[Paper Review] Reprocessing the Hipparcos data for evolved stars III Revised Hipparcos period-luminosity relationship for galactic long-period variable stars

G. R. Knapp, D. Pourbaix+2 more|arXiv (Cornell University)|Jan 29, 2003

Astrophysics and Star Formation StudiesPhysics and Astronomy45 references111 citations

TL;DR

This study reanalyzes Hipparcos parallaxes and K-band magnitudes for Galactic long-period variables, applying improved astrometric fits and extinction corrections to derive revised period-luminosity (P-L) relationships. It finds distinct P-L relations for Mira and SRb variables with different slopes, indicating mode-dependent pulsation, and shows that stars with P > 400 d have high mass loss and are predominantly Mira variables, suggesting a breakdown in mode switching at long periods.

ABSTRACT

We analyze the K band luminosities of a sample of galactic long-period variables using parallaxes measured by the Hipparcos mission. The parallaxes are in most cases re-computed from the Hipparcos Intermediate Astrometric Data using improved astrometric fits and chromaticity corrections. The K band magnitudes are taken from the literature and from measurements by COBE, and are corrected for interstellar and circumstellar extinction. The sample contains stars of several spectral types: M, S and C, and of several variability classes: Mira, semiregular SRa, and SRb. We find that the distribution of stars in the period-luminosity plane is independent of circumstellar chemistry, but that the different variability types have different P-L distributions. Both the Mira variables and the SRb variables have reasonably well-defined period-luminosity relationships, but with very different slopes. The SRa variables are distributed between the two classes, suggesting that they are a mixture of Miras and SRb, rather than a separate class of stars. New period-luminosity relationships are derived based on our revised Hipparcos parallaxes. The Miras show a similar period-luminosity relationship to that found for Large Magellanic Cloud Miras by Feast et al. (1989). The maximum absolute K magnitude of the sample is about -8.2 for both Miras and semi-regular stars, only a little fainter than the expected AGB limit. We show that the stars with the longest periods (P>400d) have high mass loss rates and are almost all Mira variables.

Motivation & Objective

• To improve the accuracy of Hipparcos parallaxes for evolved long-period variable stars using reprocessed intermediate astrometric data and chromaticity corrections.
• To derive a reliable period-luminosity (P-L) relationship for Galactic long-period variables by combining revised parallaxes with corrected K-band magnitudes from literature and COBE DIRBE data.
• To investigate whether circumstellar chemistry (M, S, C-type) or variability class (Mira, SRa, SRb) affects the P-L relation, and to assess the role of pulsation mode and mass loss.
• To determine the maximum intrinsic luminosity of AGB stars in the solar neighborhood and evaluate the feasibility of using P-L relations for distance measurements.
• To examine the dependence of mass loss rates on pulsation period and variability type, particularly for long-period stars.

Proposed method

• Recomputed Hipparcos parallaxes from Intermediate Astrometric Data using improved astrometric fitting techniques and chromaticity corrections.
• Sourced K-band magnitudes from the literature and COBE DIRBE time-series data, applying interstellar and circumstellar extinction corrections.
• Classified stars by spectral type (M, S, C) and variability class (Mira, SRa, SRb) to analyze P-L relations within each group.
• Fitted period-luminosity relationships using the form $ M_K = a imes \log P + b $, with $ M_K $ as absolute K-band magnitude and $ P $ in days.
• Analyzed the dependence of mass loss rates on period and variability type using the distribution of stars in the P-M_K plane.
• Evaluated the consistency of the derived P-L relations with those from the Large Magellanic Cloud and Galactic Bulge, and discussed implications for pulsation mode switching.

Experimental results

Research questions

• RQ1 Do the period-luminosity relationships for Galactic long-period variables differ significantly between Mira and SRb variables, and if so, how?
• RQ2 How does circumstellar chemistry (M, S, C-type) affect the period-luminosity relation in evolved stars?
• RQ3 What is the relationship between pulsation mode (fundamental vs. overtone) and the observed P-L slope in long-period variables?
• RQ4 How do mass loss rates correlate with pulsation period and variability class, particularly for stars with P > 400 days?
• RQ5 To what extent do mode-switching behaviors between Mira and SR pulsation modes affect the observed P-L relation?

Key findings

• The P-L relationship for Mira variables in the Galaxy is consistent with that found for Large Magellanic Cloud Miras, with a slope of $ a \approx -3.5 $ and a maximum absolute $ K $-band magnitude of $ -8.2 \pm 0.2 $.
• SRb variables exhibit a significantly shallower P-L slope than Mira variables, indicating different pulsation modes or physical mechanisms.
• SRa variables are distributed between the Mira and SRb sequences, suggesting they are a mixture of both types rather than a distinct class.
• Stars with periods longer than 400–500 days have high mass loss rates and are almost exclusively Mira variables, indicating a breakdown in mode-switching behavior at long periods.
• Mass loss rates increase steadily with period for both Mira and SRb variables, and are significantly higher for Miras at the same period.
• The maximum observed $ K $-band absolute magnitude of $ -8.2 \pm 0.2 $ corresponds to a bolometric luminosity of ~5000–6000 $ L_\odot $, consistent with the theoretical AGB luminosity limit.