The sdB+M Eclipsing System HW Virginis and its Circumbinary Planets

For the very short-period sdB eclipsing binary HW Vir, we present new CCD photometry made from 2000 through 2008. In order to obtain consistency of the binary parameters, our new light curves were analyzed simultaneously with previously published radial-velocity data. The secondary star parameters of $M_2$=0.14 M$_\odot$, $R_2$=0.18 R$_\odot$, and $T_2$=3,084 K are consistent with those of an M6-7 main sequence star. More than 250 times of minimum light, including our 41 timings and spanning more than 24 yrs, were used for a period study. From a detailed analysis of the $O$--$C$ diagram, it emerged that the orbital period of HW Vir has varied as a combination of a downward-opening parabola and two sinusoidal variations, with cycle lengths of $P_3$=15.8 yr and $P_4$=9.1 yr and semi-amplitudes of $K_3$=77 s and $K_4$=23 s, respectively. The continuous period decrease with a rate of $-8.28\times10^{-9}$ d yr$^{-1}$ may be produced by angular momentum loss due to magnetic stellar wind braking but not by gravitational radiation. Of the possible causes of the cyclical components of the period change, apsidal motion and magnetic period modulation can be ruled out. The most reasonable explanation of both cyclical variations is a pair of light-travel-time effects driven by the presence of two substellar companions with projected masses of $M_3 \sin i_3$=19.2 M$\rm_{Jup}$ and $M_4 \sin i_4$=8.5 M$\rm_{Jup}$. The two objects are the first circumbinary planets known to have been formed in a protoplanetary disk as well the first ones discovered by using the eclipse-timing method. The detection implies that planets could be common around binary stars just as are planets around single stars and demonstrates that planetary systems formed in a circumbinary disk can survive over long time scales.