Activity of Star TOI-1408 and Mass Loss by the Atmospheres of Its Exoplanets

The properties of the TOI-1408 multiplanetary system consisting of hot Jupiter (planet (b), \((1.86 \pm 0.02){\kern 1pt} {{M}_{{{\text{Jup}}}}}\), \((2.4 \pm 0.5){\kern 1pt} {{R}_{{{\text{Jup}}}}}\)) and sub-Neptune (planet (c), \((2.22 \pm 0.06){\kern 1pt} {{R}_{ \oplus }}\), \((7.6 \pm 0.2){\kern 1pt} {{M}_{ \oplus }}\)) orbiting a star of spectral class F have been considered. Measurements of radial velocities have also indicated the existence of an additional celestial body with an orbital period of several thousand days. The TOI-1408 system has made it possible to study the migration processes of hot Jupiter-type planets in cases, where less massive planet (c) is closer to the star than more massive one (b). Based on archival measurements of the TOI-1408 brightness (DASCH project), we have estimated the length of the possible cyclic long-term variability of the object (~10 500 days). The analysis of the brightness variability of TOI-1408 according to the Kamogata Wide-field Survey (KWS) archive has led to the detection of peaks in the power spectrum corresponding to a rotation period of ~7.5 days. The mass loss of the planets atmospheres, which have been established for two values of parameter \(\log R_{{{\text{HK}}}}^{'}\) (\( - 4.94\) and \( - 4.59\)) corresponding to the maxima of the bimodal distribution of this parameter for low and high activity for stars of spectral class F, has been estimated. The mass loss of planet (b) (hot Jupiter) can reach \(2.3 \times {{10}^{{11}}}\) g/s and of the sub-Neptune—planet (c) can reach \(2.7 \times {{10}^{{10}}}\) g/s for the value of \(\log R_{{{\text{HK}}}}^{'} = - 4.59\). The obtained data have been in good agreement with the results for exoplanets of the corresponding types (including for hot Jupiter HD 189733 b and warm Neptune GJ 436 b).