Hipparcos period-luminosity relations for Miras and semiregular variables

We present period-luminosity diagrams for nearby Miras and semiregulars, selecting stars with parallaxes better than 20 per cent and well-determined periods. Using K-band magnitudes, we find two well-defined P-L sequences, one corresponding to the standard Mira P-L relation and the second shifted to shorter periods by a factor of about 1.9. The second sequence only contains semiregular variables, while the Mira sequence contains both Miras and semiregulars. Several semiregular stars show double periods in agreement with both relations. The Whitelock evolutionary track is shown to fit the data, indicating that the semiregulars are Mira progenitors. The transition between the two sequences may correspond to a change in pulsation mode or to a change in the stellar structure. Large amplitude pulsations leading to classical Mira classification occur mainly near the tip of the local AGB luminosity function.

💡 Research Summary

In this paper Bedding and Zijlstra exploit the high‑precision parallaxes provided by the Hipparcos mission to construct period‑luminosity (P‑L) diagrams for a carefully selected sample of nearby long‑period variables (LPVs). The authors restrict the sample to stars with relative parallax errors ≤ 20 %, a variability flag of at least 2 in the Hipparcos catalogue, spectral types M or S (excluding carbon stars), and well‑determined periods longer than 50 days. After cross‑checking periods against the General Catalogue of Variable Stars, the AFOEV, VSOLJ, and Mattei et al. (1997), the final list comprises six Mira variables and eighteen semiregular variables (SRs), seven of which exhibit two independent periods.

K‑band magnitudes are taken from van Leeuwen et al. (1997) for the Miras and from Kerschbaum & Hron (1994) and other literature sources for the SRs. Although many SR magnitudes are single‑epoch, the low K‑band amplitudes of SRs limit the induced scatter to ≲ 0.1 mag, far smaller than the ≈ 0.26 mag scatter seen for Miras in the LMC.

The authors explicitly address the Lutz‑Kelker bias, using Koen (1992) to estimate that the systematic shift in absolute K magnitude is at most ≈ 0.1 mag for the poorest parallaxes in the sample. This bias is comparable to the photometric scatter and does not affect the main conclusion that two distinct P‑L sequences are present.

Figure 1 shows the K‑band P‑L diagram. The solid line is the LMC Mira relation from Feast (1996): MK = −3.47 log P + 0.91 (adopting an LMC distance modulus of 18.56). The Hipparcos Miras and a subset of SRs lie on this line, confirming that they share the same pulsation mode (either fundamental or first overtone). A second, parallel sequence is offset to shorter periods by a factor of ≈ 1.8–1.9 (or equivalently ≈ 0.9 mag brighter at a given period). This second sequence contains only SRs, reproducing the “Wood & Sebo” sequence identified in the LMC and in MACHO data for the Galactic bulge.

Seven stars display double periods. In five cases the longer period aligns with the Mira sequence while the shorter period falls on the SR sequence, yielding period ratios between 1.76 and 1.90. These ratios provide valuable constraints for pulsation models and suggest a possible mode switch (e.g., from first overtone to fundamental) or a structural adjustment that changes the period while the luminosity remains roughly constant.

The authors then compare the data with the Whitelock evolutionary track, originally derived from LPVs in globular clusters. The track has a slope consistent with Vassiliadis & Wood (1993) AGB evolutionary models and, when shifted upward by 0.8 mag, passes through the bulk of the SR points, linking them to the Mira sequence at the point where the two lines intersect. This supports the long‑standing hypothesis that SRs are the progenitors of Miras, with the transition occurring near the tip of the local AGB luminosity function where large‑amplitude pulsations develop.

Two interpretations are offered for the bifurcation into separate sequences: (1) a change in dominant pulsation mode (e.g., from first overtone in SRs to fundamental in Miras) causing a sudden period increase, or (2) an adjustment in stellar structure (e.g., core mass growth, envelope mass loss) that alters the period independently of mode. The presence of double‑mode stars that occupy both sequences lends weight to the mode‑change scenario, but the authors acknowledge that the evidence is not conclusive.

In summary, the paper demonstrates that (i) a significant fraction of SRs share the same P‑L relation as Miras, implying a common pulsation mode; (ii) the remaining SRs define a second, parallel P‑L sequence shifted to shorter periods by a factor of ~1.9; (iii) many SRs exhibit double periods whose ratios (≈ 1.8–1.9) are consistent with a mode transition; (iv) the Whitelock evolutionary track fits the data, reinforcing the view that SRs evolve into long‑period Miras; and (v) the separation into two sequences likely reflects either a pulsation‑mode switch or a structural readjustment during AGB evolution. These findings provide robust observational constraints for theoretical models of AGB pulsation, mass loss, and stellar evolution.