X-ray Luminosities of Optically-Selected Cataclysmic Variables and Application to the Galactic Ridge X-ray Emission

0.41 MB·English

by  R. C. Reis

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed11December 2013 (MNLATEXstylefilev2.2)
X-ray Luminosities of Optically-Selected Cataclysmic Variables and
Application to the Galactic Ridge X-ray Emission
R. C. Reis 1⋆, P. J. Wheatley2†, B. T. Ga¨nsicke2, & J. P. Osborne3
1InstituteofAstronomy,MadingleyRoad,Cambridge,CB30HA
2DepartmentofPhysics,UniversityofWarwick,Coventry,CV47AL
3
3UniversityofLeicester,UniversityRoad,Leicester,LE17RH
1
0
2

n
11December 2013
a
J

7 ABSTRACT
BystudyingSwiftX-rayspectraofanoptically-selected,non-magneticsampleofnearbycat-
]
aclysmic variables (CVs), we show that there is a population with X-ray luminosity much
E
lowerthanaccountedforin existingstudies.We findanaverage0.5-10.0keVluminosityof
H
8×1029ergs−1 which is an order of magnitude lower than observedin previoussamples.
.
h Lookingattheco-addedX-rayspectrumoftwentyCVs,weshowthatthespectralproperties
p ofthisoptically-selected,lowX-rayluminositysample–likelycharacteristicofthedominant
- populationofCVs–resemblesthatoftheirbrightercounterpart,aswellastheX-rayemission
o
originatingintheGalacticridge.ItisarguedthatifthespacedensityofCVsisgreaterthan
r
t thecurrentestimates,asitisindeedpredictedbypopulationsynthesismodels,thenCVscan
s
significantlycontributetotheGalacticridgeemission.
a
[
Keywords:

1 Stars:CataclysmicVariables(CVs)-X-rays:GRXE
v
3
1
2
1 1 INTRODUCTION 2009)orii)originatingfromdiffusegasregionssuchasmolecular
. clouds illuminated by X-rays from point sources (e.g. Murakami
1 Theserendipitousdetectionin1962ofanalmostuniformCosmic
etal.2000)orbombardedbylow-energycosmic-rayelectrons(e.g.
0 X-ray Background (CXB) is regarded as one of the first discov-
Yusef-Zadehetal.2002), and/or non-thermal processes inthein-
3 eriesof extrasolar X-rayastronomy (Giacconi et al. 1962) and is
1 terstellar medium (e.g. Dogiel et al. 2002). Theapparent thermal
thought to be mostly due to unresolved active galactic nuclei to-
: spectrumof theGRXE(Koyama et al.1986) impliesanemitting
v getherwithtypeIasupernovae(e.g.Zdziarski1996;Draper&Bal-
plasmawithtemperatureofafew keV.Theenergydensityofthis
i lantyne 2009; Moretti et al. 2009). A decade later the possibility
X hypothetical plasma is over two orders of magnitude higher than
ofaGalacticcomponenttothetotalmeasuredCXBwassuggested
thatofnormalinterstellarmatteranditstemperatureistoohighfor
r (Cooke, Griffiths & Pounds 1970). Ensuing observations showed
a ittobegravitationallyboundtotheGalacticplane(Koyamaetal.
that this Galacticcomponent tothe X-ray background isconcen-
1996).FurthermoreDogieletal.(2002)showedthattheenergyre-
tratedneartheGalacticdisk,coveringacontinuousridgeofwidth quiredtoreplenishtheoutflowingplasmaisashighas1042ergs−1
∼10deg.extendingalongtheGalacticplanefortensofdegrees–
whichisequivalenttothereleaseofkineticenergyfromonesuper-
theGalacticRidgeX-rayEmission(GRXE,seee.g.Worralletal.
novaoccurringevery30yearsintheGalacticplaneregion.Withan
1982;Warwicketal.1985,1988).
expected rateof 2-3 supernovae per century inthewholeGalaxy
NumerousauthorshavemodelledtheGRXEspectrumasorig-
(Tammann1982),thisleadstotheunlikelyrequirementthatallthe
inating from two collisionally-ionised plasma components (e.g.,
energyassociatedwithsupernovae intheGalaxygoesintoexclu-
Koyamaetal.1986,1996;Kanedaetal.1997):Asoftcomponent
sivelyheatingthishypotheticaldiffuseplasma.
(kT∼0.8keV)possiblyproducedbysupernovashockwaves(e.g.
The absence of a plausible heating mechanism to this hy-
Kaneda et al. 1997) and a hard (kT∼ 8 keV) component whose
pothetical diffuse thermal plasma, and the similarities of the X-
originisstillatopicofmuchdiscussion.Severalexplanationsfor
ray spectra of the ridge and CVs, led many to believe that the
the nature of this hard component have been suggested, amongst
ridgeemissionisstillmost likelytoarisefromasyet unresolved
them:i)asuperpositionofdiscrete,faintX-raysourcessuchascat-
sourcessuchascataclysmicvariables(CVs)andotheraccretingbi-
aclysmic variables (Worrall et al. 1982; Revnivtsev et al. 2006a,
narysystems(Munoetal.2004;Revnivtsevetal.2007).Anultra-
deep (1 Ms) Chandra ACIS-I study of the Galactic centre region
⋆ E-mail:[email protected] (Revnivtsevetal.2009)hassuccessfullyresolvedover80percent
† E-mail:[email protected] ofthediffuseemissionintodiscretesourcesat 6–7keV(seealso
(cid:13)c 0000RAS
2 Reis etal.
Hong2012;Yuasaetal.2012),howeverthenatureofthesesources FortheSwiftsurveypresentedhere,weselected16CVsfrom
remainsuncertain(e.g.Warwicketal.2011) andthecontribution SDSSDR5inwhichtheopticalspectrumisdominatedbyemission
of CVs to the total GRXE luminosity function is still known. A fromacoolwhitedwarf.Thesespectrahavebeenskysubtracted,
key uncertainty is the X-ray luminosity function of CVs. Previ- corrected for telluric absorption and spectrophotometrically cali-
ous studies were suggestive of mean CV X-ray luminosities of bratedbytheSpectro2dpipeline(Stoughtonetal.2002).Thissam-
log(< L >) ∼ 31.5 (Mukai & Shiokawa 1993; Verbunt et al. ple was supplemented by four additional low-mass transfer sys-
x
1997) in the hard band (2.0–10.0keV), with at least an order of tems withsimilar optical properties: V455And (Araujo-Betancor
magnitudespreadaboutthismeanvalue.WorkdoneonASCAdata etal.2005),PQAnd(Schwarzetal.2004;Pattersonetal.2005a),
(Yamauchi etal.1996) concluded thatforCVstobeaccountable REJ1255+266(Watsonetal.1996;Wheatleyetal.2000a;Patter-
fortheGRXEthesources’2.0–10.0keVluminositycouldnotbe son et al. 2005c) and ASAS0025+1217 (aka FL Psc, Templeton
higherthan2×1033ergs−1.Basedonmodelcalculations,Tanaka etal.2006;Ishiokaetal.2007).Theobjectnamesandcoordinates
etal.(1999)showedthattheridgeemissionrequiresaclassofhard ofthe20SwifttargetsarelistedinTable1.Ourtargetsformarepre-
sourceswithaluminosityinthe1029−30ergs−1range,thusmak- sentativesampleofspectroscopicallyselectedlow-luminosityCVs
ingCVsapparentlytooluminousasaclass. withdistancesintherange∼75−400 pc(seeSect. 4.1).
Sazonov et al. (2006) found CVscontributingonly at L &
x
1031ergs−1,buttheirsamplewasX-rayselectedandweremostly
consistent of magnetic CVs, and thus biased tohigh X-ray lumi-
nosities.Ontheotherhand,amorerecentstudybyBycklingetal.
(2010) usedadistance-limitedsampleofnon-magnetic CVswith
known distances and found systematically low luminosities con-
centratedaroundLx ≈1030.5ergs−1.However,eventhissample 3 OBSERVATIONSANDDATAREDUCTION
wasbiasedtohigh accretionratesbyrelianceoninhomogeneous
selectioncriteriasuchasdwarfnovaoutburst. Oursampleof20optically-selected, non-magnetic CVswereob-
Until recently, the population of known CVshas been dom- servedusingtheX-RayTelescope,XRT(0.2-10.0keV) onboard
inated by systems discovered because they displayed copious ac- the Swift Gamma-Ray Burst Explorer (Gehrels et al. 2004). The
cretionactivity,eitherintheformofoutbursts,orX-rayemission variousobservations,listedinTable1,werereducedusingthetools
(Ga¨nsickeetal.2002, 2005a). Incontrasttothis,population syn- providedintheHEASOFTv6.9softwarepackage. Alldatawere
thesismodelshavelongpredictedthattheCVpopulationshouldbe extractedinthephotoncounting(PC)modewiththestandardgrade
dominated (>95%) by short-period low-luminosity systems with selection(0–12) for thismode. For each observation animage in
extremely low-mass donor stars (Kolb 1993; Howell et al. 2001) the 0.2-10.0keV band was obtained from which a spectrum was
andthusshouldhaveaverageX-rayluminosities. 1030ergs−1. extractedfromacircularregionofradius47”,correspondingto90
Overthepastyears,theSloanDigitalSkySurvey(SDSS)hasiden- percentofthepointspreadfunctionat1.5keV.Backgroundspectra
tifiedasubstantialnumberofCVswhoseopticalspectraaredomi- wereextractedfromanannularregioncentredontheX-raysource
natedbyacoolwhitedwarf(e.g.Szkodyetal.2009),implyingvery of inner and outer radius of 50” and 200” respectively. Response
low secular average accretion rates (Townsley & Bildsten 2003; files(version10)weredownloaded1andusedforspectralanalysis.
Townsley&Ga¨nsicke 2009; Ga¨nsicke etal.2009), andthat have When looking at the spectrum of each individual target we used
extremelylow-massdonorstars(Littlefairetal.2006b,2008).This the ftool2 GRPPHA to provide a minimum of 4 counts per bin
sampleofoptically-selected,non-magneticCVsprovidethemeans andthusprovidetwoormoreindependentspectralbins.Following
to measure the X-ray luminosity of CVs towards the low-end of thisrequirementonlysourceswith8ormorecountswereindivid-
their luminosity function and thus to better assess their contribu- ually analysed in this manner. Model fits were minimised using
tiontotheGalacticridgeX-rayemission. Cashstatistics(C-statinXSPEC;Cash1979)duetothelownum-
InthefollowingsectionswepresentresultsonSwift-XRTob- berofcountsperbin.Allspectralanalyseswereperformedusing
servationsmadeonasampleof20CVswhoseopticalspectraare XSPECv12.7.0(Arnaud1996).
dominated by the white dwarf, indicative of low accretion rates. The source and background event files were used to calcu-
Thesearethesystemsexpectedtodominateinnumbersthepopu- late count-rates, R, for each target in the 0.5-10.0keV energy
lationofCVs. band. Thenet counts werecomputed fromthetotalcounts inthe
sourceregionlessthebackgroundcount,scaledbytheratioofthe
source/background area.Thecount-rateforeachindividual target
wascomputedusingthetotallive-timeandtheuncertaintiesareas-
2 TARGETSAMPLE sumedtofollowsimplePoissonstatistics.Table1listthenetcounts
for the various observations. In order to analyse the sample as a
TheSloanDigitalSkySurvey(SDSS;Yorketal.2000)isanimag-
group,inSect.4.2weco-addedalltheindividualspectrausingthe
ingandspectroscopicsurveyofthehighGalacticlatitudeskyvis-
ftool XSELECT. For the co-added spectrum, a minimum of 20
iblefromtheNorthernhemisphere. Webasedourtargetselection
onDataRelease5(DR5),whichcoveredover8,000deg2ofthesky countsperbinwereusedandmodelfitswereminimisedusingχ2
statistics.
and performed spectroscopy on over 1million objects (Adelman-
McCarthyetal.2006).Althoughtheprinciplegoalofthissurvey
istosurveythelarge-scaledistributionofgalaxiesandquasars,it
hasalsoprovidedvastamountofdataonstars.DuetoCVshaving
non-stellar colours they are serendipitously discovered by SDSS.
Szkody et al. (2011) have identified close to 300 CVs, of which
∼ 45haveaverylowmassaccretionrateandarethusdominated 1 http://heasarc.nasa.gov/docs/heasarc/caldb/data/swift/xrt/index.html
bythewhitedwarf. 2 http://heasarc.gsfc.nasa.gov/ftools/
(cid:13)c 0000RAS,MNRAS000,000–000
The LuminosityFunctionofCVs and theGRXE 3
Table1.Systemproperties
Target RA(2000) Dec(2000) Porb g Live Counts ModelFluxa Distanceb Distancec Luminosity References
time(s) [0.5–10keV] ×10−13 [0.5–10.0keV]
(min) mag. ergcm−2s−1 (pc) (pc) ×1029(ergs−1)
SDSS0131–0901 013132.39 -090122.3 81.5 18.3 4940 23.9 2.0±0.5 240 219±72 13.8±6.4 1
SDSS0137–0912 013701.06 -091234.9 79.7 18.7 4493 16.2 1.5±0.4 230 263±86 9.4±4.6 2
SDSS0843+2751 084303.99 +275149.7 85.5 18.9 476 <1d <0.3 240 288±95 <1.8 3,4
SDSS0904+0355 090403.48 +035501.2 86.0 19.3 5670 16.8 1.2±0.3 260 347±114 9.9±4.8 5
SDSS0904+4402 090452.09 +440255.4 19.4 4367 1.0 0.09±0.01 320 363±119 1.2±0.5 6
SDSS0919+0857 091945.11 +085710.0 81.3 18.2 167 <1d <2 220 209±69 <11 6,7
SDSS1137+0148 113722.25 +014858.6 109.6 18.7 3798 11.8 1.3±0.4 220 263±86 7.4±0.4 8
SDSS1238–0339 123813.73 -033933.0 80.5 17.8 4106 40.3 4.1±0.8 180 174±57 15.7±7.0 9
SDSS1339+4847 133947.12 +484727.5 82.5 17.7 4051 16.7 1.7±0.5 170 166±54 5.9±2.8 10
SDSS1457+5148 145758.21 +514807.9 77.92 19.6 6293 14.8 1.0±0.3 320 398±131 11.9±5.8 11
SDSS1501+5501 150137.22 +550123.4 81.9 19.4 4800 11.6 1.0±0.3 300 363±119 10.7±5.5 12
SDSS1507+5230 150722.33 +523039.8 66.6 18.3 7002 15.6 0.9±0.3 225 219±72 5.6±2.7 12,13,14
SDSS1556–0009 155644.24 -000950.2 106.7 18.0 7463 42.8 2.4±0.4 135 191±63 5.2±2.3 7,15
SDSS1610–0102 161033.64 -010223.3 80.5 19.0 9400 18.8 0.8±0.2 240 302±99 5.7±2.7 16,17
SDSS1702+3229 170213.26 +322954.1 144.1 17.9 6840 25.7 1.5±0.4 180 - 6.0±2.8 18,19
SDSS2048–0610 204817.85 -061044.8 87.3 19.4 14734 68.6 1.9±0.3 270 363±119 16.8±7.3 20,21
ASAS0025+1217 002511.07 +121712.1 ≃80 17.4v 3309 53.8 6.7±1.2 125 145±47 12.6±5.5 22,23
PQAND 022929.54 +400240.2 ≃80 19.0v 13215 16.5 0.5±0.1 150±50 302±99 1.4±1.0 24,25
RE1255+266 125510.56 +264226.9 ≃120? 19.2 4298 8.8 0.8±0.3 180±50 326±107 3.3±2.2 26,27
V455And 233401.45 +392141.0 81.1 16.5v 8666 16.0 0.8±0.2 90±15 95±31 0.7±0.3 28
Notes:aFluxeswerecalculatedassumingtheflux–countraterelationshipgiveninthetext(seeSect.4.3.1)inthe0.5–10keVrange.bdistancesobtainedby
modellingtheopticalSDSSspectra,asdescribedintheSect.4.1,withuncertaintiesof20%,exceptforthelastfourtargets,wherepublisheddistanceestimates
aregiven.ThedistanceslistedinthiscolumnareusedintheX-rayanalysis.cdistancesobtainedfrom<Mg>=11.6±0.7(Gaensickeetal.2009),except
forSDSS1702+3229,whoseperiodistoolongtoadoptthisabsolutemagnitude.v V-bandmagnitude.d 1σupperlimit.References:1 Southworthetal.
(2007);2Pretoriusetal.(2004);3Pattersonetal.(1998);4 Katoetal.(2004);5Woudtetal.(2005);6Dillonetal.(2008);7Thorstensenetal.inprep;
8 Pattersonetal.(2003);9 Zharikovetal.(2006);10 Ga¨nsickeetal.(2006b);11 Uthasetal.(2012);12 Littlefairetal.(2008);13 Littlefairetal.(2007);
14Pattersonetal.(2008);15Woudtetal.(2004);16Woudt&Warner(2004);17Copperwheatetal.(2009);18Littlefairetal.(2006a);19Boydetal.(2006);
20 Woudtetal.(2005);21 Dillonetal.inprep;22 Templetonetal.(2006);23 Ishiokaetal.(2007);24 Pattersonetal.(2005b);25 Vanlandingham etal.
(2005);26Wheatleyetal.(2000b);27Pattersonetal.(2005d);28Araujo-Betancoretal.(2005)
Figure1.Threecomponentsmodel(whitedwarf,opticallythindisc,secondarystar)oftheaverageopticalspectrumofSDSS1339+4842(left,Sp(2)=M8,
Twd =12500K,Td =6500K,Σd =1.7×10−2gcm−2andd=170pc)andSDSS1137+0148(right,Sp(2)=M6.5,Twd =13000K,Td =6500K,
Σd = 3.5×10−2gcm−2andd= 220pc).Theobserveddataareshowningrey,theindividualthreecomponentsasdottedblacklines,andthesummed
modelassolidblackline.
4 ANALYSISANDRESULTS (1997, 1999, 2006b), here we provide only a brief summary.
The white dwarf is represented by model spectra computed with
the TLUSTY/SYNSPEC codes of Lanz & Hubeny (1995), with
4.1 Distanceestimates
a fixed radius R = 8.7 × 108cm implied by the Hamada
wd
In order to calculate the luminosity distribution of the sample it & Salpeter (1961) mass-radius relation for an assumed mass of
wasnecessarytoobtainanapproximatedistancetoeachindividual Mwd = 0.6M⊙. The secondary star is represented by observed
source.Thiswasdonefollowingtwodifferentapproaches. templatescoveringspectraltypes(Sp(2))M0.5toM9fromBeuer-
Thefirstmethodconsistsoffittingathree-component model mann et al. (1998) and L0 to L8 from Kirkpatrick et al. (2000,
accounting for the flux contributions of the white dwarf, the ac- 1999). TheradiusofthesecondarystarisestimatedfromRoche-
cretion disc, and the companion star to the optical spectra of lobe geometry, and depends primarily on the orbital period. Or-
the 16 CVs for which SDSS spectroscopy is available. A de- bitalperiodmeasurementsareavailableformostofthetargets(Ta-
taileddescriptionofthisapproachcanbefoundinGa¨nsickeetal.
(cid:13)c 0000RAS,MNRAS000,000–000
4 Reis etal.
1
0
0.
V V
nts/sec/ke 10−3 nts/sec/ke 10−3
u u
o o
d c d c
ormalize 10−4 ormalize 10−4
N N
2 5
Ratio 11.5 Ratio 11.
5
0. 1 2 5 0.5 1 2 5
Energy (keV) Energy (keV)
Figure2.Swift-XRTX-raybackgroundsubtractedspectrumofcombinedsources.Left:Data/modelofsimpleone-temperaturethermalplasmawithatem-
peratureof∼6keV.Thismodelprovidedapoorfitwithχ2/ν =31.3/19andexhibitedresidualatenergies <1.2keV.Right:Data/modelratiofortwo-
∼
temperaturethermalplasmawithtemperaturesof8+10and0.62+0.16keVaswellasphotoelectricabsorption.Thisprovidedthebestfit(χ2/ν=11.3/17)
−3 −0.24
forthecombineddata.
ble1),anditisapparentthatmostofthesystemsarelocatedclose (MEKAL model in XSPEC; Mewe et al. 1986; Liedahl et al.
tothe80minperiod minimum,for whichweadopt R = 8.6× 1995) havingatemperatureof≈ 6keV(Model 1;Table2).This
2
109cm. For SDSS1137+0148 (RZLeo), SDSS1556–0009, and model provides a poor fit with χ2/ν = 31.3/19 and exhibited
SDSS1702+3229, weassume1.28×1010 cm,1.17×1010 cm, residualatenergies <1keV.Amuchimprovedfitwasachievedby
∼
and 1.53 ×1010 cm, respectively. Free parameters in the three- theadditionofasecondthermalplasmamodel(inasimilarman-
component model are the white dwarf temperature T , the dis- ner to e.g. van Teeseling & Verbunt 1994; Wheatley et al. 1996)
wd
tance d, the temperature T and column density Σ of the disk, absorbedbyaneutralhydrogencolumn(WABS3;Model2,Fig.2,
d d
as well as the spectral type of the secondary star. The parame- right), however, it was found that the value of N is degenerate
H
ters were varied in a forward-modelling approach until all three with the plasma temperature. Nonetheless, for a typical value of
spectral components in the observed spectrum were consistently N =4×1020cm−2 (Baskillet al.2005), wefindatemperature
H
reproduced,Fig.1showstwoexamplefits(SDSS1137+0148 and of0.62+0.16keV,consistentwiththevaluesfoundbyBaskilletal.
−0.24
SDSS1337+0148), and Table1 lists the distances determined by (2005)forasampleof34CVsusingasimilarmodel.Wehavethus
thesefits.Theuncertaintyofthedistancesdeterminedinthisway fixedthevalueofN to4×1020cm−2whenestimatingtheerrors
H
is estimated to be ≃ 20% (see Howell et al. 2002; Szkody et al. presentedinTable2.
2002;Ga¨nsickeetal.2005b,2006a,b,foradetaileddescriptionof Thebestfittingmodelforthissampleoflow-luminosityCVs
themethodemployedhereandassociateduncertainties.). ishereinterpretedasatwocollisionally-ionisedplasmawithtem-
FourofourtargetshavenoSDSSspectrum,andTable1lists peraturesof8+10 and0.62+0.16keV.Ofcourse, thefact thatwe
−3 −0.24
previouslypublisheddistanceestimatesandreferences. havetwotemperaturesdoesnotnecessarilyimplythepresenceof
Asasecondmethodofestimatingthedistancestoourtargets two discrete components in the X-ray spectrum as this likely a
weadoptedthemeanabsolutemagnitudeforshort-periodCVswith simpleapproximationtocommoncoolingflowmodelswhichsuc-
white dwarf dominated spectra, < Mg >= 11.6 ± 0.7, which cessfullyrepresentthespectraofmoreluminousCVs(e.g.Wheat-
Ga¨nsicke et al. (2009) established largely based on systems for ley et al. 1996; Mukai et al. 2003; Baskill et al. 2005; Byckling
which ultraviolet spectroscopy is available, and which leads to a et al. 2010). The results presented here for the spectral proper-
∼ 30% uncertainty in the distance. The distances corresponding tiesofoursampleofnon-magnetic,lowluminosityCVsareagain
totheobservedgandV magnitudesarealsolistedinTable1,with consistent with that of the Galactic ridge emission (e.g. Koyama
theexceptionofSDSS1702+3229,whoseorbitalperiodistoolong etal.1986;Kanedaetal.1997).Usingthebest-fitmodel,acount-
toqualifyforthismethod.Forallsystems,bothdistanceestimates rateof4.0±0.2×10−3s−1resultedina0.5–10keVunabsorbed
agreewithinthequotederrors.Wenotethatanindependentanaly- energy flux4 of 1.6 ±0.2×10−13ergcm−2s−1. These values
sisofHSTspectroscopyofSDSS1507+5230ledtoadistancees- were used as conversion factors between the 0.5–10keV count
timateof250±50pc,(Uthasetal.2011)entirelyconsistentwith rate and flux in the following section. We note here that for the
bothofourownvalues(Table1). only object common in both our sample and that of Byckling
For the determination of the X-ray luminosities carried out et al. (2010) (namely ASAS0025+12), the luminosity found here
in §4.3, we adopted the distances based on our three-component ofL0.5−10 = (1.3±0.6)×1030ergs−1 (Table1),basedonthe
model for the 16 systems with SDSS spectra, and the published methodologydescribedabove,isfullyconsistentwiththevalueof
distancesfortheremainingfoursystems. L2−10 =(1.6+−30..88)×1030ergs−1foundintheirwork,evenwhen
consideringthedifferentenergyrangeusedinthiswork.
4.2 Spectralanalysis
In order to investigate the spectral nature of the twenty optically
selectedCVsweco-addedtheirindividual spectrausingtheftool
XSELECT. The combined spectrum was then grouped so as to
3 Using the standard BCMC cross-sections (Balucinska-Church & Mc-
provideaminimumoftwentycountsper energybinandthusen-
Cammon1992)andANGRabundances(Anders&Grevesse1989).
abletheuseofχ2statistics.Figure2(left)showstheaveragespec- 4 UnabsorbedfluxobtainedusingtheXSPECmodelCFLUXconvolved
trum fitted with a simple one-temperature thermal plasma model withModel2fromTable2.
(cid:13)c 0000RAS,MNRAS000,000–000
The LuminosityFunctionofCVs and theGRXE 5
Figure3.Left:Histogramofcountsdetectedintheenergyband0.5–10.0keV. Right:Sameasbeforebutforthefluxobtainedusingtherate–fluxconversion
factorasdescribedinSect.4.3.1.
Table2.Modelparametersforthecombinedsourcespectra.
Parameter Model1 Model2
NH(×1020cm−2) – 4
kT1keV 5.8+−21..02 8+−130
Norm1(×10−5) 8.2+−00..87 7.2±0.8
kT2keV – 0.62+−00..1264
Norm2(×10−5) – 0.8±0.3
χ2/ν 31.3/19 11.3/17
Notes–Model1isthesingle-temperaturethermalplasmamodelMEKAL
inXSPEC.Model2assumesatwo-temperaturethermalplasmawithpho-
toelectricabsorption(WABS(MEKAL+MEKAL)inXSPEC).Thevalue
ofNHwasfrozenat4×1020cm−2.Thequotederrorcorrespondstoa90
percentconfidencelevelforoneparameterofinterest(∆χ2=2.71).
4.3 X-rayphotometry
4.3.1 Energyfluxes
Figure4.X-rayluminositydistributionforasampleofoptically-selected
Ahistogramofthenumberofsourcesasafunctionofthecountsin CVs (blue). Only sources with observed fluxes consistently greater than
the0.5–10.0keVenergyrangeisshowninFig.3(Left).Inorderto zeroareincludedinthehistogram.Themagentaandcyanarrowsshowsthe
obtainanestimateoftheenergyflux(in ergcm−2s−1)weused upperlimitsforSDSS0843+2751andSDSS0919+0857respectively. The
thespectralmodeldescribedintheprevioussectiontocomputean meanGaussiandistribution(solidblue)has< log(L0.5−10) >= 29.78
with a variance of 0.16. For comparison with previous, X-ray selected
averageconversionfactorbetweencount-rate(R)andenergyfluxin
surveys, we show in green the (renormalised) Gaussian distribution ob-
therange0.5−10keV.Wefind(Sect.4.2)thatforthecombined
tained for the 46 sources catalogued by the ROSAT all sky survey (de-
spectrum of all twenty sources, a two-temperature optically thin
rived from Verbunt et al. 1997 scaled to the 0.5-10keV range used in
plasmamodelabsorbedbyaneutralhydrogencolumnequivalentto thiswork.Thisillustrative, X-rayselected, distribution hasameanvalue
NH≈4×1020cm−2yieldsaconversionfactorfortheunabsorbed of< log(L2−10) >= 30.96andavarianceof0.78,clearlyhigherthan
energyfluxofF(0.5−10) =(4.1±0.4)×10−11×R ergcm−2s−1, oursample.
whereRisthecount-rateinthe0.5–10keVenergyband.Asacon-
sistencycheck weused thismodel tofittheindividual spectraof
the4observationswithover40counts(seeTable2)allowingonly
amultiplicativeconstanttovary.Thisresultedinvaluesforthecon-
versionfactorvaryingfromapproximately3.8to4.6×10−11,in SDSS0843+2751andSDSS0919+0857werenotusedinthecon-
agreementwiththevalueabove.Thefluxesforthevarioustargets structionofthehistogramduethesourceshavingacountratecon-
obtainedasdescribedarealsolistedinTable1andshowninFig.3 sistentwithzero,possiblyresultingfromtheirshortexposuretime
(Right). (see Table 1). However the upper limits to their luminosities are
displayed with magenta and cyan arrows respectively. The solid
redlineshowstheGaussiandistributionforthemean(0.5–10keV)
4.3.2 Luminositydistribution
log-luminositywith< log(L0.5−10) >= 29.78andavarianceof
Table1liststhecalculated0.5–10.0keVluminositiesofalltwenty 0.16.Forcomparison,inFig.4weshowingreenthe(renormalised)
sources.Thelargeerrorinthesevaluesaretheresultofpropagated luminositydistributionobtainedfromtheX-rayselectedROSATall
errors in both the distance and flux. A histogram of the number skysurveycataloguefromVerbuntetal.(1997)afterscalingtothe
of sources as a function of log-luminosity is displayed in Fig. 4. 0.5-10keVrangeusedhereassumingModel2(outlinedinTable2
anddescribedin§4.2).
(cid:13)c 0000RAS,MNRAS000,000–000
6 Reis etal.
Figure5.Left: X-rayluminosity (0.5-10keV)versus orbital periods forthe samplepresented inthis work (red)andthat ofByckling etal. (2010, their
Fig.7)(black).The2-10keVfluxquotedinthelatterwasconvertedtothe0.5-10keVrangeusingthemodeldetailedinTable2.Right:Cumulativesource
distributionasafunctionofX-rayluminosityforoursample(red)andforthatpresentedinBycklingetal.(2010,theirFig.6)(black).Thedashedlineshows
thepowerlawN(>L)=k(L/Lt)−α,wherek=2.39×10−7pc−3andLt=3×1030ergs−1asperBycklingetal.(2010).
5 DISCUSSION X-rayluminosityfunctioninanoptically-selectedsampleofCVs
havingparallax-baseddistancemeasurements.Inthatstudy,theau-
SuggestionsthattheGalacticridgeX-rayemissionisdiffusecame thorsfindapeakintheluminosityfunctionat∼1030−31ergs−1,
about due to failure in fully resolving the emission into point systematicallylower thanprevious –X-rayselected–studiesbut
sources (e.g. Ebisawa et al. 2001). Non-magnetic CVs have also stillmoreluminousthantheresultfoundhere.Figure5(left)shows
beendismissedasamaincontributor totheGRXE(e.g.Sazonov theBycklingetal.(2010)sample(black)togetherwithourresults
et al. 2006; Revnivtsev et al. 2006b) due to suggestions that the (red)fortheLuminosity–Orbitalperiodplane.Itisclearthatweare
overall population is too luminous, with a mean X-ray luminos- probingadifferentparameterspacetoBycklingetal.(2010),with
itygreaterthan∼ 1031ergs−1 (e.g.Eracleousetal.1991;Rich- overallloworbitalperiodsasexpectedformoreevolved,andthus
man1996;Verbuntetal.1997;Baskilletal.2005).Wearguehere intrinsicallyfainter,systems.WealsoshowinFig.5(right)thecu-
that the latter is likely a result of a selection bias in their X-ray mulativedistribution–LogN(>L )whereL istheluminos-
Vol Vol
luminosity function caused by the predominant use of X-ray se- itypercubicparsecvolumeasafunctionofLogL.Forthesample
lected samples. By studying an optically-selected sample of non- of Byckling et al. (2010), we assume a volume out to 200 pc, in
magnetic,intrinsicallyfaintCVs,wefindapopulationoflowX-ray accordancetothepreviousauthors.Forthesamplepresentedhere,
luminosityCVs,havinganaverageluminosityof< L0.5−10 >= thefurthestobjectislocated∼400pcaway(Table2).However,as
8×1029ergs−1 whichstillresemblestheX-rayspectrumofthe oursampleisnotcompleteouttothisradius,weestimateacorrec-
GalacticRidge.Thispopulation,iffoundtoexistinlargenumbers, tionfactorbynotingthatSDSScovered8,000deg2 (∼ 20%;see
couldbeastrongcontributortotheoverallGRXEbelow∼10keV. §2)oftheskyandoursampleuses16outofthe30lowluminosity
The X-ray spectra of CVs are often characterised by a two- systemsdetectedinDR5.Asthesizeofthepopulation presented
temperature plasma model (see e.g. Mukai & Shiokawa 1993; here is still highly uncertain, the normalisation of the logN–logS
Baskill et al. 2005). In Sect. 4.2 we showed that the combined plot,andwithitthespacedensityofthesesystems,shouldbeinter-
spectrum of this sample of twenty low-luminosity CVs has the pretedwithextremecaution. Nonetheless, theseresultsshow that
same spectral characteristics as that of the better known, high- the sample presented in this work fills the gap between the only
luminosity CVs (Fig. 2). This two-temperature spectrum closely low-luminosityoutlier(GWLibatL2−10 ∼ 5×1028ergs−1)in
resemblesthatoftheGalacticridgeX-rayemission(Mukai&Sh- thesampleofBycklingetal.(2010),andthepeakoftheirdistribu-
iokawa 1993). Eighteen out of the twenty sources in our sample tionat∼1030−31ergs−1.
weredetected withSwiftXRTand werefound tohave X-raylu- It was shown by Pretorius et al. (2007) and Pretorius &
minositiesintherange1028−30ergs−1.Figure4showsthisdis- Knigge(2012)thatthevastmajorityofCVscouldbefainterthan
tributiontogetherwiththeupperlimitofthetwosourceshavinga ∼5×1029ergs−1–andthusyetundetected–basedonthelim-
countrateconsistentwithzero.Thepeakofthedistributionforthe itstotheirCVspacedensityasfoundfromROSATsurveys.Muno
optically-selectedsampleusedhereisconsiderablylowerthanthat etal.(2004)showedthattoaccountforthediffuseemissionwithin
presented by Verbunt et al. (1997) of < log(L2.0−10) >= 30.8 20pc of the Galactic centre, approximately 0.2% of stellar mass
(showningreeninFig.4),especiallyafter considering thelarger wouldhavetobehardX-raysourceswithL >3×1029ergs−1.
x
energyrangeusedhere(Fig.3).Thisdifferenceisclearlyaresult Thetotalstellarmasswithin20pcoftheGalaxycentreisestimated
ofthedifferentbiasesintheselectionofthetwosamples. as≈108M⊙(Launhardtetal.2002)andhence≈2×105sources
Byckling et al. (2010) presented a thorough analysis of the wouldbeneededinthatregion.Thisisequivalenttoasourceden-
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