Mildly relativistic X-ray transient 080109 and SN2008D: Towards a continuum from energetic GRB/XRF to ordinary Ibc SN
aa r X i v : . [ a s t r o - ph ] J a n D RAFT VERSION N OVEMBER
1, 2018
Preprint typeset using L A TEX style emulateapj v. 08/22/09
MILDLY RELATIVISTIC X-RAY TRANSIENT 080109 AND SN 2008D:TOWARDS A CONTINUUM FROM ENERGETIC GRB/XRF TO ORDINARY IBC SN
D. X U , Y. C. Z OU , AND
Y. Z. F AN Draft version November 1, 2018
ABSTRACTWe analyze the hitherto available space-based X-ray data as well as ground-based optical data of the X-raytransient 080109/SN 2008D. From the data we suggest that ( i ) The initial transient ( .
800 sec) is attributed tothe reverse shock emission of a mildly relativistic ( Γ ∼ a few) outflow stalled by the dense stellar wind. ( ii )The subsequent X-ray afterglow ( . × sec) can be ascribed to the forward shock emission of the outflow,with a kinetic energy ∼ erg, when sweeping up the stellar wind medium. ( iii ) The late X-ray flattening( & × sec) is powered by the fastest non-decelerated component of SN 2008D’s ejecta. ( iv ) The localevent rate of X-ray transient has a lower limit of ∼ . × yr - Gpc - , indicating a vast majority of X-raytransients have a wide opening angle of & ◦ . ( v ) Transient 080109/SN 2008D indicates a continuum fromGRB-SN to under-luminous GRB-/XRF-SN to X-ray transient-SN and to ordinary Ibc SN (if not every Ibc SNhas a relativistic jet), as shown in Figure 2 of this Letter . Subject headings: gamma rays: bursts - supernovae: individual: SN 2008D - radiation mechanisms: non-thermal INTRODUCTION
During the past decade, long-duration ( & γ - raybursts (GRBs), including the subclass of X-ray flashes(XRFs), have been found (1) to be driven by the core-collapseof massive stars (Wooseley et al. 19993); thus (2) to be as-sociated with a rare variety ( ∼ SWIFT OBSERVATIONS AND DATA ANALYSISElectronic address: [email protected] (YZF) Dark Cosmology Centre, Niels Bohr Institute, University of Copen-hagen, Juliane Maries Vej 30, 2100, Copenhagen, Denmark The Racah Inst. of Physics, Hebrew University, Jerusalem 91904, Israel Department of Physics, Huazhong University of Science and Technol-ogy, 430074 Wuhan, China Neils Bohr International Academy, Niels Bohr Institute, University ofCopenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing210008, China
During
Swift /XRT follow-up observations of Ib SN 2007uybeginning at 13:32:49 UT on Jan 9, 2008, an X-ray transient(Transient hereafter) was identified and reported on Jan 10.58(Berger & Soderberg 2008a). X-ray emission was already un-derway at time of trigger. Both Transient 080109 and SN2007uy are in the same host galaxy, NGC2770, at z = 0 . Swift /BAT field of view for approx-imately 30 minutes prior to the XRT observation but nevertriggered BAT (Burrows et al. 2008).Since trigger, the Transient was observed to rise to a maxi-mum flux about 65 seconds, and then subsequently decay untilthe end of the first orbit, roughly 500 seconds afterwards. Wereduced the XRT data in a standard way using the Swift anal-ysis software (HEAsoft 6.4) and calibration data. The con-tamination by a source close to the Transient and pile-up havebeen corrected.A general spectral softening was seen during the first orbit.Taking a mean spectrum, the data can be well fitted by eitheran absorbed power-law Γ = 2 . ± . N H = 7 . + . - . × cm - ( χ do f = 15 . /
20) with respect to theGalactic number 1 . × cm or by an absorbed blackbodyspectrum with kT = 0 . ± .
05 keV in the restframe ( χ do f =24 . / Γ ∼ . σ ) and U (3.0 σ ) filters.After a data gap of 2 days, the source brightened and showedup in both optical and UV. The source then faded until day ∼ . EARLY SPECTROSCOPY AND ITS EVOLUTION
Two spectra were obtained at the ESO VLT equipped withFORS2 starting 07:17 UT on Jan 11. As pointed in Male-sani et al. (2008), the overall spectral shape rules out a sig-nificant non-thermal afterglow component, but a SN one in-stead. The presence of broad features reveal SN 2008D’semergence, but the features are not as broad as in the earli- U B V O p t i c a l Lu m i no s i t y ( e r g s - ) Time since onset (sec) X -r a y Lu m i no s i t y ( e r g / s ) (0.3-10 KeV)~t -1.1 ~t F IG . 1.— Comparison of X-ray transient 080109/SN 2008D (squares) andXRF 060218/SN 2006aj (stars). Data of XRF 060218/SN 2006aj are takenfrom Campana et al. (2006). Upper : Temporal evolution of the X-ray lumi-nosity in 0.3-10 keV.
Lower : The U (grey), B (blue), and V (red) lightcurvesfor two events. Data of Transient 080109 have not been corrected for extinc-tion. est spectra of GRB/XRF-associated SNe such as SN 1998bwand SN 2006aj.SN 2008D is distinguished for its apparent Ic → Ib spectro-scopic evolution. It was classified as peculiar type-Ic on Jan11, and then as a type-Ic with possibly some He as seen inNIR spectra on Jan 13-15, and later to a type-Ib on Jan 21(Modjaz et al. 2008 and reference therein). This evolution isreminiscent of SN 2005bf (Folatelli et al. 2006). INTERPRETATION OF THE FOLLOW-UPS
Real onset time and Spectrum for the first orbit
Though it’s impossible to know the exact onset time ofthe Transient, we may get a rough estimate about this time-back shift. First, non-trigger of BAT approximately 30 min-utes prior to the XRT trigger and association with SN 2008Dgive us confidence that Transient 080109 is a dwarf outburstcompared with previous bursts featuring low ν F ν peak energysuch as XRF 060218. Second, the existence of a main outburst30 minutes earlier would make the first orbit lightcurve looklike a very sharp flare with a decay index ∼
20 covering theeorder of magnitudes in luminosity. Its profile is not similar tothe Fast-Rise-Exponential-Decay one typical for GRB/XRF.Considering the above two factors, a back shift of tens to ∼
200 sec is generally acceptable and doesn’t affect the tem-poral decay laws after 1000 sec. In this work, we adopt a backshift of ∼
100 sec.Should a shock break-out be responsible for the first or-bit observation, according to the equation L = Ω ( γ ct ) σ T rest ,where L ∼ erg s - is the isotropic luminosity, Ω is thesolid angle for the outburst, γ is the Lorentz factor for the out-burst with respect to the observer, σ is the Stefan-Boltzmann constant, T rest is the temperature in the restframe, we thenhave T obs ∼ . Ω / t / γ keV , where T obs is the measured temperature. To match the mea-sured T = 0 .
73 keV, a jet-like outflow with Ω < - is needed,which renders the shock break-out model unacceptable in thisevent. The X-ray transient powered by the reverse shock of themildly relativistic outflow
The Transient lightcurve is smooth and decays as t - . . Thesmoothness largely disfavors that these X-ray photons arepowered by internal shocks, and the steep decline rules outthat the transient is from the forward shock of an outflow.We consider a mild-relativistic ( Γ i ∼
3) outflow with aluminosity L m ∼ Ω - o erg s - decelerated by the stel-lar wind medium, where Ω o is the solid angle of the ini-tial transient outflow. The density profile of the stellar windis n = 3 × A ∗ R - , where the free wind parameter A ∗ =[ ˙ M / - M ⊙ yr - ][ v w / (10 cm s - )], ˙ M is the mass loss rateof the progenitor, and v w is the velocity of the stellar wind(Li & Chevalier 1999). Because of the low luminosity of theoutflow while the high density of the stellar wind, the forward-shocked material would move sub-relativistically (i.e., Γ fr ∼
1) while the reverse shock is mild-relativistic. The reverseshock region is thus very hot and has a very large sidewaysexpansion velocity of ∼ c , the speed of light. As a result, af-ter the reverse shock crosses the outflow, the shocked outflowwill have a large solid angle Ω ≫ Ω o if Ω o is small. So forsimplicity we treat the outflow as isotropic.Now we estimate the synchrotron radiation of the reverseshock at a distance R r ∼ cT ∼ cm. As usual, we as-sume ǫ e and ǫ B fractions of the shock energy given to theelectrons and magnetic field, respectively (Sari et al. 1998).The minimum Lorentz factor of the reverse shock acceler-ated electrons is γ m , r ∼ ( Γ i - ǫ e ( p - m p / [( p - m e ] ∼ p ∼ . B r ∼ [2( ǫ B /ǫ e ) L m / ( R c )] / ∼ × Gauss ( ǫ B /ǫ e ) / L / , R - , .The typical synchrotron radiation frequency ν m , r ∼ . × Hz γ , r B r ∼ × Hz, which is in the soft X-ray bandand matches the observation. The cooling Lorentz factor is γ c , r ∼ . × / ( B t ) ≪ γ m , r , so the reverse shock is in thefast cooling phase. At a first glimpse, one might interpretthe ∼ t - . decline as the high latitude emission of the re-verse shock. But this requires either a sub-relativistic outflowwith a very sharp energy distribution from the outflow cen-ter to the outflow side or a Γ fr ≥ a few. The validity of theformer option is hard to estimate. The latter is also difficultto function because Γ fr ≈ . L / , A - / ∗ , - . A Γ fr ∼ L m ∼ erg s - A ∗ , which is too high to match the observa-tion.In this work we interpret the steep X-ray decline as thedimmer and dimmer reverse shock emission powered by theweaker and weaker outflow. Within this scenario, the outflowis very likely to be mildly relativistic. If Γ i ∼ tens - hundreds, γ m , r ∼ - and ν m , r would be ∼ -
500 keV. As a result,the XRT spectrum should be ∝ ν - . , which is inconsistent The convention Q x = Q / x has been adopted in cgs. with the observed value. A marginally relativistic ( Γ i ∼ . The early X-ray afterglow ( . × sec) powered bythe forward shock of the Transient outflow We calculate the synchrotron radiation of the sub-relativistic forward shock when it sweeps up the surround-ing stellar wind medium. The minimum Lorentz factor of theshocked electrons, the magnetic field and the cooling Lorentzfactor are γ m ≈ C p β ǫ e , - , B ≈
15 Gauss β R - ǫ / , - A / ∗ , - ,and γ c ≈ β - R ǫ - , - A - ∗ , - t - , respectively, where C p ≡ p - / ( p - F ν , max ≈ βǫ / , - A / ∗ , - D - , . , (1) ν m ≈ . × Hz β C R - ǫ , - ǫ / , - A / ∗ , - , (2) ν c ≈ . × Hz β - R ǫ - / , - A - / ∗ , - t - , (3)where D L is the luminosity distance of the source. So the X-ray flux can be estimated as F ν X = F ν , max ν / ν ( p - / ν - p / = 4 . × - µ Jy ν - p / , β (5 p - / ǫ p - , - ǫ ( p - / , - A ( p + / ∗ , - D - , . C p - R (4 - p ) / t - . (4)If β ∼ const., i.e., the outflow hasn’t been decelerated sig-nificantly, we have R ≈ β ct and F ν X ∝ t (2 - p ) / . The de-cline is thus too shallow to be consistent with the detected ∝ t - . for the early X-ray afterglow. We then consider analternative in which the outflow with a energy distribution E ( ≥ β Γ ) ∝ ( β Γ ) - k has entered the Sedov regime, thus wehave β ∝ t - + k and R = + k + k β ct ∝ t + k + k . Accordingly, Eqs. (1-3)read F ν , max ∝ t - + k , ν m ∝ t - + k + k , and ν c ∝ t , respectively. Thelight curves are of F ν ∝ t + k + k ) for ν < ν m < ν c , t - + k [1 + ( p - + k )2 ] for ν m < ν < ν c , t - + k [1 + ( p - + k )2 ] + for ν > max { ν c , ν m } . (5)So the early X-ray afterglow decline F ν X ∝ t - . suggests avery small k ∼ . p ∼ .
2, implying that the outflowalmost has a very flat energy distribution (i.e., the Transientejecta is likely expanding with a single bulk Lorentz factor).So we assume E tran ≈ πβ R nm p c , which yields β ∼ . E / tran , . A - / ∗ t - / . (6)Eq.(4) thus reduces to F ν X ∼ . µ Jy ǫ . , - E . tran , . t - . , (7)which is consistent with the XRT flux ∼ . µ Jy at 10 Hzat t ∼ sec (see Fig.1). The outflow energy inferred aboveis E tran ∼ × erg, which is larger than the isotropic energyof the X-ray transient by a factor of 10 and is reasonable. Till here we have shown that a mild-relativistic outflow withan energy ∼ × erg can account for the Transient andthe early X-ray afterglow self-consistently, which implies thatthere was no energetic outburst before the X-ray transient.Should it happen, there would be a bright X-ray afterglowcomponent, which actually could outshine the current data.On the other hand, an earlier outburst would sweep up thestellar wind medium and leave a very low density bubble. TheTransient outflow thus cannot get decelerated effectively andcannot account for the following X-ray afterglow data. The late X-ray afterglow ( & × sec) powered by thesupernova shock After & × sec, the X-ray lightcurve gets flattening.We interpret this flattening as the shock emission of the fastestcomponent of the SN ejecta, which moves with a velocity ∼ . ∼ sec or even longer, we have F ν X ∝ t (2 - p ) / ∼ t - . , which is consistent with the observed flattening (see Fig.1).The observed X-ray flux at ∼ Hz at t ∼ s is ∼ . µ Jy, which requires β ≈ . / (2 p - ǫ (1 - p ) / (2 p - , - A - ( p + / [4(2 p - ∗ , - . A reasonable choice of A ∗ ∼ ǫ e , - ∼
1, and β ∼ . E SN ( β ≥ . ∼ π nR β m p c ∼ × erg A p - p - ∗ ǫ - p )2 p - e , - t . (8)For comparison, we plot in Figure 2 the identified energydistribution of the outflows associated with XRTr 080109/SN2008D, together with those of ordinary Ic SNe and the hy-pernovae associated with energetic GRBs/XRFs. At firstglimpse, the main difference between the ordinary Ic SNeand the GRB/XRF-associated ones is the energy of the (mild-)relativistic outflow. The radio afterglow: the supernova shock model
Radio emission below the self-absorption frequency, ν a ,would be suppressed significantly. Through the standardtreatment (Rybicki & Lightman 1979), for ν a < ν m < ν c , wehave ν a ≈ . × Hz β - / t - ǫ - , - ǫ / , - A / ∗ , - . While for ν m < ν a < ν c , we have ν a ≈ . × Hz β p - p + t - ǫ - pp + e , - ǫ p + p + B , - A p + p + ∗ , - . (9)The latter seems to be more realistic and considered here.The radio afterglow thus will peak when the observation fre-quency, ν obs , crosses ν a at t peak ∼ × s ( ν a .
64 GHz ) - β p - p + ǫ - pp + e , - ǫ p + p + B , - A p + p + ∗ , - . (10)For typical parameters ǫ e , - ∼ ǫ B , - ∼ β ∼ . A ∗ ∼ we expect the SN radio afterglow will peak at ∼ days .Using Eq. (1) the peak flux can be estimated as F ν radio , peak ∼ . (11)For ν m < ν radio < ν a < ν c , F ν radio ∝ β t / . For β ∼ const.,we have F ν radio ∝ t / , increasing with time rapidly. The Log ( K i ne t i c E ne r g y > ) ( e r g ) Velocity of ejecta ( ) mild-RL radio/hypernovaX-ray/X-ray transient non-RL optical/hypernovaoptical-radio/Ibc SN moderate-RL / ultra-RL -ray/GRB/XRF NA/X-ray transient F IG . 2.— Energy distribution for Transient 080109-SN 2008D as well asfor GRB-HN, under-luminous GRB-/XRF-HN, and ordinary Ibc SNe. RLand NA represent “relativistic” and “not available”, respectively. Part of datafrom Soderberg et al. (2006) and Kaneko et al. (2006). Sudden drop ofthe energy distribution in GRB 031203 and XRF 060218 after the promptemission might be due to the geometry correction and/or a high GRB/XRFefficiency. Transient 080109/SN 2008D marks a transition between popula-tions of ordinary Ibc SNe and under-luminous GRB-/XRF-HN. We cautionthat X-ray transients may account for a majority of Ibc SN events. current two data reported in GCN (Soderberg et al. 2008;van der Horst et al. 2008) do suggest a quick rise of the radioflux and support our assumption β ∼ const. For β ∝ t - / (3 + k ) ,we have F ν radio ∝ t / - / (3 + k ) . As long as the observation fre-quency is above ν a , the light curve is described by Eq.(5). CONCLUSION AND DISCUSSION