CoKon 65-28

Non-Periodic Phenomena in Variable Stars
IAU Colloquium, Budapest, 1968

THE PROBLEM OF IRREGULAR VARIATIONS IN MAGNETIC STARS
Introductory Report by

T. JARZEBOWSKI
Astronomical Institute, Wroclaw, Poland

At the prelude of this short introductory report I would like to pay
attention to the fact that the magnetic stars do not seem to be the proper
subject for our Colloquium devoted to "non-periodic phenomena in variable
stars". As a matter of fact, the investigations of the latest few years have
revealed periodicity in many magnetic stars, which were hitherto treated to
be irregular; thus the number of non-cyclic phenomena in magnetic stars has
considerably decreased.
We shall present in this paper the most important observational data
on the variability of the magnetic stars, emphasizing the facts that indicate
non-periodicity of variations*.

* All problems on magnetic stars are presented in detail in the following
reviews: Babcock 1958a, 1960, Gollnow 1965, Jarzebowski 1965, Mestel 1965,
Ledoux and Renson 1966, Jarzebowski 1969.

OBSERVATIONAL DATA

The presence of a magnetic field has been firmly established in the case
of about 100 stars (Babcock 1958a, b, Gollnow 1962, Preston and Pyper 1965).
It is generally believed that all peculiar stars possess magnetic fields (although
the magnetic field can only be measured in the case of sharp-line peculiar
stars); the number of stars with peculiar spectra exceeds 800 (Bertaud 1959,
1960, 1965). In this paper we shall include under discussion all investigated
peculiar stars.
The variations of the following parameters have been observed in magnetic
(peculiar) stars:
1. the magnetic field
2. the light
3. the color index
4. the equivalent width
5. the line profile
6. the cross-over effect
7. the radial velocity
8. the polarization of the light (probably)
So far, 47 stars are known, in the case of which some of these parameters
are varying periodically. The stars and their periods are listed in Table 1.

Table 1

Periodic A_p Stars

Variable Variable Variable
Star Period param. Star Period param. Star Period param.

HD 124224 0.521d l, s 21 Per 2.883d* m*, l* HD 125248 9.296d m, l, s, V
kappa Psc 0.580d l HD 224801 3.740d l HD 215441 9.488d l
HD 219749 0.723d* l* ADS 16252 3.770d s 10 Aql 9.78d* l*
56 Ari 0.728d l, s, V* HD 25354 3.900d l HD 173650 10.1d m*, l, s*, V
52 Her 0.96d* m*, l* 15 Cnc 4.116d* l* 41 Tau 11.94d l
HD 133029 1.054d* m*, l* HD 10783 4.133d m, l, V* 78 Vir 12.26d* m*, l*
HD 140728 1.305d* l* epsilon UMa 5.089d l, s, V HD 192678 18d* l*
chi Ser 1.596d l, s 17 Com 5.09d* m*, l* beta Cr B 18.50d m
21 Aql 1.71d* l* 49 Cnc 5.43d* l* 73 Dra 20.275d m,l, s, V*
iota Cas 1.741d l, s alpha^2 CVn 5.469d m, l, s, V HD 4174 40.0d m*, l
HD 215038 2.036d l HD 98088 5.905d m, s, v (b) HD 8441 106.27d m*, v (b)
HD 4778 2.156d s HD 153882 6.009d m, l HD 221568 160d l, s, V
21 Com 2.2d* l*, s* HD 32633 6.431d m, l HD 188041 226d m, s
pi Boo 2.444d* s* HD 71866 6.800d m, l, s gamma Equ 314d* m*
HD 34452 2.466d l, s* kappa Cnc 6.91d* l* HD 187474 2500d m
gamma Ari 2.607d l, s 53 Cam 8.028d m, l, s

The symbols denote: m = periodic magnetic field variations,
l = periodic light variations,
s = periodic spectral variations,
v = periodic radial velocity variations (b = a binary star with the same period).
The asterisk indicates an uncertain value.
The new data on the periods have been taken from the following papers: Jarzebowski 1960a, b, 1961, 1964,
Wehlau 1962, Rakos 1962b, 1963, Steinitz 1964, Renson 1965, 1966, 1967, Osawa et al. 7965, Stepien 1968b.

Variations of the magnetic field. Periodic variations of the magnetic
field have been stated in the case of 12 stars; in the case of 9 others the
periodic field variations are probable but not firmly established. In nearly
all remaining magnetic stars (about 80) the observations indicate variations
of the magnetic field. It has not been shown, as yet, that there is a star with
constant magnetic field. On the other hand - it has not been proved that
there exist magnetic stars with irregular field variations*.

* Babcock has subdivided the magnetic stars into three classes denoted
as alpha, beta and gamma (alpha-periodic magnetic variables, beta-irregular
variables with the reversing of polarity, gamma-irregular with constant
polarity). The sense of this division is very doubtful now.

We have, however, to call our attention to some facts:
1. In the case of several magnetic stars - e.g. HD 173650 (P = 10.1d),
or HD 4174 (P = 40^d) - there are difficulties in fitting the magnetic
observations to the period derived from luminosity variations. This seems to
indicate the possibility of some irregularities.
2. In the magnetic star 73 Dra the period of variations (20.3d) is known
for a long time. The magnetic measurements by Preston (1967a) follow this
period, but the measurements by Babcock (made over ten years earlier) do
not form a smooth curve and indicate only the negative polarity (Berg 1967).
This is illustrated in Figure 1. We have rather to eliminate the supposition
that Babcock's measurements are of lower accuracy, and thus, we have to
accept that some secular magnetic field variations are taking place.

Fig. 1. The variations of the magnetic field of 73 Dra.
Bottom: the measurements by Preston plotted with the period
of 20.2754d.
Top: Babcock's magnetic field observations plotted with
the same period.

3. Babcock's magnetic measurements of the star 78 Vir seem to follow
the probable 12-day period of luminosity variations, but the dispersion of
individual points is very large, bringing into question the periodicity
(Stepien 1968b).
4. Recent observations by Preston (1967a) indicate that the amplitude
of magnetic variation of beta CrB (P = 18.5d) is varying; there is evidence
of some secular changes of the amplitude in a period of the order of 10 years.
In this place we have to mention that also Adam (1965) reported secular
decrease of the amplitude of the magnetic field of HD 125248 (P = 9.3d).
Adam's result seems to be, however, inconclusive, because the successive
measurements were made by using different apparatus - and in such a case
some divergence of the results can be expected (op. e.g. Preston and Pyper
1965).
Variations in light and color. Periodic luminosity variations have been
stated in the case of about 40 peculiar stars. The amplitudes are very small
- most often of the order of one, two or three hundredths of a magnitude,
and do not exceed 0.2m. The small value of the amplitude does not permit,
very often, to distinguish the large scatter and the true deviations from
periodicity (e.g. HD 153882, Chugainov 1961) - although the observational
data indicate in some cases such deviations. On the other hand, we cannot
say - by the same reason - that the light of any peculiar star is constant.
We shall now summarize the most interesting observational data.
1. In several magnetic (peculiar) stars the variations are very regular
and the amplitude is increasing towards the short wavelength (the curves U,
B, V, U-B, and B-V are all in phase). As an example we can here name
HD 124224 (P = 0.5d, Hardie 1958), or HD 215441 (the star with the strongest
magnetic field, P = 9.5d, Stepien 1968b). In many cases a double wave is
conspicuous (e.g. 56 Ari, P 0.7d, Hardie et al. 1963).
2. The majority of the peculiar stars shows, however, non-typical
luminosity variations. One of the characteristic facts is that the amplitude in
yellow is sometimes much larger than in blue. As an example let us mention
the two peculiar stars: alpha^2CVn (P = 5.5d, Jarzebowski 1969), and 73 Dra
(P = 20.3d, Stepien 1968a); both the stars show also a double wave on the
V curve.
3. In a few cases a phase shift is conspicuous. This was firstly stated for
53 Cam (the star with a strong magnetic field, varying with a period of 8 days);
the V curve lags here considerably with respect to the B curve (Jarzebowski
1960b, Rakos 1962b), while the U light maximum nearly coincides with the
V light minimum (Preston and Stepien 1968b), Fig. 2. A similar case is
presented by the peculiar star HD 221568 (P = 160^d) recently investigated
by Osawa et al. (1965) and by Kodaira (1967); the changes in V are almost
exactly reflected in the changes in B in an opposite sense as we see in
Figure 3. The authors also report the possibility of some irregularities in the
luminosity variations of this star.

Fig. 2. The magnetic and light variations of 53 Cam, based on the data of Babcock,
Preston, Stepien, Jarzebowski, and Rakos (Preston and Stepien 1968b).

Fig. 3. Light variations of HD 221568 from October 1964 to March 1965
(Osawa et al. 1965).

4. An interesting case is presented by the M-type magnetic star HD 4174,
in the case of which the deviations from strict periodicity are undoubtful
(Jarzebowski 1964, 1969). Three sets of photometric observations of this star
are presented in Figure 4. We see that the observational data of 1962/63 and
of 1965 can be described with the slightly variable period of 40 days, but the
data of 1964 do not fit this period and are rather irregular. It may be noted
that the magnetic variations of this star probably also follow the semi-regular
40-day luminosity period.

Fig. 4. Luminosity variations of the M-type magnetic star HD 4174 during
three sets of observations (Jarzebowski 1969).

5. Besides the luminosity variations discussed on here (with periods given
in Table 1) some of the peculiar stars show additional brightness fluctuations
over very short intervals. It was stated in the case of four stars that these
variations can be described by a period (Bahner et al. 1957, Rakos 1962a,
1963). The following values of the short periods were found: 0^h 32^m (21 Com),
1^h 34^m (HD 71866), 1^h 46^m (HD 32633), and 2^h 04^m (HD 224801). These
shortperiod fluctuations in some phases disappear and display conspicuous
irregularities (Fig. 5).

Fig. 5. Short interval brightness fluctuations of 21 Com observed
on 28 March 1956 (Bahner et al. 1957).

Spectral variations. Apart from the fact that the lines of elements such
as Si, Cr, Mn, Sr, and the rare earths are abnormally intense -- spectral
variations have been well established in many peculiar stars.
The following variations have been observed in the spectra of peculiar
stars:
1. The line intensity variations. This phenomenon is generally most
conspicuous in the case of those elements which are abnormally strong (i.e. Si,
Cr, Mn, Sr, rare earths). In about 20 cases periodicity of these variations has
been established (see Table 1). The phase relationship between the variations
of different elements may change from star to star and, further, some elements
may show a double wave. There is also no uniform relationship between the line
intensity and the magnetic variation.
2. The profiles of some magnetic stars show remarkable variations in width
and depth. The profile variations are generally correlated with the intensity
variations. In several cases it was possible to detect periodicity; for instance
in 53 Cam (P = 8.0d) most of the lines being much wider when the field is of
negative polarity.
3. The cross-over effect. This effect appears as a difference in sharpness
of the profiles when the right-handed polarized spectrum is compared with
the left-handed (in the first spectrum the lines tend to be broad and shallow,
in the other - sharp and deep). The cross-over effect is mainly observed in
periodic magnetic variables; the sharpness of the profiles is periodically varying
with the sign of the magnetic field. Let us note, however, that in the case
of 78 Vir it was not possible to find the correlation between this effect and the
presumable 12-day period of variations (Stepien 1968b).
Are there irregularities in the spectral variations?
This problem is rather undecided (here the same questions arise as in the
case of luminosity and magnetic variations). The present observational data
do not contradict the possibility that there are magnetic (peculiar) stars
showing irregular spectrum variations, or variations that are not simply
correlated with the magnetic changes (Babcock 1960). It may also be noted
in this place that in several magnetic stars the possibility of some secular
spectral changes was reported (for instance the lines of some elements are
intense according to the HD Catalogue and weak according to Babcock etc.).
Finally, we have to announce a very interesting fact recently found by Wood
(1965, 1967, 1968): the rapid Balmer-line variations. Using the photoelectric
narrow-band photometer Wood has discovered the variations of the equivalent
widths of H beta, H gamma, and H delta in several peculiar stars (HD 215441,
HD 224801, 73 Dra, epsilon UMa). The variations seem to be irregular, but the
existence of quasi-periods of the order of half an hour is not excluded. In the
case of HD 224801, for instance, time variations of about 10 per cent with a
quasi-period of about 35 min have been observed (the oscillations may become
unrecognizable after several cycles), Fig. 6.

Fig. 6. Fluctuations of the equivalent width of H beta in the spectrum
of magnetic star HD 224801 on 29 Aug. 1963 (bottom: the comparison star).
From the paper by Wood, 1968.

Radial velocity variations. Over ten magnetic stars belong to spectroscopic
binaries. In HD 98088 the period of revolution equals the period of magnetic
variation; a similar case presents, probably, HD 8441 (Renson 1966). In the
other spectroscopic binaries the period of velocity variations differs from the
period of magnetic, light or spectrum variations. For example, in beta Cr B the
period of magnetic variation is 18.5 days while the period of orbital revolution
- 3833 days, in HD 125248 the corresponding values are 9.3 days and 1618 days;
in kappa Cnc this difference is much smaller: the period of orbital revolution
being 6.39 days while the period of light variation seems to amount to 6.91 days
(Stepien 1968b). The problem of the possible binary nature of magnetic stars
matters much for the "binary-star hypothesis" which was put forward by Renson (1963).
The binary nature of peculiar stars has also been set up by van den Heuvel (1967)
and by Guthrie (1968).
Apart from the spectroscopic binaries, most of the peculiar stars show small
fluctuations in differential radial velocity of the order of a few km/s. These
radial displacements depend on the chemical element considered and are often
correlated with the variations in line intensity. In several cases the
variations follow the period of magnetic or spectrum variations (see Table 1).
This periodicity is especially conspicuous in alpha^2 CVn,
but we have to note that:
1. it is evident only for a group of elements, 2. for some elements secondary
maxima occur, 3. there are elements showing nearly no velocity variations
(cp. Jarzebowski 1965). In other stars the probable period of velocity
variation differs from the main period (e.g. in HD 224801, Rakos 1963), while
in the majority of cases no regularities in the velocity fluctuations could be
detected.

The polarization of the light. Thiessen, in 1961, reported the variations
in polarization for the star HD 71866 of the same period as the variations in
brightness and magnetic field. Polosuhina and Lebedeva (1966) have investigated
the 34 kG magnetic star HD 215441; they reported the existence of a possible
correlation between the percentage of polarization and the magnitude in the 9.5d
photometric period.
On the other hand, the investigations by Serkowski (1965), Elvius and
Engberg (1967), Hiltner and Mook (1967) did not reveal definite indication
of variable plane polarization in magnetic stars.
With reference to the problem of the variations of polarization we have
to keep in mind that the degree of polarization we are observing for the
magnetic variables remains very small and seldom exceeds the mean error.
Thus we have rather to conclude that within the accuracy of the present
technics of observations there is probably no variable polarization in stars
with variable magnetic fields.

CONCLUSIONS

Recapitulating the here discussed observational data we conclude that there
are still many magnetic stars in the case of which the variations of magnetic
field, light, radial velocity, or the spectral variations are non-periodic.
It may well be, however, that thorough observations can reveal in the future
the periodicity of variations.
The results of investigations of the latest few years seem to lead to the
following statement: if a star is carefully studied, there is the probability of
finding periodic or semiperiodic variations.
When considering this question we have, however, to take note of the
fact that, generally speaking, it is much easier to find a period of variations
than to prove that the variations are irregular.
On the other hand, it is sometimes very difficult to distinguish between
true irregularity and the errors of observations (though, in some cases the
irregularities seem to be undoubtful - as for instance in the case of HD 4174,
Fig. 4).
At the end we shall add one general remark. The conclusion on the
periodicity of variations in magnetic stars may be regarded as a new support
for the oblique rotator theory. This theory requires, of course, constancy of
the period of variations. Such constancy of the period has been stated in the
case of stars that are investigated for a long time (e.g. alpha^2 CVn, 73 Dra,
HD 125248). Rakos (1968) suggested variations of the period in a few stars, but
the deviations seem to lie within the limits of errors. On the basis of the
present observational data we have rather to conclude that the mean value
of the period is constant, but overlapping of some irregularities is possible.

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DISCUSSION

Detre: If the magnetic period is not constant, this fact alone must not be
regarded as contrary to the oblique rotator theory because the magnetic
fields can show some displacements relative to the photosphere.
Theoretically, the oblique rotator theory is not quite satisfactory because
an oblique rotator represents an unstable configuration. But as recent
results by Preston and B�hm Vitense have given, values near to pi/2 for
the angle of obliquity we may unite the oblique rotator model with the
solar model: the star has a relatively weak polar dipole field and a strong
equatorial dipole field. According to Mestel, such a configuration might
be stable.
Jarzebowski: Yes, if we accept the oblique rotator model, we should have to
make the assumptions mentioned by you.
The sun, as we know, does not however fit to this model. Bumba, Howard
and Smith have recently investigated how the sun would appear as a
magnetic star viewed near the plane of its equator. They found that the
27-day rotation period is impossible to detect.