Infrared period-luminosity relations of Galactic Miras based on multi-epoch photometry and the Gaia parallax uncertainty

Summary

This paper establishes period–luminosity (PL) relations for Galactic Miras in nine near-infrared bands using multi-epoch photometry and Gaia parallaxes, and tests the reliability of Gaia parallax uncertainties for these stars.

Data and Methods:

• The sample combines two multi-epoch IR catalogues: the COBE/DIRBE catalogue of variable stars (Price et al. 2010) and the WISE/unTimely catalogue (Meisner et al. 2023). Pulsation periods were taken from the Karlsson compilation of 510 solar-neighbourhood Miras, based on contemporaneous optical observations.

• Gaia DR3 parallax distances from Bailer-Jones et al. (2021) were used. A gold sample was defined with relative parallax uncertainty ≤ 10% and a period available from Karlsson. This yielded 110 stars with DIRBE observations (91 M-, 9 MS/S-, 10 C-type) and 312 stars with unTimely observations (253 M-, 28 MS/S-, 30 C-type, one unknown). The W2 gold sample was further restricted to 152 stars due to saturation effects for sources brighter than W2 = 1.4 mag.

• Photometry was de-reddened using the 3D extinction map of Gontcharov (2017) and the extinction law of Xue et al. (2016). The star R For was excluded from the DIRBE sample because it was in a faint dust-obscuration phase during DIRBE observations.

Results – PL Relations:

• The paper presents well-defined PL relations of the form M0 = b × (log P − 2.38) + a for nine bands: 2MASS J, DIRBE [1.25], 2MASS H, 2MASS KS, DIRBE [2.2], unTimely W1, DIRBE [3.5], unTimely W2, and DIRBE [4.9]. Slopes become steeper and zero points brighter with increasing wavelength.

• The scatter around the W1 relation is 0.327 mag and around the DIRBE [2.2] relation is 0.313 mag. Using single-epoch 2MASS KS data increases the scatter to 0.378 mag, corresponding to an additional variability-induced scatter of 0.209 mag, consistent with a mean KS amplitude of 0.59 mag.

• The Galactic Miras are fainter than LMC Miras by 0.2–0.3 mag, and the Galactic PL relations are steeper, confirming the results of Sanders (2023). The zero point in the DIRBE [2.2]/KS band agrees with Whitelock et al. (2008) to within 0.1 mag, but the slope is steeper (b ≈ −4.0 vs −3.5).

• A Wesenheit index W[2.2],[1.25]−[2.2] was constructed. C stars are brighter by 0.2 mag and S stars fainter by 0.2 mag relative to the M-star trend.

Synthetic SEDs and Derived Relations:

• Synthetic SEDs were constructed from the PL relations at log(P) = 2.2, 2.3, 2.4, 2.5, 2.6, and 2.7. Blackbody fits (excluding WISE bands, which deviate due to saturation issues) yielded:

• Period–temperature relation: T bb = 2895.3/(log P − 1.2580) + 279.3, ranging from 3353 K at log P = 2.2 to 2287 K at log P = 2.7.

• Period–bolometric-luminosity relation: log(L*/L⊙) = 3.506 − 1.044 log(P) + 0.4551 log(P)2, ranging from 2584 L⊙ to 10079 L⊙.

• Period–radius relation: R*/R⊙ = −534.0/(log P − 3.228) − 371.1, ranging from 150 R⊙ to 639 R⊙.

Testing Gaia Parallax Uncertainties:

Three independent tests were performed:

1. Scatter around the PL(K) relation: Using COLIBRI evolutionary model tracks with masses 1.0–5.0 M⊙ and the non-linear pulsation models of Trabucchi et al. (2021), the intrinsic width of the PL relation was modelled. The observed scatter of 0.313 mag is fully consistent with the Gaia uncertainties (EIF = 1.0), with better agreement at EIF = 1.3 and marginal agreement at EIF = 1.7. Larger EIFs (>2) are safely excluded.

2. Comparison with VLBI parallaxes: The sample of Andriantsaralaza et al. (2022) was revisited with improved pulsation periods (Table 4). The stars form a well-defined PL(W1) relation, extending to long-period OH/IR stars (NSV 17351, P = 1108 d). For stars with σ̟/̟ < 0.1 in both catalogues (22 stars), the one-sided EIF is 4.59, but excluding U Her and RW Lep reduces it to 2.27. For the faint subsample (G > 7.922 mag), the one-sided EIF is 1.76. A two-sided EIF (applied to both Gaia and VLBI uncertainties) is 1.89 for the full sample and 1.64 for the faint sample.

3. 47 Tuc globular cluster LPVs: Using 41 LPVs in 47 Tuc, the spread in parallaxes compared to the combined uncertainties yields an EIF of 1.34–1.35. This is somewhat larger than the 1.11–1.16 expected from El-Badry et al. (2021) for the G magnitude range of these stars. The parallax uncertainty increases for brighter (more extended) stars and for stars near the cluster centre.

Stars with Changing Pulsation Periods:

Miras with continuously, suddenly, or meandering changing periods generally follow the fundamental-mode PL(W1) relation closely. Exceptions include R Cen (likely an intermediate-mass HBB star with an overestimated Gaia distance), RU Tau (below the relation), and RU Vul (possibly transitioning to overtone pulsation).

Conclusions:

• The Gaia parallax uncertainties for Galactic Miras are underestimated by factors between 1.0 and 1.7, most likely 1.3. Large error inflation factors (>2) reported in the literature are unrealistic.

• For stars with σ̟/̟ > 0.1, distances tend to be overestimated (parallaxes underestimated), as these stars lie systematically above the PL relations.

• The W2 band flux is significantly overestimated due to saturation, so the PL(W2) relation should be used with caution.

• The PL relations and derived period–temperature, period–bolometric-luminosity, and period–radius relations are useful empirical tools for studying AGB variables.

Based on this paper, here are specific improvements for AI systems:

• Multi-epoch photometry integration: Combine data from multiple IR catalogs (DIRBE, unTimely/WISE, 2MASS) with Gaia parallaxes and optical period measurements to construct period-luminosity relations.

• Automated outlier detection: Identify stars with circumstellar dust obscuration (like R For) that deviate from PL relations, and flag stars with unreliable photometry (e.g., W2 saturation effects).

• Synthetic SED construction: Generate mean spectral energy distributions at any period using derived PL relations across nine IR bands, enabling blackbody fitting for temperature, luminosity, and radius estimates.

• Period-temperature relation: Use Eq. 4 (T bb = 2895.3/(log P - 1.2580) + 279.3) to estimate effective temperatures of Miras from their pulsation periods.

• Period-bolometric luminosity relation: Apply Eq. 5 to estimate luminosities from periods, useful for distance determination and stellar evolution studies.

• Period-radius relation: Use Eq. 6 (R/R sun = -534.0/(log P - 3.228) - 371.1) to estimate stellar radii, valuable for modeling extended atmospheres.

• Error inflation factor (EIF) estimation: Implement the three-test methodology (PL scatter with COLIBRI models, VLBI comparison, 47 Tuc cluster analysis) to quantify whether Gaia parallax uncertainties are underestimated for AGB stars.

• Distance bias correction: Detect and correct systematic overestimation of distances for stars with σ π/π > 0.1, which tend to appear above PL relations by 0.3-0.6 magnitudes.

• Brightness-dependent uncertainty assessment: Automatically evaluate whether brighter stars have more severely underestimated parallax uncertainties (finding: no significant difference).

• Period change classification: Automatically identify Miras with continuous, sudden, or meandering period changes and verify they still follow fundamental-mode PL relations.

• Mode identification: Distinguish fundamental-mode pulsators from first-overtone pulsators (e.g., BX Eri, RT Vir, RX Boo, V637 Per) based on their position in PL diagrams.

• Long-period extension validation: Confirm that OH/IR stars with periods >1000 days (like NSV 17351) follow the same near-IR PL relations as shorter-period Miras.

• Galactic vs. LMC comparison: Quantify that Galactic Miras are fainter by 0.2-0.3 magnitudes and have steeper PL slopes than LMC Miras, enabling population and metallicity effect studies.

• Chemical type separation: Analyze differences between M, S, and C-type stars in Wesenheit indices (finding 0.4 magnitude difference between S and C stars).

• PL-based distance estimation: Use derived PL relations (Table 1) to estimate distances to Miras from apparent magnitudes and periods, particularly useful for stars with poor parallaxes.

• Wesenheit index application: Apply the reddening-free index W[2.2],[1.25]-[2.2] = [2.2] - 0.686×([1.25]-[2.2]) for distance determination without extinction corrections.

• Sample selection optimization: Identify criteria for selecting optically bright Miras with well-determined periods (requiring ≥20 clear maxima) to minimize variability-induced scatter in PL studies.

• Saturation limit detection: Automatically identify photometric saturation limits (e.g., W2 < 1.4 mag) and exclude affected sources.

• COLIBRI model comparison: Use the model grid (masses 1.0-5.0 M sun, [Fe/H] = -0.03) to test whether observed PL scatter matches theoretical predictions, validating AGB evolutionary models.

• Thermal pulse phase identification: Use position relative to PL relations to infer which phase of thermal pulse cycle a star is in.

Miras and other long-period variable (LPV) stars on the AGB follow period-luminosity (PL) relations. These relations have been difficult to study for Galactic LPVs because their distances were poorly known in the past. We aim to establish the PL relations of solar-neighbourhood Miras for several near-IR photometric bands. To this end, we used multi-epoch photometry from the DIRBE and unTimely/WISE catalogues, Gaia parallax distances, and contemporary pulsation periods obtained from optical observations of a well-selected sample of solar-neighbourhood Miras. We show that clearly defined PL relations in the nine investigated near-IR bands emerge from our data, and we report the slopes and zero-point magnitudes. We find that Galactic Miras are fainter in the near-IR than their Large Magellanic Cloud siblings. We derive average period-temperature, period-bolometric-luminosity, and period-radius relations from fits to synthetic SEDs constructed from the PL relations. By applying AGB evolutionary models, the scatter of stars around the PL sequences can also be used to test whether the parallax uncertainties quoted in the Gaia catalogue are realistic. Furthermore, we performed such tests based on a comparison with parallaxes obtained with the VLBI and with a sample of LPVs in the globular cluster 47 Tuc. We conclude that, for Galactic Miras with a fractional parallax uncertainty of <0.1 in the Gaia catalogue, the parallax uncertainty is underestimated by factors between 1.0 and 1.7, and most likely by about1.3. For more uncertain parallaxes, we find evidence that the distances (parallaxes) are generally overestimated (underestimated). Nevertheless, we find strong evidence that the large error-inflation factors reported for AGB stars in the literature are unrealistic. Our results lend confidence to the parallax measurements of these highly extended, variable stars.