Radio Photospheres of Long‐Period Variable Stars

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 radio 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 0 080 ± 0 015 and a brightness temperature of 1500 ± 570 K. Our observations suggest that long-period variables have a "radio photosphere" near 2 R * , where R * is the stellar radius (defined by line-free regions of the optical spectrum). For the physical conditions expected in the radio photosphere, free electrons, obtained predominantly from the ionization of potassium and sodium, provide the dominant opacity through free-free interactions with neutral H and H 2 . 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 × 10 13 cm, where the density and temperature are ≈ 1.5 × 10 12 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 radio photosphere to less than ±150 K and ±4 × 10 12 cm. Also, any periodic shocks or disturbances near 2 R * probably propagate outward at less than ≈ 5 km s -1 and/or are mostly damped. The radio 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 radio photosphere. Our study suggests that the density and temperature in the SiO shell are ≈ 5 × 10 10 cm -3 and ≈ 1300 K, respectively. Extrapolating our model outward to ≳10 14 cm radius, where significant dust is detected at 10 μm wavelength and H 2 O masers are found, gives densities ≲3 × 10 9 cm -3 and temperatures ≲1100 K. Based on the sample of stars we observed, it appears that the flux density at radio 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.