A long-term optical and X-ray ephemeris of the polar EK Ursae Majoris
K. Beuermann (1), J. Diese (2), S. Paik (3), A. Ploch (2), J. Zachmann, (2), A.D. Schwope (4), F.V. Hessman ((1) Institut fuer Astrophysik,, Goettingen, Germany, (2) Max-Planck-Gymnasium, Goettingen, Germany, (3), Felix-Klein-Gymnasium, Goeqttingen, Germany

TL;DR
This study provides a precise long-term optical and X-ray ephemeris for the polar EK UMa, showing no significant period change over 17 years and offering insights into its accretion geometry.
Contribution
It presents a combined optical and X-ray analysis to derive a stable ephemeris and constrain period variations in EK UMa, a polar system.
Findings
The orbital period is P=0.0795440225(24) days.
No significant period change over 17 years (Delta P = -0.14+-0.50 ms).
X-ray dips lag optical minima by 9.5+-0.7 degrees, informing accretion geometry.
Abstract
We searched for long-term period changes in the polar EK UMa using new optical data and archival X-ray/EUV data. An optical ephemeris was derived from data taken remotely with the MONET/N telescope and compared with the X-ray ephemeris based on Einstein, Rosat, and EUVE data. A three-parameter fit to the combined data sets yields the epoch, the period, and the phase offset between the optical minima and the X-ray absorption dips. An added quadratic term is insignificant and sets a limit to the period change. The derived linear ephemeris is valid over 30 years and the common optical and X-ray period is P=0.0795440225(24) days. There is no evidence of long-term O-C variations or a period change over the past 17 years Delta P = -0.14+-0.50 ms. We suggest that the observed period is the orbital period and that the system is tightly synchronized. The limit on Delta P and the phase constancy…
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