Abstract

We present Very Large Telescope (VLT) and Magellan spectroscopy and New Technology Telescope photometry of nine faint cataclysmic variables (CVs) which were spectroscopically identified by the Sloan Digital Sky Survey (SDSS). We measure orbital periods for five of these from the velocity variations of the cores and wings of their Hα emission lines. Four of the five have orbital periods shorter than the 2–3 h period gap observed in the known population of CVs. SDSS J004335.14−003729.8 has an orbital period of Porb= 82.325 ± 0.088 min; Doppler maps show emission from the accretion disc, bright spot and the irradiated inner face of the secondary star. In its light curve, we find a periodicity which may be attributable to pulsations of the white dwarf. SDSS J163722.21−001957.1 has Porb= 99.75 ± 0.86 min. By combining this new measurement with a published superhump period, we estimate a mass ratio of q≈ 0.16 and infer the physical properties and orbital inclination of the system. For SDSS J164248.52+134751.4, we find Porb= 113.60 ± 1.5 min. The Doppler map of this CV shows an unusual brightness distribution in the accretion disc which would benefit from further observations. SDSS J165837.70+184727.4 had spectroscopic characteristics which were very different between the SDSS spectrum and our own VLT observations, despite only a small change in brightness. We measure Porb= 98.012 ± 0.065 min from its narrow Hα emission line. Finally, SDSS J223843.84+010820.7 has a comparatively longer period of Porb= 194.30 ± 0.16 min. It contains a magnetic white dwarf and, with g= 18.15, is brighter than the other objects studied here. These results continue the trend for the fainter CVs identified by the SDSS to be almost exclusively shorter period objects with low mass transfer rates.

1 INTRODUCTION

Cataclysmic variables (CVs) are interacting binary stars containing a white dwarf primary component in a close orbit with a low-mass secondary star which fills its Roche lobe. In most of these systems, the secondary component is hydrogen rich and transfers material to the white dwarf via an accretion disc. Comprehensive reviews of the properties of CVs have been given by Warner (1995) and Hellier (2001).

The evolution of CVs is thought to be governed primarily by the loss of orbital angular momentum due to gravitational radiation (Paczyński 1967) and magnetic braking (Verbunt & Zwaan 1981; Rappaport, Joss & Webbink 1982). These effects are predicted to cause CVs to evolve towards shorter orbital periods until a minimum value of about 80 min, at which point the secondary stars become degenerate and the CVs evolve back to longer periods (e.g. Patterson 1998).

The distribution of orbital periods of the observed population of CVs has a characteristic ‘period gap’ (Whyte & Eggleton 1980; Knigge 2006) in the interval between 2.2 and 3.2 h. The deficiency in the number of systems in this period range is thought to result from the sudden cessation of magnetic braking due to structural changes in CV secondary stars (Spruit & Ritter 1983). The number of CVs shortwards of this period gap is observed to be roughly equal to the number which is longward of the gap (e.g. Downes et al. 2001; Ritter & Kolb 2003).

Unfortunately, theoretical studies of the population of CVs have consistently predicted that the vast majority of these objects should have short periods (Porb≲ 2 h) due to their relatively longer evolutionary time-scale (de Kool 1992; de Kool & Ritter 1993; Kolb 1993; Kolb & de Kool 1993; Politano 1996; Kolb & Baraffe 1999; Howell, Nelson & Rappaport 2001; Politano 2004; Willems et al. 2005), culminating in a strong ‘spike’ in the population at a minimum period of about 65 min. The remarkable differences between the predicted and observed populations of CVs have not yet been satisfactorily explained, although it is clear that observational selection biases have a lot to answer for.

To understand these selection biases, and to discover what the properties of the intrinsic population of CVs are, we are conducting a research programme to characterize the sample of CVs identified by the Sloan Digital Sky Survey (SDSS1; York et al. 2000). A total of 212 of these objects have been found spectroscopically from an initial selection based on single-epoch photometric colour indices (Szkody et al. 2002,2003,2004,2005,2006,2007). This sample is therefore not biased towards CVs which are variable or strong X-ray emitters, and also has a much wider coverage of colour space than previous large-scale surveys (Green, Schmidt & Liebert 1986; Chen et al. 2001; Aungwerojwit et al. 2006). Results and further discussion of our project to measure the orbital periods of SDSS CVs can be found in Gänsicke et al. (2006), Southworth et al. (2006, hereafter Paper I), Southworth et al. (2007a,b), Southworth, Townsley & Gänsicke (2008), Dillon et al. (2008a) and Littlefair et al. (2006a,b,2007,2008).

In this work, we present time-resolved spectroscopy and photometry of nine CVs, and measure orbital period for five of these. We will abbreviate the names of the targets to SDSS J0043, SDSS J0337, SDSS J1601, SDSS J1637, SDSS J1642, SDSS J1658, SDSS J1659, SDSS J2232 and SDSS J2238. Their full names and ugriz apparent magnitudes are given in Table 1. In Fig. 1, we have plotted their SDSS spectra for reference.

Table 1

Apparent magnitudes of our targets in the SDSS ugriz passbands. gspec are apparent magnitudes we have calculated by convolving the SDSS flux-calibrated spectra with the g passband function. They are obtained at a different epoch to the ugriz magnitudes measured from the imaging observations, but are less reliable as they are affected by ‘slit losses’, and any errors in astrometry or positioning of the spectroscopic fibre entrance.

SDSS name Short name Reference u g r i z gspec 
SDSS J004335.14−003729.8 SDSS J0043 Szkody et al. (2004) 20.18 19.86 19.81 19.97 19.84 19.95 
SDSS J033710.91−065059.4 SDSS J0337 Szkody et al. (2007) 19.64 19.54 19.72 19.97 20.14 23.27 
SDSS J160111.53+091712.6 SDSS J1601 Szkody et al. (2006) 19.96 20.11 20.12 20.22 19.74 20.39 
SDSS J163722.21−001957.1 SDSS J1637 Szkody et al. (2002) 16.83 16.60 16.59 16.75 16.84 20.57 
SDSS J164248.52+134751.4 SDSS J1642 Szkody et al. (2007) 18.48 18.64 18.50 18.42 18.21 18.03 
SDSS J165837.70+184727.4 SDSS J1658 Szkody et al. (2006) 20.51 20.07 20.12 20.09 19.68 19.71 
SDSS J165951.68+192745.6 SDSS J1659 Szkody et al. (2006) 16.84 16.73 16.78 16.86 16.96 17.12 
SDSS J223252.35+140353.0 SDSS J2232 Szkody et al. (2004) 17.74 17.66 17.80 17.88 17.97 23.16 
SDSS J223843.84+010820.7 SDSS J2238 Szkody et al. (2003) 18.29 18.15 18.08 18.18 18.17 18.27 
SDSS name Short name Reference u g r i z gspec 
SDSS J004335.14−003729.8 SDSS J0043 Szkody et al. (2004) 20.18 19.86 19.81 19.97 19.84 19.95 
SDSS J033710.91−065059.4 SDSS J0337 Szkody et al. (2007) 19.64 19.54 19.72 19.97 20.14 23.27 
SDSS J160111.53+091712.6 SDSS J1601 Szkody et al. (2006) 19.96 20.11 20.12 20.22 19.74 20.39 
SDSS J163722.21−001957.1 SDSS J1637 Szkody et al. (2002) 16.83 16.60 16.59 16.75 16.84 20.57 
SDSS J164248.52+134751.4 SDSS J1642 Szkody et al. (2007) 18.48 18.64 18.50 18.42 18.21 18.03 
SDSS J165837.70+184727.4 SDSS J1658 Szkody et al. (2006) 20.51 20.07 20.12 20.09 19.68 19.71 
SDSS J165951.68+192745.6 SDSS J1659 Szkody et al. (2006) 16.84 16.73 16.78 16.86 16.96 17.12 
SDSS J223252.35+140353.0 SDSS J2232 Szkody et al. (2004) 17.74 17.66 17.80 17.88 17.97 23.16 
SDSS J223843.84+010820.7 SDSS J2238 Szkody et al. (2003) 18.29 18.15 18.08 18.18 18.17 18.27 
Figure 1

SDSS spectra of the CVs studied in this work. For this plot, the flux levels have been smoothed with 10-pixel Savitsky–Golay filters. The units of the abscissae are 10−21W m−2nm−1, which correspond to 10−17erg s−1cm−2Å−1.

Figure 1

SDSS spectra of the CVs studied in this work. For this plot, the flux levels have been smoothed with 10-pixel Savitsky–Golay filters. The units of the abscissae are 10−21W m−2nm−1, which correspond to 10−17erg s−1cm−2Å−1.

2 OBSERVATIONS AND DATA REDUCTION

A log of observations is given in Table 2. The reduced data and velocity measurements presented here will be made available at the CDS (http://cdsweb.u-strasbg.fr/) and at http://www.astro.keele.ac.uk/~jkt/.

Table 2

Log of the observations presented in this work. The acquisition magnitudes were measured from the VLT/FORS2 acquisition images and are discussed in Section 2.2. The passbands for the acquisition magnitudes are indicated, where ‘V’ denotes the Johnson V band and ‘Wh’ indicates that no filter was used.

Target Date (UT) Start time (UT) End time (UT) Telescope and instrument Optical element Number of observations Exposure time (s) Mean magnitude 
SDSS J0043 2007 08 16 07:47 10:25 VLT / FORS2 1200R grism 21 400 V= 19.9 
SDSS J0043 2007 08 17 07:13 09:03 VLT / FORS2 1200R grism 14 440 V= 19.8 
SDSS J0043 2005 10 08 05:05 06:49 APO 3.5 m / DIS unfiltered 175 15–20 V= 19.8 
SDSS J0337 2007 08 17 09:20 10:18 VLT / FORS2 1200R grism 600 V= 21.4 
SDSS J1601 2007 08 10 23:25 00:10 NTT / SUSI2 unfiltered 36 60 Wh= 20.1 
SDSS J1637 2007 08 16 01:18 04:06 VLT / FORS2 1200R grism 20 600–400 V= 20.3 
SDSS J1637 2007 08 16 23:28 00:40 VLT / FORS2 1200R grism 480 V= 20.6 
SDSS J1642 2007 08 06 23:38 02:55 NTT / SUSI2 V filter 262 30 V= 19.5 
SDSS J1642 2007 08 07 23:21 04:21 NTT / SUSI2 V filter 414 28 V= 19.6 
SDSS J1642 2007 08 17 00:48 03:41 VLT / FORS2 1200R grism 29 300 V= 18.5 
SDSS J1658 2007 08 15 00:17 03:23 VLT / FORS2 1200R grism 19 480 Wh= 19.5 
SDSS J1658 2007 08 15 23:33 01:01 VLT / FORS2 1200R grism 12 400 V= 20.1 
SDSS J1659 2007 08 11 00:19 02:45 NTT / SUSI2 V filter 166 30–60 V= 17.0 
SDSS J2232 2005 08 11 00:10 05:34 NOT / ALFOSC unfiltered 177 60 Wh= 22.1 
SDSS J2232 2006 07 21 02:03 05:12 NOT / ALFOSC unfiltered 109 60 Wh= 21.8 
SDSS J2232 2007 08 15 03:37 06:10 VLT / FORS2 1200R grism 14 600 V= 21.4 
SDSS J2238 2007 08 14 07:27 09:44 Magellan / IMACS 600 ℓ mm−1 grism 22 300  
SDSS J2238 2007 08 15 07:24 09:51 Magellan / IMACS 600 ℓ mm−1 grism 17 300  
SDSS J2238 2007 08 16 07:39 09:42 Magellan / IMACS 600 ℓ mm−1 grism 19 300  
Target Date (UT) Start time (UT) End time (UT) Telescope and instrument Optical element Number of observations Exposure time (s) Mean magnitude 
SDSS J0043 2007 08 16 07:47 10:25 VLT / FORS2 1200R grism 21 400 V= 19.9 
SDSS J0043 2007 08 17 07:13 09:03 VLT / FORS2 1200R grism 14 440 V= 19.8 
SDSS J0043 2005 10 08 05:05 06:49 APO 3.5 m / DIS unfiltered 175 15–20 V= 19.8 
SDSS J0337 2007 08 17 09:20 10:18 VLT / FORS2 1200R grism 600 V= 21.4 
SDSS J1601 2007 08 10 23:25 00:10 NTT / SUSI2 unfiltered 36 60 Wh= 20.1 
SDSS J1637 2007 08 16 01:18 04:06 VLT / FORS2 1200R grism 20 600–400 V= 20.3 
SDSS J1637 2007 08 16 23:28 00:40 VLT / FORS2 1200R grism 480 V= 20.6 
SDSS J1642 2007 08 06 23:38 02:55 NTT / SUSI2 V filter 262 30 V= 19.5 
SDSS J1642 2007 08 07 23:21 04:21 NTT / SUSI2 V filter 414 28 V= 19.6 
SDSS J1642 2007 08 17 00:48 03:41 VLT / FORS2 1200R grism 29 300 V= 18.5 
SDSS J1658 2007 08 15 00:17 03:23 VLT / FORS2 1200R grism 19 480 Wh= 19.5 
SDSS J1658 2007 08 15 23:33 01:01 VLT / FORS2 1200R grism 12 400 V= 20.1 
SDSS J1659 2007 08 11 00:19 02:45 NTT / SUSI2 V filter 166 30–60 V= 17.0 
SDSS J2232 2005 08 11 00:10 05:34 NOT / ALFOSC unfiltered 177 60 Wh= 22.1 
SDSS J2232 2006 07 21 02:03 05:12 NOT / ALFOSC unfiltered 109 60 Wh= 21.8 
SDSS J2232 2007 08 15 03:37 06:10 VLT / FORS2 1200R grism 14 600 V= 21.4 
SDSS J2238 2007 08 14 07:27 09:44 Magellan / IMACS 600 ℓ mm−1 grism 22 300  
SDSS J2238 2007 08 15 07:24 09:51 Magellan / IMACS 600 ℓ mm−1 grism 17 300  
SDSS J2238 2007 08 16 07:39 09:42 Magellan / IMACS 600 ℓ mm−1 grism 19 300  

2.1 VLT spectroscopy

Spectroscopic observations were obtained in 2007 August using the FORS2 spectrograph (Appenzeller et al. 1998) and Very Large Telescope (VLT) at European Southern Obseratory (ESO) Paranal, Chile. The 1200R grism was used for all observations, giving a wavelength interval of 5870–7370 Å with a reciprocal dispersion of 0.73 Å pixel−1. From measurements of the full widths at half-maximum (FWHMs) of arc-lamp and night-sky spectral emission lines, we estimate a resolution of 1.6 Å at Hα.

The data were reduced using optimal extraction (Horne 1986) as implemented in the pamela2 code (Marsh 1989), and the starlink3 packages figaro and kappa.

The wavelength calibration of the spectra was obtained using one arc spectrum per night, taken during daytime as a part of the standard calibration routines for FORS2. As, in Paper I, we have found that flexure of the spectrograph can cause night-time spectra to shift by up to 42 km s−1 (1.2 pixel) depending on elevation. We have removed this trend from each spectrum by measuring the position of the O i night sky emission line at 6300.304 Å (Osterbrock et al. 1996). Offsets calculated using other lines (e.g. O i 6363.78 Å) always agree to within 0.1 pixel.

The VLT spectra cover the Hα and He i 6678 and 7065 Å lines. The average continuum-normalized Hα profile for each object is plotted in Fig. 2.

Figure 2

The averaged Hα emission-line profiles of the seven CVs for which we present spectroscopy. The spectra have had their continuum level normalized to unity. The orbital motion was removed from the spectra of SDSS J1658 before its mean spectrum was constructed.

Figure 2

The averaged Hα emission-line profiles of the seven CVs for which we present spectroscopy. The spectra have had their continuum level normalized to unity. The orbital motion was removed from the spectra of SDSS J1658 before its mean spectrum was constructed.

2.2 VLT photometry

The observing procedure of FORS2 included obtaining target acquisition images. Exposure times were generally 20 s and the observations used either Johnson V or were unfiltered. We have extracted differential photometry from these images using the starlink package gaia, taking special care to select comparison stars from the SDSS data base with colours as close to our target CVs as possible in order to minimize colour effects. The V-band apparent magnitudes of the comparison stars were calculated from the g and r magnitudes using the transformations provided by Jester et al. (2005).

2.3 Magellan spectroscopy

Time-resolved spectroscopy of SDSS J2238 was obtained in 2007 August using the Inamori-Magellan Areal Camera and Spectrograph (IMACS; Bigelow & Dressler 2003) on the 6.5-m Magellan Baade Telescope at Las Campanas Observatory (Table 2). IMACS was employed in long-camera mode, using a 600-line mm−1 grating centred at 5550 Å. This instrumental setup yielded a reciprocal dispersion of 0.76 Å pixel−1 in the spectral interval 3920–7100 Å. The spectra were obtained dispersed along the short axis of four of the eight SITe CCDs in the IMACS mosaic detector. On August 14, most spectra were obtained with a 0.7-arcsec slit width which yielded a spectral resolution of 1.7 pixel (1.3 Å). The other data were obtained with a 1.2-arcsec slit width that provided a spectral resolution of 3.5 pixel (2.7 Å). Weather conditions during were generally good, with seeing ranging from 0.7 to 1.2-arcsec FWHM.

The IMACS frames were bias and flat-field corrected with standard iraf routines. The spectra were extracted from each CCD frame with the irafkpnoslit package. The wavelength calibration was derived from cubic spline fits to HeNeAr lamp spectra bracketing the target spectra. The root mean square deviation of the fits was always less than 0.05 Å.

2.4 NTT photometry

SDSS J1601, SDSS J1642 and SDSS J1659 were observed using the New Technology Telescope (NTT) at ESO La Silla, Chile. Time-series imaging photometry was obtained using the SUSI2 high-resolution imager (D'Odorico et al. 1998). The observing run was affected by cloud, wind, snow and ice. For SDSS J1642 and SDSS J1659, we used a Johnson V filter. For SDSS J1601, we obtained unfiltered photometry and took care to avoid regions of the CCD where fringing was strong. The CCD was binned by factors of 3 in both directions, giving a spatial resolution of 0.24 arcsec pixel−1.

Debiasing and flat-fielding of the raw images was performed with the starlink software packages convert and kappa. Optimal and aperture differential photometry (Naylor 1998) was measured from the reduced images with the multiphotom script (Southworth, Maxted & Smalley 2004a), which uses the autophotom package (Eaton, Draper & Allen 1999) to obtain time-series photometry. Differential magnitudes were converted into apparent mangitudes in way described in Section 2.2.

2.5 NOT photometry

Light curves of SDSS J2232 were obtained in 2005 August and 2006 July using the Nordic Optical Telescope (NOT) and the Andalucía Faint Object Spectrograph and Camera (ALFOSC) imaging spectrograph. The observations were unfiltered, windowed, and binned by a factor of 2 in both directions. The detector was an EEV 2 × 4k pixel CCD with an unbinned plate scale of 0.19 arcsec pixel−1.

These data were reduced using the pipeline described by Gänsicke et al. (2004), which performs bias and flat-field corrections within midas4 and uses the SExtractor package (Bertin & Arnouts 1996) to perform aperture photometry for all objects in the field of view. Differential magnitudes were converted into apparent magnitudes in the same way as for our NTT and VLT photometry.

2.6 APO photometry

A light curve of SDSS J0043 was observed on 2005 October 8 using the 3.5-m telescope at Apache Point Observatory (APO) and dual imaging spectrograph (DIS) in imaging mode. With this instrument, the blue and red portions of the beam are split by a dichroic at 5550 Å. We present here the blue-arm photometry, which is unfiltered but sensitive to light in the wavelength interval 3500–5550 Å. The CCD had a plate scale of 0.4 Å pixel−1, and windowing was used to decrease the readout time. We used a standard iraf reduction to extract sky-subtracted light curves from the CCD frames using weighted circular aperture photometry (O'Donoghue et al. 2000).

3 DATA ANALYSIS

3.1 Radial-velocity measurement

We measured radial velocities (RVs) from emission lines in the spectra of our targets5 by cross-correlation with single and double Gaussian functions (Schneider & Young 1980; Shafter 1983), as implemented in molly. In each case, we tried a range of different widths and separations for the Gaussians in order to verify the consistency of our results (see Paper I for further details).

3.2 Orbital period measurement

The RVs and light curves for each CV were searched for periods using periodograms computed by the Scargle (1982) method, analysis of variance (AoV; Schwarzenberg-Czerny 1989) and orthogonal polynomials (ORT; Schwarzenberg-Czerny 1996), as implemented within the tsa6 context in midas. In general, two Fourier terms were used for ORT, which is appropriate for the relatively simple variation exhibited by these objects.

To find the final values of the orbital periods, and to investigate the aliases in the periodograms, we fitted circular spectroscopic orbits (sine curves) to the data using the sbop7 program, which we have previously found to give reliable error estimates (Southworth et al. 2005). The parameters of the final spectroscopic orbits are given in Table 3, and grey-scale plots of the trailed spectra are shown in Fig. 3.

Table 3

Circular spectroscopic orbits found using sbop. Phase zero corresponds to the blue-to-red crossing point of the RVs; because we are measuring emission lines from the accretion disc, this usually has a phase offset with respect to inferior conjunction of the white dwarf (see Section 4.5).

Target Orbital period (day) Reference time (HJD) Velocity amplitude (km s−1Systemic velocity (km s−1σrms (km s−1
SDSS J0043 0.057 1702 ± 0.000 061 2454 328.871 40 ± 0.000 71 50.0 ± 2.8 13.1 ± 2.0 11.8 
SDSS J1637 0.067 391 ± 0.000 13 2454 326.6720 ± 0.0043 24.4 ± 1.6 −9.1 ± 1.2 6.0 
SDSS J1642 0.078 89 ± 0.0011 2454 329.552 38 ± 0.000 74 105.9 ± 2.4 −55.1 ± 2.4 12.7 
SDSS J1658 0.068 0638 ± 0.000 045 2454 327.547 03 ± 0.000 37 125.3 ± 3.5 −41.5 ± 2.4 13.5 
SDSS J2238 0.134 932 ± 0.000 11 2454 326.8701 ± 0.0013 170.7 ± 5.1 −23.0 ± 4.0 27.3 
Target Orbital period (day) Reference time (HJD) Velocity amplitude (km s−1Systemic velocity (km s−1σrms (km s−1
SDSS J0043 0.057 1702 ± 0.000 061 2454 328.871 40 ± 0.000 71 50.0 ± 2.8 13.1 ± 2.0 11.8 
SDSS J1637 0.067 391 ± 0.000 13 2454 326.6720 ± 0.0043 24.4 ± 1.6 −9.1 ± 1.2 6.0 
SDSS J1642 0.078 89 ± 0.0011 2454 329.552 38 ± 0.000 74 105.9 ± 2.4 −55.1 ± 2.4 12.7 
SDSS J1658 0.068 0638 ± 0.000 045 2454 327.547 03 ± 0.000 37 125.3 ± 3.5 −41.5 ± 2.4 13.5 
SDSS J2238 0.134 932 ± 0.000 11 2454 326.8701 ± 0.0013 170.7 ± 5.1 −23.0 ± 4.0 27.3 
Figure 3

Grey-scale plots of the continuum-normalized and phase-binned trailed spectra of the five CVs for which we obtained orbital periods. Darker shading indicates stronger emission. The upper plots show the Hα lines. The lower plots show the He i 6678 Å lines, with the same velocity scale but different intensity scale. The He i spectra have been smoothed with a Savitsky–Golay filter for display purposes.

Figure 3

Grey-scale plots of the continuum-normalized and phase-binned trailed spectra of the five CVs for which we obtained orbital periods. Darker shading indicates stronger emission. The upper plots show the Hα lines. The lower plots show the He i 6678 Å lines, with the same velocity scale but different intensity scale. The He i spectra have been smoothed with a Savitsky–Golay filter for display purposes.

In some cases, to assess the likelihood of the point of highest power corresponding to the actual orbital period we have performed bootstrapping simulations (see Paper I) by randomly resampling the data with replacement and calculating a new periodogram a total of 1000 times (Press et al. 1992). The fraction of periodograms in which the highest peak fell close to a particular alias can be interpreted as the likelihood of that alias being correct. However, in these cases we expect the resulting probabilities for the correct peak to be quite conservative (i.e. too low) for two reasons. First, because the simulated data sets necessarily contain fewer unique epochs than the original data some temporal definition is sacrificed. The bootstrapping periodograms are often clearly inferior to those calculated from the actual data, confirming this picture. Secondly, when picking the best alias interactively we use more information than just the periodogram (including the shape of the phased radial RV curve).

At the suggestion of the referee we have also performed Monte Carlo simulations, using the same approach as in Southworth, Maxted & Smalley (2004b) and Southworth et al. (2004c). These have the advantage that they do not suffer from a loss of time information, but the drawback that a sine curve is assumed to be a good representation of the data. This is not always the case for CVs, which often have substantial non-Keplerian kinematical effects. We find, as expected, that Monte Carlo simulations generally give a higher significance level (by a factor of 2 in percentage terms) to the highest peak in a periodogram.

4 RESULTS FOR EACH SYSTEM

4.1 SDSS J004335.14−003729.8

SDSS J0043 was found to be a CV by Szkody et al. (2004) from an SDSS spectrum which shows a blue continuum with narrow Balmer emission lines. There are very broad Balmer absorption lines attributable to the white dwarf component of the system, but no identifiable features arising from the secondary star. Szkody et al. (2004) obtained nine low-resolution spectra of SDSS J0043 over 2.7 h using the APO 3.5-m telescope and Double Beam Spectrograph. RVs from the Hα and Hβ emission lines yielded orbital periods of about 1.5 and 1.2 h, respectively.

We obtained a total of 35 VLT spectra of SDSS J0043 (21 on one night and 14 on the next night). The Hα line is relatively narrow (about 1000 km s−1) but is clearly double peaked and variable (Fig. 2). RV measurements consistently give orbital periods close to 82 min, and the best results are found using a single Gaussian of width 1500 km s−1. Data from the first night alone give Porb= 82.4 ± 2.4 min. Including the spectra from the second night too gives Porb= 82.325 ± 0.088 min. The adjacent 1-d aliases at 77.75 and 87.49 min differ from the first-night period by 2σ, so are unlikely to be correct but cannot be ruled out. Bootstrapping simulations (which we expect to be conservative) give a probability of 75 per cent that we have identified the orbital period correctly, and respectively 6 and 19 per cent that the peaks at 77.75 and 87.49 min are actually the orbital period. Monte Carlo simulations give a probability of 89 per cent for this period, and probabilities of 2 and 9 per cent for the other peaks. The parameters of the final spectroscopic orbit are given in Table 3 and the orbit and Scargle periodogram are plotted in Fig. 4.

Figure 4

Upper panel: Scargle periodogram of the RVs of SDSS J0043 measured using a single Gaussian with width 1500 km s−1. The measured period and uncertainty from the data of the first night only are indicated with an error bar at the top of the plot. Lower panel: measured RVs (filled circles) compared to the best-fitting spectroscopic orbit (solid line).

Figure 4

Upper panel: Scargle periodogram of the RVs of SDSS J0043 measured using a single Gaussian with width 1500 km s−1. The measured period and uncertainty from the data of the first night only are indicated with an error bar at the top of the plot. Lower panel: measured RVs (filled circles) compared to the best-fitting spectroscopic orbit (solid line).

A diagram of the phase-binned trailed spectra of SDSS J0043 shows that the relative strengths of the double peaks is variable (Fig. 3) and that there is emission in the form of an S-wave from the bright spot on the edge of the accretion disc (Smak 1985). The He i 6678 Å emission line is narrow and single peaked (Fig. 3) and has the same phasing as the emission from the bright spot in Hα.

4.1.1 Photometry of SDSS J0043: does it contain a pulsating white dwarf?

Fig. 5 shows the light curve we have obtained of SDSS J0043. A periodogram of these data shows a peak at a frequency near to 400 cycle d−1. A fit to this peak results in a period of 207 ± 1 s and an amplitude of 17 ± 5 mmag. This period is within the range of values typically exhibited by ZZ Ceti stars (pulsating white dwarfs), but the amplitude is large for this type of star (Winget 1998; Mukadam et al. 2004). These observations therefore suggest that the white dwarf in SDSS J0043 is a ZZ Ceti star. More extensive data are needed for confirmation.

Figure 5

Upper panel: light curve of SDSS J0043 given as fractional change in intensity. Lower panels: amplitude spectrum of the light curve (left-hand side) and the window function (right-hand side).

Figure 5

Upper panel: light curve of SDSS J0043 given as fractional change in intensity. Lower panels: amplitude spectrum of the light curve (left-hand side) and the window function (right-hand side).

4.1.2 Doppler tomography of SDSS J0043

The complexity of the Hα emission line observed for SDSS J0043 prompted us to decompose the emission into velocity space using Doppler tomography. A Doppler map of this line was computed using the maximum entropy method (Marsh & Horne 1988) and is shown in Fig. 6. The χ2 value for the Doppler map was chosen to be marginally larger than the value for which noise features start to be visible. SDSS J0043 is not eclipsing, so the exact orientation of the map is not known. The velocity modulation of emission lines from the accretion discs of CVs are habitually offset in phase from the true motion of the white dwarf (e.g. Stover 1981; Steeghs et al. 2007). We therefore adopted the spectroscopic orbit and experimented with phase offsets of 0.10–0.25, a range which covers the values found in most studies of eclipsing CVs. The best-fitting calculated spectra and residuals are shown in Fig. 7.

Figure 6

Doppler map of the Hα emission line from SDSS J0043. Strong emission is coloured red and weak to no emission is blue. The Roche lobe of the mass donor is indicated by a solid curve, and the centre of mass of the system and individual stars are shown with crosses. The dots indicate the velocity of the accretion stream and the Keplerian velocity of the disc along the path of the stream. They are positioned at every 0.01RRL, decreasing from RRL= 1.0 at the mass donor, where RRL is the radius of the Roche lobe of the white dwarf.

Figure 6

Doppler map of the Hα emission line from SDSS J0043. Strong emission is coloured red and weak to no emission is blue. The Roche lobe of the mass donor is indicated by a solid curve, and the centre of mass of the system and individual stars are shown with crosses. The dots indicate the velocity of the accretion stream and the Keplerian velocity of the disc along the path of the stream. They are positioned at every 0.01RRL, decreasing from RRL= 1.0 at the mass donor, where RRL is the radius of the Roche lobe of the white dwarf.

Figure 7

Comparison between the 35 observed spectra (left-hand panel) and the best-fitting representation for the Doppler map (centre panel). The residuals (right-hand side) are shown in the right-hand panel.

Figure 7

Comparison between the 35 observed spectra (left-hand panel) and the best-fitting representation for the Doppler map (centre panel). The residuals (right-hand side) are shown in the right-hand panel.

The Doppler map in Fig. 6 shows a circular emission feature at large velocities which comes from the accretion disc of SDSS J0043. There is no emission at low velocities which could be attributed to the white dwarf. However, there is an emission peak at (VX, VY) = (100, 0) which may arise from the irradiated inner face of the secondary star. We have overplotted several features on the Doppler map to illustrate this interpretation. The Roche lobe of the secondary is shown with a solid line, the centres of mass of the system and of the two stars are shown by crosses, and the velocity of the accretion stream and the Keplerian velocity of the accretion disc are indicated by dots with a constant spacing in position. We have adopted KWD= 50 km s−1 for the white dwarf velocity amplitude (Table 3). To position the inner Lagrangian point of the secondary on the emission peak, we used a phase offset of 0.21 (corresponding to a clockwise rotation of the map of 76°) and a secondary star velocity amplitude of K2= 200 km s−1. This interpretation leads to a mass ratio of forumla, which is larger than expected and unlikely to be real. We discuss this further below.

The accretion disc has two regions of enhanced emission in the Doppler map. The one at (VX, VY) = (−350, 100) is in the path of the accretion stream from the secondary star's surface at the inner Lagrangian point, supporting our interpretation of the map. Doppler maps of helium emission can be useful indicators of the velocity of this bright spot, so a map of the He i 6678 Å emission was constructed (not shown) using the same procedure as for the Hα map. This displays only one significant feature: a spot of emission centred on roughly (VX, VY) = (−250, 150) which confirms that this emission region is arising from the bright spot in SDSS J0043.

The second region of enhanced emission from the accretion disc, at (VX, VY) = (−100, −350), is not a typical feature of Doppler maps of CV emission lines. This has no immediate explanation in the accepted picture of the structure of short-period CVs, but has previously been seen in some AM CVn system (e.g. Roelofs et al. 2006). A second oddity for this system is that the placement of the inner emission feature on the substellar point of the secondary star required K2= 200 km s−1, which with KWD= 50 km s−1 results in q= 0.25, much larger than the expected value of q∼ 0.1 for a CV with Porb= 82 min (Knigge 2006). The latter difficulty could be explained by the former: the region of enhanced emission at (VX, VY) = (−100, 350) will distort the Hα profiles and thus the velocities measured from them. The spectroscopic orbit measured above is therefore unlikely to accurately represent the motion of the white dwarf. This caveat is supported by the phase difference of 0.21 between the spectroscopic orbit we measured from the Hα emission and the velocity variation of the irradiated face of the secondary star, which in our experience is on the large side for short-period CVs. If KWD were only 25 km s−1 then the mass ratio would become roughly q= 0.12, which is a reasonable value for this system. An alternative explanation is that the degenerate component has a low mass of MWD∼ 0.4 M, which would make it a helium-core white dwarf.

4.2 SDSS J033710.91−065059.4

A spectrum of SDSS J0337 was presented by Szkody et al. (2007) which identified it as a CV with narrow Balmer emission lines. The apparent magnitude of SDSS J0337 was much brighter when it was observed during the SDSS imaging observations (g= 19.54) than when the SDSS spectrum was subsequently acquired (gspec= 23.3). This is probably due to the system being in a higher state during the imaging observations, an explanation which is supported by the brightness of SDSS J0337 in our acquisition image (V≈ 21.4) being midway between the two SDSS magnitudes.

SDSS J0337 was the last object studied during our VLT observing run, and there was only time to obtain seven spectra over 1 h. These show a sharp Hα emission line (Fig. 2) with a FWHM of only about 500 km s−1, with weaker narrow He i emission lines at 5876, 6678 and 7065 Å. We cannot detect any RV motion in the Hα line, to an upper limit of 15 km s−1. The narrow emission lines and lack of observable RV variation are consistent with a low orbital inclination for the SDSS J0337 system. A plot of its RVs, measured using a single Gaussian of width 600 km s−1, is shown in Fig. 8. Obtaining the orbital period of this object may take a substantial amount of telescope time.

Figure 8

RVs measured for SDSS J0337 by cross-correlation against a single Gaussian function with FWHM 600 km s−1.

Figure 8

RVs measured for SDSS J0337 by cross-correlation against a single Gaussian function with FWHM 600 km s−1.

4.3 SDSS J160111.53+091712.6

SDSS J1601 was discovered to be a CV by Szkody et al. (2006) and has a spectrum characterized by strong Balmer and weak He i emission lines which are slightly double peaked (Fig. 1). We obtained 45 min of NTT unfiltered photometry, which shows a variation of amplitude about 0.2–0.3 mag (Fig. 9). The mean magnitude is consistent with the SDSS imaging and spectroscopic values. The variation is suggestive of a sinusoidal variation with a period similar to the duration of the observations. Further photometry of SDSS J1601 has a good chance of yielding a measurement of the orbital period of this binary.

Figure 9

NTT unfiltered photometry of SDSS J1601. The magnitudes are differential with respect to a comparison star and have been offset by the r magnitude of the comparison star. Differential magnitudes for the comparison minus check stars are shown offset by +21.3 mag.

Figure 9

NTT unfiltered photometry of SDSS J1601. The magnitudes are differential with respect to a comparison star and have been offset by the r magnitude of the comparison star. Differential magnitudes for the comparison minus check stars are shown offset by +21.3 mag.

4.4 SDSS J163722.21−001957.1

SDSS J1637 is a faint CV (V≈ 20.5) which was in a high state when observed by the SDSS imaging survey (g= 16.60). The flux level of its SDSS spectrum (Szkody et al. 2002) (gspec= 20.6) is similar to its apparent magnitude in our VLT acquisition observations (V= 20.3 and 20.6). Szkody et al. (2002) observed the system several times (the exact number is not given) and found it at 20th magnitude each time. A superoutburst of SDSS J1637 was observed by G. Bolt8 with a mean magnitude of V≈ 15.5 on the night of 2004 March 28. A superhump period of 0.06927 ± 0.0006 d (99.75 ± 0.86 min) was measured by G. Bolt from CCD photometry.9

We obtained 28 VLT spectra of SDSS J1637 over two nights, 20 of which were taken over 3 h on the first night. These show a strong Hα emission line with FWHM of only about 800 km s−1, and much weaker He i emission at 6678 and 7065 Å. RV measurements with both single and double Gaussians of various widths are in good agreement with each other, and formally the best results are obtained using a single Gaussian of FWHM 500 km s−1. RV measurements from the first night yield a period of 98.2 ± 2.1 min. Adding in the second night gives a best period of 97.0 min with 1-d aliases at 90.2 and 104.9 min. Using the measurements from the first night to select the best alias gives an orbital period of 97.04 ± 0.19 min (Fig. 10). Bootstrapping simulations give a (conservative) probability of 80 per cent that the orbital period refers to the 97-min peak in the periodogram, and a 19 per cent probability that the 105-min alias is actually the correct period. Monte Carlo simulations are more confident, yielding an 88 per cent probability for the 97-min peak and a 10 per cent probability for the 105-min alias. The 97-min period receives further support from the observed superhump period for SDSS J1637, so can be unambiguously assigned to the orbital period of the system.

Figure 10

Upper panel: Scargle periodogram of the RVs of SDSS J1637 measured using a single Gaussian with width 500 km s−1. The measured period and uncertainty from data from the first night only are indicated with a thick line. Lower panel: measured RVs (filled circles) compared to the best-fitting spectroscopic orbit (solid line).

Figure 10

Upper panel: Scargle periodogram of the RVs of SDSS J1637 measured using a single Gaussian with width 500 km s−1. The measured period and uncertainty from data from the first night only are indicated with a thick line. Lower panel: measured RVs (filled circles) compared to the best-fitting spectroscopic orbit (solid line).

4.4.1 The physical properties of SDSS J1637

There is strong evidence that the superhumps observed in CVs during superoutburst arise from the precession of an elliptical accretion disc (Vogt 1982; Whitehurst 1988), where the superhump period is the beat period between the orbital and precession periods. The ratio of the orbital and superhump periods is observed to depend on mass ratio in CVs (Patterson 1998), allowing the physical properties of SDSS J1637 to be estimated.

From measurements of the orbital and superhump periods of SDSS J1637, we find a superhump period excess (Patterson 1998) of ε(q) = 0.028 ± 0.009. Using the calibration presented by Patterson (1998), we obtain from this q= 0.167. The updated calibration given by Knigge (2006) results in q= 0.161 ± 0.037, which is in agreement (but remember that the different calibrations have many objects in common). Estimating a white dwarf mass of MWD= 0.8 M (Smith & Dhillon 1998; Littlefair et al. 2008) results in a secondary star mass of M2= 0.13 M, in agreement with the properties of the semi-empirical CV secondary star sequence presented by Knigge (2006).

The measured spectroscopic orbit for SDSS J1637 has a low velocity amplitude of only 24.4 ± 1.6 km s−1 (Table 3). The phase-binned and trailed Hα and He i 6678 Å spectra show no large variation with orbital phase (Fig. 3). SDSS J1637 has the largest Hα and He i emission line equivalent widths of all of the objects we have studied with the VLT, which points to a very weak continuum. The Hα emission line is strong, narrow and single peaked. These results suggest that the SDSS J1637 binary system has a relatively low orbital inclination when observed from Earth. If the masses of the white dwarf and secondary star are 0.8 and 0.13 M (see above), the velocity amplitude we have measured implies an orbital inclination of roughly 40°.

4.5 SDSS J164248.52+134751.4

SDSS J1642 was discovered to be a CV by Szkody et al. (2007) and has double-peaked Balmer and He i emission lines. Weak emission at He ii 4686 Å is also visible in the SDSS spectrum. Szkody et al. (2007) presented seven low-resolution APO 3.5-m telescope spectra taken over an 80-min period and estimated an orbital period (70 ± 7 min, which is close to the duration of the observations) from RV measurements of the Hα and Hβ lines.

We obtained 8 h of V-filter photometry of SDSS J1642 over two nights in 2007 August using the NTT and SUSI2 imager. Exposure times of 30 s were used, giving an observing cadence of 43 s. This object is quite variable in brightness: it was at magnitude g= 18.64 in the SDSS imaging data, gspec= 18.0 during its SDSS spectrum, averaging V= 19.5 on the night of 2007 August 6, and during the next night increased from V= 19.8 to 19.3 over 5 h. Its apparent magnitude on our VLT acquisition image on the night of 2007 August 17 was V= 18.5.

The light curves from the two NTT nights are shown in Fig. 11. Periodic variation is seen during both nights, as well as a steady increase in brightness over the second night and quite a lot of flickering (Bruch 1992,2000). Scargle periodograms show a small forest of peaks in the region between zero and 15 cycles d−1 (Fig. 11, panel 3) and it is not clear for these data if any of the peaks relates to the orbital period.

Figure 11

NTT V-filter photometry of SDSS J1642. The upper two panels show the light curves from the individual nights as well as differential photometry between the two comparison stars used (offset to appear in the plot). The third panel shows the Scargle periodogram of the combined data from the two nights, and the spectroscopic orbital period value is indicated at the top of the plot. The bottom panel shows the data phased with the photometric period of 110.6 min (grey dots) and combined into 25 phase bins (black filled circles). In most cases, the error bars are smaller than the points.

Figure 11

NTT V-filter photometry of SDSS J1642. The upper two panels show the light curves from the individual nights as well as differential photometry between the two comparison stars used (offset to appear in the plot). The third panel shows the Scargle periodogram of the combined data from the two nights, and the spectroscopic orbital period value is indicated at the top of the plot. The bottom panel shows the data phased with the photometric period of 110.6 min (grey dots) and combined into 25 phase bins (black filled circles). In most cases, the error bars are smaller than the points.

We observed SDSS J1642 for 3 h with VLT/FORS2 on the night of 2007 August 17, obtaining 29 spectra with exposure times of 300 s. The Hα emission line is strong and has double peaks separated by 750 km s−1 (measured from the average spectrum). The He i 6678 Å line is weaker and its double peaks have a greater separation of 1220 km s−1. The best RV measurements were obtained using the double Gaussian method with FWHMs 300 km s−1 and separation 2100 km s−1, giving an orbital period of Porb= 113.6 ± 1.5 min (Table 3).

The RV curve is not sinusoidal (Fig. 12) and formally the best orbital fit has an eccentricity of e= 0.09 ± 0.03 (giving σrms= 11.2 km s−1 compared to σrms= 12.7 km s−1 for a circular orbit) and an orbital period of 113.4 min. It is difficult to find a reason for an interacting close binary star to have an eccentric orbit, and we do not believe that this is the case for SDSS J1642. Many CVs have emission-line RV variations which do not match the motion of the white dwarf component (Stover 1981; Steeghs et al. 2007), and an apparently significant non-zero orbital eccentricity may result from the same distortion mechanisms. We therefore adopt the orbital period from the circular RV orbit, which in this case is in excellent agreement with the period from the eccentric-orbit alternative. The spectra have been phase binned with this period and shown as a trailed grey-scale plot in Fig. 3. The emission shows clear double peaks at both Hα and He i 6678 Å.

Figure 12

Upper panel: Scargle periodogram of the RV of SDSS J1642 measured using a double Gaussian with width 300 km s−1 and separation 2100 km s−1. Lower panel: measured RVs (filled circles) compared to the best-fitting spectroscopic orbit (solid line).

Figure 12

Upper panel: Scargle periodogram of the RV of SDSS J1642 measured using a double Gaussian with width 300 km s−1 and separation 2100 km s−1. Lower panel: measured RVs (filled circles) compared to the best-fitting spectroscopic orbit (solid line).

Using the orbital period we measured from the VLT spectra, we can now select the peak(s) in the light curve periodogram which may correspond to this value. The two highest peaks are at periods of 110.6 and 119.7 min (Fig. 11), which agree with the spectroscopic period to within 2σ and 4σ, respectively. The former of these has a period of 110.60 ± 0.16 min. This might represent the orbital period of the system, but the data in hand are insufficient to be sure. We therefore adopt the spectroscopic value, Porb= 113.6 ± 1.5 min, as the orbital period of SDSS J1642.

4.5.1 Doppler tomography of SDSS J1642

The trailed spectra for SDSS J1642 (Fig. 3) show that the He i 6678 Å emission line appears to be wider than the Hα line. We have therefore calculated Doppler maps for SDSS J1642, in the same way as for SDSS J0043 (Section 4.1.2), to investigate this further. The maps are plotted in Fig. 13 and indeed show that the accretion disc seems to span a wider range of velocities in He i 6678 and 7065 Å than for Hα. These higher velocities imply that the helium emission comes from a physically smaller part of the disc, specifically the hotter annuli closer to the white dwarf surface.

Figure 13

Doppler maps of the Hα (left-hand panel), He i 6678 Å (centre panel) and He i 7065 Å (right-hand panel) emission lines from SDSS J1642. The symbols are overplotted in the same way as for Fig. 6.

Figure 13

Doppler maps of the Hα (left-hand panel), He i 6678 Å (centre panel) and He i 7065 Å (right-hand panel) emission lines from SDSS J1642. The symbols are overplotted in the same way as for Fig. 6.

A second feature of the Hα Doppler map (but not the He i maps) is an inner emission feature that, by analogy with SDSS J0043 and many other CVs, can be attributed to the surface of the secondary star. The interpretations of the maps in Fig. 13 assume K2= 350 km s−1 and a phase offset of 0.15. In this interpretation, the lower velocities of the accretion disc in the Hα map overlap that of the inner emission feature, which violates Kepler's third law. The disparity between the Hα and He i Dopper maps, and the apparent violation of Kepler's third law, can both be explained by the breakdown of the assumption that all emitting material is optically thin. If the accretion disc is optically thin to He i emission but partially optically thick for Hα, it is quite possible that the detected Hα emission is biased towards lower velocities.

The Hα map also shows a region of strong emission coming from the accretion disc, on the side opposite to the bright spot and reminiscent of the Doppler maps of SDSS J0043 (Section 4.1). Our spectroscopic observations only cover 1.5 orbital periods of this system, and the region of strong emission could be caused by brightness variations which change between different orbits (which is not taken into account when calculating the Doppler maps). Additional observations are needed to further investigate the unusual characteristics of SDSS J1642.

4.6 SDSS J165837.70+184727.4

SDSS J1658 was discovered to be a CV by Szkody et al. (2006) and its SDSS spectrum shows the strong Balmer emission and weaker He i emission lines typical of short-period CVs. The Balmer emission is single peaked and the He i emission is weakly double peaked.

We obtained 31 VLT spectra of SDSS J1658 over two consecutive nights in 2007 August. At the times of the SDSS imaging observations and our spectroscopy, the system had an apparent g or V magnitude of ∼20. However, the spectroscopic characteristics of SDSS J1658 are very different in our observations compared to the SDSS spectrum (where it was at magnitude gspec= 19.7). Fig. 14 shows that the emission lines in the SDSS spectrum are remarkably strong and broad (e.g. Hα has FWHM 35 Å and equivalent width 360 Å) but in the VLT data are extremely weak (7 and 25 Å, respectively). Spectral features from both stellar components are visible in the mean VLT spectrum: we see a broad Hα absorption from the white dwarf photosphere and a wide 7150–7350 Å dip which betrays the presence of an M-type secondary star (Fig. 14).

Figure 14

Main panel: the mean spectrum of SDSS J1658 from our VLT observations (black line), normalized unity using a straight-line fit. A template M5 star is shown, with a red line, for comparison. Inset panel: a comparison between our mean VLT spectrum (black line) and the SDSS spectrum of SDSS J1658 (blue line) in the region of the Hα and He i 6678 Å lines.

Figure 14

Main panel: the mean spectrum of SDSS J1658 from our VLT observations (black line), normalized unity using a straight-line fit. A template M5 star is shown, with a red line, for comparison. Inset panel: a comparison between our mean VLT spectrum (black line) and the SDSS spectrum of SDSS J1658 (blue line) in the region of the Hα and He i 6678 Å lines.

At the time of the SDSS spectrum, SDSS J1658 was clearly in a state of much higher accretion level than during the other observations. This is manifested in the vastly stronger emission lines from the accretion disc, but the disc still contributed very little continuum light so the CV was only slightly brighter at that time. The stellar components are not clearly visible in the SDSS spectrum due to the wider emission lines and much lower signal-to-noise ratio than our mean VLT spectrum.

The RV motion of the Hα line in our spectra is straightforward to detect. Single-Gaussian measurements were made and the best FWHM was found to be 400 km s−1, giving an orbital period of 98.29 ± 0.79 min from 19 spectra on the first night only. Including the spectra from the second night gives the expected alias pattern centred on a period of 98.05 min with 1-d aliases at 91.48 and 105.70 min. We can therefore unambiguously identify the central peak in the periodogram with the orbital motion of the binary, resulting in a final period of Porb= 98.012 ± 0.065 min. The spectroscopic orbit is plotted in Fig. 15 and its parameters are given in Table 3.

Figure 15

Upper panel: Scargle periodogram of the RVs of SDSS J1658 measured using a single Gaussian with width 400 km s−1. Lower panel: measured RVs (filled circles) compared to the best-fitting spectroscopic orbit (solid line).

Figure 15

Upper panel: Scargle periodogram of the RVs of SDSS J1658 measured using a single Gaussian with width 400 km s−1. Lower panel: measured RVs (filled circles) compared to the best-fitting spectroscopic orbit (solid line).

The velocity amplitude we have measured from the Hα emission, K1= 125.3 ± 3.5 km s−1, is too high to be attributed to the white dwarf, and is far too narrow to arise from the full accretion disc. We therefore tentatively assign it to the secondary star. An additional constraint on the system is that the full width at zero intensity of the Hα line in the SDSS spectrum (roughly 3200 km s−1) arises from material in orbit around the white dwarf. We have constructed a constraints diagram in a similar fashion as for SDSS J121607.03+052013.9 (Paper I) and SDSS J013132.39−090122.2 (Southworth et al. 2007b), and required that our measured velocity amplitude is attributable to some part of the secondary star. We find that there is a small region of parameter space where the system could satisfy all our constraints, involving a large white dwarf mass (1.0 M or more) and a low orbital inclination (10°–30°). This solution also allows the secondary star to have a mass near to 0.15 M, which is the value expected for a CV with a period of 98 min (Knigge 2006). This is only a rough investigation: more detailed studies would require a more accurate measurement of the emission-line full width at zero intensity when the system is again in the high state. An alternative explanation is that the narrow emission comes from some other structure in the system.

Our VLT data for SDSS J1658 have characteristics reminiscent of the spectrum of the low-inclination CV RE J1255+266 presented by Watson et al. (1996), which shows wide absorption from the white dwarf and very narrow Balmer emission. In the case of RE J1255+266, the narrow emission arises from the accretion disc and has a much lower velocity amplitude than the one we measure for SDSS J1658.

4.7 SDSS J165951.68+192745.6

SDSS J1659 was found to be a CV by Szkody et al. (2006) from an SDSS spectrum which has the extremely blue continuum and weak single-peaked emission lines which are characteristic of a high mass transfer rate (e.g. Rodríguez-Gil, Schmidtobreick & Gänsicke 2007a; Rodríguez-Gil et al. 2007b). We obtained 2.5 h of V-filter NTT photometry of SDSS J1659 (Fig. 16) as a brighter (g= 17.12) backup target during cloudy conditions. There is flickering (Bruch 1992,2000) but no clear coherent periodicity in these data.

Figure 16

NTT V-filter photometry of SDSS J1659 obtained in cloudy conditions. Differential magnitudes for SDSS J1659 minus comparison star are shown as filled circles with error bars, offset by the V magnitude of the comparison. Differential magnitudes for the comparison minus the check star are shown offset at the bottom of the plot.

Figure 16

NTT V-filter photometry of SDSS J1659 obtained in cloudy conditions. Differential magnitudes for SDSS J1659 minus comparison star are shown as filled circles with error bars, offset by the V magnitude of the comparison. Differential magnitudes for the comparison minus the check star are shown offset at the bottom of the plot.

4.8 SDSS J223252.35+140353.0

SDSS J2232 was found at magnitude g= 17.7 by the SDSS imaging survey. It was subsequently selected for spectroscopic follow-up, and the SDSS spectrum (Szkody et al. 2004) shows Balmer emission lines emanating from a much fainter object (gspec= 23.2). This indicates that SDSS J2232 is a dwarf nova which was in outburst at the time of the SDSS imaging observations but in quiescence during the SDSS spectroscopic observation. On our VLT acquisition image SDSS J2232 was in quiescence at a magnitude of V= 21.4, whereas it was at magnitudes 22.1 and 21.8 during our visits to it with the NOT.

The NOT light curves cover time intervals of about 3 and 5 h, separated by slightly less than 1 yr. Both show a variation with a period in the region of 135 min. The light curves and Scargle periodograms are shown in Fig. 17. Fitting sine curves to the data results in periods of 131 ± 3 min for the 2005 data and 132 ± 6 min for the 2006 observations. With the VLT we obtained 14 Hα spectra over 2.5 h, but then discontinued our observations for scheduling reasons. The resulting RVs (Fig. 18) are consistent with orbital motion with a period longer than 4 h.

Figure 17

Upper panels: NOT unfiltered light curves of SDSS J2232. The comparison minus check magnitudes are shown in each panel offset to a magnitude of 20.4. Lower panels: Scargle periodograms of the two light curves.

Figure 17

Upper panels: NOT unfiltered light curves of SDSS J2232. The comparison minus check magnitudes are shown in each panel offset to a magnitude of 20.4. Lower panels: Scargle periodograms of the two light curves.

Figure 18

RVs measured for SDSS J2232 using a double Gaussian function with FWHMs 500 km s−1 and separation 2000 km s−1.

Figure 18

RVs measured for SDSS J2232 using a double Gaussian function with FWHMs 500 km s−1 and separation 2000 km s−1.

The SDSS spectrum of SDSS J2232 has a very low signal but has a significant contribution from the secondary star. A simple fit to the the SDSS spectrum (see Paper I) indicates a secondary component with a spectral type of M4 and a magnitude r= 23.4 (Fig. 19). We would therefore expect to see an ellipsiodal modulation in the light curve of this system, with a period of half of the orbital period. The observed periodicity of roughly 135 min implies an orbital period of about 270 min, consistent with the RVs measured from our VLT spectra. We therefore suggest that SDSS J2232 is a dwarf nova with Porb∼ 4.5 h. These properties are similar to those of the well-studied dwarf novae U Gem (Porb= 254.7 min and secondary spectral type ∼M4; Naylor, Allan & Long 2005; Echevarría, de la Fuente & Costero 2007) and GY Cnc (252.6 min and M3; Gänsicke et al. 2000; Thorstensen 2000).

Figure 19

Compison between the SDSS spectrum of SDSS J2232 (grey line; the data have been smoothed) and a template SDSS spectrum of an M4 dwarf (blue line).

Figure 19

Compison between the SDSS spectrum of SDSS J2232 (grey line; the data have been smoothed) and a template SDSS spectrum of an M4 dwarf (blue line).

The distance to this system can be estimated using Roche geometry. Assuming MWD= 0.6 and q= 0.5 gives a secondary star radius of about 2.5 × 108m. Accounting for the flux ratio between the SDSS spectrum of SDSS J2232 and a template M4 dwarf spectrum (and the flux from the white dwarf and the accretion disc), we find a distance of about 2.7 kpc. Alternatively, adopting a secondary spectral type of M4 gives an absolute visual magnitude of MV= 11.3. The SDSS magnitude r= 23.4 converts to V= 24.0, which then results in a distance of roughly 3.5 kpc. A distance of approximately 3 kpc puts SDSS J2232 about 2 kpc from the Galactic plane. This is well into the Galactic thick disc, which has a scale height close to 1 kpc (Veltz et al. 2008). Further observations to assess the membership of SDSS J2232 in this old stellar population may be very rewarding.

4.9 SDSS J223843.84+010820.7 (Aqr 1)

SDSS J2238 was found to be a CV by Berg et al. (1992) in the course of the Large Bright Quasar Survey (Foltz et al. 1987). It was given the provisional name of Aqr 1 in the now-frozen catalogue of Downes et al. (2001). An SDSS spectrum was presented by Szkody et al. (2003), along with seven intermediate-resolution spectra and 3.75 h of unfiltered time-series photometry with exposure times of 600 s. An orbital period of ∼2 h was estimated from the spectra (although they only cover 1.75 h), and no periodic variation was noted in the photometry. The He ii 4686 Å emission in the SDSS spectrum was strong enough for Szkody et al. (2003) to suggest that the object may be a magnetic CV.

Woudt, Warner & Pretorius (2004) presented 15 h of unfiltered photometry of SDSS J2238 over five nights, obtained using the South African Astronomical Observatory (SAAO) 1.9-m telescope and the University of Cape Town (UCT) high-speed photometer. They found periodicities at 6.7284 and 193.5 min, the second of which was found to be the ‘probable’ orbital period. The first of these was attributed to the spin period of the white dwarf, confirming the magnetic nature of the object.

We obtained a total of 59 spectra over three consecutive nights (Table 2) using the IMACS spectrograph on the Magellan Baade telescope (Section 2.3). RV measurements of the Hα line indicate an orbital period of 194 min for all widths of Gaussian functions tried. The best results are found using a single Gaussian of width 850 km s−1. A Scargle periodogram of these observations is highly aliased (Fig. 20) but bootstrapping simulations give a probability of 88 per cent that the highest peak is the correct one. Fitting a spectroscopic orbit to the RVs gives an orbital period of Porb= 194.30 ± 0.16 min. Whilst, this solution gives a scatter in the observations of σrms= 27.3 km s−1, the alternative alias periods of 171 and 224 min have scatter of 35.0 and 34.1 km s−1, respectively.

Figure 20

Upper panel: Scargle periodogram of the RVs of SDSS J2238 measured using a single Gaussian with FWHM 850 km s−1. Lower panel: measured RVs (filled circles) compared to the best-fitting spectroscopic orbit (solid line).

Figure 20

Upper panel: Scargle periodogram of the RVs of SDSS J2238 measured using a single Gaussian with FWHM 850 km s−1. Lower panel: measured RVs (filled circles) compared to the best-fitting spectroscopic orbit (solid line).

Our orbital period of 194.30 min is in good agreement with the ‘probable orbital period’ obtained by Woudt et al. (2004), which supports both our alias discrimination and their interpretation. The discrepant value of ∼2 h favoured by Szkody et al. (2003) is probably due to the shortage of observational data available to that study. The parameters of the final spectroscopic orbit are given in Table 3 and phase-binned and trailed spectra around the Hα and He I 6678 Å emission lines are shown in Fig. 3. The 6.7-min photometric periodicity found by Woudt et al. (2004) is not resolved by our spectra, which have a cadence of 5.5 min.

5 SUMMARY AND DISCUSSION

We have presented time-resolved photometry and spectroscopy of nine faint CVs which were identified by the SDSS. For five of these systems we have determined orbital periods (Table 4), and four of these are shorter than the 2–3 h period gap apparent in the known population of CVs. This work brings the total number of SDSS CVs with measured orbital periods to approximately 110 of the total population of 212 objects.

Table 4

Summary of the orbital periods obtained for the objects studied in this work.

Object Period (min) Notes 
SDSS J0043 82.325 ± 0.088 VLT spectroscopy 
SDSS J0337  Faint, no RV motion noted 
SDSS J1601 Short period More photometry needed 
SDSS J1637 97.04 ± 0.19 VLT spectroscopy 
SDSS J1642 113.6 ± 1.5 VLT spectroscopy 
SDSS J1658 98.012 ± 0.065 VLT spectroscopy, low state 
SDSS J1659  NTT photometry 
SDSS J2232  VLT spectroscopy, period may be ∼4.5 h 
SDSS J2238 194.30 ± 0.16 Magellan spectroscopy 
Object Period (min) Notes 
SDSS J0043 82.325 ± 0.088 VLT spectroscopy 
SDSS J0337  Faint, no RV motion noted 
SDSS J1601 Short period More photometry needed 
SDSS J1637 97.04 ± 0.19 VLT spectroscopy 
SDSS J1642 113.6 ± 1.5 VLT spectroscopy 
SDSS J1658 98.012 ± 0.065 VLT spectroscopy, low state 
SDSS J1659  NTT photometry 
SDSS J2232  VLT spectroscopy, period may be ∼4.5 h 
SDSS J2238 194.30 ± 0.16 Magellan spectroscopy 

From VLT spectroscopy of SDSS J0043, we found an orbital period of Porb= 82.325 ± 0.088 min, placing this object close to the observed minimum period for hydrogen-rich CVs. Its spectrum shows a strong contribution from the white dwarf in the system, indicating that the accretion disc is faint and the mass transfer rate is low. We have used Doppler tomography to decompose the spectra into a Doppler map in velocity space. The map shows a circular accretion disc and an inner emission peak. The latter feature can be attributed to the irradiated inner face of the secondary star, if the velocity amplitude measured from the Hα emission-line overestimates the motion of the white dwarf by a factor of 2. The Doppler map shows enhanced emission from two bright regions on the accretion disc. If the inner emission peak does indeed come from the secondary star, one of these bright regions is in the correct position to be a bright spot caused by the mass transfer stream impacting the disc. This interpretation is supported by its presence in a Doppler map of the He i 6678 Å line. The second region of enhanced emission is in an unusual position in velocity space and its origin is not straightforwardly explicable. A short light curve of SDSS J0043 shows evidence of a variation with a period of 207 ± 1 s and an amplitude of 17 ± 5 mmag. The white dwarf component may be a ZZ Ceti-type pulsating star.

SDSS J1637 was observed with the VLT during quiescence, resulting in an orbital period measurement of Porb= 97.01 ± 0.19 min. This object is a dwarf nova which has previously been observed in superoutburst, when superhumps with a period of 99.75 ± 0.86 min were detected. Using the calibrations presented by Patterson (1998) and Knigge (2006), we find q≈ 0.16 from these two period measurements. Assuming a white dwarf mass of 0.8 M gives an estimated secondary mass of 0.13 M. This is in good agreement with the expected properties of a CV with Porb= 97 min, and together with the velocity amplitude from the Hα emission line point to the system having an orbital inclination of roughly 40°.

SDSS J1642 was studied both photometrically with the NTT and spectroscopically with the VLT. The VLT data yield an unambiguous period of Porb= 113.6 ± 1.5 min. The NTT photometry shows a number of features and results in a periodogram with a small forest of peaks at frequencies below 15 cycle d−1. The spectroscopic period is in best agreement with the peak corresponding to a period of 110.60 ± 0.16 min, but we prefer the spectroscopic value for our final orbital period measurement. Doppler maps of the Hα and He i emission lines reveal a clear accretion disc and bright spot as well as weak emission from the secondary star. More surprisingly, the He i maps show an accretion disc with much higher velocities than those for Hα, indicating that the emitting region for He i is physically smaller and closer to the white dwarf than for Hα. The Hα map also shows strong emission arising from the part of the disc opposite the bright spot, but the short duration of our spectroscopic observations means this unusual feature could be caused by brightness variation which differ from orbit to orbit.

SDSS J1658 is perhaps the most unusual system studied in this work. Its SDSS spectrum shows the strong emission-lines characteristic of a short-period CV whose light is dominated by a hydrogen-rich accretion disc. However, our VLT spectra show a much weaker and narrower central emission line, and broad absorption features arising from both the white dwarf and secondary star, but no flux which could be unambiguously assigned to an accretion disc. The object was only 0.4-mag fainter during our observations than when the SDSS spectrum was taken, so the strong emission lines in that spectrum were accompanied by only weak continuum flux from the accretion disc. The velocity variation of the narrow Hα emission in our VLT spectra yields a period measurement of Porb= 98.012 ± 0.065 min, confirming that this object is a short-period binary star system. The velocity amplitude (125 km s−1) is too large for the white dwarf, so we have attempted to assign it to the secondary star. The observational constraints can be satsified in this scenario if the white dwarf is massive (≲1 M) and the orbital inclination is low (10°–30°).

A modest number of photometric and spectroscopic observations of SDSS J2232 suggest that this is a dwarf nova with an orbital period close to 4.5 h. From the flux contribution of the secondary star we infer a distance of roughly 3 kpc, corresponding to distance of 2 kpc from the Galactic plane. Further investigation is needed to prove its membership of this old stellar population.

We obtained 59 Magellan spectra of SDSS J2238, which is the brightest of the five objects for which we determine orbital periods in this work. Velocity measurements of its Hα emission line give a period of Porb= 194.30 ± 0.16. This value is in good agreement with a published photometric period, which also confirmed that the system contains a magnetic white dwarf with a rotational period of 6.7284 min.

These observations provide further confirmation that the faintest of the CVs identified by the SDSS have predominantly short orbital periods. Theoretical population studies of CVs predict a huge population of faint short-period CVs which has not previously been detected. Our observations are now uncovering this ‘quiet majority’ of the CV population. The unusual characteristics of several of the objects studied in this work show that even the short-period CVs demonstrate impressively varied behaviour, many aspects of which cannot easily be explained in the standard picture of CV structure. Our project to study the SDSS CV population is invaluable for extending our knowledge of these fascinating objects.

2
pamela and molly were written by TRM and can be found at http://www.warwick.ac.uk/go/trmarsh.
3
Starlink software can be accessed from http://starlink.jach.hawaii.edu/.
5
The reduced spectra and RVs presented in this work will be available at the CDS (http://cdsweb.u-strasbg.fr/) and at http://www.astro.keele.ac.uk/~jkt/.
7
Spectroscopic Binary Orbit Program, written by P. B. Etzel, http://mintaka.sdsu.edu/faculty/etzel/.
8
vsnet-superoutburst alert number 2306.
9
vsnet-superoutburst alert number 2310.

The reduced spectra and RV measurements presented in this work will be made available at the CDS (http://cdsweb.u-strasbg.fr/) and at http://www.astro.keele.ac.uk/~jkt/. Based on observations made with ESO Telescopes at the La Silla and Paranal Observatories under programme ID 079.D-0024. Some data presented here have been taken using ALFOSC, which is owned by the Instituto de Astrofisíca de Andalucía (IAA) and operated at the NOT under agreement between IAA and the NBIfAFG of the Astronomical Observatory of Copenhagen.

JS and CMC acknowledge financial support from PPARC in the form of a postdoctoral research assistant position. DS acknowledges an STFC Advanced Fellowship. The following internet-based resources were used in research for this paper: the ESO Digitized Sky Survey; the NASA Astrophysics Data System; the simbad data base operated at CDS, Strasbourg, France; and the arxiv scientific paper preprint service operated by Cornell University.

Funding for the SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the US Department of Energy, the Japanese Monbukagakusho and the Max Planck Society. The SDSS website is http://www.sdss.org/.

REFERENCES

Appenzeller
I.
et al.,
1998
,
The Messenger
 ,
94
,
1
Aungwerojwit
A.
et al.,
2006
,
A&A
 ,
455
,
659
Berg
C.
Wegner
G.
Foltz
C. B.
Chaffee
J.
F. H.
Hewett
P. C.
,
1992
,
ApJS
 ,
78
,
409
Bertin
E.
Arnouts
S.
,
1996
,
A&AS
 ,
117
,
393
Bigelow
B. C.
Dressler
A. M.
,
2003
, in
Iye
M.
Moorwood
A. F. M.
, eds,
Proc. SPIE, Vol. 4841
,
Instrument Design and Performance for Optical/Infrared Ground-based Telescopes
 .
SPIE
, Bellingham, p.
1727
Bruch
A.
,
1992
,
A&A
 ,
266
,
237
Bruch
A.
,
2000
,
A&A
 ,
359
,
998
Chen
A.
O'Donoghue
D.
Stobie
R. S.
Kilkenny
D.
Warner
B.
,
2001
,
MNRAS
 ,
325
,
89
De Kool
M.
,
1992
,
A&A
 ,
261
,
188
De Kool
M.
Ritter
H.
,
1993
,
A&A
 ,
267
,
397
Dillon
M.
et al.,
2008a
,
MNRAS
 ,
386
,
1568
D'Odorico
S.
Beletic
J. W.
Amico
P.
Hook
I.
Marconi
G.
Pedichini
F.
,
1998
, in
D'Odorico
S.
, ed.,
Proc. SPIE, Vol. 3355
,
Optical Astronomical Instrumentation
 .
SPIE
, Bellingham, p.
507
Downes
R. A.
Webbink
R. F.
Shara
M. M.
Ritter
H.
Kolb
U.
Duerbeck
H. W.
,
2001
,
PASP
 ,
113
,
764
Eaton
N.
Draper
P. W.
Allen
A.
,
1999
, Starlink User Note 45.9
Echevarría
J.
De La Fuente
E.
Costero
R.
,
2007
,
AJ
 ,
134
,
262
Foltz
C. B.
Chaffee
J.
F. H.
Hewett
P. C.
MacAlpine
G. M.
Turnshek
D. A.
Weymann
R. J.
Anderson
S. F.
,
1987
,
AJ
 ,
94
,
1423
Gänsicke
B. T.
Fried
R. E.
Hagen
H.-J.
Beuermann
K.
Engels
D.
Hessman
F. V.
Nogami
D.
Reinsch
K.
,
2000
,
A&A
 ,
356
,
L79
Gänsicke
B. T.
Araujo-Betancor
S.
Hagen
H.-J.
Harlaftis
E. T.
Kitsionas
S.
Dreizler
S.
Engels
D.
,
2004
,
A&A
 ,
418
,
265
Gänsicke
B. T.
et al.,
2006
,
MNRAS
 ,
365
,
969
Green
R. F.
Schmidt
M.
Liebert
J.
,
1986
,
ApJS
 ,
61
,
305
Hellier
C.
,
2001
,
Cataclysmic Variable Stars: How and Why they Vary, Springer-Praxis books in Astronomy and Space Science
 .
Springer Verlag
, New York
Horne
K.
,
1986
,
PASP
 ,
98
,
609
Howell
S. B.
Nelson
L. A.
Rappaport
S.
,
2001
,
ApJ
 ,
550
,
897
Jester
S.
et al.,
2005
,
AJ
 ,
130
,
873
Knigge
C.
,
2006
,
MNRAS
 ,
373
,
484
Kolb
U.
,
1993
,
A&A
 ,
271
,
149
Kolb
U.
Baraffe
I.
,
1999
,
MNRAS
 ,
309
,
1034
Kolb
U.
De Kool
M.
,
1993
,
A&A
 ,
279
,
L5
Littlefair
S. P.
Dhillon
V. S.
Marsh
T. R.
Gänsicke
B. T.
,
2006a
,
MNRAS
 ,
371
,
1435
Littlefair
S. P.
Dhillon
V. S.
Marsh
T. R.
Gänsicke
B. T.
Southworth
J.
Watson
C. A.
,
2006b
,
Sci
 ,
314
,
1578
Littlefair
S. P.
Dhillon
V. S.
Marsh
T. R.
Gänsicke
B. T.
Baraffe
I.
Watson
C. A.
,
2007
,
MNRAS
 ,
381
,
827
Littlefair
S. P.
et al.,
2008
,
MNRAS
 ,
388
,
1582
Marsh
T. R.
,
1989
,
PASP
 ,
101
,
1032
Marsh
T. R.
Horne
K.
,
1988
,
MNRAS
 ,
235
,
269
Mukadam
A. S.
et al.,
2004
,
ApJ
 ,
607
,
982
Naylor
T.
,
1998
,
MNRAS
 ,
296
,
339
Naylor
T.
Allan
A.
Long
K. S.
,
2005
,
MNRAS
 ,
361
,
1091
O'Donoghue
D.
Kanaan
A.
Kleinman
S. J.
Krzesinski
J.
Pritchet
C.
,
2000
,
Balt. Astron.
 ,
9
,
375
Osterbrock
D. E.
Fulbright
J. P.
Martel
A. R.
Keane
M. J.
Trager
S. C.
Basri
G.
,
1996
,
PASP
 ,
108
,
277
Paczyński
B.
,
1967
,
Acta Astron.
 ,
17
,
287
Patterson
J.
,
1998
,
PASP
 ,
110
,
1132
Politano
M.
,
1996
,
ApJ
 ,
465
,
338
Politano
M.
,
2004
,
ApJ
 ,
604
,
817
Press
W. H.
Teukolsky
S. A.
Vetterling
W. T.
Flannery
B. P.
,
1992
,
Numerical recipes in FORTRAN 77. The art of scientific computing
 ,
2nd edn
.
University Press
, Cambridge
Rappaport
S.
Joss
P. C.
Webbink
R. F.
,
1982
,
ApJ
 ,
254
,
616
Ritter
H.
Kolb
U.
,
2003
,
A&A
 ,
404
,
301
Rodríguez-Gil
P.
Schmidtobreick
L.
Gänsicke
B. T.
,
2007a
,
MNRAS
 ,
374
,
1359
Rodríguez-Gil
P.
et al.,
2007b
,
MNRAS
 ,
377
,
1747
Roelofs
G. H. A.
Groot
P. J.
Marsh
T. R.
Steeghs
D.
Nelemans
G.
,
2006
,
MNRAS
 ,
365
,
1109
Scargle
J. D.
,
1982
,
ApJ
 ,
263
,
835
Schneider
D. P.
Young
P.
,
1980
,
ApJ
 ,
238
,
946
Schwarzenberg-Czerny
A.
,
1989
,
MNRAS
 ,
241
,
153
Schwarzenberg-Czerny
A.
,
1996
,
ApJ
 ,
460
,
L107
Shafter
A. W.
,
1983
,
ApJ
 ,
267
,
222
Smak
J.
,
1985
,
Acta Astron.
 ,
35
,
351
Smith
D. A.
Dhillon
V. S.
,
1998
,
MNRAS
 ,
301
,
767
Southworth
J.
Maxted
P. F. L.
Smalley
B.
,
2004a
,
MNRAS
 ,
349
,
547
Southworth
J.
Maxted
P. F. L.
Smalley
B.
,
2004b
,
MNRAS
 ,
351
,
1277
Southworth
J.
Zucker
S.
Maxted
P. F. L.
Smalley
B.
,
2004c
,
MNRAS
 ,
355
,
986
Southworth
J.
Smalley
B.
Maxted
P. F. L.
Claret
A.
Etzel
P. B.
,
2005
,
MNRAS
 ,
363
,
529
Southworth
J.
Gänsicke
B. T.
Marsh
T. R.
De Martino
D.
Hakala
P.
Littlefair
S.
Rodríguez-Gil
P.
Szkody
P.
,
2006
,
MNRAS
 ,
373
,
687
(Paper I)
Southworth
J.
Gänsicke
B. T.
Marsh
T. R.
De Martino
D.
Aungwerojwit
A.
,
2007a
,
MNRAS
 ,
378
,
635
Southworth
J.
Marsh
T. R.
Gänsicke
B. T.
Aungwerojwit
A.
Hakala
P.
De Martino
D.
Lehto
H.
,
2007b
,
MNRAS
 ,
382
,
1145
Southworth
J.
Townsley
D. M.
Gänsicke
B. T.
,
2008
,
MNRAS
 ,
388
,
709
Spruit
H. C.
Ritter
H.
,
1983
,
A&A
 ,
124
,
267
Steeghs
D.
Howell
S. B.
Knigge
C.
Gänsicke
B. T.
Sion
E. M.
Welsh
W. F.
,
2007
,
ApJ
 ,
667
,
442
Stover
R. J.
,
1981
,
ApJ
 ,
249
,
673
Szkody
P.
et al.,
2002
,
AJ
 ,
123
,
430
Szkody
P.
et al.,
2003
,
AJ
 ,
126
,
1499
Szkody
P.
et al.,
2004
,
AJ
 ,
128
,
1882
Szkody
P.
et al.,
2005
,
AJ
 ,
129
,
2386
Szkody
P.
et al.,
2006
,
AJ
 ,
131
,
973
Szkody
P.
et al.,
2007
,
AJ
 ,
134
,
185
Thorstensen
J. R.
,
2000
,
PASP
 ,
112
,
1269
Veltz
L.
et al.,
2008
,
A&A
 ,
480
,
753
Verbunt
F.
Zwaan
C.
,
1981
,
A&A
 ,
100
,
L7
Vogt
N.
,
1982
,
ApJ
 ,
252
,
653
Warner
B.
,
1995
,
Cataclysmic Variable Stars. Cambridge Astrophysics Series
 ,
Cambridge Univ. Press
, Cambridge, UK
Watson
M. G.
Marsh
T. R.
Fender
R. P.
Barstow
M. A.
Still
M.
Page
M.
Dhillon
V. S.
Beardmore
A. P.
,
1996
,
MNRAS
 ,
281
,
1016
Whitehurst
R.
,
1988
,
MNRAS
 ,
232
,
35
Whyte
C. A.
Eggleton
P. P.
,
1980
,
MNRAS
 ,
190
,
801
Willems
B.
Kolb
U.
Sandquist
E. L.
Taam
R. E.
Dubus
G.
,
2005
,
ApJ
 ,
635
,
1263
Winget
D. E.
,
1998
,
J. Phys.: Condens. Matter
 ,
10
,
11247
Woudt
P. A.
Warner
B.
Pretorius
M. L.
,
2004
,
MNRAS
 ,
351
,
1015
York
D. G.
et al.,
2000
,
AJ
 ,
120
,
1579