Long term multiwavelength study of
Hipparcos Mira variable stars
By
Sean P. Patterson
Advisor:
Dr. Lee Anne Willson
ABSTRACT
From the visual and infrared light curves we are trying to find the phase changes and
correlate them to Infrared shift and magutdes to see what is happing to Mira type stars as
they age. Most of the radiation in the star is in the Infrared. The method being used O-C
and fitting mean light curves. All mira variables pulsate undergoing rapid mass loss. In
the conclusion we show that the magnitude has a positive correlation with the phase shift.
I.
Introduction
Studies of Mira variables are of considerable importance in
stellar astrophysics because they are pulsating stars
undergoing rapid mass loss.
During one cycle, which
typically lasts from 200-500 days, these stars undergo
significant changes in their observable properties.
At
some point in their lives, many if not most stars go
through an unstable phase that leads to pulsation.
They
are evolving through the tip of the asymptotic giant branch
(AGB) in the H-R diagram and are affected by two
significant processes. In the interior, helium shell
flashes cause large excursions in their luminosity’s and
period on a timesscale of ten of thousands of years. In the
outer layers, pulsation-enhanced mass loss, which reduces
their envelope masses and drives their evolution to the
white dwarf.
The atmospheres of Mira variables are very
deep and there effective diameters change markedly with
wavelength because of the opacity effects.
The massive
winds of Miras are believed to be driven by a combination
of dust formation and shocks induced by stellar pulsation.
(Willson). Understanding the nature of shocks and measuring
their properties is essential to understanding the physics
of pulsation and mass loss from pulsating stars.
This paper presents an analysis of visible and IR
(JHKL) data for 2 Long Period Variables (LPV).
The four
pulsating variables chosen are classified as Miras.
All
Miras stars are Long period variables that exhibit a very
large change in visible light because they are cool (less
than or equal to 3000K), and so most of their radiation
lies in the infrared.
We are studying the Mira stars
instead the irregular stars because to understand any star
you must first start with the simplest model then expand
upon that, Mira are relatively well-behaved long period
variable.
II.
Data Search
For this study we required stars that had already been
studied intensively, so that both IR data and visual data
were available for many cycles.
A search of the SIMBAD
database located many useful papers about mass-loss rates
and infrared photometry.
The American Association of
Variable Star Observers (AAVSO) has a long-term program to
monitor hundreds of Miras by using observations from
amateur astronomers around the world.
Using the AAVSO data
obtained from the World Wide Web we obtained evaluated
visual light curves.
The Infrared data was obtained from
Patricia Whitelock who works at the South African
Astronomical Observatory.
III. Data Analysis
The method used for computing the analysis is fitting
mean light curves.
To find the mean light curve you must
take the regular light curves and the period and epoch.
The period is the time interval for some regular event to
take place.
Epoch is the phase at 0.
The period and Epoch
was received from General Catalogue of Variable Stars
(GCVS) data, which was the most accurate data that could be
found.
The formula for finding the phase plus the cycle is
(Julian Date – Epoch)/Period.
Then you take the phase from
that by just subtracting the integer from the phase plus
cycle.
That will superimpose all data in one phase.
To
get the so-called cardboard cutout, I then take all the
points in each bin and get a mean point.
That will produce
the mean light curve.
For the (J, H, K, L) light curve I
took 1/10 of a cycle.
For the visual light curve 1/20,
because there were considerably more points.
In phasing I phased with the most defined structure,
if there was no defined structure you must look at the
cycle before and after.
Usually the best phasing comes
when you are fitting it to he rising or falling branch of
the curve.
Then an O-C (Observed minus Calculated) method
to detect the presence of systematic changes in the periods
of variable stars. The calculated portion of the O-C is
equal to (E+nP).
The observed is basically my job to find
the amount of shift and subtract it from the calculated-C
analysis begins with an assumption that he period is
constant.
A plot of the residuals is the O-C.
Results:
R Horologii was the most stable star I worked with; in
the visible and infrared there was not many random points.
The O-C curve showed that the period changes we used early
in the star but for more recent data the period we used
turns out to be correct.
R Hor phase diagram is also shows
a positive correlation.
S Pictoris is very different. The regular light curve
was not too well defined, and the O-C results were in a
positive correlation but not a very high positive
correlation.
There was a sizable gap in the Infrared data
that may have influenced the results. Also in S Pic there
were not that many points to phase with, so that in a lot
of cycles I had only three points to work with in odd
locations on the lightcurve.
There were many instances
were it was questionable were the phase could go.
In the
visual phasing of S Pic, in contrast, I had very good
phasing thoughout the light curve and very few
uncertainties.
After finding all of the phasing for the stars,
playing with the data made me think, what if the magnitude
had to do with the phase shift, I acted on my idea and
plotted a correlation between the magnitude and phase
shift.
The correlation shows the they are related.
three of the highest points in the magnitude.
I took
The first
highest point could be a bad point, the amateur observer
may have thought the star was bright,
I used the
assumption that if two or more people observed the
magnitude at about same place that point is real. After
doing that the correlation is higher.
I also took the
Infrared and did the same correlation graph.
positive correlation.
Conclusion:
Again a
In conclusion the method of fitting mean light curves,
our results were that we have made a independent discovery
of the Harrington effect in a different way. We also used
the infrared data to find a postive correlation. The
magnitude of the light curve shows directly the phase shift
of the cycle.
In the future of this project, further
testing of this theory and trying to see if the is a
pattern that can be used to predict the next cycle phase
shift and magnitude.
References
Alvarez, R and Plez, B
Near-infrared narrow-band
photometry of M-giant and Mira stars: models meet
observations
Bertre, T Le and Winters, J.M.
On the relations between
infrared colors and mass loss for Mira stars
Harrington, J. Patrick.
Period Variabless
Variations in the Maxima of Long
P. De Laverny et al.: Long-term UBV (RI) monitoring of 12
Southern Hemisphere Long Period Variables
P.G. Tuthill, W.C. Danchi, D.S. Hale, J.D. Monnier and C.H.
Townes
NEAR AND MID-INFRARED SUBARCESECOUND STRUCTURE
OF THE DUSTY SYMBIOTIC STAR R AQUARII
Tej, Anandmayee,
Chandrasekhar, T. Ashok, N.M
The Angular
diameter of the mira variable R Leonis at 3.36 and 2.2
microns
Wood, B.E and Karovska M.
Studying the pulsation of mira
variables in the Ultraviolet