SDSS J123813.73-033933.0, a cataclysmic variable evolved beyond the period minimum

We present infrared JHK photometry of the cataclysmic variable SDSS J123813.73-033933.0 (SDSS1238)and analyze it along with optical spectroscopy, demonstrating that the binary system is most probably comprised of a massive white dwarf with Teff=12000+/-1000 K and a brown dwarf of spectral type L4. The inferred system parameters suggest that this system may have evolved beyond the orbital period minimum and is a bounce-back system. SDSS1238 stands out among CVs by exhibiting the cyclical variability (brightenings). These are not related to specific orbital phases of the binary system and are fainter than dwarf novae outbursts, that usually occur on longer timescales. This phenomenon has not been observed extensively and, thus, is poor understood. The new time-resolved, multi-longitude photometric observations of SDSS1238 allowed us to observe two consecutive brightenings and to determine their recurrence time. The period analysis of all observed brightenings during 2007 suggests a typical timescale that is close to a period of ~9.3 hours. However, the brightenings modulation is not strictly periodic, possibly maintaining coherence only on timescales of several weeks. The characteristic variability with double orbital frequency that clearly shows up during brightenings is also analyzed. The Doppler mapping of the system shows the permanent presence of a spiral arm pattern in the accretion disk. A simple model is presented to demonstrate that spiral arms in the velocity map appear at the location and phase corresponding to the 2:1 resonance radius and constitute themselves as a double-humped light curves. The long-term and short-term variability of this CV is discussed together with the spiral arm structure of an accretion disk in the context of observational effects taking place in bounce-back systems.