INVERSE COMPTON X-RAY EMISSION FROM SUPERNOVAE WITH COMPACT PROGENITORS: APPLICATION TO SN2011fe

Over the past two decades, the utility of Type Ia supernovae (SNe Ia) as standardizable candles for tracing the expansion history of the universe has been underscored by the increasing resources dedicated to optical/near-IR discovery and follow-up campaigns (Riess et al. 1998; Perlmutter et al. 1999). At the same time, the nature of their progenitor system(s) has remained elusive, despite aggressive studies to unveil them (see, e.g., Hillebrandt & Niemeyer 2000). The second nearest Ia SN discovered in the digital era, SN 2011fe (Nugent et al. 2011b) located at d_L = 6.4 Mpc (Shappee & Stanek 2011), represents a natural test bed for a detailed SN Ia progenitor study.²¹ The best studied Type Ia SN at early times before SN 2011fe, SN 2009ig, demonstrated how single events can provide significant insight into the properties of this class of explosions (Foley et al. 2012).

The fundamental component of SN Ia progenitor models is an accreting white dwarf (WD) in a binary system. Currently, the most popular models include (1) a single-degenerate (hereafter SD) scenario in which a massive WD accretes material from a H-rich or an He-rich companion, potentially a giant, a subgiant, or a main-sequence star (Whelan & Iben 1973; Nomoto 1980). Mass is transferred either via Roche-lobe overflow (RLOF) or through stellar winds. Alternatively, (2) models invoke a double sub-M_Ch WD binary system that eventually merges (double-degenerate model, DD; Iben & Tutukov 1984; Webbink 1984).

In SD models, the circumbinary environment may be enriched by the stellar wind of the donor star or through non-conservative mass transfer in which a small amount of material is lost to the surroundings. Winds from the donor star shape the local density profile as ρ_CSM∝R⁻² over a ≲ 1 parsec region encompassing the binary system. Theoretical considerations indicate that the wind-driven mass-loss rate must be low, since an accretion rate of just ∼3 × 10⁻⁷ M_☉ yr⁻¹ is ideal for the WD to grow slowly up to M_Ch and still avoid mass-losing nova eruptions (steady burning regime; Nomoto et al. 1984). Strong evidence for the lack of a wind-stratified medium and/or the detection of a constant local density (with a typical interstellar medium (ISM) density of n_CSM ≈ 0.1–1 cm⁻³) may instead point to a DD model.

Arising from the interaction of the SN shock blast wave with the circumbinary material, radio and X-ray observations can potentially discriminate between the two scenarios by shedding light on the properties of the environment, shaped by the evolution of the progenitor system (see, e.g., Boffi & Branch 1995; Eck et al. 1995). Motivated thus, several dozen SNe Ia at distances d ≲ 200 Mpc have been observed with the Very Large Array (Panagia et al. 2006; Hancock et al. 2011; A. Soderberg, in preparation), the Chandra X-ray Observatory (Hughes et al. 2007), and the Swift X-Ray Telescope (XRT; Immler et al. 2006; Russell & Immler 2012) revealing no detections to date.²² These limits were used to constrain the density of the circumbinary material, and in turn the mass-loss rate of the progenitor system. However, these data poorly constrain the WD companion, due in part to the limited sensitivity of the observations (and the distance of the SNe). The improved sensitivity of the Expanded Very Large Array coupled with a more detailed approach regarding the relevant radio and X-ray emission (and absorption) processes in Type Ia supernovae, has enabled the deepest constraints to date on a circumbinary progenitor as discussed in our companion paper on the recent Type Ia SN 2011fe/ PTF11kly (Chomiuk et al. 2012; see also Horesh et al. 2012).

Here, we report a detailed panchromatic study of SN 2011fe bridging optical/UV and gamma-ray observations. Drawing from observations with the Swift and Chandra satellites as well as the Interplanetary Network (IPN; Hurley 2010), we constrain the properties of the bulk ejecta and circumbinary environment through a self-consistent characterization of the dynamical evolution of the shockwave. First, we present optical/UV light curves for the SN indicating that the object appears consistent with a "normal" SN Ia. Next we discuss deep limits on the X-ray emission in the month following the explosion. We furthermore report gamma-ray limits (25–150 keV) for the shock breakout pulse. In the Appendix, we present an analytic generalization for the inverse Compton (IC) X-ray luminosity expected from hydrogen-poor SNe that builds upon previous work by Chevalier & Fransson (2006) and Chevalier et al. (2006) but is broadly applicable for a wide range of shock properties, metallicities, photon temperatures, and circumstellar density profiles (stellar wind or ISM; see the Appendix). We apply this analytic model to SN 2011fe to constrain the density of the circumbinary environment, and find that our limits are a factor of ∼10 deeper than the results recently reported by Horesh et al. (2012).

Observations are described in Section 2; limits on the SN progenitor system from X-ray observations are derived and discussed in Section 3 using the IC formalism from the Appendix. We combine our radio (Chomiuk et al. 2012) and X-ray limits to constrain the post-shock energy density in magnetic fields in Section 4, while the results from the search of a burst of gamma-ray radiation from the SN shock breakout is presented in Section 5. Conclusions are drawn in Section 6.

SN 2011fe was discovered by the Palomar Transient Factory on 2011 August 24.167 UT and soon identified as a very young Type Ia explosion in the Pinwheel galaxy (M101; Nugent et al. 2011a). From early-time optical observations, Nugent et al. (2011b) were able to constrain the SN explosion date to August 23, 16: 29 ± 20 minutes (UT). The SN site was fortuitously observed both by the Hubble Space Telescope and by Chandra on several occasions prior to the explosion in the optical and X-ray band, giving the possibility to constrain the progenitor system (Li et al. 2012; Liu et al. 2012). Very early optical and UV photometry has been used by Brown et al. (2011) and Bloom et al. (2012) to infer the progenitor and companion radius and nature, while multi-epoch high-resolution spectroscopy taken during the evolution of the SN has been employed as a probe of the circumstellar environment (Patat et al. 2011b). Limits on the circumstellar density have been derived from deep radio observations in our companion paper (Chomiuk et al. 2012), where we consistently treat the shock parameters and evolution. Here we study SN 2011fe from a complementary perspective, bridging optical/UV, X-ray, and gamma-ray observations.

Swift observations were acquired starting from August 24, 1.25 days since the onset of the explosion. Swift-XRT data have been analyzed using the latest release of the HEASOFT package at the time of writing (v11). Standard filtering and screening criteria have been applied. No X-ray source consistent with the SN position is detected in the 0.3–10 keV band either in promptly available data (Horesh et al. 2012; Margutti & Soderberg 2011b) or in the combined 142 ks exposure covering the time interval 1–65 days (see Figure 1). In particular, using the first 4.5 ks obtained on August 24, we find a point-spread function (PSF) and exposure-map-corrected²³ 3σ count-rate limit for the undetected SN ≲  4 × 10⁻³ counts s⁻¹. For a simple power-law spectrum with photon index Γ ∼ 2 and Galactic neutral hydrogen column density $\rm {NH}=1.8\times 10^{20}\,\rm {cm^{-2}}$ (Kalberla et al. 2005) this translates into an unabsorbed 0.3–10 keV flux F = 1.5 × 10⁻¹³ erg s⁻¹ cm⁻² corresponding to a luminosity L = 7 × 10³⁸ erg s⁻¹ at a distance of 6.4 Mpc (Shappee & Stanek 2011). Collecting data between 1 and 65 days after the explosion (total exposure of 142 ks) we obtain a 3σ upper limit of 2 × 10⁻⁴ counts s⁻¹ (F = 7.4 × 10⁻¹⁵ erg s⁻¹ cm⁻² and L = 3.6 × 10³⁷ erg s⁻¹). Finally, extracting data around maximum light (the time interval 8–38 days), the X-rays are found to contribute less than 3 × 10⁻⁴ counts s⁻¹ (3σ limit and total exposure of 61 ks) corresponding to F = 1.1 × 10⁻¹⁴ erg s⁻¹ cm⁻² and L = 5.9 × 10³⁷ erg s⁻¹.

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We observed SN 2011fe with the Chandra X-ray Observatory on August 27.44 UT (day 4 since the explosion) under an approved DDT proposal (PI: Hughes). Data have been reduced with the CIAO software package (version 4.3), with calibration database CALDB (version 4.4.2). We applied standard filtering using CIAO threads for ACIS data. No X-ray source is detected at the SN position during the 50 ks exposure (Hughes et al. 2011), with a 3σ upper limit of 1.1 × 10⁻⁴ counts s⁻¹ in the 0.5–8 keV band, from which we derive a flux limit of 7.7 × 10⁻¹⁶ erg s⁻¹ cm⁻² corresponding to L = 3.8 × 10³⁶ erg s⁻¹ (assuming a simple power-law model with spectral photon index Γ = 2). 3σ upper limits from Swift and Chandra observations are shown in Figure 2.

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The SN was clearly detected in Swift-UVOT observations. Photometry was extracted from a 5'' aperture, closely following the prescriptions by (Brown et al. 2009; see Figure 2). Pre-explosion images of the host galaxy acquired by UVOT in 2007 were used to estimate and subtract the host galaxy light contribution. Our photometry agrees (within the uncertainties) with the results of Brown et al. (2011). With respect to Brown et al. (2011) we extend the UVOT photometry of SN 2011fe to day ∼60 since the explosion. Due to the brightness of SN 2011fe, u, b, and v observations strongly suffer from coincidence losses (Breeveld et al. 2010) around maximum light (see Brown et al. 2011 for details): supernova templates from Nugent et al. (2002) were used to fit the u and b light curves and infer the SN luminosity during those time intervals in the u and b bands. For the v band, it was possible to (partially) recover the original light curve applying standard coincidence loss corrections: however, due to the extreme coincidence losses, our v-band light curve may still provide a lower limit for the real SN luminosity in the time interval 8–37 days since the explosion. In Figure 2, we present the Swift-UVOT six-filter light curves, and note that the re-constructed v band is broadly consistent with the Nugent template.²⁴ We adopted a Galactic reddening of E(B − V) = 0.01 (Schlegel et al. 1998).

In the case of the "golden standard," Ia SN 2005cf (which is among the best studied Ia SNe), the V band is found to contribute ∼20% to the bolometric luminosity (Wang et al. 2009), with limited variation over time. For SN 2011fe, we measure at day 4 a v-band luminosity L_v ∼ 10⁴¹ erg s⁻¹, corresponding to L_bol ≈ 5 × 10⁴¹ erg s⁻¹ and note that at this time the luminosity in the v, b, u, w1, and w2 bands accounts for ≈0.5 L_bol. We therefore assumed that the v, b, u, w1, and w2 bands represent²⁵  ≈0.5L_bol. In the following we explicitly provide the dependence of our density limits on L_bol, so that it is easily possible to re-scale our limits to any L_bol value. Given that the optical properties point to a normal SN Ia (J. T. Parrent et al., in preparation) we adopt fiducial parameters M_ej = 1.4 M_☉ and E = 10⁵¹ erg for the ejecta mass and SN energy, respectively, throughout this paper.

X-ray emission from SNe may be attributed to a number of emission processes including (1) synchrotron, (2) thermal, (3) IC, or (4) a long-lived central engine (see Chevalier & Fransson 2006 for a review). It has been shown that the X-ray emission from stripped supernovae exploding into low-density environments is dominated by IC on a timescale of weeks to a month since explosion, corresponding to the peak of the optical emission (Björnsson & Fransson 2004; Chevalier & Fransson 2006). In specific cases, this has been shown to be largely correct (e.g., SN 2008D, Soderberg et al. 2008; SN 2011dh, Soderberg et al. 2011).

In this framework, the X-ray emission is originated by upscattering of optical photons from the SN photosphere by a population of relativistic electrons (e.g., Björnsson & Fransson 2004). The IC X-ray luminosity depends on the density structure of the SN ejecta, the structure of the circumstellar medium (CSM), and the details of the relativistic electron distribution responsible for the upscattering. Here we assume the SN outer density structure ρ_SN∝R⁻ⁿ with n ∼ 10 (Chevalier & Fransson 2006), as found for SNe arising from compact progenitors (as a comparison, Matzner & McKee 1999 found the outermost profile of the ejecta to scale as ρ_SN∝R^−10.2. See Chomiuk et al. 2012; A. Soderberg, in preparation for a discussion)²⁶; the SN shock propagates into the CSM and is assumed to accelerate the electrons in a power-law distribution n_e(γ) = n₀γ^−p for γ > γ_min. Radio observations of Type Ib/c SNe indicate p ∼ 3 (Chevalier & Fransson 2006). However, no radio detection has ever been obtained for a Type Ia SN so that the value of p is currently unconstrained: this motivates us to explore a wider parameter space p ≳ 2.1 (Figure 3) as seen for mildly relativistic and relativistic explosions (e.g., gamma-ray bursts (GRBs); Panaitescu & Kumar 2000; Yost et al. 2003; Curran et al. 2010). Finally, differently from the thermal or synchrotron mechanisms, the IC luminosity is directly related to the bolometric luminosity of the SN (L_IC(t)∝L_bol(t)): the environment directly determines the ratio of the optical to the X-ray luminosity, so that possible uncertainties on the distance of the SN do not affect the IC computation; it furthermore does not require any assumption on magnetic field related parameters.

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For a population of optical photons with effective temperature T_eff, the IC luminosity at frequency ν reads (see the Appendix):

$$\begin{eqnarray} \frac{dL_{\rm {IC}}}{d\nu }&\sim& 0.2\left (\frac{h}{3.6k} \right)^\frac{3-p}{2} \nonumber\\ &\times& \frac{(p-2)\sigma _T \epsilon _e\rho _{{\rm CMS}} v_s^2 \gamma _{\rm {min}}^{(p-2)} T_{\rm {eff}}^{\frac{p-3}{2}} \nu ^{\frac{1-p}{2}} \Delta R}{m_e c^2}L_{\rm {bol}}(t),\quad\quad \end{eqnarray} \tag{ 1 }$$

where ΔR is the extension of the region containing fast electrons; ρ_CSM is the circumstellar medium density the SN shock is impacting on, which we parameterize as a power law in shock radius ρ_CSM∝R^−s; together with ρ_SN, ρ_CSM determines the shock dynamics, directly regulating the evolution of the shock velocity v_s ≡ v_s(t, n, s), shock radius R ≡ R(t, n, s) and γ_min ≡ γ_min(t, n, s) as derived in the Appendix. For the special case of p = 3, (dL_IC/dν)∝ν⁻¹, its dependence on T_eff cancels out and it is straightforward to verify that Equation (1) matches the predictions from Chevalier & Fransson (2006, their Equation (31) for s = 2 (wind medium)). In the following we use Equation (1) and the L_bol(t) evolution calculated from Swift-UVOT observations of SN 2011fe (Section 2) to derive limits on the SN environment assuming different density profiles. We assume _e = 0.1, as indicated by well-studied SN shocks (Chevalier & Fransson 2006). Each limit on the environment density we report below has to be re-scaled of a multiplicative factor (0.1/_e)^{(p − 1)} for other _e values.

3.1. Wind Scenario

3.2. ISM Scenario

3.3. Implications

While the IC emission model discussed here is primarily sensitive to CSM density, the associated radio synchrotron emission is sensitive to both the CSM density and _B (post-shock energy density in magnetic fields). As a consequence, when combined with radio observations of synchrotron self-absorbed SNe, deep X-ray limits can be used to constrain the _B versus ambient density parameter space (Chevalier & Fransson 2006; Katz 2012). This is shown in Figure 4 for a wind (upper panel) and ISM (lower panel) environment around SN 2011fe: the use of the same formalism (and assumptions) allows us to directly combine the radio limits from Chomiuk et al. (2012) with our results. We exclude the values of _B < 0.02 coupled to $\dot{M}>2\times 10^{-9}\,{M_{\odot }\, \rm yr^{-1}}$ for a wind medium, while _B < 0.1 for any $\dot{M}>5\times 10^{-10}\,{M_{\odot }\ \rm yr^{-1}}$. In the case of an ISM profile, X-ray limits rule out the _B < 2 × 10⁻³ n_CSM > 150 cm⁻³ parameter space.

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The exact value of the microphysical parameters _B and _e is highly debated both in the case of non-relativistic (e.g., SNe) and relativistic (e.g., GRBs) shocks: equipartition (_B/_e ∼ 1) was obtained for SN 2002ap from a detailed modeling of the X-ray and radio emission (Björnsson & Fransson 2004) while significant departure from equipartition (_e/_B ≈ 30) has recently been suggested by Soderberg et al. (2011) to model SN 2011dh. The same is true for SN 1993J, for which _B/_e ≫ 1 (Fransson & Björnsson 1998). In the context of relativistic shocks, GRB afterglows seem to exhibit a large range of _B and _e values (e.g., Panaitescu & Kumar 2001); furthermore, values as low as _B ∼ 10⁻⁵ have recently been be suggested by Kumar & Barniol Duran (2010) from accurate multi-wavelength modeling of GRBs with GeV emission. It is at the moment unclear if this is to be extended to the entire population of GRBs. On purely theoretical grounds, starting from relativistic MHD simulations Zhang et al. (2009) concluded _B ∼ 5 × 10⁻³: this result applies to GRB internal shocks, the late stage of GRB afterglows, transrelativistic SN explosions (like SN 1998bw; Kulkarni et al. 1998), and shock breakout from Type Ibc supernova (e.g., SN 2008D; Soderberg et al. 2008). It is not clear how different the magnetic field generation and particle acceleration might be between relativistic and non-relativistic shocks.

Figure 4 constitutes the first attempt to infer the _B value combining deep radio and X-ray observations of a Type Ia SN: better constraints on the parameters could in principle be obtained if X-ray observations are acquired at the SN optical maximum light. In the case of SN 2011fe we estimate that a factor ∼10 improvement on the density limits would have been obtained with a Chandra observation at maximum light.

Shock breakout from WD explosions is expected to produce a short (≈1–30 ms) pulse with typical ∼ MeV photon energy, luminosity ∼10⁴⁴ erg s⁻¹, and energy in the range 10⁴⁰–10⁴² erg (Nakar & Sari 2012). Such an emission episode would be easily detected if it were to happen close by (either in the Milky Way or in the Magellanic Clouds), while SN 2011fe exploded ∼6.4 Mpc away (Shappee & Stanek 2011). Given the exceptional proximity of SN 2011fe we nevertheless searched for evidence of high-energy emission from the shock breakout using data collected by the nine spacecrafts of the IPN (IPN Mars Odyssey, Konus-Wind, RHESSI, INTEGRAL (SPI-ACS), Swift-BAT, Suzaku, AGILE, MESSENGER, and Fermi-GBM).

The IPN is full sky with temporal duty cycle ∼100% and is sensitive to radiation in the range 20–10⁴ keV (Hurley 2010). Within a two-day window centered on August 23 a total of three bursts were detected and localized by multiple instruments of the IPN. Out of these three confirmed bursts, one has localization consistent with SN 2011fe. Interestingly, this burst was detected by Konus, Suzaku, and INTEGRAL (SPI-ACS) on August 23 13:28:25 UT: for comparison, the inferred explosion time of SN 2011fe is 16: 29 ± 20 minutes (Nugent et al. 2011b). The IPN error box area for this burst is 1.4 sr. The poor localization of this event does not allow us to firmly associate this burst with SN 2011fe: from Poissonian statistics we calculate a ∼10% chance probability for this burst to be spatially consistent with SN 2011fe. A more detailed analysis reveals that SN 2011fe lies inside the Konus–INTEGRAL triangulation annulus but outside the Konus–Suzaku triangulation annulus. Furthermore, at the inferred time of explosion, SN 2011fe was slightly above the Fermi-Gamma-ray Burst Monitor (GBM) horizon, but no burst was detected (in spite of the stable GBM background around this time). We therefore conclude that there is no statistically significant evidence for a SN-associated burst down to the Fermi-GBM threshold (fluence ∼4 × 10⁻⁸ erg cm⁻² in the 8–1000 keV band).³⁰

The early photometry of SN 2011fe constrains the progenitor radius to be R_p ≲ 0.02 R_☉ (Bloom et al. 2012). Using the fiducial values E = 10⁵¹ erg, M_ej = 1.4 M_☉, the shock breakout associated with SN 2011fe is therefore expected to have released E_BO ≲ 3 × 10⁴¹ erg over a timescale t_BO ≲ 2 ms with luminosity L_BO ≳ 7 × 10⁴³ erg s⁻¹ at typical T_BO ≳ 250 keV (see Nakar & Sari 2012; their Equation (29)). At the distance of SN 2011fe, the expected fluence is as low as ∼5 × 10⁻¹¹ erg cm⁻² which is below the threshold of all gamma-ray observatories currently on orbit (the weakest burst observed by BAT had a 15–150 keV fluence of ∼6 × 10⁻⁹ erg cm⁻²). For comparison, the Konus–Suzaku–INTEGRAL burst formally consistent with the position of SN 2011fe was detected with fluence ∼3 × 10⁻⁶ erg cm⁻² and duration of a few seconds (peak flux of ∼4 × 10⁻⁷ erg s⁻¹ cm⁻²). If it were to be connected with the SN, the associated 3 s peak luminosity would be L ∼ 2 × 10⁴⁵ erg s⁻¹ and total energy E ∼ 10⁴⁶ erg (quantities computed in the 20–1400 keV energy band) which are orders of magnitudes above expectations.

For t > t_BO, the temperature and luminosity drop quickly (see Nakar & Sari 2012 for details): in particular, for t > t_NW the emitting shell enters the Newtonian phase. For SN 2011fe we estimate t_NW ∼ 0.3s (Nakar & Sari 2012; their Equation (30)); for R_p ≲ 0.02 R_☉ the luminosity at t = 10 × t_NW is L(t_NW) ≳ 1 × 10⁴¹ erg s⁻¹ with typical emission in the soft X-rays: T(t_NW) ≳ 0.2 keV. At later times L∝t^−0.35 (Nakar & Sari 2012) while T rapidly drops below the Swift-XRT energy band (0.3–10 keV). Swift-XRT observations were unfortunately not acquired early enough to constrain the shock breakout emission from SN 2011fe. UV observations were not acquired early enough either: after ∼1 hr the UV emission connected with the shock breakout is expected to be strongly suppressed due to the deviation from pure radiation domination (e.g., Rabinak et al. 2011). It is, however, interesting to note the presence of a "shoulder" in the UV light curve (Margutti & Soderberg 2011a) particularly prominent in the uvm2 filter for t < 4 days (see Brown et al. 2011; their Figure 2) whose origin is still unclear (see, however, Piro 2012). A detailed modeling is required to disentangle the contribution of different physical processes to the early UV emission (and understand which is the role of the "red leak"—see, e.g., Milne et al. 2010—of the uvm2 filter in shaping the observed light curve).

The collision of the SN ejecta with the companion star is also expected to produce X-ray emission with typical release of energy E_x ∼ 10⁴⁶–10⁴⁷ erg in the hours following the explosion (a mechanism which has been referred to as the analog of shock breakout emission in core collapse SNe; Kasen 2010). According to Kasen (2010), in the most favorable scenario of a red giant companion of M ∼ 1 M_☉ at separation distance a = 2 × 10¹³ cm, the interaction timescale is ∼5 hr after the SN explosion and the burst of X-ray radiation lasts 1.9 hr (with a typical luminosity ∼6 × 10⁴⁴ erg s⁻¹): too short to be caught by our Swift-XRT re-pointing 1.25 days after the explosion. We furthermore estimate the high-energy tail of the longer lasting thermal optical/UV emission associated to the collision with the companion star to be too faint to be detected either: at t ∼ 1.5 days, the emission has T_eff  ≲  25, 000 K and peaks at frequency ν ≲ 3 × 10¹⁵ Hz (Equation (25) from Kasen 2010). Non-thermal particle acceleration might be a source of X-rays at these times, a scenario for which we still lack clear predictions: future studies will help understand the role of non-thermal emission in the case of the collision of an SN with its companion star.

IC emission provides solid limits on the environment density which are not dependent on assumptions about the poorly constrained magnetic field energy density (i.e., the _B parameter; see also Chevalier & Fransson 2006; Horesh et al. 2012). This is different from the synchrotron emission, which was used in our companion paper (Chomiuk et al. 2012) to constrain the environment of the same event from the deepest radio observations ever obtained for an SN Ia. The two perspectives are complementary: the use of the same assumptions and of a consistent formalism furthermore allows us to constrain the post-shock energy density in magnetic fields versus ambient density parameter space (see Figure 4). This plot shows how deep and contemporaneous radio and X-rays observations of SNe might be used to infer the shock parameters.

The IC luminosity is, however, strongly dependent on the SN bolometric luminosity: L_IC(t)∝L_bol(t). Here we presented the deepest limit on the ambient density around a Type Ia SN obtained from X-ray observations. Our results directly benefit from: (1) unprecedented deep Chandra observations of one of the nearest Type Ia SNe, coupled with (2) a consistent treatment of the dynamics of the SN shock interaction with the environment (see the Appendix; Chomiuk et al. 2012), together with (3) the direct computation of the SN bolometric luminosity from Swift/UVOT data.

In particular we showed that:

• 1.  
  Assuming a wind profile the X-ray non-detections implies a mass loss $\dot{M}<2\times 10^{-9}\,{M_{\odot }}\ {\rm yr^{-1}}$ for v_w = 100 km s⁻¹. This is a factor of ∼10 deeper than the limit reported by Horesh et al. (2012). This rules out symbiotic binary progenitors for SN 2011fe and argues against Roche lobe overflowing subgiants and main-sequence secondary stars if a fraction ≳ 1% of the transferred mass is lost at the Lagrangian points and the WD is steadily burning.
• 2.  
  Were SN 2011fe to be embedded in an ISM environment, our calculations constrain the density to n_CSM < 160 cm⁻³.

Whatever the density profile, the X-ray non-detections are suggestive of a clean environment around SN 2011fe, for distances in the range ∼(0.2–5) × 10¹⁶ cm. This is either consistent with the bulk of material (transferred from the donor star to the accreting WD or resulting from the merging of the two WDs) to be confined within the binary system or with a significant delay ≳ 10⁵ yr between mass loss and SN explosion (e.g., Justham 2011; Di Stefano et al. 2011). Note that in the context of DD mergers, the presence of material on distances 10¹³–10¹⁴ cm (as recently suggested by, e.g., Fryer et al. 2010; Shen et al. 2012) has been excluded by Nugent et al. (2011b) based on the lack of bright, early UV/optical emission.

We furthermore looked for bursts of gamma rays associated with the shock breakout from SN 2011fe. We find no statistically significant evidence for an SN-associated burst for fluences >6 × 10⁻⁷ erg cm⁻². However, with progenitor radius R_p < 0.02 R_☉ the expected SN 2011fe shock breakout fluence is ≈5 × 10⁻¹¹ erg cm⁻², below the sensitivity of gamma-ray detectors currently on orbit.

The proximity of SN 2011fe coupled to the sensitivity of Chandra observations, make the limits presented in this paper difficult to be surpassed in the near future for Type Ia SNe. However, the generalized IC formalism of the Appendix is applicable to the entire class of hydrogen-poor SNe, and will provide the tightest constraints to the explosion environment if X-ray observations are acquired around maximum light (see Figure 2) for Type I supernovae (Ia, Ib, and Ic).

We thank Harvey Tananbaum and Neil Gehrels for making Chandra and Swift observations possible. We thank Re'em Sari, Bob Kirshner, Sayan Chakraborti, Stephan Immler, Brosk Russell, and Rodolfo Barniol Duran for helpful discussions. L.C. is a Jansky Fellow of the National Radio Astronomy Observatory. R.J.F. is supported by a Clay Fellowship. K.H. is grateful for IPN support under the following NASA grants: NNX10AR12G (Suzaku), NNX12AD68G (Swift), NNX07AR71G (MESSENGER), and NNX10AU34G (Fermi). The Konus–Wind experiment is supported by a Russian Space Agency contract and RFBR Grant 11-02-12082-ofi_m. P.O.S. acknowledges partial support from NASA Contract NAS8-03060.

Ambient electrons accelerated to relativistic speed by the SN shock are expected to upscatter optical photons from the SN photosphere to X-ray frequencies via IC, see, e.g., Chevalier et al. (2006) and Chevalier & Fransson (2006). Here we generalize Equation (31) from Chevalier & Fransson (2006) for a population of relativistic electrons with arbitrary distribution n_e(γ) = n₀γ^−p for γ > γ_min, both for an ISM (Equation (A6)) and a wind (Equation (A8)) scenario.

Using the IC emissivity given by Felten & Morrison (1966), their Equation (27), the IC luminosity reads:

$$\begin{equation} \frac{dL_{\rm {IC}}}{d\nu }=2.1\sigma _{\rm {T}} c \left (\frac{h}{3.6k}\right)^{\frac{3-p}{2}}R^2 n_0 \Delta R \rho _{\rm {rad}} T_{\rm {eff}}^{\frac{p-3}{2}} \nu ^{\frac{1-p}{2}}, \end{equation} \tag{ A1 }$$

where ρ_rad(t) = (L_bol(t)/4πR²c) is the energy density of photons of effective temperature T_eff which are upscattered to ∼3.6γ²kT_eff; ΔR is the extension of the region containing fast electrons while R is the (forward) shock radius. The emission is expected to originate from a shell of shocked gas between the reverse and the forward shock which are separated by the contact discontinuity at R_c (Chevalier & Fransson 2006). For ρ_SN∝R⁻ⁿ with n = 10 the forward shock is at 1.239 R_c (1.131 R_c) while the reverse shock is at 0.984 R_c (0.966 R_c) in the case of a wind (ISM) environment (Chevalier 1982). The fraction of the volume within the forward shock with shocked gas is 0.5 (0.4) corresponding to a sphere of radius ΔR ∼ 0.8R (ΔR ∼ 0.7R) for an assumed wind (ISM) density profile.

If a fraction _e of the post-shock energy density goes into non-thermal relativistic electrons, from $\int _{\gamma _{\rm {min}}}^{\infty }\gamma \cdot n_e(\gamma)d\gamma = 9/8 \epsilon _e \rho _{{\rm CSM}}v_s^2$ we have

$$\begin{equation} n_0=\frac{9(p-2) \epsilon _e \rho _{{\rm CSM}} v_s^2 \gamma _{\rm {min}}^{(p-2)}}{8m_e c^2} \end{equation} \tag{ A2 }$$

for p > 2. Combining Equation (A1) with Equation (A2), we obtain Equation (1). The temporal evolution of L_IC directly depends on L_bol(t), T_eff(t), v_s(t), R(t), and γ_min(t). The properties of the SN and of its progenitor determine L_bol(t), T_eff(t), and the profile of the outer ejecta ρ_SN∝R⁻ⁿ. We assume n ∼ 10 throughout the paper (e.g., Chevalier & Fransson 2006). The environment sets the ρ_CSM profile, which we parameterize as ρ_CSM ≡ A · R^−s. Both the SN explosion properties and the environment determine the shock dynamics: evolution of the shock radius R(t), shock velocity v_s(t) and, as a consequence γ_min(t). Under those conditions the shock interaction region can be described by a self-similar solution (Chevalier 1982) with the shock radius evolving as R∝t^{((n − 3)/(n − s))} which implies

$$\begin{equation} v_s(t)=\left (\frac{n-3}{n-s}\right) \frac{R(t)}{t}. \end{equation} \tag{ A3 }$$

The shock velocity directly determines γ_min. From Soderberg et al. (2005), assuming that all electrons go into a power-law spectrum with spectral index p:

$$\begin{equation} \gamma _{\rm {min}}(t)= \frac{9\epsilon _e}{8\eta } \left(\frac{m_p}{m_e}\right) \left(\frac{v_s(t)}{c}\right)^2 \left(\frac{\mu _i}{N_e/N_i}\right) \left(\frac{p-2}{p-1}\right), \end{equation} \tag{ A4 }$$

where η is the shock compression parameter, N_e (N_i) is the electron (ion) number density, and μ_i is the average number of nucleons per atom. We furthermore define g(Z) ≡ (μ_i/(N_e/N_i)). For Solar metallicity g(Z_☉) ≈ 1.22. In the following, we assume η ≈ 4 (Chevalier & Fransson 2006), Z = Z_☉.

A.1. ISM Scenario

The self-similar solutions for the interaction of the SN ejecta with an ISM-like CSM (s = 0 and ρ_CSM ≡ A/R^s = A) lead to (Chevalier 1982; A. Soderberg, in preparation)

$$\begin{eqnarray} v_s(t)&=&2.4\times 10^9 \left(\frac{A}{\rm {g\, cm^{-3}}} \right)^{-0.1} \left(\frac{E}{10^{51}\,\rm {erg}} \right)^{0.35} \nonumber\\ \ms \ms &&\times \left(\frac{M_{{\rm ej}}}{1.4\, M_{\odot }} \right)^{-0.25} \left(\frac{t}{s} \right)^{-0.29}\, \rm {cm\,s^{-1}}, \end{eqnarray} \tag{ A5 }$$

where M_ej is the mass of the ejected material and E is the energy of the supernova explosion. Equations (A2)–(A5), together with Equation (A1), predict an IC luminosity:

$$\begin{eqnarray} \frac{dL_{\rm {IC}}}{d\nu }&=& f_{\rm {ISM}}(p, Z) \epsilon _e^{p-1} \left(\frac{M_{{\rm ej}}}{1.4\,M_{\odot }} \right)^{\frac{1-2p}{4}} \left(\frac{A}{\rm {g\,cm^{-3}}} \right)^{(1.1-0.2p)} \nonumber\\ \ms \ms &&\times \left(\frac{E}{10^{51}\,\rm {erg}} \right)^{(0.7p-0.35)} \left(\frac{t}{s} \right)^{(1.29-0.58p)} \nonumber\\ \ms \ms &&\times T_{\rm {eff}}^{\frac{p-3}{2}}\nu ^{\frac{1-p}{2}} \left(\frac{L_{\rm {bol}}}{\rm {erg\,s^{-1}}}\right) \,\,\rm {\frac{erg}{s\,Hz}} \end{eqnarray} \tag{ A6 }$$

with f_ISM(p, Z) ≈ 2.0 × 10⁷(10³)^{(1.1 − 0.2p)}(1.3 × 10⁻¹¹)^{((3 − p)/2)} × (53.9/(2 + p))^{(p − 2)}(p − 2)^{(p − 1)}g(Z)^{(p − 2)}. In the body of the paper, A will be reported in (hydrogen) particles per cm³.

A.2. WIND Scenario

For s = 2 (ρ_CSM ≡ A/R²) the self-similar solutions lead to (Chevalier 1982, A. Soderberg, in preparation)

$$\begin{eqnarray} v_s(t)&=&6.6\times 10^{11} \left(\frac{A}{\rm {g \,cm^{-1}}}\right)^{-0.12} \left(\frac{E}{10^{51}\,\rm {erg}}\right)^{0.43} \nonumber\\ &&\times \left(\frac{M}{1.4\,M_{\odot }}\right)^{-0.31} \left(\frac{t}{s}\right)^{-0.12}\,\,\, \rm {cm\,s^{-1}}. \end{eqnarray} \tag{ A7 }$$

Combining Equations (A2), (A3), (A4), and (A7) with Equation (A1) we obtain

$$\begin{eqnarray} \frac{dL_{\rm {IC}}}{d\nu }&=& f_{\rm {WIND}}(p, Z) \epsilon _e^{p-1} \left(\frac{M_{{\rm ej}}}{1.4\,M_{\odot }} \right)^{(0.93-0.62p)} \nonumber\\ \ms &&\times \left(\frac{A}{\rm {g\,cm^{-1}}} \right)^{(1.36-0.24p)} \left(\frac{E}{10^{51}\,\rm {erg}} \right)^{(0.86p-1.29)} \nonumber\\ \ms &&\times \left(\frac{t}{s} \right)^{-(0.24p+0.64)} T_{\rm {eff}}^{\frac{p-3}{2}}\nu ^{\frac{1-p}{2}} \left(\frac{L_{\rm {bol}}}{\rm {erg\,s^{-1}}}\right) \,\,\rm {\frac{erg}{s\,Hz}} \nonumber\\ \end{eqnarray} \tag{ A8 }$$

with f_ISM(p, Z) ≈ 6.7 × 10⁻⁷10^{(0.24p − 1.36)}(1.3 × 10⁻¹¹)^{((3 − p)/2)}((5.6 × 10⁵)/(2 + p))^{(p − 2)}(p − 2)^{(p − 1)}g(Z)^{(p − 2)}.

Note that $\rho _{{\rm CSM}}\equiv A/R^2\equiv \dot{M}/ (4\pi v_w R^2)$, so that $A=\dot{M}/(4\pi v_w)$, where $\dot{M}$ and v_w are the mass-loss rate and the wind velocity of the SN progenitor, respectively. In the body of the paper, for the wind scenario, we refer to A in terms of mass-loss rate for a given wind velocity so that it is easier to connect our results to known physical systems.