Phase-resolved spectroscopy of four AM CVn systems obtained with the William Herschel Telescope and the Gran Telescopio de Canarias ( GTC ) is presented .
SDSS J120841.96+355025.2 was found to have an orbital period of 52.96 \pm 0.40 min and shows the presence of a second bright spot in the accretion disc .
The average spectrum contains strong Mg i and Si i/ii absorption lines most likely originating in the atmosphere of the accreting white dwarf .
SDSS J012940.05+384210.4 has an orbital period of 37.555 \pm 0.003 min .
The average spectrum shows the Stark broadened absorption lines of the DB white dwarf accretor .
The orbital period is close to the previously reported superhump period of 37.9 min .
Combined , this results in a period excess \epsilon =0.0092 \pm 0.0054 and a mass ratio q = 0.031 \pm 0.018 .
SDSS J164228.06+193410.0 displays an orbital period of 54.20 \pm 1.60 min with an alias at 56.35 min .
The average spectrum also shows strong Mg i absorption lines , similar to SDSS J120841.96+355025.2 .
SDSS J152509.57+360054.50 displays an period of 44.32 \pm 0.18 min .
The overall shape of the average spectrum is more indicative of shorter period systems in the 20-35 minute range .
The accretor is still clearly visible in the pressure broadened absorption lines most likely indicating a hot donor star and/or a high mass accretor .
Flux ratios for several helium lines were extracted from the Doppler tomograms for the disc and bright spot region , and compared with single-slab LTE models with variable electron densities and path lengths to estimate the disc and bright spot temperature .
A good agreement between data and the model in three out of four systems was found for the disc region .
All three systems show similar disc temperatures of \sim 10 500 K. In contrast , only weak agreement between observation and models was found for the bright spot region .