Asteroseismology and interferometry of the F7V spectroscopic binary $χ$ Draconis A in the TESS CVZ
We present a detailed analysis of the asteroseismic main-sequence benchmark star $χ$ Dra A in the TESS northern CVZ. We aim to derive stellar mass and radius from asteroseismic modelling of individual mode frequencies and test the asteroseismic mass and radius against an independent dynamical mass and interferometric radius measurement. We determined the dynamical mass of $χ$ Dra using 618 radial velocity measurements obtained with the SONG telescope at Tenerife, and 53 relative astrometric measurements. With the PAVO beam combiner at CHARA, we obtained the interferometric radius of $χ$ Dra A. We determined asteroseismic parameters from 16 sectors of 20-sec cadence TESS photometry. We determined $T_{\rm eff}=6277\pm30$ K, $\rm [Fe/H] =-0.51\pm0.03$ dex, and $[α/\rm Fe]=0.08\pm0.03$ dex from the spectroscopic analysis. For the dynamical fit we obtained a mass of $M_{\rm A}=1.028 \pm 0.004$ $\rm M_{\odot}$ for $χ$ Dra A, and $M_{\rm B}=0.735 \pm 0.003$ $\rm M_{\odot}$ for $χ$ Dra B. Combining the derived interferometric angular diameter with dynamical parallax yields an interferometric radius of $R_{\rm A} = 1.159^{+0.029}_{-0.028}$ $\rm R_{\odot}$. In the TESS power spectrum, we identified 38 individual oscillating modes. Using these modes, we modelled the star with nine independent pipelines to test the resulting model mass and radius against our independently calculated mass and radius. All models yielded masses slightly lower than the dynamical mass. Using asteroseismic scaling relations, we found that scaling masses from corrected scaling relations best reproduce the dynamical mass. The combination of spectroscopy, interferometry, and asteroseismology has yielded precise results for the main component of the $χ$ Dra system, making it one of the best-characterised main-sequence solar-like oscillators.