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Period evolution of Very Long Period Variables: The Semiregulars
L. SABIN , A. A. ZIJLSTRA
University of Manchester, School of Physics  Astronomy
P.O Box 88 Manchester M60 1QD, United Kingdom
Email: [email protected]
[email protected]
Introduction
Like the Miras , the Semiregulars are red giant or supergiant pulsating stars, but oscillating with less regularity as indicated by
their name. They are divided in different classes: SRa, SRb, SRc, SRd (super giants), from the most to the less regular shape
of their light curve. The study of the period changes in these variable stars will not only reveal the action (or not) of physical
processes such as thermal pulses, magnetism, convection . . . etc via the observation of stable or unstable behavior in the
long run, but also we could be able to notice the differences or similarities with the Mira-type stars. The effect on the mass
loss which is characteristic of the AGB stars may therefore be investigated. The study will concern stars with periods greater
than 450 days as their long-period evolution is more likely to permit us to see perturbations in their behavior.
The Sample
1000
600
800
Name
Type
dlnP/dt
(dd-1)
dlnP/dt
(y-1)
AB Cyg
SRb
1.5210-06
5.5410-04
RW Cyg
SRc
-4.3310-06
-1.5810-03
S Aur
SR
-2.2310-07
-8.1310-05
S Per
SRc
-5.8010-07
-2.1210-04
ST Psc
SRb
1.5310-05
5.6010-03
SW Gem
SRa
3.0610-06
1.1210-03
V Hya
SRa
6.4810-08
2.3710-05
T Cnc
SRb
8.8310-08
3.2310-05
W Per
SRc
5.8110-06
2.1210-03
SY Per
SRa
2.1910-06
7.9910-04
TW Peg
SRb
3.9610-07
1.4510-04
500
600
400
-0.5
0
0.5
1.0
1.5
-0.4
2.0
-0.2
-0.1
-0.08-0.04 0
0.04 0.08
0.1
0.2
-5
(dlnP/dt) / 10
-5
(dlnP/dt)/10
750
Meandering behaviour: V Cam-type trend
Semiregulars
Miras
1000
MIRAS
500
750
Period (days)
550
500
250
Period (days)
250
-1
Continuous decrease or increase
550
450
ST Psc: Continuous increase
6
2.445x10Julian date
2.450x10
6
1
(dlnp/dt)/10
2
0
-10
-5
0
-3 -1
dlnP/dt (10 yr )
5
10
450
T CnC : Meandering trend
400
6
2.42x10
6
2.45x10
Julian date
The sign of a sudden change?
RW Cyg presents nearly the same period
evolution as the Mira R Cen, but we must
underline the fact that the star has been
observed over only 30 years regarding to 88
for R Cen. So we have to be careful while
dealing with this object. Moreover, while for R
Cen the decrease in period is accompanied by
a decrease in amplitude, this is not the case
for RW Cyg.
RW Cyg: Sudden drop ?
600
The different classes of evolutionary trend.
The high level of perturbation observed while
studying the Semiregulars’ period evolution,
prevents us to establish a very good
classification of the different observable
trends. Nevertheless, even with our small
sample, we can find nearly the same
categories as found for the Miras.
0
-5
550
Period (days)
Period (d)
Period
Period (days)
We used a linear fitting to define the change (by
dlnP/dt: the slope over the mean period). In
order to compare these variations to the ones of
the Miras we define the same method of
calculation and the same significant threshold
for the period change : 2 (1σ dlnP/dt error:
0.0002, in days) (Templeton, Mattei and Willson
2005). It appears that the SRs are very unstable
and more than the miras.
6
MIRAS
500
The period evolution
2.440x10
C stars
S stars
O stars
SEMIREGULARS
Period (days)
The Semiregulars with period longer than 450
days are not in high number: using the
database of the AAVSO and the AFOEV we
found 26 stars corresponding to our criterion.
The study of the light curves of these stars
involving the use of the wavelet analysis
(developed by Foster- 1996) allows the correct
visualization of periodic variations in only 11
of them. This is due, in part, to the fact that
the stars present close modes of pulsation (
believed to be the 1st and 2nd overtone) and
there is a phenomenon of aliasing preventing
us to have a correct analysis.
The case of ST Psc is not common as the
star presents a nearly straight increase of
90 days over 33 years. Other SRs (S Aur, S
Per for example) show that kind of rise or
fall but the evolution is characterised by
oscillating motions. They will therefore be
put in the category of meandering stars
like the V Del-type Miras.
Comparative study
6
2.43x10
6
2.44x10Julian date
6
2.45x10
6
2.46x10
Interpretation
We can see that the period evolution of the
Semiregular stars can be described nearly in
the same way as for the Miras. The
meandering and continuous trends are the
most represented, part from the time we
consider as truthful the analysis for such a
biased type of signal. The denomination of the
stars (SRa., SRb...etc) does not seem to play a
role in the type of period evolution. The
correlation between these changes and
thermal pulses is not so obvious: among the
stars studied by Lebzelter and Hron (2003), SW
Gem and TW Peg do not present Technetium;
the other stars have not been studied.
Moreover the presence of close modes of
pulsation prevents us to have a correct
analysis of the light curve.
We can see that the Semiregulars are more
unstable than the Miras. It may be due to the
fact that the SRs (may) pulsate according
the first overtone (and are most often
accompanied with a second one) while the
Miras are believed to pulsate in the
fundamental mode. Both groups present
almost the same trends: continuous
changes, (possible) sudden drops and more
often meandering behaviours. The particular
study of the period evolution for both types
of stars shows that most of the SRs and
nearly half of the O-rich and C-rich Miras
studied; show an increasing trend in their
behaviour: the period is rising. So if the
process responsible for this phenomenon is
a thermal pulse, we can say that the stars
are experiencing the consequences of one
which has occurred some times ago. The
stars showing decreasing period changes,
may present the short moment after the
appearance of the pulse when the
temperature is still high, and the luminosity
drops. The small variations (meandering
stars) could be due to other phenomena. The
Very Long Period Variables can be seen,
regarding their period instability, as the
witnesses of the physical changes occurring
in AGB stars . We must nevertheless also
quote the particularly unstable behaviour of
52 Mira-type stars with a period between 200
and 450 days. They have been taken out of a
panel of 547 Mira stars (Templeton et al.
2005).
References
Lebzelter T. and Hron J., 2003, AA
411,533-542.
Templeton M.R., Mattei ,J.A.,Willson L.A.,
2005, AJ, 130:776-788
Zijlstra A.A and Bedding T.R,
2002,JAAVSO,31,2
We acknowledge the AAVSO and the
AFOEV for the data as well as all the
observers who provide them.