Non-Periodic Phenomena in Variable Stars
IAU Colloquium, Budapest, 1968
HOT, VERY SHORT-PERIOD ERUPTIVE BINARIES
Introductory Report by
J. SMAK
Institute of Astronomy, Polish Academy of Sciences, Warsaw, Poland
ABSTRACT
Some problems connected with the interpretation of the photometric and
spectroscopic observations of the U Geminorum type stars are discussed.
1. INTRODUCTION
In order to discuss the non-periodic or irregular phenomena displayed by
a given group of stars one should have a good knowledge of all regular
properties and basic physical processes known to occur in these objects.
In the case of hot, very short-period eruptive binaries the situation is
still quite unsatisfactory in this respect. Within each group we observe
a considerable diversity of basic physical characteristics and a
large variety of occurring phenomena. Several excellent review articles
on these objects have appeared recently (e.g. Kraft 1963, 1966,
Mumford 1967) and therefore there seems to be no reason for presenting
another review of this type. Instead an attempt will be made here to
discuss only some selected problems connected with the interpretation of
the apparently most homogeneous group of objects, namely of the U Geminorum
type stars.
2. SOME BASIC PROPERTIES
Due to the work of Kraft (1962) it is now well established that all U
Geminorum type variables are binaries. Their orbital periods range from
about 3 hours to about 9 hours. At minimum light, i.e. between the
outbursts, the spectrum of U Geminorum type variables consists of the
following components: (a) the blue, hot continuum usually associated
with the blue component of the system; however, no spectral features
belonging to this component are seen in the spectrum and it is difficult
to tell what fraction of the hot continuum may belong to it; (b) strong,
emission lines, primarily those of H, He I, and Ca II, which are interpreted
as being due to a rotating gaseous ring around the blue component; as a rule
these emission lines are observed to be double when the orbital inclination
is close to 90 deg (e.g. in U Gem); (c) absorption lines belonging to the red
component; these lines are visible only in some systems, being undetectable
in the others (at least in the blue region of the spectrum), thus indicating
that the relative luminosity of the red star is quite different in different
systems. In order to explain the existence of the ring it is necessary
to postulate (Kraft 1962, 1963, Krzeminski 1965) that the red component is
in contact with its Roche lobe and is loosing mass through the inner
Lagrangian point; this mass, together with the momentum it carries, is
responsible - directly or indirectly - for the formation of the ring.
It is really unfortunate that among all U Geminorum type variables
studied until now there is no single object that would simultaneously be
a double-line spectroscopic binary and an eclipsing variable. This
leaves us with some crude estimates only of stellar masses and radii.
Two stars, namely U Gem and SS Cyg, can be considered in order to
illustrate the existing situation. In U Gem no lines of the red
component are visible and therefore no direct estimate is available for
the mass-ratio M_b/M_r (b and r stand for the blue and red components,
respectively). On the other hand, the star is known to be an eclipsing
variable (Krzeminski 1965) and therefore the orbital inclination is
close to i = 90 deg. Taking the mass-ratio as an unknown parameter we can
obtain a set of solutions for M_b and M_r (Krzeminski 1965, Paczynski
1965). With M_b/M_r = 0.9, which is the average value for the double-line
U Geminorum type binaries, we get M_b = 1.1 M_Sun and M_r = 1.2 M_Sun.
Larger mass-ratios would lead to larger masses but there is a limit set up by
the resulting radius of the gaseous ring; namely, if we require that the
ring should be within the Roche lobe of the blue component, then we get
that the mass-ratio cannot be larger than about 1.0. On the other hand,
however, it is possible that the mass-ratio is smaller than 0.9 and that
the masses are smaller than those given above. SS Cyg is a double-line
spectroscopic binary with M_b/M_r = 0.9 (Joy 1956). No eclipse has been
detected, however, in spite of many searches and the orbital inclination
is an unknown parameter. With i = 70 deg we get M_b = 0.22 M_Sun and M_r = 0.24
M_Sun while with i = 30 deg we get M_b = 1.44 M_Sun and M_r = 1.60 M_Sun.
3. PERIOD CHANGES
Walker and Chincarini (1968) have recently found that the orbital period
of SS Cyg is increasing with time. The observed rate of the period
variation is A = +9.54d X 10^-11, where A is the coefficient in the usual
formula
Zero Phase = T_0 + PE + AE^2. (1)
An inspection of the O-C diagram for U Gem (Fig. 1) shows that the
orbital period of this star is also increasing; the data presented in
Fig. 1 lead to A ~~ +2.0d X 10^-11. Since SS Cyg and U Gem are rather
typical examples of the U Geminorum type variables, it is tempting to
conclude that the lengthening of the orbital period may be a common
characteristic of the entire class.
Period changes in close binary systems are usually interpreted as a
result of the exchange of mass or of the loss of mass from the system.
Much work has been done recently in this field (cf., for example,
Kruszewski 1966). The rate of the period variation can be related to the
rate of the mass transfer (or mass loss) provided the mechanism of the
mass transfer (or mass loss) can be properly identified. Let us see then
what conclusions can be obtained in this respect for SS Cyg and U Gem
under different assumptions concerning the mechanisms involved.
Fig. 1. The (O-C) diagram for U Gem. Observed moments of minima are from
Krzeminski (1965, 1968), Mumford (1968), and Paczynski (1965). Elements
are those by Krzeminski (1965).
Case I. Mass exchange between the components with no exchange
between the orbital and rotational momenta. Fixing our attention on the red
component we can write the following relation between the observed rate
(A) of period variations and the rate of the mass loss (or mass gain):
d log M_r / dt = 52.9 A/P^2 (M_r/M_b-1)^-1; (2)
in this and in the following formulae we express t in years and A and P
in days. We may easily note that with the mass-ratio being larger than
1 and with A being positive, the mass of the red component should be
expected to increase. This is in conflict with the indication given
above unless we can assume that (a) it is the blue component that is
responsible for the eruption activity, and (b) a considerable amount of
mass is transferred from the blue to the red component during an
outburst. While the assumption (a) may still be correct (see Section 5),
the assumption (b) cannot be given any direct or indirect support on the
basis of the available data. Besides, it should be kept in mind that to
the simple mechanism considered here should not be given too much
credence.
Case II. Mass exchange between the components with exchange between the
orbital and rotational momenta. No single, analytical expression similar
to Eq. (2) can be given in this case. Instead Eq. (2) can be replaced
with (see, e.g., Kruszewski 1966):
d log M_r / dt = -158.7 A/P^2 k-1 (1+(M_r/M_b-1), (3)
where the coefficient k can be determined only from the numerical
integrations and depends not only on the mass-ratio but also on the
asynchronism parameter, f, of the mass ejecting component. With A being
positive, the sign of the right-hand side of Eq. (3) is now determined
only by the sign of k. Let us assume that the red component is loosing
mass and let us see whether this is consistent with Eq. (3), i.e.
whether k can be positive when the mass-ratio is larger than 1.
Numerical data published by Kruszewski (1966, Table I; see also
Kruszewski 1964) show that this can happen as long as the mass-ratio does
not exceed about 1.2-1.3, provided the value of f is positive, i.e. when
the mass loosing component rotates faster than in the case of synchronism.
For example, with M_b/M_r ~= 1.1 we get k ~= +0.4 when f = + 0.1,
and k ~= +1 when f = +0.5. Thus our assumption about the mass loss
from the red component is consistent with the observed direction of the
period variations, provided its rotation is faster than in the case of
synchronism. It should be added, however, that this by itself is not an
argument in favor of our assumption for if we assumed that the blue
component is loosing mass our conclusions would be similar, even
regardless of the value of f (compare with Case I).
Case III. Isotropic mass loss from the system (Jeans mode). In this case
we have:
d log (M_r + M_b) / dt = -79.3 A/P^2 . (4)
It is irrelevant here which of the two components is loosing mass, the
effect being always the same - namely the increase of period. Situation
becomes more complicated, however, when we wish to include the angular
momentum effects. A second term appears then in the right-hand side of
Eq. (4), which is proportional to dlog h_0/dt, where h_0 is the angular
momentum per unit reduced mass. Therefore depending on the amount of
momentum carried away by the ejected matter the period may either
increase or decrease. In other words, without going into the details of
the angular momentum effects it is impossible to decide whether the
observed increase of period in the case of SS Cyg and U Gem is, or is
not consistent with the pure mass loss hypothesis. In particular, no
much weight should be given to the rate of mass loss computed with the
help of Eq. (4). Finally, adopting such a possibility would require
neglecting the contribution to the observed period variations due to the
mass exchange which is certainly taking place in these systems.
We are not going to consider here the most complicated case of
simultaneous mass exchange and mass loss. No simple description can be
given in such a case mostly because of the difficulties connected with
the angular momentum effects. It should be noted that all the analytical
considerations published in the past (e.g. Huang 1956) were necessarily
of rather restricted and/or approximate character and their results
should never be blindly applied to any specific case.
To summarize, the observed increase of period in SS Cyg and U Gem cannot
be used as an argument in favor, or against any of the possible
mechanisms of the mass exchange and/or mass loss. Situation becomes
slightly better, however, when we try to interpret the numerical results
obtained from Eqs. (2-4). First, it turns out that the rates of mass
exchange (or mass loss), as computed from Eqs. (2), (3), or (4) for
either SS Cyg or U Gem, are practically of the same order, namely
between 10^-7 and 10^-6 M_Sun per year. These estimates depend on the
adopted values of the masses themselves which were taken to be of the
order of 1 M_Sun. At least one possibility can now be shown incompatible
with the estimates given above. It is the possibility of the sudden mass
loss from the system during the outbursts. The amount of mass loss per
outburst would be of the order of 10^-7 M_Sun, that is only one order of
magnitude less than in the case of some novae (see McLaughlin 1960),
which is clearly incompatible with the lack of any direct observational
evidence for mass ejection during an outburst. Therefore if the mass
loss is to be responsible for the observed period variations it should
mostly be of continuous character (Walker and Chincarini 1968).
Unfortunately, no convincing conclusions can be obtained at the present
moment with respect to the mass transfer phenomena.
4. COLORS, HOT SPOTS, ETC.
The aim of this section is to mention some unexplained photometric
properties of the U Geminorum type variables. Fig. 2 shows the light and
color curves of U Gem at minimum light (i.e. between the outbursts). The
following features of these curves are worth mentioning (Krzeminski
1965, Mumford 1964, Paczynski 1965): (a) a total primary eclipse, with
no major variations in (B-V), but with a strong excess in (U-B); (b)
nearly constant light and colors between phases 0.1P-0.6P; (c) a
shoulder in the light curves between phases 0.6P-0.1P; a similar shoulder is
present in the (B-V) curve (i.e. the amplitude of the shoulder is larger
in B than in V), while the (U-B) curve shows a minimum in this interval
of phases. Other examples of stars showing a shoulder in their light curves
are: Z Cam (Kraft, Krzeminski, and Mumford 1968), RR Pic which is a nova (van
Houten 1966), and VV Pup which is an extremely short-period nova-like
object (Thackeray, Wesselink, and Oosterhoff 1950, Herbig 1960,
Krzeminski 1965, Walker 1965). Following Herbig's (1960) interpretation
of VV Pup, it is now commonly accepted that the shoulder is due to a hot
spot located on the surface of the hotter component symmetrically with
respect to the line joining the components.
Fig. 2. The V, B-V, and U-B curves of U Gem on JD 2438056 (after
Paczynski 1965).
Using the UBV data available for different stars we can easily determine
the photometric properties of such hot spots. First, we can assume that
the observed brightness and colors outside of the shoulder are due to
the combined light of the two components including the gaseous ring
around the blue star. Second, from the observed brightness and colors on
top of the shoulder we can determine the relative luminosity and colors
of the hot spot. The results are given in Table 1 and shown in Fig. 3.
Let us discuss them briefly.
Fig. 3. Colors of U Gem, Z Cam, and W Pup at phases 0.2P-0.5P are shown
as filled circles. Colors of hot spots in U Gem and Z Cam are shown as open
circles. The standard main sequence relation and the black body line
(with the temperature in 1000 K units marked) are shown for comparison.
(a) Colors of the combined light of the two components (plus the ring),
as seen at phases 0.2P-0.5P, are peculiar; all three objects shown in Fig. 3
are situated 0.3-0.5 mag. above the black body line in the two-color diagram.
No quantitative estimates of the influence of the hydrogen emission lines and
continuum on colors of these objects are available but it seems almost
improbable that they could be responsible for the entire ultraviolet excess,
unless we could assume that the bound-free and free-free emission of hydrogen
dominates in the continuous spectrum. But even this explanation could hardly
be accepted for Z Cam where the absorption lines of the red component are seen
in the combined spectrum what indicates rather high contribution of light
from that component.
(b) Relative luminosities of hot spots (expressed in units of light at
phases 0.2P-0.5P) are very large. In the most extreme case of VV Pup the hot
spot would seem to radiate much more energy than the "rest" of the system
(i.e. the two stars plus the ring). And if such a hot spot is confined to a
small region on the surface of the blue star we are forced to conclude that
the surface brightness of the spot is at least one order of magnitude higher
than that of the star itself.
(c) Colors of the hot spots are peculiar. In the case of U Gem and Z Cam
(see Fig. 3) the (B-V) colors are bluer while the (U-B) colors - redder than
those of the combined light of the two components; in the case of VV Pup both
- (B-V) and (U-B) - are much redder. In all cases it is hard to see how the
observed colors could be reconciled with the extremely high surface brightness
of the hot spot.
Table 1
Photometric Data
U Gem^1 Z Cam^2 VV Pup^3
Colors at phi = 0.2P-0.5P, B-V +0.30 +0.55 +0.05
U-B -1.00 -0.80 -1.10
Amplitude of the shoulder. A_v 0.60 0.15 1.40
Colors at phi = 0.8P, B-V +0.15 +0.45 +0.30
U-B -0.80 -0.80 -0.80
Relative luminosity
of the hot spot, I_v 0.7 0.2 2.60
Colors of the hot spot, B-V 0.00 +0.05 +0.40
U-B -0.55 -0.40 +0.60
Photometric data from:
1. U Gem - Krzeminski (1965), Mumford (1964, 1967), and Paczynski (1965).
2. Z Cam - Krzeminski`s observations on JD 2439138 (Kraft, Krzeminski, and
Mumford 1968).
3. VV Pup - Walker's observations on JD 2438474 (Walker 1965).
Note: All photometric data have been rounded up to the nearest 0.05 mag.
While all these questions remain with no answers at the present moment
it seems quite clear that the peculiarities discussed in this section
may be deeply connected with the basic physical processes taking place
in these systems.
5. ORIGIN OF OUTBURSTS
Although the problem of the origin of outbursts in the U Geminorum
type variables is rather of theoretical nature, there is one basic question to
which an answer should be given on the basis of the observational data.
The question is: which of the two components is responsible for the outburst
activity. Photometric observations of U Gem during its outbursts seemed to
leave no doubt that the eruption occurs in the red component (Krzeminski
1965, see also Paczynski 1965). Indeed, the eclipses become shallower during
the rising branch and disappear almost completely at maximum; their width
increases sharply during an outburst and decreases slowly afterwards. All this
can be explained if we assume that the outburst consist of a large increase
in the surface brightness of the red star and a moderate increase of its radius.
Recent spectroscopic observations of SS Cyg made by Walker and Chincarini
(1968) seem, however, to contradict the photometric arguments collected for U Gem.
Their observations made during the rise to maximum, some 3 mag. above the
minimum level, show that the absorption lines characteristic of that phase
display radial velocity variations which are in phase with the radial velocity
of the blue component observed at minimum. This means that the relative
luminosity contributed by this component (or rather by its gaseous envelope)
must be at least comparable with that of the red star. Thus Walker and
Chincarini conclude that the outburst is associated with the blue star.
Both pieces of evidence are very convincing. It seems, however, that
there is no need to postulate that two, completely different mechanisms
operate in U Gem and SS Cyg. It is very likely that an increase in the
surface brightness and of the radius of the red star, as postulated in
Krzeminski's model, is accompanied by an increase in brightness of the
blue star (for example due to accretion of mass transferred from the red
star). It may happen, then, that at some specific phase of the outburst
the ratio of luminosities is already much different from that at minimum
- this would account for shallower eclipses - but the luminosity of the
blue star (plus its envelope) is still high enough to contribute to the
combined spectrum. Needless to say an extensive series of spectroscopic
observations made during the outburst are badly needed to solve this
problem.
In conclusion, the author wishes to thank Drs. W. Krzeminski and B.
Paczynski for many day-to-day discussions; many of their ideas have been
incorporated into the present report. Specific thanks go to Dr.
Krzeminski for his unpublished observational data.
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Herbig, G. H., 1960, Astrophys. J., 132, 76.
Huang, S.-S., 1956, Astr. J., 61, 49.
Joy, A. H., 1956, Astrophys. J., 124, 317.
Kraft, R. P., 1962, Astrophys. J., 135, 408.
Kraft, R. P., 1963, Adv. Astr. Astrophys., 2, 43.
Kraft, R. P., 1966, Trans. I. A. U., XIIB, 519.
Kraft, R. P., Krzeminski, W., Mumford, G. S., 1968, Astr. J., 73, S21.
Kruszewski, A., 1964, Acta Astr., 14, 241.
Kruszewski, A., 1966, Adv. Astr. Astrophys., 4, 233.
Krzeminski, W., 1965, Astrophys. J., 142, 1051.
Krzeminski, W., 1968, Unpublished.
McLaughlin, D. B., 1960, Stellar Atmospheres, ed. J. L. Greenstein
(Chicago: University of Chicago Press), 585.
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DISCUSSION
Feast: Could you tell us what is the evidence for mass exchange in one
direction between the stars rather than in the other direction?
Smak: The presence of the rotating gaseous ring around the blue
component implies that there must be a transfer of mass and of momentum
from the red to the blue star. We do not quite know, however, what is
happening during an outburst. If one can assume that the outburst is
associated with the blue component, then it is very likely that some
amount of mass could be transferred in another direction.
Lortet-Zuckermann: What are the exposure time and the linear dispersion
of Kraft's spectra showing the doubling of the emission lines?
Bakos: Why do you think that a mass loss of 10^-7 mSun/year is too high?
It is less than the mass of the earth and I believe that the blue star
could absorb it without appreciable changes in its spectrum.
Smak: I think this figure is acceptable as long as we assume that this
is the amount of mass transferred from one component to the other,
without any considerable sudden mass loss from the system, or that this
is a continuous outflow of mass from the system. But I do not think it
could be associated with a sudden mass loss from the system during an
outburst only, because there is no direct spectroscopic indication
pointing to such a large outflow of mass.