We present medium-resolution VLT/FORS2 spectroscopy of six cataclysmic variables discovered by the Sloan Digital Sky Survey .
We determine orbital periods for SDSS J023322.61+005059.5 ( 96.08 \pm 0.09 min ) , SDSS J091127.36+084140.7 ( 295.74 \pm 0.22 min ) , SDSS J103533.02+055158.3 ( 82.10 \pm 0.09 min ) , and SDSS J121607.03+052013.9 ( most likely 98.82 \pm 0.16 min , but the one-day aliases at 92 min and 107 min are also possible ) using radial velocities measured from their H \alpha and H \beta emission lines .
Three of the four orbital periods measured here are close to the observed 75–80 min minimum period for cataclysmic variables , indicating that the properties of the population of these objects discovered by the SDSS are substantially different to those of the cataclysmic variables found by other means .
Additional photometry of SDSS J023322.61+005059.5 reveals a periodicity of approximately 60 min which we interpret as the spin period of the white dwarf , suggesting that this system is an intermediate polar with a low accretion rate .
SDSS J103533.02+055158.3 has a period right at the observed minimum value , a spectrum dominated by the cool white dwarf primary star and exhibits deep eclipses , so is an excellent candidate for an accurate determination of the parameters of the system .
The spectroscopic orbit of SDSS J121607.03+052013.9 has a velocity amplitude of only 13.8 \pm 1.6 km s ^ { -1 } , implying that this system has an extreme mass ratio .
From several physical constraints we find that this object must contain either a high-mass white dwarf or a brown-dwarf-mass secondary component or both .