[Paper Review] Petersen diagram for RRd stars in the Magellanic Clouds

B. L. Popielski, W. A. Dziembowski+1 more|arXiv (Cornell University)|Nov 23, 2000

Stellar, planetary, and galactic studies1 references10 citations

TL;DR

This study explains the observed narrow, curved band of RRd stars in the Petersen diagram using evolutionary and pulsation models with metallicity [Fe/H] = (-2, -1.3), showing that mass spread at fixed metallicity accounts for the band's width. The models successfully reproduce the LMC and SMC data, supporting a brighter RR Lyrae luminosity scale with ⟨MV⟩ ≈ 0.5 mag and a distance modulus of 18.4 mag for the LMC.

ABSTRACT

RRd stars from the Magellanic Clouds form a well-defined band in the Petersen diagram. We explain this observed band with our evolutionary and pulsation calculations with assumed metallicity [Fe/H]=(-2,-1.3). Vast majority of RRd stars from LMC is confined to a narrower range of (-1.7,-1.3). The width of the band, at specified fundamental mode period, may be explained by mass spread at given metallicity. The shape of the band reflects the path of RRd stars within the RR Lyrae instability strip. We regard the success in explaining the Petersen diagram a support for our evolutionary models, which yield, mean absolute magnitude in the mid of the instability strip, , in the range 0.4 to 0.65 mag implying distance modulus to LMC of 18.4 mag.

Motivation & Objective

• To explain the observed narrow, curved band of RRd stars in the Petersen diagram using theoretical models.
• To constrain the metallicity and mass distribution of RRd stars in the LMC and SMC based on their position in the Petersen diagram.
• To test the consistency of evolutionary and pulsation models with observed period ratios and luminosities.
• To assess the impact of convection, nonlinearity, and abundance mixtures on period ratio predictions.
• To support a brighter RR Lyrae luminosity scale and distance modulus for the LMC.

Proposed method

• Evolutionary models of horizontal branch stars were computed with fixed hydrogen abundance X = 0.76 and varying metallicity [Fe/H] = (-2, -1.3).
• Linear, non-adiabatic pulsation calculations were performed to determine radial mode periods and the period ratio R = P1/P0.
• The mixing-length parameter α was varied (α = 1 and α = 2) to assess its impact on period ratios and model placement in the Petersen diagram.
• Effects of different heavy element abundance mixtures (e.g., oxygen-enhanced) were evaluated to estimate their influence on metallicity calibration.
• Nonlinear effects were corrected by applying a -4×10⁻⁴ adjustment to observed period ratios to infer linear values.
• Model predictions were compared with observed RRd stars in the LMC, SMC, and globular clusters to validate the theoretical framework.

Experimental results

Research questions

• RQ1 Why do RRd stars in the Magellanic Clouds form a well-defined, narrow band in the Petersen diagram?
• RQ2 What range of metallicities and masses is required to reproduce the observed period ratio and period distribution of RRd stars in the LMC and SMC?
• RQ3 How do uncertainties in convection treatment (α), nonlinearity, and abundance mixtures affect the inferred metallicity and period ratio?
• RQ4 Can the observed band be explained by mass spread at constant metallicity, and what does this imply for stellar evolution models?
• RQ5 Does the model support a brighter RR Lyrae luminosity scale, and what is the implied distance modulus to the LMC?

Key findings

• The observed RRd band in the Petersen diagram is successfully reproduced by models with metallicity [Fe/H] = (-2, -1.3), with a strong concentration in the LMC at (-1.7, -1.3).
• The width of the band is explained by a spread in stellar masses at fixed metallicity, not by metallicity variation alone.
• The models yield a mean absolute V-magnitude ⟨MV⟩ ≈ 0.5 mag, supporting a brighter RR Lyrae luminosity scale and a distance modulus of 18.4 mag for the LMC.
• The choice of mixing-length parameter α significantly affects model placement, with α = 2 shifting the upper metallicity limit from [Fe/H] = -1.3 to -1.2.
• Nonlinear effects reduce the inferred period ratio by approximately 4×10⁻⁴, corresponding to a 10% decrease in inferred Z or a 0.15 dex decrease in [Fe/H].
• Uncertainties in metallicity inference due to convection, nonlinearity, and abundance mixtures are estimated at ±0.5 dex, which can be reduced with further refinement.