From solar-like to mira stars: a unifying description of stellar pulsators in the presence of stochastic noise

ABSTRACT We discuss and characterize the power spectral density properties of a model aimed at describing pulsations in stars from the main-sequence to the asymptotic giant branch. We show that the predicted limit of the power spectral density for a pulsation mode in the presence of stochastic noise is always well approximated by a Lorentzian function. While in stars predominantly stochastically driven the width of the Lorentzian is defined by the mode lifetime, in stars where the driving is predominately coherent the width is defined by the amplitude of the stochastic perturbations. In stars where both drivings are comparable, the width is defined by both these parameters and is smaller than that expected from pure stochastic driving. We illustrate our model through numerical simulations and propose a well-defined classification of stars into predominantly stochastic (solar-like) and predominately coherent (classic) pulsators. We apply the model to the study of the Mira variable U Per, and the semiregular variable L2 Pup and, following our classification, conclude that they are both classical pulsators. Our model provides a natural explanation for the change in behaviour of the pulsation amplitude-period relation noted in several earlier works. Moreover, our study of L2 Pup enables us to test the scaling relation between the mode line width and effective temperature, confirming that an exponential scaling reproduces well the data all the way from the main sequence to the asymptotic giant branch, down to temperatures about 1000 K below what has been tested in previous studies.

Astrometry and infrared observations of the Mira variable stars AP Lyncis, V837 Herculis, and BX Camelopardalis: Implications for the period–luminosity relation of the Milky Way

AP Lyn and V837 Her are long-period Mira variable stars in the Milky Way. We performed VLBI Exploration of Radio Astrometry (VERA) phase-referenced observations towards H2O masers associated with AP Lyn and V837 Her. The annual parallaxes of AP Lyn and V837 Her were obtained to be 2.008 ± 0.038 mas and 1.090 ± 0.014 mas, corresponding to distances of 498 ± 10 pc and 917 ± 12 pc, respectively. From our multi-epoch infrared observations using the Kagoshima University 1 m telescope, we derived the mean J-, H-, and K′-band magnitudes of AP Lyn, V837 Her, and an additional long-period Mira variable BX Cam, whose parallax is known. We derived their pulsation periods to be 433 ± 1 d, 520 ± 1 d, and 458 ± 1 d, respectively, using the K′-band light curves. The MK–log P relation of long-period Mira variables seem to be violated by Mira variable stars with larger-than-expected MK values (like OZ Gem) in the Milky Way because of circumstellar extinction leading to an observed dimming effect. AP Lyn, V837 Her, and BX Cam (like OZ Gem) are dimming from the trend to O-rich stars in the Large Magellanic Cloud. This implies that the high metallicity of the Milky Way galaxy increases the opacity of the Mira-type variable stars and strengthens mass loss.

Trigonometric parallax of O-rich Mira variable star OZ Gem (IRAS 07308+3037): A confirmation of the difference between the P–L relations of the Large Magellanic Cloud and the Milky Way

OZ Geminorum (OZ Gem) is a galactic Mira variable in the Milky Way (MW). We measured its annual parallax with VLBI Exploration of Radio Astrometry to be π = 0.806 ± 0.039 mas, corresponding to a distance of D = 1.24 ± 0.06 kpc. Based on multi-epoch infrared observations with the Kagoshima University 1 m telescope, we also derived the mean J-, H-, and K′-band magnitudes of OZ Gem to be 5.75 ± 0.47 mag, 4.00 ± 0.16 mag, and 2.65 ± 0.16 mag, respectively. We derived a pulsation period of OZ Gem as 592 ± 1 d from the K′-band lightcurve. From the period–luminosity (P–L) relation and two-color diagram of the Large Magellanic Cloud (LMC), the property of OZ Gem suggests that OZ Gem is assigned among the carbon-rich Mira variables. However, our optical spectroscopic observational results (with the 1.5 m Kanata telescope) confirmed OZ Gem to be an oxygen-rich Mira star with the detection of multiple titanium oxide transition absorption lines. We suggest that OZ Gem is a low-mass star evolving to an OH/IR star with large mass loss and dust formation. It is predicted that the lower limit to the initial mass of AGB stars for developing the C-rich surface chemistry is larger in the MW than in the LMC because of larger metallicity, and OZ Gem is likely to be the first example to prove this. Our results highlight the necessity of deriving the PL relation of the Milky Way with high accuracy.

Annual parallax measurement of the Mira variable star BX Camelopardalis with VERA

We report the results of astrometric VLBI observations toward the Mira variable star BX Cam using the VERA VLBI array. The observation was performed from 2012 February to 2014 November. The parallax obtained is 1.73 ± 0.03 mas corresponding to a distance of 0.58 ± 0.01 kpc. The parallax of this source was reported in Gaia DR2 as 4.13 ± 0.25 mas, and there is a 240% difference between these two measurements. Astrometric results from our VLBI observations show that we exactly traced the angular motions of the seven maser spots in BX Cam. We calculated the stellar luminosities using both parallaxes, and obtained luminosities of $L_{\ast }^{\mathrm{VERA}} = 4950\pm 170\, L_{\odot }$ and $L_{\ast }^{\mathrm{Gaia}} = 870\pm 110\, L_{\odot }$. These deduced luminosities also support the validity of the parallax that we determined with VERA. Evaluating the two parallaxes, we conclude that the parallax of 1.73 ± 0.03 mas from the VERA observations is correct for BX Cam. We obtained the systemic motion of BX Cam as (μαcos δsys, ${\mu }_{\delta }^{\mathrm{sys}}$) = (13.48 ± 0.14, −34.30 ± 0.18) mas yr−1. The total of 73 H2O maser spots detected from our VLBI observations shows a spatial distribution of 30 au × 80 au, with a strong elongation along the north–south direction. They show outflows with a three-dimensional velocity of 14.79 ± 1.40 km s−1. From a comparison between the time variations of the V-band magnitudes and the H2O masers, we found that the variation of the H2O masers is relevant to that seen in the V band even though the H2O masers do not recover their maximum flux in each cycle.

Mid-IR spectra of the M-type Mira variable R Tri observed with the Spitzer IRS

ABSTRACT We present analysis of mid-infrared (IR) spectra of the oxygen-rich Mira variable R Tri. The data were taken with the Spitzer Infrared Spectrometer (IRS) as part of a study tracking how Mira variables’ regular pulsations affect circumstellar envelopes. We detected strong emission lines at 13.87, 16.18, and 17.6 $\hbox{$\mu $m}$, and one strong absorption feature at 14.98 $\hbox{$\mu $m}$. The emission features at 13.87 and 16.18 $\hbox{$\mu $m}$ are excited vibrational bands of CO2, while the absorption feature is the fundamental ν2 band. The 17.6 $\hbox{$\mu $m}$ emission feature has a completely different character than the molecular lines and we report its identification as Fe i fluorescence. We used a two-slab model with the radiative transfer code radex to model the CO2 Q-branch bandheads. Our results indicate a slab of gas with T∼600 K located at ∼3–4 R*. The cool temperature discrepancy with the radius provides observational evidence for the previously theoretical ‘refrigeration zone’.