Astronomy&Astrophysicsmanuscriptno.30038_ap (cid:13)cESO2017 January12,2017 LettertotheEditor X-ray orbital modulation of a white dwarf accreting from an L dwarf The system SDSSJ121209.31+013627.7 B.Stelzer1,D.deMartino2,S.L.Casewell3,G.A.Wynn3,andM.Roy3 1 INAF-OsservatorioAstronomicodiPalermo,PiazzadelParlamento1,I-90134Palermo,Italy e-mail:[email protected] 2 INAF-OsservatorioAstronomicodiCapodimonte,SalitaMoiariello16,I-80131Napoli,Italy 7 3 DepartmentofPhysicsandAstronomy,UniversityofLeicester,Leicester,LE17RH,UK 1 0 ReceivedXXX;acceptedXXX 2 n ABSTRACT a J InanXMM-NewtonobservationofthebinarySDSSJ121209.31+013627.7,consistingofawhitedwarfandanLdwarf,wedetectX- 1 rayorbitalmodulationasproofofaccretionfromthesubstellarcompanionontothemagneticwhitedwarf. Weconstrainthesystem 1 geometry (inclination as well as magnetic and pole-cap angle) through modelling of the X-ray light curve, and we derive a mass accretionrateof3.2·10−14M⊙/yrfromtheX-rayluminosity(∼3·1029erg/s).FromX-raystudiesofLdwarfs,apossiblewinddriven ] fromahypothesizedcoronaonthesubstellardonorisordersofmagnitudetooweaktoexplaintheobservedaccretionrate,whilethe R radiusoftheLdwarfiscomparabletoitsRochelobe(0.1R ),makingRoche-lobeoverflowthelikelyaccretionmechanisminthis ⊙ S system. . h Keywords. X-rays:binaries,Accretion,stars:whitedwarfs,stars:browndwarfs,stars:individual:SDSSJ121209.31+013627.7 p - o 1. Introduction donor mass of ∼ 0.06M . This means that the systems that r ⊙ t have evolved beyond the period minimum, so-called period- sSensitive wide-field surveys such as SDSS and UKIDSS have a bouncers, have a substellar donor. Binary population synthe- boostedthenumberofknownwhitedwarf(WD)main-sequence [ sis revealedthatperiod-bouncingWDLD binariesare expected (MS) binaries. In the majority of these systems the non- to be the greater portion(∼ 70%) of the whole CV population 1degeneratecomponentisanMdwarf. (Howelletal.2001). Thepredictedhighabundanceofsuchsys- v Over 2000 systems consisting of a WD and an tems is at oddswith the very low detectionrate. Systems with 4 9M dwarf (henceforth WDMD binaries) are known averylow-masscompanionaredifficulttoidentifybecausethe (Rebassa-Mansergasetal. 2013), but only about a dozen 8 contrast between the WD and L dwarf at optical and infrared binariesthatconsistofaWDandanLdwarf(WDLDbinaries) 2 wavelengthsislow.OnlyafewbinariescomposedofaWDand 0(see Sect. 3 for accreting systems and Casewell 2014, for aBDareconfirmedspectroscopically. .a summary of detached systems). This might be due to the 1difficulty of detecting such faint very late-type companions in The type of binary interaction in close WD / MS systems 0 is tied to the evolutionary state. During the CV phase, ac- thespectralenergydistribution(SED)ofWDs. 7 cretion occursthroughRoche-lobeoverflow, while in detached Similar to their higher-mass siblings, the WDMD binaries, 1 systems wind accretion may take place. A handful of sys- :theWDLDsystemscomprisebothwide(separationtenstothou- vsandsofAU)andclosebinaries(period<10h). Onlyahandful tems showing very weak mass accretion (< 10−13M⊙/yr, e.g. i Schmidtetal. 2007) were defined as low accretion rate polars Xofthemareclose systems(period∼100min)in whichthelow- (LARPs; Schwopeetal. 2002). However, in most of them the masscompanionmusthavesurvivedacommon-envelopephase r donor is underfilling its Roche lobe, meaning that they are a(Nordhaus&Spiegel 2013). The progenitors of wide systems in a pre-CV phase, and they must be accreting from a wind composedofWDandbrowndwarf(BD),theAU-scaleBD-MS (Schwopeetal.2009). Magneticsiphonsthatchanneltheentire binaries,arealsorarelydiscovered,andtheydefinetheso-called wind of the donorontothe WD have been proposedto explain ‘brown dwarf desert’ (Marcy&Butler 2000), suggesting that thisclassofsystemswithastronglymagneticWD butweakor systems composed of WD and BD form rarely. However, the absentX-rayemission(Webbink&Wickramasinghe2005). much more frequent WDMD binaries evolve into cataclysmic variables (CVs), and subsequently, both the binary separation Accretion rates of WD binaries can be inferred from the andthedonormassdecreaseovertime,whichconvertsthedonor X-ray luminosity or from the broad-band UV to optical/near- intoaclose-insubstellarobject. IRspectralenergydistribution(SED)arisingfromtheaccretion Whenthedonorstarleavesthermalequilibriumandstartsto disk. Hα emission provides only an upper limit to the accre- expand in response to its mass loss, the orbital evolution of a tionrate, sincethislinecanalsohavea significantcontribution CV reverses. The period minimum that represents this change fromthedonorstar’schromosphericactivityoritsirradiationby is observed and theoretically predicted to be at P ∼ 82min the WD. For the same reason, detection of X-rays at low lev- orb (Gänsickeetal. 2009; Kniggeetal. 2011), corresponding to a els(L ≤ 1029erg/s)fromWDbinarieswithM-dwarfdonorsis x Articlenumber,page1of5 not sufficient to diagnose accretion. However, magnetic activ- Table1.X-raycountrateandpulsedfraction(PFsine)fromasinefitfor EPIC/pndataindifferentenergybands. itydropssharplyatlate-Mspectraltypes(e.g.Westetal.2004), andthecoronalX-rayemissionlevelsofLdwarfsaregenerally below the current sensitivity limits (Stelzeretal. 2006). Only Energy Band netsourcerate PF one verynearbyL dwarf hasbeen detected in X-raysso far, at sine [keV] label [cts/s] aleveloflogL [erg/s]= 25.4(Audardetal.2007). Therefore, x 0.2−12.0 B 0.0615±0.0021 1.0 anX-raydetectionofaWDLDbinaryclearlypointsataccretion, 0.2−1.0 S 0.0323±0.0015 0.94±0.03 whetherthroughwindorRoche-lobeoverflow. Onlyoneshort- 1.0−2.0 M 0.0188±0.0012 0.93±0.05 periodWDLDsystemhasbeendetectedasX-rayemittersofar, 2.0−12.0 H 0.0104±0.0009 1.0 SDSSJ121209.31+013627.7(SDSS1212), which has been re- portedasaweakSwiftsourcebyBurleighetal.(2006). SDSS1212is a magnetic WDLD binary (spectral type DA Binsize = 300s +L5/L8)withanaveragefieldstrengthof7MG(Schmidtetal. 0.20 2005;Farihietal.2008).Schmidtetal.(2005)foundnarrowHα s/s] 0.15 0.2−12.0 keV (broad) emission with periodic radial velocity variation (P ∼ 90min) [ct 0.10 andlargeamplitudeconsistentwithanoriginintheLdwarf’sir- ate 0.05 radiatedatmosphere. Photometricvariabilityatthesameperiod R 0.00 athnadttrhoeurgehilsyainhoatnstpi-opthoansethweiWthDthseuHrfaαceem(Bisusriloenigahlseotailn.d2i0c0at6e)s. s/s] 00..1250 0.2−1.0 keV (soft) ct 0.10 The Ks -band light curve was shown by Debesetal. (2006) to e [ 0.05 be more consistent with cyclotron emission from a magnetic at R 0.00 pole than with irradiation of a companion star. The authors atolsothenoetxepdeactecdleaSrEeDxcoefssthienWthDe,HwahnicdhKwsabsasnpdesctwroisthcorpeiscpaellcyt s/s] 00..1250 1.0−2.0 keV (medium) ct 0.10 confirmed by Farihietal. (2008) to be due to a late-L dwarf. e [ 0.05 Burleighetal.(2006)determinedthatinan11kslongSwiftob- at R 0.00 servationSDSS1212hadacountrateof2.6·10−3cts/s. Theyfit- 0.20 teelds,tbhuetSthweifatcXc-rreatiyonspmecetcrhuamniwsmith(wvairnidouvssoRnoec-hteemlopbeera)tcuoruelmdondo-t cts/s] 00..1105 2.0−12.0 keV (hard) be established. The photon statistics were also insufficient for e [ 0.05 studyingtheX-raylightcurve. Rat 0.00 Here we report on an XMM-Newton observation of 3.2 SDSS1212fromwhichwe unambiguouslyconfirmthatitisan s] B band s/ accreting WDLD system. We derive an improved estimate for [ct 2.5 itsmassaccretionrateanddiscusstheresultintheframeworkof e evolutionaryscenariosforthissystem. Rat 1.8 0 5000 10000 15000 20000 25000 Time [s] 2. XMM-Newtonobservationsandanalysis XMM-Newton observedSDSS1212on 6 June 2015for 22ksec (obs-id0760440101) with all EPIC instruments using the thin filterandwiththeOpticalMonitor(OM)infastmodeusingthe Fig. 1. OM B-band light curve and EPIC/pn X-ray light curve of SDSS1212with1σerrorsinfourenergybandsaslabelledintheup- Bbandfilter. per left of each panel. X-ray light curves represent the background- WerestricttheanalysistoEPIC/pn,whichprovidesthehigh- subtracted source signal (black) and for comparison the background estsensitivityoftheEPICdetectors. Thedataanalysiswascar- signal(red).Thebinsizeis300s. riedoutwithXMM-Newton’sStandardScienceAnalysisSystem (SAS)version15.0.0. Theobservationisnotaffectedbyflaring particlebackground,thereforeweusedthefullexposuretimeof 22ksecfortheanalysis.Wefilteredthedataforpixelpatterns(0 epiclccorr,whichalsocorrectsforinstrumentaleffects.Wethen ≤pattern≤12),qualityflag(flag=0),andeventschannels(200 barycentre-correctedthephotonarrivaltimesusingtheSAStool ≤PI≤15000). Sourcedetectionwasperformedinthreeenergy barycen. bands:0.2−1.0keV(S),1.0−2.0keV(M),and2.0−12.0keV(H) Thelightcurveshowsaclearperiodicmodulationinallen- usingacustomizedprocedurebasedonthestepsimplementedin ergy bands with larger amplitude for softer emission (Fig. 1). theSAStaskedetect_chain. ThenetEPIC/pnsourcecountrates The modulation does not appear to be sinusoidal, displaying aregiveninTable1. WenotethatSDSS1212isalsodetectedin on-off behaviour that is typical of strongly magnetized accret- theMOScamerasatanetcountrateof0.0167±0.0010cts/sand ing WDs or AMHer systems (Cropper 1990). In the mini- 0.0178±0.0010cts/sinthebroadbandforMOS1andMOS2, mum the counts drop to zero, suggesting that the area of ac- respectively. cretion, the pole cap, is completely occulted by the WD. All Forthespectralandtemporalanalysisweallowedonlypixel energy bands show flickering typical of X-ray emission from patternswithflag≤4. We definedacircularphotonextraction CVs. Lomb-Scargle periodogram analysis of the broad band region with radius of 30′′ centred on the EPIC/pn source posi- (0.2−12keV)lightcurveyieldsaperiodofP =88.3±0.6min. orb tion.Thebackgroundwasextractedfromanadjacentcircularre- This value and its 1σ error were derived with a bootstrap ap- gionwithradiusof45′′onthesameCCDchip.Thebackground proach from 5000 simulated broad band light curves drawn subtractionofthelightcurvewascarriedoutwiththeSAStask randomly from the count rates and errors. This period is in Articlenumber,page2of5 B.Stelzer etal.:X-rayorbitalmodulationofawhitedwarfaccretingfromanLdwarf Table 2. Best-fit parameters for the EPIC/pn spectrum of SDSS1212and values corresponding to upper and lower 90% confidenceranges. e at 2.5 nt r tbabs·apec ou 2 N kT Z c H zed 1.5 χ2red(dof) [cm−2] [keV] [Z⊙] ali 1.13(22) 2.35.1·1020 2.623.58 0.110.44 m 1 0.0 1.99 0.0 or N V 0.5 e k 2 0 1 0.1000 0.2- 0 0.5 1 1.5 2 Phase V ke0.0100 s/ s/ nt Fig.2. Barycentre-correctedX-ray(EPIC/pn0.2−12keV)lightcurve ou ofSDSS1212foldedusingtheephemerisofBurleighetal.(2006)and m.c0.0010 theperioddeterminedfromtheX-raysignal.Thebinsizeis450s.The or n best-fitmodelisshowninred. err0.00012 d)/ 1 mo 0 good agreement with published periods for the Hα emission − −1 bs −2 (93.6±14.4min; Schmidtetal. 2005), the near-IRphotometry o ( 0.3 0.5 1.0 2.0 3.0 (87.84±1.44min;Debesetal.2006),andtheopticalphotometry Energy [keV] (88.428±0.001min;Burleighetal.2006). Tofirstapproximationwefittedasinusoidtothelightcurve Fig.3. Time-averaged EPIC/pnX-rayspectrumof SDSS1212with fromwhichwedeterminedthepulsedfraction(PF)takinginto best-fittingone-temperatureapecmodel(solidblueline)andresiduals. account the uncertainties on y-offset and amplitude of the sine curve. Thevaluesobtainedfortheindividualenergybands(see Table1)areconsistentwiththe100%PFobservedinpolars. The phase-folded X-ray light curve of SDSS1212is dis- theabundanceisfixedtothevalueobtainedfromthe1T-model, played in Fig. 2 together with a geometric modelbased on the theadditionallow-temperaturecomponentturnsouttobecom- one presented by Wynn&King (1992) and Brinkworthetal. pletelyunconstrained. Weconcludethattheobservedspectrum (2004),whichdescribesdirectaccretionfromadonorontoaWD does not provide information on a possible multi-temperature magnetosphere with a post-shock region characterized through environment. There is therefore no evidence for an additional the anglebetweenmagneticand rotationaxis(m), thepole-cap lower temperature blackbody component such as the one typi- openinghalf-angle(b),andthesysteminclination(i).Weranthe cally used to represent a soft excess in X-ray spectra of polars model over a range of parameter space to determine the likely and intermediate polars (<< 0.1keV, see e.g. Beuermannetal. valuesfortheseangles,assumingasinglepoletoberesponsible 2012;Bernardinietal.2012). Suchacomponentwouldalsobe for the variation. The modelling was performed on the X-ray physicallyunacceptableasitwouldbelocallysuper-Eddington. light curve with a bin size of 150s. We found 80◦ & i & 70◦, We showinFig.3theobservedEPIC/pnspectrumtogether 110◦ & m & 100◦, andb ≃ 30◦. Thesevaluesmeetthecriteria with the 1T-model. The total galactic absorption in the direc- fortheself-occultationasinWynn&King(1992)andreferences tionofSDSS1212is∼2·1020cm−2(Dickey&Lockman1990), therein.Weconfirmedthesizeoftheaccretionregionusingdif- consistentwiththevaluedeterminedfortheEPIC/pnspectrum. ferentbinningswithlowertime-resolution.Wealsoexploredthe Giventhedistanceof120pc(Burleighetal.2006),theintrinsic effectsofaverticalextentofthecolumnupto1R obtaining absorptionofthesourcemustbeverylow. WD anupperlimitof0.2R andnomajoreffectonthevaluesofthe The X-ray flux is 1.510−13erg/cm2/s, taking into account wd otherparameters. Asmallverticalextentoftheemissionregion the bolometric correction to the 0.001 − 100keV range, and is also suggestedby the factthat the fluxdropsto zeroand the 1.310−13erg/cm2/sforthe0.2−12keVrange.Thislattervalue ingressandtheegressaresteep. is similar to the value obtained by Burleighetal. (2006) from The EPIC/pn spectrum of SDSS1212was first fitted with theSwiftspectrum(1.210−13erg/cm2/s)foranabsorbed1T fit. single-component models: a power law, a black body, or an DespitethelowstatisticsoftheSwiftdata,thesemeasurements, optically thin model, none of which adequately describes the taken about one decade apart, indicate that the X-ray source spectral shape. When we add a simple absorber (tbabs) and is rather stable in time. With the distance (d = 120pc) from leave the abundance free to vary, the thermal apec model pro- Burleighetal.(2006),wedeterminethebolometricX-raylumi- vides a reasonable fit. However, the 90% confidence level of nosity to logL [erg/s] = 29.4. From the X-ray luminosity we x the abundance is compatible with zero, which is an unphysi- derivea mass accretion rate of M˙ ∼ 2.610−14M /yr; where acc ⊙ cal result (see Table 2). We also tested representations with we have used a slightly higher WD mass than Burleighetal. two spectral components. In particular, the spectrum is com- (2006)(0.8M ;seeSect.3forajustification)andacorrespond- ⊙ patible with an absorbed two-temperature (2T) thermal model inglysmallerradius(R =7·108cm).ThisvalueforM˙ only WD acc [tbabs· (apec + apec)], whichyieldsa better χ2 than the one- includesthekineticenergyconvertedintoX-rayluminosity.The red temperature(1T)model. However,similartothecaseofthe1T- valueishigherwhencontributionsfromcyclotronemissionand model,theabundancecannotbeconstrainedbythefit.If,inturn, luminosityofthehotspotareconsidered. Articlenumber,page3of5 The X-ray count rate in the minimum of the light curve thatwemeasuredalowerlimitof3·10−14M /yr). Thisleaves ⊙ (0.35 ≤ φ ≤ 0.65) is 0.0046cts/s with a standard deviation of Roche-lobe overflow as the most likely origin for the mass 0.0086cts/s. ThiscorrespondstoanupperlimitoftheX-raylu- transfer. minosity. Withthecount-to-fluxconversionfactorderivedfrom Farihietal. (2008) estimated the L-dwarf radius as 0.09R ⊙ thetime-averagedX-rayspectrum,weobtainlogL [erg/s]= and calculated the Roche lobe to be R = 0.11R . However, x,min L ⊙ 27. Thisvaluecanbeunderstoodtorepresenttheupperlimitto this is based on the assumption that the WD mass is 0.6M , ⊙ anypossibleresidualemission. a value typical of a non-magnetic, isolated WD. There is evi- B-bandphotometryacquiredwiththeOMinfastmode,si- dence that WDs in CVs have higher masses than single WDs multaneously with the X-ray observations, was extracted with and those in detached systems (Zorotovicetal. 2011). More- the SAS task omfchain, and the time series was barycen- over, single magnetic WDs have also been found to be more tre corrected. A Lomb-Scargle periodogram analysis did not massive than non-magnetic WDs (Ferrarioetal. 2015). Con- yield a significant periodicity, and when folded on the X- sideringthatthenon-magneticCVSDSS1433+1011–withan ray period, no phase-related variability is seen (Fig. 1, lowest L-dwarf companion – has a mass of 0.868M (Littlefairetal. ⊙ panel). At the time of the OM observation, SDSS1212was at 2008,HernándezSantistebanetal.2016),assumingamassof∼ B =18.28±0.08mag, which is consistent with the SED pro- 0.8M forSDSS1212isthereforeplausible. Forthisvalue,us- OM ⊙ videdbyDebesetal.(2006)andwiththeu′ andg′ photometry ingEq.5fromBreedtetal.(2012),wedetermineR =0.10R , L ⊙ shown by Burleighetal. (2006). The optical light curve pre- whichisclosertotheL-dwarfradius.Ourdetectionofaccretion, sentedbyBurleighetal.(2006)showedonlyaweakmodulation and thus the presence of an X-ray emitting region on the WD, (. 10% in u′ and ∼ 4% in g′). Given the low statistics of the alsoprovidesanexplanationfortheHαemissionpreviouslyob- OM data, it is therefore not surprising that no significant vari- served from SDSS1212, as due to irradiation of the donor by abilityisdetectedinourB-bandlightcurve. theX-rayemissionfromtheaccretingWD.Asaresultoftheir- radiationtheLdwarfmaybeinflated,makingRoche-lobefilling evenmorelikely. 3. Discussion To conclude, SDSS1212presents the characteristics of the To date, only four period-bounce candidates have long-sought class of period-bounce CVs (cool WD, substellar infrared detections: EFEri (Schwopeetal. 2007), donor mass, and weak accretion), and it is located in the ob- SDSSJ 143317.78+101123.3 (Littlefairetal. 2013; servationallystillnearlyunpopulated‘boomerang’regionofCV HernándezSantistebanetal. 2016), WZSge (Harrison 2016), evolution models (e.g. Howelletal. 2001) that awaits observa- and SDSS1212(Farihietal. 2008). SDSSJ 1433+1011 and tionalconfirmation. SDSS1212isthefirstWDLDbinaryfound WZSge are non-magnetic CVs, while EFEri has been the to exhibit clear accretion-induced X-ray variability at a very textbookexampleforaLARP,butisalsoconsideredacandidate low accretion rate. The WDLD binary EFEri has long been period bouncer (Schwopeetal. 2007; Schwope&Christensen knowntoshowX-rayorbitalmodulationduringhighstates(e.g. 2010). The X-ray luminosity of EFEri (2 · 1029erg/s; see Pattersonetal.1981),butinitscurrentlowstatetheX-rayemis- Schwopeetal.2007)isremarkablysimilartoourmeasurement sioncouldnotbefoundtobemodulatedattheWDspin/binary forSDSS1212. However,noX-rayvariabilityhasbedetected orbit(Schwopeetal.2007). forEFEriduringitsextendedlowstate,implyingthataccretion TheX-rayorbitalmodulationofSDSS1212suggeststhatac- (almost) stopped. Our detection of X-ray orbital modulation creting WDLD systems may be easy to identify in the X-ray in SDSS1212, consistent with its binary period found with bandthroughthemagneticallyconfinedaccretionflowontothe othermethods, providesunambiguousproofforaccretionfrom polar regions of the WD. Sensitive searches for X-rays from the L dwarf onto the WD and establishes this system as a new WDLDbinariescanthereforebeexpectedtoprovidefurtherex- benchmark for interacting binaries consisting of a WD and a amples of pulsed emission, ensuing determination of mass ac- substellarcompanionwithlowaccretionrates. cretionratesatveryweaklevels,andthecharacterizationofthe TheX-rayluminosityofSDSS1212,bothduringourXMM- multi-wavelengthpropertiesofthesofarwidelyelusiveclassof Newton observation in 2015 and during the Swift observation period-bounceCVs. nineyearsbefore,isseveralordersofmagnitudehigherthanthat Acknowledgements. DDM acknowledges financial support from ASI INAF ofanysingleLdwarf(< 1026erg/s;seeAudardetal. 2007and I/037/12/0. SLCacknowledges supportfromtheUniversity ofLeicester Col- thecompilationbyCooketal.2014),clearlyrulingoutcoronal legeofScienceandEngineering. emissionfromtheultracoolcompanion.Togetherwithitsorbital modulation,thehighX-rayluminosityofSDSS1212thereforeis anotherclearpieceofevidenceforaccretionontothemagnetized References WD. Following the lines of argument in Audard,M.,Osten,R.A.,Brown,A.,etal.2007,A&A,471,L63 Bernardini,F.,deMartino,D.,Falanga,M.,etal.2012,A&A,542,A22 Webbink&Wickramasinghe (2005), the mass flux driven Beuermann,K.,Burwitz,V.,&Reinsch,K.2012,A&A,543,A41 by coronal X-ray emission from an L dwarf with an assumed Breedt,E.,Gänsicke,B.T.,Girven,J.,etal.2012,MNRAS,423,1437 logLx[erg/s] ∼ 25 would be 10−16M⊙/yr at most. The Brinkworth,C.S.,Burleigh,M.R.,Wynn,G.A.,&Marsh,T.R.2004,MNRAS, detectionof windsfromlate-typestarsrequireshigh-resolution 348,L33 UV spectroscopy and is at present not possible for L dwarfs. Burleigh,M.R.,Marsh,T.R.,Gänsicke,B.T.,etal.2006,MNRAS,373,1416 Casewell,S.L.2014,Mem.Soc.Astron.Italiana,85,731 A very small number of late-type stars have measured wind Cook,B.A.,Williams,P.K.G.,&Berger,E.2014,ApJ,785,10 accretionrates,includingtwoMdwarfsthatshowmuchsmaller Cropper,M.1990,SpaceSci.Rev.,54,195 M˙ than expected from the empirical M˙ vs F relation for Debes, J.H.,López-Morales, M.,Bonanos, A.Z.,&Weinberger, A.J.2006, w w x solar-type stars (Woodetal. 2015). Extrapolating from that ApJ,647,L147 relationto low F , foranadoptedlogL [erg/s] ∼ 25fortheL Dickey,J.M.&Lockman,F.J.1990,ARA&A,28,215 x x Farihi,J.,Burleigh,M.R.,&Hoard,D.W.2008,ApJ,674,421 dwarf, its wind would be ≈ 10−17M /yr, making it difficultto ⊙ Ferrario,L.,deMartino,D.,&Gänsicke,B.T.2015,SpaceSci.Rev.,191,111 provide the observed accretion rate of SDSS1212(considering Gänsicke,B.T.,Dillon,M.,Southworth,J.,etal.2009,MNRAS,397,2170 Articlenumber,page4of5 B.Stelzer etal.:X-rayorbitalmodulationofawhitedwarfaccretingfromanLdwarf Harrison,T.E.2016,ApJ,816,4 HernándezSantisteban, J.V.,Knigge, C.,Littlefair, S.P.,etal.2016, Nature, 533,366 Howell,S.B.,Nelson,L.A.,&Rappaport,S.2001,ApJ,550,897 Knigge,C.,Baraffe,I.,&Patterson,J.2011,ApJS,194,28 Littlefair,S.P.,Dhillon,V.S.,Marsh,T.R.,etal.2008,MNRAS,388,1582 Littlefair,S.P.,Savoury,C.D.J.,Dhillon,V.S.,etal.2013,MNRAS,431,2820 Marcy,G.W.&Butler,R.P.2000,PASP,112,137 Nordhaus,J.&Spiegel,D.S.2013,MNRAS,432,500 Patterson,J.,Williams,G.,&Hiltner,W.A.1981,ApJ,245,618 Rebassa-Mansergas, A., Schreiber, M.R., &Gänsicke, B.T.2013, MNRAS, 429,3570 Schmidt,G.D.,Szkody,P.,Henden,A.,etal.2007,ApJ,654,521 Schmidt,G.D.,Szkody,P.,Silvestri,N.M.,etal.2005,ApJ,630,L173 Schwope, A.D.,Brunner, H.,Hambaryan, V.,&Schwarz, R.2002,inAstro- nomicalSocietyofthePacificConferenceSeries,Vol.261,ThePhysicsof Cataclysmic Variables andRelated Objects, ed. B.T.Gänsicke, K.Beuer- mann,&K.Reinsch,102 Schwope,A.D.&Christensen,L.2010,A&A,514,A89 Schwope,A.D.,NebotGomez-Moran,A.,Schreiber,M.R.,&Gänsicke,B.T. 2009,A&A,500,867 Schwope,A.D.,Staude,A.,Koester,D.,&Vogel,J.2007,A&A,469,1027 Stelzer,B.,Micela,G.,Flaccomio,E.,Neuhäuser,R.,&Jayawardhana,R.2006, A&A,448,293 Webbink,R.F.&Wickramasinghe,D.T.2005,inAstronomicalSocietyofthe PacificConferenceSeries,Vol.330,TheAstrophysicsofCataclysmicVari- ablesandRelatedObjects,ed.J.-M.Hameury&J.-P.Lasota,137 West,A.A.,Hawley,S.L.,Walkowicz,L.M.,etal.2004,AJ,128,426 Wood,B.E.,Linsky,J.L.,&Güdel,M.2015,inAstrophysicsandSpaceScience Library,Vol.411,CharacterizingStellarandExoplanetaryEnvironments,ed. H.Lammer&M.Khodachenko,19 Wynn,G.A.&King,A.R.1992,MNRAS,255,83 Zorotovic,M.,Schreiber,M.R.,&Gänsicke,B.T.2011,A&A,536,A42 Articlenumber,page5of5