COMMUNICATIONS MITTEILUNGEN
FROM THE DER
KONKOLY OBSERVATORY STERNWARTE
OF THE DER UNGARISCHEN AKADEMIE
HUNGARIAN ACADEMY OF SCIENCES DER WISSENSCHAFTEN
BUDAPEST - SZABADSAGHEGY
No. 94.
(Vol. 11, Part 1)
PERIOD CHANGES
OF BRIGHT SOUTHERN CEPHEIDS
L. SZABADOS
BUDAPEST. 1989
ISBN 963 8361 30 1
HU ISSN 0238 - 2091
PERIOD CHANGES OF BRIGHT SOUTHERN CEPHEIDS
ABSTRACT
O-C diagrams have been constructed for 44 bright southern Cepheids, mainly
for studying the effects of duplicity on the pulsation period. Because
the light-time effect in the O-C diagrams of binary Cepheids has to be
accompanied with properly phased variations in the gamma-velocity, the
radial velocities of the programme stars have been studied, as well.
Light-time effect is found or suspected in eleven cases (V496 Aql, AX
Cir, AG Cru, BG Cru, BF Oph, AP Pup, AT Pup, Y Sgr, AP Sgr, R TrA, and V
Vel), and a preliminary value of the orbital period is suggested for 14 Cepheid
binaries (V496 Aql, AX Cir, AG Cru, Y Oph, BF Oph, AP Pup, AT Pup, U
Sgr, Y Sgr, AP Sgr, BB Sgr, RV Sco, R TrA, and V Vel). The phenomenon
of the phase jump (i.e. the return of the pulsation period to an earlier
value) is present in the O-C diagram of eight Cepheid binaries (U Aql,
YZ Car, KN Cen, S Mus, S Nor, Y Oph, U Sgr, and V350 Sgr).
INTRODUCTION
Period changes of more than a hundred northern Cepheids were
studied in a series of papers (Szabados, 1977, 1980, 1981, 1983, and 1984).
The large number of the programme stars and the homogeneous method of the
analysis enabled the determination of the period changes as a function of
the pulsation period. A general agreement of the observed period changes
with the theoretically calculated values was found. In addition to the
frequently occurring parabolic O-C diagrams corresponding to the continuous
period change as a result of the stellar evolution, two special kinds of
period variations were also revealed in several cases, both of them being
characteristic of binary Cepheids:
1. light-time effect due to the orbital motion,
2. stepwise O-C graph, i.e. rejump (return) of the pulsation period to an
earlier value. In what follows, the term "phase jump" will be used for this
phenomenon.
This paper is dealing with a similar study: period changes of 44
(mostly bright) southern Cepheids are discussed here. Because the southern
Cepheid variable stars were observed on rare occasions before the
photoelectric era, secular period variations have remained undiscovered
in most cases. The time interval of less than fifty years covered with
photoelectric observations is not long enough to reveal the evolutionary
period changes unambiguously (there are, however, some exceptions). At the
same time, due to their accuracy, these photoelectric observations can be
used successfully for searching for both light-time effect and phase jump
in the O-C diagrams.
For this reason the sample of stars studied here is arbitrarily chosen:
it contains the bright southern Cepheids for which presence of a companion
has been suspected or discovered. In addition, some other bright Cepheids
without any evidence for duplicity have also been included, considering
that any evolutionary period changes are likely to be expected in these
very bright Cepheids with the longest available coverage of photometric
observations.
The current ephemerides (the moment of the light maximum, and the value
of the pulsation period) are also determined, and these pieces of
information may be useful for planning future observations in any
wavelength interval, or for determining their phases.
Due to the inhomogeneous (and arbitrary) selection of the programme
stars, the statistical study of the period changes has not been attempted.
Instead, duplicity effects are placed in the centre of interest. Because
the most straightforward way to discover the presence of a companion is to
detect variations in the mean radial velocity (so called gamma-velocity), the
radial velocity data are also analysed and intercompared with the relevant
parts of the O-C diagrams.
O-C DIAGRAMS
In order to study the period changes, all the available photometric
observations have been analysed. At the final step, however, the results
based on visual observations were omitted because of their very low
accuracy. Nevertheless, there are one or two cases where the very early
visual data have been used but after J.D.2420000 only the photographic and
photoelectric observations were taken into account.
Homogeneity of the O-C diagrams has been achieved by re-analysing all
observations without accepting the originally published moments of normal
maxima. The new moments of normal maxima were determined by fitting the
master light curve to the light curve to be analysed. The master light
curve has been the most reliable seasonal light curve available in the
literature for the given star (mostly but not necessarily from the paper by
Moffett and Barnes, 1984). Whenever it was possible, the longer
observational series were grouped into seasonal light curves.
Depending on the number and quality of the observations and the
distribution of the data points, a weight has been assigned to each light
curve. This weight is 3 for the master curves and other best quality light
curves, and 2 or 1 is assigned to the light curves of poorer coverage
and/or showing wide scatter. Note that these weights were determined before
performing the curve fitting procedure, i.e. without knowing how much the
corresponding O-C residual will deviate from the final O-C curve.
The weight was never larger than 1 in the case of the photographic
observations, and there are numerous O-C residuals in the tables of this
paper where no weight has been assigned (these are based on visual or
photographic observations without exception). These latter O-C residuals
are still useful but have not been taken into account when determining the
shape of the O-C curve.
The exact calculation of the error for each O-C residual would have
been extremely time-consuming. Instead, based on the large body of the
previous O-C diagrams (Szabados, 1977, 1980, 1981) the following average
uncertainties could be deduced: for w=3, 2, and 1 the standard deviation is
about 0.002, 0.004 and 0.008 part of the pulsation period.
Throughout this study the blue (or closest to Johnson's B band) light
curves were analysed. There are quite a few series of photometric
observations obtained in red and/or infrared bands. Although these
observations are very important in some respects, they were omitted from
this study because the shape of the light curve at long wavelength differs
from the blue light curve, and the necessary corrections to be applied for
removing the systematic differences between the moments of maxima in
different spectral regions have not been determined yet.
The O-C residuals are given in tabular form and shown plotted in
figures. The successive columns in the tables of the O-C residuals contain
the following data:
1. Moment of normal maximum;
2. The corresponding epoch;
3. O-C residual (in days);
4. Type of observation and the weight assigned to the residual (pe for
photoelectric, pg for photographic, and vis for visual observations);
5. Source of the observational data.
The O-C diagram (usually the upper panel of the figure) shows the O-C
residuals listed in the corresponding table, and the curve thought to be
the best interpretation of the O-C plot is also drawn. These curves were
obtained by the weighted least squares method applied to the data points.
The weights are visualized in the figure as circles of increasing diameter.
Photoelectric observations are denoted with filled circles, while open
circles refer to the O-C residuals based on photographic observations. If
no weight has been assigned to an O-C residual, it is shown plotted as a
small dot.
RADIAL VELOCITIES
Because one of the main aims of this study is to search for light-time
effect in the O-C diagrams, it was appropriate to carry out a simultaneous
investigation of the radial velocity measurements in order to check the
results on duplicity obtained from the O-C diagrams.
The radial velocity data have been collected from the literature, and
they were analysed after the trend of the period variation had been
determined from the O-C diagram. This step is crucial because any fitting
error due to the use of an inaccurate pulsation period can be eliminated,
and only the observational (and in some cases a systematic zero-point)
error of the radial velocity measurements remains as a possible source of
error.
It is almost impossible to get rid of the systematic errors because
most of the early papers containing radial velocity data do not give enough
information for converting the data into a common system. Nevertheless,
thanks to the existence of the IAU standard radial velocity system, these
systematic errors have become much smaller in the last decades, e.g.
according to Welch et al. (1987) the zero-point correction applied to the
radial velocity measurement series of U Aql is less than 1 km/s for eight
instruments, and the correction slightly exceeds 1 km/s in only one case.
In view of this, no corrections have been applied to the observational data
analysed here, and, of course, this can be an additional source of error.
The only exception is Paddock's (1917) radial velocity measurement series,
for which Lloyd Evans (1982) introduced +4 km/s correction, and this value
is so large that it was also applied here.
The individual radial velocity series were used for constructing the
seasonal radial velocity curves using the accurate value of the pulsation
period. The centre-of-mass velocity of the Cepheid (i.e. the gamma-velocity)
was then determined in two steps. At first, the gamma-velocity of the best
radial velocity curve was determined graphically for each variable, then
these radial velocity normal curves were fitted to the properly phased
other radial velocity curves. If the gamma-velocity seemed to be constant, the
radial velocity measurement series were not always divided into seasonal
curves.
As to variability of the gamma-velocity, there is a reasonable lower limit
(4-5 km/s), and if the fluctuation of the gamma-velocity exceeds this value,
the presence of a companion to the Cepheid is suspected. It is hoped that
the above limit overestimates the real threshold of detection because much
smaller variations in the gamma-velocity can be revealed by using the recent
radial velocity measurement techniques. Unfortunately most of the available
radial velocity data have been obtained at a higher level of uncertainty.
Because the relative errors of the radial velocity measurements are
larger than those of the photometric measurements, the standard deviations
have been calculated for the individual radial velocity measurement series.
The standard deviation of the date of observation is formal, and it only
indicates the length of the observational interval. The standard deviation
of the gamma-velocity does not contain the contribution of the possible
zero-point error.
The successive columns in the tables of the gamma-velocities give the
following data:
1-2. Mean date of the observations and its standard deviation;
3-4. gamma-velocity and its standard deviation;
5. Number of radial velocity observations used;
6. Source of the observational data.
The gamma-velocity data of the individual Cepheids are plotted in most
cases in the lower panel of the figures. The plot is missing in those cases
where no obvious change in the gamma-velocity is seen. Error bars (according
to the standard deviations listed in the tables) are only shown, if the bar
exceeds the size of the circle.
REMARKS ON THE INDIVIDUAL VARIABLES
The list of the programme stars can be found in Table 1. The ordinal
number following the name of the Cepheid gives the page number where the
discussion on the given star begins. The Cepheids involved in this study
are arranged in alphabetical order of constellations, and within one
constellation, according to the IAU nomenclature of variable stars.
Table 1. Programme stars
Cepheid Page Cepheid Page Cepheid Page
U Aql 9 GH Lup 31 WZ Sgr 57
V496 Aql 10 R Mus 33 AP Sgr 58
V Car 12 S Mus 34 BB Sgr 60
YZ Car 14 S Nor 35 V350 Sgr 62
l Car 15 RS Nor 37 RV Sco 63
SY Nor 38 RY Sco 65
V Cen 17 Y Oph 39 V500 Sco 66
XX Cen 18 BF Oph 43 V636 Sco 67
AZ Cen 20 Y Sct 68
KN Cen 21 AP Pup 46 R TrA 69
AX Cir 23 AT Pup 47
S TrA 71
S Cru 24 MY Pup 49 T Vel 72
T Cru 25 U Sgr 50 V Vel 73
AG Cru 27 W Sgr 52 AH Vel 75
BG Cru 28 X Sgr 54
beta Dor 30 Y Sgr 55
It was not my intention to give a comprehensive history on each
variable. I do hope, however, that neither photoelectric or photographic,
nor radial velocity observation published in the literature escaped my
attention. The additional remarks on the individual Cepheids mostly concern
the previous studies on both the changes in the gamma-velocity and the period
variations. The available other evidence regarding the duplicity of these
stars is also discussed briefly. A systematic application of the known
duplicity tests is beyond the scope of this paper but such a study is
planned for the near future. The compilation on the binary Cepheids will be
published in due time.
Although the phase difference between the gamma-velocity variations and
the sinusoidal wave in the O-C diagram is a good indicator whether this
phenomenon can be interpreted as a light-time effect, there is an
additional criterion that makes use of the amplitude of these oscillations.
Assuming a circular orbit, the radial velocity and O-C variations have to
obey the following relationship in a binary system:
2K = a*sini*Porb^-1*3.77*10^-6 (1)
where 2K is conventionally the total amplitude of the gamma-velocity variation
(in km/s), a*sini is the projected radius of the orbit, and at the same
time this quantity is the half amplitude of the wave in the O-C diagram (in
days), and Porb is the orbital period (in days). This test is frequently
used during this study as a very strong criterion when deciding whether
light-time effect is expected or not (if the orbital period has been known
from radial velocity measurements), and to judge reality of interpreting
the O-C wave in terms of duplicity.
U Aquilae
U Aql is one of the spectroscopic binary Cepheids with known orbit
(Welch et al., 1987). According to various estimates, the companion is a
main-sequence B8-A1 star (Leonard and Turner, 1986). The radial velocity
observations have not been re-analysed here, the orbital period of 1856.4
days (Welch et al., 1987) is accepted, although the more recently published
radial velocity data (Wilson et al., 1989) may slightly alter this value.
The O-C residuals are listed in Table 2, and are shown plotted in
Figure 1. The O-C diagram of U Aql can be well approximated by two lines
showing a phase jump (i.e. rejump of the period). The O-C residuals have
been calculated with the formula:
C = 2434922.400 + 7.023958d*E (2)
+-.031 +-.000029
Figure 1. O-C diagram of U Aql
Table 2. O-C residuals for U Aql
Norm.max. Type,
JD2400000+ E O-C weight Reference
32765.994 -307 -0.051d pe 2 Eggen (1951)
33110.132 -258 -0.087 pe 3 Eggen (1951)
34950.444 + 4 -0.052 pe 1 Walraven et al. (1958)
35294.581 + 53 -0.089 pe 1 Irwin (1961)
36109.319 +169 -0.130 pe 1 Svolopoulos (1960)
37233.200 +329 -0.082 pe 2 Mitchell et al. (1964)
38673.155 +534 -0.039 pe 1 Wisniewski and Johnson (1968)
39059.541 +589 +0.030 pe 1 Wisniewski and Johnson (1968)
40253.609 +759 +0.025 pe 2 Feltz and McNamara (1980)
40801.469 +837 +0.016 pe 2 Feltz and McNamara (1980)
40822.484 +840 -0.041 pe 3 Pel (1976)
41194.809 +893 +0.015 pe 2 Feltz and McNamara (1980)
42922.639 +1139 -0.049 pe 2 Dean (1977)
43365.210 +1202 +0.012 pe 3 Moffett and Barnes (1984)
43674.270 +1246 +0.018 pe 3 Moffett and Barnes (1984)
44039.528 +1298 +0.031 pe 2 Moffett and Barnes (1984)
44467.988 +1359 +0.029 pe 2 Eggen (1985)
45563.595 +1515 -0.101 pe 1 Eggen (1985)
This period is valid after J.D.2438600, while between J.D.2432700 and
J.D.2437300 the pulsation period was 7.023920 +- 3.0*10^-5 days. The phase
jump occurred at about J.D.2438000, and it amounts to 0.1 day.
There are no early photographic observations available in the
literature, therefore the longer time-scale behaviour of the O-C diagram of
U Aql cannot be studied. According to the phase relations of the radial
velocity curves, the O-C residuals might be even more negative at about
J.D.2421840. A single straight line fitted to the photoelectric O-C
residuals is almost as good as the phase jump approximation. In view of the
values of the orbital period and the orbital radial velocity amplitude, the
expected light-time effect has such a low amplitude (see equation (1)) that
the effect cannot be detected.
V496 Aquilae
Its spectroscopic binary nature was revealed by Gieren (1982) but there
is no agreement on the type of the companion (Leonard and Turner, 1986).
The variable gamma-velocity of V496 Aql is well illustrated in Figure 2 (lower
panel), and in Table 3. There is a number of periods that fits the data
points reasonably well: 1200, 1780, 2700, 3600, 5350, and 10750 days. It is
impossible to choose the true value of the orbital period from the
available radial velocity measurements alone.
Table 3. gamma-velocities of V496 Aql
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
33918 31 6.8 0.8 15 Stibbs (1955)
34202 28 0.6 1.5 5 Stibbs (1955)
40448 27 6.8 0.4 4 Lloyd Evans (1980)
44053 10 18.0 4.0 2 Barnes et al. (1988)
44423 4 7.7 0.4 25 Gieren (1981a)
44486 46 14.5 1.6 7 Barnes et al. (1988)
44822 47 4.6 2.3 4 Barnes et al. (1988)
The O-C diagram (see Table 4 and the upper panel of Figure 2) can be
approximated by a straight line with the light-time effect superimposed on
it. The sine-wave was fitted by using the method of weighted least squares,
and the 1500 - 13000 day interval was analysed. The best fit was achieved
assuming an orbital period of 1882 +- 23 days. The moments of the light
maxima can be predicted as follows:
C = 2436017.084 + 6.807055d*E - 0.023*cos(2pi(0.00362*E - 0.006)) (3)
+-.004 +-.000008 +-.008 +-.00004 +-.031
Figure 2. Upper panel: O-C diagram of V496 Aql
Lower panel: gamma-velocities for the same Cepheid
Table 4. O-C residuals for V496 Aql
Norm.max E O-C Type, Reference
JD2400000+ weight
34567.181 -213 0.000d pe 2 Eggen et al. (1957)
35608.663 - 60 +0.002 pe 2 Walraven et al. (1958)
37187.908 +172 +0.011 pe 2 Mitchell et al. (1964)
40366.791 +639 -0.001 pe 2 Stobie (1970)
40809.275 +704 +0.024 pe 3 Pel (1976)
41122.357 +750 -0.018 pe 2 Pel (1976)
41149.613 +754 +0.010 pe 2 Feltz and McNamara (1980)
44410.200 +1233 +0.017 pe 3 Moffett and Barnes (1984)
44410.214 +1233 +0.031 pe 3 Gieren (1981b)
44621.218 +1264 +0.016 pe 2 Eggen (1985)
44907.121 +1306 +0.023 pe 1 Moffett and Barnes (1984)
This value of the orbital period is in reasonable agreement with the 1780
day period, one of the values suggested by the radial velocity data. The
amplitude of the wave is, however, twice larger than the value expected
from equation (1). This suggests that the orbital period may be longer.
More spectroscopic and photometric data are necessary to determine the
value of the orbital period unambiguously.
The O-C residuals have been calculated with the elements:
C = 2436017.084 + 6.807055d*E (4)
+-.004 +-.000008
If no sinusoidal term is assumed in the O-C diagram, then the least squares
fit results in the following formula:
C = 2436017.085 + 6.807070d*E (5)
+-.004 +-.000005
which is practically identical with the linear part of the sinusoidal fit
(i.e. with equation (4)).
V Carinae
V Car was reported to be a suspected binary (Lloyd Evans, 1968) but
later on Lloyd Evans (1982) explained the scatter in the radial velocity
data as due to the variability of the bump on the velocity curve. Here the
scatter in the radial velocity data is attributed to the variation in the
gamma-velocity (see Table 5 and the lower panel of Figure 3).
Table 5. gamma-velocities of V Car
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
34009 20 15.2 0.8 14 Stibbs (1955)
34095 20 14.0 1.2 7 Stibbs (1955)
39252 64 8.7 1.1 4 Lloyd Evans (1968)
39611 41 8.3 1.1 4 Lloyd Evans (1968)
39932 48 12.2 0.6 2 Lloyd Evans (1980)
40338 16 12.5 0.3 5 Lloyd Evans (1980)
40666 51 13.2 0.3 6 Lloyd Evans (1980)
Figure 3. Upper panel: O-C diagram of V Car
Lower panel: gamma-velocities for the same Cepheid
Table 6. O-C residuals for V Car
Norm.max. E O-C Type, Reference
JD2400000+ weight
35230.691 -332 +0.034d pe 1 Irwin (1961)
35351.218 -314 +0.021 pe 1 Walraven et al. (1958)
39630.343 +325 -0.027 pe 2 Cousins and Lagerweij (1968)
39958.494 +374 -0.013 pe 3 Cousins and Lagerweij (1968)
40742.012 +491 -0.006 pe 3 Pel (1976)
42858.163 +807 -0.003 pe 1 Dean (1977)
44425.219 +1041 +0.031 pe 2 Eggen (1985)
The O-C diagram (Table 6 and the upper panel of Figure 3) contains
very few points, and for the sake of simplicity it is approximated by a
straight line:
C = 2437453.952 + 6.696672d*E (6)
+-.009 +-.000016
Further observations are to be obtained in order to decide whether a
parabola fits better, and even the light-time effect cannot be excluded.
YZ Carinae
According to Coulson (1983) YZ Car belongs to a binary system with an
orbital period of about 850 days. Coulson also derived tentative orbital
parameters, and concluded that the companion is probably a main-sequence A0
star. The radial velocity measurements of YZ Car have not been analysed
again here.
Table 7. O-C residuals for YZ Car
Norm.max. E O-C Type, Reference
JD2400000+ weight
34725.613 - 10 +0.197d pe 2 Walraven et al. (1958)
35216.089 + 17 +0.202 pe 3 Irwin (1961)
37831.903 +161 +0.173 pe 3 Walraven et al. (1964)
41737.333 +376 +0.006 pe 3 Madore (1975)
43989.866 +500 +0.008 pe 2 Coulson and Caldwell (1985)
44280.475 +516 -0.033 pe 2 Coulson and Caldwell (1985)
44280.593 +516 +0.085 p‚ 1 EEggen (1983b)
44680.082 +538 -0.068 pe 2 Coulson and Caldwell (1985)
44771.006 +543 +0.028 pe 2 Eggen (1983b)
45007.127 +556 -0.004 pe 3 Coulson and Caldwell (1985)
45715.615 +595 +0.027 pe 2 Coulson and Caldwell (1985)
Figure 4. O-C diagram of YZ Car
The O-C diagram has been constructed on the basis of the available
observations listed in Table 7. The plot of the O-C residuals (see Figure
4) can be well approximated by two sections of straight lines showing the
phenomenon of the phase jump seen in numerous binary Cepheids.
The O-C residuals have been calculated with the elements:
C = 2434907.072 + 18.165573d*E (7)
+-.071 +-.000137
The previous value of the pulsation period (between J.D.2434700 and
2437900) was 18.165412 + 2.0*10^-5 days, therefore it can be stated that the
star returned to the same pulsation period after an 0.16 day phase jump,
occurred at about J.D.2440000.
Another fact worth mentioning is that the pulsation period differs
considerably from the value given in the GCVS (Kholopov et al., 1985-1987).
Coulson (1983) used an almost correct value of the pulsation period but did
not call the attention explicitly to the correction to be applied to the
period in the catalogue.
l Carinae
Figure 5. O-C diagram of l Car
The gamma-velocity of this long period Cepheid can be considered as being
constant (see Table 8), therefore the individual values of the gamma-velocity
are not plotted in a diagram.
The O-C diagram (see Table 9 and Figure 5) is based on only the
photoelectric normal maxima. The previous values of the pulsation period
can be followed in Parenago's (1956) paper. The O-C residuals have been
calculated with the formula:
C = 2440736.230 + 35.551341d*E (8)
+-.015 +-.000397
Table 8. gamma-velocities of l Car
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
17441 402 2.2 0.8 17 Jacobsen (1934)
21655 25 2.0 0.8 15 Jacobsen (1934)
22435 19 1.8 0.6 28 Jacobsen (1934)
34086 61 1.0 0.7 21 Stibbs (1955)
35641 19 0.7 1.0 5 Lloyd Evans (1968)
37722 52 4.4 0.7 21 Dawe (1969)
39238 33 0.9 1.1 4 Lloyd Evans (1968)
39901 38 2.0 0.3 5 Lloyd Evans (1980)
40307 61 3.2 0.2 12 Lloyd Evans (1980)
40663 44 0.0 0.3 6 Lloyd Evans (1980)
Table 9. O-C residuals for l Car
Norm.max. E O-C Type, Reference
JD2400000+ weight
33807.235 -195 +3.516d pe 2 Eggen et al. (1957)
34766.489 -168 +2.884 pe 2 Eggen et al. (1957)
35228.242 -155 +2.470 pe 2 Irwin (1961)
35263.849 -154 +2.526 pe 1 Walraven et al. (1958)
37751.037 - 84 +1.120 pe 2 Lake (1962)
38141.594 - 73 +0.612 pe 1 Feinstein and Muzzio (1969)
38461.577 - 64 +0.633 pe 1 Feinstein and Muzzio (1969)
38852.400 - 53 +0.391 pe 1 Feinstein and Muzzio (1969)
39563.259 - 33 +0.223 pe 3 Feinstein and Muzzio (1969)
39563.437 - 33 +0.401 pe 3 Landolt (1971)
40629.547 - 3 -0.029 pe 2 Eggen (1971)
40736.226 0 -0.004 pe 3 Pel (1976)
41127.387 + 11 +0.092 pe 2 Pel (1976)
41731.656 + 28 -0.012 pe 3 Madore (1975)
41838.299 + 31 -0.023 pe 3 Dean et al. (1977)
42549.300 + 51 -0.048 pe 2 Dean et al. (1977)
43189.300 + 69 +0.027 pe 3 Dean (1981)
Two values of the pulsation period are apparent in Figure 5: before
J.D.2440000 the period was 35.531758 +- 6.21*10^-4 days, while after this epoch
the value of the period has been 35.551341 +- 3.97*10^-4 days. Although Figure
5 suggests a continuous period increase, a parabolic fit was not attempted
because the early part of the O-C diagram (Parenago, 1956) would contradict
to this interpretation.
V Centauri
Although Gieren (1982) found no evidence for the variable gamma-velocity,
according to the present study variability in the gamma-velocity cannot be
ruled out (see Table 10 and the lower panel of Figure 6). Especially
Stibbs' (1955) seasonal curves suggest a short period (several hundred
days) variation.
Table 10. gamma-velocities of V Cen
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
33848 22 -25.1 1.1 9 Stibbs (1955)
34165 54 -19.5 1.1 8 Stibbs (1955)
39268 37 -23.9 1.0 5 Lloyd Evans (1968)
40371 28 -23.2 0.3 4 Lloyd Evans (1980)
40759 15 -20.8 0.3 3 Lloyd Evans (1980)
44422 4 -23.9 0.4 26 Gieren (1981a)
Figure 6. Upper panel: O-C diagram of V Cen
Lover panel: gamma-velocities for the same Cepheid
Table 11. O-C residuals for V Cen
Norm.max. E O-C Type, Reference
JD2400000+ weight
16162.649 -4395 -0.364d pg 1 Shapley (1930)
17953.707 -4069 -0.305 pg 1 Shapley (1930)
20272.216 -3647 -0.205 pg 1 Shapley (1930)
21794.004 -3370 -0.216 pg 1 Shapley (1930)
23986.101 -2971 -0.170 pg 1 Shapley (1930)
24260.903 -2921 -0.061 pg 1 Voute (1927b)
24656.476 -2849 -0.046 pg 1 Voute (1927b)
25035.485 -2780 -0.113 pg 1 Voute (1927b)
25793.717 -2642 -0.034 pg 1 Dartayet et al. (1949)
26139.928 -2579 +0.064 pg 1 Dartayet et al. (1949)
34869.621 - 990 +0.011 pe 3 Walraven et al. (1958)
35193.758 - 931 +0.011 pe 3 Irwin (1961)
40335.980 + 5 -0.021 pe 3 Stobie (1970)
40748.007 + 80 -0.034 pe 3 Pel (1976)
42852.197 + 463 +0.007 pe 2 Dean (1977)
44417.952 + 748 +0.012 pe 3 Gieren (1981b)
44494.877 + 762 +0.023 pe 2 Eggen (1985)
The O-C diagram (Table 11 and the upper panel of Figure 6) shows one
period change. The O-C residuals have been computed using the ephemeris:
C = 2440308.532 + 5.493861d*E (9)
+-.005 +-.000007
The period change occurred at about J.D.2427000, and before that epoch the
pulsation period was 5.494058 +- 2.6*10^-5 days.
XX Centauri
Spectroscopic binary nature of XX Cen was discovered by Coulson et
al. (1985). The value of the orbital period was determined recently
(Szabados, 1989), its value is 909.4 +- 29.0 days.
According to equation (1), no detectable light-time effect is expected
in the O-C diagram, therefore the phase shift mentioned by Coulson et al.
(1985) is not caused by the orbital motion but, instead, it reflects the
strong period change determined here.
The O-C residuals have been calculated with the formula:
C = 2440366.125 + 10.954027d*E (10)
+-.010 +-.000027
As is seen in the O-C diagram (see Table 12 and Figure 7), the period of
XX Cen is continuously decreasing as follows:
P = 10.954027d - 15.5d*10^-7*E (11)
+-.000027 +-.6
where the E epoch number is the same as in equation (10).
Table 12. O-C residuals for XX Cen
Norm.max E O-C Type, Reference
JD2400000+ weight
26398.368 -1275 -1.373d pg 1 van Gent and Oosterhoff (1948)
27691.409 -1157 -0.907 pg 1 van Gent snd Oosterhoff (1948)
34812.261 - 507 -0.172 pe 1 Walraven et al. (1958)
35206.584 - 471 -0.194 pe 3 Irwin (1961)
35469.522 - 447 -0.153 pe 1 Walraven et al. (1958)
37846.692 - 230 -0.007 pe 3 Walraven et al. (1964)
40377.080 + 1 +0.001 pe 3 Stobie (1970)
41110.923 + 68 -0.076 pe 2 Grayzeck (1978)
41592.936 + 112 -0.040 pe 1 Grayzeck (1978)
41768.228 + 128 -0.012 pe 2 Madore (1975)
42874.573 + 229 -0.024 pe 3 Dean (1977)
44068.488 + 338 -0.098 pe 3 Coulson et al. (1985)
44659.979 + 392 -0.125 pe 3 Coulson et al. (1985)
45010.518 + 424 -0.114 pe 3 Coulson et al. (1985)
Figure 7. O-C diagram of XX Cen
AZ Centauri
AZ Cen may be a spectroscopic binary because Balona found a strongly
discordant gamma-velocity in comparison with other radial velocity
measurements (Gieren, 1982). Unfortunately Balona's observations have
remained unpublished, and the available radial velocity data show a
constant gamma-velocity (see Table 13).
The O-C residuals have been computed with the formula:
C = 2435223.389 + 3.212279d*E (12)
+-.011 +-.000004
It should be emphasized that this pulsation period strongly differs from
that given in the GCVS (Kholopov et al., 1985-1987). The O-C diagram is
parabolic (see Table 14, and Figure 8) showing a continuous decrease in the
period. The instantaneous value of the pulsation period can be obtained
from the formula:
P = 3.212279d - 9.79d*10^-8*E (13)
+-.000004 +-.35
where the E epoch number is the same as in equation (12).
Table 13. gamma-velocities of AZ Cen
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
34138 33 -12.1 0.9 11 Stibbs (1955)
43178 4 -11.5 0.4 7 Stobie and Balona (1979)
43311 37 -13.1 0.3 10 Stobie and Balona (1979)
43531 4 -12.5 0.6 4 Stobie and Balona (1979)
44423 4 -12.7 0.4 22 Gieren (1981a)
Figure 8. O-C diagram of AZ Cen
Table 14. O-C residuals for AZ Cen
Norm.max. E O-C Type, Reference
JD2400000+ weight
23253.740 -3726 -0.697d pg 1 de Jager (1947)
34709.464 - 160 +0.040 pe 1 Walraven et al. (1958)
35220.172 - 1 -0.005 pe 3 Irwin (1961)
35451.504 + 71 +0.043 pe 2 Walraven et al. (1958)
40738.672 +1717 -0.200 pe 3 Pel (1976)
41795.508 +2046 -0.204 pe 3 Dean et al. (1977)
42540.691 +2278 -0.270 pe 3 Dean et al. (1977)
43179.904 +2477 -0.300 pe 3 Stobie and Balona (1979)
44316.936 +2831 -0.415 pe 1 Eggen (1985)
44400.508 +2857 -0.362 pe 3 Gieren (1981b)
44634.956 +2930 -0.410 pe 1 Eggen (1985)
45055.732 +3061 -0.443 pe 1 Eggen (1985)
KN Centauri
The presence of a companion to the Cepheid KN Cen has been suspected on
various grounds: large UV excess (Walraven et al., 1964), peculiar loop in
the two-colour diagram (Stobie, 1970; Madore, 1977; and Pel, 1978), the
shape of the Ca II K line (Lloyd Evans, 1968), and finally the companion
was revealed with the help of an IUE spectrum (B”hm Vitense and Proffitt,
1985). The available radial velocity observations also give evidence for
the binary nature (see Table 15 and the lower panel of Figure 9). This
variation has not been reported before.
Table 15. gamma-velocities of KN Cen
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
41539 194 -48.8 4.5 6 Grayzeck (1978)
43975 5 -40.8 0.4 6 Coulson and Caldwell (1985)
44400 56 -40.0 0.4 9 Coulson and Caldwell (1985)
44703 35 -39.5 0.3 16 Coulson and Caldwell (1985)
45092 2 -38.0 0.5 3 Coulson and Caldwell (1985)
The O-C residuals (see Table 16 and upper panel of Figure 9) have been
calculated with the elements:
C = 2436242.009 + 34.029641d*E (14)
+-.195 +-.000787
Table 16. O-C residuals for KN Cen
Norm.max. E O-C Type, Reference
JD2400000+ weight
34638.470 - 47 -4.146d pe 2 Walraven et al. (1958)
35216.974 - 30 -4.146 pe 3 Irwin (1961)
35250.816 - 29 -4.333 pe 1 Walraven et al. (1958)
37871.756 + 48 -3.676 pe 1 Walraven et al. (1964)
40356.990 +121 -2.606 pe 2 Stobie (1970)
41106.302 +143 -1.946 pe 3 Pel (1976)
41582.839 +157 -1.824 pe 2 Grayzeck (1978)
44034.776 +229 -0.021 pe 2 Coulson and Caldwell (1985)
44647.361 +247 +0.031 pe 3 Coulson and Caldwell (1985)
45123.728 +261 -0.017 pe 3 Coulson and Caldwell (1985)
Figure 9. Upper panel: O-C diagram of KN Cen
Lower panel: gamma-velocities for the same Cepheid
Three values of the pulsation period could be determined:
before J.D.2437000 P = 34.026583d +- .003999d
between J.D.2437000 and J.D.2444000 P = 34.047490d +- .001315d
after J.D.2444000 P = 34.029641d +- .000787d .
The first and the third value is nearly the same, i.e. a phase jump
occurred, although not very suddenly.
Additional photometric and radial velocity measurements on this binary
Cepheid are urgently needed both for confirming the rejump in the pulsation
period, and in order to determine the orbital period.
AX Circinis
Its composite spectrum was discovered by Jaschek and Jaschek (1960).
Lloyd Evans (1971) revealed the spectroscopic binary nature of AX Cir,
while B”hm Vitense and Proffitt (1985) were able to detect the companion
using IUE spectra.
The variable gamma-velocity is shown in the lower panel of Figure 10 (see
also Table 17). The observed extrema of the gamma-velocity correspond to the
full amplitude of the gamma-velocity variation, as is seen in the O-C wave to
be discussed below (see Figure 10).
Table 17. gamma-velocities of AX Cir
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
38570 6 -17.7 0.9 6 Evans (1965)
39618 50 -26.0 1.1 4 Lloyd Evans (1968)
39900 33 -26.4 0.2 7 Lloyd Evans (1980)
40258 11 -26.8 0.6 2 Lloyd Evans (1980)
40387 46 -30.9 0.2 14 Lloyd Evans (1980)
40745 71 -33.3 0.2 15 Lloyd Evans (1980)
Table 18. O-C residuals for AX Cir
Norm.max. E O-C Type, Reference
JD2400000+ weight
38220.425 + 4 -0.006d pe 3 Cousins and Evans (1967)
39533.527 +253 +0.043 pe 3 Cousins and Evans (1967)
39617.878 +269 +0.021 pe 3 Mauder and Sch”ffel (1968)
42855.659 +883 -0.008 pe 3 Dean (1977)
42971.687 +905 +0.007 pe 3 Dean (1977)
44474.595 +1190 +0.023 pe 2 Eggen (1985)
45381.576 +1362 -0.005 pe 2 Eggen (1985)
The O-C residuals listed in Table 18 have been computed with the
formula:
C = 2438199.338 + 5.273306d*E (15)
+-.002 +-.000008
A sinusoidal term is superimposed on the straight line in the O-C graph. A
weighted least squares fit applied to the O-C residuals resulted in the
Figure 10. Upper panel: O-C diagram of AX Cir
Lower panel: gamma-velocities for the same Cepheid
value of 4600 +- 83 days for the orbital period. The moments of the normal
maxima can be predicted as follows:
C = 2438199.338 + 5.273306d*E - 0.032cos(2pi(0.00115*E + 0.222)) (16)
+-.002 +-.000008 +-.002 +-.00002 +-.018
Although each parameter (amplitude, phase, period) of this wave are in
agreement with the pattern of the gamma-velocity changes, further observations
are desirable to confirm or refine the above value of the orbital period.
S Crucis
The gamma-velocity of S Cru seems to be constant (see Table 19).
Table 19. gamma-velocities of S Cru
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
33832 9 -6.0 1.3 6 Stibbs (1955)
34167 46 -6.9 1.1 8 Stibbs (1955)
40383 46 -5.0 0.2 7 Lloyd Evans (1980)
44423 4 -7.8 0.4 25 Gieren (1981a)
Figure 11. O-C diagram of S Cru
Table 20. O-C residuals for S Cru
Norm.max. E O-C Type, Reference
JD2400000+ weight
25785.558 -1959 -0.286d pg 1 Dartayet et al. (1949)
26109.086 -1890 -0.366 pg 1 Dartayet et al. (1949)
34921.939 - 11 +0.034 pe 1 Walraven et al. (1958)
35208.046 + 50 +0.053 pe 2 Irwin (1961)
40310.536 +1138 -0.145 pe 3 Stobie (1970)
40774.862 +1237 -0.126 pe 3 Pel (1976)
42852.392 +1680 -0.253 pe 1 Dean (1977)
44414.058 +2013 -0.347 pe 3 Gieren (1981b)
45126.915 +2165 -0.365 pe 2 Eggen (1985)
The O-C residuals (listed in Table 20) have been computed with the
elements:
C = 2434973.495 + 4.689970d*E (17)
+-.015 +-.000007
As is seen in Figure 11, the pulsation period is continuously decreasing.
The instantaneous value of the period is:
P = 4.689970d - 1.747d*10^-7*E (18)
+-.000007 +-.109
where the E epoch number is the same as in equation (17).
T Crucis
On the basis of the available radial velocity measurements, variability
in the gamma-velocity can be suspected (see Table 21 and the lower panel of
Figure 12). Jaschek and Jaschek (1956) found strong Ca II emission which
may be partly caused by the presence of the companion.
Table 21. gamma-velocities of T Cru
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
33831 9 -5.5 1.1 8 Stibbs (1955)
34106 19 -7.8 1.1 9 Stibbs (1955)
40363 34 -12.8 0.3 6 Lloyd Evans (1980)
Table 22. O-C residuals for T Cru
Norm.max E O-C Type, Reference
JD2400000+ weight
25794.799 -1299 -0.022d pg 1 Dartayet et al. (1949)
26117.971 -1251 -0.044 pg 1 Dartayet et al. (1949)
33814.110 - 108 +0.052 pe 2 Eggen et al. (1957)
34871.193 + 49 +0.023 pe 3 Eggen et al. (1957)
34958.726 + 62 +0.025 pe 1 Walraven et al. (1958)
35214.551 + 100 -0.012 pe 2 Irwin (1961)
40318.333 + 858 +0.008 pe 1 Stobie (1970)
40742.458 + 921 -0.059 pe 3 Pel (1976)
41819.814 +1081 -0.014 pe 3 Dean et al. (1977)
42102.620 +1123 -0.002 pe 3 Dean et al. (1977)
42587.418 +1195 +0.006 pe 2 Dean et al. (1977)
43260.823 +1295 +0.091 pe 1 Dean (1981)
Figure 12. Upper panel: O-C diagram of T Cru
Lower panel: gamma-velocities for the same Cepheid
The O-C diagram contains very few data points (see Table 22). The
residuals have been calculated with the elements:
C = 2434541.243 + 6.733196d*E (19)
+-.010 +-.000011
The photographic observations have also been taken into account in the
fitting procedure. If the deviations from the straight line (see Figure 12,
upper panel) are caused by a light-time effect, the gamma-velocity variations
may well exceed the range observed so far. In any case, more photometric
and spectroscopic observations are needed.
AG Crucis
Gieren (1982) already noted that AG Cru might belong to a spectroscopic
binary. The present study based on the same radial velocity data (see Table
23 and the lower panel of Figure 13) confirm his conclusion. The presence
of a blue companion is also suspected in Pel's (1978) photometry.
Table 23. gamma-velocities of AG Cru
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
34154 41 -4.4 0.8 17 Stibbs (1955)
40577 199 -6.5 0.3 5 Lloyd Evans (1980)
44423 4 -8.5 0.4 23 Gieren (1981a)
Table 24. O-C residuals for AG Cru
Norm.max. E O-C Type, Reference
JD2400000+ weight
27439.121 -1947 +1.523d pg O'Herne (1937)
34778.239 - 34 -0.026 pe 2 Walraven et al. (1958)
35219.538 + 81 -0.012 pe 3 Irwin (1961)
39559.471 +1212 -0.013 pe 3 Landolt (1971)
40760.517 +1525 -0.027 pe 3 Pel (1976)
41098.205 +1613 -0.018 pe 2 Pel (1976)
42894.075 +2081 +0.017 pe 2 Dean (1977)
44421.305 +2479 +0.020 pe 3 Gieren (1981b)
Although the O-C diagram contains very few data points (see Table 24
and the upper panel of Figure 13), a sine wave can be reliably fitted to
the O-C residuals. Moreover, the parameters of the light-time effect wave
are in agreement with the changes in the gamma-velocity. The O-C residuals
have been computed with the elements:
C = 2434908.732 + 3.837254d*E (20)
+-.001 +-.000001
and the moments of the light maxima can be predicted as follows:
C = 2434908.732 + 3.837254*E - 0.026d*cos(2pi(0.000604*E + 0.110)) (21)
+-.001 +-.000001 +-.001 +-.000008 +-.012
Figure 13. Upper panel: O-C diagram of AG Cru
Lower panel: gamma-velocities for the same Cepheid
The orbital period is 6350 +- 90 days. According to the phase relations no
radial velocity observation of AG Cru was performed during the epochs when
the Cepheid was strongly moving away on its orbit. Therefore the expected
amplitude of the gamma-velocity variations may reach 10 km/s (see equation 1).
If the first O-C residual is correct, a period change might have
occurred before J.D.2435000, but O'Herne's (1937) photographic normal maximum
seems to be of very low quality (this O-C residual has not been plotted in
Figure 13).
BG Crucis
According to the available radial velocity observations, BG Cru is a
new spectroscopic binary. Its duplicity can also be suspected on the basis
of the extremely low amplitude light variations in the ultraviolet band
(Dean, 1981). In addition to the data points listed in Table 25 (shown
plotted in the lower panel of Figure 14), there is one more series of
radial velocity observations (Lunt, 1921). These latter data, however,
cannot be used because the moments of these three observations have not
been published. The average value of these radial velocity measurements is
-14.9 km/s, being more positive than any other gamma-velocity determined for
BG Cru.
Figure 14. Upper panel: O-C diagram of BG Cru
Lower panel: gamma-velocities for the same Cepheid
Table 25. gamma-velocities of BG Cru
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
19902 1 -17.4 2.0 2 Campbell and Moore (1928)
21449 175 -26.2 1.2 4 Campbell and Moore (1928)
40449 9 -19.9 0.4 3 Lloyd Evans (1980)
40728 62 -24.4 0.2 16 Lloyd Evans (1980)
43178 4 -20.9 0.4 9 Stobie and Balona (1979)
43319 29 -20.0 0.3 10 Stobie and Balona (1979)
43533 4 -19.6 0.3 10 Stobie and Balona (1979)
Table 26. O-C residuals for BG Cru
Norm.max. E O-C Type, Reference
JD2400000+ weight
39327.323 -319 -0.009d pe 1 Stobie and Alexander (1970)
40393.683 0 +0.023 pe 3 Stobie and Alexander (1970)
40771.369 +113 -0.018 pe 1 Cousins and Lagerwey (1971)
41112.338 +215 -0.007 pe 3 Cousins and Lagerwey (1971)
43181.468 +834 -0.021 pe 3 Stobie and Balona (1979)
43562.551 +948 -0.008 pe 2 Dean (1981)
43636.112 +970 +0.014 pe 2 Eggen (1985)
43997.102 +1078 -0.010 pe 3 Arellano Ferro (1981)
44622.258 +1265 +0.057 pe 1 Eggen (1985)
More than ten values could be determined as possible orbital periods
using a least squares sinus fit but after comparing these values with the
O-C diagram to be discussed below, three values remained as the most
probable ones: 4050, 4950, and 6650 days.
The O-C residuals have been computed with the formula:
C = 2440393.660 + 3.342720d*E (22)
+-.008 +-.000010
Although the light-time effect is apparent (see Table 26 and the upper
panel of Figure 14), an exact determination of the orbital period cannot be
carried out because of the limited time interval covered with photometric
observations. The pattern of the O-C graph is in agreement with a nearly
5000 day long orbital period. Both much shorter and much longer values can
be excluded.
beta Doradus
The gamma-velocity of this Cepheid variable is constant (see Table 27).
Lloyd Evans (1968) could not find any variation larger than 3 km/s in the
gamma-velocity of beta Dor either. Moreover, this star has not been suspected as
having a companion by any other method.
Table 27. gamma-velocities of beta Dor
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
16619 191 5.1 1.3 6 Lunt (1924)
17297 798 7.9 0.7 12 Applegate (1927)
19129 921 6.1 1.7 4 Lunt (1924)
21712 564 8.0 0.3 54 Applegate (1927)
22815 136 6.9 0.5 35 Lunt (1924)
34024 29 8.8 0.6 23 Stibbs (1955)
40281 514 7.9 0.5 13 Lloyd Evans (1968,1980)
Table 28. O-C residuals for beta Dor
Norm.max. E O-C Type, Reference
JD2400000+ weight
25639.776 -1551 +0.108d pg Dartayet et al. (1949)
25993.962 -1515 -0.033 pg Dartayet et al. (1949)
26397:617 -1474 +0.082 pg Dartayet et al. (1949)
34438.765 - 657 -0.031 pe 1 Eggen et al. (1957)
34812.843 - 619 +0.035 pe 2 Eggen et al. (1957)
35216.360 - 578 +0.013 pe 2 Irwin (1961)
35570.654 - 542 -0.021 pe 1 Walraven et al. (1958)
40511.600 - 40 +0.028 pe 2 Hutchinson et al. (1975)
40796.967 - 11 -0.035 pe 3 Hutchinson et al. (1975)
40924.940 + 2 -0.014 pe 3 Pel (1976)
41732.014 + 84 -0.019 pe 3 Dean et al. (1977)
43198.610 + 233 +0.056 pe 1 Dean (1981)
43493.849 + 263 +0.022 pe 2 Eggen (1985)
43887.415 + 303 -0.109 pe 1 Schmidt and Parsons (1982)
44665.128 + 382 +0.053 pe 2 Eggen (1985)
Figure 15. O-C diagram of beta Dor
The early part of the O-C diagram of beta Dor was published by Iroshnikov
(1958). In the present study the O-C residuals have been calculated with
the elements:
C = 2440905.269 + 9.842425d*E (23)
+-.008 +-.000024
The photoelectric part of the O-C diagram (see Table 28 and Figure 15) can
be well approximated by a straight line, assuming a constant period during
the last decades. A parabolic fit to these O-C residuals (including the
photographic points at about J.D.2426000) would contradict to the O-C
pattern determined by Iroshnikov (1958).
GH Lupi
The variation in the gamma-velocity of GH Lupi has not been reported yet.
Although the effect is not very large, it can be readily detected
especially in the radial velocity observational series obtained by Coulson
and Caldwell (1985) (see Table 29 and the lower panel of Figure 16). This
variation might have been hidden till now because the pulsation period was
not known accurately enough. The unusually low amplitude light variation
Table 29. gamma-velocities of GH Lup
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
41602 214 -21.5 4.5 6 Grayzeck (1978)
43974 5 -15.0 0.4 7 Coulson and Caldwell (1985)
44408 52 -16.0 0.3 10 Coulson and Caldwell (1985)
44721 32 -16.9 0.3 17 Coulson and Caldwell (1985)
45092 2 -18.9 0.6 4 Coulson and Caldwell (1985)
Table 30. O-C residuals for GH Lup
Norm.max. E O-C Type, Reference
JD2400000+ weight
38202.145 -315 -0.474d pg Strohmeier (1967)
41088.014 - 4 -0.047 pe 3 Pel (1976)
41413.010 + 31 +0.221 pe 1 Grayzeck (1978)
44029.154 +313 -0.017 pe 3 Coulson and Caldwell (1985)
44455.880 +359 -0.076 pe 3 Coulson and Caldwell (1985)
44651.017 +380 +0.224 pe 1 Eggen (1985)
44734.257 +389 -0.038 pe 3 Coulson and Caldwell (1985)
45142.455 +433 -0.069 pe 2 Coulson and Caldwell (1985)
45569.543 +479 +0.233 pe 1 Eggen (1985)
Figure 16. Upper panel: O-C diagram of GH Lup
Lower panel: gamma-velocities for the same Cepheid
may be also due to the presence of a companion. Pel's (1978) photometry
gives evidence for a red companion.
The O-C residuals listed in Table 30 and plotted in Figure 16 (upper
panel) have been computed by the formula:
C = 2441125.173 + 9.277948d*E (24)
+-.056 +-.000167
This value of the pulsation period, assumed to be constant between
J.D.2441000 and 2445600, considerably differs from the value given in the
GCVS (Kholopov et al., 1985-1987). A change in the period might have
occurred before J.D.2441000, if the photographic O-C residual obtained
from Strohmeier's (1967) data is real.
R Muscae
The Cepheid R Muscae is probably a spectroscopic binary (Lloyd Evans,
1982). This earlier conclusion is confirmed here (see Table 31 and the
lower panel of Figure 17). There is, however, no sign of any companion in
the study made by Eichendorf et al. (1982) covering an exceptionally wide
wavelength range.
The O-C residuals listed in Table 32 have been calculated with the
elements:
C = 2426496.033 + 7.510159d*E (25)
+-.020 +-.000028
As is readily seen in Figure 17, R Mus has a continuously increasing
period:
P = 7.510159d + 1.25d*10^-7*E (26)
+-.000028 +-.10
where the E epoch number is the same as in equation (25). The photographic
O-C residuals were also taken into account during the fitting procedure. A
sine-wave superimposed on the parabola was also searched for but without
any physically acceptable result.
Table 31. gamma-velocities of R Mus
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
33832 9 +4.2 1.2 7 Stibbs (1955)
34125 31 +2.4 1.2 7 Stibbs (1955)
40389 43 -2.0 0.2 14 Lloyd Evans (1980)
40727 67 +1.3 0.2 18 Lloyd Evans (1980)
Table 32. O-C residuals for R Mus
Norm.max E O-C Type, Reference
JD2400000+ weight
19346.327 - 952 -0.035d pg Hertzsprung (1928)
26105.508 - 52 +0.003 pg 1 Dartayet et al. (1949)
26473.501 - 3 -0.002 pg 1 Dartayet et al. (1949)
34141.479 +1018 +0.104 pe 1 Eggen et al. (1957)
34839.906 +1111 +0.086 pe 3 Walraven et al. (1958)
34907.506 +1120 +0.094 pe 3 Eggen et al. (1957)
35207.854 +1160 +0.037 pe 3 Irwin (1961)
37836.518 +1510 +0.145 pe 3 Walraven et al. (1964)
42853.512 +2178 +0.359 pe 2 Dean (1977)
43596.970 +2277 +0.305 pe 3 Eggen (1985)
44648.445 +2417 +0.358 pe 3 Eggen (1985)
Figure 17. Upper panel: O-C diagram of R Mus
S Muscae
This Cepheid has long been known as a spectroscopic binary. Its orbital
period is 506 days (Lloyd Evans, 1971). The presence of a blue companion is
predicted by the two-colour diagrams (Stobie, 1970; Dean, 1977; Pel, 1978).
B”hm-Vitense and Proffitt (1985) detected the effect of the companion in
the IUE spectrum of S Mus. The radial velocity observations of S Muscae are
not re-discussed here.
Figure 18. O-C diagram of S Mus
Table 33. O-C residuals for S Mus
Norm.max. E O-C Type, Reference
JD2400000+ weight
26128.045 -1467 -0.081d pg 1 Dartayet et al. (1949)
26466.032 -1432 -0.190 pg 1 Dartayet et al. (1949)
33807.521 - 672 -0.206 pe 1 Eggen et al. (1957)
34541.889 - 596 +0.012 pe 1 Eggen et al. (1957)
34628.743 - 587 -0.073 pe 2 Walraven et al. (1958)
34918.458 - 557 -0.155 pe 3 Eggen et al. (1957)
35227.609 - 525 -0.120 pe 3 Irwin (1961)
37845.449 - 254 -0.106 pe 3 Walraven et al. (1964)
40308.825 + 1 +0.002 pe 3 Stobie (1970)
42859.006 + 265 -0.024 pe 2 Dean (1977)
43602.870 + 342 +0.030 pe 2 Eggen (1985)
44694.391 + 455 -0.015 pe 2 Eggen (1985)
45148.433 + 502 +0.013 pe 1 Eggen (1985)
The light curve of this Cepheid is double-peaked. The moment of the
first maximum was used when constructing the O-C diagram. The O-C residuals
listed in Table 33 have been calculated with the elements:
C = 2440299.163 + 9.659875d*E (27)
+-.012 +-.000036
The O-C diagram in Figure 18 can be best approximated by two almost
parallel lines. The phase jump occurred at about J.D.2439000, before that
epoch the pulsation period was 9.659899 +- 4.0*10^-5 days (taking into
account the photographic O-C residuals, as well). The value of the phase
jump was about 0.1 day, and after the phase jump the elements given in
equation (27) have been valid. The parabolic fit would be somewhat worse.
The amplitude of the light-time effect expected according to equation (1)
is about 0.01 day, therefore this effect can hardly be pointed out in the
O-C diagram of S Muscae.
S Normae
S Nor is one of the most important stars among the Cepheid variables
because of its membership in the open cluster NGC 6087. This calibrating
Cepheid may belong to a spectroscopic binary system (Breger, 1970). Its
duplicity is also suspected on the basis of photometric evidence (Madore,
1977). The gamma-velocities listed in Table 34, including more recent than
Breger's data suggest a variation with a period of either 3300 or 6350 days
(see the lower panel of Figure 19). Even longer periods can be excluded
because the corresponding light-time effect is not seen in the O-C diagram
(see below).
Table 34. gamma-velocities of S Nor
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
18418 11 -5.8 1.0 5 Campbell and Moore (1928)
33905 22 +3.8 0.9 12 Stibbs (1955)
34213 22 +3.5 1.2 7 Stibbs (1955)
38514 44 +5.6 0.3 12 Feast (1967)
38619 7 +9.4 0.5 5 Feast (1967)
38953 17 +7.1 0.1 20 Breger (1970)
39288 121 +8.0 1.9 2 Lloyd Evans (1968)
40377 29 +3.4 0.2 8 Lloyd Evans (1980)
40814 12 +3.1 0.3 3 Lloyd Evans (1980)
41412 4 +2.6 7.1 3 Grayzeck (1978)
41793 4 -2.4 5.8 4 Grayzeck (1978)
45772 198 +5.9 0.2 10 Mermilliod et al. (1987)
46286 53 +5.8 0.1 13 Mermilliod et al. (1987)
Table 35. O-C residuals for S Nor
Norm.max. E O-C Type, Reference
JD2400000+ weight
16580.963 -2813 +0.767d pg Shapley (1930)
18199.911 -2647 +0.511 pg Shapley (1930)
20248.050 -2437 +0.259 pg Shapley (1930)
21350.020 -2324 -0.001 pg Shapley (1930)
23203.204 -2134 -0.123 pg Shapley (1930)
24276.419 -2024 +0.125 pg 1 ten Bruggencate (1927a)
24676.279 -1983 +0.061 pg 1 ten Bruggencate (1927a)
25037.357 -1946 +0.232 pg 1 ten Bruggencate (1927a)
34576.828 - 968 +0.052 pe 3 Walraven et al. (1958)
35230.372 - 901 +0.062 pe 3 Irwin (1961)
36830.115 - 737 +0.109 pe 2 Fernie (1961)
37844.464 - 633 +0.016 pe 3 Walraven et al. (1964)
38888.164 - 526 +0.012 pe 3 Breger (1970)
39268.525 - 487 -0.042 pe 3 Breger (1970)
39678.266 - 445 +0.021 pe 2 Schmidt (1971)
41424.213 - 266 -0.042 pe 1 Grayzeck (1978)
41882.705 - 219 0.000 pe 3 Dean et al. (1977)
42545.994 - 151 +0.001 pe 3 Dean et al. (1977)
43492.182 - 54 +0.027 pe 3 Dean (1981)
43784.761 - 24 -0.021 pe 2 Eggen (1980)
The O-C residuals have been computed with the ephemeris:
C = 2444018.884 + 9.754244d*E (28)
+-.009 +-.000024
Figure 19. Upper panel: O-C diagram of S Nor
Lower panel: gamma-velocities for the same Cepheid
The O-C diagram is approximated by two sections of almost parallel lines
(see Table 35 and the upper panel of Figure 19). Before the phase jump the
most reliable photographic observations have been taken into account in the
fitting procedure which resulted in the period P = 9.754190 + 3.0*10^-5 days.
The phase jump might have occurred at about J.D.2437500, and it amounted to
0.06 day. The observed changes in the gamma-velocity are too small to cause any
noticeable light-time effect, assuming an orbital period of several
thousand days.
RS Normae
RS Nor has been completely neglected spectroscopically: there is not a
single radial velocity measurement published in the literature. The
situation is not much better as far as photometric observations are
concerned, because the O-C diagram (see Table 36 and Figure 20) contains a
few scattered points. Madore (1977) gives evidence for a B8 dwarf
photometric companion.
The O-C residuals have been computed with the elements:
C = 2435308.175 + 6.198136d*E (29)
+-.009 +-.000012
Table 36. O-C residuals for RS Nor
Norm.max. E O-C Type, Reference
JD2400000+ weight
25583.330 -1569 +0.030d pg 1 Kruytbosch (1930b)
34737.872 - 92 -0.074 pe 1 Walraven et al. (1958)
35227.600 - 13 +0.001 pe 3 Irwin (1961)
35332.962 + 4 -0.006 pe 1 Walraven et al. (1958)
40768.737 + 881 +0.004 pe 3 Pel (1976)
41103.449 + 935 +0.017 pe 2 Pel (1976)
Figure 20. O-C diagram of RS Nor
The early photographic observations were also used when determining the
average pulsation period.
SY Normae
An early type photometric companion to this Cepheid was suspected by
Madore (1977). A companion was later found using IUE measurements
(B”hm-Vitense and Proffitt,1985) but it cannot be ruled out that these two
stars form only an optical pair. Radial velocity measurements would be very
important in order to find the physical relation between the two stars, if
it really exists. The only available radial velocity data published by
Grayzeck (1978) are not suitable for drawing any conclusion.
The O-C residuals listed in Table 37 and plotted in Figure 21 have been
calculated with the elements:
C = 2440731.750 + 12.645687d*E (30)
+-.004 +-.000016
The pulsation period has been stable since J.D.2434700. It is worth
mentioning that the moment of the normal maximum given in equation (30)
strongly differs from the value given in the GCVS (Kholopov et al.,
Table 37. O-C residuals for SY Nor
Norm.max. E O-C Type, Reference
JD2400000+ weight
25600.646 -1197 +5.783d pg Kruytbosch (1930a)
34750.337 - 473 -0.003 pe 3 Walraven et al. (1958)
35218.235 - 436 +0.005 pe 3 Irwin (1961)
40390.261 - 27 -0.055 pe 1 Stobie (1970)
40769.693 + 3 +0.006 pe 3 Pel (1976)
41111.126 + 30 +0.005 pe 3 Pel (1976)
41591.643 + 68 -0.014 pe 2 Grayzeck (1978)
41920.457 + 94 +0.012 pe 3 Madore (1975)
Figure 21. O-C diagram of SY Nor
1985-1987). This deviation is probably caused by Kruytbosch's (1930a)
ephemeris. Unfortunately the original photographic observations have not
been published, therefore it cannot be decided whether there was a real
period change, or Kruytbosch published an erroneous ephemeris.
Y Ophiuchi
Y Oph belongs to a spectroscopic binary system. Its orbital period was
determined by Abt and Levy (1978) as being 2612 days. Evans and Lyons
(1986) questioned this value of the orbital period, and even doubted the
variability in the gamma-velocity. The presence of a blue photometric
companion is suspected by Pel (1978) but such a blue star is not seen in an
IUE spectrum (Evans and Lyons, 1986). All the available radial velocity
data were subjected to a period analysis which resulted in the value of
1222.5 +- 10 days for the orbital period. The gamma-velocities are listed in
Table 38, and the orbital radial velocity curve folded with the recently
determined period is shown in Figure 22. In this figure open circles denote
Table 38. gamma-velocities of Y Oph
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
17066 27 -4.9 0.3 42 Albrecht (1907)
17440 6 -9.4 2.0 2 Albrecht (1907)
25356 13 -4.8 1.0 5 Sanford (1935)
26549 32 -1.0 0.6 14 Sanford (1935)
26911 35 -8.3 0.8 7 Sanford (1935)
27226 45 -11.8 0.6 11 Sanford (1935)
34482 29 -7.0 0.6 12 Abt (1954)
34599 32 -7.9 1.1 4 Abt (1954)
40365 36 -5.8 0.2 9 Lloyd Evans (1980)
40718 25 -7.8 0.5 4 Abt and Levy (1978)
40762 50 -6.4 0.2 7 Lloyd Evans (1980)
40792 28 -7.3 0.4 4 Evans and Lyons (1986)
41110 23 -6.3 0.5 3 Evans and Lyons (1986)
41116 36 -7.2 0.6 4 Abt and Levy (1978)
41534 79 -6.1 0.3 6 Abt and Levy (1978)
42228 86 -6.5 0.2 3 Abt and Levy (1978)
42565 35 -7.3 0.3 2 Abt and Levy (1978)
42900 27 -10.1 0.5 6 Abt and Levy (1978)
43281 26 -8.2 0.5 4 Abt and Levy (1978)
43350 46 -9.4 1.1 13 Wilson et al. (1989)
43639 46 -5.1 1.0 17 Barnes et al. (1987)
43976 5 -5.8 0.5 5 Coulson and Caldwell (1985)
44013 58 -10.1 1.1 12 Barnes et al. (1987)
44049 4 -9.0 0.5 3 Evans and Lyons (1986)
44181 3 -10.0 1.0 2 Coulson and Caldwell (1985)
44415 47 -6.4 0.4 9 Coulson and Caldwell (1985)
44446 23 -7.9 0.5 3 Evans and Lyons (1986)
44449 1 -12.5 1.3 1 Beavers and Eitter (1986)
44759 36 -8.8 0.6 4 Coulson and Caldwell (1985)
44819 25 -6.2 0.7 2 Evans and Lyons (1986)
45092 2 -7.2 0.7 3 Coulson and Caldwell (1985)
45388 1 -9.5 2.7 3 Barnes et al. (1987)
45501 21 -8.6 0.3 6 Evans and Lyons (1986)
45875 I -9.9 0.7 1 Evans and Lyons (1986)
those low weight gamma-velocities that are based on one or two radial velocity
measurements. The semi-amplitude of the orbital radial velocity variations
is 1.60 + 0.47 km/s. In spite of its low amplitude, the orbital effect
seems to be real because its consequences also appear in the O-C diagram
(see below).
The early part of the O-C diagram was constructed by Detre (1970). In
the present paper all the photoelectric and photographic series of
observations are discussed. The O-C residuals listed in Table 39 have been
calculated with the elements:
C = 2439853.173 + 17.126908d*E (31)
+-.033 +-.000139
Table 39. O-C residuals for Y Oph
Norm.max E O-C Type, Reference
JD2400000+ weight
25077.192 -863 +4.541d pg ten Bruggencate (1927b)
32781.493 -413 +1.733 pe 2 Eggen (1951)
33106.646 -394 +1.475 pe 3 Eggen (1951)
34322.185 -323 +1.003 pe 3 Abt (1954)
34733.130 -299 +0.902 pe 2 Walraven et al. (1958)
35281.188 -267 +0.899 pe 3 Irwin (1958)
35691.858 -243 +0.524 pe 2 Prokof'yeva (1961)
37079.101 -162 +0.487 pe 2 Mitchell et al. (1964)
37472.819 -139 +0.286 pe 1 Mitchell et al. (1964)
37815.507 -119 +0.436 pe 1 Williams (1966)
38603.166 - 73 +0.257 pe 1 Wisniewski and Johnson (1968)
39014.145 - 49 +0.190 pe 3 Wisniewski and Johnson (1968)
39682.123 - 10 +0.219 pe 3 Schmidt (1971)
40401.559 + 32 +0.325 pe 1 Feltz and McNamara (1980)
40778.016 + 54 -0.010 pe 3 Pel (1976)
40812.402 + 56 +0.122 pe 1 Feltz and McNamara (1980)
40829.354 + 57 -0.053 pe 2 Evans (1976)
41188.978 + 78 -0.093 pe 2 Feltz and McNamara (1980)
42953.217 +181 +0.074 pe 3 Dean (1977)
43038.950 +186 +0.172 pe 2 Dean (1981)
43312.747 +202 -0.061 pe 3 Moffett and Barnes (1984)
43672.337 +223 -0.136 pe 2 Moffett and Barnes (1984)
44015.145 +243 +0.133 pe 3 Moffett and Barnes (1984)
44032.132 +244 -0.007 pe 2 Coulson and Caldwell (1985)
44443.162 +268 -0.022 pe 3 Coulson and Caldwell (1985)
44460.261 +269 -0.050 pe 3 Eggen (1983b)
44871.342 +293 -0.015 pe 3 Coulson and Caldwell (1985)
46292.876 +376 -0.014 pe 3 Berdnikov (1987)
46601.179 +394 +0.004 pe 1 Lloyd et al. (1987)
Table 40. Changes in the pulsation period of Y Oph
J.D. interval P
2432781 - 2433106 17.113288d
+-.000010
34733 - 35281 17.126813d
+-.000007
35281 - 35691 17.111255d
+-.000001
39014 - 39682 17.127643d
+-.000001
40778 - 46601 17.126908d
+.000139
Figure 22. Orbital velocity curve of Y Oph
Figure 23. O-C diagram of Y Oph
The O-C diagram (see Figure 23) is of complex structure. It is approximated
with sections of straight lines, representing two characteristic periods:
either 17.112 or 17.127 days. Table 40 summarizes the individual periods
and the time intervals in which the given period was valid.
The alternating periods can be considered as a special case of the
phase jump: there is an interval of finite length when the star pulsates
with another period before returning to the "original" pulsation period. As
in the previous cases, the phase jump is a characteristic feature of binary
Cepheids. Moreover, the final part of the O-C diagram (after J.D.2440000)
shows unusually wide scatter, if approximated by a single period. The
dashed lines, however, suggest that this part also consists of several
phase jumps, and the predominant period is the shorter one (17.112 days).
The cyclic occurrence of this pulsation period can also be suspected, the
cycle length being about 2400 days in the first case, and about 1200 days
in the second case (N.B. the orbital period determined above is just over
1200 days). This phenomenon cannot be interpreted as a light-time effect
because of the large amplitude but it gives a further support to the
reality of the 1222.5 day spectroscopic orbital period, and calls the
attention that the binary companion is able to control the changes in the
pulsation period.
BF Ophiuchi
According to Mianes (1963) and Balona (1977), BF Oph has a red
photometric companion, while Gieren (1982) already suspected the
spectroscopic binary nature of this Cepheid. The analysis of the available
radial velocity data (see Table 41) suggests an orbital period of 4420 +- 80
days. The orbital velocity curve is shown in Figure 24. Although the plot
of the data is not too convincing, this period is also supported by the
features in the O-C diagram (see below).
Table 41. gamma-velocities of BF Oph
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
25597 219 -32.5 2.6 4 Joy (1937)
26152 45 -33.2 2.2 5 Joy (1937)
33905 21 -30.0 1.1 9 Stibbs (1955)
34199 14 -31.8 1.5 5 Stibbs (1955)
40559 210 -29.4 0.2 13 Lloyd Evans (1980)
44233 207 -28.3 1.1 13 Barnes et al. (1988)
44423 4 -29.2 0.4 22 Gieren (1981a)
44945 295 -28.2 2.3 4 Barnes et al. (1988)
Figure 24. Orbital velocity curve of BF Oph
Figure 25. Upper panel: O-C diagram of BF Oph
Lower panel: gamma-velocities for the same Cepheid
The O-C residuals listed in Table 42 have been calculated with the
elements:
C = 2444435.105 + 4.067698d*E (32)
+-.005 +-.000001
The O-C diagram (Figure 25) can be best represented by a sine-wave
superimposed on a parabola. The moments of the normal maxima can be
predicted as follows:
C = 2444435.105 + 4.067698d*E - 4.87d*10^-9*E^2 - 0.017d*cos(2n(0.000904*E+0.046)) (33)
+-.005 +-.000001 +-.89 +-.005 +-.000073 +-.081
Table 42. O-C residuals for BF Oph
Norm.max. E O-C Type, Reference
JD2400000+ weight
15618.712 -7084 -0.820d pg Shapley (1930)
16558.440 -6853 -0.731 pg Shapley (1930)
17180.773 -6700 -0.755 pg Shapley (1930)
18030.957 -6491 -0.720 pg Shapley (1930)
18572.053 -6358 -0.628 pg Shapley (1930)
19479.214 -6135 -0.564 pg Shapley (1930)
20069.022 -5990 -0.572 pg Shapley (1930)
20870.376 -5793 -0.554 pg Shapley (1930)
21541.624 -5628 -0.477 pg Shapley (1930)
22440.589 -5407 -0.473 pg Shapley (1930)
23351.842 -5183 -0.384 pg Shapley (1930)
24149.199 -4987 -0.296 pg Shapley (1930)
25320.776 -4699 -0.216 pg Shapley (1930)
26781.021 -4340 -0.275 pg O'Connell (1937)
27269.159 -4220 -0.260 pg O'Connell (1937)
34790.528 -2371 -0.065 pe 1 Walraven et al. (1958)
35229.827 -2263 -0.077 pe 3 Irwin (1961)
37113.244 -1800 -0.005 pe 1 Mitchell et al. (1964)
37471.204 -1712 -0.002 pe 2 Mitchell et al. (1964)
39549.798 -1201 -0.002 pe 2 Takase (1969)
40338.898 -1007 -0.035 pe 3 Stobie (1970)
40761.959 - 903 -0.015 pe 3 Pel (1976)
42856.824 - 388 -0.014 pe 2 Dean (1977)
44361.869 - 18 -0.017 pe 3 Moffett and Barnes (1984)
44414.749 - 5 -0.018 pe 3 Gieren (1981b)
44809.332 + 92 -0.001 pe 3 Eggen (1985)
Here only the photoelectric O-C residuals have been taken into account.
According to the cosine term, the orbital period is 4500 +- 360 days, being
in a very good agreement with the spectroscopic value. The amplitude and
the phase of the wave is also adequate to the spectroscopic binary
interpretation of the gamma-velocity changes. It is worth mentioning that,
according to this value of the orbital period, BF Oph has not been observed
spectroscopically during the orbital phases when the Cepheid is strongly
moving away from us, i.e. the amplitude of the gamma-velocity variations is
larger than observed so far.
A simple parabolic fit applied to the whole set of O-C residuals
resulted in the pulsation period as a function of time:
C = 4.067665d - 4.12d*10^-8*E (34)
+-.000008 +-.22
where the E epoch number is the same as in equations (32) and (33).
AP Puppis
This Cepheid is likely to be a spectroscopic binary with one of the
largest orbital velocity amplitude (see Table 43 and the lower panel of
Figure 26). The extremely large shift between Joy's (1937) and the more
recent radial velocity data was already noted by Lloyd Evans (1982) but no
subsequent radial velocity observations followed this discovery.
The O-C residuals have been calculated with the elements:
C = 2440689.133 + 5.084274d*E (35)
+-.019 +-.000027
Table 43. gamma-velocities of AP Pup
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
28620 27 46.1 2.3 5 Joy (1937)
33980 26 17.0 0.7 21 Stibbs (1955)
34138 36 18.5 3.0 2 Stibbs (1955)
40335 17 13.7 0.3 4 Lloyd Evans (1980)
40629 8 13.0 0.4 3 Lloyd Evans (1980)
Figure 26. Upper panel: O-C diagram of AP Pup
Lower panel: gamma-velocities for the same Cepheid
Table 44. O-C residuals for AP Pup
Norm.max. E O-C Type, Reference
JD2400000+ weight
35182.832 -1083 -0.032d pe 1 Irwin (1961)
35299.806 -1060 +0.003 pe 2 Walraven et al. (1958)
40740.008 + 10 +0.032 pe 3 Pel (1976)
42854.964 + 426 -0.070 pe 1 Dean (1977)
The small number of the photometric observational series (see Table 44 and
the upper panel of Figure 26) does not allow a reliable search for the
light-time effect expected in this binary system. The plot of the O-C
residuals can be approximated by a free-hand sinusoidal term (taking into
account the phases prescribed by the gamma-velocity variations) suggesting a
long (about 9000 - 10000 days) orbital period, and a slightly shorter
pulsation period than used in equation (35). Any further photometric and/or
spectroscopic observations may play a decisive role in determining the
orbital period of this neglected star.
AT Puppis
The changing gamma-velocity of AT Pup was first reported by Gieren (1985).
His conclusion is confirmed here (see Table 45 and the lower panel of
Figure 27).
Figure 27. Upper panel: O-C diagram of AT Pup
Lower panel: gamma-velocities for the same Cepheid
Table 45. gamma-velocities of AT Pup
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
28614 25 24.2 2.6 4 Joy (1937)
34019 42 29.1 0.8 16 Stibbs (1955)
34163 20 28.2 1.5 5 Stibbs (1955)
45042 2 20.6 0.5 20 Gieren (1985)
Table 46. O-C residuals for AT Pup
Norm.max. E O-C Type, Reference
JD2400000+ weight
30750.437 -1499 -0.015d pg Erleksova (1961)
34142.642 - 990 -0.234 pg Erleksova (1961)
35215.887 - 829 -0.034 pe 1 Irwin (1961)
35589.121 - 773 -0.034 pe 3 Walraven et al. (1958)
37648.645 - 464 +0.043 pe 2 Mitchell et al. (1964)
40741.152 0 +0.046 pe 3 Pel (1976)
42893.867 + 323 +0.005 pe 1 Dean (1977)
44513.455 + 566 +0.027 pe 1 Eggen (1985)
45046.576 + 646 -0.042 pe 3 Gieren (1985)
The O-C residuals have been calculated with the ephemeris:
C = 2440741.106 + 6.664879d*E (36)
+-.011 +-.000020
Gieren's (1985) observations made in 1981 were omitted because there can be
a systematic error of unknown origin in the published moments of the
observations in the case of each of the three stars (AT Pup, T Vel, V Vel)
studied here from his sample. Such an error is not present in Gieren's 1982
observations, both the O-C residual, and the light curve is the most
reliable among the observations on AT Pup. This latter statement is also
true for the 1982 observations on T Vel and V Vel.
The wave-like pattern of the photoelectric O-C residuals (see Table 46
and the upper panel of Figure 27), together with the variation in the
gamma-velocity, is in accord with a very long (about 20000 days) orbital
period. From the radial velocity observations alone the orbital period can
be much shorter but in that case the light-time effect interpretation of
the O-C diagram fails.
MY Puppis
No variability in the gamma-velocity of MY Pup is seen in the available
data (see Table 47).
The O-C residuals have been computed with the elements:
C = 2441043.597 + 5.694998d*E (37)
+-.013 +-.000031
The plot of the O-C residuals (see Table 48 and Figure 28) can be well
approximated by a parabola. This is the only star in this sample where
Table 47. gamma-velocities of MY Pup
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
24422 301 11.4 1.0 5 Neubauer (1929)
43172 56 13.4 0.2 23 Stobie and Balona (1979)
43533 4 12.8 0.4 9 Stobie and Balona (1979)
Table 48. O-C residuals for MY Pup
Norm.max. E O-C Type, Reference
JD2400000+ weight
24421.80 -2919 +1.90d vr 1 Neubauer (1929)
39107.348 - 340 +0.050 pe 1 Stobie (1972)
41043.599 0 +0.002 pe 3 Stobie (1972)
43184.919 + 376 +0.003 pe 3 Stobie and Balona (1979)
44284.122 + 569 +0.071 pe 1 Eggen (1985)
44568.948 + 619 +0.147 pe 1 Eggen (1985)
Figure 28. O-C diagram of MY Pup
radial velocity measurements were also used when determining the shape of
the O-C graph. The period change has been so strong since the twenties that
it could not be avoided making exceptions lacking suitable photometric
observations. The continuously increasing period can be calculated as
follows:
P = 5.694998 + 4.47d*10^-7*E (38)
+-.000031 +-.12
where E corresponds to the epoch number used in equation (37).
U Sagittarii
U Sgr is the other "classical" cluster-member Cepheid, it belongs to
the open cluster M25. Duplicity of U Sgr has long been debated, the various
pieces of evidence are summarized by Leonard and Turner (1986). Gieren
(1982) suspected the variation in the gamma-velocity, preferring a long
orbital period, similarly to an earlier study performed by Wallerstein
(1960). Table 49 summarizes the gamma-velocities of U Sgr. Joy's (1937) and
Hayford's (1932) data have been omitted because of much lower quality of
those early observations. The 800 - 8000 day interval was studied when
searching for the possible orbital period. The best curve was obtained at
Porb = 4550 +- 230 days. The gamma-velocities folded with this period are shown
Table 49. gamma-velocities of U Sgr
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
33916 33 3.5 0.8 14 Stibbs (1955)
34202 27 5.1 2.1 3 Stibbs (1955)
37223 151 3.8 0.6 11 Jacobsen (1970)
38200 28 3.7 2.0 2 Jacobsen (1970)
38955 19 6.8 0.5 14 Breger (1967)
39314 1 5.0 2.0 1 Jacobsen (1970)
39377 5 3.5 1.9 2 Lloyd Evans (1968)
40392 49 3.0 0.2 7 Lloyd Evans (1980)
40816 12 1.4 0.4 3 Lloyd Evans (1980)
43361 42 3.4 1.2 12 Wilson et al. (1989)
43668 31 7.1 1.2 11 Barnes et al. (1987)
44015 61 2.7 1.4 8 Barnes et al. (1987)
44112 146 2.9 0.2 6 Mermilliod et al. (1987)
44423 4 0.1 0.4 26 Gieren (1981a)
45182 18 2.0 0.5 2 Mermilliod et al. (1987)
45880 3 2.0 0.3 4 Mermilliod et al. (1987)
46275 10 2.6 0.1 30 Mermilliod et al. (1987)
Figure 29. Orbital velocity curve of U Sgr
Table 50. O-C residuals for U Sgr
Norm.max E O-C Type, Reference
JD2400000+ weight
14496.341 -2316 +0.336d vis Pickering (1904)
15946.443 -2101 +0.214 pg Shapley (1930)
17329.147 -1896 +0.146 pg Shapley (1930)
18475.855 -1726 +0.165 pg Shapley (1930)
19609.067 -1558 +0.179 pg Shapley (1930)
20459.006 -1432 +0.219 pg Shapley (1930)
21308.978 -1306 +0.292 pg Shapley (1930)
23244.642 -1019 +0.075 pg Shapley (1930)
24674.684 - 807 +0.129 pg Voute and ten Bruggencate (1927)
24694.765 - 804 -0.026 pg Shapley (1930)
25059.149 - 750 +0.116 pg Voute and ten Bruggencate (1927)
33133.030 + 447 -0.042 pe 2 Eggen (1951)
34758.595 + 688 -0.078 pe 2 Walraven et al. (1958)
35284.729 + 766 -0.071 pe 3 Irwin (1961)
35952.493 + 865 -0.085 pe 2 Johnson (1960)
36782.149 + 988 -0.092 pe 3 Sandage (1960)
37099.195 +1035 -0.072 pe 3 Wampler et al. (1961)
37119.444 +1038 -0.059 pe 2 Mitchell et al. (1961)
37180.138 +1047 -0.072 pe 2 Mitchell et al. (1964)
37800.793 +1139 +0.022 pe 1 Williams (1966)
38920.467 +1305 -0.012 pe 2 Wisniewski and Johnson (1968)
39675.918 +1417 -0.026 pe 2 Schmidt (1971)
40788.948 +1582 +0.041 pe 3 Pel (1976)
40829.379 +1588 0.000 pe 1 Feltz and McNamara (1980)
42448.200 +1828 -0.034 pe 2 Dean et al. (1977)
43486.971 +1982 -0.028 pe 3 Dean (1981)
43608.399 +2000 -0.014 pe 3 Moffett and Barnes (1984)
44411.081 +2119 -0.014 pe 3 Gieren (1981b)
44458.345 +2126 +0.033 pe 3 Eggen (1985)
44721.388 +2165 +0.012 pe 3 Berdnikov (1986)
Figure 30. Upper panel: O-C diagram or U Sgr
Lower panel: gamma-velocities for the same Cepheid
in Figure 29 (the zero phase is arbitrarily chosen at J.D.2400000). In this
figure open circles denote those gamma-velocities which are only based on two
velocity measurements. Assuming that this orbital period is correct, the
full amplitude of the orbital radial velocity variation is 2K = 3.6 +- 1.3
km/s.
Although Figure 29 is not fully convincing, i.e. another value of the
orbital period cannot be excluded, the O-C diagram gives a further support
to binary nature of U Sgr. The O-C residuals have been computed with the
elements:
C = 2430117.955 + 6.745229d*E (39)
+-.030 +-.000016
As is seen in Figure 30 (based on the data listed in Table 50), the O-C
diagram can be characterized by a phase jump occurred at about J.D.2437500.
Before the phase jump (of an amplitude of 0.07 day) the pulsation period
was 6.745192 +- 1.5d*10^-5 days. This pattern of the O-C diagram cannot be
explained with a light-time effect because its expected amplitude is less
than 0.01 day. According to numerous other cases, the rejumping period is a
typical feature of binary Cepheids, therefore duplicity of U Sgr can be
stated beyond doubt.
W Sagittarii
This Cepheid belongs to a multiple star system: at present four
components are identified (Babel et al., 1989, and references therein). The
Cepheid itself is a member of a spectroscopic binary system in this
hierarchy. The orbital period is 1780 +- 5 days, and the orbital velocity
amplitude is the least among the well-studied spectroscopic binary
Cepheids (K = 2.35 +- 0.47 km/s, - Babel et al., 1989).
The O-C residuals have been calculated with the elements:
C = 2443374.622 + 7.594904d*E (40)
+-.006 +-.000008
The O-C diagram (see Table 51 and Figure 31) can be well described
assuming a constant period. Although Babel et al. (1989) approximate the
Table 51. O-C residuals for W Sgr
Norm.max. E O-C Type, Reference
JD2400000+ weight
14491.629 -3803 +0.427d vis Pickering (1904)
15220.531 -3707 +0.218 pg Shapley (1930)
16306.666 -3564 +0.282 pg Shapley (1930)
17392.573 -3421 +0.118 pg Shapley (1930)
18471.022 -3279 +0.090 pg Shapley (1930)
19640.603 -3125 +0.056 pg Shapley (1930)
20605.127 -2998 +0.027 pg Shapley (1930)
21782.113 -2843 +0.197 pg Shapley (1930)
23232.817 -2652 -0.120 pg Shapley (1930)
24440.488 -2493 -0.038 pg Shapley (1930)
24577.282 -2475 +0.047 pg Voute (1927a)
25443.229 -2361 +0.175 pg Shapley (1930)
34572.151 -1159 +0.023 pe 2 Walraven et al. (1958)
34868.304 -1120 -0.026 pe 3 Eggen et al. (1957)
35248.090 -1070 +0.015 pe 3 Irwin (1961)
37253.091 - 806 -0.039 pe 1 Mitchell et al. (1964)
37883.539 - 723 +0.033 pe 3 Walraven et al. (1964)
38650.553 - 622 -0.039 pe 2 Wisniewski and Johnson (1968)
40017.674 - 442 0.000 pe 3 Cousins and Lagerweij (1968)
42858.147 - 68 -0.022 pe 2 Dean (1977)
43617.650 + 32 -0.009 pe 3 Moffett and Barnes (1984)
43754.383 + 50 +0.016 pe 3 Babel et al. (1989)
45508.797 + 281 +0.007 pe 3 Babel et al. (1989)
Figure 31. O-C diagram of W Sgr
O-C graph by a parabola (continuous period increase), the parabolic fit to
the data in Table 51 has been of much lower accuracy as compared with the
linear fit. No effect of duplicity is seen in the O-C diagram, since the
amplitude of the light-time effect is much smaller than the limit of
detection.
X Sagittarii
X Sgr belongs to a spectroscopic binary system with an orbital period
of 507.25 days (Szabados, 1989). Because the effect of the orbital motion
on the radial velocity variations is rather small, the value of the orbital
period is tentative, and needs confirmation. Nevertheless, a blue
photometric companion to X Sgr has been suspected by Pel (1978).
The O-C residuals listed in Table 52 have been calculated with the
elements:
C = 2440741.492 + 7.012777d*E (41)
+-.015 +-.000028
Table 52. O-C residuals for X Sgr
Norm.max. E O-C Type, Reference
JD2400000+ weight
15531.897 -3595 +1.338d pg 1 Shapley (1930)
16422.246 -3468 +1.065 pg 1 Shapley (1930)
17228.609 -3353 +0.958 pg 1 Shapley (1930)
17922.830 -3254 +0.914 pg 1 Shapley (1930)
18652.136 -3150 +0.892 pg 1 Shapley (1930)
19144.481 -3037 +0.793 pg 1 Shapley (1930)
20152.889 -2936 +0.910 pg 1 Shapley (1930)
20888.857 -2831 +0.537 pg 1 Shapley (1930)
21569.130 -2734 +0.570 pg 1 Shapley (1930)
22501.724 -2601 +0.465 pg 1 Shapley (1930)
23329.154 -2483 +0.387 pg 1 Shapley (1930)
24353.118 -2337 +0.486 pg 1 Shapley (1930)
24514.329 -2314 +0.403 pg 1 Voute (1927a)
25440.009 -2182 +0.396 pg 1 Shapley (1930)
34871.956 - 837 +0.158 pe 1 Eggen et al. (1957)
35222.549 - 787 +0.112 pe 3 Irwin (1961)
35250.607 - 783 +0.119 pe 2 Walraven et al. (1958)
37129.933 - 515 +0.021 pe 2 Mitchell et al. (1964)
39051.428 - 241 +0.015 pe 3 Wisniewski and Johnson (1968)
40762.530 + 3 0.000 pe 3 Pel (1976)
42852.333 + 301 -0.005 pe 3 Dean (1977)
43658.808 + 416 0.000 pe 3 Moffett and Barnes (1984)
44437.218 + 527 -0.007 pe 3 Eggen (1985)
Figure 32. O-C diagram of X Sgr
As is seen in Figure 32, the O-C diagram of X Sgr is parabolic. The
parabola fitted to the photographic and photoelectric O-C residuals has
resulted in the following temporal variation in the pulsation period:
P = 7.012777d + 1.65*10^-7*E (42)
+-.000028 +-.21
where the E epoch number is the same as in equation (41). It has to be
noted, however, that the period increase used to be even stronger during
the visual observations made by Schmidt (Hertzsprung, 1934) in the last
century.
Y Sagittarii
Table 53. gamma-velocities of Y Sgr
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
16615 173 +1.5 1.1 8 Duncan (1908)
18152 22 +2.7 0.6 27 Duncan (1908)
22691 368 -6.0 0.6 24 Duncan (1922)
23377 165 -6.0 0.4 22 ten Bruggencate (1930)
23550 363 -3.0 0.5 16 Campbell and Moore (1928)
24134 141 -4.9 0.6 14 ten Bruggencate (1930)
25089 90 -3.5 0.6 15 ten Bruggencate (1930)
25794 20 -4.0 0.5 16 ten Bruggencate (1930)
40380 47 -3.3 0.2 8 Lloyd Evans (1980)
40765 51 -1.8 0.2 7 Lloyd Evans (1980)
43354 45 -1.1 1.2 12 Wilson et al. (1989)
43649 41 -3.6 1.1 14 Barnes et al. (1987)
44014 62 -2.7 1.4 8 Barnes et al. (1987)
44796 1 -6.6 1.3 1 Beavers and Eitter (1986)
The changing gamma-velocity of Y Sgr was first reported by ten Bruggencate
(1930). The recent determination of the gamma-velocities confirms this
conclusion (see Table 53 and the lower panel of Figure 33). The pattern of
the gamma-velocity changes suggests a very long (P > 10000 days) orbital
period.
Table 54. O-C residuals for Y Sgr
Norm.max. E O-C Type, Reference
JD2400000+ weight
14499.428 -4549 +0.205d vis Pickering (1904)
18176.856 -3912 -0.010 vis Nijland (1923)
18962.147 -3776 +0.101 vis Nijland (1923)
24712.345 -2780 +0.012 pg ten Bruggencate (1928)
25070.247 -2718 -0.035 pg ten Bruggencate (1928)
25439.689 -2654 -0.089 pg ten Bruggencate (1928)
29839.040 -1892 -0.054 pg Filin (1950b)
30681.845 -1746 -0.163 pg Filin (1950b)
31449.885 -1613 +0.018 pg Filin (1950b)
32408.117 -1447 -0.131 pg Filin (1950b)
33118.360 -1324 -0.014 pe 2 Eggen (1951)
33141.471 -1320 +0.004 pg Filin (1950b)
34879.244 -1019 -0.011 pe 2 Walraven et al. (1958)
35271.837 - 951 -0.008 pe 3 Irwin (1961)
36097.317 - 808 -0.121 pe 1 Svolopoulos (1960)
37130.873 - 629 0.000 pe 2 Mitchell et al. (1964)
37800.726 - 513 +0.141 pe 1 Williams (1966)
38937.984 - 316 +0.043 pe 1 Wisniewski and Johnson (1968)
40779.682 + 3 +0.033 pe 3 Pel (1976)
40820.055 + 10 -0.008 pe 2 Feltz and McNamara (1980)
42881.153 + 367 -0.006 pe 2 Dean (1977)
43441.162 + 464 -0.015 pe 3 Moffett and Barnes (1984)
44041.585 + 568 -0.024 pe 3 Moffett and Barnes (1984)
44821.027 + 703 +0.012 pe 1 Eggen (1985)
Figure 33. Upper panel: O-C diagram of Y Sgr
Lower panel: gamma-velocities for the same Cepheid
The O-C residuals have been computed with the elements:
C = 2440762.329 + 5.773380d*E (43)
+-.009 +-.000013
The light-time effect expected in such a long period spectroscopic binary
is present in the O-C diagram (see Table 54 and the upper panel of Figure
33) but the limited time-base of the photoelectric observations does not
allow the successful determination of the long orbital period. A cycle
length as long as 10000 - 12000 days is in accordance with the
photoelectric O-C residuals but a much longer period cannot be ruled out,
either.
WZ Sagittarii
The available radial velocity measurements might indicate a variable
gamma-velocity (see Table 55 and the lower panel of Figure 34). Joy's (1937)
first two observations have not been taken into account here. Further good
quality radial velocity data are necessary.
Table 55. gamma-velocities of WZ Sgr
JD sigma v gammma sigma n Reference
2400000+ [d] [km/s] [km/s]
25985 282 -10.6 1.8 8 Joy (1937)
44327 231 -12.5 2.8 3 Barnes et al. (1988)
44589 297 -18.3 0.2 21 Coulson and Caldwell (1985)
Figure 34. Upper panel: O-C diagram of WZ Sgr
Lower panel: gamma-velocities for the same Cepheid
Table 56. O-C residuals for WZ Sgr
Norm.max. E O-C Type, Reference
JD2400000+ weight
15929.289 -896 +0.025d pg Shapley (1930)
17022.168 -846 +0.414 pg Shapley (1930)
18114.435 -796 +0.192 pg Shapley (1930)
19250.773 -744 +0.341 pg Shapley (1930)
21129.367 -658 -0.147 pg Shapley (1930)
23183.108 -564 -0.286 pg Shapley (1930)
24450.260 -506 -0.422 pg Shapley (1930)
24865.634 -487 -0.194 pg Voute (1930a)
25805.161 -444 -0.208 pg Voute (1930a)
29956.518 -254 -0.311 pg Filin (1950b)
30983.476 -207 -0.293 pg Filin (1950b)
32010.500 -160 -0.209 pg Filin (1950b)
32971.974 -116 -0.125 pg Filin (1950b)
33124.977 -109 -0.071 pe 2 Eggen (1951)
34632.661 - 40 -0.022 pe 2 Walraven et al. (1958)
35244.562 - 12 +0.084 pe 2 Irwin (1961)
37232.733 + 79 -0.075 pe 2 Mitchell et al. (1964)
37910.227 +110 +0.075 pe 3 Walraven et al. (1964)
41908.570 +293 -0.093 pe 1 Madore (1975)
42870.045 +337 -0.009 pe 2 Dean (1977)
43372.555 +360 -0.044 pe 3 Dean (1981)
44399.590 +407 +0.051 pe 3 Coulson and Caldwell (1985)
44486.967 +411 +0.029 pe 3 Moffett and Barnes (1984)
44508.828 +412 +0.040 pe 1 Eggen (1983b)
44923.961 +431 +0.027 pe 3 Coulson and Caldwell (1985)
45776.012 +470 -0.064 pe 3 Berdnikov (1986)
The O-C residuals have been computed with the elements:
C = 2435506.675 + 21.849789d*E (44)
+-.017 +-.000053
The pulsation period has been constant since the early photoelectric
observations (see Table 56 and the upper panel of Figure 34), while before
J.D.2433000 some changes occurred in the period. However, those earlier
variations were not secular ones (such long period Cepheids usually show
much larger continuous period changes indicating stellar evolution
(Szabados, 1981)).
AP Sagittarii
The present study confirms Gieren's (1982) statement concerning the
variable gamma-velocity of AP Sgr. The data in Table 57 (shown plotted in the
lower panel of Figure 35) were analysed for possible periodicity. A number
of periods (5625, 6725, 7200, and 7500 days) describe the variable
gamma-velocity reasonably well, the most probable value of the orbital period
Table 57. gamma-velocities of AP Sgr
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
21733 1 - 6.4 4.5 1 Joy (1937)
24694 700 -18.9 2.6 3 Joy (1937)
26313 157 -18.3 2.0 6 Joy (1937)
39279 19 -19.7 0.8 6 Lloyd Evans (1968)
40592 219 -18.6 0.2 10 Lloyd Evans (1980)
44062 2 - 8.3 2.3 4 Barnes et al. (1988)
44423 4 -14.7 0.4 22 Gieren (1981a)
44579 168 -13.5 1.4 9 Barnes et al. (1988)
Table 58. O-C residuals for AP Sgr
Norm.max E O-C Type, Reference
JD2400000+ weight
16021.186 -3959 -0.053d pg Shapley (1930)
17381.853 -3690 +0.035 pg Shapley (1930)
18469.235 -3475 -0.035 pg Shapley (1930)
19652.935 -3241 +0.113 pg Shapley (1930)
20750.509 -3024 +0.119 pg Shapley (1930)
21640.649 -2848 +0.066 pg Shapley (1930)
23679.094 -2445 +0.171 pg Shapley (1930)
25868.992 -2012 -0.009 pg 1 Voute (1930b)
29829.379 -1229 +0.030 pg Filatov (1966)
31280.959 - 942 -0.012 pg Filatov (1966)
32540.355 - 693 -0.037 pg Filatov (1966)
33369.887 - 529 -0.003 pg Filatov (1966)
34391.562 - 327 -0.027 pg Filatov (1966)
34720.309 - 262 -0.045 pe 2 Walraven et al. (1958)
35276.695 - 152 -0.030 pe 2 Irwin (1961)
36010.163 - 7 +0.040 pg Filatov (1966)
37208.869 + 230 +0.020 pe 1 Mitchell et al. (1964)
39282.603 + 640 +0.009 pe 1 Takase (1969)
40370.067 + 855 +0.021 pe 2 Stobie (1970)
40794.903 + 939 -0.008 pe 3 Pel (1976)
44077.489 +1588 -0.010 pe 3 Moffett and Barnes (1984)
44426.508 +1657 +0.013 pe 3 Gieren (1981b)
44492.235 +1670 -0.013 pe 3 Moffett and Barnes (1984)
44659.170 +1703 +0.011 pe 2 Eggen (1985)
being the longest one (see the discussion below).
The O-C residuals listed in Table 58 have been calculated with the
elements:
C = 2436045.528 + 5.057916d*E (45)
+-.004 +-.000003
The O-C diagram (see the upper panel of Figure 35) shows a wave-like
pattern, the weighted least squares fit to the data points results in the
following formula for predicting the moments of the normal maxima:
C = 2436045.528 + 5.057916d*E - 0.035d*cos(2pi(0.000665*E + 0.151)) (46)
+-.004 +-.000003 +-.006 +-.000017 +-.024
Figure 35. Upper panel: O-C diagram of AP Sgr
Lower panel: gamma-velocities for the same Cepheid
indicating an orbital period of 7608 + 194 days. The combination of the
photometric and spectroscopic evidence (including the amplitude and phase
relations) suggests that the orbital period is near 7500 days.
BB Sagittarii
The Cepheid BB Sgr may be a coronal member of the open cluster Cr394
(Turner and Pedreros, 1985). Its spectroscopic binary nature was first
suspected by Gieren (1982), and later on confirmed by Barnes et al. (1988).
Gieren assumes a red companion to BB Sgr. The study of the available
observational data confirms the changing gamma-velocity (see Table 59 and the
lower panel of Figure 36) but the orbital period cannot be determined yet.
The O-C residuals have been calculated with the elements:
C = 2436053.475 + 6.637005d*E (47)
+-.009 +-.000005
Table 59. gamma-velocities of BB Sgr
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
25558 368 + 8.6 2.6 4 Joy (1937)
26314 158 - 1.5 2.3 5 Joy (1937)
39284 16 + 7.5 0.8 6 Lloyd Evans (1968)
40407 44 + 8.2 0.3 4 Lloyd Evans (1980)
40799 27 + 7.3 0.3 5 Lloyd Evans (1980)
44062 2 +15.1 4.0 2 Barnes et al. (1988)
44423 4 + 4.1 0.4 24 Gieren (1981a)
44486 45 +11.1 1.8 6 Barnes et al. (1988)
44821 44 + 8.3 2.3 4 Barnes et al. (1988)
Table 60. O-C residuals for BB Sgr
Norm.max. E O-C Type, Reference
JD2400000+ weight
15644.972 -3075 +0.287d pg 1 Shapley (1930)
16680.382 -2919 +0.325 pg 1 Shapley (1930)
17788.766 -2752 +0.329 pg 1 Shapley (1930)
18837.317 -2594 +0.233 pg 1 Shapley (1930)
19958.922 -2425 +0.184 pg 1 Shapley (1930)
21067.273 -2258 +0.155 pg 1 Shapley (1930)
22096.026 -2103 +0.173 pg 1 Shapley (1930)
23337.157 -1916 +0.184 pg 1 Shapley (1930)
25819.325 -1542 +0.112 pg 1 Voute (1930d)
34938.469 - 168 +0.011 pe 1 Walraven et al. (1958)
35283.586 - 116 +0.004 pe 2 Irwin (1961)
36756.971 + 106 -0.027 pe 1 Weaver et al. (1961)
37141.943 + 164 -0.001 pe 1 Mitchell et al. (1964)
40374.151 + 651 -0.014 pe 1 Stobie (1970)
40447.184 + 662 +0.012 pe 1 Lloyd Evans and Stobie (1971)
40805.592 + 716 +0.021 pe 3 Pel (1976)
41157.395 + 769 +0.063 pe 1 Feltz and McNamara (1980)
42239.185 + 932 +0.021 pe 3 Dean et al. (1977)
42551.084 + 979 -0.019 pe 3 Dean et al. (1977)
43526.814 +1126 +0.071 pe 2 Dean (1981)
44409.527 +1259 +0.063 pe 3 Moffett and Barnes (1984)
44422.808 +1261 +0.070 pe 3 Gieren (1981b)
44721.439 +1306 +0.035 pe 2 Turner and Pedreros (1985)
44907.311 +1334 +0.071 pe 3 Moffett and Barnes (1984)
45040.034 +1354 +0.054 pe 3 Turner and Pedreros (1985)
45212.646 +1380 +0.104 pe 3 Eggen (1985)
Figure 36. Upper panel: O-C diagram of BB Sgr
Lower panel: gamma-velocities for the same Cepheid
The pattern of the O-C diagram (see Table 60 and the upper panel of Figure
36) shows a continuously increasing period:
P = 6.637005d + 7.2d*10^-8*E (48)
+-.000005 +-.6
where the E epoch number has to be calculated from the zero-point indicated
in equation (47). A check on the presence of a possible light-time effect
was also performed, and there is weak evidence for an approximately 4550
day orbital period (using only the photoelectric O-C residuals). Although
this value is consistent with the tendency of the gamma-velocity changes, a
completely different orbital period cannot be ruled out.
V350 Sagittarii
Its spectroscopic binary nature was suspected by Lloyd Evans (1971),
later on confirmed by Gieren (1982), and Lloyd Evans [1982). The orbital
period was determined recently (Szabados, 1989), and its value is 1129
days.
The O-C residuals listed in Table 61 have been computed with the
ephemeris:
C = 2435317.170 + 5.154178d*E (49)
+-.020 +-.000012
The O-C diagram in Figure 37 offers two obvious approximations: a phase
jump, or a parabolic O-C graph. Equation (49) has been obtained assuming
that the first approximation is correct. In this case the former value of
the pulsation period was 5.154139 +- 1.9*10^-5 days. The 0.06 day phase jump
Table 61. O-C residuals for V350 Sgr
Norm.max. E O-C Type, Reference
JD2400000+ weight
25560.345 -1893 +0.034d pg Voute (1930c)
26106.715 -1787 +0.061 pg Voute (1930c)
33075.072 - 435 -0.031 pe 1 Eggen (1951)
34940.902 - 73 -0.013 pe 2 Walraven et al. (1958)
35306.827 - 2 -0.035 pe 2 Irwin (1961)
37244.780 + 374 -0.053 pe 2 Mitchell et al. (1964)
40373.404 + 981 -0.015 pe 1 Stobie (1970)
40435.281 + 993 +0.012 pe 1 Feltz and McNamara (1980)
41136.257 +1129 +0.020 pe 1 Feltz and McNamara (1980)
42883.488 +1468 -0.015 pe 1 Dean (1977)
44373.048 +1757 -0.013 pe 2 Moffett and Barnes (1984)
44414.287 +1765 -0.007 pe 3 Gieren (1981b)
44888.487 +1857 +0.008 pe 2 Moffett and Barnes (1984)
44919.423 +1863 +0.019 pe 2 Eggen (1985)
Figure 37. O-C diagram of V350 Sgr
occurred between J.D.2437500 and 2440000. If, however, the continuous
period increase interpretation is accepted, the pulsation period can be
calculated as follows:
P = 5.154168d + 3.04d*10^-8*E (50)
+-.000004 +-.58
where the E epoch number has to be calculated according to equation (49).
Additional observations are necessary to decide which of the above
interpretations is the correct one.
RV Scorpii
Moffett and Barnes (1987) found almost 6 km/s discrepancy between their
own and the previous gamma-velocity determinations. The variable gamma-velocity
is also seen in the present study (see Table 62 and the lower panel of
Figure 38).
The O-C residuals have been computed with the elements:
C = 2434925.379 + 6.061352d*E (51)
+-.009 +-.000004
The whole data set (see Table 63) can be well approximated by a parabola,
Table 62. gamma-velocities of RV Sco
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
18433 15 -23.0 1.2 7 Paddock (1917)
25104 238 -17.7 1.8 7 Joy (1937)
25983 338 -20.9 2.3 5 Joy (1937)
33942 145 -18.8 0.8 15 Stibbs (1955)
40530 213 -21.6 0.2 7 Lloyd Evans (1980)
44055 9 -13.0 1.6 7 Barnes et al. (1988)
44423 4 -18.9 0.4 24 Gieren (1981a)
44456 18 - 7.5 2.0 5 Barnes et al. (1988)
44798 1 -14.4 2.8 3 Barnes et al. (1988)
Table 63. O-C residuals for RV Sco
Norm.max. E O-C Type, Reference
JD2400000+ weight
14474.195 -3374 -0.181d vis 1 Pickering (1904)
16274.495 -3077 -0.103 pg 1 Shapley (1930)
18141.361 -2769 -0.133 pg 1 Shapley (1930)
19638.618 -2522 -0.030 pg 1 Shapley (1930)
20753.897 -2338 -0.040 pg 1 Shapley (1930)
23196.583 -1935 -0.079 pg 1 Shapley (1930)
24342.277 -1746 +0.020 pg 1 Shapley (1930)
24711.873 -1685 -0.127 pg 1 Voute (1927c)
25075.607 -1625 -0.074 pg 1 Voute (1927c)
34901.138 - 4 +0.005 pe 1 Walraven et al. (1958)
35240.579 + 52 +0.011 pe 3 Irwin (1961)
37277.192 + 388 +0.009 pe 1 Mitchell et al. (1964)
40344.212 + 894 -0.015 pe 3 Stobie (1970)
40780.652 + 966 +0.008 pe 3 Pel (1976)
41574.662 +1097 -0.019 pe 3 Dean et al. (1977)
41950.453 +1159 -0.032 pe 3 Dean et al. (1977)
43538.527 +1421 -0.032 pe 3 Dean (1981)
44023.428 +1501 -0.039 pe 3 Gieren (1981b)
44247.691 +1538 -0.046 pe 3 Moffett and Barnes (1984)
44835.688 +1635 0.000 pe 2 Eggen (1985)
Figure 38. Upper panel: O-C diagram of RV Sco
Lower panel: gamma-velocities for the same Cepheid
corresponding to a continuously decreasing period:
P = 6.061352d - 2.75*10^-8*E (52)
+-.000004 +-.54
where the E epoch number is calculated according to equation (51). The O-C
residuals based on the photoelectric observations made after J.D.2440000
seem to form a part of a wave superimposed on the parabola, indicating a
possible light-time effect. Assuming an orbital period of about 8000 days,
this interpretation is in agreement with the trend of the gamma-velocity
variations (see Figure 38). Further observations are needed before carrying
out a more thorough analysis.
RY Scorpii
RY Sco is a member of a visual triple star system (Proust et al.,
1981). The faint companions may or may not influence the photometric
behaviour of this Cepheid. A blue photometric companion was reported by
Madore (1977) and Pel (1978) but Bohm-Vitense and Proffitt (1985) failed to
find any evidence for a blue companion using IUE spectra. The available
spectroscopic data do not allow to draw any conclusion regarding the
variation in the gamma-velocity (see Table 64).
Table 64. gamma-velocities of RY Sco
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
22868 1 -17.7 4.5 1 Joy (1937)
25515 270 -17.2 1.8 7 Joy (1937)
27034 315 -17.2 4.5 2 Joy (1937)
33934 94 -19.3 1.0 10 Stibbs (1955)
40579 242 -20.5 0.3 4 Lloyd Evans (1980)
44123 158 -15.4 1.8 6 Barnes et al. (1988)
44250 198 -17.8 0.2 18 Coulson and Caldwell (1985)
44785 149 -17.6 0.3 17 Coulson and Caldwell (1985)
Table 65. O-C residuals for RY Sco
Norm.max. E O-C Type, Reference
JD2400000+ weight
16415.032 -583 +8.149d pg Shapley (1930)
17938.584 -508 +7.690 pg Shapley (1930)
19563.398 -428 +6.893 pg Shapley (1930)
20762.244 -369 +6.850 pg Shapley (1930)
23281.083 -245 +5.991 pg Shapley (1930)
24439.079 -188 +5.739 pg Shapley (1930)
25047.825 -158 +4.881 pg Wallenquist (1928)
26673.167 - 78 +4.611 pg Wallenquist (1928)
31019.120 +136 +2.053 pg Filatov (1966)
33335.314 +250 +1.751 pg Filatov (1966)
35244.432 +344 +0.775 pe 2 Irwin (1961)
35244.615 +344 +0.958 pg Filatov (1966)
35487.784 +356 +0.286 pe 1 Mitchell et al. (1964)
38251.601 +492 +0.563 pg Filatov (1966)
40343.964 +595 -0.049 pe 3 Stobie (1970)
41075.606 +631 +0.068 pe 3 Pel (1976)
41908.631 +672 -0.033 pe 1 Madore (1975)
44062.665 +778 +0.066 pe 1 Moffett and Barnes (1984)
44326.737 +791 -0.024 pe 3 Coulson and Caldwell (1985)
44529.910 +801 -0.052 pe 2 Moffett and Barnes (1984)
44875.432 +818 +0.027 pe 3 Coulson and Caldwell (1985)
Figure 39. O-C diagram of RY Sco
The O-C residuals listed in Table 65 have been calculated with the
elements:
C = 2428253.527 + 20.320144d*E (53)
+-.101 +-.000139
Figure 39 shows that the above elements are only valid after J.D.2440000.
Before that epoch the pulsation period cannot be characterized by a single
value.
V500 Scorpii
The discrepancy between the gamma-velocities reported by Moffett and
Barnes (1987) is confirmed here (see Table 66 and the lower panel of
Figure 40). Madore (1977) assumed a blue photometric companion. Such a
companion is not suspected on the basis of Pel's (1978) photometry, nor in
Table 66. gamma-velocities of V500 Sco
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
34182 37 -14.0 0.9 12 Stibbs (1955)
44359 343 -7.4 1.3 10 Barnes et al. (1988)
Table 67. O-C residuals for V500 Sco
Norm.max E O-C Type, Reference
JD2400000+ weight
34729.921 -1038 -0.038d pe 1 Walraven et al. (1958)
35251.730 - 982 +0.028 pe 3 Irwin (1961)
37282.750 - 764 -0.023 pe 2 Mitchell et al. (1964)
37869.731 - 701 -0.003 pe 3 Walraven et al. (1964)
44335.597 - 7 -0.023 pe 3 Moffett and Barnes (1984)
44782.853 + 41 +0.025 pe 3 Eggen (1985)
Figure 40. Upper panel: O-C diagram of V500 Sco
Lower panel: gamma-velocities for the same Cepheid
the study of an IUE spectrum obtained by Bohm-Vitense and Proffitt (1985).
The O-C residuals listed in Table 67 have been computed with the
elements:
C = 2444400.838 + 9.316839d*E (54)
+-.010 +-.000015
The O-C diagram (in the upper panel of Figure 40) simply shows a constant
period.
V636 Scorpii
This Cepheid belongs to a spectroscopic binary system with an orbital
period of 1318 days (Lloyd Evans, 1971). The blue companion has been
discovered in an IUE study (Bohm-Vitense and Proffitt, 1985).
Table 68. O-C residuals for V636 Sco
Norm.max. E O-C Type, Reference
JD2400000+ weight
34743.483 -827 +0.064d pe 2 Walraven et al. (1958)
35232.792 -755 -0.001 pe 3 Irwin (1961)
37849.532 -370 -0.051 pe 3 Walraven et al. (1964)
40350.817 - 2 -0.010 pe 2 Stobie (1970)
42852.033 +366 -0.038 pe 2 Dean (1977)
44456.179 +602 +0.049 pe 2 Eggen (1985)
45020.306 +685 +0.037 pe 1 Eggen (1985)
45706.740 +786 -0.012 pe 1 Eggen (1985)
Figure 41. O-C diagram of V636 Sco
The O-C residuals listed in Table 68 have been calculated with the
elements:
C = 2440364.421 + 6.796859d*E (55)
+-.011 +-.000018
The O-C diagram plotted in Figure 41 has been approximated by a straight
line. According to equation (1) no detectable light-time effect is
expected.
Y Scuti
The variable gamma-velocity of Y Scuti was first noticed by Moffett and
Barnes (1987). Their conclusion is confirmed here (see Table 69 and the
lower panel of Figure 42). The orbital period can be as long as several
thousand days because the radial velocity data obtained by Barnes et al.
(1988) cover three consecutive years, and no obvious change in the
gamma-velocity is seen in their data.
The O-C residuals have been calculated with the elements:
C = 2434947.209 + 10.341483d*E (56)
+-.007 +-.000008
Photographic observations were also taken into account in the fitting
procedure. The O-C graph can be best represented by a straight line (see
Table 70 and the upper panel of Figure 42). The number of the O-C residuals
Table 69. gamma-velocities of Y Sct
JD sigma v gammma sigma n Reference
2400000+ [d] [km/s] [km/s]
25362 371 12.0 2.6 4 Joy (1937)
28080 425 3.5 2.0 6 Joy (1937)
44521 339 18.5 1.3 11 Barnes et al. (1988)
Table 70. O-C residuals for Y Sct
Norm.max. E O-C Type, Reference
JD2400000+ weight
16342.813 -1799 -0.068d pg 1 Shapley (1930)
18028.602 -1636 +0.059 pg 1 Shapley (1930)
19631.411 -1481 -0.062 pg 1 Shapley (1930)
21337.791 -1316 -0.026 pg 1 Shapley (1930)
23220.027 -1134 +0.060 pg 1 Shapley (1930)
24347.261 -1025 +0.072 pg 1 Shapley (1930)
29869.583 - 491 +0.042 pg 1 Filin (1950a), Solov'yov (1956)
31317.362 - 351 +0.014 pg 1 Filin (1950a), Solov'yov (1956)
32610.015 - 226 -0.019 pg 1 Filin (1950a), Solov'yov (1956)
33106.422 - 178 -0.003 pg 1 Filin (1950a)
33178.761 - 171 -0.054 pg 1 Solov'yov (1956)
34833.443 - 11 -0.010 pe 1 Walraven et al. (1958)
36767.263 + 176 -0.047 pe 2 Weaver et al. (1961)
37491.251 + 246 +0.037 pe 2 Ponsen and Oosterhoff (1966)
40841.857 + 570 +0.003 pe 3 Pel (1976)
44285.578 + 903 +0.010 pe 3 Moffett and Barnes (1984)
44947.444 + 967 +0.021 pe 3 Moffett and Barnes (1984)
45495.492 +1020 -0.030 pe 1 Berdnikov (1986) '
45878.138 +1057 -0.019 pe 3 Berdnikov (1986)
Figure 42. Upper panel: O-C diagram of Y Sct
Lower panel: gamma-velocities for the same Cepheid
obtained from photoelectric observations is not enough to reveal the
light-time effect expected in this case.
R Trianguli Australis
Its spectroscopic binary nature was already suspected by Gieren (1982).
His conclusion is confirmed here (see Table 71 and the lower panel of
Figure 43). It has to be noted that the gamma-velocity obtained from Paddock's
Table 71. gamma-velocities of R TrA
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
18432 24 -16.4 0.9 13 Paddock (1917)
33849 23 - 7.5 1.1 8 Stibbs (1955)
34172 44 -10.2 1.2 7 Stibbs (1955)
39265 36 -14.9 0.8 6 Lloyd Evans (1968)
40364 28 -12.9 0.3 4 Lloyd Evans (1980)
40792 12 -14.1 0.3 4 Lloyd Evans (1980)
44423 4 -13.1 0.4 26 Gieren (1981a)
Table 72. O-C residuals for R TrA
Norm.max. E O-C Type, Reference
JD2400000+ weight
16259.101 -7252 +0.032d pg 1 Shapley (1930)
18119.820 -6703 +0.033 pg 1 Shapley (1930)
20278.701 -6066 -0.062 pg 1 Shapley (1930)
21648.047 -5662 +0.012 pg 1 Shapley (1930)
23810.290 -5024 -0.110 pg 1 Shapley (1930)
25728.752 -4458 +0.015 pg 1 Dartayet et al. (1949)
34920.515 -1746 +0.032 pe 1 Walraven et al. (1958)
35201.826 -1663 +0.032 pe 3 Irwin (1961)
40339.938 - 147 -0.015 pe 1 Stobie (1970)
40770.398 - 20 +0.006 pe 3 Pel (1976)
42410.823 + 464 +0.016 pe 3 Dean et al. (1977)
43234.389 + 707 -0.015 pe 3 Dean (1981)
44417.257 +1056 -0.008 pe 3 Dean (1981)
44681.614 +1134 -0.015 pe 3 Eggen (1985)
Figure 43. Upper panel: O-C diagram of R TrA
Lower panel: gamma-velocities for the same Cepheid
(1917) observations still has the most negative value, although a +4 km/s
correction has been applied to his data as discussed in the Introduction.
The O-C residuals have been calculated with the ephemeris:
C = 2440838.178 + 3.389287d*E (57)
+-.007 +-.000002
The O-C residuals listed in Table 72 and shown plotted in the upper panel
of Figure 43 suggest an orbital period of about 3500 days, if the wave-like
pattern of the photoelectric O-C residuals is caused by a light-time
effect. This value is in accord with the gamma-velocity variations but further
photometric and spectroscopic observations are necessary to confirm that
the above hypothesis is correct.
S Trianguli Australis
The variability of the gamma-velocity may or may not be real (see Table 73
and the lower panel of Figure 44). Gieren (1982) also noticed these changes
but the question on the spectroscopic binary nature of S TrA is still open.
Table 73. gamma-velocities of S TrA
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
18416 12 2.0 0.8 7 Campbell and Moore (1928)
20680 2 3.5 2.0 2 Campbell and Moore (1928)
33855 23 8.1 1.1 8 Stibbs (1955)
34173 38 5.0 1.1 8 Stibbs (1955)
39265 36 2.2 1.0 S Lloyd Evans (1968)
40554 202 3.6 0.4 3 Lloyd Evans (1980)
44423 4 4.3 0.4 23 Gieren (1981a)
Table 74. O-C residuals for S TrA
Norm.max. E O-C Type, Reference
JD2400000+ weight
15895.762 -3928 -0.053d pg 1 Shapley (1930)
17995.176 -3596 -0.030 pg 1 Shapley (1930)
20277.932 -3235 -0.045 pg 1 Shapley (1930)
21745.045 -3003 +0.024 pg 1 Shapley (1930)
24027.839 -2642 +0.048 pg 1 Shapley (1930)
25482.306 -2412 +0.118 pg 1 Dartayet et al. (1949)
25798.453 -2362 +0.091 pg 1 Dartayet et al. (1949)
34575.331 - 974 0.000 pe 3 Walraven et al. (1958)
35207.668 - 874 -0.010 pe 3 Irwin (1961)
37092.091 - 576 +0.021 pe 1 Eggen (1961)
40342.320 - 62 -0.011 pe 3 Stobie (1970)
40753.357 + 3 0.000 pe 3 Pel (1976)
41518.515 + 124 +0.019 pe 2 Dean et al. (1977)
42176.137 + 228 +0.001 pe 3 Dean et al. (1977)
42555.556 + 288 +0.012 pe 3 Dean et al. (1977)
43605.266 + 454 +0.027 pe 1 Eggen (1985)
43681.122 + 466 +0.001 pe 1 Dean (1981)
44420.971 + 583 +0.005 pe 3 Gieren (1981b)
44642.260 + 618 -0.027 pe 3 Eggen (1985)
Figure 44. Upper panel: O-C diagram of S TrA
Lower panel: gamma-velocities for the same Cepheid
The O-C residuals have been computed with the elements:
C = 2440734.386 + 6.323465d*E (58)
+-.003 +-.000005
As one can see in the upper panel of Figure 44 (based on the data listed in
Table 74), a period change occurred between J.D.2426000 and 2434500. The
former value of the pulsation period was 6.323570 + 1.8*10^-5 days.
T Velorum
Gieren (1985) suspects the presence of a red companion on the basis of
the amplitude of the light variation in different colours. The gamma-velocity
study performed here (see Table 75 and the lower panel of Figure 45) is
still inconclusive as far as variability in the gamma-velocity is concerned.
The O-C residuals have been calculated with the elements:
C = 2440713.286 + 4.639819d*E (59)
+-.004 +-.000004
Table 75. gamma-velocities of T Vel
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
34063 53 8.6 0.7 20 Stibbs (1955)
40473 190 6.3 0.3 5 Lloyd Evans (1980)
45042 2 5.2 0.5 20 Gieren (1985)
Table 76. O-C residuals for T Vel
Norm.max E O-C Type, Reference
JD2400000+ weight
18201.069 -4852 +0.185d pg Hertzsprung (1937)
26302.088 -3106 +0.080 pg Hertzsprung (1937)
33786.067 -1493 +0.031 pe 1 Eggen et al. (1957)
34741.844 -1287 +0.005 pe 1 Walraven et al. (1958)
34843.895 -1265 -0.020 pe 2 Eggen et al. (1957)
35205.814 -1187 -0.007 pe 2 Irwin (1961)
40745.774 + 7 +0.009 pe 3 Pel (1976)
41803.658 + 235 +0.015 pe 3 Dean et al. (1977)
42555.282 + 397 -0.012 pe 3 Dean et al. (1977)
44299.894 + 773 +0.028 pe 3 Eggen (1985)
44800.940 + 881 -0.027 pe 2 Eggen (1985)
45052.229 + 933 -0.008 pe 3 Gieren (1985)
Figure 45. Upper panel: O-C diagram of T Vel
Lower panel: gamma-velocities for the same Cepheid
The O-C residuals listed in Table 76 and shown plotted in the upper panel
of Figure 45 show constancy of the period, at least in the photoelectric
era. Hertzsprung's (1937) observations suggest that the pulsation period of
T Vel is increasing. Further observations will decide whether a parabolic
fit is better. Similarly to AT Pup, Gieren's (1985) observations made in
1981 have not been taken into account (see the remarks on AT Pup).
V Velorum
Pel (1978) suspects a blue photometric companion to this Cepheid.
Variability of the gamma-velocity is suspected here (see Table 77 and the
lower panel of Figure 46).
Table 77. gamma-velocities of V Vel
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
34092 45 -29.0 0.8 17 Stibbs (1955)
39245 40 -30.7 1.1 4 Lloyd Evans (1968)
40381 23 -29.4 0.3 4 Lloyd Evans (1980)
40690 57 -27.5 0.3 6 Lloyd Evans (1980)
45042 2 -26.3 0.4 21 Gieren (1985)
Table 78. O-C residuals for V Vel
Norm.max. E O-C Type, Reference
JD2400000+ weight
34809.091 -1356 +0.001d pe 2 Walraven et al. (1958)
35233.090 -1259 +0.009 pe 2 Irwin (1961)
40268.520 - 107 -0.002 pe 3 Stobie (1970)
40766.834 + 7 +0.013 pe 3 Pel (1976)
41789.624 + 241 -0.021 pe 3 Dean et al. (1977)
42585.158 + 423 -0.017 pe 3 Dean et al. (1977)
44412.289 + 841 +0.018 pe 3 Eggen (1985)
45037.336 + 984 +0.006 pe 3 Gieren (1985)
Figure 46. Upper panel: O-C diagram of V Vel
Lower panel: gamma-velocities for the same Cepheid
The O-C residuals have been calculated with the elements:
C = 2440736.224 + 4.371043d*E (60)
+-.003 +-.000006
These elements have been obtained by a linear least squares fit to the O-C
residuals listed in Table 78. The upper panel of Figure 46, however, shows
that a light-time effect interpretation of these data is also possible.
Assuming an orbital period of about 7500 days, the gamma-velocity variations
are properly phased with respect to the O-C wave. Similarly to AT Pup and T
Vel, Gieren's (1985) photometric observations obtained in 1981 have not
been taken into account here (see the remark on AT Pup).
AH Velorum
AH Vel belongs to a binary system based on both photometric (Gieren,
1980b) and spectroscopic (Lloyd Evans, 1968 and 1982, and Gieren, 1980a)
criteria. The orbital period cannot be determined yet. The individual
gamma-velocities are listed in Table 79 and shown plotted in the lower panel of
Figure 47.
The O-C residuals have been calculated with the elements:
C = 2442035.703 + 4.227231d*E (61)
+-.007 +-.000007
Table 79. gamma-velocities of AH Vel
JD sigma v gamma sigma n Reference
2400000+ [d] [km/s] [km/s]
33979 22 25.8 0.7 18 Stibbs (1955)
34108 38 28.5 1.3 6 Stibbs (1955)
39230 44 22.5 0.8 6 Lloyd Evans (1968)
39643 72 21.3 0.8 7 Lloyd Evans (1968)
39899 30 23.0 0.2 8 Lloyd Evans (1980)
40300 54 23.2 0.2 12 Lloyd Evans (1980)
40653 49 21.0 0.2 9 Lloyd Evans (1980)
42036 7 24.5 0.3 37 Gieren (1977)
Table 80. O-C residuals for AH Vel
Norm.max. E O-C Type, Reference
JD2400000+ weight
33889.864 -1927 +0.035d pe 2 Eggen et al. (1957)
34824.060 -1706 +0.013 pe 1 Walraven et al. (1958)
35.187.584 -1620 -0.005 pe 3 Irwin (1961)
40256.017 - 421 -0.022 pe 3 Stobie (1970)
40725.254 - 310 -0.007 pe 3 Pel (1976)
41765.136 - 64 -0.024 pe 3 Dean et al. (1977)
42035.677 0 -0.026 pe 3 Gieren (1980a)
43895.726 + 440 +0.041 pe 1 Eggen (1980)
44681.992 + 626 +0.042 pe 3 Eggen (1983a)
Figure 47. Upper panel: O-C diagram of AH Vel
Lower panel: gamma-velocities for the same Cepheid
Although a constant period is assumed here (see the upper panel of Figure
47 and Table 80), neither a parabolic O-C graph, nor a light-time effect
with a very long orbital period can be excluded. Further photometric and
radial velocity observations are needed as for most of the previously
discussed Cepheids.
GENERAL REMARKS
Because the sample of Cepheids studied here is inhomogeneous and is not
large enough, any statistics concerning the period changes, including a
comparison with previous results, may lead to false conclusions. It is,
however, important to note that all kinds of period changes known from
earlier studies are observed here, too. Particularly important among them
are: the continuous period increase or decrease (due to stellar evolution),
the wave-like pattern of the O-C graph (due to the light-time effect in
binary systems), and the phase jump (return to an earlier value of the
pulsation period). This latter kind of period change also occurs in binary
Cepheids.
Table 81 summarizes the results on the period changes and variability
of the gamma-velocity of the Cepheids studied here. Because the normal maxima
published in the GCVS (Kholopov et al., 1985-1987) were only modified in
the discussion on the individual variables instead of transferring them to
a more recent epoch, it is worthwhile to give the actual values of the
normal maximum and the pulsation period valid for e.g. J.D.2445000, taking
into account the period variations when necessary. The successive columns
of Table 81 give the following data:
1. Name of the Cepheid
2. Moment of the normal maximum just following J.D.2445000
3. Pulsation period at J.D.2445000
4. Characteristic features in the O-C diagram (~: light-time effect, -:
decreasing period, +: increasing period)
5. Variability in the gamma-velocity
6. Value of the orbital period
7. Reference to the paper where the value cited in the previous column has
been published.
There are four stars in this sample for which the catalogued value of
the pulsation period needs a considerable correction: YZ Car, AZ Cen, KN
Cen, and GH Lup. In addition, the starting epoch needs a big correction in
the case of SY Nor.
Light-time effect has been discovered in the O-C diagram of V496 Aql,
AX Cir, AG Cru, BG Cru (uncertain), BF Oph, AP Pup, AT Pup, Y Sgr, AP Sgr,
R TrA, and V Vel. A preliminary value of the orbital period has been
suggested on the basis of the light-time effect and/or the variations in
the gamma-velocity for the following Cepheids: V496 Aql, AX Cir, AG Cru, Y
Oph, BF Oph, AP Pup, AT Pup, U Sgr, Y Sgr, AP Sgr, BB Sgr, RV Sco, R TrA,
and V Vel. A phase jump is revealed in the O-C diagram of U Aql, YZ Car, KN
Cen, S Mus, S Nor, Y Oph, U Sgr, and V350 Sgr. If an O-C diagram can be
equally well represented by a phase jump or a constant period of another
value, the phase jump interpretation is preferred here. This more or less
provocative step may encourage others to observe these stars
photometrically. Similarly, some of the orbital periods, and even the
variation in the gamma-velocity assumed for a particular Cepheid variable can
be doubted. In any case, more regular photometric and radial velocity
observations would be desirable on each Cepheid studied here.
Even if some of the orbital periods suggested in Table 81 is not well
determined, the half of the programme stars belongs to spectroscopic binary
systems. Keeping in mind that the spectroscopic binaries can only be
revealed in favourable cases (depending on the value of the orbital
inclination), and that the binary nature can also be discovered on the
Table 81. Summary on the periods, period changes, and duplicity
Cepheid Norm.max. P O-C diagram v gamma Porb Source
JD2400000+ [gay]
U Aql 45001.780 7.023958d linear with phase jump variable 1856.4 Welch et al. (1987)
V496 Aql 45002.397 6.807055 linear ~ variable 1780þn present paper
V Car 45001.101 6.696672 linear variable
YZ Car 45007.131 18.165573 linear with phase jump variable ~ 850 Coulson (1983)
l Car 45002.391 35.551341 two linear sections constant
V Cen 45000.289 5.493861 two linear sections variable ?
XX Cen 45010.493 10.953370 parabolic ( - ) variable 909.4 Szabados (1989)
AZ Cen 45001.112 3.211981 parabolic ( - ) variable ?
KN Cen 45021.656 34.029641 linear with phase jump variable
AX Cir 45001.903 5.273306 linear ~ variable ~ 4600 present paper
S Cru 45000.251 4.689596 parabolic ( - ) constant
T Cru 45004.630 6.733196 linear variable
AG Cru 45000.710 3.837254 linear ~ variable ~ 6350 present paper
BG Cru 45003.271 3.342720 linear ~: variable
Beta Dor 45009.560 9.842425 linear constant
GH Lup 45003.355 9.277948 linear : variable
R Mus 45001.446 7.510467 parabolic ( + ) variable
S Mus 45003.522 9.659875 linear with phase jump variable 506 Lloyd Evans (1971)
S Nor 45004.063 9.754244 linear with phase jump variable
RS Nor 45002.060 6.198136 linear not observed!
SY Nor 45005.992 12.645687 linear one series only
Y Oph 45008.372 17.126908 linear with phase jumps variable 1222.5 present paper
Table 81. (cont.)
Cepheid Norm.max. P O-C diagram v gamma Porb Source
JD2400000+ [day]
BF Oph 45000.515 4.067510d parabolic ~ ( - ) variable ~ 4500 present paper
AP Pup 45000.597 5.084274 linear ~ variable ~ 10000 present paper
AT Pup 45006.629 6.664879 linear ~ variable ~ 20000 present paper
MY Pup 45001.729 5.695309 parabolic ( + ) constant
U Sgr 45004.675 6.745229 linear with phase jump variable 4550 present paper
W Sgr 45007.526 7.594904 linear variable 1780 Babel et al. (1989)
X Sgr 45005.293 7.012877 parabolic ( + ) variable 507.25 Szabados (1989)
Y Sgr 45005.763 5.773380 linear ~ variable >= 10000: present paper
WZ Sgr 45011.333 21.849789 linear + earlier changes variable ?
AP Sgr 45003.097 5.057916 linear ~ variable ~ 7500 present paper
BB Sgr 45000.224 6.637102 parabolic ( + ) variable ~ 4550 ? present paper
V350 Sgr 45002.267 5.154178 linear with phase jump variable 1129 Szabados (1989)
RV Sco 45005.369 6.061306 parabolic ( - ) variable ~ 8000 ? present paper
RY Sco 45017.646 20.320144 linear with period change variable ?
V500 Sco 45006.433 9.316839 linear variable
V636 Sco 45006.676 6.796859 linear variable 1318 Lloyd Evans (1971)
Y Sct 45009.472 10.341483 linear variable
R TrA 45000.222 3.389287 linear ~ variable ~ 3500 present paper
S TrA 45002.725 6.323465 linear with period change variable ?
T Vel 45000.479 4.639819 linear constant
V Vel 45002.362 4.371043 linear ~ variable ~ 7500 present paper
AH Vel 45003.219 4.227231 linear variable
basis of a number of photometric methods not discussed here, the following
conclusion may not be an exaggeration: the frequency of Cepheid binaries is
higher than thought ever since these variables have been known as pulsating
stars.
The author is grateful to Drs. M. Kun and B. Szeidl for their comments,
advice and encouragement during the various stages of this project. Thanks
are also due to Mr. A. Holl and Dr. K. Olah for computer-related advice,
and Mrs. I. Nemeth for preparing the figures.
Budapest - Szabadsaghegy, June 26, 1989.
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