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The Change of the Orbital Periods Across Eruptions and the Ejected Mass For Recurrent Novae CI Aquilae and U Scorpii

I report on the cumulative results from a program started 24 years ago designed to measure the orbital period change of recurrent novae (RNe) across an eruption. The goal is to use the orbital period change to measure the mass ejected during each eruption as the key part of trying to measure whether the RNe white dwarfs are gaining or losing mass over an entire eruption cycle, and hence whether they can be progenitors for Type Ia supernovae. This program has now been completed for two eclipsing RNe; CI Aquilae (CI Aql) across its eruption in 2000 and U Scorpii (U Sco) across its eruption in 1999. For CI Aql, I present 78 eclipse times from 1991-2009 (including four during the tail of the 2000 eruption) plus two eclipses from 1926 and 1935. For U Sco, I present 67 eclipse times, including 46 times during quiescence from 1989-2009, plus 21 eclipse times in the tails of the 1945, 1999, and 2010 eruptions. The eclipse times during the tails of eruptions are systematically and substantially shifted with respect to the ephemerides from the eclipses in quiescence, with this being caused by shifts of the center of light during the eruption. These eclipse times are plotted on an O-C diagram and fitted to models with a steady period change (Pdot) between eruptions (caused by, for example, conservative mass transfer) plus an abrupt period change (DeltaP) at the time of eruption. For CI Aql, the best fit is DeltaP=-3.7^{+9.2}_{-7.3} X 10^{-7}. For U Sco, the best fit is DeltaP=(+43+-69) X 10^{-7} days. These period changes can directly give a dynamical measure of the mass ejected (M_ejecta) during each eruption with negligible sensitivity to the stellar masses and no uncertainty from distances. For CI Aql, the one-sigma upper limit is M_ejecta < 10 X 10^{-7}$ M_sun. For U Sco, I derive M_ejecta=(43+-67) X 10^{-7} M_sun.