SDSS 1355+0856: A detached white dwarf + M star binary in the period gap discovered by the SWARMS survey
Carles Badenes, Marten H. van Kerkwijk, Mukremin Kilic, Steven J. Bickerton, Tsevi Mazeh, Fergal Mullally, Lev Tal-Or, Susan E. Thompson
aa r X i v : . [ a s t r o - ph . S R ] O c t Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 21 September 2018 (MN L A TEX style file v2.2)
SDSS 1355 + ⋆ . Carles Badenes † Marten H. van Kerkwijk , Mukremin Kilic , Steven J. Bickerton ,Tsevi Mazeh , Fergal Mullally , Lev Tal-Or , Susan E. Thompson Department of Physics and Astronomy and Pittsburgh Particle Physics, Astrophysics and Cosmology Center (PITT PACC), Universityof Pittsburgh, 3941 O’Hara St, Pittsburgh PA 15260, USA Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada. Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, 440 W. Brooks St., Norman, OK, 73019, USA Institute for the Physics of Mathematics of the Universe (IPMU), The University of Tokyo, Chiba 277-8582, Japan School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel SETI Institute/NASA Ames Research Center, Moffett Field, CA 94035, USA
Accepted 0000. Received 0000; in original form 0000
ABSTRACT
SDSS 1355+0856 was identified as a hot white dwarf (WD) with a binary companionfrom time-resolved SDSS spectroscopy as part of the ongoing SWARMS survey. Follow-up observations with the ARC 3.5m telescope and the MMT revealed weak emissionlines in the central cores of the Balmer absorption lines during some phases of the orbit,but no line emission during other phases. This can be explained if SDSS 1355+0856 isa detached WD+M dwarf binary similar to GD 448, where one of the hemispheres ofthe low-mass companion is irradiated by the proximity of the hot white dwarf. Basedon the available data, we derive a period of 0 . ± . . ± .
01 M ⊙ , a secondary mass between 0 .
083 and 0 .
097 M ⊙ , and an inclinationlarger than 57 ◦ . This makes SDSS 1355+0856 one of the shortest period post-commonenvelope WD+M dwarf binaries known, and one of only a few where the primary islikely a He-core white dwarf, which has interesting implications for our understandingof common envelope evolution and the phenomenology of cataclysmic variables. Theshort cooling time of the WD (25 Myr) implies that the system emerged from thecommon envelope phase with a period very similar to what we observe today, and wasborn in the period gap of cataclysmic variables. Key words: binaries: close – binaries: spectroscopic - stars: individual: SDSS1355+0856– white dwarfs.
The common envelope (CE) phase remains one of the keyopen issues in stellar evolution. Several important classesof astrophysical sources go through at least one CE phaseat some point in their lifetime, including cataclysmic vari-ables (CVs), low mass X-ray binaries, detached binary whitedwarfs (WDs), AM CVn stars, and very likely the not-yet-identified progenitors of Type Ia supernovae (SN Ia). Duringthe CE phase, the two components of a binary system comeinto contact and create a shared atmosphere that is ejected ⋆ Observations reported here were obtained at the MMT Ob-servatory, a joint facility of the Smithsonian Institution and theUniversity of Arizona † E-mail: [email protected] through friction, leading to a loss of energy and a dras-tic reduction of the orbital period (Paczynski 1976). Dueto the challenges involved in performing accurate numeri-cal simulations of the CE phase (Taam & Sandquist 2000;Ricker & Taam 2012), theoretical studies have been largelyrestricted to simplified analytic calculations. One prescrip-tion that has gained wide acceptance is the so-called α formalism, where the eponymous parameter represents thefraction of the orbital energy loss that is consumed in un-binding the common envelope (see Webbink 2006, for a re-view), but even the fundamental aspects of this prescrip-tion are still being revised (see Ivanova & Chaichenets 2011;De Marco et al. 2011; Zorotovic et al. 2011b; Davis et al.2012).The most useful constraints on CE evolution come fromstatistical studies of the properties of post-CE binaries: peri- c (cid:13) C. Badenes et al. −16 −16 −16 −16 F l u x [ e r g c m − s − A − ] Teff= 32500Klogg= 7.50SDSS1355+0856 MMT Coadd −60 −40 −20 0 20 40 60 ∆ λ [A]2•10 −16 −16 −16 −16 F l u x + o ff s e t [ e r g c m − s − A − ] H γ H δ H ε H9H10
Figure 1.
Co-added MMT spectrum of SDSS 1355+0856, together with the best-fit atmosphere model ( T eff = 32500 K, log g = 7 . ods, mass ratios, and demographics. Zorotovic et al. (2010)compiled a sample of all post-CE WD+main sequence starbinaries (WDMS) known at the time: 35 from the SDSScatalogue of Rebassa-Mansergas et al. (2010) plus 25 fromthe literature, with periods ranging between 0 .
08 and 21 . α formalism, with α between 0 . . M . .
48 M ⊙ ; Sweigart & Gross1978) are of particular interest, because they anchor the lowvalues of α (Zorotovic et al. 2011a), and they have shorterperiods and less massive secondaries than their C/O coreWD counterparts (Zorotovic et al. 2011b). The final fate ofthese systems is also puzzling, because few, if any, CVs areknown to have a He core WD primary, suggesting they mightevolve into classical novae with exceptionally rare outbursts(Shen et al. 2009).In this paper, we report on SDSS J135523 .
92 +085645 . . In the DR7 SDSS WD catalogue (Kleinman et al. 2009),SDSS 1355+0856 is classified as an isolated DA WD with T eff = 33158 ±
175 K and log g = 7 . ± .
04. To verifythe basic properties of the WD, we performed an indepen-dent fit to a high S/N co-added spectrum obtained afterremoving RV shifts from the MMT exposures without de-tected line emission (see Table 2 and Section 3 for details)using the latest version of the DA WD atmosphere mod-els by Detlev Koester (Finley et al. 1997; Koester 2010).Our fitted parameters are close to those of Kleinman et al.: T eff = 32500 ±
250 K and log g = 7 . ± .
05 (see Figure1). The system was identified as a candidate short-periodbinary by the SWARMS survey from the large RV shifts(roughly a hundred km s − ) found between the four SDSSsub-exposures, which were taken with a temporal baselineof three days.Because SWARMS often detects significant RV shiftsfrom known WDMS binaries, we routinely cross-check allour candidate binaries against the SDSS WDMS cata-logue of Rebassa-Mansergas et al. (2012) and remove anymatches from our follow-up schedule to maximize the effi-ciency in our discovery of short-period double WD systems.SDSS 1355+0856, however does not appear in the SDSSWDMS catalogue. Rebassa-Mansergas et al. (2010) describethe procedure they follow to identify WDMS binaries among Avialable on-line at http://sdss-wdms.org c (cid:13) , 000–000 DSS 1355 + F l u x [ − e r g c m − s − A − ] Teff= 32500Klogg= 7.50SDSS1355+0856 SDSS Coadd
Figure 2.
SDSS spectrum of SDSS 1355+0856, together with thebest-fit atmosphere model ( T eff = 32500 K, log g = 7 . ν [Hz]10 −14 −13 −12 −11 −10 ν F ν [ e r g s − c m − ] ugrizYJHK FUVNUV UKIDSSSDSSGalexBB T=32500 KWD ModelM Star Models0.080.090.10
Figure 3.
Spectral energy distribution for SDSS 1355+0856. Thedotted black line is a blackbody spectrum with T = 32500 K,normalized to match the observed flux in the g band. The solidblack line is a WD model from Holberg et al. (2006), with T eff =35000 K, log g = 7 .
5, and the same normalization. The solid redlines represent low-mass star models from Baraffe et al. (1998),labeled by mass in M ⊙ . the SDSS spectra. A key ingredient is the fitting of all can-didate objects with WD atmosphere models: any spectrathat are well-fit by a WD model in the blue but not in thered are potential WDMS binaries. Rebassa-Mansergas et al.(2010) calculate the χ in the red (7000 to 9000 ˚A) andin the blue (4000 to 7000 ˚A), and flag any spectra with χ r /χ b > . χ r /χ b = 0 .
74. This explains why the systemis not listed in the SDSS WDMS catalogue. For obviousreasons, it is hard to constrain the presence of low-mass M-type companions with hot WD primaries; see Figure 9 ofRebassa-Mansergas et al. (2010) and the accompanying dis-cussion for more details.In addition to the SDSS broadband photometry,SDSS 1355+0856 has NUV and FUV fluxes from
Galex (Morrissey et al. 2007) and Y , J , H , and K IR photome-
Table 1.
Observational Properties of SDSS 1355+0856Parameter ValueR.A. (J2000) 13h 55m 23 . ◦ ′ . ′′ SED (GALEX/SDSS/UKIDSS)
F UV ± µ Jy NUV ± µ Jy u . ± .
01 mag g . ± .
01 mag r . ± .
02 mag i . ± .
02 mag z . ± .
03 mag Y . ± .
02 mag J . ± .
04 mag H . ± .
07 mag K . ± .
15 magSpectral Parameters (MMT) T eff ±
350 Klog g . ± . P . ± . T . ± . K a ± − γ a − ± − K e − ±
13 km s − ∆ γ e − a − ± − Derived Parameters M . ± .
01 M ⊙ M . M .
097 M ⊙ i > ◦ t Cool,WD
25 Myr try from UKIDSS (Lawrence et al. 2007, see Table 1). Thebroadband SED is reasonably well fit by a blackbody spec-trum with T = 32500 K, although the measured fluxes in thered and near IR present small deviations with respect to thebest isolated WD model in the grid of Holberg & Bergeron(2006) ( T eff = 35000 K, log g = 7 .
5, see Figure 3). When theWD model is normalized to match the measured g flux, theSED of SDSS 1355+0856 is brighter than the model by ∼ z and J , and ∼ H . It is hard to ex-plain this flux excess as the contribution of a low-mass stellarcompanion, because the WD model does match the flux inthe K band. A possible explanation for the excess is that theIR data points were taken at different orbital phases, andthat the excess in J and H comes from the irradiated sideof the companion, but given the known issues with the ac-curacy of UKIDSS photometry for objects fainter than ∼ We observed SDSS 1355+0856 with the Dual Imaging Spec-trograph on the 3.5m Astrophysical Research Consortiumtelescope at Apache Point Observatory on February 9 and14, 2010. Variable cloud coverage and pointing issues due c (cid:13)000
5, see Figure 3). When theWD model is normalized to match the measured g flux, theSED of SDSS 1355+0856 is brighter than the model by ∼ z and J , and ∼ H . It is hard to ex-plain this flux excess as the contribution of a low-mass stellarcompanion, because the WD model does match the flux inthe K band. A possible explanation for the excess is that theIR data points were taken at different orbital phases, andthat the excess in J and H comes from the irradiated sideof the companion, but given the known issues with the ac-curacy of UKIDSS photometry for objects fainter than ∼ We observed SDSS 1355+0856 with the Dual Imaging Spec-trograph on the 3.5m Astrophysical Research Consortiumtelescope at Apache Point Observatory on February 9 and14, 2010. Variable cloud coverage and pointing issues due c (cid:13)000 , 000–000 C. Badenes et al. to strong winds resulted in extremely noisy spectra. ClearRV shifts were apparent in some spectra, but in other casesthe line cores had strange shapes, probably because of in-adequate pointing, and the RVs could not be determinedwith confidence. Because of these issues, we revisited SDSS1355+0856 with the 6.5m Multiple Mirror Telescope (MMT)at Mt. Hopkins observatory. We used the Blue ChannelSpectrograph to obtain moderate resolution spectroscopyof SDSS 1355+0856 on March 19 and 21, 2010. We op-erated the spectrograph with the 832 line mm − gratingin second order and a 1 ′′ slit, providing wavelength cov-erage 3600 ˚A to 4500 ˚A and a spectral resolution of 1.0˚A. We obtained all observations at the parallactic angle,with a comparison lamp exposure paired with every ob-servation. We flux-calibrated using blue spectrophotomet-ric standards (Massey et al. 1988). Our observing and re-duction procedures were similar to the ones described inKilic et al. (2010). The superior quality of the MMT datarevealed weak but clear emission lines in some of the spectra,but no evidence of line emission in others (see Figure 4). The behaviour of the line emission revealed by the MMTdata and shown on Figure 4 implies that the companionof SDSS 1355+0856 cannot be a degenerate object, andis probably a faint main sequence star or a brown dwarf.The absence of line emission in some of the spectra canbe understood if the system is a binary similar to GD 448(Marsh & Duck 1996), where one hemisphere of the low-mass main sequence companion is irradiated by the proxim-ity of the hot WD. This results in line emission only duringthe phases in which most of the irradiated side of the sec-ondary is visible, i.e. when the RV of the primary is increas-ing between its minimum and its maximum values. In thisscenario, the secondary would not contribute much flux tothe red part of the SDSS spectrum (Figure 2), especiallyif most or all of the SDSS sub-exposures were taken duringphases in which the irradiated hemisphere was not facingthe observer.To verify the irradiated companion hypothesis, we fittedall the MMT spectra with a two-component model consist-ing of the best-fit WD atmosphere model from the Koestergrid (absorption component), and a set of six equal-strengthGaussian lines in the Balmer series, from H γ to H10 (emis-sion component). For these fits, we scanned over possibleRVs v a and v e for the absorption and emission components,respectively. For each pair of RV values we fitted for theemission to absorption flux ratio, F e /F a (forced to be pos-itive), as well as an overall normalisation, described as athird-order polynomial in wavelength. We then determinedthe best-fit values of the RVs and their uncertainties by aparabolic fit to the χ surface around the best-fit location,taking F e /F a and its uncertainty from the fit to the nearestgrid point. For all spectra, we found good fits, with reduced χ values around 0.8. The resulting values are listed in Table2, where we have corrected all times and radial velocities tothe barycenter of the Solar System.In seven of the 19 spectra (MMT 5, 6, 7, 8, 12, 13, and18; used to construct the spectrum in Fig. 1), our proce-dure did not detect any line emission: at the best-fit v a , the addition of an emission component made for a worse fit atany value of v e . Since random chance should lead to somenon-zero contributions from the emission component even inspectra that can be described by the absorption componentalone, we inspected these fits more closely. We concludedthat the absence of spurious detections of an emission com-ponent even at unreasonable values of v e results from ourbest-fit WD model slightly underpredicting the depths ofthe line cores (see Fig. 1), so that the best-fit emission com-ponent would have a negative flux, which our fit routinedoes not allow. This is a minor effect that we did not try tocorrect for, but we note that it implies that our F e /F a fluxratios are slightly biased towards low values.For the spectra with clear emission (MMT 1, 2, 3, 4,9, 10, 11, 14, 15, 16, and 17), we find that the strength ofthe emission lines varies quite a bit, with the lines appear-ing stronger at superior conjunction of the companion (seeFigure 4 for an ilustration of this variation in the case ofH γ - other lines show similar behaviour). The overlap be-tween the cores of the emission and absorption lines makesthe determination of the component RVs somewhat chal-lenging, which results in measurements that are more noisythan would be expected in a single-lined system with spectraof similar quality.We used the RVs to derive orbital solutions of the form v = γ + K sin 2 π ( t − T ) /P for each component. To get thebest possible constraints on the binary period, we fitted theemission and absorption RVs jointly, assuming that theyhave the same period and anomaly, but are in antiphase.In our procedure, we scan a grid in period, at each pointfitting for T , the semi-amplitude of the absorption compo-nent K a , its systemic velocity γ a , the semi-amplitude of theemission component K e , and the difference in systemic ve-locity ∆ γ = γ e − γ a . Our best-fit orbital solution, shownin Figure 5, has a reduced χ of 1.97 (for 25 d.o.f.), i.e.it is formally not acceptable. This is likely due to inac-curacies of the spectral model. Since the residuals had noobvious phase dependencies, we compensated for the poorquality of the fit by increasing all errors by √ .
97. We finda period of 0 . ± . T = 55275 . ± . χ minima in the periodogramme (see Figure 6). However,we can only exclude the alias at 0.12112 d at the 2 σ level(the two fits differ by ∆ χ = 3 . K a = 64 ± − and K e = − ±
13 kms − for the absorption and emission components, respec-tively. The systemic velocity for the absorption componentis γ a = − ± − , and that for the emission compo-nent identical within the uncertainties, ∆ γ = − ±
18 kms − . This orbital solution nicely confirms the irradiated com-panion hypothesis. The spectra without detected line emis-sion are only found between phases 0.25 and 0.75, in thepart of the orbit where the RV of the absorption compo-nent is decreasing and the irradiated side of the companionis partially or totally occulted by the rest of the star. Out-side of this phase range, a larger fraction of the irradiatedside of the companion is in view, and the line emission canbe easily detected. This scenario makes a specific predic-tion about the strength of the line emission, which should c (cid:13) , 000–000 DSS 1355 + −1000 −500 0 500 1000Velocity [km s −1 ]0.00.51.01.52.02.53.03.5 N o r m a li z ed F l u x + o ff s e t MMT 18MMT 11MMT 17MMT 10MMT 16MMT 4MMT 15MMT 3MMT 14MMT 2 −1000 −500 0 500 1000Velocity [km s −1 ]0.00.51.01.52.02.53.03.5 N o r m a li z ed F l u x + o ff s e t MMT 1MMT 0MMT 9MMT 8MMT 7MMT 6MMT 5MMT 13MMT 12
Figure 4.
MMT spectra of SDSS 1355+0856 around the H γ line, ordered by phase (top to bottom and left to right). No line emissionwas detected in spectra MMT 18, 12, 13, 5, 6, 7, and 8. The red line is our best-fir model (see Section 3 for details). peak around phase 0, fall down gradually as the system ap-proaches quadrature (phase 0.25), stay low until quadratureis reached again (phase 0.75), and then increase again. Thisis indeed the behaviour of the F e /F a ratio in the MMT spec-tra of SDSS 1355+0856 when it is folded through the best-fitorbital solution (see Figure 7). The numerical value of thisratio is arbitrary, because it depends on the normalizationof the emission and absorption models that we used to fitthe spectra, but qualitatively its orbital evolution matchesthat of the equivalent width in the line emission of GD 448(Marsh & Duck 1996; Maxted et al. 1998). For GD 448, theequivalent widths of the emission lines do not go to zero be- tween phases 0.25 and 0.75, but that is expected given therelatively low orbital inclination of the system (29 . ◦ ± . ◦ Maxted et al. 1998). The absence of detectable line emis-sion during these phases and the larger RVs imply a higherinlcination for SDSS 1355+0856.
For the values of T eff and log g determined from the co-added SDSS spectrum, the models of Panei et al. (2007) forHe WDs give a mass of M = 0 . ± .
01 M ⊙ , and those c (cid:13) , 000–000 C. Badenes et al.
Table 2.
Spectroscopic RVs for SDSS 1355+0856 from the MMT spectraSpectrum MJD (bar.) v a (km s − ) v e (km s − ) F e /F a MMT 0 55275.3824 − . ± . . ± . . ± . − . ± . . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . − . ± . . ± . . ± . . ± . − . ± . . ± . − . ± . − . ± . . ± . . ± . . ± . . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . . ± . . ± . −400−300−200−1000100200300 R V [ k m s − ] SDSS 1355+0856 P=0.1143 dK a =64 km s −1 ; K e =261 km s −1 R e s i dua l s Figure 5.
Orbital solution for SDSS 1355+0856. The red circlesrepresent the RVs of the absorption component (WD), and theblue squares represent the RVs of the emission component in thespectra with F e /F a >
0. The value of γ a ( −
23 km s − ) has beenmarked with a horiozontal dotted line. of Holberg & Bergeron (2006) for C/O WDs give a slightlylower value of M = 0 . ± .
01 M ⊙ . Since these valuesare both below the ∼ .
48 M ⊙ threshold for C ignition in astellar core (Sweigart & Gross 1978), we conclude that theprimary in the SDSS 1355+0856 system is most likely a hotHe-core WD, and we adopt the mass given by the He-coremodels (however, see Prada Moroni & Straniero 2009, forthe possibility that it might be a hybrid CO-He WD).Even without considering the RVs measured for the lineemission component, the mass of the companion is tightlyconstrained by the broadband SED of the system and themass function of the WD primary derived from the absorp-tion RVs. A quick comparison between the SED shown inFigure 3 and the theoretical models of Baraffe et al. (1998)rules out companions more massive than ∼ . ⊙ , whichwould lead to noticeable excess flux in the IR, especiallyin the J , H , and K bands. More formally, we can set an χ Figure 6.
Periodogramme for the orbital solution of SDSS1355+0856, with indication of the best-fit period (0 . E m i ss i on t o A b s o r p t i on R a t i o Figure 7.
Behaviour of the F e /F a ratio in the MMT spectra ofSDSS 1355+0856 as a function of orbital phase. The dashed linerepresents the model light curve discussed in Section 4.c (cid:13) , 000–000 DSS 1355 + upper limit on M by requiring that the K -band flux pre-dicted by the stellar models does not exceed the observedflux from UKIDSS by more than a factor 10. This generoustolerance should accomodate both the issues identified withtheoretical low-mass stellar models (Casagrande et al. 2008;Kraus et al. 2011) and the uncertainties associated with theUKIDSS photometry (Leggett et al. 2011). By interpolat-ing on the mass grid of the Baraffe et al. (1998) models,we determine a conservative upper limit of 0 .
097 M ⊙ for M . The mass function for the primary also puts constraintson the companion mass, requiring M sin i = 0 . ± . ⊙ , where the error bar reflects the observational uncer-tainty in the values of K and M . From these limits, wecan conclude that the nondegenerate companion of SDSS1355+0856 is a low-mass main sequence star with a massbetween 0 .
083 and 0 .
097 M ⊙ , above the upper mass limitfor brown dwarfs. The star should have a spectral type be-tween M5 and M8 (Baraffe & Chabrier 1996), and be fullyconvective (Reiners & Basri 2009). Our faliure to detect asignificant offset between the RV curve of the WD and thatof the line emission from the companion (∆ γ = − ±
18 kms − in our fit) does not allow us to put further constraintson the component masses using gravitational redshift, al-though this should be possible with data of higher quality(see discussion in Maxted et al. 1998, their Section 3.4, forthe case of GD 448).The RV curve that we have measured for the line emis-sion provides an independent confirmation of our estimatefor the companion mass. To interpret these RV measure-ments we need to account for the fact that the line emissiondoes not originate from the entire surface of the compan-ion, so the center of light for the line emission does notcorrespond to the center of mass for the star, but is shiftedtowards the WD. This means that the measured semiampli-tude of the emission component, K e , is only a lower limitto the true semiamplitude of the RV curve of the com-panion ( K ). This effect has been observed in other sys-tems with hot WD primaries like GD 448 (Marsh & Duck1996) and SDSS J212531.92 − K e /K = 1 − f ( R /a ), where a is the orbital radius ofthe companion around the barycentre of the system, R is the companion radius, and f is a dimensionless factorthat depends on the extent of the irradiated area on thesurface of the companion and on the orbital inclination ofthe binary (van Kerkwijk et al. 2011). In practice, the or-bital inclination has a very small effect on the value of f for i & ◦ (MunozDarias et al. 2005; van Kerkwijk et al.2011). We can estimate f by assuming the emission fromthe irradiated hemisphere is proportional to the incidentflux from the primary. For an irradiating source at a largedistance, the integral has an analytic solution at quadra-ture, and f = 3 π/
16 = 0 .
59, with higher values of f If thestars are closer together. For SDSS 1355+0856, we expect R ≃ . R ⊙ (for a very low-mass M dwarf, Baraffe et al.1998), a ≃ . R ⊙ (for a total mass of ∼ . M ⊙ ), andthus R /a = 1 /
8. For that value, numerical integrationyields f = 0 .
66 at quadrature, with a range of ± .
02 for1 / < R /a < /
6. From Figure 7, one sees that such a
80 60 40 20 00.060.080.100.120.14 80 60 40 20 0i [degrees]0.060.080.100.120.14 M [ M s un ] i > 57 o (Orbit) M < 0.097 M sun (SED)Primary RVsSecondary RVs Figure 8.
Observational constraints on M and i for SDSS1355+0856. The horizontal dashed line is the upper limit on M derived from the SED (Figure 3). The vertical dashed line is thelower limit on i imposed by the measured value of K e . The shadedregions above and to the right of these lines are forbidden by thedata. The solid red line represents the constraint on M sin i fromthe mass function of the primary, with the dotted red lines indi-cating standard 1 σ uncertainties. The solid blue line representsthe constraint from the measured value of K e and the light curvemodel shown in Figure 7. The (rather large) uncertainty on thisconstraint is not shown. model reproduces the flux ratio between the emission andabsorption components in our spectral fits quite well. Tryingdifferent inclinations, we find that the absence of emissionat phases 0.3–0.7 requires an inclination i & ◦ (for smallerinclination, the flux at phase 0.3 would exceed 20% of themaximum flux). After some algebra, we can write an expres-sion for M which depends strongly on measured parametersand weakly on R and sin i : M = M K K e + 2 πf sin i ( R /P ) . (1)For the nominal values of M , f , K , and K e , and i = 90 ◦ ,this yields M = 0 .
10 M ⊙ , which agrees quite nicely with ourconstraints from the mass function of the primary and theSED. Unfortunately, the error bars on K and K e are largeenough that this method cannot refine our M estimate anyfurther, just confirm it. In any case, the measured value of K e does put an upper limit on the orbital inclination,sin i > K + K e (2 πG ( M + M ) /P ) / , (2)which translates to i > ± ◦ (or a lower limit of 57 ◦ ), withthe uncertainty on the inclination angle is again dominatedby the errors on K and K e . The limit is in line with ourexpectations from the mass constraints and the emission linelightcurve. We summarize our constraints on M and i inFigure 8.The picture that emerges from our analysis of SDSS1355+0856 is that of a binary similar to GD 448(Marsh & Duck 1996; Maxted et al. 1998). The two sys-tems have almost identical component masses and period,but SDSS 1355+0856 has a somewhat higher inclination,leading to higher RVs and no detectable line emission be-tween phases 0.25 and 0.75. The cooling age of the WD inSDSS 1355+0856 is ∼
25 Myr (Panei et al. 2007), abouthalf the value for GD 448. This cooling time is much shorter c (cid:13) , 000–000 C. Badenes et al. than both the thermal timescale of the companion ( ∼ ∼ q (0 .
21) impliesthat mass transfer will be stable (Paczynski 1971; King et al.1996). At this point, SDSS 1355+0856 will become one of therare CVs with likely He-core WD primaries, possibly leadingto a few exceptionally long classical nova events (Shen et al.2009). The period and component masses of the systemare such that it will contribute to future demographic con-straints of CE evolution (see discussion in Zorotovic et al.2011b), but we leave that analysis for further work.
ACKNOWLEDGMENTS
We wish to thank Detlev Koester for making his WD at-mosphere models available to us. Balmer/Lyman lines inthe Koester WD models were calculated with the modifiedStark broadening profiles of Tremblay & Bergeron (2009),kindly made available by the authors. We are indebted toScott Kleinman, who made his WD catalogue available tous in advance of publication. We are grateful to EduardoBravo, Avishay Gal-Yam, Shri Kulkarni, Dan Maoz, ThomasMatheson, Gijs Nelemans, Benny Trakhtenbrot, and SharonXuesong Wang for discussions.Funding for the SDSS and SDSS-II has been providedby the Alfred P. Sloan Foundation, the Participating In-stitutions, the National Science Foundation, the U.S. De-partment of Energy, the National Aeronautics and SpaceAdministration, the Japanese Monbukagakusho, the MaxPlanck Society, and the Higher Education Funding Councilfor England. The SDSS Web Site is .The SDSS is managed by the Astrophysical Research Con-sortium for the Participating Institutions. The Participat-ing Institutions are the American Museum of Natural His-tory, Astrophysical Institute Potsdam, University of Basel,University of Cambridge, Case Western Reserve Univer-sity, University of Chicago, Drexel University, Fermilab,the Institute for Advanced Study, the Japan ParticipationGroup, Johns Hopkins University, the Joint Institute forNuclear Astrophysics, the Kavli Institute for Particle As-trophysics and Cosmology, the Korean Scientist Group, theChinese Academy of Sciences (LAMOST), Los Alamos Na-tional Laboratory, the Max-Planck-Institute for Astronomy(MPIA), the Max-Planck-Institute for Astrophysics (MPA),New Mexico State University, Ohio State University, Uni-versity of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and theUniversity of Washington.
Facilities:
MMT (Blue Channel Spectrograph); ARC3.5m Telescope (Dual Imaging Spectrograph).
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