X-RAY EMISSION FROM SUPERNOVAE IN DENSE CIRCUMSTELLAR MATTER ENVIRONMENTS: A SEARCH FOR COLLISIONLESS SHOCKS

Circumstellar matter (CSM) around supernova (SN) progenitors may play an important role in the emission and propagation of energy from SN explosions. The interaction of the SN radiation with optically thin CSM shells may generate emission lines, with widths that are representative of the shell velocity or the velocity of the shocked cool gas in the post-shock region, as in Type IIn SNe (SNe IIn; Schlegel 1990; Kiewe et al. 2012; see Filippenko 1997 for a review of SN classification). The interaction of SN ejecta with the CSM can power the light curves of SNe by transformation of the SN kinetic energy into photons. In cases where a considerable amount of optically thin (and ionized) material is present around the exploding star, synchrotron, and free–free radiation can emerge, and inverse-Compton scattering can generate X-ray photons (e.g., Chevalier & Fransson 1994; Horesh et al. 2012; Krauss et al. 2012).

For the Type IIn SN PTF 09uj, Ofek et al. (2010) suggested that a shock breakout can take place in an optically thick wind (see also Grassberg et al. 1971; Falk & Arnett 1977; Chevalier & Irwin 2011; Balberg & Loeb 2011). This will happen if the Thomson optical depth within the wind profile is ≳ c/v_sh, where c is the speed of light and v_sh is the shock speed. Ofek et al. (2010) showed that shock breakout in wind environments produces optical displays that are brighter and have longer timescales than those from the surfaces of red supergiants (e.g., Colgate 1974; Matzner & McKee 1999; Nakar & Sari 2010; Rabinak & Waxman 2011; Couch et al. 2011). Chevalier & Irwin (2011) extended this picture. Specifically, they discussed CSM with a wind profile in which the wind has a cutoff at a distance R_w. If the optical depth at R_w is ≲ c/v_s, then the SN light curve will have a slow decay (e.g., SN 2006gy; Ofek et al. 2007; Smith et al. 2007). If the optical depth at R_w is ≳ c/v_s, then it will have a faster decay (e.g., SN 2010gx; Pastorello et al. 2010a; Quimby et al. 2011b). Moriya & Tominaga (2012) investigated shock breakouts in general wind-density profiles of the form ρ∝r^−w. They suggested that, depending on the power-law index w, shock breakouts in wind environments can produce bright SNe without narrow emission lines (e.g., SN 2008es; Gezari et al. 2009; Miller et al. 2009).

Recently Katz et al. (2011) and Murase et al. (2011) showed that if the progenitor is surrounded by optically thick CSM, then a collisionless shock is necessarily formed during the shock breakout. Moreover, they argued that the energy emitted from the collisionless shock in the form of high-energy photons and particles is comparable to the shock-breakout energy. Furthermore, this process may generate high-energy (≳ 1 TeV) neutrinos. Although Katz et al. (2011) predicted that the photons are generated with energy typically above 60 keV, it is reasonable to assume that some photons will be emitted with lower energy due to reprocessing of photons (see below) and the continuum nature of the radiation. Chevalier & Irwin (2012) showed that Comptonization and inverse-Compton scattering of the high-energy photons is likely to play an important role, and that the high-energy photons will be absorbed.

Svirski et al. (2012) discuss the X-ray emission from collisionless shocks. They show that at early times the X-rays will be processed into the optical regime by the Compton process. Therefore, at early times, the optical emission will be about 10⁴ times stronger than the high-energy emission. With time, the X-ray emission will become stronger, while the optical emission will decay. They conclude that for a CSM with a steady wind profile (w = 2), X-ray emission may peak only at late times, roughly 10–50 times the shock-breakout timescale. The shock-breakout timescale, t_br, is roughly given by the diffusion timescale at the time of shock breakout. This timescale is also equivalent to the radius at which the shock breaks out (r_br) divided by the shock velocity (v_s; Weaver 1976). If the main source of optical photons is due to diffusion of the shock-breakout energy, the SN optical light rise time, t_rise, will be equivalent to the shock-breakout timescale. Therefore, X-ray flux measurements and spectra of SNe embedded in dense CSM starting from the explosion until months or years after maximum light are able to measure the properties of the CSM around the SN progenitors and the progenitor mass-loss history. This unique probe into the final stages of massive star evolution has been only partially exploited, at best.

Herein, we analyze the X-ray data for 28 SNe with light curves that may be powered by a shock breakout from dense CSM, and for which Swift/XRT (Gehrels et al. 2004) observations exist. We use this sample to search for X-ray signatures of collisionless shocks—emission at late times (months to years after peak optical luminosity). We suggest that these signals were observed in several cases, most notably in SN 2010jl (Chandra et al. 2012b). Finally, we review the conditions for a shock breakout in CSM with a wind profile, and we discuss the importance of bound-free absorption and the possibility of detecting radio emission from such SNe.

The structure of this paper is as follows. In Section 2 we present the SN sample, while Section 3 presents the X-ray observations. We review and discuss the model in Section 4, and consider the observations in the context of the model in Section 5. We summarize our conclusions in Section 6.

Our sample is based on SNe found by amateur astronomers and several surveys, including the Lick Observatory Supernova Search (Li et al. 2000; Filippenko et al. 2001), the Catalina Real-time Transient Survey (Drake et al. 2009a), Pan-STARRS1 (PS1; Kaiser et al. 2002), and the Palomar Transient Factory¹⁷ (PTF; Law et al. 2009; Rau et al. 2009). Two SNe, PTF 09drs and PTF 10tel, are reported here for the first time. We note that many of the nearby or luminous SNe found by PTF are also observed by Swift.

We selected a sample of SNe in which the main source of energy may be explained by diffusion of the explosion shock energy through optically thick CSM around the progenitor. First, we include SNe IIn within 200 Mpc. Objects that belong to this class show relatively narrow (intermediate width) hydrogen emission lines, an indication of the presence of optically thin material somewhere around the progenitor. However, it is unlikely that all SNe showing relatively narrow hydrogen emission lines in their spectra are powered mainly by the diffusion of shock energy in an optically thick environment. One reason is that some SNe IIn show X-ray emission near maximum optical light, which is not expected when optically thick CSM is present (see Section 4). Furthermore, Moriya & Tominaga (2012) suggest that not all SNe powered by interaction of the ejecta with slowly moving material will necessarily have narrow emission lines in their spectrum. We note that some of the SNe IIn in our sample are peculiar (e.g., SN 2010jp/PTF 10aaxi; Smith et al. 2012).

Another relevant, but rare, class of objects are SNe Ibn. This class is defined by the lack of hydrogen lines and the presence of narrow helium emission lines. The only SN of this type in our sample is SN 2006jc (Nakano et al. 2006; Foley et al. 2007; Pastorello et al. 2008; Smith et al. 2008).

The third class of SNe we investigate here is the small group of hydrogen-poor superluminous SN (SLSN-I; see review in Gal-Yam 2012). Quimby et al. (2011b) used spectra of several such events found by PTF, at intermediate redshift (z ≈ 0.5), to show that these events, as well as SCP 06F6 (Barbary et al. 2009) and SN 2005ap (Quimby et al. 2007), are spectroscopically similar. This group of SNe continues to grow with new discoveries (e.g., Chomiuk et al. 2011; Leloudas et al. 2012), and their hosts were studied by Neill et al. (2011). Although the nature of these events is not understood (e.g., Kasen & Bildsten 2010), Quimby et al. (2011b) suggested that they may be powered by a pulsational pair-instability SN (Rakavy et al. 1967; Woosley et al. 2007). According to this hypothesis, the SN ejecta interact with a dense shell of material, enriched with intermediate-mass elements, that was expelled by the progenitor during previous explosions (see also Ginzburg & Balberg 2012). This model is tentatively supported by observations of SN 2006oz (Leloudas et al. 2012) that may show a dip in the light curve followed by rebrightening. Moriya & Maeda (2012) interpret the dip as an increase in the opacity due to ionization of the massive shell/CSM as it interacts with the ejecta.

Our sample, presented in Table 1, consists of eight SLSN-I objects, 19 SNe IIn, and a single SN Ibn. We note that the spectra of SNe having PTF names, as well as some other SNe, are available online from the WISeREP¹⁸ Web site (Yaron & Gal-Yam 2012).

Table 1. SN Sample

Name	Type	αJ2000	δJ2000	trise	MR	z	tpeak	NH	LX		FAPmin
		(deg)	(deg)	(day)	(mag)		(MJD)	(1020 cm−2)	(erg s−1)
PTF 09atu	SLSN-I	247.60229	+23.64029	30:	−22.5	0.501	55060	4.05	<1.9 × 1044	0.7	1.00
PTF 09cnd	SLSN-I	243.03725	+51.48782	50	−22.8	0.258	55080	1.67	<8.0 × 1042	0.02	1.00
PTF 09cwl/SN 2009jh	SLSN-I	222.29200	+29.41983	50	−22.5:	0.349	55060	1.51	<1.1 × 1044	0.4	1.00
SN 2010gx/PTF 10cwr	SLSN-I	171.44448	−8.82810	20	−21.7:	0.231	55280	3.78	<9.9 × 1042	0.07	1.00
PTF 10hgi	SLSN-I	249.44601	+6.20898	50	−20.3	0.096	55370	6.06	<5.1 × 1042	0.1	1.00
PTF 11dij	SLSN-I	207.74069	+26.27856	40:	−21.1:	0.143	55690	1.21	<4.6 × 1042	0.06	1.00
PTF 11rks	SLSN-I	24.93962	+29.92417	20	−21.0	0.20	55945	5.27	<5.4 × 1042	0.07	1.00
PS 1-12fo	SLSN-I	146.55379	+19.84131	>14	−21.0:	0.175	55956	2.79	<1.8 × 1043	0.2	1.00
SN 2006jc	Ibn	139.36667	+41.90889	<15	−17.8	0.006	54020	1.00	∼1.5 × 1041	0.04	0.00
PTF 09drs	IIn	226.62567	+60.59427	40:	−17.8:	0.045	55210	1.72	<4.4 × 1042	1.2	1.00
SN 2010jl/PTF 10aaxf	IIn	145.72221	+9.49494	15..23	−20.6	0.011	55500	3.05	∼1.8 × 1041	0.004	0.00
SN 2010jp/PTF 10aaxi	IIn	94.12770	−21.41001	<19	−14.6:	0.01	55520	11.0	<1.2 × 1040	0.06	0.04
SN 2010jj/PTF 10aazn	IIn	31.71774	+44.57156	15..53	−18.0:	0.016	55530	9.38	<1.2 × 1041	0.03	1.00
SN 2010bq/PTF 10fjh	IIn	251.73066	+34.15964	15..45	−18.5	0.032	55310	1.79	<1.2 × 1042	0.2	1.00
PTF 11iqb	IIn	8.52015	−9.70498	10:	−18.4	0.013	55780	2.79	∼7.9 × 1040	0.01	0.00
SN 2007bb	IIn	105.28108	+51.26592	<15	−17.6:	0.021	54192	7.04	<2.8 × 1041	0.09	0.07
SN 2007pk	IIn	22.94613	+33.61503	<14	−17.3:	0.017	54423	4.72	<1 × 1041	0.04	0.00
SN 2008cg	IIn	238.56313	+10.97361	30..60	−19.4:	0.036	54583:	3.65	<2.6 × 1041	0.02	1.00
SN 2009au	IIn	194.94167	−29.60208	⋅⋅⋅	−16.5:	0.009	54901:	6.42	<3.5 × 1040	0.03	0.15
SN 2010al	IIn	123.56629	+18.43839	<35	−16.0:	0.0075	55268:	3.92	∼2.2 × 1041	0.3	0.00
SN 2011ht	IIn	152.04413	+51.84917	50	−16.8	0.004	55880	0.78	∼7.2 × 1039	0.05	0.00
SN 2011hw	IIn	336.56058	+34.21642	⋅⋅⋅	−19.1:	0.023	55883:	10.2	<5.1 × 1040	0.004	1.00
PTF 10tel	IIn	260.37782	+48.12983	17	−18.5	0.035	55450	2.34	<7.2 × 1041	0.1	1.00
SN 2011iw	IIn	353.70083	−24.75044	<40	−18.1:	0.023	55895:	1.61	<1.0 × 1041	0.02	1.00
SN 2005db	IIn	10.36163	+25.49767	<18	−16.8:	0.0153	53570:	4.17	∼5.3 × 1040	0.04	0.00
SN 2005av	IIn	311.15658	−68.75294	<19	−17.8:	0.0104	53453:	4.85	<8.1 × 1039	0.02	1.00
SN 2003lo	IIn	54.27133	−5.03814	⋅⋅⋅	−15.8:	0.0079	53005:	4.87	<6.3 × 1039	0.01	1.00
SN 2002fj	IIn	130.18792	−4.12736	<90	−18.5	0.0145	52532	3.12	<4.9 × 1040	0.007	1.00

Notes. The sample of SNe with Swift X-ray observations. Type refer to SN type, α_J2000 and δ_J2000 are the J2000.0 right ascension and declination, respectively. t_rise is the approximate rise time of the SN optical light curve. The rise time is deduced from various sources including PTF and Katzman Automatic Imaging Telescope (KAIT; Filippenko et al. 2001) photometry and the literature listed in the references. The colon sign indicates an uncertain value. M_R is the approximate absolute R-band magnitude at maximum light (ignoring K-corrections). z refers to the object redshift. If the galaxy is nearby and has a direct distance measurement in the NASA Extragalactic Database (NED), we replaced the observed redshift by the redshift corresponding to the luminosity distance of the galaxy. t_peak is the MJD of maximum light and N_H is the Galactic neutral hydrogen column density for the source position (Dickey & Lockman 1990). L_X is the X-ray luminosity or the 2σ upper limit on the X-ray luminosity in the 0.2–10 keV band. L_X/L_opt is the ratio between the X-ray measurements or limit (L_X) and the peak visible-light luminosity. Finally, FAP_min is the minimum false-alarm probability value over all the observations of the source. Sources with FAP_min < 0.01 indicate a possible detection of an X-ray source at the position of the SN. As discussed in the text, some of these possible detections are chance coincidences or due to emission from the SN host galaxy. References. PTF 09atu: Quimby et al. (2011b). PTF 09cnd: Quimby et al. (2011b); Chandra et al. (2009); Chandra et al. (2010). PTF 09cwl: SN 2009jh; Quimby et al. (2011b); Drake et al. (2009b). SN 2010gx: PTF 10cwr; Mahabal et al. (2010); Quimby et al. (2010a); Pastorello et al. (2010b); Quimby et al. (2011). PTF 10hgi: Quimby et al. (2010b). PTF 11dij: Drake et al. (2011a); Drake et al. (2011b); Quimby et al. (2011c). PTF 11rks: Quimby et al. (2011a). PS1-12fo: Drake et al. (2012); Smartt et al. (2012); Maragutti et al. (2012). PTF 09drs: Reported here for the first time. SN 2010jl: PTF 10aaxf; Newton & Puckett (2010); Stoll et al. (2011). SN 2010jp: PTF 10aaxi; A peculiar SN IIn; Maza et al. (2010); Challis et al. (2010b); Smith et al. (2012). SN 2010jj: PTF 10aazn; Rich (2010b); Silverman et al. (2010a). SN 2010bq: PTF 10fjh; Duszanowicz (2010); Challis et al. (2010a). PTF 11iqb: Parrent et al. (2011); Horesh et al. (2011). SN 2007bb: Joubert & Li (2007); Blondin et al. (2007). t_peak and t_rise are based on unpublished KAIT photometry. SN 2007pk: A peculiar SN IIn (Parisky & Li 2007). t_peak and t_rise are based on unpublished KAIT photometry. SN 2008cg: Drake et al. (2008); Blondin & Calkins (2008); Filippenko et al. (2008); Spectrum is similar to SN 1997cy (Filippenko et al. 2008). SN 2009au: Pignata et al. (2009); Stritzinger et al. (2009). SN 2010al: Spectrum is similar to SN 1983K with He ii, N iii, and H i emission lines; Rich (2010a); Stritzinger et al. (2010); Silverman et al. (2010b). SN 2011ht: Boles et al. (2011); Prieto et al. (2011); Roming et al (2012). SN 2011hw: Dintinjana et al. (2011). PTF 10tel: Reported here for the first time. SN 2011iw: Mahabal et al. (2011). SN 2005db: Blanc et al. (2005); Monard (2005b); Kiewe et al. 2012). SN 2005av: Monard (2005a); Salvo et al. (2005). SN 2003lo: Puckett et al. (2004); Matheson et al. (2004). SN 2002fj: Monard & Africa (2002); Hamuy (2002).

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For each Swift/XRT image of an SN, we extracted the number of X-ray counts in the 0.2–10 keV band within an aperture of 72 (3 pixels) radius centered on the SN position. We chose a small aperture in order to minimize any host-galaxy contamination. We note that this aperture contains ∼37% of the source flux (Moretti et al. 2004). The background count rates were estimated in annuli around each SN, with an inner (outer) radius of 50'' (100''). For each SN that has Swift/XRT observations, we searched for Chandra observations. The Chandra observations were analyzed in a similar manner with an extraction aperture of 2'' and background annuli with an inner (outer) radius of 15'' (40''). All of the Swift/XRT X-ray measurements are listed in Table 2 (the full table is available in the online version). In addition, in Table 2, for each object we give the count rate in up to four superepochs: (1) all of the observations taken prior to maximum light, or discovery date if time of maximum light is not known; (2) all of the observations taken between maximum light and 300 days after maximum light; (3) all of the observations taken more than 300 days after maximum light; and (4) all of the observations at the position of the SN.

In each epoch, and superepoch, we also provide an estimator for the false-alarm probability (FAP), which is the probability that the X-ray counts are due to the X-ray background rather than a source. This probability is estimated as 1 minus the Poisson cumulative distribution to get a source count rate smaller than the observed count rate, assuming the expectancy value of the Poisson distribution equal to the background counts. We note that the median background counts in our background annuli is six counts (within an exposure). However, the background annuli area is about 340 times larger than the photometric aperture area. Therefore, the contribution of the errors in the background to the uncertainty in the source counts is negligible. We note that in some cases X-ray emission from the host galaxy will tend to produce some seemingly significant, but actually "false alarm" detections under these assumptions. Furthermore, many nuclear X-ray sources like active galactic nuclei (AGNs), as well as X-ray sources in general, tend to significantly vary with time (e.g., González-Martín & Vaughan 2012). This fact makes it very hard to distinguish between X-ray emission from an SN and its host galaxy. An example for such confusion is demonstrated in the case of SN 2007pk discussed in this paper.

In cases in which FAP ⩽0.01, we also estimated the 2σ upper limit on the count rate (Gehrels 1986). The count-rate measurements or upper limits are converted to luminosity in the 0.2–10 keV band using the PIMMS¹⁹ web tool and assuming that (1) the aperture in which we extracted the source photometry contains 37% of the source photons (Moretti et al. 2004); (2) Galactic neutral hydrogen column density at the position of the sources as listed in Table 1 (Dickey & Lockman 1990); (3) a spectrum of N_ph(E)∝E^−0.2, where N(E) has units of photons cm⁻² s⁻¹ (motivated in Section 4); and (4) the luminosity distance to each SN calculated using the redshift listed in Table 1 together with H₀ = 70.4 km s⁻¹ Mpc⁻¹, Ω_m = 0.268, Ω_Λ = 0.716, and Ω_K = 0.986 (the third-year WMAP+SNLS cosmology; Spergel et al. 2007).

Several objects listed in Table 2 show count rates which may deviate from zero. Here we discuss the observations of all seven sources that have FAP ⩽0.01 in at least one of the epochs or superepochs. We note that Table 2 contains 305 epochs and superepochs; therefore, we expect about three random false detections. Interpretation of these observations is discussed in Section 5.

SN 2010jl/PTF 10aaxf (Figure 1). This SN has a large number of Swift/XRT observations, as well as Chandra/ACIS-S observations in five epochs (Chandra et al. 2012b), of which three are public (PIs: D. Pooley; Tremonti). The host, SDSSJ094253.43+092941.9, is an irregular star-forming galaxy. The binned Swift/XRT and Chandra light curves, as well as the PTF R-band light curve, are presented in Figure 1.

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SN 2006jc (Figure 2). This is the only SN in our sample that belongs to the rare class of Type Ibn SNe. SN 2006jc has a large number of Swift/XRT and Chandra observations. The SN is detected on multiple epochs and its X-ray light curve is presented in Figure 2 (see also Immler et al. 2008). It was detected in X-rays soon after maximum optical light and reached a maximum X-ray luminosity of about 1.5 × 10⁴⁰ erg s⁻¹ at ∼100 days after maximum optical light, ≳ 6 times the SN rise time. SN 2006jc was observed by Chandra on several occasions. We reduced a 55 ks Chandra observation with 306 photons at the SN location taken 87 days after maximum light. Given the limited number of photons we did not attempt to fit complex models. We found that the spectrum is well fitted by an N_ph(E)∝E^−0.2 power law and with negligible absorbing column density. The spectra and the best-fit model are presented in Figure 3. Regardless of the exact spectral shape, the spectrum is hard. Marginalizing over all the free parameters, we find a 2σ upper limit of N_H < 1.26 × 10²¹ cm⁻², in excess of the Galactic column density.

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SN 2011ht (Figure 4). This SN took place about 21'' from the center of UGC 5460. It was observed on multiple epochs using Swift/XRT, and Roming et al. (2012) reported a detection of an X-ray source at the SN position. The binned Swift/XRT X-ray light curve of this SN is shown in Figure 4. Apparently the light curve rises, peaks ∼40 day after maximum optical light, and then declines. However, the uncertainties in the flux measurements are large and the light curve is consistent with being flat (i.e., a best-fit flat model gives χ²/dof = 1.23/4). Moreover, recently Pooley (2012) reported on a 9.8 ks Chandra observation²⁰ of this SN. He argued that the emission detected by Roming et al. (2012), which is shown in Figure 4, is from a nearby source found 47 from the SN location.

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SN 2010al (Figure 5). This SN was found 12'' from the center of the spiral galaxy UGC 4286. It was observed on multiple epochs using Swift/XRT with a total integration time of 35 ks, and is detected in the combined image with a mean luminosity of ∼7 × 10³⁹ erg s⁻¹. Figure 5 presents the binned Swift/XRT light curve. Although the light curve peaks around 30 days after maximum light, it is consistent with being flat (i.e., a best-fit flat model gives χ²/dof = 0.15/2).

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SN 2005db. This SN was observed on three epochs, about two years after maximum light (676–695 days), using Swift/XRT. The combined image, with an exposure time of 13.6 ks, shows a faint source (five photons) with an FAP of 2 × 10⁻⁴ per trial. However, given the fact that we have 305 observations, the FAP over all the trials is only about 0.06. Using the Galactic column density (Table 1) and assuming a power-law spectrum N_ph(E)∝E^−0.2, the unabsorbed flux is (1.97^+1.7_−0.72) × 10⁴⁰ erg s⁻¹. Chandra observed this target twice at 722.7 and 1051.4 days after maximum light (PI: D. Pooley), with integrations of 3.0 and 5.0 ks, respectively. Using the same assumptions as above, we put a 2σ upper limit on the unabsorbed flux of 1.4 × 10⁴⁰ erg s⁻¹ for both epochs. To conclude, given the uncertainties, the Chandra upper limits are consistent with the possible Swift detection. However, given that this source has a single detection, we cannot firmly conclude that the detection is real.

PTF 11iqb. This SN has multi-epoch Swift/XRT observations taken between about −13 and 28 days relative to maximum light. The SN is detected in a single epoch ∼24 days after maximum light, with an FAP of 1.4 × 10⁻³ per trial. However, given that we are reporting 305 individual X-ray observations, the FAP over all the trials is 0.45. The SN was not detected at the last epoch, 28 days after maximum light.

SN 2007pk (Figure 6). This SN has a large number of Swift/XRT observations, as well as a Chandra observation (PI: D. Pooley). Immler et al. (2007) reported a tentative detection in the images taken between MJD 54417.09 and 54420.04. The light curve of the source extracted at the SN position is shown in Figure 6. The light curve shows a brightening, with a peak around MJD 54461, and a full width at half-maximum intensity of about 40 days. However, the SN is about 7'' from the center of the spiral host galaxy, NGC 579, and the centroids of the Swift/XRT positions in individual exposures are clustered around the galaxy nucleus, rather than at the SN position. We note that emission from the center of NGC 579 is clearly detected in the Chandra observation and that there is some emission at the source position. However, the latter may be due to diffuse emission from NGC 579. Therefore, without conclusive evidence that the emission is from the SN, here we assume that the observed flare as well as the quiescent X-ray emission from the position of the source is due to AGN activity in NGC 579. In Table 1, we adopted an upper limit on the X-ray luminosity of SN 2007pk, which is based on the average luminosity observed from the direction of the source, presumably due to AGN activity.

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Several recent works discuss the possibility of detecting X-ray emission from SN collisionless shocks in optically thick wind environments (Katz et al. 2011; Murase et al. 2011; Chevalier & Irwin 2012; Svirski et al. 2012). Here, we review the main processes relevant to shock breakout in wind-profile CSM (Section 4.1), emission from collisionless shocks including the importance of bound-free absorption (Section 4.2), and the possibility of detecting radio emission (Section 4.3). In Section 5 we discuss our observations in the context of this model.

4.1. Shock-breakout Conditions in Wind-profile CSM

Here, we assume that the CSM around the progenitor has a wind-density profile ρ = Kr⁻², where is the mass-loading parameter, is the progenitor mass-loss rate, and v_w is the progenitor wind speed. The Thomson optical depth, τ, due to an ionized progenitor wind between the observer and a spherical surface at radius r from the star center is

Here κ_0.34 is the opacity in units of 0.34 cm² g⁻¹, is the mass-loss rate in units of 0.1 M_☉ yr⁻¹, v_{w, 10} is the wind speed in units of 10 km s⁻¹, and r₁₅ is the radius in units of 10¹⁵ cm. We note that this relation is correct up to a factor of order unity (see Balberg & Loeb 2011). The photons in the radiation-dominated and radiation-mediated shock from the SN explosion break out when τ ≈ c/v_s (e.g., Weaver 1976; Ofek et al. 2010), where c is the speed of light and v_s is the shock velocity. At this optical depth, the photon diffusion time becomes shorter than the hydrodynamical timescale (i.e., r/v_s) and the photons can diffuse outward faster than the ejecta. Therefore, the condition for the shock breakout to take place in a steady-wind environment (w = 2) is

where τ₃₀ is the Thomson optical depth in units of 30 and r_☉ is the radius in units of the solar radius.

Figure 7 shows the radius versus the mass-loading parameter at which τ ≈ 30 (Equation (2); i.e., v_s = 10⁴ km s⁻¹; solid black line). For example, this plot suggests that the critical mass-loading, above which the shock will break out in the wind environment, is ∼6 × 10⁻⁴ M_☉ yr⁻¹ v⁻¹_{w, 10} for a 500 R_☉ red supergiant. Assuming v_s = 10⁴ km s⁻¹, systems found above the solid line will have a shock breakout in a wind profile (the two cases discussed by Chevalier & Irwin 2011). Objects found in regions below the τ ≈ 2/3, black dashed-dotted line, will have a shock breakout within the stellar surface and the wind will not influence the diffusion of energy from the shock breakout. Finally, systems below the solid line (τ ≈ 30) and above the dashed-dotted line (τ ≈ 2/3) will have a shock breakout below the stellar surface, but the wind can play a role in the diffusion of the shock energy (e.g., Nakar & Sari 2010).

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We note that, in order to form an SN IIn, we require optically thin material, which is ionized by the SN radiation field. Therefore, we speculate that SNe IIn can be found below and above the τ ≈ 2/3 line, and that not all SNe IIn are powered by shock breakout in dense CSM environments.

4.2. X-Ray Emission from Collisionless Shocks

Katz et al. (2011) showed that if the shock width (Δr) at radius r is on the order of r (i.e., the Thomson optical depth varies on scales on the order of the radius r), the radiation-mediated and radiation-dominated shock will transform into a collisionless shock, and hard X-ray photons will be generated. It is reasonable to assume that some of this energy will be produced in the 1–10 keV X-ray regime. We note that the exact spectrum was not calculated self-consistently and, therefore, is not known.

Chevalier & Irwin (2012) and Svirski et al. (2012) showed that, during the first several shock-breakout timescales after the shock breakout, the optical depth is too large for the hard X-rays to escape. They found that the most efficient processes in blocking the hard X-rays (∼100 keV) are likely (1) cooling of the electrons by inverse-Compton scattering on soft photons generated by the pre-shocked material and (2) Compton scattering. On average, for each Compton scattering, the photon loses a fraction of its energy which is comparable to 4k_BT_e/(m_ec²) (e.g., Lang 1999). Here k_B is the Boltzmann constant, T_e is the electron temperature, and m_e is the electron mass. Svirski et al. (2012) argued that when the Thomson optical depth declines to τ ≈ 5, the hard X-ray emission (∼100 keV) will be Comptonized to the 1–10 keV X-ray band and may diffuse out of the CSM. Since the optical depth in a wind profile (w = 2) decreases as r⁻¹ (Equation (1)), the collisionless-shock signature will be observable in the X-ray regime only when the optical depth decreases by an order of magnitude (i.e., the shock radius increases by an order of magnitude). Given that the shock velocity falls as t^−1/5, they argued that this should happen roughly between 10 and 50 times the shock-breakout timescale. For reference, we show the τ = 5 line in Figure 7 (dashed line, assuming v_s = 10⁴ km s⁻¹). Such late-time emission may be relevant only if the collisionless shock is still important at late times and if the Comptonization remains the dominant process.

Chevalier & Irwin (2012) consider the effect of bound-free absorption. Since above 0.5 keV, metals with a high ionization potential dominate the bound-free absorption, full ionization is required in order to avoid absorption by this process. They argued that an ionization parameter of ∼1000 is needed to achieve full ionization (including the metal atoms' inner electrons). They estimate that full ionization is achieved for shocks with velocity v_s ≳ 10⁴ km s⁻¹. In order to estimate the effect of bound-free absorption, we need to evaluate the density of the CSM.

Assuming a hydrogen-rich material, the particle density in a wind profile is given by

where 〈μ_p〉 is the mean number of protons per particle (mean molecular weight). For our order-of-magnitude calculation, we assume 〈μ_p〉 = 1. In a wind profile, the column density between the radius r and the observer is

Assuming the gas in the pre-shocked wind is neutral, the bound-free optical depth in the 0.03–10 keV region is roughly given by (e.g., Behar et al. 2011)²¹

where σ(E) is the bound-free cross section as a function of energy E and E₁ is the energy in keV. This approximation is valid when the material is neutral. However, since above ∼0.5 keV metals with a high ionization potential dominate the absorption, this formula is still valid, to an order of a magnitude, above 0.5 keV when some (or even one) of the inner electrons of the metals are bound. In Figure 7 we show the lines at which τ_bf ≈ 1 at 1 keV and 10 keV, and at which τ_bf ≈ 30 at 1 keV. Comparison of Equations (1) and (5) suggests that at the time of shock breakout the bound-free cross section in the ∼0.5–8 keV range is larger than the Thomson cross section. We note that this may modify the properties of the shock breakout and its spectrum. Moreover, the τ_bf = 1 line at 1 keV is located far below the τ = 5 line. This suggests that if the pre-shocked wind is not completely ionized (e.g., v_s ≲ 10⁴ km s⁻¹), then soft (≲ 1 keV) X-ray emission is not expected in the simple case of a spherically symmetric wind (w = 2) profile, even at late times. Moreover, the τ_bf = 1 at 10 keV line is located slightly below the τ = 5 line. Therefore, bound-free absorption is likely important even at late stages. This may indicate that ∼10 keV X-rays may escape the wind on a timescale somewhat longer than suggested by Svirski et al. (2012), and that observations at energies above 10 keV may be more effective (e.g., by the NuSTAR mission; Harrison et al. 2010).

All of the order-of-magnitude calculations presented so far assume a wind-density profile with w = 2. However, we note that if the CSM profile falls faster than r⁻², or alternatively if the wind is not spherically symmetric or is clumpy, then the column density may fall faster than r⁻¹ in some directions (e.g., Equation (4)), and it will enable the X-rays to escape earlier than predicted by Svirski et al. (2012) for the w = 2 case.

So far we have discussed the emission of X-rays from optically thick environments. However, X-rays can also be generated in optically thin environments. Following Immler et al. (2008), the X-ray emission from an optically thin region is given by

where Λ(T) is the effective cooling function in the 0.2–10 keV range. Assuming optically thin thermal plasma with a temperature in the range 10⁶–10⁸ K (Raymond et al. 1976), we adopt a value of Λ(T) ≈ 3 × 10⁻²³ erg cm³ s⁻¹. Substituting Equation (3) into Equation (6) we get

Figure 7 also shows lines of equal optically thin X-ray emission. They are plotted only to the right-hand side of the τ ≈ 2/3 line, being relevant only for optically thin regions. This suggests that in the case of a shock breakout in an optically thick CSM (τ ≳ c/v_s) with a wind profile, the optically thin X-ray emission will be generated at late times roughly equal to c/v_s times the shock breakout timescale. We note that, in a wind profile, X-ray emission from optically thin material is expected to decay with the radius and therefore with time (see Figure 7).

4.3. Radio Emission from Collisionless Shocks

The shock going through the CSM may generate synchrotron radiation peaking at radio frequencies (e.g., Slysh 1990; Chevalier & Fransson 1994; Chevalier 1998; Horesh et al. 2012; Krauss et al. 2012; Katz 2012). However, if the material is ionized or partially ionized then the free–free optical depth may block this radiation. In order to test if a radio signature is expected, we need to estimate the free–free optical depth (e.g., Chevalier 1981) which, for a ionized CSM with a wind profile, is given by (Lang 1999, Equation (1.223))

where ν₁₀ is the frequency in units of 10 GHz. The free–free optical depth is so large that radio emission is not expected. However, if in some regions the CSM density profile falls significantly faster than r⁻², then the free–free absorption may be low enough for radio emission (e.g., synchrotron) to escape the CSM. We predict that if the CSM is ionized, then due to the effect of free–free absorption, the synchrotron radio emission generated in the shocked CSM may have a relatively steep radio spectrum. Therefore, it is preferable to search for this emission at high frequencies and late times after maximum light. However, the existence of radio emission is likely to be very sensitive to the exact properties of the CSM, such as density profile, symmetry, and homogeneity. We speculate that good candidates for radio emission will be SNe in which the wind filling factor is low, or asymmetric, or alternatively when the wind is ejected in a relatively short eruption, and therefore may have a steep density profile (see Section 5).

We note that Van Dyk et al. (1996) presented a search for radio emission among 10 SNe IIn. None of the SNe in their sample was detected at radio wavelengths, but these observations were conducted 2–14 yr after the SN explosion. However, some SNe IIn were detected as bright radio sources a few years after maximum light. Examples include SN 1986J (Rupen et al. 1987; Leibundgut et al. 1991b) and SN 1978K (Ryder et al. 1993; Chugai et al. 1995).

As shown in Table 2 and Figures 1–5, several SNe in our sample show X-ray emission in the 0.2–10 keV range. Some SNe are presumably detected (and maybe peaking) in X-rays near maximum optical light (e.g., SN 2011ht; SN 2010al). However, the X-ray luminosity of SN 2011ht (see Roming et al. 2012) and SN 2010al at maximum visible light is about 0.05 and 0.3 (respectively) of their visible-light luminosity. These X-ray luminosities are higher than predicted by Svirski et al. (2012; X-rays 10⁻⁴ of optical) for the CSM shock-breakout case. Moreover, although the X-ray light curves are consistent with a nonvariable luminosity, it is possible that they are peaking near maximum optical light. Therefore, we suggest that the optical light curves of SN 2011ht and SN 2010al, which are SNe IIn, are likely not powered by a shock breakout in CSM.

As previously reported, SN 2010jl (Chandra et al. 2012b) and SN 2006jc (Immler et al. 2007) are detected in X-rays and are peaking at late times, respectively ≳ 10 t_rise and ≳ 6 t_rise. Moreover, the X-ray luminosity at maximum visible light is about 10⁻³ of the visible-light luminosity. This is roughly consistent with the predictions of Svirski et al. (2012). We discuss these SNe in detail in Sections 5.1 and 5.2.

Two other SNe in our sample, PTF 11iqb and SN 2005db, have marginal X-ray detections. Therefore, we cannot make any firm conclusion regarding the reality and nature of this emission.

As indicated in the column L_X/L_opt in Table 1, the rest of the SNe in our sample, including all of the SLSN-I events, do not have late-time observations and/or sufficiently deep limits to evaluate their nature. Our upper limits are mostly obtained at early times (≲ 3 t_rise) after the SN explosion, or at very late times (≳ 37 t_rise). We note that all of the observations of the hydrogen-poor luminous SNe were obtained at ≲ 2 t_rise after optical maximum light.

Recently, Chandra et al. (2012a) reported on X-ray and radio observations of another Type IIn event, SN 2006jd. This event is listed as an SN IIb in the IAUC SN list²² and, therefore, was not included in our sample. We note that the X-ray observations started about a year after the explosion, so there is no measurement of L_X/L_opt during optical maximum light.

We conclude that deeper X-ray observations, over longer periods of time after maximum optical light, are required in order to understand the nature of SN IIn and SLSN-I events. The current null detection of hydrogen-poor luminous SNe in X-rays cannot be used to reject the CSM-interaction model proposed by Quimby et al. (2011b).

5.1. SN 2010jl (PTF 10aaxf)

5.2. SN 2006jc

We present a search for X-ray emission from 28 SNe in which it is possible that the shock breakout took place within a dense CSM. Most SNe have been observed with X-ray telescopes only around maximum optical light. SNe in our sample that have clear X-ray detections include SN 2006jc (Immler et al. 2008), SN 2010jl (Chandra et al. 2012b), SN 2011ht (Roming et al. 2012), and SN 2010al. Two additional objects, PTF 11iqb and SN 2005db, have questionable detections. The SNe in our sample that do have late-time observations were either also detected at early times or observed serendipitously at very late times. In that respect, our first conclusion is that a search for X-ray emission both at early and late times from SNe is essential for constraining the properties of the CSM around their progenitors.

Our analysis suggests that some SNe IIn/Ibn, most notably SN 2010jl, have optical light curves that are likely powered by a shock breakout in CSM, while some other SNe IIn do not. However, for most of the SNe in our sample, including all of the SLSN-I events, the observations are not conclusive. Specifically, the lack of X-ray detection of SLSN-I events cannot rule out the interaction model suggested by Quimby et al. (2011b; see also Ginzburg & Balberg 2012). We conclude that deeper observations at later times are required in order to further test this model and to estimate the fraction of SNe IIn which are powered by optically thick emission.

Given the limits found in this paper and our current understanding of these events, it will be worthwhile to monitor SNe IIn (as well as other classes of potentially interacting SNe; e.g., SNe IIL) with X-ray and radio instruments at timescales ≳ 10 times the rise time of the SN. In most cases presented in this paper, the SN rise time is in the range 10–50 days. Therefore, the recommended timescale to conduct X-ray and radio observations is between three months and two years after the SN maximum light. Given the X-ray luminosities reported in Table 1, we suggest that a luminosity sensitivity of better than ∼10⁴¹ erg s⁻¹ is required in order to detect X-ray emission from these SNe.

We argue that in some cases bound-free absorption will play an important role at early and late times. Therefore, observations with the recently launched Nuclear Spectroscopic Telescope Array (NuSTAR; Harrison et al. 2010) in the 6–80 keV band may be extremely useful to test the theory and to study the physics of these collisionless shocks. Moreover, in the cases where bound-free absorption is important (e.g., v_s ≲ 10⁴ km s⁻¹; Chevalier & Irwin 2012), the spectral X-ray evolution as a function of time can be use to probe the column density above the shock at any given time, and to deduce the density profile outside the shocked regions. We also argue that in some cases, if the CSM has a steep density profile (e.g., SN 2010jl), it may be possible to detect radio emission.

Finally, we note that Katz et al. (2011) and Murase et al. (2011) predict that the collisionless shocks will generate TeV neutrinos. The detection of such neutrinos using IceCube (Karle et al. 2003) will be a powerful tool to test this theory and explore the physics of collisionless shocks.

We thank Ehud Nakar, Boaz Katz, and Nir Sapir for many discussions, and the anonymous referee for constructive comments. This paper is based on observations obtained with the Samuel Oschin Telescope as part of the Palomar Transient Factory project, a scientific collaboration between the California Institute of Technology, Columbia University, Las Cumbres Observatory, the Lawrence Berkeley National Laboratory, the National Energy Research Scientific Computing Center, the University of Oxford, and the Weizmann Institute of Science. E.O.O. is incumbent of the Arye Dissentshik career development chair and is grateful to support by a grant from the Israeli Ministry of Science. M.S. acknowledges support from the Royal Society. A.C. acknowledges support from LIGO, which was constructed by the California Institute of Technology and the Massachusetts Institute of Technology with funding from the National Science Foundation and operates under cooperative agreement PHY-0757058. S.R.K. and his group are partially supported by the NSF grant AST-0507734. A.G. acknowledges support by the Israeli, German–Israeli, and the U.S.–Israel Binational Science Foundations, a Minerva grant, and the Lord Sieff of Brimpton fund. The National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, provided staff, computational resources, and data storage for the PTF project. P.E.N. acknowledges support from the U.S. Department of Energy Scientific Discovery through Advanced Computing program under contract DE-FG02-06ER06-04. J.S.B.'s work on PTF was supported by NSF/OIA award AST-0941742 ("Real-Time Classification of Massive Time-Series Data Streams"). L.B. is supported by the NSF under grants PHY 05-51164 and AST 07-07633. M.M.K. acknowledges generous support from the Hubble Fellowship and Carnegie-Princeton Fellowship. A.V.F.'s supernova group at UC Berkeley is supported by Gary & Cynthia Bengier, the Richard & Rhoda Goldman Fund, the Christopher R. Redlich Fund, the TABASGO Foundation, and NSF grants AST-0908886 and AST-1211916. KAIT and its ongoing operation were made possible by donations from Sun Microsystems, Inc., the Hewlett-Packard Company, AutoScope Corporation, Lick Observatory, the NSF, the University of California, the Sylvia & Jim Katzman Foundation, and the TABASGO Foundation.