A Dynamical Study of the Black Hole X-ray Binary Nova Muscae 1991

1 MB·English

by  Jianfeng Wu

DRAFTVERSIONJANUARY5,2016
PreprinttypesetusingLATEXstyleemulateapjv.05/12/14
ADYNAMICALSTUDYOFTHEBLACKHOLEX-RAYBINARYNOVAMUSCAE19911
JianfengWu2,JeromeA.Orosz3,JeffreyE.McClintock2,DannySteeghs4,2,Pene´lopeLonga-Pen˜a4,PaulJ.Callanan5,LijunGou6,
LuisC.Ho7,8,PeterG.Jonker9,10,2,MarkT.Reynolds11,ManuelA.P.Torres9,10
ApJinpress
ABSTRACT
5
We present a dynamical study of the Galactic black hole binary system Nova Muscae 1991 (GS/GRS
1
1124−683). We utilize 72 high resolution Magellan Echellette (MagE) spectra and 72 strictly simultane-
0
ousV-bandphotometricobservations;thesimultaneityisauniqueandcrucialfeatureofthisdynamicalstudy.
2
The data were takenon two consecutivenightsand coverthe full10.4-hourorbitalcycle. The radialveloci-

c tiesofthesecondarystararedeterminedbycross-correlatingtheobjectspectrawiththebest-matchtemplate
e
spectrum obtained using the same instrument configuration. Based on our independent analysis of five or-
D
dersof the echellette spectrum, the semi-amplitudeof the radialvelocityof the secondaryis measuredto be
1 K2=406.8±2.7kms−1,whichisconsistentwithpreviouswork,whiletheuncertaintyisreducedbyafactor
3 of3.Thecorrespondingmassfunctionis f(M)=3.02±0.06M⊙.Wehavealsoobtainedanaccuratemeasure-
mentoftherotationalbroadeningofthestellarabsorptionlines(vsini=85.0±2.6kms−1)andhencethemass

] ratioofthesystemq=0.079±0.007.Finally,wehavemeasuredthespectrumofthenon-stellarcomponentof
E
emissionthatveilsthespectrumofthesecondary.Inafuturepaper,wewilluseourveiling-correctedspectrum
H ofthesecondaryandaccuratevaluesofK andqtomodelmulti-colorlightcurvesanddeterminethesystemic
2
. inclinationandthemassoftheblackhole.
h
Subjectheadings: blackholephysics—stars: blackholes—binaries:general—X-rays:binaries
p
-
o
1. INTRODUCTION sientsystemsthataredistinguishedbytheirshortorbitalperi-
r
t ods,P<12hr.(Forasketchtoscaleofnineofthesesystems,
s Mass is the fundamental parameter for a black hole. Ac-
a cordingtotheNo-HairTheorem(e.g.,Israel1967;Hawking includingtheprototypeA0620−00,see Figure1inMcClin-
[ 1971),massandspintogetherprovideacompletedescription tock et al. 2014.) NovaMus was discoveredduring its 1991
ofan astrophysicalblack hole. An accuratemeasurementof outburst independently by the Ginga (Makino et al. 1991)
3
andGRANAT(Lund&Brandt1991)missions. Eightdaysaf-
v mass is a prerequisite for measuring black hole spin via the
ter discovery, it reached a peak X-ray intensity of 8 Crab in
2 continuum-fittingmethod (see McClintock et al. 2014 for a
the1–6keVband(Ebisawaetal. 1994). Overthecourseof
8 review).Stellar-massblackholesintheMilkyWayandneigh-
eightmonths,thesourcepassedthroughallthecanonicalX-
9 boringgalaxiesarediscoveredinX-raybinarysystems,some
raystatesbeforereturningtoitsquiescentstate(Ebisawaetal.
0 ofwhicharepersistentX-raysources,whileothersareX-ray
1994;Remillard&McClintock2006).Esinetal.(1997)used
0 transients which have gone through one or more X-ray out-
the1991outburstdataforNovaMustodevelopamodelofthe
. bursts(Remillard&McClintock2006). Abouttwodozenof
1 states that combines the standard model of a thin accretion
these black holes have been dynamically confirmed to have
0 disk(Shakura&Sunyaev1973)andtheadvection-dominated
massesintherangeM=5–30M .
5 ⊙ accretionflow(ADAF)model(Narayan&Yi1994).
X-rayNovaMuscae1991(hereafterNovaMus),withanor-
1
Interestingly, hard X-ray observations of NovaMus made
: bitalperiodof10.4hr,isoneofaboutadozenblack-holetran-
v at the peak of the outburst revealed evidence for positron-
i electron annihilation in the form of a relatively narrow and
X [email protected] variable emission line near 500 keV (Sunyaev et al. 1992;
r 1Thispaperincludesdatagatheredwiththe6.5meterMagellanTele- Goldwurmetal. 1992).Kaiser&Hannikainen(2002)argued
a scopeslocatedatLasCampanasObservatory,Chile.
that the line could be generated by annihilation in the bipo-
2Harvard-Smithsonian Center for Astrophysics, 60 Garden Street,
laroutflowof the system. Mart´ın etal. (1996)suggestedan
Cambridge,MA02138,USA
3Department of Astronomy, San Diego State University, 5500 Cam- alternativemechanism,namely,Liproductionneartheblack
panileDrive,SanDiego,CA92182,USA hole that givesrise to a 476 keV nuclear line; their support-
4DepartmentofPhysics,UniversityofWarwick,Coventry,CV47AL, ing evidence is their detection of a relatively strong lithium
UK absorptionlinel 6708intheopticalspectrum.
5DepartmentofPhysics,UniversityCollegeCork,Cork,Ireland
Soonafter its discovery,NovaMuswas consideredto be a
6NationalAstronomicalObservatories,ChineseAcademyofSciences,
Beijing100012,China strong candidate for a black hole binary based on its X-ray
7Kavli Institute for Astronomy and Astrophysics, Peking University, spectralpropertiesand lightcurve, and its similarities to the
Beijing100871,China prototypeblack-holeX-raytransientA0620−00(McClintock
8DepartmentofAstronomy,SchoolofPhysics,PekingUniversity,Bei- & Remillard 1986). Following the discovery of the optical
jing100871,China
counterpart(DellaValleetal. 1991),theblackholenatureof
9SRON, Netherlands Institute for Space Research, Sorbonnelaan 2,
theprimarywasestablishedinthecustomarywaybymeasur-
3584CA,Utrecht,TheNetherlands
10DepartmentofAstrophysics/IMAPP,RadboudUniversityNijmegen, ingthemassfunction:
Heyendaalseweg135,6525AJ,Nijmegen,TheNetherlands
11DepartmentofAstronomy,UniversityofMichigan,1085S.Univer- PK3 Msin3i
sityAvenue,AnnArbor,MI48109,USA f(M)≡ 2 = , (1)
2p G (1+q)2
2 WUETAL.
where K is the semi-amplitude of the velocity curve of the mountedonthe6.5-meterMagellan/ClayTelescopeattheLas
2
secondary,iistheorbitalinclinationangleofthebinaryand Campanas Observatory (LCO) in Chile. All the data were
q is the ratio of the companion star mass M to that of the taken on the nights of 2009 April 25–26 UT. A total of 72
2
compact primary M. Three dynamical studies performed in spectrawereobtained,eachwithanintegrationtimeof600s.
quiescencefoundavalueforthemassfunction(theminimum Duringthesametwonights,andwiththesamesetup,weob-
mass of the compact primary) of ≈ 3M (Remillard et al. tained spectra of 38 stars, principally K dwarfs, that serve
⊙
1992;Oroszetal. 1996;Casaresetal.1997),whichiswidely asradialvelocitytemplates. The seeingwas similar onboth
consideredto be the maximumstable mass ofa neutronstar nights,withatypicalvalueof≈0.7′′andarangeof0.5′′–1.3′′.
(Kalogera&Baym1996). EachMagEspectrumconsistsof15orders(correspondingto
Orosz et al. (1994)obtained a quite uncertain estimate of sequencenumbers#6–20). The full wavelengthcoverageof
themassratioq≡M2/M bymeasuringtheradialvelocityof the instrument is 3100–11000A˚, with order #20 at the blue
theHa emissionline. Casaresetal. (1997)madea conven- end(centralwavelength3125A˚)andorder#6attheredend
tionalanddirectmeasurementofthemassratiobymeasuring (centralwavelength9700A˚).Thespatialscaleis≈0.3′′/pixel.
therotationalbroadeningofthephotosphericabsorptionlines Thespectraldispersionincreasesfrom0.2A˚ perpixelforor-
ofthesecondary;theyobtainedaresultthatisconsistentwith
der#20to0.7A˚ perpixelfororder#6,whilethevelocitydis-
thatofOroszetal. (1994).
persionis22kms−1 perpixelforallorders. Forourchosen
The inclination angle i is usually estimated by modeling
theellipsoidalmodulationofthelightcurvesofthesecondary 0.85′′ slit, the spectral resolutionis ≈1 A˚ at 5000 A˚, corre-
star after a system has returned to its quiescent state. This spondingto≈60kms−1.
modelingis complicatedin the case of the short-periodsys- TheMagEdatawerereducedusingthepipelinedeveloped
tems because the stellar component of light is significantly by Carnegie Observatories12, which performs bias correc-
contaminated by the emission from the accretion disk; this tion, flat-fielding, and wavelength calibration. The bias was
so-called “disk veiling,” can be quite significant (&50% in corrected using the overscan region of the detectors. Three
theV-band)andvariablein“active”quiescentstates(Cantrell sets of flats were utilized in the calibration: 1) order defini-
etal. 2010).Oroszetal. (1996)estimatedadiskcontribution tion flats taken with the Xe-Flash lamps; 2) blue flats to de-
at∼5000A˚ thatcouldbeashighas50%. Meantime,using fine the flat field at the blue end of a spectrum (also taken
differentdata, Casares et al. (1997)estimated a disk contri- with the Xe-Flash lamps); and 3) red flats to define the flat
butionatHal 6563of15%,suggestingthatdiskveilingmay fieldattheredendofaspectrumandtocorrectthefringing,
be less significant at longer wavelengths. Based on this no- whichweretakenwiththeQflamps. Thewavelengthcalibra-
tion, Gelino et al. (2001) modeled near-infrared (J and K) tionwasperformedusingarcspectraobtainedwithThorium-
lightcurvesofNovaMusassumingthatthediskcontribution Argonlamps. The RMS residualof the wavelengthsolution
could be ignoredin these bands, and they thereby estimated is<0.05A˚ fororders#8–18and<0.1A˚ fortheremaining
thesystemicinclinationtobei=54◦±1.5◦;theirestimateof orders.Theperformanceofwavelengthcalibrationwasexam-
blackhole mass (whichalso dependson the mass ratio q) is ined using sky emission lines; the relative wavelengthoffset
M=6.95±0.6M⊙. isnegligible.
TheseestimatesofiandMarequiteuncertainbecausethey The mean MagE spectrum of NovaMus in the observer’s
restontheassumptionthattheeffectsofveilingarenegligible rest-frameisshowninFig.1,whichcoversspectrathatspan
inthenear-infrared,whilethereisconsiderableevidencethat orders#9–14(∼4300–7000A˚).Thespectrumineach order
itmaynotbe(e.g.,Reynoldsetal. 2007,2008;Kreidberget was normalized by a fifth-order polynomial. In the analysis
al. 2012).Inthispaper,weobtainthefirstdetailedandsecure thatfollows,wemainlyusethedataintheseordersbecauseof
measurementofthespectrumofthenon-stellarcomponentof theirgoodsignal-to-noise(S/N)ratioandgenerallackofsky
lightthatveilsthestellarspectrum.Whilethisachievementis emissionlinesandtelluricabsorptionfeatures(relativetored-
inpartduetothequalityandquantityofourdata,itisbased derorders). Themostprominentfeaturesinthespectrumare
primarily on the strict simultaneity of our spectroscopic and thebroad,double-peakedBalmerlinesHal 6563,Hbl 4861
photometricobservations.Thesimultaneityiscrucialbecause andHgl 4341,whicharethecanonicalsignaturesofablack-
oftheaperiodicvariabilityofthenon-stellarcomponent.Our holeaccretiondisk. Also presentarebroaddisklinesofHe,
twootherprincipalresultsareagreatlyrefinedmeasurement notablyHe I l 5875. Other featuressuch as Na D ll 5890–
oftheK-velocityandthefirstrobustmeasurementofthemass 5896,diffuseinterstellar bands(DIB) at l 5780,l 6280, and
ratio q, which differssignificantly fromthe earlier estimates telluricfeaturesredwardofl 6850arealsoevident.
mentionedabove.
Thispaperisstructuredasfollows. Observationsanddata 2.2. OpticalPhotometry
reductionaredescribedin§2. Wederivethemassfunctionvia Photometricdatawereobtainedduringthesameobserving
aradialvelocityanalysisin§3. Themassratioisdetermined runusingtheduPont2.5mtelescope,whichisalsolocatedat
viarotationalbroadeningin§4. Thediskveilingisalsomea- LCO.Seventy-twoV-bandimageswereacquired;bydesign,
suredinthissection.ThelightcurveofNovaMusispresented each10-minexposurewasstrictlysimultaneous(timediffer-
in §5. Finally, we discuss our results in §6. The light curve ence<1s)withitscorrespondingMagEspectroscopicobser-
modelingand the determinationof the inclination and black vation13. Thetypicalseeingwas≈0.7′′(witharangeof0.6–
holemasswillbepresentedinasubsequentpaper. 1.1′′). Weusedthe2048×2048Tek#5CCD,whichprovided
afieldofviewof8.85′×8.85′ at0.259′′ perpixel. Biascor-
2. OBSERVATIONANDDATAREDUCTION rection and flat-fielding were performed with standard IRAF
2.1. MagellanEchelletteSpectroscopy
12Seehttp://code.obs.carnegiescience.edu/mage-pipeline.
The spectroscopic data were obtained using the Magel- 13Theonlyexceptionisthefirstimagewhoseexposuretimewasonly60
lan Echellette spectrograph (MagE; Marshall et al. 2008) seconds.
ADynamicalStudyofNovaMuscae1991 3
FIG.1.—ThemeanMagellan/MagEspectrumofNovaMusintheobserver’srestframe,coveringMagEorders#9–14(4000–7000A˚).Broadanddouble-peaked
Balmerlines(Ha ,Hb ,Hg,andHd )areprominentinthespectrum.HeIl 5875emissionisalsoevident.Theweak,broademissionfeaturesredwardofHg and
Ha arelikelytobeHeIl 4471andl 6678,respectively. TheNaDll 5890–5896doublet,DIBfeaturesatl 5780andl 6280(whichalsohasastrongtelluric
component),aswellasthetelluricfeatureatl 6860arealsolabeled. TheNovaMusspectrumcoveringthefullMagEwavelengthrange(∼3000–10000A˚)is
availableintheonlinejournalinelectronicform.
tasks (zerocombine, flatcombine, and ccdproc). The estimateoftheuncertaintyinthezero-pointis0.05mag.
centroidof the opticalcounterpartwas determinedusing the
CIAO routine wavdetect (Freeman et al. 2002), and the
quality of the centroiding was confirmed visually. Aperture
photometry was performed using the IDL procedure aper. 3. RADIALVELOCITYANALYSIS
The radius of the aperture was fixed to eight pixels (2.1′′),
TheradialvelocityK ofthesecondarystarwasdetermined
2
whichisthelargestaperturethatsecurelyexcludessignificant
by sequentially cross-correlating the 72 object spectra with
contaminationof NovaMusby a faint field star. Choosing a
thespectrumofatemplatestar. Thiswasdoneinturnforin-
smalleraperture(e.g.,∼5pixels)wouldprovideverysimilar
dividualechellette orders, rather than using a single merged
results. We first produceda lightcurveofNovaMusrelative
spectrum. The best quality results were obtained for order
to nearbyfield starsandthenderivedan absolutecalibration
#12(covering∼4700–5500A˚),asexpectedsincestrongstel-
relativetoapairofnearby(24′′ and41′′)standardstars. Our
larabsorptionfeaturesarepresentinthisorder(e.g.,the Mg
4 WUETAL.
TABLE1
RADIALVELOCITYANALYSISRESULTS
Order# K2 g T0−2454900 No.of c 2/n l Coverage MaskedFeatures
(kms−1) (kms−1) (d) ObjectSpectra (A˚)
9a 413.6±4.3 17.4±3.1 46.90550±0.00072 39 1.55 6300–7300 Hal 6563,6820–7020A˚,7150–7200A˚
10 409.5±2.7 19.4±2.0 46.90351±0.00044 72 0.92 5680–6630 NaDll 5890,5896,DIBl 6280
OIl 6300,Hal 6563
11 413.0±3.1 15.2±2.3 46.90258±0.00051 67 0.74 5170–6000 OIl 5577,NaDll 5890,5896
12 401.2±2.6 9.7±1.9 46.90327±0.00044 72 0.87 4700–5500 Hbl 4861
13 407.0±4.2 17.0±3.1 46.90211±0.00069 57 0.92 4370–5100 Hbl 4861
14 403.9±3.9 9.2±2.9 46.90086±0.00068 63 1.02 4060–4730 Hgl 4341
Average 406.8±2.2 14.2±2.1 46.90278±0.00042
NOTE.—Thequoteduncertaintiesareatthe1s levelofconfidence.
aThebest-fitparametersfororder#9werenotincludedincalculatingtheaverageparametervalues;forthisorder,thewavelengthranges6820–
7020A˚ and7150–7200A˚ weremaskedtoavoidstrongtelluricabsorptionfeaturesandskyemissionlines.
(that is given in the same database)14. The star at the peak
ofthisordereddistributionandhavingthemaximumTDRis
HD 170493 with B−V =1.11, corresponds to an effective
temperatureT ≈4400K(Allen’sAstrophysicalQuantities,
eff
4thedn.).WethereforechooseHD170493asthemastertem-
plate for our cross-correlationanalysis. Potentialsystematic
effectsrelatedtothischoiceoftemplatearediscussedin§6.1.
3.2. FittingtheRadialVelocityCurve
WithHD170493asthetemplate,wefirstcross-correlated
eachofthe72spectrafororder#12. Forboththeobjectand
template spectra, we masked out the region around the Hb
emission line, and also ∼100 A˚ at both ends of each order
becausetheS/N intheseregionsispoor. Wefurthermorere-
quiredthattheTDRvalueforacorrelationexceed2.5(similar
to the criterion in Orosz et al. 1996). All 72 spectra for or-
FIG.2.—TheaverageTDRvalueofthecross-correlationbetweenthespec- der#12deliveredreliablemeasurementsofradialvelocity,as
trumofeachtemplatestarandNovaMusfororder#12,plottedagainstthe illustrated in the middle-rightpanel of Fig. 3. We fitted the
B−Vcolorofthestar.ThetemplatestarwiththehighestaverageTDRvalue
radialvelocitycurvewiththefollowingmodel,
isHD170493,withB−V=1.11,whichcorrespondstoaspectraltypeof
∼K5withTeff≈4400K,basedonthescaleofB−Vcolorvs.Teffvs.Spec- t−T
traltype,whichisshownatthetopofthefigure. V(t)=g +K cos(2p 0), (2)
2
P
featuresat∼5200A˚ region),and it is relatively freeof con- whereg isthesystemicvelocityofintheheliocentricframe,t
taminatingtelluricandinterstellarfeatures.
is the observation time in Heliocentric Julian Days (HJDs),
and T is the time of maximum radial velocity; the ra-
3.1. ChoosingtheBestTemplateSpectrum 0
dial velocity we used for the template star HD 170493 is
The cross-correlation analysis was performed using the g =−55.07±0.07kms−1. Weinitiallyfixedtheorbitalpe-
0
software package fxcor as implemented in the IRAF pack- riodto thespectroscopicvaluegivenbyOroszetal. (1996),
age.ThetaskfxcorreturnstheparameterRdefinedbyTonry P=0.4326058(31)d. Then, using our value of T and the
0
&Davis(1979;TDRhereafter)providesanestimateofS/N: oneinOroszetal. weobtainedarefinedvalueoftheorbital
thehighertheTDRvalue,thebetterthequalityofthecross- period: P=0.43260249(9)d. Thisperiodandotherbest-fit
correlation. Fromamongourdozensoftemplatespectra,we parametersarelistedinTable1.
chosetheonethatgivesthehighestTDRvalue,whilefocus- AsacheckonourvaluefortheK-velocity,weperformedan
ingontheNovaMusdatafororder#12. Specifically,we: (1) independentanalysisusingthexcorprocedureintheMOLLY
selectedaK-typetemplatespectrumthatgivesrelativelyhigh packagedevelopedbyT.Marsh15 inplaceoffxcorinIRAF.
valuesofTDRandcross-correlateditagainstthe72spectraof We again analyzed only the data for order #12 and used the
NovaMus;(2)wevelocity-shiftedalltheNovaMusspectrato same template spectrum (HD 170493) as before. Both the
therestframeofthetemplatestarandsummedthem;(3)we objectandtemplatespectrawererebinnedtothesameveloc-
thencross-correlatedthissummedspectrumagainstallofour ity dispersion using the vbin procedure, and were normal-
template spectra in turn and selected the template spectrum ized using a fifth-orderpolynomial, as requiredby the xcor
thatyieldedthemaximumTDRvalue. procedure. Fitting a Gaussian to the profile of the cross-
TheresultsofthisanalysisaresummarizedinFig.2,which correlation function using the MOLLY procedure mgfit, we
shows how TDR varies among the template stars, which we
have ordered by their B−V color given in the SIMBAD 14Weassumethatthereddeningofthesetemplatestarcanbeignoreddue
database;weregardthephotometriccolorasamoreaccurate totheirproximitytotheSun(.100pc).
measure of the effective temperature than the spectral type 15Seehttp://deneb.astro.warwick.ac.uk/phsaap/software/molly/html/INDEX.html.
ADynamicalStudyofNovaMuscae1991 5
FIG.3.—TheradialvelocitiesofNovaMusrelativetothespectraltemplateHD170493,inMagEorders#9–14.Thebest-fitradialvelocitycurvesandresiduals
foreachorderareshown.
6 WUETAL.
4. ROTATIONALVELOCITYANDDISKVEILING
TABLE2 MEASUREMENTS
ORBITALPARAMETERSFORNOVAMUS
4.1. RotationalBroadeningandMassRatio
Parameter Value
As the next step toward measuring the mass of the black
OrbitalperiodP(days) 0.43260249±0.00000009 hole, we obtain a precise estimate of the mass ratio q. For
K2velocity(kms−1) 406.8±2.7 ashort-period,mass-exchangebinarylikeNovaMus,onecan
g velocity(kms−1) 14.2±6.3 quiteconfidentlyassumethatthesystemistidally-lockedand
T0,spectroscopic(HJD−2454900) 46.90278±0.00062 thatthesecondaryfillsitsRochelobe(Wade&Horne1998).
Massfunction f(M)(M⊙) 3.02±0.06
vsini(kms−1) 85.0±2.6 Inthiscase,qcanbesimplydeterminedbymeasuringthero-
Massratioq 0.079±0.007 tationalbroadeningof the stellar photosphericlines. Specif-
NOTE. —Thequoteduncertainties areatthe1s levelofconfi- ically, one measures the radial component of the rotational
denceandincludeanallowanceforsystematicerror;see§6.1. velocity of the secondary star, vsini and uses the following
equation(Wade&Horne1998),
obtained values for both the K-velocity and its uncertainty
(K2=402.9±1.3kms−1)thatareconsistentwiththoseob- vsini =0.462q1/3(1+q)2/3. (3)
tainedusingtheIRAFroutines. K2
InordertoobtainamoreprecisevalueofK ,weanalyzed
2
Inmeasuringvsini weusethemethodofoptimalsubtrac-
datafororders#10and#11(whichlietotheredoforder#12)
andorders#13and#14,againmaskingout∼100A˚ atboth tion. Fig. 4 illustrates the principle of the method using the
data for orders #10 and #12. Before doing the optimal sub-
ends of each order; the wavelength ranges of the orders are
traction, we first normalized both the object and template
given in Table 1. As before, we masked out disk emission
spectra using a 5th-order polynomial. The spectra of Nova-
lines(mainlyBalmerlines), andwe alsomaskedouta num-
Muscontainscontributionsfromboththesecondary(numer-
berofstrongtelluricandinterstellarfeatures,whicharelisted
ousrotationally-broadenedabsorptionfeatures)andtheaccre-
in Table 1). As was the case for order #12discussed above,
tiondisk(broaddiskemissionlineslikeHa ).Thebest-match
all 72 objectspectra for order #10 yieldedreliable measure-
templatespectrumwillhavevirtuallythesamesetofabsorp-
mentsofradialvelocity(i.e.,TDR>2.5);theradialvelocity
tionfeaturesasNovaMus;however,thefeaturesintheobject
curve for this order is shown in Fig. 3. For the other three
spectrum will be shallower because they are diluted by the
orders, some object spectra were rejected because: (1) the
disk continuum emission. In obtaining the best match of a
TDR value for the correlation was ≤ 2.5; (2) the fit to the
given template spectrum to the object spectrum, one repeti-
cross-correlationpeak didnotconverge;or (3)the valueob-
tainedforthe radialvelocityliesmorethan >3s awayfrom tively performsa pair of operations. First, one broadensthe
∼ narrow-linetemplatespectrum,andthenmultipliesthespec-
thefittedcurve.16 Thevelocitydataforeachorderindividu-
trum by the factor f (06 f 61), which represents the
allywerefittedtothesamemodelusedfororder#12(Eqn.2). star star
fractionofthelightcontributedbythesecondary.Finally,one
For each of the five orders, Table 1 lists the best-fit parame-
subtractsthetrialtemplatespectrumfromthespectrumofNo-
ters, valuesof reduced c 2 and the numberof usefulspectra.
vaMusanddeterminesquantitatively(seebelow)thetemplate
Usingpreciselythevelocityuncertaintiesreturnedbyfxcor,
spectrum that is freest of photospheric absorption features.
weobtaingoodfitsforallfiveorders,with c 2/n valuesthat
The results of such an analysis for two orders are shown in
are close to unity. We note that there are small differences
Fig.4.Theresidualspectrumfororder#10(upperpanel)only
amongthebest-fitparametersatthelevelof∼3–4s level. showsthebroadHa disklineandtheDIBatl 6280.Theonly
Table 2 provides a summary of the orbital parameters.
clear spectral feature in the residual spectrum of order #12
The error-weighted mean of K2 among the five orders is (Fig.4;lowerpanel)istheFeIImultiplet42atl 4924,l 5018,
406.8±2.2kms−1. Afterincludingourestimateofthesys- andl 5169(Moore1972),afeaturethatisalsopresentinthe
tematicerror(see§6.1),weobtainfortheradialvelocitysemi- spectraofA0620−00(Marshetal.1994)andtheneutron-star
amplitudeK2 =406.8±2.7kms−1. UsingthisvalueofK2, transientEXO0748−676(Rattietal. 2012).
the orbitalperiodP (Table 2) and Eqn.(1), we derivea pre- In practice, we use the spectrum of our velocity-template
cise valueforthe mass functionof f(M)=3.02±0.06M⊙, starHD170493andthephase-averagedspectraofNovaMus
therebyconfirmingthe blackholenatureof the compactob- foreachordertoincreasetheS/N.Beforeaveragingthespec-
ject. tra fora givenorder,we shifted the individualspectrato the
In addition to orders #10–14, and as discussed in the fol- restframeofHD 170493usingthe datain Table 1. We first
lowing section, we also performeda radial velocity analysis broadenedthe template spectrum using a grid of trial values
oforder#9forthepurposeofmeasuringthemassratioqand from 5 to 300 km s−1 in steps of 5 km s−1. We also arti-
investigatingtheeffectsofdiskveiling. Thebest-fitparame- ficially smearedthe templatespectrumusingthe appropriate
tersfororder#9areincludedinTable1. However,wedonot phase and integration time in order to simulate the velocity
includetheresultsforthisorderinourfinaldeterminationof smearingduringan observationofNovaMus. A c 2 test was
the radialvelocity parametersbecause relativelyfew spectra
performedontheresidualspectrumtodetermineaminimum
generatedusefulvelocitydata(39outof72)andbecausethe
andthecorrespondingapproximatevalueofvsini.Now,start-
qualityofthefitisrelativelypoor(c 2/n =1.55). ing with this approximate value, we repeated the procedure
withatrialgridextendingfrom60to120kms−1 instepsof
1kms−1. Makinguseoftherbroadandoptsubtasksinthe
16Onlyfivedatapointsinallfiveorderslie >3–4s awayfromthefitted MOLLY, curves of vsini vs. c 2 were generated (see Fig. 5)
∼
curve;removingtheseradialvelocitypointsdoesnotsignificantlychangethe andfitted witha 3rd-orderpolynomial;ouradoptedvalueof
fittedvaluesoftheparameters. vsinicorrespondstotheminimumofthefittedcurve. Allthe
ADynamicalStudyofNovaMuscae1991 7
FIG.4.—Theresultsofapplyingtheoptimalsubtractionprocedurefororder#10(upperpanel)andorder#12(lowerpanel). Eachpanelcontainstheaverage
normalized spectrum ofNovaMus, thenormalized spectrum ofthetemplate starHD170493, andtheresidual spectrum after optimal subtraction. TheHa
emissionlineandstrongDIBfeaturearelabeledfororder#10. TheupperpanelalsocontainstheaveragedHa emissionlineintheobserver’sframe,which
showsthecharacteristicdouble-peakedprofile.TheFeIImultiplet42featuresintheresidualspectrumoforder#12arelabeledinthelowerpanel.Allthespectra
aresmoothedwitha5-pixelboxcarforthepurposeofpresentation.
8 WUETAL.
FIG.5.—MeasurementoftherotationalvelocityvsiniinMagEorders#9–14. Foreachorder,theupperpanelshowsthecurveofvsinivs. c 2,whichwe
fittedwithacubicpolynomial. Ouradoptedvalueofvsiniisthevaluecorrespondingtotheminimuminc 2.Thelowerpanelillustratesthemethodweusedto
estimatetheuncertaintyinvsiniviathebootstrapmethoddescribedinthetext.ThehistogramofvsiniisfittedwithaGaussianindeterminingtheuncertainty.
emission lines, interstellar features, and telluric features are
maskedoutduringtheoptimalsubtraction. TABLE3
The effectof limb darkeningneedsto be properlyconsid- LIMBDARKENINGCOEFFICIENTANDROTATIONALVELOCITY
ered in the optimalsubtraction. Since this effectvarieswith
Order# Centrall (A˚) u(limbdarkening) vsini(kms−1) DiskVeiling(%)
wavelength,wecalculatedalinearlimbdarkeningcoefficient
for each order of the MagE spectra based on the data given 9 6800 0.706 83.8±7.5 40.3±3.4
10 6130 0.762 87.2±3.5 51.4±1.3
byClaretetal. (2012).Weretrievedfromtheirtablethelimb
11 5590 0.808 88.6±4.5 56.7±1.4
darkening coefficients for theUBVRI bands. For the effec- 12 5140 0.845 82.8±3.5 59.3±1.0
tivetemperatureofthecompanionstar,weadoptedthevalue 13 4750 0.878 79.4±5.9 55.8±2.1
T =4400K.Thestar’ssurfacegravitylogg(incm−2 s−1) 14 4400 0.908 85.5±7.1 69.1±1.5
eff Average 85.0±1.3
issecurelyintherange4.0–4.5,andforeachbandweadopted
theaverageofthetabulatedvaluesofthelimbdarkeningcoef- NOTE.—Thequoteduncertaintiesareatthe1s levelofconfidence.
ficientforlogg=4.0andlogg=4.5. Finallywelinearlyin-
terpolatedbetweentheUBVRI bandsusingthecentralwave-
a Gaussian distribution(see Fig. 5). The mean of the Gaus-
length of each order, thereby obtaining the values we adopt
for the limb darkening coefficients (see the third column in sian distributionis veryclose (within 1 km s−1) to the fitted
Table 3), which range from 0.71 (Order #9) to 0.91 (Order valuesofvsinidiscussedabove. Foreachorder,wetakethe
#14). meanoftheGaussiandistributionasthefinalmeasurementof
vsini andthestandarddeviationofthemeans astheuncer-
tainty. The measured values of vsini for six orders (#9–14)
arepresentedinFig.5andTable3).
Theerror-weightedmeanvsiniofallsixordersishvsinii=
We utilized the bootstrap method to determine the uncer-
tainty in vsini following Steeghs & Jonker (2007)and Ratti 85.0±1.3 km s−1. After including an allowance for sys-
etal. (2013). We generated500simulatedNovaMusspectra tematic uncertainty, related to the choice of template spec-
usingtheMOLLYtaskboot.Thebootstrapmethodrandomly trum and the limb darkening coefficient (see §6.1), our fi-
selectsdata pointsfromtheoriginalspectrumwhile keeping nal adopted value is vsini= 85.0±2.6 km s−1. Using this
thesametotalnumberofdatapointsinthespectrum.Foreach value and our K-velocity for the secondary (K2 = 406.8±
simulatedspectrum,vsiniwasmeasuredfollowingthesame 2.7 km s−1; §3.2), and Eqn. (3), we obtain for the mass
procedure as described above. The 500 vsini values follow ratio the value q = 0.079±0.007. Using this mass ra-
ADynamicalStudyofNovaMuscae1991 9
FIG.7.—ThesimplisticspectralenergydistributionofNovaMus,decom-
posed into the secondary star component (red line) and the accretion disk
component(blueline). Thepinklineshowsthesumofthetwocomponents.
ThesolidblueandpinklinescovertheobservedwavelengthrangeforMagE
orders#9–14.Thedashedlinesareextrapolationstolongerwavelengths.The
starcomponentisrepresentedbya4400Kblackbodyspectrum.Theblueline
representsapower-lawmodelobtainedbyfittingtheobservedrelativefluxof
diskemission(filledbluesquares)inthesixorders,excludingthedatapoint
fororder#13(thesecondbluesquarefromtheleft),,whichisaclearoutlier.
Theblackdottedlinesshowtheeffective wavelengths oftheR,I,J,H,K
bands.Ourestimateofthediskveilingfactorineachbandisalsolabeled.
disk veiling factor. These alternative measurementsof f ,
disk
areconsistentwithin∼1s (forallorders)withthevaluesde-
termined as described aboveusing the phase-averagedspec-
tra. Wenotethatforfiveofthesixorders f isgreaterthan
disk
0.5,i.e.,thediskisbrighterthanthesecondarystar.
FIG.6.—Measurementofthediskveilingfractioninorder#9–14.Ineach Fig. 6 indicates that the disk veiling factor generally de-
panel,thedottedlineindicatesthediskveilingfraction(labeledbythe“mean creases with increasing wavelength, i.e., the disk veiling is
veiling1”value)oftheaveragedspectrum. Thehistogramshowsourdisk lesssignificantforredderwavebands. However,thisdoesnot
veilingmeasurementsforindividualspectra; thedashedlineindicates their
necessarilymeanthatdiskveilingcanbeignored,eveninthe
meanvalueasobtainedfromthehistogram(labeledbythe“meanveiling2”
value). J and K bands, as claimed by Gelino et al. (2001)and oth-
ers. Weutilizeasimplisticspectralenergydistribution(SED)
tio and the value of the mass function given in §3.2, the modelandanextrapolationtoillustratethispoint(seeFig.7).
massesofthe blackholeandsecondarystar areM=3.52± Our crude SED by no means represents an accurate model
0.07(sin−3i)M⊙ andM2=0.28±0.03(sin−3i)M⊙, respec- ofthediskemission. Forthestellarcomponent,weassumed
tively. blackbodyemissionat4400K(redlineinFig.7;see§3and
Fig. 2), and we then computedthe relative disk flux in each
4.2. DiskVeiling
order(filledbluesquares)basedonourmeasurementsof f .
disk
The disk veiling factor f , i.e., the fraction of the total Wefittedtheseestimatesofdiskfluxusingapower-lawmodel
disk
lightthatisnon-stellar,isalsodeterminedbytheoptimalsub- torepresenttheSEDofthediskcomponentandthenextrapo-
traction method. For each order, we first broaden the HD latedthepowerlawintothenear-infrared(dashedblueline).
170493 template spectrum using the values of vsini deter- At shorter wavelengths, the disk component does indeed
mined in §4.1, and then optimally subtract it from the spec- decreaserapidlywith increasingwavelengthso thatthe stel-
trum of NovaMus. The proceduregives the fractionof light lar component becomes dominant as one approaches the R-
duetothesecondarystar, f ,forthetemplatespectrumthat band. However, at longer wavelengths the blackbody com-
star
corresponds to the minimum value of c 2. The disk veiling ponentbeginstofallrapidly,anddiskveilingreachesamin-
factoristhensimply f =1−f . Asindeterminingvsini imum(≈40%) at around1 m m and then beginsto increase.
disk star
we computed fdisk using for each order the averaged, rest- Forourdata and thiscrudemodel, we estimate that fdisk for
frame spectrum of NovaMus. The values we adopt for the theI,J,H,K bandsisintherangeof40–60%(seetheblack
diskveilingfactorforthesixordersareindicatedinFig.6by dottedlinesinFig.7),whichisconsistentwiththeestimates
dottedlinesandarelistedinthelastcolumnofTable3. ofReynoldsetal.(2008)forNovaMusof40–50%inthenear-
As a check on the robustness of our measured values of infrared.Wenotethat fdiskinthenear-infraredcouldbelower
f ,werepeatedtheoptimalsubtractionprocedureforeach than our estimate if the disk component of emission has a
disk
spectrumindividually,usingonlythosespectrathatproduced thermalspectrumthatfallsbelowtheextrapolatedpower-law
a reliable measurement of radial velocity (see §3). A his- spectrum,whichweassume. However,weconcludethatitis
togramof f foreachorderisshowninFig. 6; the dashed notwarrantedto assume thattheeffectsofveilingarenegli-
disk
lineineachpanelrepresentstheweightedmeanvalueofthe gibleinthenear-infrared.
10 WUETAL.
FIG.8.—Theoriginal(leftpanel)andphase-binned(rightpanel)V-bandlightcurvesofNovaMus,acquiredwiththeduPont2.5-mTelescope.Intheleftpanel,
theopen(filled)circlesarethephotometrydatapointsobtainedduringthefirst(second)nightofobservation.Theerrorbarinthelowerleftcornerrepresentsthe
typicaluncertainty.Intherightpanel,thelightcurveisbinnedinto20phasebins,eachofwhichhasthreeorfourindividualdatapoints.
5. LIGHTCURVE HD107493becauseitgavethemaximumTDRvalue(§3.1),
obviouslythisspectrumisnotidenticaltothatoftheRoche-
Ourcalibratedandphase-foldedV-bandlightcurve,which
lobe-fillingcompanionstar. Focusingonthehigh-qualitydata
wasobtainedinexposuresthatobtainedsimultaneouslywith
fororder#12,werepeatedouranalysisforsixothertemplate
the spectroscopic exposures (see §2.2), is shown in Fig. 8.
spectra with TDR values > 60 (see Fig. 2); the results are
Zerophotometricphase,whichisequivalentto0.75spectro-
summarized in Table 4. The spread in the values of K is
scopic phase, corresponds to the inferior conjunction of the 2
secondary. Two versions of the light curve are shown, un- <0.8kms−1,whichissignificantlysmallerthanthestatisti-
binned and binned into 20 phase bins, each with 3–4 data caluncertainty. AsourestimateofthesystematicerrorinK2
pointsperbin. associatedwith the choiceof thetemplate, we take thestan-
During our observations, NovaMus was ∼0.5 magnitude darddeviationofthesevenvaluesofK2,whichis0.3kms−1.
brighteronaveragein theV-bandthanit wasin earlierpho- In like manner, we obtain estimates of systematic error of
tometric monitoring campaigns (e.g., during 1992–1995, as 4.2kms−1 forg ,andof0.00013dayforT .
0
reportedbyOroszetal. 1996).OurV-bandlightcurveshows A second source of systematic uncertainty is the effect of
substantial aperiodic flickering (see §6.2). Nevertheless, the the different widths of the photospheric lines for NovaMus
phase-binnedlightcurveexhibitsthecharacteristicsignatures whicharerotationallybroadened,andfortheslowly-rotating
of ellipsoidal modulation, with two minima at phases ∼0.0 template star, which are narrow. To assess this effect, we
and∼0.5andtwomaximaatphases∼0.25and∼0.75.The broadenedthe lines of our chosen template (HD 107493)to
twomaximadonothaveequalamplitudeasonewouldexpect 85 km s−1 (§4.1) and repeated the radial velocity analysis.
foranidealellipsoidalmodulation,whichcouldbecausedby ThechangeinK is0.5kms−1 (Table4),whichweadoptas
2
a hotspotin the accretiondisk. Such unequalmaximahave ourestimate ofsystematicerror;we obtainsimilar estimates
frequently been observed in the light curves of other black of systematic error for g and T of 0.8 km s−1 and 0.00020
0
holebinariesin quiescence,e.g.,A0620−00(McClintock& day,respectively.
Remillard1986;Cantrelletal. 2010).
Foreachofthethreeparametersinquestion,weobtainour
finalestimate oferror,whichis givenin Table 2, bylinearly
6. DISCUSSION addingthelargerofthetwosystematicerrorsdiscussedabove
6.1. AssessmentofSystematicUncertainties ontothestatisticalerrorobtainedin§3.2(giveninTable1).
We identify sources of systematic error, and obtain esti-
mates of their magnitude, first for the orbital parameters K
2
andT andthesystemicvelocityg ,andthenfortherotational
0
6.1.2. RotationalVelocity
velocityvsini.
Weidentifytwosourcesofsystematicuncertaintyforvsini,
namely,the valueadoptedforthe limb darkeningcoefficient
and the choice of template spectrum. Again, using the data
6.1.1. OrbitalParametersandSystemicVelocity for order #12, we considered an uncertainty of ±0.1 in our
Wefirstconsidertheuncertaintyassociatedwiththechoice adoptedvalueof0.845(Table3)andfindthatthiscorresponds
of template spectrum. While we chose the spectrum of to an uncertainty of ≤ 1.5 km s−1 (see Table 5). We then