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Spectroscopically resolving the Algol triple system

Algol ($β$ Persei) is the prototypical semi-detached eclipsing binary and a hierarchical triple system. From 2006 to 2010 we obtained 121 high-resolution and high-S/N échelle spectra of this object. Spectral disentangling yields the individual spectra of all three stars, and greatly improved elements both the inner and outer orbits. We find masses of $M_{\rm A} = 3.39\pm0.06$ M$_\odot$, $M_{\rm B} = 0.770\pm0.009$ M$_\odot$ and $M_{\rm C} = 1.58\pm0.09$ M$_\odot$. The disentangled spectra also give the light ratios between the components in the $B$ and $V$ bands. Atmospheric parameters for the three stars are determined, including detailed elemental abundances for Algol A and Algol C. We find the following effective temperatures: $T_{\rm A} = 12\,550\pm120$ K, $T_{\rm B} = 4900\pm300$ K and $T_{\rm C} = 7550\pm250$ K. The projected rotational velocities are $v_{\rm A} \sin i_{\rm A} = 50.8\pm0.8$ km/s, $v_{\rm B} \sin i_{\rm B} = 62\pm2$ km/s and $v_{\rm C} \sin i_{\rm C} = 12.4\pm0.6$ km/s. This is the first measurement of the rotational velocity for Algol B, and confirms that it is synchronous with the orbital motion. The abundance patterns of components A and C are identical to within the measurement errors, and are basically solar. They can be summarised as mean metal abundances: [M/H]$_{\rm A} = -0.03\pm0.08$ and [M/H]$_{\rm C} = 0.04\pm0.09$. A carbon deficiency is confirmed for Algol A, with tentative indications for a slight overabundance of nitrogen. The ratio of their abundances is (C/N)$_{\rm A} = 2.0\pm0.4$, half of the solar value of (C/N)$_{\odot} = 4.0\pm0.7$. The new results derived in this study, including detailed abundances and metallicities, will enable tight constraints on theoretical evolutionary models for this complex system.