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Mon.Not.R.Astron.Soc.000,1–11(2015) Printed29thJanuary2016 (MNLATEXstylefilev2.2) Detached cataclysmic variables are crossing the orbital period gap M. Zorotovic1⋆, M. R. Schreiber1,2, S. G. Parsons1, B. T. Gänsicke3, 6 A. Hardy1, C. Agurto-Gangas1,4, A. Nebot Go´mez-Morań5, 1 A. Rebassa-Mansergas6 and A. D. Schwope7 0 2 1 Institutode F´ısica y Astronom´ıa, Universidad de Valpara´ıso, Av. Gran Bretanã 1111, Valpara´ıso, Chile n 2 MillenniumNucleus“Protoplanetary Disksin ALMAEarly Science”,Universidad de Valpara´ıso, Casilla 36-D, Santiago, Chile a 3 Department of Physics, Universityof Warwick, Coventry, CV47AL, UK J 4 Max-Planck-Institutfur extraterrestrische Physik, Giessenbachstrasse 1, 85748 Garching, Germany 5 Observatoire Astronomique de Strasbourg, Universitéde Strasbourg, CNRS, UMR 7550, 11 rue de l’Université,F-67000 Strasbourg, France 8 6 Departament de F´ısica, UniversitatPolitècnica de Catalunya, c/Esteve Terrades 5, 08860 Castelldefels, Spain 2 7 Leibniz-Institutfu¨r Astrophysik Potsdam (AIP), Ander Sternwarte 16, 14482 Potsdam, Germany ] R S Accepted2016January27.Received2016January26;inoriginalform2015December14 . h p ABSTRACT - o A central hypothesis in the theory of cataclysmic variable (CV) evolution is the need r to explainthe observedlack ofaccretingsystems inthe ≃2−3h orbitalperiodrange, t s known as the period gap. The standard model, disrupted magnetic braking (DMB), a reproduces the gap by postulating that CVs transform into inconspicuous detached [ white dwarf (WD) plus main sequence (MS) systems, which no longer resemble CVs. 1 However, observational evidence for this standard model is currently indirect and v thus this scenario has attracted some criticism throughout the last decades. Here 5 we perform a simple but exceptionally strong test of the existence of detached CVs 8 (dCVs). If the theory is correct dCVs should produce a peak in the orbital period 7 distribution of detached close binaries consisting of a WD and an M4−M6 secondary 7 star. We measured six new periods which brings the sample of such binaries with 0 knownperiodsbelow10hto52systems.Anincreaseofsystemsinthe≃2−3horbital . 1 periodrangeisobserved.Comparingthisresultwithbinarypopulationmodelswefind 0 thattheobservedpeakcannotbereproducedbyPCEBsaloneandthattheexistence 6 of dCVs is needed to reproduce the observations. Also, the WD mass distribution in 1 the gap shows evidence of two populations in this period range,i.e. PCEBs and more : v massive dCVs, which is not observed at longer periods. We therefore conclude that i CVs are indeed crossing the gap as detached systems, which provides strong support X for the DMB theory. r a Key words: Binaries:close–novae,cataclysmicvariables–whitedwarfs–stars:low- mass – stars: evolution 1 INTRODUCTION (1983)proposedadisruptedmagneticbraking(DMB)scenario assuming that MB turns off when the donor star be- Cataclysmic variables (CVs) are close binaries in which a comes fully convective at P ≃ 3h. Systems above the gap main-sequence (MS) donor transfers mass to a white dwarf orb are driven closer due to GR and efficient MB. Due to the (WD). The evolution of CVs is driven by angular mo- strong mass transfer caused by MB the donors are driven mentum loss due to gravitational radiation (GR) and the out of thermal equilibrium. Once the donor star becomes much stronger magnetic braking (MB). The observed or- fully convective, at the upper edge of the gap, MB stops bitalperioddistributionofCVshasanapparentlackofsys- or at least becomes inefficient. This causes a drop in the tems in the ≃ 2−3h orbital period range, known as the mass-transfer rate, which allows the donor star to relax to period gap.Inordertoexplainthisdeficit,Rappaport et al. a radius which is smaller than its Roche lobe radius. The system detaches, mass transfer stops and it becomes a detached white dwarf plus main sequence (WD+MS) binary, ⋆ E-mail:[email protected](MZ) (cid:13)c 2015RAS 2 M. Zorotovic et al. evolving towards shorter periods only via GR. At P ≃2h massdistributionofdetachedsystemsinthe≃2−3hperiod orb the Roche lobe has shrunk enough to restart mass transfer range shows evidence for a combined population of PCEBs and the system appears again as a CV at the lower edge of and dCVs(more massive) in the period gap. thegap. TheDMBscenarionotonlyexplainstheperiodgap,but alsoagreeswellwithseveralotherobservedcharacteristicsof 2 THE SPECTRAL TYPES OF DETACHED CVs.Themodeladequatelyreproducesthehigheraccretion CVS ratesofsystemsabovetheperiodgap(Townsley & Bildsten 2003; Townsley & Gänsicke 2009) and the larger radii of If the standard theory of CV evolution is correct and CVs donor stars in CVs above the gap with respect to their are crossing the ≃ 2−3h gap as detached systems, a peak MSradii(Knigge et al.2011).Inaddition,thereisevidence of systems should show up in the orbital period distribu- for a discontinuity in the braking of single stars (Bouvier tion of detached PCEBs with secondary stars of spectral 2007;Reiners& Basri2008)and/orachangeinthefieldto- types that are expected for dCVs. Detached CVs should pology(Reiners& Basri2009;Saunderset al.2009)around have secondary stars with similar spectral types across the the fully convective boundary. Also in wide WD+MS bin- entire period gap, because MB is assumed to stop when aries a significant increase in the activity fraction of M- the secondary star becomes fully convective and the mass dwarfs at the fully convective boundary has been observed remains constant while they are detached within the gap. (Rebassa-Mansergas et al. 2013), which supports the idea Single M-dwarfs become fully convective at Msec≃ 0.35M⊙ thatfullyconvectivestarsinwidebinariesarenotspundown (Chabrier & Baraffe 1997) which correspond to a spectral asquicklyasearlierMdwarfs.Finally,thepredictionofthe type of M3−M4 (Rebassa-Mansergas et al. 2007). However, DMB scenario of a steep decrease of the number of post in most CVs above the period gap the spectral type of common envelope binaries (PCEBs) at the fully convective the secondary star is significantly later than the spectral boundary(Politano & Weiler2006)isinagreementwiththe type expected for a zero-age MS star with the same mass observations (Schreiberet al. 2010). (e.g., Baraffe & Kolb 2000). The mass at which a mass- However,thesepiecesofevidencesupportingthestand- losingstarbecomesfullyconvectiveissmallerthanforsingle ard theory of CV evolution based on the DMB scenario starsorsecondarystarsindetachedsystems.Usingobserva- are rather indirect and the hypothesis that CVs are really tionalconstraintsfromalargesampleofCVs,Knigge(2006) crossing the gap as detached systems has been frequently find the fully convective boundary for CVs to be at M = sec challenged (e.g., Clemens et al. 1998;Andronovet al. 2003; 0.2±0.02M⊙, which according to Rebassa-Mansergas et al. Ivanova& Taam 2003). In addition, the standard scenario (2007)correspondstoaspectraltypeof∼M6.However,the forCVevolutionisfacingseveralmajorproblems,themost exactmassatwhichaCVsecondarystarbecomesfullycon- severebeingthat thepredictedWD masses in CVsare sys- vectivewill differfrom system to system.For example, it is tematically smallerthantheobservedones(Zorotovic et al. affectedbythetimethesystemspentasaCVbeforereach- 2011a).Schreiberet al.(2016)recentlysuggested arevision ingthefullyconvectiveboundary.Ifitstartedmasstransfer of the standard model of CV evolution incorporating an veryclosetotheupperedgeoftheperiodgap,withthesec- empiricalprescriptionforconsequentialangularmomentum ondary being close to fully convective, the secondary star loss(CAML),i.e.angularmomentumlossgeneratedbymass may be only slightly out of thermal equilibrium when be- transfer,andshowedthattheWDmassproblemandseveral comingfullyconvectivecomparedtoasystemwithalonger others can be solved if CAML is assumed to increase as a mass transfer history. This implies that dCVs may cover a function of decreasing WD mass. range of secondary masses with Msec∼ 0.2−0.35M⊙ which A direct test of the main prediction of the standard roughly corresponds to spectral types later than ∼ M4−M6 scenarioofCVevolutionhasbeensuggested byDaviset al. accordingtoRebassa-Mansergas et al.(2007).Thisfitswith (2008):ifMBisdisruptedattheupperboundaryofthegap the spectral type range for PCEBs that start mass trans- causing CVs to stop mass transfer, these systems should fer within the period gap if we use the mass spectral-type show up in population studies of detached WD+MS binar- relation from Rebassa-Mansergas et al. (2007) for detached ies. In particular, the deficit of CVs in the ≃2−3h orbital systems. Therefore, we decided to search for the peak pro- periodrangeshouldimplyanexcessofshort-perioddetached duced by dCVs in the orbital period distribution of a large WD+MS binaries in the same period range. Observation- and unbiased sample of close detached WD+MS binaries ally identifying this peak would provide clear evidence for with secondaries of spectral type M4−M6 assuming an un- thestandardtheoryofCVevolutionandmayevenallowto certainty of half a subclass. distinguishbetweentheclassicalstandardmodelandthere- However, we are aware of the fact that spectral types visedversionbySchreiberet al.(2016)asthelatterpredicts of dCVsas well as spectral-typemass and spectral-typera- theCVs crossing thegap to contain more massive WDs. dius relations are notoriously uncertain. Therefore we per- We here present the results of an observational search formedseveraltestsmovingthespectral-typerangeassumed forclosedetachedWD+MSbinariestestingifthepredicted for dCVs one class towards earlier/later spectral types and peak at orbital periods of ≃ 2−3h exists. Comparing the findthat theconclusions of thispaper remain identical. observational results with those predicted by binary population models, we find that the existence of detached CVs (dCVs) is required to reproduce the observations, and we 3 THE OBSERVED SAMPLE therefore conclude that indeed CVs are crossing the gap as detached systems. In addition, as predicted by the revised In what follows we describe our observational sample. We modelproposedbySchreiberet al.(2016),theobservedWD also present the details of the observations, data reduction (cid:13)c 2015RAS,MNRAS000,1–11 Detached CVs are crossing the period gap 3 Table 1.SixSDSSWD+MSbinarieswithneworbitalperiodmeasurements.Uncertainties intheperiodsaregiveninparentheses. System Porb γ K2 Teff MWD Sp2 [d] [km/s] [km/s] [K] [M⊙] SDSSJ111459.93+092411.0 0.2102534(1) -8.2±1.6 143.9±2.1 10324±172 0.610±0.115 M5 SDSSJ113006.11-064715.9 0.3085042(7) 15.5±3.6 120.1±4.8 11139±192 0.520±0.076 M5 SDSSJ121928.05+161158.7 0.674080(1) -3.2±0.9 153.8±1.4 7123±103 0.930±0.124 M6 SDSSJ143017.22-024034.1 0.18140900(9) -28.5±1.7 167.4±2.1 10802±436 0.640±0.201 M5 SDSSJ145238.12+204511.9 0.10621803(3) -44.1±1.1 356.5±1.4 − >0.89 M4 SDSSJ220848.32+003704.6 0.103351(9) 8.3±0.7 228.4±1.0 − >0.33 M5 and period determination for six systems. We analysed the 10h. This brings our sample size to 52. In the following we observed orbital period distribution and the possible biases describethe observationsand data reduction. that affect oursample. WeselectedsixsystemsfromourcatalogueofWD+MS binaries and observed them with the Very Large Telescope (VLT)UT1equippedwithFORS2(Appenzelleret al.1998) 3.1 Systems from the SDSS PCEB survey on the nights of 2014 May 16-18 and 2015 July 2-4, in order to determine their orbital periods. We used the long Our observational sample is mostly based on the results slit mode with a 0.7” slit, 2x2 binning, the 1028z grism of a large project we performed over the last decade. The and the OG590 filter, resulting in a wavelength coverage of SloanDigitalSkySurvey(SDSS)sampleofspectroscopically 7700−9500˚Awithadispersionof0.8˚A/pixel.Thedatawere identified WD+MS binary stars (Rebassa-Mansergas et al. reducedusingthestandardESOreductionpipeline.Wealso 2012) contains 2316 systems up to data release 8. The applied a telluric correction to the data using observations majority (∼ 3/4) of these systems are wide binaries of theDQWD GJ 440 taken at thestart of each night. We that never underwent a CE event (Schreiberet al. 2010; measuredtheRVoftheMdwarfineachspectrumbyfitting Rebassa-Mansergas et al. 2011; Nebot Gómez-Morán et al. theNaiabsorptiondoubletat∼8200˚Awithacombination 2011). We carried out a radial velocity (RV) sur- ofastraightlineandtwoGaussiansoffixedseparation,typ- vey to identify the PCEBs within the SDSS sample ically reaching a precision of 5-10kms−1 in each individual (Schreiberet al. 2010), and measured their orbital peri- spectrum. We then determined the orbital periods of the ods to constrain theories of close binary evolution binaries by fitting a constant plus sine wave to the velocity (Nebot Gómez-Morán et al.2011).Thetargetselectiondur- measurements over a range of periods and computing the ing this large observational project was mostly determined χ2 of the resulting fit. In Fig. 1 we show the phase-folded by observing constraints and otherwise random, i.e. was RVcurvesandcorrespondingfitsforthesesystems.Table1 mostly independent of the secondaries spectral type. Only lists the results of these fits and the parameters of the sys- in a few cases we targeted systems with a certain spectral tems, where the WD temperatures and masses are taken type, e.g. when we were trying to measure the increase of fromRebassa-Mansergas et al.(2012)and3Dmodelcorrec- systems across the fully convective boundary we preferen- tions have been applied for systems with temperatures be- tially observed systems with M2−M4 secondary stars. low 12000K (Tremblay et al. 2013). SDSSJ1452+2045 and The close binaries discovered in the above described SDSSJ2208+0037shownoabsorptionfeaturesfromtheWD projectcontainingM4−M6secondarystarswithorbitalperi- in the SDSSspectra, meaning that the masses and temper- ods measured through RVsor from ellipsoidal/reflection ef- aturescannotbereliablydetermined.HowevertheRVsemi- fect (25) are complemented with 22 eclipsing systems iden- amplitudecanbeusedtodeterminealowerlimitontheWD tified by combining our spectroscopic WD+MS identifica- mass, which is providedin Table 1. tionfromSDSSwithphotometryfromarchivalCatalinaSky Surveydata(Drakeet al.2010;Parsons et al.2013b,2015). This way we established a sample of 47 PCEBs with an or- bitalperiod below10handcompanionswith spectraltypes 3.3 Observed period distribution M4−M6. Our final sample contains 52 close WD+MS binaries with Wealso includedin our sample11 systems with earlier orbitalperiodsP 610handspectraltypesM4−M6.Their spectral types(M2−M3) and orbital periods below 10h, se- orb parametersaswellasanexplanationofhowtheclosebinary lectedinthesameway,asacontrolgroup.Wedonotexpect naturehasbeenrevealedandhowtheperiodhasbeenmeas- to see any detached systems in the period gap for this con- uredarelistedinTableA1intheAppendix.Themassesand trolgroup,becausePCEBswithcompanionsinthisspectral- temperatures of WDs cooler than 12000K have been up- typerange should start mass transfer at longer periods. datedbasedon3Dmodelcorrections(Tremblay et al.2013) exceptin somesystemswheretheinclination isconstrained by the eclipse which places a limit on the WD mass that is 3.2 VLT/FORS survey of dCVs more accurate than themass estimated from thespectra. Tocomplementthesamplethatextractedfromprevioussur- The left panel in Fig. 2 shows the observed orbital veys,wecarriedoutadedicatedsearchofcloseWD+MSsys- period distribution of close detached WD+MS binaries in tems with M4−M6 companions to search for dCVs crossing our sample with secondary stars in the spectral-type range the gap. We measured 6 periods, five of them shorter than M4−M6(top)andM2−M3(bottom).Thehatchedareacor- (cid:13)c 2015RAS,MNRAS000,1–11 4 M. Zorotovic et al. Figure 1.Phase-foldedRVcurves forthe sixsystems withperiodspresented inthis paper. Thegreylineineach panel shows thesine fittothedata(seeTable1formoredetails).ThepanelbeloweachRVcurveshowstheresidualstothisfit. respondstotheperiodgapaccordingtoKnigge(2006).The ever, as shown in Nebot Gómez-Morán et al. (2011, their binninghasbeen chosen tocoverthewhole gap in onlyone Figure10) the detection probability of close binarity only bin(2.15−3.18h).Apeakcanbeobservedatthepositionof significantlydecreasesatperiodslongerthanaboutoneday. theperiod gap for systems containingM4−M6 companions. Therefore, for the majority of systems (35) in our sample On the other hand, the period distribution of PCEBs with which have been identified as close binaries through RV secondariesinthespectral-typerangeM2−M3onlycontains measurements, we can clearly exclude observational biases systems with periods above the gap. This confirms that we toaffect our results. have selected the correct spectral-type range to search for dCVs and that our results are not affected by the uncer- Eclipse light curves led to the discovery of the close tainty of the spectral type of the secondary star, which is binary nature in 17 systems in our sample. As shown by typically roughly half a subclass (Rebassa-Mansergas et al. Parsons et al. (2013b), the baseline and cadence of the 2007). archival Catalina data is typically good enough to detect eclipsing systems with orbital periods of about a day, so the detection probability again should not affect our results.However,thedetectionprobabilityisnottheonlypos- 3.4 Possible observational biases sible bias towards shorter periods in the case of eclipses. The close WD+MS binaries in our sample have been iden- The smaller the orbital period, the wider the range of in- tifiedthroughRVvariationsoreclipsesintheirlightcurves. clinations that produce an eclipse. In other words, there is Bothmethodsimplyanobservationalbiastowardsshortor- alargerfraction ofeclipsingsystemsat shorterorbitalperi- bitalperiodsthatwehavetoconsiderbeforecomparingthe ods.ThishasbeenshowninParsons et al.(2013b,Figure4), observedperioddistributionwiththeresultsofbinarypop- where a comparison between the period distribution of all ulation models. SDSS spectroscopically confirmed eclipsing PCEBs and all SystemswithshorterperiodsshowlargerRVvariations SDSS PCEBs from Nebot Gómez-Morán et al. (2011) has andthereforetheirclosenatureiseasiertodetermine.How- beenperformed.Totestwhetherthelatterbiascouldaffect (cid:13)c 2015RAS,MNRAS000,1–11 Detached CVs are crossing the period gap 5 Figure 2. Left: Observed period distribution for detached WD+MS binaries. The upper and bottom panels show the distribution for different ranges of spectral types for the main-sequence companion. The corresponding ranges are labelled in the top right corner of each panel. The hatched area represents the location of the period gap (2.15−3.18h, Knigge 2006). Right: Orbital period distribution forthesimulatedpopulationofPCEBswithsecondarystarsinthecorrespondingspectral-typeranges.Thesolidlinecorrespondstothe simulationswithαCE=0.25,thedottedlinetoαCE=0.5,andthedashedlinetoαCE=1.0. ourresults,weinvestigatedthefractionofeclipsingsystems WD mass. This bias does not affect the relative distribu- in our observational sample and found that 40% of thesys- tionofWDmassesasitisindependentoftheorbitalperiod tems with M4−M6 companions are known to be eclipsers: (i.e.eachorbitalperiodbinisequallybiased).Inthecaseof 50% of the systems in the period gap and 38% above (see eclipsing systems, the identification probability is virtually Table A1in theAppendix).This confirmsthat thefraction independentof theWD mass. of eclipsing systems is larger in the bin with the shortest periods, although we can not excludethat thisis caused by the low number of systems. Also, in some of these systems 4 BINARY POPULATION MODELS their close nature was initially revealed from RV variations and their eclipsing nature was subsequentlydiscovered. We The observed period distribution of close but detached foundthatthefractionofsystemsthatwerediscoveredtobe WD+MSsystems with secondary spectral typesof M4−M6 closesolelyduetotheireclipsingnatureissimilarinthegap showsapeakatthepositionoftheorbitalperiodgap.Inor- and outside (33% and 30%, respectively). This means that dertoevaluateifthispeakprovidesevidenceforCVscross- the potential bias towards shorter periods caused by close ing the gap as detached system we performed Monte Carlo systemsidentifiedthrougheclipsesisnotimportantandcan simulationsofthepopulationofWD+MSPCEBsanddCVs not be responsible for the peak observed at the position of intheperiodgap.Inwhatfollows wedescribethedetailsof theperiod gap in theupper-left panelof Fig. 2. ourpopulation models. While we can exclude that our sample is significantly biased with respect to the orbital period, the situation is 4.1 PCEBs differentconcerningthetemperatureoftheWDsinoursys- An initial MS+MS binary population of 107 systems tems. If the WD is colder than ∼ 8000K it becomes very was generated. We assumed the initial-mass function of difficulttomeasureitstemperaturefrom SDSSspectra,be- Kroupaet al. (1993) in the range 0.8 −9M⊙ for the dis- causenohydrogenabsorptionlinesarepresent,which leads tribution of primary masses plus a flat initial mass-ratio to a clear bias against old systems. The two systems in our distribution (Sanaet al. 2009) for secondary masses, with olobwser8v0e0d0Ksam(SpDleSSwJit0h13W8−D001te6mapnedraStuDrSesSJs1ig2n1i0fi+c3a3n4t7ly) baree- a lower limit of Msec= 0.05M⊙. A flat distribution in loga ranging from 3 to 104R⊙ was used for the orbital separa- eclipsing and the WD temperatures were determined from tions (Popova et al. 1982; Kouwenhovenet al. 2009) and a theircolours.ThisbiasagainstsystemscontainingcoldWDs constant star formation rate was assumed with an upper hastobetakenintoaccount when comparingobserved and limit of 10Gyrs. simulated populations. As in Schreiberet al. (2016), the systems were first Finally, given the importance of the WD mass for our evolveduntiltheendof theCE phaseusingthebinary-star understanding of CV evolution, we consider possible biases evolution (BSE) code from Hurley et al. (2002). Three dif- affecting this parameter. The RV method for identifying ferentvaluesoftheCEefficiencywereconsidered:α =0.25, CE close binaries causes a bias towards systems with larger α =0.5, and α =1.0. The subsequent evolution of these CE CE WD masses because, for a given secondary mass and or- zero-agePCEBswasperformedwithourowncode.Allzero- bital period, the velocity of the secondary increases with age PCEBs were evolved to their current periods assuming (cid:13)c 2015RAS,MNRAS000,1–11 6 M. Zorotovic et al. systemic angular momentum loss due to MB and GR (if towardsshorterperiodswhenthereisnomasstransfer.How- Msec>0.35M⊙)orGRonly(ifMsec60.35M⊙).Thenormaliz- ever, as the star formation rate is constant and we do not ationfactorsforMBandGRarebasedontheobservational take into account old (cool) systems, these factors should constraintsderivedbyKnigge et al.(2011).Ifasystemfilled notaffecttheorbitalperioddistributionforthePCEBpop- its Rochelobe it was not considered as a PCEB any more. ulation. The spectral-type mass conversion was performed The spectral-type range of the MS star was conver- as in thecase of PCEBs. ted into a mass range based on the relation presented in Rebassa-Mansergas et al. (2007). The range M4−M6 corresponds to masses for the companion in the range 0.17− 5 COMPARISON WITH THE OBSERVATIONS 0.35M⊙, which is consistent with the mass range used by Daviset al. (2008). Furthermore, this corresponds to the To compare the simulated populations with the observa- mass range of secondary stars that will commence mass tions we excluded systems with old WDs that are too transfer within the gap. PCEBs in this mass range are as- cool to be reliably detected through observations, be- sumed to evolve towards shorter periods due to GR only. cause the observed sample is strongly biased against such The spectral-type range M2−M3 used for comparison cor- systems. The detectability of a WD against a compan- responds toa mass range of 0.35−0.45M⊙ for thecompan- ion of the same spectral type depends mostly on the ion. These systems are brought into contact mainly due to WD effective temperature and only little on its mass MBandthereforeevolvefastertowardsasecondmasstrans- (Zorotovic et al. 2011a). Therefore, applying a temperat- ferphase.Thesesystemswillstartthesecondmasstransfer ure limit of 8000K to all our systems seems reasonable phaseat periods abovethegap andtherefore wedonot ex- for comparing observed and simulated populations. We es- pect to see any such system within thegap. timated the effective temperature of the WDs using the cooling tracks by Althaus& Benvenuto (1997)1 for heliumcore WDs (if MWD<∼0.5M⊙) and Fontaineet al. (2001)2 for 4.2 Cataclysmic Variables carbon/oxygen-core WDs (if MWD>∼0.5M⊙). The temperat- uresoftheWDsinPCEBsanddCVswerecalculatedinthe To estimate the impact of dCVs on the predicted popu- sameway.WenotethattheeffectivetemperatureoftheWD lation of close detached systems with secondary spectral in a dCV might be affected by compressional heating dur- types of M4−M6 we extended the binary population syn- ingthepreviousCVphase(Sion1995;Townsley & Bildsten thesis model described above by incorporating CV evolu- 2004; Townsley & Gänsicke 2009). However, it is not clear tion following Schreiberet al. (2016). Once the secondary howlongittakesfortheWDtocooldownaftermasstrans- starfillsitsRochelobeitisinflatedtoalargerradiusbased fer stops. If the time-scale is longer or comparable to the on the Mass-Radius relation for CVs above the gap given time a dCV spends in the gap, i.e. if the effective temper- by Knigge et al. (2011). We stop MB when the secondary ature of a dCV is higher than the cooling temperature, the star reaches 0.2M⊙ and the system becomes a dCV which numberofdCVsproducedbythesimulationscanbeslightly evolvesthrough theperiod gap only via GR. underestimated. AsshowninSchreiberet al.(2016),thesimulatedpop- WestartourcomparisonbyusingPCEBsonlytotestif ulationofCVsisstronglyaffectedbythecriticalmassratio thepeak observed at theposition of theperiod gap for sys- thatisassumedforhavingstablemasstransfer.Apartfrom tems with M4−M6 companions can be reproduced without the intrinsic angular momentum loss due to GR and MB, assuming dCVscrossing thegap. consequentialangularmomentumloss(CAML),i.e.angular momentum loss due to mass transfer and mass loss dur- ing the nova eruptions, can play an important role. Two 5.1 PCEBs differentmodelsforCAMLaresimulated:theclassicalnon- In the right panel of Fig. 2 we show the simulated orbital conservative model for CAML (cCAML) where the change period distribution for PCEBs. The different lines corres- in angular momentum is given by pond to different values of the CE efficiency. The upper J˙ M 2 M˙ panel,whichcontainssystemswithM4−M6secondarystars, CAML = sec sec (1) J M (M +M )M shows a trend to have more systems towards shorter peri- WD WD sec sec ods with a drop in the period gap, independent of the CE (see e.g. King & Kolb 1995), and an empirical CAML efficiency parameter. In contrast, the bottom panel shows (eCAML) modelgiven by adecreaseofsystemswith M2−M3secondarystarstowards J˙ 0.35 M˙ shorterperiodsandnonewithinthegap.Thisisexpectedbe- CAML = sec (2) causesystemswithearlierspectraltypeshavemoremassive J M M WD sec secondaries that fill their Rochelobes at longer periods. (Schreiberet al.2016)thatrecentlyhasshowntosolvesev- Whiletheobservedandpredicteddistributionsfor sys- eralproblemsbetweenpredictionsandobservationsofCVs, tems with M2−M3 secondary stars agree quite well in not especiallythedisagreementbetweenobservedandpredicted showing any system within the gap (and keeping in mind WDmasses. IntheeCAML modelweadjusted thenormal- thattheobservedsampleisadmittedlysmall),theobserved izationfactorsforMBandGRinordertoobtainmasstrans- peak at the period gap for systems with spectral types fer rates in CVs that are consistent with the ones obtained withthecCAMLmodel.Thefactorsweusedare0.43forMB and1.67forGR(insteadof0.66and2.74,respectively,from 1 http://fcaglp.fcaglp.unlp.edu.ar/evolgroup/TRACKS/tracks_heliumcore_prev.h Knigge et al. 2011). This means that systems evolve slower 2 http://www.astro.umontreal.ca/~bergeron/CoolingModels (cid:13)c 2015RAS,MNRAS000,1–11 Detached CVs are crossing the period gap 7 Figure 3. Same as in Fig. 2 but including the population of dCVs in the period gap for our two models: cCAML (left) and eCAML (right).ThedifferentstylesoflinescorrespondtodifferentvaluesfortheCEefficiency:αCE=0.25(solid),αCE=0.5(dotted),andαCE=1.0 (dashed). M4−M6 is in contrast to the drop expected from our simu- hand panel compares observations with PCEBs + dCVs lationsofthePCEBpopulationifdCVsdonotexist.Inthe fromtheeCAMLmodel.Differentstylesoflinescorrespond next section we evaluate if this is better reproduced if we to the three different CE efficiencies used in the simula- includedCVs. tions. The KS probabilities are also listed in the upper left corner of each panel. According to the KS test, the cumulative distribution of observed systems and PCEBs is dif- 5.2 Including dCVs ferent with a confidentlevel of at least 98.4% dependingon Figure3shows thesimulatedorbitalperiod distributionfor the value of the CE efficiency that is assumed. The corres- the combined population of PCEBs and dCVs in the same ponding KS probability is less than 0.02 and we therefore spectral-type ranges as in Fig. 2. As expected, the distri- conclude that the two samples are different. In the case of butions of the systems with M2−M3 secondaries (bottom PCEBs + dCVs, both models show larger KS probabilit- panels) do not change because no detached systems with ies when a small CE efficiency is assumed (αCE = 0.25). M2−M3secondariesareproducedbyCVevolution.Thedif- For the cCAML model the KS probability is 0.670 while ferencebetweenthedistributionsintheleftandrightpanels for the eCAML it is 0.234. Based on these values, we can in this range is purely due to the normalization factors for not exclude any of the two models. However, the probab- MB and GR assumed in each model. ilities drop dramatically if we use larger values for the CE The predicted orbital period distributions for close de- efficiencyandall themodels with αCE=0.5orαCE =1.0can tached systems with secondaries of spectral type M4−M6, be rejected with a confidence level larger than 98%. This however, are significantly affected. The number of systems is consistent with recent studies that show that low values in the orbital period range of the period gap is clearly in- of αCE seem to work best for PCEBs with M-dwarf second- creased. This effect is strongest for small values of α and aries (e.g., Zorotovic et al. 2010; Toonen & Nelemans 2013; CE stronger in the cCAML model than in the eCAML model. Camacho et al. 2014). We also performed the KS tests for Comparingwiththeobserveddistribution(Fig.2,leftpanel) thesimulatedandobservedsystemswithsecondarystarsin itseemsthatespeciallymodelsassumingsmallvaluesforα the spectral-type range M2−M3. Comparing with the pre- CE provideabetteragreementbetweentheoryandobservations dicted PCEB sample the KS probabilities are larger than than is reachable with PCEBs alone. 0.1 for both CAML models and for the three values of the However, given the still relatively low number of sys- CE efficiency assumed in our simulations. This means that temsinoursample,weneedtocarefullyinvestigatewhether there are no statistically significant differences in the two this apparent improvement provides statistically robust distributions,i.e. observations and predictionsagree. evidencefortheexistenceofdCVscrossingthegap.Tothat end,weperformedaKolmogorov-Smirnov(KS)testbetween the observed and simulated period distributions. Figure 4 6 DISENTANGLING DETACHED CVS AND shows the cumulative distributions of orbital periods for PCEBS oursimulations(black)andtheobservedsystems(red)with MScompanionsinthespectral-typerangeM4−M6.Theleft In the previous section we showed that PCEBs alone can panel compares the observational sample with our PCEB not be responsible for the observed peak at the position of simulations (without dCVs), middle shows the comparison the period gap in the observed period distribution of de- withPCEBs+dCVsfromthecCAMLmodel,andtheright- tached close WD+MS systems with secondaries of spectral (cid:13)c 2015RAS,MNRAS000,1–11 8 M. Zorotovic et al. Figure 4. Comparison between the observed (red) and simulated (black) cumulative distribution of orbital periods. Left panel: only PCEBs; middle panel: PCEBs + dCVs from the cCAML model; right panel: PCEBs + dCVs from the eCAML model. The different styles of linesineach panel correspond todifferent CEefficiencies: αCE=0.25(solidline),αCE =0.5(dotted line)andαCE =1.0(dashed line).ThevaluesintheupperleftcornerofeachpanelaretheKSprobabilities. typeM4−M6. If therewere only PCEBs, one should expect simulationswithdCVsasecondpopulationisclearlyvisible to see a drop in thenumberof systems in this bin, because inthe≃2−3horbitalperiodrange.InthecaseofthecCAML PCEBs with secondary stars in this spectral type range fill model (middle panel), a second peak is evident at ∼ 0.5− their Roche lobes within the gap. The inclusion of dCVs 0.6M⊙ and systems with more massive WDs become more in the gap can reproduce the observed peak, and the size frequent at these periods. In the eCAML model the second of the expected peak depends strongly on the model that peak is not as pronounced as in the cCAML model, but weassume forCAML and ontheefficiencyfor CEejection. occursathighermasses(∼0.8−0.9M⊙).Thisisbecausethe Only with a small value for α does the KS test show no eCAML model is more restrictive than the cCAML model CE significant differences between the observed and simulated with respect to the stability limits for mass transfer and distributionswithdCVs,inagreement withZorotovic et al. therefore produces less CVs (and subsequently less dCVs) (2010).Based onthecurrentdata,wecannotdecidewhich but with higher WD masses, which is more consistent with of the two models for CAML we tested should be preferred theobserved WD mass distribution of CVs. as both models produce reasonable agreement with the observations. However, our results clearly show that CVs are From theobservational sample we seethat thepopula- crossingthegapasdetachedsystems,whichprovidesfurther tionofsystemswithmassiveWDs(>0.8M⊙)isconcentrated evidencefortheDMBmodel.Thequestionthatimmediately atthelocationoftheperiodgap.WeobtainanaverageWD arises from this result is: is there a way of observationally massof0.66±0.12M⊙ inthegapand0.50±0.02M⊙ outside distinguishing a normal PCEB from a dCV in the period the gap, with standard deviations of 0.35M⊙ and 0.15M⊙ gap?Whilethesecondarystars ofdCVsshouldbeindistin- respectively,forthesystemswithM4−M6companions.This guishable from those of PCEBs with M4−M6 secondaries, is consistent with having some dCVs with massive WDs in theWD parameter distributionsmay providenewinsights. the period gap and seems to provide further support for the eCAML model. However, the tendency of having high- mass WDs in the gap needs to be interpreted with cau- tion because of two reasons: first, our sample is too small 6.1 WD masses to provide a statistically significant result. Second, it has AsshowninZorotovic et al.(2011a),theWDmassdistribu- beenpreviouslyfoundthatsomeofthemassesderivedfrom tion of CVs and PCEBs is very different. WDs in CVs are, spectra may overestimate significantly the truevalue, espe- on average, more massive and there is a lack of low-mass cially if the spectrum is dominated by the MS star com- WDs(helium-coreWDs).Ifsomeof thesystemswithin the ponent (Parsons et al. 2013b). This is almost certainly the period gap are in fact dCVs, one should expect to have a case for SDSSJ0052−0053, the system in the gap with the largeraverageWDmassinthisperiodrangethanatlonger most massive WD (1.26M⊙). However, for two other gap periods. systemswith MWD >1M⊙ theWD isclearly visible in their InFigure5weshowthedistributionofWDmassesand SDSSspectra, meaning that these systems quitelikely con- orbitalperiodsfortheobservedsystemswithmeasuredWD tainmassiveWDs.Oneofthesesystems,SDSSJ1013+2724, mass(reddots)andforoursimulationsassumingα =0.25 isinfactaneclipsingsystemandParsons et al.(2015)noted CE (grey scale density). In the simulation that only includes that the sharp ingress and egress eclipse features are in PCEBs (left panel) the systems are concentrated at low- agreement with asmall (hencemassive) WD.Thelarge RV mass WDsin all period ranges, exhibitingasingle peak (at semi-amplitudeofSDSSJ1452+2045(oneofthenewsystems ∼ 0.40−0.45M⊙) and a continuous decrement of systems presentedinthispaper)alsoplacesalowerlimitonthemass towards more massive WDs. Ontheother hand,in ourtwo of this DC WD of 0.89M⊙. In summary, there seems to be (cid:13)c 2015RAS,MNRAS000,1–11 Detached CVs are crossing the period gap 9 Figure 5.Relationbetween WDmassandorbitalperiod.Theintensityofthegreyscalerepresents thedensityofsimulatedobjectsin each bin, on alinear scale, and normalizedto one for the bin that contains most systems. The red dots are the observed systems with availableWDmasses.ThetwoverticalarrowscorrespondtoSDSSJ1452+2045andSDSSJ2208+0037forwhichalowerlimitfortheWD masshasbeencalculated basedontheRVsemi-amplitude. an excess of systems containing fairly massive WDs with servedsystemswiththelowesttemperaturesarenotrepres- periodsinthegapandthesemaywellbedCVscrossingthe ented in this figure because our simulations exclude cold gap. (< 8000K) WDs. The average temperature seems to increase towards shorter periods in all our models and there is no distinctive behaviour at periods corresponding to the 6.2 WD effective temperatures period gap. The simulation that only includes PCEBs (left panel)looksalmostidenticaltotheonewithdCVsfromthe Asecondpossibility todistinguish dCVsandPCEBs might eCAML model (right panel) while the cCAML model pre- betheeffectivetemperatureoftheWD.Incomparisonwith dicts a small increase of the number of hotter WDs in the CVs above the period gap, dCVs should be cooler because orbital period range of the gap. This is because this model CVs suffer from compressional heating of the outer layers produces the largest fraction of dCVs compared to PCEBs (Sion1995).Ontheotherhand,dCVsshouldbehotterthan at these periods. However, in general the predicted distri- PCEBs in the same orbital period range, because the ini- butions of WD temperatures are not significantly different tial mass of thesecondary star must havebeen higher than and,inagreementwiththis,theobservedWDtemperatures thelimitfornon-fullyconvectivesecondaries(Msec>∼0.35M⊙) do not show any significant tendency either. The observed in order to start mass transfer above the gap. This means WD effective temperature average is ∼ 13000±1300K in thatangularmomentumlossaftertheCEphasewasmainly thegap and∼17000±1600K,outsidethegap,with stand- driven by MB. PCEBs in the orbital period range of the ard deviations of ∼ 4000K and ∼ 9500K respectively. The period gap, however, need to have less massive secondaries dispersioninboth,observationsandsimulations,issubstan- in order to still be detached systems in this period range (≃2−3h).ThismeansthataftertheCEphasetheybecome tial.WethereforeconcludethattheWDtemperatureisnot asuitableparametertoidentifydCVswithintheperiodgap. closer only due to GR and therefore they evolve slower towards shorter periods. This effect, however, might be com- pensated by the fact that systems with more massive com- panionstendtoemergefromtheCEphaseatslightlylonger 7 CONCLUSION periods(e.g.,Zorotovic et al.2011b,2014).Whichofthetwo effects is stronger is uncertain because it depends on, e.g., We have measured six new periods of close detached the initial orbital period, the star formation rate, the CE WD+MSbinaries with secondary stars in thespectral type efficiency or thestrength of MB and GR. rangeM4−M6,whichshouldcorrespondtothespectraltype Figure 6showstherelation between WDeffectivetem- rangeofsecondarystarsindetachedCVscrossingtheorbital perature and orbital period for our simulations with α = period gap. These new measurements bring the sample of CE 0.25 (grey scale density plot) and for the observed systems suchbinarieswithmeasuredorbitalperiodto52systems.A with available WD temperatures (red dots). The two ob- clearpeakintheorbitalperioddistributioncanbeobserved (cid:13)c 2015RAS,MNRAS000,1–11 10 M. Zorotovic et al. Figure6.RelationbetweentheWDeffectivetemperatureandorbitalperiod.Theintensityofthegreyscaleforthesimulationsmeans thesameasinFig.5.ThereddotsaretheobservedsystemswithavailableWDtemperatures. at theposition oftheorbital period gap, in agreement with References thepredictionsfromthedisruptedmagneticbrakingmodel. Althaus,L. G., Benvenuto,O. G., 1997, ApJ, 477, 313 Comparing the observed period distribution with the res- Andronov,N.,Pinsonneault, M., Sills, A.,2003, ApJ,582, ultsofbinarypopulationmodels wefindthat thispeakcan 358 not be explained without assuming that CVs are crossing Appenzeller,I., et al., 1998, TheMessenger, 94, 1 thegapasdetachedsystems.Thereforeweconcludethatin- Baraffe, I., Kolb,U., 2000, MNRAS,318, 354 deedCVsbecomedetachedbinariesattheupperedgeofthe period gap, which supports the idea that magnetic braking Bouvier,J.,2007,inBouvier,J.,Appenzeller,I.,eds.,IAU becomes inefficient at thefully convectiveboundary. Symposium,vol.243 of IAU Symposium, p.231 We also see clear signs of a different WD mass distri- Camacho, J., Torres, S., Garc´ıa-Berro, E., Zorotovic, M., butionin thegap andat longerperiods. TheWDmass dis- Schreiber, M. R., Rebassa-Mansergas, A., Nebot Gómez- tribution of systemswithin thegap shows a second peak at Morán, A., Gänsicke, B. T., 2014, A&A,566, A86 larger masses which is consistent with having two popula- Chabrier, G., Baraffe, I.,1997, A&A,327, 1039 tionsin thisperiod range,i.e. normalPCEBs andthemore Clemens, J. C., Reid, I. N., Gizis, J. E., O’Brien, M. S., massive detached CVs crossing the gap, in agreement with 1998, ApJ,496, 352 themodel recently proposed bySchreiberet al. (2016). Davis, P. J., Kolb, U.,Willems, B., Gänsicke, B. T., 2008, MNRAS,389, 1563 Drake, A.J., et al., 2010, ArXiv:astro-ph/1009.3048 Fontaine,G., Brassard, P., Bergeron, P., 2001, PASP,113, 409 Green, R. F., Richstone, D. O., Schmidt, M., 1978, ApJ, ACKNOWLEDGEMENTS 224, 892 Hurley,J.R.,Tout,C.A.,Pols,O.R.,2002,MNRAS,329, We thank Fondecyt for their support under the grants 897 3130559 (MZ), 1141269 (MRS), and 3140585 (SGP). The Ivanova,N.,Taam, R.E., 2003, ApJ,599, 516 research leading to these results has received funding from theEuropeanResearchCouncilundertheEuropeanUnion’s King, A.R., Kolb, U.,1995, ApJ, 439, 330 Seventh Framework Programme (FP/2007-2013) / ERC Knigge, C., 2006, MNRAS,373, 484 GrantAgreementn.320964(WDTracer).Thisresearchwas Knigge, C., Baraffe, I.,Patterson, J., 2011, ApJ,194, 28 also partially funded by MINECO grant AYA2014-59084-P Kouwenhoven,M.B.N.,Brown,A.G.A.,Goodwin,S.P., and by the AGAUR (ARM). The results presented in this Portegies Zwart, S.F., Kaper, L., 2009, A&A,493, 979 paper are based on observations collected at the European Kroupa,P.,Tout,C. A.,Gilmore, G., 1993, MNRAS,262, Southern Observatory under programme IDs 093.D-0441 545 and 095.D-0739. Nebot Gómez-Morán, A., et al., 2009, A&A,495, 561 (cid:13)c 2015RAS,MNRAS000,1–11