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Orbital periods of cataclysmic variables identified by the SDSS. VII. Four new eclipsing systems

We present photometry of nine cataclysmic variable stars identified by the Sloan Digital Sky Survey, aimed at measuring the orbital periods of these systems. Four of these objects show deep eclipses, from which we measure their orbital periods. The light curves of three of the eclipsing systems are also analysed using the LCURVE code, and their mass ratios and orbital inclinations determined. SDSS J075059.97+141150.1 has an orbital period of 134.1564 +/- 0.0008 min, making it a useful object with which to investigate the evolutionary processes of cataclysmic variables. SDSS J092444.48+080150.9 has a period of 131.2432 +/- 0.0014 min and is probably magnetic. The white dwarf ingress and egress phases are very deep and short, and there is no clear evidence that this object has an accretion disc. SDSS J115207.00+404947.8 and SDSS J152419.33+220920.1 are nearly identical twins, with periods of 97.5 +/- 0.4 and 93.6 +/- 0.5 min and mass ratios of 0.14 +/- 0.03 and 0.17 +/- 0.03, respectively. Their eclipses have well-defined white dwarf and bright spot ingress and egress features, making them excellent candidates for detailed study. All four of the orbital periods presented here are shorter than the 2-3 hour period gap observed in the known population of cataclysmic variables.


Introduction
Cataclysmic variables (CVs) are interacting binary stars containing a white dwarf primary component in a close orbit with a lowmass 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). CVs are thought to evolve from longer to shorter orbital periods through the loss of orbital angular momentum, before reaching a minimum period caused by the changes in the structure of the mass donor and evolving back to longer periods. However, theoretical population synthesis models of this scenario (de Kool 1992;de Kool & Ritter 1993;Kolb 1993;Kolb & de Kool 1993;Politano 1996Politano , 2004Kolb & Baraffe 1999) are unable to reproduce the orbital period distribution of the observed population of CVs (Downes et al. 2001;Ritter & Kolb 2003).
This disagreement may mainly be due to observational selection effects favouring the discovery and analysis of longerperiod CVs, which are intrinsically much brighter than their shorter-period colleagues. We are therefore working on the characterisation of the population of CVs discovered by the Sloan Digital Sky Survey (SDSS 1 ; see Szkody et al. 2007 and references therein), which were identified spectroscopically so should be much less affected by these selection biases. Further information and previous results can be found in Gänsicke et al. (2006), Southworth et al. (2006Southworth et al. ( , 2007aSouthworth et al. ( ,b, 2008a and Dillon et al. (2008). A major recent result of our project is the identification of the long-predicted pile-up of objects at the minimum 1 http://www.sdss.org/ period (the 'period spike'), which is discussed in detail by Gänsicke et al. (2009).
In this work we present and analyse time-resolved photometry of four CVs which we have discovered to show eclipses. We abbreviate the names of the targets to SDSS Jnnnn, where nnnn are the first four digits of right ascension. The full and abbreviated names, references and ugriz apparent magnitudes are given in Table 1. In Fig. 1 we plot their SDSS spectra for reference. In Sect. 8 we also present light curves of five SDSS CVs for which we did not find periodic brightness variations.

Observations and data reduction
Most of the observations presented in this work were obtained in 2009 January using the New Technology Telescope (NTT) at ESO La Silla, equipped with the EFOSC2 focal-reducing instrument 2 (Buzzoni et al. 1984). We used EFOSC2 in imaging mode and with a Loral 2048×2048 px 2 CCD binned 2×2, giving a field of view of 4.4×4.4 arcmin 2 at a plate scale of 0.26 ′′ px −1 . All images were obtained with a B Tyson filter (ESO filter #724), which has a central wavelength of 4445 Å and a FWHM of 1838 Å.
Additional observations were obtained in 2009 February (classical observing) and May (service mode) at the William Herschel Telescope (WHT) at La Palma. For these we used the Auxiliary Port focal station, which was equipped at the time with the EEV 4200×2048 px 2 CCD destined for the ACAM instrument 3 . The CCD was binned 4×4 and windowed down to the Table 1. Apparent magnitudes of our targets in the SDSS ugriz passbands. g spec 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 SDSS ugriz magnitudes, but are affected by 'slit losses' and any errors in astrometry or positioning of the spectroscopic fibre entrance. central 2048×2100 pixels, which reduced the dead time between exposures to only 5 s whilst still properly sampling the seeing conditions (plate scale 0.27 ′′ px −1 ) and available field of view (a circle of 1.8 arcmin in diameter). We used the Johnson V filter for all WHT observations. The data were reduced using standard methods, with a pipeline written in idl 4 (Southworth et al. 2009b,c,d). Aperture photometry was performed using the astrolib/aper procedure 5 , which originates from daophot (Stetson 1987). For the NTT we were able to set the photometry apertures by eye and fix their positions, whereas for the WHT they were set by eye and adjusted according to the offset between each image and the reference image found by cross-correlation.
Light curves of SDSS J0906 were obtained on the nights of 2008/01/17 and 2008/01/19 using the Isaac Newton Telescope (INT) and Wide Field Camera (WFC) equipped with a g filter. These data were reduced using the pipeline described by Gänsicke et al. (2004), which performs aperture photometry via the SExtractor package (Bertin & Arnouts 1996).
The instrumental differential magnitudes have been transformed to BV apparent magnitudes using formulae from Jordi et al. (2006). Given the non-standard nature of the spectral energy distribution of CVs, and the B Tyson filter used at the NTT, the resulting apparent magnitudes are uncertain by at least a few tenths of a magnitude.

Light curve modelling
We have modelled the observed eclipses of SDSS J0750, SDSS J1152 and SDSS J1524 in order to explore the physical properties of these systems. For this analysis we used lcurve, a code developed to fit light curves of eclipsing bi- Table 3. Parameter determinations from our lcurve fits for SDSS J0750, SDSS J1152 and SDSS J1524. The radius of the WD and the radial position of the bright spot are given as fractions of the orbital semimajor axis, a.  nary stars containing a degenerate object. A complete description of lcurve is given in Copperwheat et al. (2009). The binary is defined by four components: white dwarf, secondary star, accretion disc and bright spot. We obtained initial fits using the Nelder-Mead downhill simplex and Levenberg-Marquardt methods (Press et al. 1992). We then used a Markov Chain Monte Carlo (MCMC) algorithm for final minimisation and determination of uncertainties (see Copperwheat et al. 2009). We list the parameter determinations from these fits in Table 3. We include the following quantities: mass ratio (q), or- Table 4. Times of eclipse for the objects studied in this work, and the residuals with respect to the calculated linear ephemerides. The timings below were measured using the simple mirror-image method (Sect. 4) in order to maximise their archival value. bital inclination (i), time of white dwarf mid-eclipse (T 0 ), and the white dwarf radius and bright spot position expressed as fractions of the orbital semi-major axis (r WD and r BS ). We use the bright spot position as an indicator of the accretion disc radius, since we assume that the bright spot lies at the outer edge of the accretion disc. lcurve implements a wealth of additional parameters which are needed for modelling high-precision data. The discovery data presented in this work are insufficient to constrain these parameters, so we fixed them at values which we have found to be physically appropriate in detailed modelling of other eclipsing systems (Copperwheat et al. 2009;Pyrzas et al. 2009;Nebot Gómez-Morán et al. 2009;Southworth et al. 2009a). Our fits are therefore only indicative, and definitive results will require high-quality follow-up light curves. We discuss the results for each system below.

SDSS J075059.97+141150.1
SDSS J0750 was identified by Szkody et al. (2007) as a CV from its SDSS spectrum, which shows a blue continuum with broad and double-peaked hydrogen Balmer and He I emission lines (Fig. 1). To our knowledge no other information is available in the literature for this object beyond a few catalogued magnitude measurements.
We observed SDSS J0750 on the night of 2009/01/20 using NTT/EFOSC2, detecting two eclipses in 4.5 hr of observing (Fig. 2). It was in fact undergoing an eclipse whilst we tried to acquire it, although this was not clear at the time. We observed it again on subsequent nights during the same run, and with the shown on all panels except the bottom one, which contains the WHT data (V filter). The solid line represents our best lcurve fit to the WHT data, and the residuals of the fit are plotted offset from zero for clarity. Note that the time axis has been stretched to suit each panel.
WHT/ACAM a month later, in order to extend the time interval on which our orbital period measurement is based.
For each eclipse, a mirror-image of the light curve was shifted until the respective ascending and descending branches were in the best agreement. The time defining the axis of reflection was taken as the midpoint of the eclipses, and uncertainties were estimated based on how far this could be shifted before the agreement was visually poorer. We have fitted a linear ephemeris to these times of minimum light, finding Min I (HJD) = 2454853.62932(11) + 0.09316415(54) × E where E is the cycle number and the parenthesised quantities indicate the uncertainty in the last digit of the preceding number. This corresponds to an orbital period of 134.1564 ± 0.0008 min. The measured times of minimum light and the observed minus calculated values are given in Table 4.

Photometric model for SDSS J0750
We have modelled the WHT/ACAM light curve, which has the highest observing cadence, using the lcurve code (Sect. 3). The best fit is shown in Fig. 2 and the parameters of the fit are given in Table 3. The relatively featureless light variation makes this quite a difficult object, and our mass ratio measurement is correspondingly uncertain (Table 3).
The photometric determination of parameters in CVs is dependent on measurement of the phase widths of the eclipses of the white dwarf and bright spot. The phase width of the white dwarf eclipse is intrinsically linked to i and q, causing these two parameters to be degenerate (Bailey 1979). This degeneracy can be broken using the observed ingress and egress phases of the bright spot, but in the SDSS J0750 light curve these features are rather weakly defined. This causes a large uncertainty in the position of the bright spot and thus the mass ratio. Highspeed photometry of several eclipses should be sufficient to provide a clear detection of the bright spot ingress and egress, and thus obtain a precise mass ratio (e.g. Littlefair et al. 2006Littlefair et al. , 2008Copperwheat et al. 2009).

SDSS J092444.48+080150.9
SDSS J0924 is another new discovery from the SDSS survey, identified by Szkody et al. (2005) due to a spectrum which shows strong and narrow Balmer emission and hints of the secondary star towards the red end. The presence of strong He II is John Southworth et al.: Orbital periods of cataclysmic variables identified by the SDSS. 5 indicative of a magnetic system, but polarimetric observations revealed no polarisation. Szkody et al. (2005) presented followup observations comprising 11 spectra, which indicated an orbital period in the region of 2.1 hr, and 3.75 hr of photometry which showed clear variability but no eclipses.
We observed SDSS J0924 on the night of 2009/01/24 using the NTT, obtaining a light curve covering 3.75 hr. These data cover two eclipses, which are approximately 2.5 mag deep and 10 min long (Fig. 3). We observed one additional eclipse on each of the two following nights, plus one more on the night of 2009/02/16 with the WHT. The eclipse midpoints were obtained as above and a straight line fitted to them to determine an ephemeris: Min I (HJD) = 2454856.71933(11) + 0.09114110(94) × E which equates to an orbital period of 131.2432 ± 0.0014 min. The measured times of minimum light and the observed minus calculated values are given in Table 4.
The ascending and descending branches of the eclipses of SDSS J0924 are extremely quick and are not resolved by our data, even though the WHT observations have a mean cadence of 15.2 s. The dominant light source in the system is therefore very small, which requires it to be all or part of the white dwarf. The Balmer emission lines indicate that there is mass transfer occuring in this system, but the eclipse morphology indicates that any accretion disc is rather faint. This is clear evidence that the white dwarf is magnetic and its field is disrupting the disc. This system is very well suited to the measurement of the radius of the white dwarf, although this would need high-speed photometry obtained using a large telescope. We did not attempt to model the light curve; our data do not resolve the eclipse ingress and egress shapes so the lcurve solutions would be indeterminate.
It is not clear why eclipses were not detected by Szkody et al. (2005), although it must be remembered that the telescope available to these authors was much smaller (1.0 m versus 3.6 m). Dr. A. Henden (private communication) has kindly supplied the data from Szkody et al. for a closer inspection. We find that their light curve closely matches the morphology of our own data from the night of 2009/01/24, and that it is possible to align the two eclipses we observed on that night with two short gaps in Szkody et al.'s data. Their non-detection therefore can be attributed to either bad luck with the observing conditions or equipment, or to accidental rejection of data where SDSS J0924 was in eclipse and thus below the detection limit of individual images.

Spectral energy distribution of SDSS J0924
The secondary star dominates the optical spectrum of SDSS J0924 at longer wavelengths, exhibiting potassium and sodium absorption lines as well as strong TiO bandheads characteristic of mid-to-late M dwarfs. We have determined the star's spectral type using an M dwarf template library (Rebassa-Mansergas et al. 2007). These templates were scaled and subtracted from the SDSS spectrum of SDSS J0924, and the smoothest residual spectrum was obtained for a spectral type of M2±0.5 (Fig. 4). Two SDSS spectra are available for this object, and they give consistent results. From this best-fitting template, we calculated f TiO , the flux difference between the bands 7450-7550 Å and 7140-7190 Å (Beuermann 2006). For the orbital period of SDSS J0924, and an assumed mass ratio of q = 0.25, we find R 2 = 0.23 M ⊙ (only weakly dependent on q). Using the polynomial expressions of Beuermann (2006), we find a distance of d = 650 ± 30 pc.   (Schlegel et al. 1998), E B−V = 0.047 (upper pair). Black triangles: UKIDSS yJHK fluxes. Gray lines: best-fitting M2 secondary star spectrum from Fig. 4 and a white dwarf with T eff = 17 000 K and log g = 8.3, scaled for d = 650 pc, as a plausible match to the observed ultraviolet fluxes. SDSS J0924 has also been detected in the ultraviolet (UV) Medium Imaging Survey by GALEX (Morrissey et al. 2007) and in the infrared (IR) by UKIDSS (Lawrence et al. 2007). The UV-optical-IR spectral energy distribution is shown in Fig. 5. For a distance of 650 pc, the UV fluxes are consistent with a 15 000-20 000 K white dwarf, depending on its surface gravity (and hence mass). This temperature range is entirely consistent with that observed in a number of magnetic CVs (Townsley & Gänsicke 2009). Assuming a canonical mass for a CV white dwarf, M wd = 0.8 M ⊙ and an effective temperature of 17 000 K, we find a good match to the GALEX fluxes and the blue upturn of the SDSS spectrum (Fig. 5). For a system at the lower edge of the period gap, Beuermann et al. (1998) and Knigge (2006) suggest that the companion should be an M4 dwarf. The spectral type of the companion star determined from the SDSS spectrum, M2, is hence too early for the orbital period of the system. This suggests that the donor star is somewhat evolved, similar to the dwarf nova QZ Ser, a P orb = 119.8 min CV which harbours a K4±2 companion star (Thorstensen et al. 2002). Ultraviolet spectroscopy of SDSS J0924 would allow us to probe the abundance ratio of nitrogen to carbon, which is expected to be enhanced in such stars by nuclear processing (Gänsicke et al. 2003) 6. SDSS J115207.00+404947.8 The SDSS spectrum of SDSS J1152 shows a blue continuum with broad double-peaked Balmer emission features, leading Szkody et al. (2007) to identify it as one of the population of SDSS CVs. The large separation of the double peaks is a telltale signature of a high orbital inclination, whilst the shallow Balmer absorption outside the emission lines is a clear sign of the underlying white dwarf.
The spectral features of SDSS J1152 are a reliable indicator of a high-inclination short-period CV with a low mass transfer rate (e.g. SDSS J1035; Southworth et al. 2006 andLittlefair et al. 2006), and our observations indeed reveal two deep eclipses recurring on a period close to the minimum found Only the second eclipse is plotted in the lower panel, as these data are much better than those from the first eclipse. The best fit (solid line in the lower panel) is compromised by the slightly different shape of the first eclipse (not shown) compared to the second eclipse.
in hydrogen-rich CVs (Fig. 6). Due to poor weather we were unable to obtain additional data, so the ephemeris is not precise: Min I (HJD) = 2454879.5388(2) + 0.06770(28) × E corresponding to an orbital period of 97.5 ± 0.4 min.
The phased light curve in Fig. 6 clearly shows that the bright spot and the white dwarf are eclipsed. This makes SDSS J1152 a good candidate for measurement of its physical properties: we have modelled our data using lcurve (Sect. 3) and find that the mass ratio is well-defined even though our observations are rather noisy. High-quality follow-up observations of SDSS J1152 are strongly encouraged. 7. SDSS J152419.33+220920.1 SDSS J1524 was discovered to be a CV by Szkody et al. (2009), from an SDSS spectrum which is very similar to that of SDSS J1152. Szkody et al. stated that the deep central absorption in the centres of the double-peaked Balmer emission made it a candidate eclipsing system. Our follow-up photometry, obtained over 2.75 hr on the night of 2009/05/06 using the WHT in service mode, confirms this suggestion. We observed two eclipses, which have a depth of 2.2 mag and a duration of 5.6 min and show clear structure due to the eclipse of the bright spot and of the white dwarf (Fig. 7). We find an ephemeris of Min I (HJD) = 2454957.6499(1) + 0.06500(32) × E corresponding to an orbital period of 93.6 ± 0.5 min. The measured times of minimum light are given in Table 4. SDSS J1524 is strongly reminiscent of SDSS J1152, and our lcurve models of the two systems are very similar (Table 3). Our modelling of the eclipses of SDSS J1524 was hindered by flickering, which causes the two eclipses to have different shapes. SDSS J1524 is, however, an excellent candidate for detailed characterisation using high-speed photometry, as flickering can be averaged out by observing several eclipses.
Since our observations were taken we have become aware that Dr. J. Patterson has independently discovered eclipses in SDSS J1524 6 . An outburst has also been detected by the 6 See http://cbastro.org/ Fig. 9.
Catalina Sky Survey (CSS Drake et al. 2009) using a 0.7 m Schmidt telescope, which allows us to classify this system as a dwarf nova.

Five SDSS cataclysmic variables showing no periodic brightness variations
During our NTT observing run we obtained light curves of five CVs which did not display any clear periodic variability. Their spectra are shown in Fig. 8, the log of observations is given in Table 2, and our light curves are plotted in Fig. 9. Orbital period measurements of these objects will require spectroscopic observations, mostly with a large telescope. We obtained a single 2.75 hr light curve of SDSS J0310 : there is a hint of a brightness variation at 76 min but it is not significant enough to claim a detection. SDSS J0310 appears to outburst quite frequently. It was at magnitude g = 15.5 in the SDSS imaging observations, but at g spec = 22.0 in the subsequent SDSS spectroscopic observations. Szkody et al. then found it to be in outburst during their follow- up spectroscopic observations. An outburst was also observed by Berto Monard 7 , where superhumps were visible with a period of either 0.0643(3) d or its one-day alias of 0.0687(3) d 8 .
We observed SDSS J0743 (Szkody et al. 2006) on the night of 2009/01/23, for 2 hr then another 1 hr after a gap of 2 hr. The light curve shows nothing out of the ordinary. One outburst has been seen for this CV in 2006 October, by the CSS (Drake et al. 2009), where it increased in brightness by at least 5 mag. SDSS J0746 was found to be a CV by Szkody et al. (2006) and is another object which was much brighter when the SDSS observed it photometrically (g = 18.2) than spectroscopically (g spec = 21.2). The CSS has detected two outbursts in which the object became as bright as magnitude 16 (Drake et al. 2009). Nakajima 9,10 and Maehara 11 have reported a measurement of the superhump period of 0.06666(3) d. Our own light curve covers a total 3.75 hr over two observing sequences on the night of 2009/01/23 (Fig. 9). We confirm that SDSS J0746 is a very variable object, but in this case we find only stochastic variations with a total amplitude of 1.3 mag and attributable to the phenomenon of flickering (Bruch 1992(Bruch , 2000. We observed SDSS J0758 (Szkody et al. 2009) for only 2.3 hr in two segments on the night of 2009/01/25. The light curve shows some variation but our data are insufficient to be useful for period measurement. We have a short sequence of spectroscopic observations from 2008 February which indicate a period of about 80 min and will be presented in a later paper. SDSS J0906 was found to be a CV by Szkody et al. (2005) from an SDSS spectrum which shows moderately weak Balmer line emission. Twelve outbursts, of amplitude roughly 3 mag, have been seen by the CSS (Drake et al. 2009), which makes it a frequently-outbursting system. Our 5.75 hr of NTT observations, in three blocks over two nights, show 0.2 mag brightness variations but nothing which is clearly periodic. We have also obtained 4.8 hr of INT photometry of this system (Fig. 10) which shows similar characteristics.

Summary and discussion
We have presented NTT/EFOSC2 and WHT/ACAM time-series photometry of nine CVs identified by the SDSS, from which we find four of them to be eclipsing systems. We also present light curves of five SDSS CVs which do not show identifiable periodic phenomena. Our results are summarised in Table 5. SDSS J0750 has an orbital period of 134.1564 min, which puts it in an interesting situation close to the lower edge of the 2-3 hr period gap in the observed population of CVs (Whyte & Eggleton 1980;Knigge 2006). This period gap is commonly explained through the phenomenon of disrupted magnetic braking (Spruit & Ritter 1983), which requires CVs to migrate through the gap without undergoing mass transfer. A prediction of this scenario is that CVs with orbital periods of 2 hr have secondary star masses essentially the same as those with periods of 3 hr; SDSS J0750 fits the bill perfectly as a 2 hr CV whose donor mass can be measured precisely.
SDSS J0924 has an orbital period of 131.2432 min. It displays strong He II emission and has an extremely faint or missing accretion disc, so is very likely to be a magnetic CV. As magnetic CVs evolve differently from their non-magnetic cousins (Webbink & Wickramasinghe 2002), SDSS J0924 is precluded from investigations of the disrupted magnetic braking scenario. Instead, the shape of the eclipse suggests that it will be possible to measure the radius of the WD directly. Our own observations have a cadence of 15 s and do not resolve the ingress and egress of the WD. Light curves with a substantially higher time resolution, such as can be provided by ULTRACAM , will be necessary. SDSS J1152 and SDSS J1524 are near-identical twins, for which we find orbital periods of 97.5 and 93.6 min and mass ratios of 0.14 and 0.17, respectively. Ingress and egress features of both the WD and the bright spot are clearly visible in our light curves, which makes these objects very well suited to photometric determinations of their physical properties (e.g. Littlefair et al. 2007Littlefair et al. , 2008.
Five of our nine targets did not exhibit identifiable periodic brightness variations; of these SDSS J0746 shows a remarkable flickering activity with an amplitude of at least 1.3 mag. Timeresolved spectroscopy is needed to measure the orbital periods of these objects, which will require 8m-class telescopes.
All four of the orbital periods measured in this work are shorter than the 2-3 hr period gap observed in the general CV 7 vsnet-alert number 8239 8 vsnet-gcvs number 614 9 vsnet-alert number 11069 10 vsnet-outburst number 10022 11 vsnet-alert number 11075 population. This is an increasingly common feature of the SDSS sample of CVs, and further evidence that previous samples are much less complete for the shorter-period faint systems than for the longer-period and generally much brighter objects ). The SDSS CV sample is a unique window into the physical properties and evolutionary history of this faint but dominant population of CVs.