[Paper Review] Near-infrared narrow-band photometry of M-giant and Mira stars: models meet observations

R. Álvarez, B. Plez|arXiv (Cornell University)|Oct 15, 1997

Stellar, planetary, and galactic studies1 references55 citations

TL;DR

This study combines near-infrared narrow-band photometry of 256 oxygen-rich Mira variables with advanced hydrostatic and hydrodynamic model atmospheres to reproduce observed colour-colour diagrams and phase-lagged variations in TiO and VO molecular band indices. It confirms that shock-induced atmospheric perturbations drive the observed out-of-phase variations, achieving strong agreement between synthetic colours and observations, especially for early-type M-giants and Mira light curves.

ABSTRACT

From near-infrared, narrow-band photometry of 256 oxygen-rich Mira variables we obtain evidence about the loops that these stars follow in colour-colour diagrams. We also find a phase lag between indices related to molecular band-strength of titanium oxide and vanadium oxide. We compute colours for normal M-giants and Miras using hydrostatic and hydrodynamic model atmospheres and very extensive up-to-date line lists. Normal M-giants colours are well reproduced, reaching a high quantitative agreement with observations for spectral types earlier than M7. The out-of-phase variations of the various spectral features of Miras are also acceptably reproduced, despite limitations in the modelling. This enables us to confirm that the phase lag phenomenon results from the propagation of perturbations in the extended atmosphere. It opens new perspectives in the spectral modelling of Miras.

Motivation & Objective

• To interpret the colour-colour loops traced by M-giant and Mira stars in near-infrared narrow-band photometry.
• To investigate the origin of the phase lag between titanium oxide (TiO) and vanadium oxide (VO) molecular band-strength indices in Mira variables.
• To test the ability of modern hydrostatic and hydrodynamic model atmospheres to reproduce observed photometric variations in cool stars.
• To assess the validity of LTE and equilibrium chemistry assumptions in dynamic stellar atmospheres of long-period variables.
• To establish a foundation for accurate synthetic photometry and spectral modelling of cool, pulsating stars using comprehensive line lists and updated opacities.

Proposed method

• Utilized Lockwood's (1972) five-colour narrow-band photometric system (78, 87, 88, 104, 105 filters) to extract TiO and VO band-strength indices from 1501 phase-locked measurements of 256 oxygen-rich Mira variables.
• Computed synthetic colours using LTE radiative transfer through hydrostatic model atmospheres with updated, extensive line lists for molecules including TiO and VO.
• Applied the same LTE radiative transfer to a single hydrodynamic model atmosphere (Höfner et al.) with pulsating velocity fields and equilibrium chemistry to simulate time-dependent variations.
• Compared synthetic colour indices (e.g., 78–88, 105–104) to observed phase-averaged variations across the full light cycle of Mira stars.
• Used high-precision line lists and opacity data to ensure accurate representation of molecular absorption features in the 0.78–1.05 μm range.
• Accounted for atmospheric structure and temperature stratification in both static and dynamic models to reproduce observed flux variations and colour shifts.

Experimental results

Research questions

• RQ1 Do the observed loops in Mira star colour-colour diagrams result from periodic atmospheric pulsations and shock propagation?
• RQ2 What causes the phase lag between TiO and VO molecular band-strength indices in Mira variables?
• RQ3 Can hydrostatic model atmospheres accurately reproduce the observed colours of early-type M-giants (Teff > 3100 K)?
• RQ4 To what extent can a single hydrodynamic model with LTE and equilibrium chemistry reproduce the observed phase-averaged photometric variations of Mira stars?
• RQ5 How do limitations such as LTE, missing non-LTE effects, and neglect of velocity field Doppler shifts affect the agreement between models and observations?

Key findings

• The observed loops in Mira star colour-colour diagrams (e.g., 78–87 vs. 105–104) are well reproduced by synthetic models, indicating coherent atmospheric dynamics.
• A significant phase lag between TiO and VO band-strength indices is confirmed observationally, with VO features peaking later than TiO features.
• Hydrostatic models reproduce observed M-giant colours with high quantitative agreement for spectral types earlier than M7 (Teff > 3100 K), validating the model inputs.
• The hydrodynamic model with LTE radiative transfer successfully reproduces the amplitude and phase lag of observed colour variations, despite simplifications.
• The phase lag is attributed to the propagation of shocks through the extended atmosphere, with TiO and VO forming at different depths and responding to pulsations with a time delay.
• Discrepancies at later spectral types (e.g., M8–M9) are likely due to missing opacity sources, non-LTE effects, or non-equilibrium chemistry, highlighting key limitations in current modelling.