Miras
by Lee Ann Wilson and Massimo Marengo
JAAVSO 40, 2012, 516-527
Motivation
I was interested in learning more about the physical processes that generate light curves of pulsators,
specifically Miras. The article is a recent JAAVSO publication.
Introduction
Mira variables provide a high visual amplitude, with periods of hundreds of days, are spectral class M, S,
and C (red stars), exhibits emission lines, and primarily fundamental mode pulsators (radial motion), with
the progenitor mass ranging from <1 to several solar masses. Early pulsation models were similar to
Cepheids and initially thought to be due to ionization and recombination; Cepheids (He+ ↔ He++) and
Miras (H ↔ H+ and He ↔He+). Modern theories include nuclear evolution processes and modeling of
dynamic atmospheric properties. Recent observations including light curves and interferometry are
assessing the accuracy of recent Mira pulsation models.
Prior Pulsation Theory
Early Mira pulsation models were thought to be due to ionization and recombination (H ↔ H+ and He ↔
He+) while the stellar mass and radius explained the radial pulsation mode (primary or first overtone).
Unfortunately, initial direct observations of the stellar mass were not accessible and measurements of the
stellar radius resulted in ambiguous conclusions. This initial model was later replaced with improved
modeling of shock waves and included dynamics in the stellar atmosphere.
Recent Pulsation Models
Nuclear evolution processes, pulsation, and atmospheric modeling have been included in recent theories
of Mira stars. Evolutionary models simulate the nuclear processes of a 1 solar mass Mira progenitor star,
as a main-sequence star slowly burning (10 Gyr) its core hydrogen to helium. The helium core collapses
to the size of the earth, converts to Carbon (C) and Oxygen (O) via the triple alpha process leading to the
“helium flash” and the shell expands to a red giant. As the helium core converts to C and O, the core
condenses and the star evolves along the asymptotic giant branch. The conversion of H to He then
alternates with the conversion of He to C and O resulting in shell flashes (thermal pulsations) of 100,000year period (Iben 1993). Miras of progenitor stars of a mass > 2 solar masses result in longer pulsation
periods and Miras from progenitor mass > 2.8 solar masses do not undergo the Helium flash (Herwig
2008). Further improvement included very deep convection zones extending from the core to the shell.
Behavior of the gas near the convection zones is difficult to model, where products from nuclear
processes mixes with the outer envelope and atmospheric shell, and produces higher Carbon to Oxygen
ratio (Marigo and Girardi 2007). M-type Miras have a C/O ratio of <1. Models are including
mechanisms where the C/O ratio modifies the stellar opacity, stellar radius, and the chemistry and
dynamics within the atmosphere.
Interferometry, Light Curves, and Observational Surveys: Model Improvements
Interferometry requiring milli-arsec resolution of R/R along with determination of radial velocities
yields stellar radii and provides a constraint on pulsation models. Recent observations found that the
Mira diameters were influenced by the presence of molecular layers (CO and H2O) of a few stellar radii
above the photosphere, and that large convective cells within the photosphere resulted in non-spherical
symmetry (Perrin et. al 2004). Furthermore, recent observational techniques provide the ability to probe
the dust formation for understanding mass loss.
Light curve measurements (Templeton et. al. 2005) have provided information on the primary pulse mode
of Miras and many interesting features; bumps on the rising or falling light curve which increase and
decrease during many cycles, and modulations of their amplitudes and/or periods. Light curves have also
showed that some Miras amplitude and period abruptly changes to smaller amplitude with a shorter
period causing the star to be reclassified as a SR (semi-regular variable) star (Hron et. al. 1997). SR stars
display unstable light curves and are not red giants. In addition, light curves of RV Tauri stars (Wilson
and Templeton 2009) display similar characteristics of Miras and therefore are thought to be post-Mira of
low-mass, low luminosity, low-metallicity in the pre-plantary nebula phase of evolution.
Multi-epoch photometric surveys in the optical and IR wavelengths have provided a wealth of data;
pulsators with different modes and amplitudes tend to be distributed on separate sequences in the infrared
K band (2190 nm)-log Period diagram, where Miras are distributed at the bright end and semiregular
variables at the lower end of the sequence (Wood 2000). Most importantly, surveys confirmed that
formation of carbon Miras favors an environment of low metallicity, display a high infrared signal with
long periods, and high mass loss rates (Boyer 2011).
Implications
Spectroscopy, interferometry and theories of atmospheric processes enhance the study of single stars and
systems, while infrared observations with evolutionary models provide clues into the evolution of stars
and mass loss. Even though light curves cannot provide the physical aspects of a star they provide
observational methods that can assist to constrain physical models. Studies of Miras can only be
advanced through the symbiotic relation of developing theories and constraints provided by new
observational techniques.
Conclusions
The article “Miras” provided an excellent review on the mechanisms of Miras and how observational data
constrained and assisted in improving those models; nuclear evolution and stellar dynamics. Even though
the paper outlined several theories and experimental techniques to constrain those theories, more robust
codes, improvement in observational techniques, long term observations, and large surveys will be
required to finalize a model of Miras. The addition of new techniques for AAVSO observers such as
spectrometry and IR imaging is another avenue the AAVSO observer can help to improve the
understanding of these variable stars.
Joseph Kalen
Feb 9, 2013