Mon.Not.R.Astron.Soc.000,1–4(2013) Printed22January2014 (MNLATEXstylefilev2.2) Hydrodynamics associated to the X-ray light curve of A0620-00 ⋆ Y. Coronado, S. Mendoza 4 Instituto de Astronom´ıa, Universidad Nacional Auto´noma de M´exico, AP 70-264, DistritoFederal 04510, M´exico 1 0 2 22January2014 n a J ABSTRACT 1 From1975to 1976,anoutburstwas detected in the lightcurveof the X-raytransient 2 A0620-00 using the Ariel V and SAS-3 experiments. In this letter we model the out- ] burstwiththehydrodynamicalmodelproposedbyMendozaetal.(2009).Thephysical E modelisconstructedassummingbasicmassandmomentumconservationlawsassoci- H atedtothemotionoftheshockwavesdevelopedinsidetheexpandingrelativisticjetof the source.These internal shock waves are produced as a result of periodic variations . h of the inyected mass and velocity of the flow at the base of the jet. The observations p of this X-ray light curve present two clear bumps. The first one is modelled assuming - o periodicvariationsofthe inyectedvelocityatthe baseofthe jet,while the secondone r can either be modelled by a further velocity oscillations, or by a periodic variation of t s the mass injection rate at the base of the jet at a latter time. The fitting of the data a fixes different parameters of the model, such as the mean mass injection rate at the [ baseof the jet andthe oscillationfrequency ofthe flowas measuredonthe restframe 1 of the central source. v Key words: – Relativistic Jets – Relativistic Hydrodynamics – microquasar 5 9 3 5 . 1 INTRODUCTION nationoftheaccretiondiscwithrespecttotheorbitspanned 1 0 bytheblackholeandthestellarcompanionyieldsi=51◦± 4 On August 3rd, 1975 the low-mass X-ray binary black hole 0.9, implying a black hole mass 6.6±0.25M⊙, and an esti- 1 transientA0620-00,exhibiteditsmostpowerfuloutburstde- mateddistancetothesource1.06±0.12Kpc(Cantrell et al. tected bytheSkySurveyExperiment on board theAriel V : 2010). v satellite in X-rays (Elvis et al. 1975). On August 8th, this i micro-quasarwasalsofollowedbytheSAS-3X-rayobserva- The radio emission of A0620-00 was detected in 1975 X (Daviset al.1975;Owen et al.1976a),withnojetresolved. tory(Matilsky et al.1976).Subsequentlyitwasalsoseenin r SincemanyX-raytransientsystemscontainingablackhole a differentwavelengths,fromradiotoultraviolet(seeKuulkers have radio emission that follows their X-ray outburst with 1998,forareview).Atthattime,A0620-00becamethemost clear detections of relativistic outflows or jets (Abdoet al. powerful X-raysource in thesky for almost two months. 2009), it was clear that a jet should have been produced FivedaysafterthediscoveryofA0620-00intensevaria- in the X-ray outburst of A0620-00. Kuulkerset al. (1999) tionsontimescalesofdays,whichreachedamaximumvalue ∼50timesthatoftheCrabNebulaintheenergyintervalof inferedtheexistanceofthatjetbycompilingdifferentradio 1.5−6 KeV, suggested that the source was an an excellent observations, concluding that the speed of the jet ∼ 0.9c, where c is thevelocity of light. candidateforastellarmassblackholewithastellarcompan- ion.Thisideawas furthercorroborated bythedirectobser- Inthisletter,weassumethatthemechanismproducing vations made by McClintock & Remillard (1986) which re- theobservedlightcurveofA0620-00iscausedbyvariations solved the binary components of the source. The estimated in the injected flow at the base of the jet, which leads to distance to A0620-00 is ∼1Kpc (Shahbazet al. 1994), be- the formation of shock waves that propagate along the jet. ing one of the nearest X-ray transients objects, hosting a Thehydrodynamical jet model presented in Mendoza et al. black hole with a mass function f(m) = 3.18 ±0.16M⊙ (2009, hereafter M09) describes the motion of working sur- (McClintock & Remillard 1986; Marsh et al. 1994). faces inside a relativistic jet, which are able to fit the Usingdynamicalandstellarnumericalmodels,theincli- observed light curves of long gamma-rays bursts (lGRBs) as well as the light curve of the blazar PKS 1510-089 (Cabrera et al. 2013). The shape of the X-ray light curve ⋆ E-mail address: [email protected], ser- of the micro-quasar A0620-00 is similar to the one ob- [email protected]. served in lGRBs, showing an exponential rapid increase (cid:13)c 2013RAS 2 Y. Coronado & S. Mandoza with a slow decay. With all these, the the physical ingre- Aug75 Nov75 Feb76 60 dients of the phenomena that produces the light curve of A0620-00 can be considered similar to those ones ocurring 50 12.0 in lGRB and on PKS 1510-089, but with different physical scales of energy, sizes, masses, accretion power rates, etc. (Mirabel & Rodriguez 2002). bs] 40 9.62W/m] pSreecsteiTonnhtet3hlweetetXeb-rrraiieysflydoardgtaaesncoirsfiebtdheeathsliegfhomtllaociwunsr.vfeeaIntoufrSAeesc0t6oi2fo0nt-h0e20.hwIyne- Flux[Cra 30 7.2 −11x[10 drodynamicmodelbyM09,andusingthatmodelwefitthe 20 4.8 Flu observationaldatainSection4.Finally,theresultsofourfits 10 2.4 andthediscussion ofthemainphysicalparametersinferred by themodelling are presented in Section 5. 0 0 50 100 150 200 250 Time[Days] 2 OBSERVATIONAL DATA Figure 1. The figure shows the X-ray light curve of the micro- Theobservational1975-1976 X-raylightcurveofthemicro- quasar A0620-00. The crossess correspond to the Ariel V obser- quasar A0620-00 is shown in Figure 1 and was kindly vations, which covers the uprise of the curve and the beginning provided by Jeffrey McClintock. It consist of a composi- ofits decay. Thepoints areSAS-3observations, whichcover the firstoutburstandthebumpatthedecayingoftheburst. tion of twoindependentlightcurvesobtained byElvis et al. (1975) and Matilsky et al. (1976), with instruments on boardArielVandSAS-3respectively.Bothdatacount-rates micro-quasar A0620-00 produce internal shock waves that havebeenconvertedtofluxCrabunits,accordingtothein- travel inside the expanding relativistic jet and that these strumentsspecifications(Whitlock et al.1992).Withthisit shockwavesinturnareabletoreproduceitsobservedlight is possible to get a complete light curve of the 1975-1976 curve. outburst, including a bump in the decaying outburst. Fig- ure 1 shows the plotted data on a linear scale, with the advantage of revealing the impressive outburst of 1975 and 3 THE HYDRODYNAMICAL MODEL. a clear second bump a few days after the maximum. To convert from Crabs to mJy, we use the conversion given by Many relativistic jets show internal shock waves, which Kirsch et al. (2005) and Bradt et al. (1979) for the Ariel V are due to the interaction of the jet with inhomogeneities data (in the energy range 1 − 13 KeV) and the one in of the surrounding medium (see e.g Mendoza & Longair http://heasarc.gsfc.nasa.gov/docs/sas3 for the SAS-3 2001), the bending of jets (see e.g Mendoza & Longair satellite(intheenergyrange2−10KeV).Thisconversionis 2002) and time fluctuations in the velocity and mass of coherent with the results obtained by Kirsch et al. (2005), theejectedmaterial(cf.Rees & Meszaros1994;Jamil et al. for which 1Crab ≈ 2.4×10−11Wm−2 in the energy range 2008;Mendoza et al.2009).Inparticularthesemi-analytical 1−13KeV. model of M09 is a hydrodynamicaldescription of time fluc- In ordertocalculate theLuminosity Lwemultiply the tuations at the base of the jet that develop shock waves obtained Flux F by 4πD2δ−p, where δ := 1/Γ(v0)(1 − inside an expandingrelativistic jet. (v0/c)cosθ). For this particular case, since the inclina- ThemodelofM09produceinternalshockwavesbype- tion angle i ≈ 51◦, then the angle θ between the jet riodic oscillations of speed and mass discharge at the base and our line of sight is ≈ 39◦, with a distance to the of the jet. This mechanism injects fast fluid that overtakes source D =1Kpc (Owen et al. 1976b; Shahbazet al. 1994; slow one, producing an initial discontinuity which eventu- Cantrell et al. 2010). The beaming index p for synchrotron ally forms a working surface expanding along the jet. The radiationis3(Longair2011)andwehavechosensuchvalue extra kinetic energy inside the working surface is thus ra- in accordance to the calculations of blazars and lGRBs diated away. The efficiency converting factor between ki- (Wu et al. 2011; Mendoza et al. 2009; Cabrera et al. 2013), neticenergyandobservedradiationisassummedtobe∼1. havingin mindaunifiedradiative modelfor theflowinside This value was used by M09 and Cabrera et al. (2013) for all relativistic astrophysical jets. With this luminosity, and lGRBs and theBlazar PKS1510-089. Wehavemade such a withtheaveragejetbulkspeedofv0 =0.9c(Kuulkerset al. choice, since a micro-quasar can be considered as a scaled 1999), we are able to fit the observational data with the version of a quasar. Furthermore, A0620-00 has been the hydrodynamicalmodel of M09. most energetic X-ray micro-quasar and in this sense shares Attempts to model the light curve of A0620-00 were the same behaviour as PKS1510-089 which presented ex- made by Kuulkerset al. (1999) who noticed that this be- tremeγ-rayenergydetections.AsexplainedinSection1,the haviour might well be understood modelling many “syn- micro-quasar A0620-00 behaves as an scaled typical lGRB chrotron bubble” ejections. Since micro-quasars are thought and as such, the hypothesis used by M09 can be extended to be short scaled versions of quasars and are thus logical tothisparticularobject.Aswewilldiscussinsection5,this scaled counterparts of lGRB (Mirabel & Rodriguez 2002), assumption yields physical parameters which are coherent itisquitenaturaltomodeltheirbehaviourusingthemodel with theexpectations of typicalmicro-quasars. by M09 to model their light curve. We thus assume that Following M09, we assume that the flow is injected at velocity and mass variations at the base of the jet of the thebase of thejet with a periodic velocity v given by: (cid:13)c 2013RAS,MNRAS000,1–4 Hydrodynamical model of A0620-00 light curve 3 1st. outburst v(τ)=v0+cη2sinωτ, (1) η2/c ω m˙ Γmax 10−3 10−2d 10−9M⊙yr−1 and a periodic mass injection rate: 1.679 6.6 2.8063 2.31 2 m˙(τ)=m˙0+ǫ sinΩτ, (2) 2nd. outburst - case (a) where τ is the time measured in the proper frame of the source, the velocity v0 is the “average” velocity of the flow η′2/c ω′ m˙ Γmax iTnhsiedpeotshiteivjeet,coannsdtaωntisptahreamosectiellrastηio2nafnrdeqǫu2eanrceyoobfttahineefldobwy. 10−3 10−2d 10−9M⊙yr−1 fitting the observational data, with the particular feature 0.061 249.1 0.8391 3.61 thatη2 hastobesufficientlysmallsothatthebulkvelocity v(τ)doesnotexceedthevelocityoflight c.Themassinjec- 2nd. outburst - case (b) tion rate m˙0 is the “average” discharge of the flow at the base of thejet, and Ω is its oscillation frequency. ǫ2/c Ω m˙ Γmax 10−9M⊙y−1 10−2d 10−9M⊙yr−1 4 MODELLING THE X-RAY LIGHT CURVE 0.8959 1.5 0.7466 2.31 As previously discussed, the first outburst resembles the Table1.Obtainedvaluesforthefreeparametersofthemodelby lightcurveofatypicallGRB.Assuch,wemodelthatburst M09afterfittingwithX-rayobservationsofthelightcurveofthe byassumingm˙ =const.,incompleteaccordancetothecal- micro-quasarA062-00, accurate to within10%. Thebackground culations by M09. The bump in thedecay of thefirst burst Lorentzfactorofthebulkvelocityoftheflowwasassumedtobe is modelled in two ways. The first is by assuming a new 2.29. The maximum Lorentz factor of the flow in each outburst ejection with constant discharge added up to the first out- isrepresentedbyΓmax,andtheminimumis∼1.8−2.2. burst. The second way is by assuming an oscillating mass discharge m˙ produced at a particular time while the first outburst decays. Inthefirstburst,wherem˙ =const.,thesemi-analytical model presentedbyM09, requirestoknowthevaluesof v0, 60 Sep75 Jan76 η2,ωandm˙.The“mean”velocityvaluev0canbetakenfrom 1 2a observational data. For this particular case, we choose the 50 12.0 inferredvaluefromawidevarietyofradioobservationsmod- elledthroughejectionmechanismsbyKuulkerset al.(1999) towvahftehieloηoicnj2cheistthy,yvawi(soeτelftd)ostsathbaraeeretflLtsowohmwruieatshnlvlta(azdτlluosf=amweceatt0dool)lrtt∼vhoΓael(0vuv.eae10xr)oy×pf=efvcηr0to22e.m.ds3Tu.vhctShaheirinstivahcevtealiaootltcnuhtistheeyeiuvnvbpasauildurtlikoee- Flux[Crabs] 432000 974...6282−11Flux[10W/m] the extreme upper limit Γ(v(τ))∼ 10. As pointed by M09, 10 2.4 the mass ejection rate is related to theobserved luminosity L = m˙c2 and is obtained directly from the fits of the light 0 curve. 0 50 100 150 200 The second burst can be described by two different Time[Days] mechanisms:(a)Themassdischargem˙ iskeptconstantand the velocity is the sum of the velocity as in equation (1) Figure 2. The figure shows the fits to the X-ray light curve with an extraoscillating term η′2sinω′τ,with thesame v0, observationsofthemicro-quasarA0620-00,whichcorrespondsto η2 and ω used for the callibration of the first outburst. (b) velocityvariationsandconstantmassdischargesforthefirstand Thevelocityisthesameastheoneusedforthecallibration second outburst (model (a) -see text). The second outburst has of the first burst, and the mass discharge m˙ is allowed to anadditional oscillating velocity component as compared to the oscillate as in equation (2), with m˙0 given by the results firstone. obtained with thecallibration of thefirst outburst. Following Cabrera et al. (2013), weset a dimensionless systemofunitstoperformtherequiredfitting.Todoso,the luminosity is measured in units of the peak luminosity and thetimeinunitsoftheFWHMofeachparticularoutburst. quantity is ǫ2 which can be obtained by another regression Thissystemofunitsissuchthatforthefirstoutburstω=1 analysis. To return to the physical system of units one can and m˙ =1, with the only unknown η2 obtained by a linear recall at any particular step that the luminosity L = m˙c2 regressionanalysistowithin10%ofaccuracy.Forthecaseof (forthefirstoutburst)andthatthetimet=ω−1τ (case(a) the second outburst: (a) The only unknown is η′2 obtained of the second outburst), t = ω′−1τ and t= Ω−1τ (case (b) with a further linear regression analysis. (b) The unknown of thesecond outburst). (cid:13)c 2013RAS,MNRAS000,1–4 4 Y. Coronado & S. Mandoza Sep75 Jan76 JamilO.,FenderR.P.,KaiserC.R.,2008,inMicroquasars 60 and Beyond. 1 2b Kirsch M. G. et al., 2005, in Siegmund O. H. W., ed., So- 50 12.0 cietyofPhoto-OpticalInstrumentationEngineers(SPIE) ConferenceSeriesVol.5898,UV,X-Ray,andGamma-Ray 40 9.62m] SpaceInstrumentation for Astronomy XIV.pp 22–33 abs] W/ KuulkersE., 1998, New Astronomy Reviews, 42, 1 Flux[Cr 30 7.2−11x[10 KMuuolrkiseorns IE.,.,19F9e9n,dMerNRR.APS.,,3S0p6e,n9c1e9r R. E., Davis R. J., 20 4.8 Flu Longair M. S., 2011, High Energy Astrophysics Marsh T. R.,Robinson E. L., Wood J. H.,1994, MNRAS, 10 2.4 266, 137 Matilsky T. et al., 1976, ApJL, 210, L127 0 McClintock J. E., Remillard R. A.,1986, ApJ, 308, 110 0 50 100 150 200 Mendoza S., Hidalgo J. C., Olvera D.,Cabrera J. I.,2009, Time[Days] MNRAS,395, 1403 Mendoza S.,Longair M. S.,2001, MNRAS,324, 149 Figure 3. The figure shows the fits to the X-ray light curve observationsofthemicro-quasarA0620-00,whichcorrespondsto Mendoza S.,Longair M. S.,2002, MNRAS,331, 323 velocity variations for the first and second outburst, but with Mirabel I. F., Rodriguez L. F., 2002, Sky and Telescope, constantmassdischargeatthefirstoutburstandoscillatingmass 103, 050000 dischargeatthesecondoutburst(model (b)-seetext). Owen F. N., Balonek T. J., Dickey J., Terzian Y., Gottes- man S. T., 1976a, ApJL, 203, L15 Owen F. N., Balonek T. J., Dickey J., Terzian Y., Gottes- 5 DISCUSSION man S. T., 1976b, ApJL,203, L15 Rees M. J., Meszaros P., 1994, ApJL, 430, L93 The results of the fits to the X-ray data presented in Sec- ShahbazT.,NaylorT.,Charles P.A.,1994, MNRAS,268, tion 2 using the model by M09 are shown in Figures 2 756 and 3. The obtained values for the physical parameters of Whitlock L., Lochner J., Rhode K., 1992, Legacy, 2, 25 the model are presented in Table 1. We have also included Wu Q., Zou Y.-C., Cao X., Wang D.-X., Chen L., 2011, the maximum and minimum Lorentz factors, obtained for ApJL,740, L21 the bulk velocity of the flow. Direct inspection on the re- sults of the Table show that m˙ ∼ 10−9 −10−10M⊙yr−1, ω−1∼0.01−2dayswithamaximumLorentzfactor2.3−3.6. A00620-00 resulted to be an ideal target to test the model byMendoza et al. (2009) since it closely resembles a lGRB in this outstanding outburst in x-rays. Future tests of the model have to be done with a wide variety of Light Curves from a large collection of micro-quasars. 6 ACKNOWLEDGMENTS The authors gratefully acknowledge the kindness of Jeffrey E. McClintock for providing the observational data and for pointing to the relevant articles discussing those observa- tions. This work was supported a DGAPA-UNAM grant (PAPIITIN111513-3).YUCandSMthanksupportgranted by CONACyT:210965 and 26344. REFERENCES AbdoA. A.et al., 2009, Science, 323, 1688 Bradt H. V., Doxsey R. E., Jernigan J. G., 1979, in Baity W. A.,Peterson L. E., eds, X-ray Astronomy.pp 3–66 CabreraJ.I.,CoronadoY.,Ben´ıtezE.,MendozaS.,Hiriart D., Sorcia M., 2013, MNRAS,434, L6 Cantrell A. G. et al., 2010, ApJ, 710, 1127 Davis R. J., Edwards M. R., Morison J., Spencer R. E., 1975, Nature, 257, 659 ElvisM.,PageC.G.,PoundsK.A.,RickettsM.J.,Turner M. J. L., 1975, Nature, 257, 656 (cid:13)c 2013RAS,MNRAS000,1–4