What are Published X-ray lightcurves telling us about Young Supernova Expansion?
aa r X i v : . [ a s t r o - ph . H E ] S e p Mon. Not. R. Astron. Soc. , 1–12 (2010) Printed 16 November 2018 (MN L A TEX style file v2.2)
What are Published X-ray lightcurves telling us aboutYoung Supernova Expansion?
V. V. Dwarkadas, ⋆ and J. Gruszko, Department of Astronomy and Astrophysics, U Chicago, 5640 S Ellis Ave, Chicago, IL 60637 Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627-0171
16 November 2018
ABSTRACT
Massive stars lose mass in the form of stellar winds and outbursts. This materialaccumulates around the star. When the star explodes as a supernova (SN) the resultingshock wave expands within this circumstellar medium. The X-ray emission resultingfrom the interaction depends, among other parameters, on the density of this medium,and therefore the variation in the X-ray luminosity can be used to study the variationin the density structure of the medium. In this paper we explore the X-ray emissionand lightcurves of all known SNe, in order to study the nature of the medium intowhich they are expanding. In particular we wish to investigate whether young SNeare expanding into a steady wind medium, as is most often assumed in the literature.We find that in the context of the theoretical arguments that have been generallyused in the literature, many young SNe, and especially those of Type IIn, whichare the brightest X-ray luminosity class, do not appear to be expanding into steadywinds. Some IIns appear to have very steep X-ray luminosity declines, indicatingdensity declines much steeper than r − . However, other IIns show a constant or evenincreasing X-ray luminosity over periods of months to years. Many other SNe do notappear to have declines consistent with expansion in a steady wind. SNe with lowerX-ray luminosities appear to be more consistent with steady wind expansion, althoughthe numbers are not large enough to make firm statistical comments. The numbers doindicate that the expansion and density structure of the circumstellar medium mustbe investigated before assumptions can be made of steady wind expansion. Unless asteady wind can be shown, mass-loss rates deduced using this assumption may needto be revised. Key words: circumstellar matter; stars: massive; stars: mass-loss; supernovae: gen-eral; stars: winds, outflows; X-rays: ISM
In 1972, in a review article on supernova remnants (SNRs),Woltjer (1972) did not devote much attention to the ambi-ent medium into which the SN was expanding, suggestingthat the “importance of the swept-up matter is compara-tively minor” in the ejecta-dominated stage, as “everythingdepends on the details of the explosive process”. Chevalier(1977) also considered the interaction of SNRs only with theinterstellar medium. However, by 1982 the idea appears tohave been established that core-collapse supernovae (SNe)expand not into the interstellar medium but the wind-blowncircumstellar medium (CSM) ejected by the progenitor star.Chevalier (1982a,b) derived self-similar solutions for this in-teraction. Since then this concept has been widely tested and ⋆ E-mail: [email protected] accepted, so much so that nowadays it is commonly acceptedthat young core-collapse SNe expand into the wind-blownstructures created by their progenitor stars, and the result-ing X-ray emission is due to the forward and reverse shocksinteracting with the ambient medium (Chevalier & Fransson1994).The wind from a star is defined basically by two pa-rameters, the mass-loss rate and the wind velocity. If theseparameters are constant it is referred to as a steady wind.Another common paradigm that frequently now appearsin the literature is that young core-collapse SNe are ex-panding into steady winds. This has been used to computethe mass-loss rates of X-ray supernovae (Immler & Lewin2003; Immler & Kuntz 2005), and especially optical SNe(Smith et al. 2008, 2010; Kiewe et al. 2010). In very fewcases has an attempt been made to determine whether thewind is in fact steady, and some of the calculations were c (cid:13) Dwarkadas & Gruszko shown to be inconsistent in this respect with the resultsobtained (Dwarkadas 2011). However, a steady wind is areasonable approximation that makes analytical calculationspossible, whereas the alternative is to do much more compli-cated calculations which may not even be possible withoutsubstantially more data.A steady wind with a constant mass-loss rate ( ˙ M ) andwind velocity ( v w ) results in a density ρ = ˙ M/ (4 πr v w ).The density profile thus evolves as r − . If the wind param-eters vary with time, the density profile would deviate froman r − evolution. Thus by determining the nature of thedensity profile into which young core-collapse SNe are ex-panding, one could infer the variation in wind parameters(if any), and the nature of the progenitor mass-loss. Super-nova expansion into the surrounding medium allows a nat-ural probe into the density structure of this medium. Sincethe SN expansion velocity can be about 10-1000 times thevelocity of the surrounding medium, depending on whetherthe progenitor was a Wolf-Rayet (W-R) star or a red super-giant (RSG) star, the SN ejecta allows us to probe 10-1000years of wind evolution in 1 year of SN evolution.The X-ray emission resulting from the circumstellar in-teraction is proportional to the density structure (see § Chandra , XMM-Newton and
Swift , with Immler & Lewin (2003) listing 15SNe, Schlegel (2006) having 25 on his list, and Immler (2007)listing 32 SNe. In this paper we aim to use published X-ray light-curvesof SNe to explore the nature of the medium into which theyare evolving. We will explore what can be learned from X-ray light curves in §
2, and the limitations of this technique.In the next section 3 we show the lightcurves of X-ray SNeand fits to the data, and discuss the resulting implications.We analyze these results for individual SNe and SNe typesin §
4. Finally, in § A very thorough discussion of the evolution of the X-ray light curve from young SNe was carried out byFransson et al. (1996), in reference to SN 1993J. In thisdiscussion, and throughout this paper, we will make useof many of the results described therein. For the sake ofcompleteness, we present here a simplified analysis with ba-sic results that develops and summarizes the most impor-tant ideas. This summary follows the description given inDwarkadas et al. (2010). The expansion of a SN shock wave into the ambientmedium gives rise to a forward and reverse-shocked struc-ture, separated by a contact discontinuity (Chevalier 1982a).The shocks heat up the medium to high temperatures, pro-ducing X-ray emission. The X-ray luminosity L x from asource depends on the electron density n e , the emitting vol-ume V and the cooling function Λ L x ∼ n e Λ V (1)The density of the medium into which the SN shockwave is expanding is assumed to go as r − s , with s=2 for asteady wind. The emission arises from a thin shell of radius∆ r in between the forward and reverse shocks, at a meanradius r , whose volume V can be expressed as 4 πr ∆ r . Al-though the wind may not have been steady, the evolutionwill be self-similar as long as both the SN ejecta and the cir-cumstellar medium density profiles are described by power-laws (Chevalier 1982a). In the self-similar case, ∆ r ∝ r ,and therefore V ∝ r . For a SN in the early stages, thepost-shock temperature is going to be much larger than10 K, and the cooling function is assumed to vary as T . (Chevalier & Fransson 1994). For a strong shock, T ∝ v s ,and therefore the cooling function Λ ∝ v s ∝ r/t in the self-similar case.Therefore we get L x ∼ r − s rt r (2)which gives L x ∼ r − s t (3)For s=2 this gives the well-known result that the emis-sion decreases inversely with time, L x ∝ t − . This re-sult is inherent in the formula for mass-loss derived byImmler & Lewin (2003).In the self-similar case, with ρ ej ∝ A t − v − n and ρ cs ∝ r − s , the radius of the SN will evolve as (Chevalier 1982a) R SN ∝ t α α = ( n − / ( n − s ) (4)Using this in equation 8 gives us that in a general case, L x ∼ t − (12 − s +2 ns − n ) / ( n − s ) (5)This is a general formula that has often been used todescribe the evolution of the X-ray luminosity. An importantcaveat must be pointed out here - this formula considers thetotal X-ray emission over all temperatures. However X-raysatellites measure the emission only in a very narrow band. ROSAT covered the region between 0.4 - 2.4 keV.
Chandra and
XMM-Newton cover a slightly larger band, around 0.4-10/15 keV, but the effective area is much higher at lowerenergies. Therefore, although equation 5 shows how the X-ray luminosity will vary with time over the entire
X-rayrange, it is doubtful that this variation could be observed.We observe the variation only for that part of the luminositythat falls within a given X-ray mission’s observable band.This would have the same time dependence if and only ifthe ratio of the luminosity in that discrete band to that ofthe total X-ray region is constant.However this is not likely. As the SN expands, we expectthat the shock will sweep up more material and decelerate.The post-shock temperature, proportional to the square ofthe shock velocity, will decrease with time, and the X-ray c (cid:13) , 1–12 -rays and Young SNe expansion emission would gradually shift from high to lower temper-atures. Since X-ray satellites can detect emission mainly inthe softer bands, we would expect that the luminosity in thelower energy range would increase at the expense of that inthe higher energy range. Thus, the ratio of X-ray emissionwe observe to the total should increase over time, leading toa time dependence flatter than the overall time dependencein a steady wind of t − .In some cases, this can be derived. From above, for anon-radiative shock, the shock velocity goes as v sh ∝ t α − ,and the shock temperature therefore decreases as T sh ∝ t α − . As shown in Fransson et al. (1996), the luminosityin a given energy band with E << kT sh will then go as: L x ( E ) ∼ t − (6 − s +2 ns − n ) / ( n − s ) ∼ t − β (6)Compared to equation 5, note that this gives a flat-ter time dependence, as expected. For s = 2 we get that L x ∼ t − ( n − / ( n − . The index β is now always <
1, im-plying that the time dependence we see will not be t − butwill be flatter, and is now a function of the ejecta densitypower-law. For n >
5, as required by the Chevalier solution,0 . < β <
1. For commonly used values n=9, β = 0 . β = 0 .
77. Therefore, even for a steady wind,we are more likely to see L x ∼ t − (0 . ± . . It should benoted that for s = 2, we will not see a steeper luminositydependence than t − , or flatter than t − . .For s = 2 the situation is more complex. For s = 1,we get β = −
1, i.e. the flux is linearly increasing with time,irrespective of the value of n . Thus a decreasing wind densitycan still give rise to an increasing flux. For s = 1 . β = − . / ( n − .
5) is always negative, and thereforethat the luminosity is increasing with time, whereas the totalX-ray luminosity from equation 5 is actually decreasing withtime. Thus this clearly shows the difference between whatwe would observe with X-ray satellites, and what the totalX-ray luminosity is doing.Since we can get both decreasing and increasing lumi-nosity dependence with time, it follows that for some spe-cific values we could observe a constant luminosity withtime, i.e. β = 0. This depends on the value of the ejectadensity. For n = 9 we obtain from equation 6 that β =(13 s − / (9 − s ). Therefore, for s = 21 / ∼ .
62 theluminosity would be constant with time.If the temperature of one of the shocks, especiallythe reverse shock, is lower than about 3 × , thenthe cooling function behavior changes to Λ ∝ T − . (Chevalier & Fransson 1994). For simplicity and to illustratethe difference in evolution, we may assume that the depen-dence goes as T − . . Then we get, following the argumentabove, that the Λ dependence can be inverted, giving L x ∼ r − s tr r (7)which leads to L x ∼ r − s t (8)and therefore, assuming that r ∝ t α , we get L x ( E ) ∼ t − (2 ns − s − n +6) / ( n − s ) ∼ t − β (9)The situation becomes more complicated if the shockbecomes radiative. This has also been discussed byFransson et al. (1996). In this case the luminosity goes as L x ∼ t − (15 − s + ns − n ) / ( n − s ) (10)while, as long as the cool shell is optically thick, theluminosity in a band evolves as L x ( E ) ∼ T . e t (3 − s )( n − / ( n − s ) (11)where the luminosity is now proportional also to theelectron temperature T e with time. It is interesting to notehere that for a density gradient s = 1 . n . For s > . s < . s = 2 thetime dependence β = α , i.e. the luminosity evolution hasthe same time dependence as the radius evolution withoutcooling, although with the opposite sign.We emphasize that the light curves of young SNe ex-panding into a steady wind, observed in a narrow band ,would not be expected to have the canonical t − depen-dence that so many have postulated (Pooley et al. 2002;Immler et al. 2002; Immler & Lewin 2003; Immler & Kuntz2005; Soria & Perna 2008), but would have a flatter depen-dence that is a function of the ejecta power-law. This hasbeen very nicely shown by Fransson et al. (1996) but is rou-tinely ignored.Even though this approximate theory works nicely insome cases, it is important that we remain cognizant of itslimitations. This includes the fact that a power-law profileis assumed for both the ejecta and the surrounding windmedium; that self-similarity is assumed; and that the samecooling function is implied for both forward and reverseshocks. It is possible that one or both of the ejecta andCSM density profiles do not decrease as a power-law; thatthe solution does not depict self-similar behaviour, and thatdifferent temperatures result in different cooling functions ateach shock. While in the later case the result for each shockcould possibly be worked out in a similar manner, the totalX-ray emission from the SN would depend on details such ashow much was emanating from each shock in which temper-ature range, and would not be easy to compute analytically.Finally, such a theory computes the emission due only to cir-cumstellar interaction, and does not consider X-ray emissiondue to other mechanisms such as Inverse Compton scatter-ing or a central pulsar, or due to other components such asradiative shocks in a clumpy medium. Thus, although thereis a wide range over these ideas are applicable, it is prudentto keep the shortcomings in mind. In order to study X-ray SNe light curves, we have compileddata on SNe that was available in the literature, using pub-lished values of luminosity/flux. The time after outburst isalso taken from the literature, although in cases where dif-ferent times of explosion were listed for the same SNe indifferent papers, we have appealed to the optical light curvefor clarification. Table 1 lists the various papers from whichthe data were compiled. In some cases the data were notexplicitly listed in a table but had to be read off a fig-ure, which introduced further error in the numbers. In a c (cid:13) , 1–12 Dwarkadas & Gruszko few cases (SN 2005kd, SN 2006jd), we have downloaded thepublicly archived data-set and computed the flux, in orderto procure at least one more data-point so that we mayconstruct a light curve. In one case (SN 1993J) the mostcurrent data point is from a
Chandra observation on whichthe first author is PI. We have chosen not to include GRB-related SNe in this compilation, as their X-ray emission isnot expected to be due purely to circumstellar interaction.We have also not included SN 2008D, a very well observedSN whose early lightcurve at least was attributed to shockbreakout (Soderberg et al. 2008) and thus did not fit in withthe circumstellar model discussed herein.Figure 1 plots the datapoints for all X-ray observed SNethat we found in the literature with at least 1 published datapoint. The number is only 42, although it is rapidly increas-ing, thanks mainly to
Swift . We plot light curves for almostall published SNe with multiple data points, enabling anX-ray light curve to be constructed. As far as possible wehave constructed the light curve in the 0.4-2.4 keV or re-lated energy range, which usually has the most data for SNethat exploded during or before the
ROSAT era, and thusensures the largest duration light curves. In some cases, asmentioned in Table 1, a larger energy band is used. Most ofthese are SNe observed with
Swift . All points on a lightcurvelie in the same energy range, which is given in Table 1. Inorder to accomplish this using only published data, we hadto select the energy range in which the maximum numberof SN fluxes were quoted, which sometimes meant not usingavailable flux results lying outside the energy range. Givenour intent of assessing what the published light curves aretelling us, no attempt was made to interpolate or extrapo-late published data from a given energy range to another,which would have required assuming a spectral model thatwas generally not available.While the number of SNe is gradually increasing, it isstill not very large, with only 20 SNe found in the literaturewhich have flux values at more than one epoch (althoughlarge amounts of unpublished data exists in the archives).Given the current availability of
Chandra , XMM-Newton and especially
Swift , we hope that this situation can be rec-tified in future. Only one SN (1993J) has been observedregularly since its birth, and has the most complete lightcurve, although gaps still exist. SN 1987A is probably themost observed X-ray SN, due to its closeness and uniquenature. Hard X-ray data exist in the first 1000 days fromGinga (Inoue et al. 1991), with progressively better resolu-tion data thereafter from all the major X-ray observatories,and almost every X-ray telescope, including high-resolutiongratings.The plot shows that very few SNe possess a monotoniclight curve in the given X-ray band. This may be partiallydue to the published error bars being too optimistic, but insome cases it is evident that the light curve tends to jumparound.
Following the discussion in §
2, we fitted the light curvesof all SNe with multiple data points (Figure 1) using anexpression of the form L x = P (0) × t P (1) . The fitting wasdone using the MPFIT routine (Markwardt 2009) in theIDL programming language. In Figure 2 we show the fits for various SNe. The legend gives the value of the parameter P (1) in the expression above, which corresponds to − β from §
2. In many cases the use of a simple power-law fitting func-tion does not seem appropriate, as is evident not only fromthe large values of χ -squared that were found, but merely bycomparing the fit to the data points. It appears that a morecomplicated function is needed, or perhaps a break is neededin the power-law. In one case, SN 1978K, the fit seems en-tirely off, and it is clear that something more sophisticatedis needed. In order to study the variation of the X-ray emission withtype of SNe, we show in figure 3 the light curves of all SNeplotted as a function of the type of SN. It is clear fromthis plot that Type IIn SNe show the highest luminosities,and Type IIP SNe the lowest. These bracket the Type IIL’s,Type IIb’s and Type Ib/c. We caution that we have notincluded GRB-SNe here, and while the sample is probablyenough to make general inferences, it is still not large enoughto draw detailed statistical conclusions.
A survey of the fits to the data in figure 2 reveals the di-versity in the X-ray expansion of SNe. About half the SNedecay with β <
1, a necessary (but certainly not suffi-cient) condition if they are expanding in a steady wind.Two of them (SN 1987A and SN 1996cr) show β < β >
1. In the frameworkof the theory outlined above, these could not arise from SNexpansion into a steady wind. This group consists of 4 TypeIIn SNe, which tend to show some of the steepest decreasesin X-ray emission. Others in this category include SN 2003bgand 2008ax, which do not have enough time-sampling overeven a decade to effective judge their luminosity decrease.The steepest light curve belongs to SN 1970G, which dropsas t − . . Interestingly, many of these SNe which have steepdrop-off in light curves appear to be those from whom X-rayemission was found only late in their lifetimes, after about6 years. In this context, we point out that if the X-ray lightcurve of SN 1993J after 6 years is considered, the fall-offwould be much steeper than the gentler overall slope, as hasbeen shown in Chandra et al. (2009).We discuss some of our results in more details, in thecontext of either individual SNe or groups of SNe. In 1990, a new class of SNe was introduced by Schlegel(1990). The ’n’ denotes narrow lines, which distinguish TypeIIn from other SNe. Many of these SNe (but not all) have a c (cid:13)000
1. In the frameworkof the theory outlined above, these could not arise from SNexpansion into a steady wind. This group consists of 4 TypeIIn SNe, which tend to show some of the steepest decreasesin X-ray emission. Others in this category include SN 2003bgand 2008ax, which do not have enough time-sampling overeven a decade to effective judge their luminosity decrease.The steepest light curve belongs to SN 1970G, which dropsas t − . . Interestingly, many of these SNe which have steepdrop-off in light curves appear to be those from whom X-rayemission was found only late in their lifetimes, after about6 years. In this context, we point out that if the X-ray lightcurve of SN 1993J after 6 years is considered, the fall-offwould be much steeper than the gentler overall slope, as hasbeen shown in Chandra et al. (2009).We discuss some of our results in more details, in thecontext of either individual SNe or groups of SNe. In 1990, a new class of SNe was introduced by Schlegel(1990). The ’n’ denotes narrow lines, which distinguish TypeIIn from other SNe. Many of these SNe (but not all) have a c (cid:13)000 , 1–12 -rays and Young SNe expansion Table 1.
The list of core-collapse supernovae for which X-ray data were available and used inthis paper. The source of the data is listed, along with the energy range for the luminosity. DG11refers to this paper.SN Name Energy Range (kev) Publication1986J .5-2.5 Houck (2005)1988Z .2-2.0 Schlegel & Petre (2006)1995N .1-2.4 Chandra et al. (2005)1998S .4-2.0 Pooley et al. (2002)1978K .5-2.0 Schlegel et al. (2004); Lenz & Schlegel (2007)1993J .5-2.4 Chandra et al. (2009), DG111979C .3-2.0 Patnaude et al. (2011)2002ap .3-2.0 Sutaria et al. (2003)1994W .1-2.4 Schlegel (1999)1996cr .5-2.0 Bauer et al. (2008)1981K .5-2.0 Immler et al. (2007)1987A .5-2.0 Hasinger et al. (1996); Park et al. (2007)2010F .2-10 Russell et al. (2010)2009mk .2-10 Russell & Immler (2010)2009gj .2-10 Immler & Russell (2009)2009dd .2-10 Immler et al. (2009)2008ij .2-10 Immler et al. (2009)2008ax .2-10 Immler (2008)2008M .2-10 Immler (2010)2006jd .2-10 Immler et al. (2007), DG112006jc .2-10 Immler et al. (2008)2005kd .2-10 Immler et al. (2007); Pooley et al. (2007), DG112005ip .2-10 Immler & Pooley (2007)2004et .4-8 Rho et al. (2007)2004dj .5-8 Pooley & Lewin (2004)2002hi .5-10 Pooley & Lewin (2003)2002hh .4-8 Pooley & Lewin (2002)2001ig .2-10 Schlegel & Ryder (2002)2001gd .3-5 P´erez-Torres et al. (2005)1999em .5-8 Pooley et al. (2002)2003L .5-5 Soderberg et al. (2005)2003bg .3-10 Soderberg et al. (2006)1999gi .3-10 Schlegel (2001)1970G .3-2 Immler & Kuntz (2005)2006bp .2-10 Immler & Brown (2006); Immler et al. (2007)1941C .3-8 Soria & Perna (2008)1959D .3-8 Soria & Perna (2008)1968D .3-8 Soria & Perna (2008)1980K .5-4 Schlegel (1995); Soria & Perna (2008)2010jl 0.2-10 Immler et al. (2010)2010jr 0.2-10 Immler et al. (2010) high radio and X-ray luminosity. In fact, as is evident fromFigure 3, as a class they have the highest X-ray luminosityof all SN types.As shown in Figure 2, 4 of the Type IIns (SN 1986J, SN1988Z, SN 1998S and SN 1995N) have a very steep luminos-ity decline.
SN 1986J
X-ray flux decreases as t − . . We notehere that for 1986J, we have adopted the flux values com-puted by Houck (2005) rather than those by Temple et al.(2005). We recomputed the values for the Chandra observa-tions and find much closer agreement with the former thanthe latter.The steep value of the X-ray decline would suggest thatthe SN is expanding in a medium with a density that de-clines faster than r − . SN 1986J is also well studied in theradio range. VLBI observations (Bietenholz et al. 2010) sug-gest that the shock radius is expanding as R sh ∝ t . . Theluminosity decline and radial expansion then provide two equations which can be used to determine the slope of theejecta n and the slope of the CSM density profile s . It iseasy to show however, that there is no finite solution for n and s using equations 4 and 6. In other words, there is nocompatible solution for the case of an adiabatic shock in SN1986J.If we consider a radiative reverse shock, then it is pos-sible to get a finite solution which gives s = 2 .
72. This ap-pears to be consistent with the luminosity decline, whichindicates a very rapid slope. However, it gives a value of n = 3 .
61, which is not allowed within the Chevalier solu-tion (Chevalier 1982a). Such a low value of n is inconsis-tent with most computed models of SN outer ejecta densityprofiles (Chevalier & Soker 1989; Matzner & McKee 1999).That does not completely exclude this solution. The emis-sion could arise from the reverse shocked material collidingwith the flatter part of the ejecta density profile (i.e. the c (cid:13) , 1–12 Dwarkadas & Gruszko
Figure 1.
The X-ray lightcurves of all observed X-ray SNe found in the literature, with one or more data points. The observed rangeof luminosities spans about 5 orders of magnitude, from 10 to 10 ergs s − , excluding SN 1987A, which is a very low luminosity SNthat was observed only because of its proximity. self-similar solution is no longer valid). It is also possibleto envision scenarios such as the shock becoming suddenlyradiative, implying a transition stage, or expanding into amedium that drops steeply in density.These results seem to point to a complicated emissionstructure. An alternative solution, as suggested by Chugai(1993), is that there are two components to the emission.The basic idea is that of a SN expanding in a clumpy wind,with the clumps having a low volume filling factor. The ex-pansion of the SN in the interclump wind medium is mainlyresponsible for the radio emission and the radial expan-sion measured with VLBI, whereas the X-ray emission arisesfrom radiative shocks within the clumps. However, this stillimplies that the density of the clumps, or the number ofclumps, must decrease faster than r − in order to get theappropriate decline.Even if the SN is expanding into a clumpy wind, it isunlikely that it would have been doing so since it exploded. Ifwe assume the current luminosity decline started right fromthe SN explosion, and extrapolate the soft X-ray luminosityto 10 days after the explosion, we get that it would be about1.5 × ergs s − . This is an extremely large luminosity,especially just in the soft X-ray band, given that we wouldexpect the hard X-ray luminosity to be much larger at thisstage (indeed, at the last Chandra observation, the soft andhard luminosities were comparable). Note that if the SNreally was emitting in X-rays with this luminosity, it would have lost all its kinetic energy in a year at that rate. Evengiven the rate of luminosity decline it would have lost all itsenergy in a few years. It is clear that such a high luminositywould be unsustainable.The first X-ray detection of SN 1986J was made 8.43years after explosion, when the luminosity was almost 10 ergs s − . If we assume that the SN maintained this con-stant luminosity since explosion, it would mean that in thefirst 8.43 years it would have lost a total of 2.5 × ergsjust in the soft X-ray band. The amount lost in hard X-rayswould most likely be greater since the temperature wouldbe higher. The flux at infra-red wavelengths can be up to afactor of 100 larger than that in X-rays, especially at highertemperatures (Dwek et al. 2008), thus leading to an improb-ably high broadband flux. However it is possible that for SNeexpanding in a very dense medium, some of the dust may bedestroyed, and the IR flux may be only a few times largerthan X-rays. The broad-band flux would still be high, butnot impossibly so.A plausible inference is that the average luminosity ofSN 1986J over the first 8.43 years was lower than at 8.43years, and perhaps orders of magnitude lower. At some pointbefore 8 years the X-ray luminosity increased. In terms of theclumpy wind model, this could mean that there were fewerto no clumps in the first few years, and that the number ofclumps increased after a few years. An alternative is thatthe SN shock was evolving in a much lower density region c (cid:13) , 1–12 -rays and Young SNe expansion Figure 2.
Fits to the lightcurves of all X-ray SNe with multiple data points. The slope of the Luminosity v/s time curves, plotted on alog-log scale, is given next to each SN. The fits were calculated using the MPFIT routine in IDL (see text). earlier, and started interacting with a higher density regionat a later time. This would imply a sudden deceleration inthe shock velocity when it began expanding into the highdensity region, which is not seen in the radio VLBI data.We will explore the X-ray emission from SN 1986J in detailin a future paper.
SN 1988Z has an X-ray luminosity that decreases evenfaster than that of SN 1986J. Following the argumentsabove, a plausible model appears to be that of a SN shockwave interacting with a clumpy wind, as suggested byChugai & Danziger (1994). Not surprisingly, extrapolatingback to 10 days, we get an X-ray luminosity of 6.5 × ergs s − . At this luminosity, the SN would lose all its energyin one day, so its clear that the soft X-ray lightcurve couldnot have had the recorded decline right from the time of ex-plosion. Following the line of reasoning above for SN 1986J,it appears most likely that SN 1988Z also had a lower X-ray luminosity in the early years, which increased at a latertime. This then further suggests a lower density medium, orlack of clumps in the ambient medium, during the first fewyears. SN 1995N and
SN 1998S also have luminosity declin-ing faster than t − , although not as fast as 1986J or 1988Z.Nonetheless, it does suggest a medium that decreases fasterthan r − . Extrapolating SN 1995N luminosity back to 10days gives a luminosity of ∼ . × ergs s − , still largerthan the observed X-ray luminosity of any known X-ray SN,and unlikely (although not impossible), following the argu- ments given above for SN 1986J. SN 1998S extrapolatedback gives a luminosity of ∼ . × ergs s − , approachingthe upper limit of known X-ray luminosities. In the case of1998S the decline is not so steep, and it is possible that theluminosity could have declined with this slope since the timeof explosion.The above slopes suggest that the density into whichthe SN is expanding, whether it be due to clumps or a wind,falls faster than r − . While most Type IIns show a very highluminosity, not all of them decline so rapidly. SN 2005kdappears to rise and fall, over a time-period of only a few100 days. SN 2006jd appears to be more or less constantover 2 data points separated by a few 100 days. Neither ofthese would be consistent with an r − density in the am-bient medium. SN 1996cr, which has been studied in de-tail (Bauer et al. 2008; Dwarkadas et al. 2010; Dewey et al.2011), was increasing in X-ray luminosity for several years,before turning over, and is thought to have expanded in alow density region surrounded by a dense shell.It is clear that although there is great diversity, none ofthe Type IIn appear to be evolving into a steady wind withconstant parameters. This SN has more X-ray data than any other except SN1987A. The X-ray and radio emission has been studiedin detail by several authors, but no consensus reached c (cid:13) , 1–12 Dwarkadas & Gruszko
Figure 3.
The light curves of X-ray SNe plotted as a function of the type of SN. Type IIn SNe are the brightest as a group, thereforesuggesting that they interact with regions of higher density. Others show much more diversity, with IIP’s generally having the lowestluminosity as a class, although exceptions exist in all classes. on what kind of medium the SN is expanding in. Oneof the earliest papers which studied the X-ray light-curve(Suzuki & Nomoto 1995) suggested that the density im-mediately around the SN was decreasing as r − . . A sim-ilar result, of a density slope flatter than r − , was foundby Fransson et al. (1996). Following up on a seminal pa-per that interpreted the radio emission of 1993J in thecontext of a steady wind (Fransson & Bj¨ornsson 1998),Fransson & Bj¨ornsson (2005) asserted that both the X-rayand radio lightcurves could be fit by a self-similar expansionfor SN 1993J, with a power-law ejecta expanding into anr − medium. They criticized the hydrodynamic modelling ofSuzuki & Nomoto (1995) for using an ejecta profile that washydrodynamically unstable. However, Nymark et al. (2009),citing the same hydrodynamic models, suggested that theX-ray emission was coming partly from an adiabatic shockexpanding into CNO-enriched ejecta (which was not de-scribed simply by a power-law), and partly from a radiativeshock, with no contribution from the circumstellar shock.The calculations of Chandra et al. (2009) were consistentwith the fact that the emission was dominated by a reverseshock component, but did not need two emitting compo-nents, although they did not study the spectra. The radioand VLBI data has always been contentious, and the twodifferent views are summarized in Bartel et al. (2007) andMart´ı-Vidal et al. (2011).The soft X-ray light-curve for the first 700 days is well fit by a slope β = 0 .
34. This could fit an s = 2 solution if n = 5, but such an ejecta profile is inconsistent with explo-sion models (Suzuki & Nomoto 1995). Otherwise it cannotbe fitted with a steady wind expansion. As Fransson et al.(1996) have shown, for s ∼ . β , thus suggesting that the slope is changing at thistime. A changing density slope was used in Chandra et al.(2009) to fit the hard X-ray light curve. Overall, SN 1993Jdoes not appear to fit the expansion pattern of a shock ex-panding in a steady wind, especially since the slope of theX-ray decay steepens at later times. This SN appears to be expanding with a more or less con-stant luminosity for several years. Patnaude et al. (2011) in-terpret this steady luminosity as evidence for emission froma central black-hole component. Although without a detailedinspection of the spectra, we cannot validate or dispute theirassertion, we do wish to mention here that having a moreor less constant lightcurve is not inconsistent with the cir-cumstellar interaction model. In section 2 we have shownthat for adiabatic shocks for example, n=9, s=1.62 gives aconstant luminosity in the soft X-ray band, while for radia-tive shocks, s = 1 . c (cid:13)000
34. This could fit an s = 2 solution if n = 5, but such an ejecta profile is inconsistent with explo-sion models (Suzuki & Nomoto 1995). Otherwise it cannotbe fitted with a steady wind expansion. As Fransson et al.(1996) have shown, for s ∼ . β , thus suggesting that the slope is changing at thistime. A changing density slope was used in Chandra et al.(2009) to fit the hard X-ray light curve. Overall, SN 1993Jdoes not appear to fit the expansion pattern of a shock ex-panding in a steady wind, especially since the slope of theX-ray decay steepens at later times. This SN appears to be expanding with a more or less con-stant luminosity for several years. Patnaude et al. (2011) in-terpret this steady luminosity as evidence for emission froma central black-hole component. Although without a detailedinspection of the spectra, we cannot validate or dispute theirassertion, we do wish to mention here that having a moreor less constant lightcurve is not inconsistent with the cir-cumstellar interaction model. In section 2 we have shownthat for adiabatic shocks for example, n=9, s=1.62 gives aconstant luminosity in the soft X-ray band, while for radia-tive shocks, s = 1 . c (cid:13)000 , 1–12 -rays and Young SNe expansion a constant flux over an extended period in SN 1979C (andperhaps SN 2006jd) does not contradict the circumstellar in-teraction model, although it does indicate that the evolutionis not into a steady wind. SN 2006jc is an unusual SN that experienced a mass ejec-tion about two years before becoming a SN (Pastorello et al.2007; Foley et al. 2007). The X-ray emission (Immler et al.2008) is consistent with the SN ejecta rising as it impactsthe dense shell resulting from this mass-loss, followed by adecline as the shock crosses the dense region (see for instanceDwarkadas 2005). If it was interacting with an r − wind, itwas only for an extremely short period, but for the mostpart the profile deviates significantly from a steady wind.SN 1987A has been very well studied in the litera-ture. Its proximity, and the availability of the Hubble SpaceTelescope , has allowed us for once to optically observethe interaction. Analysis of the optical, x-ray and radiodata have shown that the SN evolved into a low densitymedium before impacting a higher density ionized HII re-gion (Chevalier & Dwarkadas 1995; Park et al. 2005, 2006,2007; Dwarkadas 2007a,b) followed by a dense shell, partof a bipolar circumstellar nebula. The evolution, and X-rayemission, is summarized in reviews by McCray (1993, 2003,2007).SN 1978K also seems to be continually bright in X-rays.Its luminosity could be considered constant on average, butappears to fluctuate by factors of a few, making it difficult toget a good linear fit. Schlegel (2006) asserts that althoughthere may not be too much luminosity evolution, spectralevolution does exist. The current X-ray light curve thoughappears inconsistent with a steady wind.SN 1970G was discovered only several thousand daysafter explosion. Although it currently has the steepest lu-minosity slope β = 3 .
08, it is not clear what the slope wasover the first 20+ years. Currently the slope does not appearconsistent with interaction with an r − medium.Schlegel (2001) analysed the X-ray emission from TypeIIP SNe, and suggested that they would not be strong X-raysources. This is consistent with the lightcurves in figure 3,which shows that Type IIPs have a low X-ray luminosity.The fits to the slopes of many of these, as well as other SNenot explicitly mentioned above, are theoretically consistentwith expansion within a steady wind. The closest to that ofa steady wind is that of SN 1994I. In most of these cases,there are either too few datapoints, or the fits are not sta-tistically good, so it is hard to judge if they are evolvingin a steady wind over an extended time period. However,Chevalier et al. (2006) have studied the X-ray emission fromType IIP’s assuming they evolve in a steady wind, and theircalculations tend to match the observations. It must be keptin mind that IIP’s evolve from RSGs, which do not have avery high wind velocity, and thus the wind will not extendvery far out from the star, perhaps a few parsecs at most.Thus we would expect that even if the SN shocks were in-teracting with winds, at some point early in their evolution(few hundred years or less) they would run out of wind ma-terial to expand in. In this paper we have plotted the X-ray lightcurves of al-most all published X-ray SNe, in the narrow energy rangesin which they were observed. Furthermore, we have fittedthese lightcurves to a function that goes as t P (1) , and derivedthe value of P (1), which we have compared to theoretical ex-pectations. In many of the cases, and especially for Type IInSNe, we find that the light-curve data in this simple theoryare not consistent with evolution into a steady wind whosedensity decreases as r − . There are of course several limi-tations to this theory. Chevalier & Fransson (2006) suggestthat the x-ray luminosities of type Ib/c SNe can only beexplained by a non-thermal mechanism, either X-ray syn-chrotron or inverse Compton. Our sample does not includeany GRB related 1b/c, and only a few non-GRB 1b/c SNethat have published data. It is thus possible for scenarios toexist where the light curve slopes, although not within therange outlined in §
2, may be consistent with a steady wind.Although such exceptions are possible, it would be unusualto assume that they would apply to all, or even most, SNe.Furthermore, if the latter is indeed true, then it suggeststhat the many tens of papers in the literature that haveused this theory need to be re-evaluated.Our plotted lightcurves are consistent with those ofSchlegel (2006) in those cases where overlap is possible. Theyare inconsistent with those of Immler (2007), who plottedlight curves of all SNe known till then with just the first andlast data point, while asserting that “all other X-ray datapoints are along the extrapolated lines”. As is evident fromfigure 1, this does not seem to represent the available data.Using that assertion, Koss & Immler (2007) went a step fur-ther, calculating the density profile of the medium into whichthe SN is evolving, and showing that the results are consis-tent with a density decline corresponding to a steady wind.Inherent in their calculation is that the SN luminosity is de-creasing as t − , which they take to mean that the ambientdensity is going as r − , although as emphasized in § t − (Pooley et al. 2002; Immler et al. 2002;Immler & Lewin 2003; Immler & Kuntz 2005; Immler 2007;Koss & Immler 2007; Soria & Perna 2008; Miller et al.2010). As shown above, and most clearly in Fransson et al.(1996), the t − dependence for a steady wind is only validover the total X-ray range, not the narrow bands in whichSNe are generally observed. Even if it were valid in the nar-row range, none of the published lightcurves are actuallydecreasing in luminosity as t − , and very few are even close.We caution therefore that the resulting mass-loss rates ob-tained in this manner from the X-ray lightcurves may beincorrect, and not reflective of the true nature of the CSM.If, as the lightcurves appear to indicate, the SNe are notevolving in an r − medium, then the calculated mass-lossrates would need to be re-calibrated. Unfortunately, if thewind is not steady, then the generally used expressions tomeasure the mass-loss rates are no longer valid, and there c (cid:13) , 1–12 Dwarkadas & Gruszko is no simple way to compute the mass-loss rate. Most tech-niques usually yield the combination ˙
M/v w - disentanglingthe magnitude, and time evolution, of either or both param-eters is a difficult task. If the deviation from a steady windis not large, a mass-loss rate obtained by assuming a steadywind may be a good approximation early on, but the dif-ference increases gradually with increasing radius from thecenter of the explosion.An r − density decline is often assumed in calculationsof mass-loss rates from optical observations (Smith et al.2008, 2010; Kiewe et al. 2010). Kiewe et al. (2010) have usedthis in fact to compute the mass-loss rates for 15 type IInSNe, and suggest that they are consistent with LBV pro-genitors. It has not been shown that such a density declineis warranted. Salamanca (2003) pointed out many years agothat the medium around Type IIn SNe does not necessar-ily decrease as r − ; this assertion was repeated for specificindividual cases by Dwarkadas (2011). If the nature of thedensity distribution plays such an important part in deter-mining the mass-loss rate and thereby categorizing the SNprogenitor, it is important that the assumption of a steadywind density decreasing as r − not be made without accom-panying proof.There exist suggestions from other sources that the cir-cumstellar medium in the immediate vicinity of massivestars does not have an r − density profile, or that such aprofile does not extend far out. In their analysis of GRBafterglows, Schulze et al. (2011) find that only a quarter ofthem appear to be evolving in a freely expanding wind, withthe rest appearing to expand in a constant density medium.Furthermore, in all cases except two, they place limits onthe freely expanding wind region of less than 1 pc, and < − profile is indicated.X-ray emission from young SNe, which is mainly ther-mal, has the simplest and most direct dependence on thedensity structure of the surrounding medium, and can beused therefore to most easily infer this density structure. Inorder to improve this analysis and make more detailed cal-culations from SN X-ray lightcurves, it is imperative that wehave detailed lightcurves, with much better time sampling,and over as wide an energy range as possible. Given theavailability of Chandra , XMM-Newton , Suzaku , and
Swift ,and that they should continue operating for many moreyears, it is urgent that we observe as many SNe as possi-ble, and for as long as possible, in X-rays.
ACKNOWLEDGMENTS
VVD would like to profusely thank John Houck and DanDewey (MKI) for help with learning to use the ISIS soft-ware, and Dan for sharing many of his scripts. A lot of theearly observations listed herein are due to Eric Schlegel, andmany of the later ones to Dave Pooley and Stefan Immler,to all of whom we are indebted. We thank the anonymousreferee for a thorough reading of the manuscript and manyinsightful comments. We are grateful to R. Chevalier forcomments on an earlier version of the paper. VVD’s research is supported by grants TM9-0004X (SN 1987A) and GO1-12095A (SN 1993J), both provided by the National Aero-nautics and Space Administration through Chandra Awardsissued by the
Chandra
X-ray Observatory Center, which isoperated by the Smithsonian Astrophysical Observatory forand on behalf of the National Aeronautics Space Adminis-tration under contract NAS8-03060. JG was supported bythe UChicago NSF REU program in summer 2010.
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