Deriving an X-ray luminosity function of dwarf novae based on parallax measurements
Kristiina Byckling, Koji Mukai, John Thorstensen, Julian Osborne
aa r X i v : . [ a s t r o - ph . S R ] J un Mon. Not. R. Astron. Soc. , 1–16 () Printed 29 August 2018 (MN L A TEX style file v2.2)
Deriving an X-ray luminosity function of dwarf novaebased on parallax measurements
K. Byckling ⋆ K. Mukai , J.R. Thorstensen and J. P. Osborne Department of Physics and Astronomy, University of Leicester, University Road, Leicester, LE1 7RH, UK NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA Department of Physics and Astronomy, 6127 Wilder Laboratory, Dartmouth College, Hanover, NH 03755-3528, USA
Accepted . Received ; in original form
ABSTRACT
We have derived an X-ray luminosity function using parallax-based distance mea-surements of a set of 12 dwarf novae, consisting of
Suzaku , XMM-Newton and
ASCA observations. The shape of the X-ray luminosity function obtained is the most accurateto date, and the luminosities of our sample are concentrated between ∼ –10 ergs − , lower than previous measurements of X-ray luminosity functions of dwarf novae.Based on the integrated X-ray luminosity function, the sample becomes more incom-plete below ∼ × erg s − than it is above this luminosity limit, and the sampleis dominated by X-ray bright dwarf novae. The total integrated luminosity within aradius of 200 pc is 1.48 × erg s − over the luminosity range of 1 × erg s − and the maximum luminosity of the sample (1.50 × erg s − ). The total absolutelower limit for the normalised luminosity per solar mass is 1.81 × erg s − M − ⊙ which accounts for ∼
16 per cent of the total X-ray emissivity of CVs as estimated bySazonov et al. (2006).
Key words: cataclysmic variables – stars: dwarf novae – X-rays: stars – X-rays:binaries – stars: distances – stars: luminosity function
Cataclysmic variables, i.e. CVs consist of an accreting whitedwarf primary and a late-type main sequence star, and ac-crete via Roche lobe overflow. CVs can be divided into sev-eral subclasses of which so called dwarf novae (DNe) are themost numerous subclass of CVs in our Galaxy. In these sys-tems, the white dwarf has a weak magnetic field strength (B . G, van Teeseling, Beuermann, & Verbunt 1996) com-pared to magnetic CVs, such as polars, and thus the for-mation of an accretion disc is possible. From time to time,the disc is seen to brighten by several magnitudes lastingfrom days to several weeks. This brightening of the disc, i.e.an outburst, is thought to be caused by disc instabilities,which are described in detail in Lasota (2001). In quiescence,DNe are sources of optical emission emanating from the ac-cretion disc and the bright spot where the material fromthe secondary hits the edge of the disc. Quiescent opticalspectra of DNe are characterized by strong Balmer emis-sion lines and weaker He I lines with some heavier elements.Also, DNe are sources of hard X-rays which are thoughtto originate from an optically thin boundary layer duringquiescence. However, during an outburst hard X-rays are ⋆ E-mail: [email protected] quenched as the boundary layer becomes optically thick andthus a source of soft X-rays and EUV emission (Pringle 1977;Pringle & Savonije 1979).At the time of the discovery of the Galactic Ridge X-ray Emission (GRXE) in 1982 (Worrall et al. 1982), dis-crete point sources were thought to be the origin of theGRXE emission. However, the origin has been debatedsince, but observational evidence gathered to date sincethe GRXE discovery supports the view that the GRXE isnot due to diffuse origin but due to discrete point sources,such as CVs and other accreting binary systems (see re-cent studies by e.g. Revnivtsev, Vikhlinin & Sazonov 2007;Revnivtsev et al. 2008). More supporting evidence was givenby the recent
Chandra study carried out by Revnivtsev et al.(2009) who resolved over 80 per cent of the GRXE into pointsources in the 6–7 keV energy range during an ultra-deep 1Msec observation.Based on
EXOSAT observations of the X-ray emissionin the Galactic Plane, Warwick et al. (1985) concluded thatif the GRXE is assumed to be originating from discrete pointsources, the bulk of the emission observed must be due to apopulation of low luminosity X-ray sources (L x < . ergs − ), such as CVs. Subsequently, Mukai & Shiokawa (1993)suggested that DNe could significantly contribute to theGRXE based on their study of an EXOSAT
Medium En- c (cid:13) RAS
K. Byckling, K. Mukai, J.R. Thorstensen, J. P. Osborne ergy (ME) DN sample. According to this study, the spacedensity of DNe is sufficiently high to account for a signifi-cant fraction of the GRXE. Later on, Ebisawa et al. (2001)resolved sources down to 3 × − erg cm − s − in their Chandra observation of the Galactic Ridge, equivalent to L x > × erg s − at 8 kpc, concluding that the numberof resolved point sources above this level is insufficient forthem to be the major contributor to the GRXE. Since theseprevious works have not completely resolved the contribu-tion of CVs to the GRXE, further studies are needed. Aswas noted by Mukai & Shiokawa (1993), unbiased and sen-sitive surveys with accurate distance measurements of CVsare needed. This way, accurate X-ray luminosity functions(XLFs) can be obtained, and the contribution to the GRXEestimated more precisely.The motivation for our work was mainly given bythe inaccuracies in the XLFs of Galactic CV populations,such as those by Baskill, Wheatley, & Osborne (2005) andSazonov et al. (2006). Baskill et al. derived an XLF using 34 ASCA observations of non-magnetic CVs (including 23 DNobservations). Their sample lacked accurate distance mea-surements as only 10 sources had parallax-based distancemeasurements. Furthermore, this sample was biased by highX-ray flux sources since
ASCA was intended to be a spectro-scopic mission and the sources in the studied sample wereknown to be X-ray bright. Also, the
ASCA study was purelyarchival without any sample selection (e.g. the distance wasnot limited) as Baskill et al. chose all non-magnetic CV ob-servations in the archive, they did not filter out sourceswhich were in an outburst state, or restrict the study toone type of objects only. The XLF study by Sazonov et al.(2006) focused on building up an XLF in the 2–10 keV rangecombining the
RXTE
Slew Survey (XSS) and
ROSAT
All-Sky Survey (RASS) observations of active binaries, CVs andyoung main sequence stars in the luminosity range ∼ . < L x < erg s − . However, uncertainties in the lumi-nosities in this study were introduced by inadequate accura-cies in the distances, for example, many of the intermediatepolars (IPs) in their sample had poorly known distances.Only a few sources had parallax measurements from, e.g.,the Hipparcos or Tycho catalogues (astrometric uncertain-ties ∼ P orb < × − pc − was dominated by low mass accretionrate, and thus short period, systems. Also, the SDSS studyby G¨ansicke et al. (2009) showed that orbital periods ofintrinsically faint Galactic CVs accumulated in the 80–86min range; they found that 20 out of 30 SDSS CVs inthis period range showed characteristics which impliedthat they are low mass accretion rate WZ Sge type DNe.As has been shown by these studies, less X-ray luminousobjects (such as DNe) dominated the studied volumes, andthus we choose to focus on DNe in this paper. It is alsoworth mentioning the study by Pretorius et al. (2007b)who carried out the ROSAT
North Ecliptic Pole (NEP)survey using a purely X-ray flux limited and a completesample of 442 X-ray sources above a flux limit of ∼ − erg cm − s − in the 0.5–2.0 keV band (only five systemswere CVs). They concluded that if the overall space densityof CVs is as high as 2 × − pc − , then the dominant CVpopulation must be fainter than 2 × erg s − .We have carried out X-ray spectral analysis of our sam-ple of 13 sources and derived an XLF in the 2–10 keV bandfor 12 of them with reliable distance measurements basedon those of by Harrison et al. (2004), Thorstensen (2003)and Thorstensen, L´epine, & Shara (2008). By using sourceswith accurate distance measurements, we minimise the erroron the luminosity. Also, we have carried out timing analy-sis for 5 sources in the sample which were recently observedby Suzaku . At the time of writing this paper, the Z Camtype star KT Per went into an outburst in January 2009,and thus we also briefly report on the
Suzaku observationsof KT Per during the outburst in Section 5.5.
Since we wanted to obtain accurate luminosities for thesources (and thus an accurate shape for the luminosity func-tion), the first step was to avoid selecting sources randomlyfrom the archive (see e.g. Baskill, Wheatley, & Osborne2005) or selecting an X-ray flux limited source sample. Theaim was to have a distance-limited sample. Thus, sourceswere not selected based on their X-ray properties, but wechose only those DNe which have accurately measured dis-tances based on trigonometric parallax measurements within ∼
200 pc. Note that by using all available distance measure-ment techniques, Patterson (priv. comm.) estimates thatcurrently there are 13 DNe within 100 pc, and ∼
33 DNewithin 200 pc from the Sun, of which the latter count isclearly incomplete. Above the 200 pc limit, ground-based c (cid:13) RAS, MNRAS , 1–16 eriving an X-ray luminosity function parallax technique does not give accurate and reliable dis-tance measurements. By using trigonometric parallax-baseddistance measurements, we are more likely to avoid biasesin the distance measurements which are present in the pre-vious, published X-ray luminosity functions. Due to the lackof ground-based parallax measurement programme for theSouthern hemisphere, our sample is limited to northern andequatorial objects. However, this selection should not intro-duce any biases in terms of the optical or X-ray luminositiesin our sample.The distance measurements of the sources chosen forthis work are based on astrometric parallaxes obtained bythe Hubble Space Telescope (HST) Fine Guidance Sensors(FGSs) (Harrison et al. 2004), and trigonometric parallaxesobtained by the ground-based 2.4 m Hiltner Telescope atthe MDM Observatory on Kitt Peak, Arizona (Thorstensen2003; Thorstensen, L´epine, & Shara 2008) and Thorstensen(in prep.). The first accurate astrometric parallaxes of DNe(SS Cyg, SS Aur and U Gem) were measured in 1999 us-ing the FGSs which can deliver high-precision parallaxeswith sub-milliarcsecond uncertainties (Harrison et al. 1999).Trigonometric parallaxes derived by ground-based observa-tions have uncertainties around 1 mas (= 10 − arcsec) orless (Thorstensen 2003; Thorstensen, L´epine, & Shara 2008)which is almost as good as the uncertainty on the FGS par-allax measurements.The second selection criterion was to restrict the sampleto sources which had been observed by X-ray imaging tele-scopes with CCDs in the energy range 0.2–10 keV. Once wehad obtained a list of targets with parallax measurements,we then looked for archival data of pointed imaging X-rayobservations of these targets in the energy range ∼ Suzaku
X-ray observa-tions. Finally, we wanted to constrain the sample to thosesources which were in their quiescent states during the obser-vations in order to avoid biases in the luminosities, and thus
AAVSO light curves of the selected sources were inspectedto confirm that the sources were in quiescence during theX-ray observations.The final source sample consists of 9 SU UMa (including2 WZ Sge systems), 3 U Gem and 1 Z Cam type DNe. Themain characteristic which separates these classes of DNe isthe outburst behaviour: U Gem type DNe outburst mainlyin timescales of every few weeks to every few months whereasSU UMa stars show normal, U Gem type DN outbursts and,in addition, superoutbursts with superhumps (variations inthe light curves at a period of a few per cent longer thanthe orbital period) in timescales of several months to years.The extreme cases, WZ Sge stars, only have superoutburstswith outburst timescales of decades without normal DN out-bursts. The defining characteristic for Z Cam stars is stand-stills, i.e., it is possible that after an outburst, they do notreturn to the minimum magnitude (unlike U Gem stars), butremain between the minimum and maximum magnitudes for10–40 days.The sources, which were included in the calculationof the X-ray luminosity function and when testing dif-ferent correlations discussed later in this paper, were ob- served with Suzaku (BZ UMa, SW UMa, VY Aqr, SS Cyg,SS Aur, V893 Sco, and ASAS J002511+1217.2),
XMM-Newton (U Gem, T Leo, HT Cas and GW Lib) and with
ASCA (WZ Sge).
Suzaku observations of BZ UMa, SW UMa,VY Aqr, SS Aur, V893 Sco and ASAS J0025 were re-quested as these observations were not in the archive.Mukai, Zietsman & Still (2009) discuss the
Suzaku observa-tions of V893 Sco in more detail. We also included Z Cam inthe source sample since it has a parallax measurement, but itappeared to be in a transition state during the observations.Thus, we have only reported the results of the spectral anal-ysis for Z Cam, but excluded it when calculating the X-rayluminosity function, and when testing correlations betweendifferent parameters. The system parameters for all the 13sources are given in Table 1.
The details of the
Suzaku , XMM , and
ASCA observationsare given in Table 2, and the data reduction methods aredescribed in the following sections.
Suzaku (Mitsuda et al. 2007), originally
Astro-E2 , waslaunched in 2005 and is Japan’s 5th X-ray astronomy mis-sion. In this paper, we will focus on the X-ray Imag-ing Spectrometer (XIS) data. The XIS consists of foursensors: XIS0,1,2,3 of which three (XIS0,2,3) containfront-illuminated (FI) CCDs, and XIS1 contains a back-illuminated (BI) CCD. The XIS0,2,3 are less sensitive tosoft X-rays than XIS1 due to the thin Si and SiO layerson the front side of the XIS0,2,3 CCDs. Since November 9,2006, the XIS2 unit has not been available for observations.The Suzaku background is low and hardly affected by softproton flares often seen in
XMM observations.The unfiltered event lists of SS Cyg and V893 Sco werereprocessed with xispi and screened in xselect with xis-repro since the pipeline version for these observations wasolder than v.2.1.6.15 which does not include correction forthe time- and energy-dependent effects in energy scale cali-bration. For all the other
Suzaku observations, the observa-tions had been processed by more recent pipeline versionsand thus reprocessing was not necessary. Pile-up was nota problem for our data since the source count rates weresafely below the pile-up limit (12 ct s − ) for point sourcesobserved in the ’Normal’ mode using Full Window . The Suzaku data reduction described below was carried out in asimilar manner for all the
Suzaku observations. The cleanedevent lists were read into xselect in which X-ray spectrawere extracted for each source. Light curves were extractedfor SW UMa, BZ UMa, SS Aur, ASAS J0025, and VY Aqrfor timing analysis studies. To include 99 per cent of theflux and to obtain the most accurate flux calibration, thespectra and light curves were extracted using a source ra-dius of 260” (250 pixels). The backgrounds were taken as anannulus centred on the source excluding the inner 4’ source http://heasarc.gsfc.nasa.gov/docs/suzaku/analysis/abc/abc.htmlc (cid:13) RAS, MNRAS , 1–16
K. Byckling, K. Mukai, J.R. Thorstensen, J. P. Osborne
Table 1.
The source sample used to derive the X-ray luminosity function (excluding *) with their inclinations, orbital periods, whitedwarf masses, distances and DN types. The types given in the last column are U Gem (UG), SU UMa (SU), WZ Sge (WZ) and ZCam (ZC). The references are: a) Thorstensen (2003), b) Thorstensen, L´epine, & Shara (2008), c) Harrison et al. (2004), d) Mason et al.(2001), e) Urban & Sion (2006), f) Friend, Connon-Smith & Jones (1990), g) Ritter & Kolb (2003), h) Horne, Wood & Stiening (1991),i) Preliminary distance estimate from Thorstensen (in prep.), and j) Templeton et al. (2006).Source Inclination P orb M WD Distance Typedeg h M ⊙ pcSS Cyg 40 ± c c f +13 − c UGV893 Sco 71 ± a a d +58 − a SUSW UMa 45 ± g b e +22 − b SUVY Aqr 63 ± a a e +15 − a SUSS Aur 40 ± c a e +10 − c UGBZ UMa 60–75 e b e +63 − b SUU Gem 69 ± c c e ± c UGT Leo 47 ± a a e +13 − a SUWZ Sge 76 ± c a e ± c SU/WZHT Cas 81 ± h b e +22 − b SUGW Lib 11 ± a a e +30 − a SU/WZZ Cam ∗ ± a a e +68 − a ZCASAS J0025 – 1.37 j – ∼ +120 − i SU Table 2.
The observation dates and the instruments used in the observations for each source. The exposure times for the
Suzaku sourceshave been obtained from the cleaned event lists, and the numbers in brackets for the
XMM sources show exposure times after filteringhigh background flares. The last column corresponds to the optical state of the source during the observations.Source ObsID Instrument T start T stop T exp StateksSS Cyg 400006010 XIS/Suzaku 2005-11-02 2005-11-02 39 QV893 Sco 401041010 XIS/Suzaku 2006-08-26 2006-08-27 18 QSW UMa 402044010 XIS/Suzaku 2007-11-06 2007-11-06 17 QVY Aqr 402043010 XIS/Suzaku 2007-11-10 2007-11-11 25 QSS Aur 402045010 XIS/Suzaku 2008-03-04 2008-03-05 19 QBZ UMa 402046010 XIS/Suzaku 2008-03-24 2008-03-25 30 QASAS 403039010 XIS/Suzaku 2009-01-10 2009-01-11 33 QJ0025KT Per 403041010 XIS/Suzaku 2009-01-12 2009-01-13 29 OBU Gem 0110070401 MOS1/XMM 2002-04-13 2002-04-13 23(22.4) Q0110070401 MOS2/XMM 2002-04-13 2002-04-13 23(22.4) QT Leo 0111970701 PN/XMM 2002-06-01 2002-06-01 13(13) QHT Cas 0111310101 PN/XMM 2002-08-20 2002-08-20 50(6.9) QGW Lib 0303180101 PN/XMM 2005-08-25 2005-08-26 22(6.7) QWZ Sge 34006000 GIS,SIS/ASCA 1996-05-15 1996-05-15 85 QZ Cam 35011000 GIS,SIS/ASCA 1997-04-12 1997-04-12 41 T region. The outer radii of the background annuli were deter-mined according to how close the calibration sources wereto the target. The response matrix files (RMFs) and ancil-lary response files (ARFs) were created and combined within xisresp v.1.10. The XIS0,2,3 source and background spec-tra and the corresponding response files were summed in addascaspec to create the total XIS0,2,3 source and back-ground spectra, and the total XIS0,2,3 response file. For thelight curves, the background areas were scaled to match thesource areas, and the scaled background light curves werethen subtracted from the source light curves in lcmath . XMM-Newton (Jansen et al. 2001) is the cornerstone mis-sion of the European Space Agency (ESA). It has been oper-ating since 1999 with three X-ray cameras (EPIC pn, MOS1and MOS2), the Optical Monitor (OM), and the ReflectionGrating Spectrometer (RGS) onboard. The X-ray camerascover the energy range 0.2–12.0 keV.The data were obtained from the
XMM-Newton
Sci-ence Archive (XSA) and the
XMM-Newton data were re-duced and analysed in the standard manner using the
XMM-Newton
Science Analysis System sas version 8.0.0. Each c (cid:13) RAS, MNRAS , 1–16 eriving an X-ray luminosity function observation was checked for high background flares in therange 10–12 keV using single pixel events ( pattern ==0 ). The high background flares were cut above 0.35 ct s − for the MOS data and above 0.40 ct s − for the pn data.The source and background extraction regions were takenfrom circular extraction areas avoiding any contaminatingbackground sources. The radii of the source regions werecalculated by using the sas task region in order to derivesource extraction radii which include ∼
90 per cent of thesource flux for each source. The background extraction re-gion (r bg = 130 arcsec) was taken from the same chip as thesource extraction region, or from an adjacent chip in caseof a crowded source chip. When extracting the X-ray spec-tra, only well-calibrated X-ray events were selected for allthe sources, i.e. for the pn spectra single and double pixelevents with pattern FLAG == 0was used. For the MOS, pattern and addascaspec . All theobservations were checked in case of pile-up by using the XMM sas task epatplot . Pile-up did not occur in any ofthe observations, but the source PSFs of HT Cas and T Leowere contaminated by out-of-time (OoT) events, introducedby these two sources. Therefore, the background regions inthe HT Cas and T Leo observations were taken from theadjacent chip in order to avoid the OoT events. These OoTevents were removed from the source X-ray spectra accord-ing to the ’ sas threads’ , i.e. the source spectra extractedfrom the OoT event lists were subtracted from the sourcespectra extracted from the original event list. The
Advanced Satellite for Cosmology and Astrophysics ( ASCA , Tanaka, Inoue & Holt 1994) was Japan’s fourthcosmic X-ray astronomy mission operating between Febru-ary 1993 and July 2000 and was the first X-ray observatorywhich carried CCD cameras. The main science goal of
ASCA was the X-ray spectroscopy of astrophysical plasmas. It car-ried four X-ray telescopes with two types of detectors locatedinside them: two CCD cameras, i.e. the Solid-state ImagingSpectrometers (SIS0 and SIS1) with spectral resolution of 2per cent at 5.9 keV at launch, and two scintillation propor-tional counters, i.e. the Gas Imaging Spectrometers (GIS2and GIS3).The
ASCA data reduction was performed in the stan-dard manner by mostly using the standard screening val- http://xmm2.esac.esa.int/sas/8.0.0/documentation/threads/EPIC OoT.html ues for the GIS and SIS instruments as described in NASA ASCA online manual . For both instruments, intervals out-side the South Atlantic Anomaly (SAA) were chosen, alsoincluding intervals when the attitude control was stable withthe upper limit of the angular distance from the target setto ang dist < br earth >
10 was applied excludingthe data taken below the 10 ◦ angle. Times of high back-ground were excluded when the PIXL monitor count ratewas 3 σ above the mean of the observation. Also, the back-ground monitor count rate of rbm cont <
500 was applied(the standard screening value is rbm cont < T DY NT < 0 k T DY NT > 32 && T SAA < 0 k T SAA > 32 ).The source extraction regions for the SIS and GIS werecentred on the source. For the GIS, a ∼ ∼ ∼ ∼ ∼ ascaarf and the SIS responsematrix files (RMFs) with sisrmg . Finally, the total SIS andGIS X-ray spectra were created by combining SIS0 and SIS1,and the GIS2 and GIS3 spectra in addascaspec , respec-tively. Since VY Aqr, SS Aur, BZ UMa, SW UMa and ASAS J0025have not been subject to previous, pointed, imaging X-rayobservations before the
Suzaku observations, we looked forperiodicities from the data of these sources. KT Per has beenobserved by the
Einstein
Observatory (C´ordova & Mason1984), but no previous X-ray spectral or timing analysisstudies have been carried out for it. In order to ensurethat these objects are not intermediate polars (IPs) andto look for orbital and spin modulation in the data, thepower spectra were calculated by using a Lomb-Scargle pe-riodogram (Scargle 1982) which is used for period analysisof unevenly spaced data. When searching over the frequencyrange 0.00001–0.03 Hz, no significant periodicities were seenat the 99 per cent confidence level. http://heasarc.gsfc.nasa.gov/docs/asca/abc/abc.htmlc (cid:13) RAS, MNRAS , 1–16
K. Byckling, K. Mukai, J.R. Thorstensen, J. P. Osborne
We carried out X-ray spectral analysis in order to study theunderlying spectra of the source sample, and, ultimately,to calculate the fluxes and luminosities of the sources. Toemploy Gaussian statistics, the X-ray spectra were binnedat 20 ct bin − with grppha and then fitted in Xspec11 (Arnaud 1996).In CVs, the power source of X-ray emission is knownto be accretion onto the white dwarf. The accreted materialis shock-heated to high temperatures ( kT max ∼ kT max to the temperatureof the optically thin cooling material which eventually set-tles onto the surface of the white dwarf (Mukai et al. 1997).Thus, when fitting X-ray spectra of CVs, cooling flow spec-tral models should represent more physically correct pictureof the cooling plasma, unlike single temperature spectralmodels. Cooling flow models have successfully been appliedto CV spectra in previous studies by e.g. Wheatley et al.(1996) and Mukai et al. (2003). In this view, the multi-temperature characteristic is our motivation for emphasizingthe cooling flow model in the rest of this work. The differen-tial emission measure dEM/dT for an isobaric cooling flowcan be described by (Pandel et al. 2005) dEMdT = 5 k ˙ M n µm p ǫ ( T, n ) , (1)where m p is the mass of a proton, µ the mean molec-ular weight ( ∼ ǫ (T,n) total emissivity per volume inunits of erg s − cm − , ˙ M accretion rate, n particle den-sity, and k the Boltzmann constant. The source of the X-rayemission above the white dwarf illuminates the surface ofthe white dwarf and thus causes a reflection, which is seenas Fe K α iron fluorescence line at 6.4 keV (George & Fabian1991). According to George & Fabian, an infinite slab reflec-tor subtending a total solid angle of Ω = 2 π where the X-raysource is located right above the slab, produces an equivalentwidth of up to ∼
150 eV for the 6.4 keV Fe K α fluorescenceline. The equivalent width of the 6.4 keV iron line dependson the total abundance of the reflector (Done & Osborne1997), the inclination angle between the surface of the re-flector and the observer’s line of sight, and the photon indexof the spectrum of the X-ray emission source (Ishida et al.2009).Even though we believe that the cooling flow -typemulti-temperature model is the correct description of thephysics of the cooling gas flow in CVs, previous workshave often used single temperature plasma models. Thus,in order to compare the effects of two different spec-tral models on the spectral fit parameters, we fitted thespectra with 1) a single temperature optically thin ther-mal plasma model ( mekal, Mewe, Lemen & van den Oord1986; Liedahl, Osterheld & Goldstein 1995) and 2) a cool-ing flow model ( mkcflow ) which was originally devel-oped to describe the cooling flows in clusters of galaxies(Mushotzky & Szymkowiak 1988), adding photoelectric ab-sorption ( wabs , Morrison & McCammon 1983) to both mod-els. In order to investigate the equivalent width of the
Table 3.
The equivalent widths of the Fe 6.4 keV line derivedby using the absorbed optically thin thermal plasma and coolingflow models. Name EW(mekal) EW(mkcflow)eV eVBZ UMa 67 +42 − < < < +37 − +52 − SW UMa 201 +124 − < +25 − +33 − T Leo 71 +38 − < +12 − +11 − VY Aqr < < < < +9 − +6 − Z Cam 120 +42 − +42 − ASAS J0025 < < σ = 10 eV. The spec-tral fits did not necessarily require the 6.4 keV line, e.g.,for SS Aur the χ ν / ν = 0.96/629 when a Gaussian line at6.4 keV was not included.The Suzaku
XIS1 and XIS0,2,3 spectra were fitted si-multaneously for each source as well as the
ASCA
GIS andSIS spectra of Z Cam and WZ Sge with the models men-tioned above. Some data sets required additional compo-nents to improve the fits. Three of the sources, HT Cas,V893 Sco and Z Cam, required partial covering absorptionmodel, pcfabs , to reduce residuals in the low energy end (be-tween ∼ χ / ν = 2.23/403.Since the fit was not statistically satisfactory, we addeda second optically thin thermal plasma component to im-prove the fit and obtained χ / ν = 1.34/401 which was goodenough for our analysis.In the spectral fitting, the parameters of the spectralmodels were tied between different instrument spectra butlet to vary free, apart from the Gaussian line energy at6.4 keV and the line width σ which were fixed. In orderto estimate the abundances, the abundance parameter ofthe models was let to vary free for most data sets. For thosesources for which abundance was significantly higher thanthe solar value, it was fixed at 1.0. An example of a sourcewith a super-solar abundance is Z Cam for which the ob- c (cid:13) RAS, MNRAS , 1–16 eriving an X-ray luminosity function Table 4.
The fit results of the absorbed optically thin thermal plasma model with a 6.4 keV Gaussian line. The errors are 90 per centconfidence limits on one parameter of interest. n H and n H are the absorption columns of the photoelectric absorption ( wabs ) andpartial covering ( pcfabs ) models, respectively. CFrac is the covering fraction of the partial covering model, kT the plasma temperatureand Ab the abundance.Name n H n H CFrac kT Ab χ ν / ν P null cm − cm − keV Z ⊙ BZ UMa < +0 . − . +0 . − . +8 . − . – – 1.62 +1 . − . +1 . − . +2 . − . +0 . − . +0 . − . +0 . − . < +0 . − . +0 . − . < +0 . − . +0 . − . × − U Gem 0.89 +0 . − . – – 0.78 +0 . − . +0 . − . × − +0 . − . T Leo 1.09 +0 . − . – – 3.55 +0 . − . +0 . − . × − V893 Sco – 80.89 +4 . − . +0 . − . +0 . − . +0 . − . < +0 . − . +0 . − . +2 . − . – – 4.88 +0 . − . +0 . − . +0 . − . – – 10.44 +0 . − . +0 . − . × − Z Cam 28.21 +2 . − . +99 . − . +0 . − . +0 . − . < +0 . − . +0 . − . tained abundance was 1.46 +0 . − . Z with the partial covering+ photoelectric absorption combined with the cooling flowmodel when the abundance was let to vary free.The measured equivalent widths of the 6.4 keV line foreach source are given in Table 3, and the results of thespectral fitting for the optically thin thermal plasma andthe cooling flow models are given in Table 4 and 5, respec-tively. These results show that in general, better χ ν / ν val-ues are achieved with the cooling flow model. For example,the improvement with the cooling flow model was statisti-cally significant for SW UMa and T Leo. Fig. 1 illustratesthe X-ray spectra of the new Suzaku
XIS observations, i.e.VY Aqr, SW UMa, BZ UMa, SS Aur, and ASAS J0025,which have been fitted with the cooling flow model absorbedby photoelectric absorption with an added 6.4 keV Gaus-sian line component. Most of the X-ray spectra show thatthe clearest, discrete emission feature seen in the spectraof our source sample is the iron Fe K α complex, except inGW Lib, for which the signal-to-noise at ∼ Since the studied sources are all within ∼
200 pc, i.e., withinthe solar neighbourhood, the effect of interstellar absorp-tion should be negligible. Thus, high measured absorptioncolumns would mainly be due to intrinsic absorption, associ-ated with the sources. For most of the sources, the measuredabsorption columns were typically of the order of a few × cm − , or even lower (10 cm − ) which indicate lowintrinsic absorption.The highest intrinsic absorption columns are found inV893 Sco, Z Cam and HT Cas when compared to the restof the source sample. All these three sources have par-tial covering absorbers n H with values of the order of10 – 10 cm − depending on the model. In additionto the partial covering absorber, Z Cam also has a sim-ple absorption component with the highest n H value, n H ∼ × cm − , within the source sample. Originally,V893 Sco was found to have high intrinsic absorption byMukai, Zietsman & Still (2009), and has a partial X-rayeclipse, also discovered by their study. Also, according tothe best-fit model of Baskill, Wheatley & Osborne (2001),Z Cam had large amounts of absorption with n H = 9 × cm − during the transition state. Baskill et al. sug- c (cid:13) RAS, MNRAS , 1–16
K. Byckling, K. Mukai, J.R. Thorstensen, J. P. Osborne
Table 5.
The fit results of the absorbed cooling flow model with a 6.4 keV Gaussian line. The errors are 90 per cent confidence limits onone parameter of interest. n H and n H are the absorption columns of the photoelectric absorption ( wabs ) and partial covering ( pcfabs )models, respectively. CFrac is the covering fraction of the partial covering model, kT max the shock temperature and Ab the abundance.Name n H n H CFrac kT max Ab χ ν / ν P null cm − cm − keV Z ⊙ BZ UMa < +1 . − . +0 . − . < +8 . − . +4 . − . +0 . − . +4 . − . +0 . − . +1 . − . – – 23.47 +4 . − . < +0 . − . +0 . − . +0 . − . – – 25.82 +1 . − . +0 . − . × − T Leo 0.68 +0 . − . – – 10.97 +0 . − . +0 . − . × − V893 Sco – 103.71 +3 . − . +0 . − . +1 . − . +0 . − . +3 . − . – – 16.47 +2 . − . +0 . − . +3 . − . – – 13.31 +3 . − . +0 . − . +0 . − . – – 41.99 +1 . − . +0 . − . × − Z Cam 31.92 +4 . − . +53 . − . +0 . − . +5 . − . < .
67 – – 14.43 +4 . − . +0 . − . gested that this absorption was associated with a clumpydisc wind. The measured shock temperatures kT max seem to be cor-related with the white dwarf masses (Fig. 2) as one wouldexpect. In Fig. 2 it has been assumed that the white dwarfmass of VY Aqr is 0.8 M ⊙ (see Table 1). ASAS J0025 isnot included in Fig. 2 since the mass estimate is currentlyunknown. SS Cyg appears to be located in the upper rightcorner due to its high-mass white dwarf and thus high shocktemperature. The shock temperatures, kT max , in Fig. 2 havebeen derived from the spectral fits of the cooling flow modelfor each source. The blue dashed line in Fig. 2 representsthe theoretical shock temperatures for given white dwarfmasses. The radii, R ∗ , of the given white dwarf masses, M ,were calculated assuming the mass-radius relation for cold,non-rotating and non-relativistic helium white dwarfs (seePringle & Webbink 1975) R ∗ = 7 . × x . − . x ) ( cm ) , (2)where x = . M ⊙ M -1. Subsequently, the theoret-ical shock temperatures, T shock , for non-magnetic CVs were calculated according to Eq. 3 for optically thin gas(Frank, King & Raine 2002) T shock = 316 GM µm H kR ∗ , (3)where m H is the mass of a hydrogen atom, µ the meanmolecular weight, and k the Boltzmann constant. As it ap-pears from Fig. 2, sources with high shock temperatures andlow luminosities are not seen. This is sensible since the X-rayluminosity is proportional to kT max and the mass accretionrate, i.e. the normalization of the cooling flow model (Eq. 1),thus we would expect to see high shock temperatures andhigh luminosities. Also, due to this proportionality, we ex-pect to see an anti-correlation between ˙ M and kT max whichindeed is seen for example in SW UMa (Fig. 3).As it appears from Fig. 2, the white dwarf mass ob-tained for T Leo by Urban & Sion (2006) is only 0.35 M ⊙ .This mass estimate may be unreliable, since as Lemm et al.(1993) argue, a low white dwarf mass would not allow super-humps to develop. See also Patterson et al. (2005) who referto previous superhump studies which have shown that themass ratio q = M /M has a key role in producing super-humps where q crit ∼ c (cid:13) RAS, MNRAS , 1–16 eriving an X-ray luminosity function − . . r m a li z ed c oun t s / s e c / k e V VY Aqr data and folded modelBI CCDFI CCD 10.5 2 5 − χ channel energy (keV) (a) VY Aqr − . . r m a li z ed c oun t s / s e c / k e V SW UMa data and folded modelBI CCDFI CCD 10.5 2 5 − χ channel energy (keV) (b) SW UMa − . . r m a li z ed c oun t s / s e c / k e V BZ UMa data and folded modelBI CCDFI CCD 10.5 2 5 − − χ channel energy (keV) (c) BZ UMa − . . r m a li z ed c oun t s / s e c / k e V SS Aur data and folded modelBI CCDFI CCD 10.5 2 5 − χ channel energy (keV) (d) SS Aur − − . r m a li z ed c oun t s / s e c / k e V ASAS J0025 data and folded modelBI CCDFI CCD 10.5 2 5 − χ channel energy (keV) (e) ASAS J0025 Figure 1.
The X-ray spectra of (a) VY Aqr, (b) SW UMa, (c) BZ UMa, (d) SS Aur, and (e) ASAS J0025 fitted with an absorbedcooling flow model and a 6.4 keV Gaussian line (upper panels). The lower panel in each figure shows the residuals. The black spectracorrespond to the front-illuminated (FI) XIS0,3 and the red ones to the back-illuminated (BI) XIS1 spectra.
We found that for most of the objects in the sample theobtained abundances were sub-solar with both models. Ingeneral, the abundances seem to be dependent on the spec-tral model: abundances are slightly lower when the spectra are fitted with the optically thin thermal plasma model. Thisis due to the single temperature characteristic of the opti-cally thin thermal plasma model, i.e. it is likely that theabundances are underestimated because the best-fit tem-perature usually converges close to the peak of the 6.7 keVHe-like Fe K α emissivity, whereas the cooling flow model c (cid:13) RAS, MNRAS , 1–16 K. Byckling, K. Mukai, J.R. Thorstensen, J. P. Osborne
10 20 30 40 50BZ UMaGW Lib HT CasSS AurSW UMa U GemT Leo V893 ScoVY AqrWZ Sge SS Cyg
Figure 2.
Mass of the white dwarf versus the shock temperature, kT max , of the source sample with 90 per cent uncertainties for kT max . The light blue dashed line represents the theoretical shocktemperatures for given white dwarf masses. The figure does notinclude ASAS J0025 since a mass estimate does not currentlyexist for this source. × − . × − . × − . × − . × − no r m highT keVSW UMa confidence contours Figure 3.
The 68, 90, and 99 per cent confidence contours ofSW UMa for the normalisation ( ˙ M ) versus the shock temperature kT max of the cooling flow model.
26 28 30 32 3402468 GW Lib WZ Sge SS AurSW UMaU GemT LeoVY AqrASASJ0025HT Cas BZ UMaV893Sco SS CygLog L(2-10 keV)
Figure 4.
A histogram showing the X-ray luminosities of thesource sample in 2–10 keV. consists of a range of temperatures outside the peak (seeMukai, Zietsman & Still 2009).
The 2–10 and bolometric 0.01–100 keV fluxes and luminosi-ties which were derived using the cooling flow model aregiven in Table 6. This shows that most of the 2–10 keV X-ray luminosities are concentrated around 10 erg s − . Thisis also seen in Fig. 4 which shows a histogram of the X-rayluminosities of our sample. Only one object, GW Lib, standsout with a very low luminosity (4 × erg s − ). The mea-sured luminosity of GW Lib is consistent with the results ob-tained by Hilton et al. (2007). Byckling et al. (2009) showedthat GW Lib was still an order of a magnitude brighter (L ∼ erg s − ) in X-rays during Swift observations two yearsafter the 2007 outburst than in 2005. But since the opticalmagnitude had not reached the quiescence level (V ∼
18) in2009, we do not consider the
Swift
Swift data does not affect the results of thispaper.One of the sources in our sample, SS Aur, has previ-ously been listed in the
RXTE
All-Sky Slew Survey cata-log where it appears more luminous in X-rays than in our
Suzaku observation (the
RXTE flux of SS Aur in 2–10 keVis ∼ × − erg cm − s − ). We suspect that the higherflux in the RXTE observation is due to other, bright sourcesin the field which overestimate the flux. E.g., the
ROSAT
Bright Source Catalogue lists a cluster of galaxies, Abell c (cid:13) RAS, MNRAS , 1–16 eriving an X-ray luminosity function Table 6.
Fluxes and luminosities in the 2–10 (absorbed) and 0.01–100 keV (unabsorbed) bands derived from the cooling flow model foreach source. Source F(2–10 keV) L(2–10 keV) F(0.01–100 keV) L(0.01–100 keV)x 10 − erg cm − s − × erg s − x 10 − erg cm − s − × erg s − BZ UMa 2.4 +0 . − . +10 . − . +0 . − . +0 . − . +0 . − . +4 . − . +0 . − . +2 . − . +0 . − . +2 . − . +0 . − . +1 . − . +0 . − . +2 . − . +1 . − . +51 . − . +0 . − . +0 . − . +1 . − . +0 . − . +0 . − . +29 . − . +1 . − . +74 . − . +0 . − . +3 . − . estimated flux of ∼ × − erg cm − s − in 2–10 keV(bremsstrahlung kT = 4 keV, Galactic n H = 1.56 × cm − as in Ebeling et al. 1996). Thus, the higher RXTE fluxof SS Aur is very likely biased by the background sourcesand not reliable.
We also analysed the
Suzaku outburst data of KT Per ob-tained in January 2009, and report the results here. KT Peris a Z Cam type dwarf nova, and was seen as an X-raysource by the
Einstein satellite in 1979 (C´ordova & Mason1984). We employed the same models which were used forthe source sample above, i.e. an absorbed optically thinthermal plasma model and an absorbed cooling flow modelwith an added 6.4 keV line. Both models yielded accept-able fits: χ ν /ν = 0.97/838 (thermal plasma) and χ ν /ν =0.95/837 (cooling flow). Fig. 5 shows the XIS1 and the com-bined XIS0,3 X-ray spectra of KT Per which have been fit-ted with an absorbed cooling flow model with a 6.4 keVGaussian line. The spectral fit parameters for the opti-cally thin thermal plasma and the cooling flow modelswith fluxes, luminosities and fit statistics are given in Ta-ble 7. The luminosities given in Table 7 are calculated for http://heasarc.gsfc.nasa.gov/Tools/w3pimms.html the distance of 180 +36 − pc (Thorstensen, L´epine, & Shara2008). Baskill, Wheatley, & Osborne (2005) noted that cool-ing flow models are often a good representation of quiescentX-ray spectra of CVs (see also Mukai et al. 2003), but notoutburst spectra. Baskill et al. applied the Xspec multi-temperature model cevmkl to their
ASCA spectra in or-der to fit a range of outburst and quiescent spectra with asingle simple model. We also investigated how this multi-temperature model combined with photoelectric absorptionand a 6.4 keV Gaussian line would fit the outburst data ofKT Per, and obtained a statistically acceptable fit: χ ν /ν =0.96/836, P = 0.819. The method which is used for calculating the height of theX-ray emission source above the white dwarf, has been ex-plained by Ishida et al. (2009) for SS Cyg. We have adoptedthe same method here in our work. As was explained inthe beginning of Section 5, an equivalent width of up to ∼
150 eV can be expected for the fluorescent Fe K α lineat 6.4 keV. In this work, we have assumed that the re-flection originates from the white dwarf surface only, thusthe reflection from the accretion disc is Ω disc /2 π = 0. Theequivalent width of 150 eV calculated by George & Fabian(1991) was assumed under the solar abundance conditions ofMorrison & McCammon (1983) where [Fe/H] = 3.2 × − . c (cid:13) RAS, MNRAS , 1–16 K. Byckling, K. Mukai, J.R. Thorstensen, J. P. Osborne − . . r m a li z ed c oun t s / s e c / k e V KT Per data and folded modelBI CCD FI CCD 10.5 2 5 − χ channel energy (keV) Figure 5.
The X-ray spectrum of KT Per fitted with an absorbed cooling flow model and a 6.4 keV Gaussian line. The lower panelshows the residuals. The black spectrum corresponds to the front-illuminated (FI) XIS0,3 and the red one to the back-illuminated (BI)XIS1 spectrum.
Table 7.
The fit parameters of KT Per derived by using an ab-sorbed optically thin thermal plasma and absorbed cooling flowmodels with a 6.4 keV iron line. The errors are 90 per cent errorsfor one parameter of interest.Parameter Thermal plasma Cooling flown H +1 . − . +2 . − . × cm − kT 5.11 +0 . − . +1 . − . (keV)Abundance 0.40 +0 . − . +0 . − . EW 52 +39 − +44 − (eV)Flux(2–10 keV) 2.55 2.62 × − erg cm − s − Flux(0.01–100 keV) 5.60 6.19 × − erg cm − s − Luminosity(2–10 keV) 1.0 1.03 × erg s − Luminosity(0.01–100 keV) 2.19 2.42 × erg s − χ ν /ν We have employed the abundances of Anders & Grevesse(1989) which are the default abundance values built in the
Xspec cooling flow and optically thin thermal plasma emis-sion models. For the solar abundances of Anders & Grevesse, the [Fe/H] composition is 4.68 × − . Ishida et al. (2009),who also employed the Anders & Grevesse abundances, cor-rected this abundance difference (see their Eq.3) using theirmeasured iron abundance of 0.37 Z . For solar abundance,the observed equivalent width of the 6.4 keV line is EW observed = 150 × . × − . × − (cid:16) Ω WD π (cid:17) Z ( eV )= 220 (cid:16) Ω WD π (cid:17) Z ( eV ) , (4)where Z is the measured elemental abundance in so-lar units Z ⊙ and Ω WD the solid angle of the white dwarfviewed from the plasma of the boundary layer. In our sam-ple, the observed equivalent widths (Table 3) are mainlybelow 150 eV and this implies that the X-ray source is lo-cated at a height h above the white dwarf surface. In thefollowing, we use the values of EW observed and abundancescalculated from the cooling flow model. As an example, the EW observed for SS Aur is 86 eV and the abundance is 1.0,thus Eq. 4 gives Ω WD /2 π = 0.39. If the X-ray source ispoint-like, the height h of the X-ray source above the whitedwarf of a radius R WD is h < R WD . As another ex-ample, we obtain Ω WD /2 π = 0.22 and h < R WD forV893 Sco ( EW observed = 45 eV, Z = 0.94 Z ). We have derived an X-ray luminosity function for 12 dwarfnovae using archival
Suzaku , XMM-Newton , and
ASCA ob-servations, and obtained new observations for BZ UMa,SW UMa, VY Aqr, SS Aur, V893 Sco and ASAS J0025with
Suzaku as originally, they were not available in thearchive. Our results show that the 2–10 keV luminosities,presented in Table 6, span a range between 4 × and1.5 × erg s − , and that most of the source luminositiesin the sample are located within 10 erg s − , see Fig. 4,whereas, the X-ray luminosities of the ASCA sample by c (cid:13) RAS, MNRAS000
Suzaku as originally, they were not available in thearchive. Our results show that the 2–10 keV luminosities,presented in Table 6, span a range between 4 × and1.5 × erg s − , and that most of the source luminositiesin the sample are located within 10 erg s − , see Fig. 4,whereas, the X-ray luminosities of the ASCA sample by c (cid:13) RAS, MNRAS000 , 1–16 eriving an X-ray luminosity function Baskill, Wheatley, & Osborne (2005) were mainly concen-trated on higher luminosities between 10 and 10 erg s − .This difference is most likely due to the fact that we did notapply X-ray selection criteria to our sample. Also, the ob-jects observed by ASCA were known to be X-ray bright, thusthe sample of Baskill et al. is very likely biased by sourceswhich are X-ray bright.In order to derive the integrated X-ray luminosity func-tion (XLF), N( > L), for 12 sources within a distance of d= 200 pc, we assumed that the luminosity function is char-acterized by a power law N( > L) = k(L/L t ) − α (see Fig. 6where the best-fit parameters α = -0.64 and k = 2.39 × − , corresponding to a threshold luminosity of L t = 3 × erg s − ). The histogram illustrates the cumulativesource distribution per pc in which a break is seen at ∼ × erg s − . This can be due to two possible scenarios:1) a single α power law describes the luminosity function ofDNe, but the sample becomes more incomplete below ∼ × erg s − than it is above this limit, or 2) the shapeof the true XLF of DNe is a broken power law with a breakat around 3 × erg s − . From these two scenarios, thefirst one is more likely since the sample contains only a fewsources below ∼ erg s − . Also, as was shown by, e.g., thestudy of G¨ansicke et al. (2009), more fainter CVs, such asWZ Sge types, are expected to exist. Based on the obtainedpower law slope, the sample is dominated by the brighterDNe: this is probably caused by the parallax measurementmethod which favours optically brighter DNe which usuallyhave high X-ray luminosities.When calculating the total, integrated luminosity ofthe sample, we restricted the calculations to the distanceof 200 pc, thus excluding BZ UMa. Integrating between theluminosities of 1 × and the maximum luminosity ofthe sample ( L max = 1.50 × erg s − ), yields the totalintegrated luminosity of 1.48 × erg s − , whereas theintegrated luminosity between the threshold luminosity 3 × and L max is 1.15 × erg s − . These two results showthat there are uncertainties in the integrated luminosities,most likely caused by the small number of sources in thesample. In order to obtain more accurate value for the in-tegrated luminosity, the power law slope ( α = -0.64) shouldbe better established. If the obtained slope is not far fromthe true power law slope of DNe in the solar neighbour-hood, estimating the integrated luminosity more accuratelyand constraining the bright luminosity end (10 erg s − )requires more DNe to be included in the sample. Since thesource density at ∼ erg s − is ∼ × − pc − ac-cording to Fig. 6, we would need to survey within a volumeof 1 × pc to find ∼
30 SS Cyg -type DNe and thusfind a statistically significant constraint for the brighter lu-minosities in the sample. This volume would correspond toa distance of ∼
620 pc with a flux limit of ∼ × − erg cm − s − .Following this, we estimated how easy it would be tohide typical DN luminosities in the solar neighbourhood. As-suming a typical dwarf nova with a 5 keV bremsstrahlungand a low Galactic n H = 1 × cm − in WebPIMMs yields a 2–10 keV flux of 5 × − erg cm − s − , corre-sponding to the ROSAT
PSPC count rate of 0.04 ct s − which is just below the detection limit (0.05 ct s − ) of ROSAT
PSPC (Voges et al. 1999). Thus, luminosities above2.4 × erg s − within 200 pc or above 6 × erg s −
28 29 30 31 32-8-7-6-5 Log(L(2-10 keV), erg/s)
Figure 6.
The cumulative source distribution (histogram) andthe integrated power law luminosity function N( > L) as a func-tion of X-ray luminosity in log L in the 2–10 keV energy band.The error bar on the top right represents a typical error on theluminosities. within 100 pc should have been found by
ROSAT and thusshould be in the RASS. However, given that sources with lu-minosities of 10 erg s − and below at a distance of 100 pcwere too faint for the RASS, and that our XLF peaks at ∼ erg s − , we conclude that there is no existing X-rayselected sample that we can use for this line of research.How far is the total luminosity of our sample from ac-counting for the total CV X-ray emissivity? In order to es-timate this, we calculated the absolute lower limit for theluminosity per cubic parsec volume (L x /vol). For a distanceof r = 200 pc, the volume V = 4/3 × π × (200 pc) =3.3 × pc , and the total summed luminosity L x of thesample is 2.39 × erg s − (without BZ UMa). Thus, thetotal absolute lower limit L x /volume = 7.24 × erg s − pc − . Normalising this value to the local stellar mass den-sity 0.04 M ⊙ pc − (Jahreiß & Wielen 1997) yields 1.81 × erg s − M − ⊙ in the 2–10 keV range. For comparison,Sazonov et al. (2006) obtained (1.1 ± × erg s − M − ⊙ (2–10 keV) for the total CV X-ray emissivity per unitstellar mass. Thus, our sample would account for ∼
16 percent of this value.And finally, how much would our sample account forthe GRXE? The Galactic Ridge X-ray emissivity estimatedby Revnivtsev et al. (2006) in the 3–20 keV range was L x /M c (cid:13) RAS, MNRAS , 1–16 K. Byckling, K. Mukai, J.R. Thorstensen, J. P. Osborne ∼ (3.5 ± × erg s − M − ⊙ , meaning that our samplewould account for 5 per cent of the Galactic Ridge X-rayemissivity. As we estimated the X-ray emissivity of all CVswithin 200 pc, we used the exponential vertical density pro-file ρ ( z ) = ρ e | z | /h , (5)of CVs with a scale height for short period systems ( h = 260 pc) as in Pretorius et al. (2007b), where z = d sin b is the perpendicular distance from the Galactic plane and b Galactic latitude. Integrating Eq.5 over a sphere with a ra-dius of 200 pc gives ∼
280 as the total number of DNe within200 pc. If the space density of DNe follows the space den-sity of CVs as in Pretorius et al. (2007b), i.e., ρ = 1.1 +2 . − . × − pc − , and if a typical DN has an X-ray luminositycorresponding to the mean luminosity (2 × erg s − )of our sample of 11 sources (BZ UMa excluded), then the2–10 keV X-ray emissivity of all DNe in the solar neighbour-hood would be 5.5 +11 . − . × erg s − M − ⊙ (these accountfor the uncertainty on the space density, assuming that thisis the dominant source of uncertainty for the X-ray emis-sivity of DNe). This would account for more than 100 percent of the GRXE emissivity. If DNe were uniformly dis-tributed in the solar neighbourhood, the X-ray emissivitywould be overestimated also in this case (by 20–30 per cent).However, in both cases, one should remember that the cal-culated X-ray emissivity of all DNe within 200 pc is likelyoverestimated by the brighter sources in our sample, thusthe calculations give excess emission. In order to understand whether the X-ray luminosity andthe various parameters (inclination i , orbital period P orb ,shock temperature kT max and white dwarf mass M WD ) arecorrelated, we carried out Spearman’s rank correlation test.Plotting X-ray luminosity versus a few of these parameters ( i and P orb ) shows that GW Lib seems to appear as an outliercompared to the rest of the sample (Fig. 7 and 8). Thus, toexplore how the presence/absence of GW Lib affects the testresults, two test cases were used: 1) GW Lib was included,and 2) GW Lib was excluded from the rest of the sample.In addition, we investigated whether a correlation betweenthe white dwarf masses M WD and the shock temperatures kT max (Fig. 2) exists, although in this case, GW Lib seemsto follow the rest of the sample, thus, carrying out test case2) was not necessary.A strong correlation was found at the 99.95 percent significance level (2.8 σ ) between the X-ray luminosi-ties and orbital periods (Fig. 7) when GW Lib is in-cluded in the sample. The correlation still holds whenGW Lib is excluded (significance is 99.67 per cent).Baskill, Wheatley, & Osborne (2005) noted that there was aweak correlation between the X-ray luminosities and the or-bital periods in their ASCA sample, concluding that the X-ray luminosity probably also correlates with long-term meanaccretion rate.The X-ray luminosity and the inclination i are not cor-related in either case (Fig. 8). The correlation between these Figure 7.
The X-ray luminosities (2.0–10.0 keV) versus orbitalperiods of the source sample. parameters was measured when the inclination of BZ UMawas set to 65 ◦ , and altering the inclination between 60 ◦ and 75 ◦ did not affect the result. Since no correlation wasfound, this result is in contrast with the discovery of anti-correlation between the emission measure and inclinationfound by van Teeseling, Beuermann, & Verbunt (1996). Itis worth noting that the ROSAT bandpass was very narrow,covering only 0.1–2.4 keV where the softer X-ray emission(and more luminous emission) is probably intrinsically ab-sorbed by the sources. In addition, an anti-correlation be-tween the X-ray luminosity and inclination was also seen byBaskill, Wheatley, & Osborne (2005) in the
ASCA sample,although, Baskill et al. noted that the inclinations might beuncertain, and this can also be the case in our sample.Finally, the white dwarf masses M WD and the shocktemperatures kT max correlate with a significance of 98.5 percent when the mass of VY Aqr is 0.80 M ⊙ , but becomes lesssignificant (97.4 per cent) if the mass is 0.55 M ⊙ . Of the restof the parameters, i.e. the X-ray luminosity L x versus kT max and M WD , kT max showed evidence of correlation with L x ata significance of 97.6 per cent when GW Lib was included inthe sample, but L x and M WD had a much lower correlationsignificance (69 per cent) when including GW Lib. For thelatter correlation test ( L x versus M WD ), the result was thesame with both M WD values for VY Aqr. Excluding GW Libdecreased the significance to 91 per cent ( L x versus kT max )and to 63 per cent ( L x versus M WD ). We have analysed the X-ray spectra of 13 dwarf novae withaccurate parallax-based distance estimates, and derived themost accurate shape for the X-ray luminosity function of c (cid:13) RAS, MNRAS , 1–16 eriving an X-ray luminosity function Figure 8.
The X-ray luminosities (2.0–10.0 keV) versus inclina-tions of the source sample.
DNe in the 2–10 keV band to date due to accurate distancemeasurements and due to the fact that we did not use anX-ray selected sample.The derived X-ray luminosities are located between ∼ –10 erg s − , showing a peak at ∼ erg s − . Thus,we have obtained peak luminosities which are lower com-pared to other previous studies of CV luminosity functions.The shape of the X-ray luminosity function of the sourcesample suggests that the two following scenarios are possi-ble: 1) the sample can be described by a power law with asingle α slope, but the sample becomes more incomplete be-low ∼ × erg s − than it is above this limit, or, 2) theshape of the real X-ray luminosity function of dwarf novaeis a broken power law with a break at around 3 × ergs − . The integrated luminosity between 1 × erg s − and the maximum luminosity of the sample, 1.50 × ergs − , is 1.48 × erg s − . In order to better constrain theintegrated luminosity and the slope of the X-ray luminos-ity function, more dwarf novae need to be included in thesample. Thus, we suggest more future X-ray imaging obser-vations of dwarf novae in the 2–10 keV band with accuratedistance measurements. The total X-ray emissivity of thesample within a radius of 200 pc is 1.81 × erg s − M − ⊙ (2–10 keV). This accounts for ∼
16 per cent of the total X-ray emissivity of CVs as estimated by Sazonov et al. (2006),and ∼ ACKNOWLEDGMENTS
This research has made use of data obtained from the
Suzaku satellite, a collaborative mission between the space agenciesof Japan (JAXA) and the USA (NASA). JO acknowledgessupport from STFC. Part of this work is based on obser-vations obtained with
XMM-Newton , an ESA science mis-sion with instruments and contributions directly funded byESA Member States and the USA (NASA). We thank thereviewer M. Revnivtsev for his helpful comments on thispaper.
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