Radio Photospheres of Long‐Period Variable Stars

Abstract

We report the detection of centimeter-wavelength emission from a sample of nearby long-period (Mira and semiregular) variables using the VLA. Six of the eight stars in the sample were detected. We find the continuum emission in the band to have a spectral index near 2.0, as expected for optically thick blackbody emission. The flux densities are a factor of ≈ 2 above the level expected from the optical photospheres of the stars. We monitored three stars over a period of nearly 2 yr and find flux density variations of less than ±15%. We partially resolved the stellar disk of W Hya and find an average diameter of 0080 ± 0015 and a brightness temperature of 1500 ± 570 K. Our observations suggest that long-period variables have a radio near 2R*, where R* is the stellar radius (defined by line-free regions of the optical spectrum). For the physical conditions expected in the free electrons, obtained predominantly from the ionization of potassium and sodium, provide the dominant opacity through free-free interactions with neutral H and H2. A simple model with a single set of physical parameters can approximate all of our centimeter-wavelength data, as well as providing plausible sizes and brightness temperatures at far-IR wavelengths. At centimeter wavelengths, unity optical depth is achieved at a radius of about 4.8 × 1013 cm, where the density and temperature are ≈ 1.5 × 1012 cm-3 and ≈ 1630 K, respectively. The lack of variability of the centimeter-wavelength flux density for stars like o Ceti, R Leo, and W Hya limits variations of the temperature and/or radius of the photosphere to less than ±150 K and ±4 × 1012 cm. Also, any periodic shocks or disturbances near 2R* probably propagate outward at less than ≈ 5 km s-1 and/or are mostly damped. The photosphere lies just outside of a molecular photosphere, seen optically in strong absorption lines of metallic oxides, and just inside of the SiO maser shell and the dust formation zone. Indeed, the inner boundary of the SiO maser emission region may be determined by continuum opacity in the photosphere. Our study suggests that the density and temperature in the SiO shell are ≈ 5 × 1010 cm-3 and ≈ 1300 K, respectively. Extrapolating our model outward to 1014 cm radius, where significant dust is detected at 10 μm wavelength and H2O masers are found, gives densities 3 × 109 cm-3 and temperatures 1100 K. Based on the sample of stars we observed, it appears that the flux density at frequencies from long-period variables can be modeled with a simple formula. Given the excellent agreement between measured and modeled flux densities, it is possible that distances can be estimated from a flux density measurement with a precision of about 10%. Since the radio-frequency emission from long-period variables has a well-defined spectrum, is very compact, and is relatively constant in time, we suggest these stars can be used to determine the absolute flux density scale for millimeter- and submillimeter-wavelength interferometers.