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Discovery of periodic dips in the light curve of GX 13+1: the X-ray orbital ephemeris of the source

The bright low-mass X-ray binary (LMXB) GX 13+1 is one of the most peculiar Galactic binary systems. A periodicity of 24.27 d with a formal statistical error of 0.03 d was observed in its power spectrum density obtained with RXTE All Sky Monitor (ASM) data spanning 14 years. Starting from a recent study, indicating GX 13+1 as a possible dipping source candidate, we systematically searched for periodic dips in the X-ray light curves of GX 13+1 from 1996 up to 2013 using RXTE/ASM, and MAXI data to determine for the first time the X-ray orbital ephemeris of GX 13+1. We searched for a periodic signal in the ASM and MAXI light curves, finding a common periodicity of 24.53 d. We folded the 1.3-5 keV and 5-12.1 keV ASM light curves and the 2-4 and 4-10 keV MAXI light curves at the period of 24.53 d finding a periodic dip. To refine the value of the period we used the timing technique dividing the ASM light curve in eight intervals and the MAXI light curve in two intervals, obtaining four and two dip arrival times from the ASM and MAXI light curves, respectively. We improved the X-ray position of GX 13+1 using a recent Chandra observation. The new X-ray position is discrepant by $\sim 7\arcsec$ from the previous one, while it is compatible with the infrared and radio counterpart positions. We detected an X-ray dip, that is totally covered by the Chandra observation, in the light curve of GX 13+1 and showed, a-posteriori, that it is a periodic dip. We obtained seven dip arrival times from ASM, MAXI, and Chandra light curves. We calculated the delays of the detected dip arrival times with respect to the expected times for a 24.52 d periodicity. Fitting the delays with a linear function we find that the orbital period and the epoch of reference of GX 13+1 are 24.5274(2) days and 50,086.79(3) MJD, respectively.(Abridged)