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Far-UV spectroscopy of the planet-hosting star WASP-13: high-energy irradiance, distance, age, planetary mass-loss rate, and circumstellar environment

Several transiting hot Jupiters orbit relatively inactive main-sequence stars. For some of those, the logR'HK activity parameter lies below the basal level (-5.1). Two explanations have been proposed so far: (i) the planet affects the stellar dynamo, (ii) the logR'HK measurements are biased by extrinsic absorption, either by the interstellar medium (ISM) or by material local to the system. We present here Hubble Space Telescope/COS far-UV spectra of WASP-13, which hosts an inflated hot Jupiter and has a measured logR'HK value (-5.26), well below the basal level. From the star's spectral energy distribution we obtain an extinction E(B-V) = 0.045+/-0.025 mag and a distance d = 232+/-8 pc. We detect at >4 sigma lines belonging to three different ionization states of carbon (C1, C2, and C4) and the Si4 doublet at ~3 sigma. Using far-UV spectra of nearby early G-type stars of known age, we derive a C4/C1 flux ratio-age relation, from which we estimate WASP-13's age to be 5.1+/-2.0 Gyr. We rescale the solar irradiance reference spectrum to match the flux of the C4 1548 doublet. By integrating the rescaled solar spectrum, we obtain an XUV flux at 1 AU of 5.4 erg s^-1 cm^-2. We use a detailed model of the planet's upper atmosphere, deriving a mass-loss rate of 1.5x10^11 g s^-1. Despite the low logR'HK value, the star shows a far-UV spectrum typical of middle-aged solar-type stars, pointing toward the presence of significant extrinsic absorption. The analysis of a high-resolution spectrum of the Ca2H&K lines indicates that the ISM absorption could be the origin of the low logR'HK value. Nevertheless, the large uncertainty in the Ca2 ISM abundance does not allow us to firmly exclude the presence of circumstellar gas.