A Radial Velocity Study of CTCV J1300-3052

0.95 MB·

by  C. D. J. Savoury

Mon.Not.R.Astron.Soc.000,1–??(2011) Printed25January2012 (MNLATEXstylefilev2.2)
A Radial Velocity Study of CTCV J1300-3052
C. D. J. Savoury1⋆, S. P. Littlefair1, T. R. Marsh2, V. S. Dhillon1, S.G. Parsons2,
C.M. Copperwheat2 and D. Steeghs2
2 1Dept of Physics and Astronomy, Universityof Sheffield, Sheffield, S3 7RH, UK
1 2Dept of Physics, Universityof Warwick, Coventry, CV47AL, UK
0
2

n SubmittedforpublicationintheMonthlyNotices oftheRoyalAstronomicalSociety25January2012
a
J

4 ABSTRACT
2
We present time-resolved spectroscopy of the eclipsing, short period cataclysmic

] variable CTCV J1300-3052. Using absorption features from the secondary star, we
R
determine the radial velocity semi-amplitude of the secondary star to be K2 = 378
S ± 6 km s−1, and its projected rotational velocity to be vsini = 125± 7 km s−1.
h. Using these parameters and Monte Carlo techniques, we obtain masses of M1 = 0.79
p ± 0.05 M⊙ for the white dwarf primary and M2 = 0.198 ± 0.029 M⊙ for the M-
- type secondary star. These parameters are found to be in excellent agreement with
o
previousmassdeterminationsfoundviaphotometricfittingtechniques,supportingthe
r
t accuracy and validity of photometric mass determinations in short period CVs.
s
a
Key words: binaries:close-binaries:eclipsing-stars:dwarfnovae-stars:lowmass,
[
stars: novae, cataclysmic variables - stars: evolution.

1
v
7
7
9 1 INTRODUCTION mass estimates for large samples of CVs. It is therefore im-
4 portant to check the validity of photometric mass determi-
Cataclysmic variable stars (CVs) are a class of interacting
. nations.
1 binary system undergoing mass transfer from a Roche-lobe
0 fillingsecondarytoawhitedwarfprimary,usuallyviaagas For objects with periods above the period gap (the
2 stream and accretion disc. Through determinations of the dearth of systems between 2.2 and 3.2 hours, see e.g.
1 massesandradiiofthecomponentstarsinCVs,itispossible Kolb & Ritter 2003, Knigge 2006), the photometric fit-
v: to test fundamental theories regarding their formation, ori- ting technique appears robust, with donor star radial ve-
i gin and evolution (e.g. Littlefair et al. 2008; Savoury et al. locities predicted by photometry in agreement with those
X
2011). foundbyothertechniques(Watson et al.2003;Feline2005;
r Savoury et al.(2011)carriedoutaphotometricstudyof Copperwheat et al. 2010). However, for objects below the
a
eclipsing CVs and found the masses and radii for both the period gap, independent tests of thephotometric technique
whitedwarfanddonorstarin14systems.Thesemasseswere are rare.Tulloch et al. (2009) found the radial velocity of
found by fitting a parameterised model to the eclipse light the white dwarf (K1) in SDSS J143317.78+101123.3 (Porb
curves. This model is based on the techniques developed =78.1mins),asmeasuredfromdiscemissionlines,tobein
by Bailey (1979), Smak (1979), Cook & Warner (1984), excellentagreementwiththephotometricvaluepredictedby
Wood et al.(1985),Wood et al.(1986),Horneet al.(1994), Littlefair et al. (2008). The agreement is encouraging, but
Littlefair et al. (2008) and Copperwheat et al. (2010) and the motion of the inner disc does not necessarily follow the
relies on just four assumptions: the bright-spot lies on the motion of the white dwarf, and so K1 estimates from disc
ballistic trajectory from the donor star; the donor star fills emission should be treated with caution (e.g. Marsh 1988).
its Roche lobe; the white dwarf is accurately described by More recently, Copperwheat et al. (2011) found the radial
a theoretical mass-radius relation; and the whole of the velocity and rotational broadening of the secondary star in
white dwarf is visible with an unmodified surface bright- OY Car (Porb = 90.9 mins) to be in good agreement with
ness.Itisphotometricmassandradiideterminationssuchas those predicted by photometric methods (Wood & Horne
thesethatareusedtocalibratetheǫ-q (super-humpexcess- 1990;Littlefair et al.2008).However,suchistheimportance
massratio)relationsofPatterson(2005),Knigge(2006)and ofmassdeterminationsinCVs,additionalverificationacross
Knigge et al.(2011),whichcanthenbeusedtoderivedonor a range of orbital periods is highly desirable.
One of the systems observed by Savoury et al. (2011)
wasCTCVJ1300-3052(hereafterCTCV1300).CTCV1300
⋆ E-mail:chris.savoury@sheffield.ac.uk is a dwarf nova that was discovered as part of the Cal´an-
(cid:13)c 2011RAS
2 C. D. J. Savoury et al.
Tololo Surveyfollow up (Tappert et al. 2004). It was found thenunderwentanoptimalextraction routine(Horne1986;
tobeeclipsing,withanorbitalperiodof128.1minutes,plac- Marsh 1989),and order merging.
ingit immediately belowtheperiod gap. Theaveragespec- Wavelength calibration was undertaken using an arc
trumshowedclearemissionlinesfromtheaccretiondiscand line spectrum which was taken from the ESO archive. The
absorptionlinesfromthedonorstar.Itisthroughabsorption wavelengthcalibration recipeusedaphysicalmodeltogen-
linessuchasthesethatwecandeterminetheradialvelocity erate a best-guess solution of the line positions on the cali-
and rotational broadening of the secondary star, which can brationframe.Theselineswerethenfittedby2DGaussians,
in turn be used to derive an independent measure of the andtheresultingpositionsoftheselineswereadjustedviaa
masses and radii of the component stars (e.g. Horne et al. polynomialfittothewholeCCD.Fromresidualstotheline
1993;Smith et al. 1998; Thoroughgood et al. 2001, 2004). fitting, we estimate that this calibration is accurate to ∼1
In this paper we present time resolved-spectroscopy of kms−1 (atλ=8183˚A).WecorrectedforflexureintheVIS
CTCV 1300anddeterminethesystemparameters.Thepa- armbymeasuringtheshiftoftheobservedskylinesrelative
rametersderivedusingspectroscopywillprovideanindepen- to theirpositions measured by Hanuschik(2003). The indi-
denttestofthephotometricmethodsusedbyLittlefair et al. vidualspectra were then moved bythese shifts, which were
(2008) and Savoury et al. (2011). typically between 10 and 35 km s−1. Wedo not attempt to
correct for flexure in the UVB and NIR arms, since we do
notattempt tomeasureradial velocities toahighdegreeof
precision in these bands.
2 OBSERVATIONS
Thetimeandwavelengthaxisofthedatawerecorrected
CTCV1300wasobservedusingX-shooter(D’Odorico et al. to theheliocentre.
2006) in service mode mounted on UT2 (Kueyen) on the
8.2-m Very Large Telescope (VLT) on the nights beginning
9Feb2010and6March2010.Intotal,weobtained48spec- 4 RESULTS
tra (24 on each night) covering 1.5 orbital cycles, and a
4.1 Average Spectra
wavelength range of ∼3000-24800 ˚A. Exposure times were
235 secondsin theUVB-arm(3000-5500 ˚A),210 secondsin TheaveragespectraofCTCV1300areshowninFig.1.The
the VIS-arm (5500-10000 ˚A), and 255 seconds in the NIR- upperpanelshowsthewavelengthrange3200-5500 ˚A(from
arm(10000-24800˚A),withdeadtimesbetweenexposuresof theUVB-arm), the centre panel shows 5750-10000 ˚A (from
approximately 8, 9 and 1 seconds, respectively. theVIS-arm),andthelowerpanel10000-13500 ˚A(fromthe
The target was observed with the 1.0”x11” slit in NIR-arm).Eachspectrumisfluxcalibrated,andtelluriccor-
the UVB-arm, the 1.2”x11” slit in the VIS-arm, and the rection has been attempted.
0.9”x11” slit in the NIR-arm. The resolving power was Throughoutthespectrumweseestrong,broad,double-
∼5100 (59 km s−1) in the UVB and NIR-arms, and ∼6700 peaked Balmer lines and several double-peaked He I lines
(45 km s−1) in the VIS-arm. Seeing conditions on both (4471, 4922, 5015, 5875, 6678, 7065 and 10830 ˚A). Broad
nights were fair, varying between 0.5 and 1.5 arcseconds, double-peaked lines such as these are typical of a high-
but with flares of up to 2.0 arcseconds. inclination accreting binary (e.g. Horne& Marsh 1986).
Observations of the standard star GD153 were used to The high ionisation line He II 4686 ˚A appears absent
flux calibrate the data and correct for telluric absorption. in the average spectrum, but is visible in the trailed spec-
The data were obtained in ‘stare’ mode rather than nod- tra (see Sections 4.2 and 4.3). Several absorption lines are
ding along the slit as is normal for long slit infra-red spec- present between 4000-4800 ˚A (see Fig. 2) which appear to
troscopy.Consequently,theskysubtractionontheNIR-arm tracethemotionofthedisc(seeSection4.2).Webelievethe
spectraissignificantlyworsethanusualwithX-shooter.We most likely cause of these absorption lines is a veil of disc
alsoobtainedspectraofthespectraltypetemplatesGJ2066 material along the line of sight, The majority of these lines
(M2V)andGJ1156 (M5V),although thesedataweretaken appeartobeFeI,FeIIandCaI.Similarfeatureshavebeen
on thenights of 11 Dec2009 and 28 Jan 2010, respectively. observed in thespectrum of OYCar by Horneet al. (1994)
and Copperwheat et al. (2011).
Theheliumlinesat4922,5015˚Aappeartoshowstrong,
narrowabsorptioncoresthatdipbelowthecontinuum,asdo
3 DATA REDUCTION & ANALYSIS
thehigher-orderBalmerlinesbetween3600-4000˚A.TheOI
DatareductionwascarriedoutusingtheX-shooterpipeline tripletat 7773˚Aisclearly visible,andalso appearstodrop
(version 1.2.2) recipes within ESORex, the ESO reduction below the continuum. Features such as these are observed
execution tool. The data for all three arms were reduced in a number of CVs (e.g Marsh 1987; Wade& Horne 1988;
with similar procedures. The required calibration frames Friend et al. 1988). These absorption cores are believed to
wereconstructedusingthestandardrecipesprovidedinthe originate through self-absorption in theaccretion disc.
pipeline. In brief, they include a map of bad pixels, a mas- The Ca II triplet at 8498, 8542 and 8662 ˚A (here-
ter bias (for the UVB and VIS-arms), a master dark (for after 8567 ˚A) is clearly present and originates from the
theNIR-arm,asdarkcontributionisnegligibleinUVBand disc, although there is evidence of emission from the irra-
VIS) and a master flat. The data was first bias and dark diated side of the donor (see Sections 4.2 and 4.3). Sim-
subtracted,beforeaninter-orderbackgroundwasfittedand ilar features have been observed in the spectrum of GW
subtracted. Science frames were then divided by the flat Lib (van Spaandonk et al. 2010). The higher orders of the
field,andthentheobjectwaslocalised ontheslit.Skysub- Paschen series are also visible from ∼8800 ˚A onwards, and
traction and cosmic ray removal took place, and the data are possibly blended with theCa II emission.
(cid:13)c 2011RAS,MNRAS000,1–??
CTCV J1300-3052 3
Figure 1.Theaverage spectra ofCTCV 1300, inthe restframeof thebinary. Theupper panel shows the UVB-arm,the centre panel
theVIS-arm,andthelowerpaneltheNIR-arm.Themostprominentfeaturesarelabelled.
Absorptionfeaturesfromthesecondarystarareclearly times(seeSection2),oneofthesebinsisemptyinboththe
visibleintheformofTiObandsaround7100˚Aand7600˚A, VISand NIR-arms.
and weak K I absorption doublet at 7664, 7699 (hereafter We divided the continuum by a polynomial and re-
7682 ˚A),11773, 12432 and12522 ˚A.However,theseregions binned the spectra onto a constant velocity-interval scale
areheavily affectedbytelluricabsorption. Theclearest fea- centredontherestwavelengthofthelines.Fig.3showsthe
turesfromthesecondarystararetheNaIdoubletsat8183, trailed spectra of the Hα, Hβ, Hγ and Hδ lines in CTCV
8194 ˚A (hereafter 8189 ˚A) and 11381, 11404 ˚A (hereafter 1300.Eachlineshowstwoclearpeaksthatvarysinusoidally
11393 ˚A), although the second of these is also heavily af- withphase,inadditiontothecharacteristics-wavebetween
fected by telluric absorption. phases 0.1–0.4 from thebright spot.
In Fig. 4 we show the trailed spectra of two Na I dou-
blets (8189 and 11393 ˚A), the Ca II triplet (8567 ˚A), the
7682˚AKIdoubletandHeII(4686˚A).Thephasesatwhich
the Na I and K I lines show maximum red-shift (φ=0.25)
4.2 Trailed Spectra
and blue-shift (φ = 0.75) suggest they originate from the
The data were phase binned into 30 bins, according to the donor star. We see evidence for emission from the donor
ephemerisofSavoury et al.(2011).TheUVB-armhascom- starintheCaIIlinesthroughacomponentinthetrailthat
pletephasecoveragealthough,duetothedifferingexposure is in phase with the Na I lines. However, this component
(cid:13)c 2011RAS,MNRAS000,1–??
4 C. D. J. Savoury et al.
Figure2.TheaveragespectraofCTCV1300between4130-4330˚A,correctedtotherestframeofthewhitedwarf.Spectratakenduring
eclipsearenotincludedintheaverage.
Figure 3.ThetrailedspectraoftheHα(topleft),Hβ (topright),Hγ (bottom left)andHδ (bottom right)linesinCTCV1300.
is only visible during phases ∼0.25-0.75, which indicates it line forest between 4130-4300 ˚A. The lines all appear to
arises from the irradiated side of the donor. The He II line move together, suggesting a common place of origin. Using
appears to follow the motion of the bright spot, as defined thesamemethodoutlinedinSection4.4,wefindthevelocity
by thes-wave in theBalmer trails. of these lines to be K = 116 ± 4 km s−1, with a phase
abs
offset of ∆φ = 0.072 ± 0.006. The high velocity (compared
In Fig. 5 we show the trailed spectra of the absorption
(cid:13)c 2011RAS,MNRAS000,1–??
CTCV J1300-3052 5
Figure4.Thetrailedspectraofthe8189and11393˚ANaIdoublets(upperleftanduppercentre,respectively),the7682˚AKIdoublet
(topright),theCaIItriplet(8498,8542˚Abottomleft,8662˚Abottom centre)andHeII(4686˚A,bottom right)inCTCV1300.Black
andwhitelinesrepresentabsorptionandemission,respectively.
review of Doppler tomography, see Marsh & Horne (1988)
and Marsh (2001).
Fig. 6 shows Doppler maps for Ca II (8498, 8542 &
8662˚A),Hα,Hβ andHeII(4686˚A).Eclipsedata(between
phases0.95and1.05) areremoved.Asystemicvelocityofγ
=-20kms−1 wasappliedtoshiftthemapsontotheK =0
x
km s−1 axis (see Section 4.4).
In each map we see a ring-like distribution of emission
centredonthewhitedwarf,whichischaracteristicofanac-
cretion disc. In the Ca II maps, we see an enhanced area
of emission at velocities intermediate to the free-fall veloc-
ity of the gas stream (lower stream) and thevelocity of the
discalongthegasstream(Keplerianvelocity,upperstream).
Thisemissionisattributedtothebrightspot.ThethreeCa
II maps all show clear emission from the donor star, which
appears to be concentrated towards the inner hemisphere,
Figure 5. Trailedspectra of the forest of FeI, FeII and CaI ab- indicatingthatirradiationissignificant.TheHαmapshows
sorptionlinesbetween4130-4300 ˚A. emission from the secondary star, a feature uncommon in
shortperiodCVs.TheHβmapshowsweakbrightspotemis-
totheexpectedmotionofthewhitedwarf,∼90kms−1,see sion.TheHeIIemissionappearstoshowemissionnearboth
the Keplerian velocity stream and at velocities intermedi-
Section 4.6) and significant phase offset suggests that these
ate to the Keplerian velocity stream and free-fall velocity
lines originate in thedisc.
stream,althoughitispossiblethatthisisanartifactarising
from limited phase coverage (Marsh & Horne 1988). If this
is a genuine feature, its position relative to the Ca II emis-
4.3 Doppler tomography
sionsuggeststhattheHeIIemissioniscausedbyamixture
Dopplertomographyisanindirectimagingtechniquewhich of gas-stream and disc material. He II bright spot emission
can be used to determine the velocity-space distribution of atKepleriandiscvelocitieshasbeenobservedinothershort
the emission in cataclysmic variables. For a comprehensive period CVs (Marsh et al. 1990; Copperwheat et al. 2011).
(cid:13)c 2011RAS,MNRAS000,1–??
6 C. D. J. Savoury et al.
Figure 6.Doppler mapsofCTCV 1300inCaII(8498, 8542, 8662˚A), Hα,Hβ andHeII(4686 ˚A)computed fromthe trailedspectra
inFigs.3and4.Datataken duringeclipsehavebeen ommitedfromthefit. Thepredicted positionofthe secondary starand thepath
of the gas stream are marked. The three crosses on the map are, from top to bottom, the centre of mass of the secondary star, the
centre ofmassof thesystem, and thewhite dwarf.These crosses,the Roche lobeofthe secondary, theKeplerianvelocity alongthe gas
stream(topcurve),andthepredictedtrajectoryofthegas-stream(bottomcurve)havebeenplottedusingthesystemparametersfound
in Section 4.6. The series of circles along the gas stream mark the distance from the white dwarf at intervals of 0.1L1, where 1.0L1 is
thesecondarystar.
4.4 Radial velocity of the secondary star a new value of K2 and γ to correct our spectra with. We
added an intrinsic error in quadrature to each error bar to
The secondary star in CTCV 1300 is visible through weak account for systematic error, and reach a reduced-χ2 of 1.
absorption lines. The strongest of these lines is the Na I
doubletat8189˚A.Inordertodeterminetheradialvelocity, aThviasluperoocfesKs2w=as3r7e9pe±ate6dkumntsi−l1K,2wcitohnvaenrgiendt.riWnseicaerrrrivoeraotf
we cross-correlated the individual spectra of CTCV 1300 22kms−1addedinquadraturetoeacherrorbar.Theradial
againstanaveragespectraofCTCV1300usinganiterative
velocitycurveobtainedusingthistechniqueisshown inthe
technique. We chose the Na I line at 8189 ˚A because it is
upperpanelof Fig. 7.
much stronger and less affected by telluric absorption than
theline at 11393 ˚A. The value of γ obtained via our auto-correlation tech-
We subtracted fits to the continuum from the individ- nique is not representative of the true systemic velocity,
ualspectraandthencorrected fortheorbitalmotion ofthe which must be determined through cross-correlation with
secondary star with a first guess of K2. For each individ- atemplatestarofknownradialvelocity.Therefore,inorder
ual spectrum, we then created a template spectrum that to verify this result and find thetrue systemic velocity (γ),
consisted of an average of all the spectra minus the spec- wethencross-correlatedagainstourM-dwarftemplatespec-
trum under study (Marsh, Robinson & Wood 1994). These trausing thesame wavelength range. Thetemplate spectra
template spectrawere then cross-correlated against theun- were artificially broadened by 46 km s−1 toaccount for the
corrected data. The velocity shifts as a function of orbital orbitalsmearingofCTCV1300throughthe210-secondVIS-
phase were then fit with a sine function according to; arm exposures, and then by the best-fitting values for the
V =γ−K2sin[2π(φ−φ0)], (1) Sroetcattioionna4l.5v.eAloncitinytroifnstihceesrerocornodfa2ry2 kstmars(−v1siwnais)afodudnedd tino
whereVisthevelocityshift,γisthesystemicvelocityofthe each error bar from the M2V cross-correlation, and 24 km
system, K2 is the radial velocity of secondary star, φ is the s−1toM5Vdata,toaccountforsystematicerrorsandreach
orbital phase, and φ0 is the phase offset. This then yielded a reduced-χ2 of 1. The radial velocity curves are shown in
(cid:13)c 2011RAS,MNRAS000,1–??
CTCV J1300-3052 7
bletat8189˚A.Thespectral-typetemplateswerebroadened
tomatchthesmearingduetoorbitalmotionofCTCV1300
through the 210 second VIS-arm exposures and rotation-
ally broadened by a range of velocities (50-200 km s−1). In
principle,theorbitalsmearingisafunctionoforbitalphase,
andthusvariesthroughouttheorbitalcycle.Weuseasingle
valueof46kms−1,whichistheaveragevalueofthesmear-
ingacrossanorbitalcycle.Wefindthatchangingthistothe
maximumandminimumpossible valuesoforbitalsmearing
required, that is the smearing at conjunction and quadra-
ture, alters the final value of vsini obtained by 3 km s−1.
This uncertainty is added in quadrature to the uncertainty
calculated below.
The value of vsini was obtained via an optimal sub-
traction routine, which subtracts a constant times the nor-
malised,broadenedtemplatespectrumfromthenormalised,
orbitally corrected CV spectrum. This constant is adjusted
to minimise the residual scatter between the spectra. The
scatter is measured by carrying out the subtraction and
then computing χ2 between the residual spectrum and a
smoothed version of itself. By finding the value of ro-
tational broadening that minimises χ2, we can obtain a
value of vsini and the spectral type of the secondary star
Figure 7. The radial velocity curve of CTCV 1300 obtained (Dhillon & Marsh 1993; Marsh, Robinson & Wood 1994).
throughauto-correlation(upperpanel), cross-correlationagainst This value of vsini should then becorrected for the intrin-
an M2 template (centre panel) and cross-correlation against an sic rotational velocity of the template star. Unfortunately
M5template(lowerpanel). a wide range of spectral-types were not available, and so
we are unable to deduce the spectral-type of the secondary
using thistechnique.
the centre panel (M2), and bottom panel (M5) of Fig. 7.
Cross-correlating against the M2 and M5 templates yield
values of K2 = 373 ± 6 km s−1 and K2 = 376 ± 7 km The value of vsini obtained using this method was
s−1, respectively. The M2 template could not be corrected foundtovarydependingonthespectral-typetemplateused
for flexure, so we only use the M5 template to derive the and thewavelength region selected for optimal subtraction.
systemic velocity for CTCV 1300. Using the radial veloci- Weattempted to includeas much of thecontinuum as pos-
tiesprovidedbyGizis et al.(2002),wefindγ =-20±5km sible around the Na I doublet, while trying to avoid tel-
s−1. For K2, we prefer the value found through the auto- luric regions. We used a wavelength range of 8080-8106,
correlation, that is K2 = 379 ± 6 km s−1. This is because 8125-8206, 8226-8245 and 8264-8285 ˚A, a limb-darkening
theaveragespectraofthedataisabettermatchtothedata coefficient of 0.5 and smoothing Gaussian of FWHM =
than theM5 and M2 templates. 15 km s−1, which were found to give the lowest values of
The radial velocity curves produced through this tech- χ2. The limb-darkening coefficient is highly uncertain, al-
niqueshowsomevariationfromasinefitbetweenphases0.4 thoughCopperwheat et al. (2011)haveshown thataltering
to 0.6, which is characteristic of irradiation suppressed ab- the limb-darkening coefficient has little effect on the value
sorption(e.g.Billington et al.1996).Marsh & Horne(1988) ofvsiniobtained.Weplotthevaluesofχ2 versusvsinifor
recommend only fitting the above data between phases 0.8 both spectral-type templates in Fig. 8. Using the M2 tem-
to 1.2, since at these phases theeffects of irradiation are at plate, we obtain a value of vsini = 129 ± 3 km s−1, while
a minimum. Fitting the auto-correlation data, we obtain a theM5 templateyieldsavalueof vsini=125 ± 4kms−1.
valueofK2 =378±6kms−1,whichweusehereafter.This Theuncertaintiesonthesevaluescomefromtheformalerror
valueisconsistentwiththevaluepredictedbySavoury et al. estimation of ∆χ2= ±1. This does not attempt to include
(2011), K2 = 372.2 ± 2.5 km s−1. Fitting the M5 and M2 systematicerrors.Becauseofthelackofavailabletemplates,
templatesbetweenthesamephasesgivesK2 =372 ±7km we estimated the spectral type of the secondary star using
s−1 and K2 = 378 ± 8 km s−1 respectively, which is again the empirical donor sequence of Knigge et al. (2011). For a
in excellent agreement with the auto-correlation data, and system with an orbital period of 128.07 minutes, we expect
consistent with thephotometric method. asecondarywithspectraltypeofM4.3.Weadoptaspectral
type of M4.5 ± 0.5. We interpolate between the two values
ofvsiniabovetoarriveat afinalvalueofvsini=125 ± 7
4.5 Rotational velocity of the secondary star
km s−1. This error takes into account both the uncertainty
The normalised spectra of CTCV 1300 were corrected for onfindingourminimumvsiniforeachtemplate(±3-4km
the orbital motion of the secondary star using the value of s−1 for each template), the uncertainty from averaging the
K2 obtainedinSection4.4.Thespectrawerethenaveraged orbitalsmearing(±3kms−1),andtheuncertaintyinspec-
togetherinordertomaximise thestrength oftheNaIdou- tral type(±0.5 spectral types).
(cid:13)c 2011RAS,MNRAS000,1–??
8 C. D. J. Savoury et al.
R2 vsini
(1+q)= . (3)
a K2
Thisgivesustwosimultaneousequationsthatcanbesolved
for q and R2/a. The orbital inclination, i, is fixed by q and
∆φ1/2,usinggeometricalarguements(e.g.Bailey1979).We
determinetheinclination via abinary chopsearch usingan
accurate model of theRoche Lobe.
Using Kepler’s Third Law, we obtain
K23Porb = M1sin3i, (4)
2πG (1+q)2
whichusingthepreviouslycalculatedvaluesofqandiyields
themassoftheprimarystar,M1.Themassofthesecondary
star, M2 and radial velocity of the primary,K1, is given by
M2 K1
q= = . (5)
M1 K2
Finally, we can calculate the radius of the secondary star
using
vsini 2πsini
= , (6)
R2 Porb
and thebinary separation, a,using equations 3 and 6.
OurMonteCarlosimulationtakes250,000valuesofK2,
∆φ1/2,vsiniandPorb,treatingeachasbeingnormallydis-
tributed about their measured values with standard devi-
ations equal to the errors on the measurements. We then
calculate the mass of each component, the inclination of
thesystem andtheradius of thesecondary staras outlined
above, omitting (K2, vsini, ∆φ1/2) triplets that are incon-
Figure 8.χ2 vsvsinifromtheoptimalsubtractiontechnique. sistent with sini 61. Each accepted M1, M2 pair is plotted
inFig.9,andthemassesandtheirerrorsarecomputedfrom
themeanandstandarddeviationofthedistributionofthese
4.6 System Parameters pairs.WefindthatM1=0.79±0.05M⊙andM2=0.198±
0.029 M⊙. These values are found to be in good agreement
Using thevaluesof K2 = 378 ± 6 km s−1 and vsini = 125 with those of Savouryet al. (2011). The values of all sys-
± 7 km s−1 found in Sections 4.4 and 4.5 in conjunction temparametersfoundfrom theMonteCarlosimulation are
with the orbital period and a measurement of the eclipse listed in Table 1, along with those of Savouryet al. (2011)
full width at half depth (∆φ1/2), we can calculate accurate for direct comparison.
system parameters for CTCV 1300.
The best measurement of the orbital period, P ,
orb
4.7 Distance
comes from Savouryet al. (2011), who determine P =
orb
0.088940717(1) days. Savouryet al. (2011) also present six By finding the apparent magnitude of the secondary star
lightcurvesofCTCV1300,fromwhichwedetermine∆φ1/2 from its contribution to the total light during eclipse, and
= 0.0791(5). byestimating theabsolutemagnitude,we cancalculate the
WeuseaMonteCarlo approach similar toHorne et al. distance (d),using theequation;
(1993),Smith et al.(1998),Thoroughgood et al.(2001)and
Thoroughgood et al. (2004) to calculate thesystem param- 5log(d/10)=mI−MI −dAI/1000, (7)
etersandtheirerrors.ForagivensetofK2,vsini,Porb and where A is the interstellar extinction in magnitudes per
I
∆φ1/2, the remaining parameters are calculated as follows. kpc. We assume the extinction is zero, as this allows a di-
R2/a can be estimated because the secondary star fills rect comparison to the distance obtained by Savoury et al.
its Roche Lobe. R2 is the secondary radius, and the a is (2011),who usedmodel generated whitedwarf fluxestoes-
the binary separation, and so we use Eggleton’s formula
timate the distance without correction for extinction. At
(Eggleton 1983), which gives the volume equivalent radius
mid-eclipse (φ = 0), the apparent magnitude of the sys-
of the Roche Lobe to an accuracy of ∼1 per cent, which is tem is 17.32 ± 0.02 around the Na I doublet, which is ap-
close to the equatorial radius of the secondary star as seen
proximately the I-band. This value is not corrected for slit
duringeclipse, losses.Thesecondarystarisfoundtocontribute58±6per
R2 0.49q2/3 cent, which gives an apparent magnitude of mI = 17.91 ±
= . (2) 0.09.Weestimatetheabsolutemagnitudeusingtheempiri-
a 0.6q2/3+ln(1+q1/3)
cal donor sequenceof Knigge et al. (2011),who assume the
The secondary star rotates synchronously with the orbital donorisonthemainsequenceandthencorrectforbloating
motion, so we can combineK2 and vsini, to get effects. From this, wetakeMI =10.32±0.14, and obtain a
(cid:13)c 2011RAS,MNRAS000,1–??
CTCV J1300-3052 9
Figure 9.Monte Carlodetermination of system parameters for CTCV 1300. Each dot represents an (M1, M2) pair. Dot-dashed lines
arelinesofconstantinclination,thesolidcurvessatisfytheconstraintsfromtheradialvelocityofthesecondarystar,K2,andthedashed
linessatisfytheconstraints oftherotational velocityofthesecondarystar,vsini.
Table 1.System parametersforCTCV1300.
Parameter MeasuredValues MonteCarloValues Savouryetal.(2011)
Porb (s) - - 0.088940717(1)
∆φ1/2 0.0791±0.0005 - not stated
K2 (kms−1) 378±6 - 372.2±2.5
vsini(kms−1) 125±7 - 122±10∗
q - 0.252±0.025 0.240±0.021
io - 85.7±1.5 86.3±1.1
M1/M⊙ - 0.79±0.05 0.736±0.014
M2/M⊙ - 0.198±0.029 0.177±0.021
R2/R⊙ - 0.223±0.011 0.215±0.008
a/R⊙ - 0.834±0.020 0.813±0.011
K1 (kms−1 ) - 95±9 90±8
Distance(pc) 330±40 - 375±13
∗ Derivedusingthevaluespublishedintable3ofSavouryetal.(2011).
distance of d = 330 ± 40 pc. This distance is found to be ofPatterson(2005),Knigge(2006)andKnigge et al.(2011)
in good agreement with that of Savoury et al. (2011), who are well founded.
obtained a valueof d = 375 ± 13 pc.
The uncertainties in the system parameters for CTCV
1300determinedinthispaper,andinSavoury et al.(2011),
are quite large in comparison to many of the other systems
publishedin Savoury et al. (2011). Thereason for thelarge
5 DISCUSSION
uncertainties in CTCV 1300 in Savoury et al. (2011) is be-
The system parameters listed in Table 1 are found to be cause the eclipse light curves used for model fitting suffer
in good agreement with those of Savouryet al. (2011). To- from heavy flickering, which causes difficulties in obtaining
gether with Copperwheat et al. (2011), this gives us confi- anaccuratevalueforthemassratio,q.Thelargeuncertain-
dencethatphotometricmassdeterminationssuchasthoseof tiesinthispaperarisebecauseoftheinterpolationtechnique
Littlefair et al.(2008)andSavoury et al.(2011)arereliable used to arrive at a value for vsini. The error on vsini (±
across a range of orbital periods, and that the ǫ-q relations 7kms−1)isthedominantsourceofuncertaintyinourfinal
(cid:13)c 2011RAS,MNRAS000,1–??
10 C. D. J. Savoury et al.
systemparameters.Inprinciple,awiderselectionofspectral Feline W., 2005, PhD Thesis, Univ.Sheffield
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6 CONCLUSIONS Horne K., 1986, PASP,98, 609
Horne K., Marsh T., 1986, MNRAS,218, 761
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1300.Thedouble-peakednatureoftheBalmerandHeIlines ApJ,426, 294
confirmsthepresenceofanaccretiondisc,whilecarefulanal- Knigge C., 2006, MNRAS,373, 484
ysis of the Na I doublet absorption lines at 8189 ˚A reveals Knigge C., Baraffe I., Patterson J., 2011, ApJS,194, 28
the radial velocity of the secondary star to be K2 = 378 ± Littlefair S., Dhillon V., Marsh T., G¨ansicke B., South-
6 km s−1 and the rotational velocity of the secondary star worth J., Baraffe I., Watson C., Copperwheat C., 2008,
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RitterH.,KolbU.,2003,VizieROnlineDataCatalog,5113
CDJS, VSD, TRM and CMC acknowledge the support of
Savoury C. et al., 2011, MNRAS,415, 2025
theScienceandTechnologyFacilitiesCouncil(STFC).SPL
Smak J., 1979, ACTA,29, 309
acknowledges the support of an RCUK Fellowship. DS ac-
Smith D., Dhillon V., Marsh T., 1998, MNRAS,296, 465
knowledges a STFC Advanced Fellowship. This article is
vanSpaandonkL.,SteeghsD.,Marsh T.,TorresM.,2010,
based upon observations carried out using the European
MNRAS,401, 1857
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Tappert C., Augusteijn T., Maza J., 2004, MNRAS, 354,
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