Inverse Compton X-Ray Emission from Supernovae with Compact Progenitors: Application to SN2011fe

Abstract

We present a generalized analytic formalism for the inverse Compton X-ray emission from hydrogen-poor supernovae and apply this framework to SN 2011fe using Swift X-Ray Telescope (XRT), UVOT, and Chandra observations. We characterize the optical properties of SN 2011fe in the Swift bands and find them to be broadly consistent with a "normal" SN Ia, however, no X-ray source is detected by either XRT or Chandra. We constrain the progenitor system mass-loss rate \dot{M}< 2\times 10^{-9}\ {M_{\odot }}\ yr^{-1} (3σ c.l.) for wind velocity vw = 100 km s-1. Our result rules out symbiotic binary progenitors for SN 2011fe and argues against Roche lobe overflowing subgiants and main-sequence secondary stars if >~ 1% of the transferred mass is lost at the Lagrangian points. Regardless of the density profile, the X-ray non-detections are suggestive of a clean environment (n CSM < 150 cm-3) for 2 × 1015 <~ R <~ 5 × 1016 cm around the progenitor site. This is either consistent with the bulk of material being confined within the binary system or with a significant delay between mass loss and supernova explosion. We furthermore combine X-ray and radio limits from Chomiuk et al. to constrain the post-shock energy density in magnetic fields. Finally, we searched for the shock breakout pulse using gamma-ray observations from theInterplanetary Network and find no compelling evidence for a supernova-associated burst. Based on the compact radius of the progenitor star we estimate that the shock breakout pulse was likely not detectable by current satellites.

Full text

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arXiv:1202.0741v1 [astro-ph.HE] 3 Feb 2012
DRAFT VERSION FEBRUARY 6, 2012
Preprint typeset using LATEX style emulateapj v. 5/2/11
INVERSE COMPTON X-RAY EMISSION FROM SUPERNOVAE WITH COMPACT PROGENITORS: APPLICATION TO
SN2011FE
R. MARGUTTI1, A. M. SODERBERG1, L. CHOMIUK1,2, R. CHEVALIER3, K. HURLEY4, D. MILISAVLJEVIC1, R. J. FOLEY1,21, J. P.
HUGHES5, P. SLANE1, C. FRANSSON6, M. MOE1, S. BARTHELMY7, W. BOYNTON8, M. BRIGGS9, V. CONNAUGHTON9, E. COSTA10, J.
CUMMINGS7, E. DEL MONTE10, H. ENOS8, C. FELLOWS8, M. FEROCI10, Y. FUKAZAWA11, N. GEHRELS7, J. GOLDSTEN12, D.
GOLOVIN13, Y. HANABATA11, K. HARSHMAN8, H. KRIMM7, M. L. LITVAK13, K. MAKISHIMA14, M. MARISALDI15, I. G.
MITROFANOV13, T. MURAKAMI13, M. OHNO11, D. M. PALMER17, A. B. SANIN13, R. STARR7, D. SVINKIN18, T. TAKAHASHI11, M.
TASHIRO19, Y. TERADA19, K. YAMAOKA20
(Dated: Accepted YEAR month day. Received YEAR month day; in original form YEAR month day)
Draft version February 6, 2012
ABSTRACT
We present a generalized analytic formalism for the inverse Compton X-ray emission from hydrogen-poor
supernovae and apply this framework to SN2011fe using Swift-XRT, UVOT and Chandra observations. We
characterize the optical properties of SN2011fe in the Swift bands and find them to be broadly consistent
with a “normal” SN Ia, however, no X-ray source is detected by either XRT or Chandra. We constrain the
progenitor system mass loss rate˙M < 2×10−9M⊙yr−1(3σ c.l.) for wind velocity vw= 100km s−1. Our result
rules out symbiotic binary progenitorsfor SN 2011feand arguesagainst Roche-lobeoverflowingsubgiants and
main sequence secondary stars if ? 1% of the transferred mass is lost at the Lagrangian points. Regardless
of the density profile, the X-ray non-detections are suggestive of a clean environment (nCSM< 150cm−3) for
2×1015? R ? 5×1016cm around the progenitor site. This is either consistent with the bulk of material being
confined within the binary system or with a significant delay between mass loss and supernova explosion. We
furthermore combine X-ray and radio limits from Chomiuk et al. 2012 to constrain the post shock energy
density in magnetic fields. Finally, we searched for the shock breakout pulse using gamma-ray observations
from the Interplanetary Network and find no compelling evidence for a supernova-associated burst. Based on
the compact radius of the progenitor star we estimate that the shock break out pulse was likely not detectable
by current satellites.
Subject headings: radiation mechanisms: non thermal
1Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cam-
bridge, MA 02138, USA.
2National Radio Astronomy Observatory, P. O. Box O Socorro, NM
87801, USA.
3Department of Astronomy, University of Virginia, Charlottesville, VA
22904-4325, USA.
4Space Sciences Laboratory, University of California, 7 Gauss Way,
Berkeley, CA 94720-7450, USA.
5Department of Physics and Astronomy, Rutgers University, Piscat-
away, NJ 08854-8019, USA.
6Department of Astronomy, Stockholm University, AlbaNova, SE-106
91 Stockholm, Sweden.
7NASA/Goddard Space Flight Center Greenbelt, MD 20771, USA.
8Department of Planetary Sciences, University of Arizona, Tucson, AZ
85721, USA.
9Physics Department, The University of Alabama in Huntsville,
Huntsville, AL 35809, USA.
10INAF/IASF-Roma, via Fosso del Cavaliere 100, 00133 Roma, Italy.
11Department of Physics, Hiroshima University, 1-3-1 Kagamiyama,
Higashi-Hiroshima, Hiroshima 739-8526, Japan.
12Applied Physics Laboratory, Johns Hopkins University, Laurel, MD
20723, USA.
13Space Research Institute, 84/32, Profsoyuznaya, Moscow 117997,
Russian Federation.
14Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-
ku, Tokyo 113-0033, Japan.
15INAF/IASF-Bologna, Via Gobetti 101, I-40129 Bologna, Italy.
16DepartmentofPhysics,Kanazawa
Kanazawa, Ishikawa 920-1192, Japan.
17Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM
87545, USA.
18Ioffe Physical-Technical Institute of the Russian Academy of Sci-
ences, St. Petersburg, 194021, Russia.
19Department of Physics, Saitama University, 255 Shimo-Okubo,
Sakura-ku, Saitama-shi, Saitama 338-8570, Japan.
University,Kadoma-cho,
20Department of Physics and Mathematics, Aoyama Gakuin University,
5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan.
21Clay Fellow.

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2 Margutti et al.
1. INTRODUCTION
Over the past two decades, the utility of Type Ia supernovae
(SNe Ia) as standardizable candles to trace the expansion his-
tory 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 dL= 6.4Mpc (Shappee & Stanek 2011),
represents a natural test bed for a detailed SN Ia progenitor
study22. 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 mostpopularmodelsinclude(i)a single-degenerate(here-
after, SD) scenario in which a massive WD accretes material
from a H-rich or He-rich companion, potentially a giant, sub-
giant or main-sequence star, (Whelan & Iben 1973; Nomoto
1980). Mass is transferred either via Roche-lobe overflow
(RLOF) or through stellar winds. Alternatively, (ii) models
invoke a double sub-MChWD binary system that eventually
merges(doubledegeneratemodel,DD;Iben & Tutukov1984,
Webbink 1984).
In SD models, the circumbinary environment may be en-
riched by the stellar wind of the donor star or through non-
conservative mass transfer in which a small amount of ma-
terial is lost to the surroundings. Winds from the donor star
shapethelocaldensityprofileasρCSM∝R−2overa?1parsec
region encompassing the binary system. Theoretical consid-
erations indicate that the wind-driven mass loss rate must be
low, since an accretionrate of just ∼3×10−7M⊙yr−1is ideal
for the WD to grow slowly up to MChand 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 density of nCSM≈ 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 observa-
tions can potentially discriminate between the two scenar-
ios 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, sev-
eral dozen SNe Ia at distances d ? 200 Mpc have been ob-
served with the Very Large Array (VLA; Panagia et al. 2006;
Hancock et al. 2011; Soderberg in prep.), the Chandra X-ray
Observatory (Hughes et al. 2007), and the Swift X-ray Tele-
scope (Immler et al. 2006; Russel & Immler, in press) reveal-
ing no detections to date23. These limits were used to con-
strain the density of the circumbinarymaterial, and in turn the
mass loss rate of the progenitor system. However these data
poorlyconstraintheWD companion,duein parttothe limited
sensitivity of the observations (and the distance of the SNe).
22The nearest Type Ia in the digital era is SN 1986G which exploded in
NGC 5128 at a distance of ∼ 4Mpc (Frogel et al. 1987).
23We note that the claimed detection of SN2005ke with the Swift-XRT
was not confirmed with follow-up Chandra observations, strongly suggesting
that the Swift/XRT source was due to contamination from the host galaxy
(Hughes et al. 2007).
FIG. 1.— Swift-XRT color combined image of the environment around
SN 2011fe. Red, green and blue colors refer to soft (0.3-1 keV), medium
(1-3 keV) and hard (3-10 keV) sources, respectively. A 40” region around
the SN is marked with a white box. Inset: Chandra 0.5-8 keV deep observa-
tion of the same region obtained at day 4 since the explosion. No source is
detected at the SN position (white circle).
The improved sensitivity of the Expanded Very Large Array
(EVLA) coupled with a more detailed approach regardingthe
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 com-
panion paper on the recent Type Ia SN2011fe/ PTF11kly
(Chomiuk et al. 2012. See also Horesh et al. 2011).
Here we report a detailed panchromaticstudy of SN2011fe
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 op-
tical/UV light-curves for the SN, indicating that the object
appears consistent with a "normal" SN Ia.
cuss deep limits on the X-ray emission in the month follow-
ing 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 the Inverse Comp-
ton (IC) X-ray luminosity expected from hydrogen poor SNe
thatbuildsuponpreviousworkbyChevalier & Fransson2006
and Chevalier et al. 2006 but is broadly applicable for a wide
range of shock properties, metallicity, photon temperatures,
and circumstellar density profiles (stellar wind or ISM; see
Appendix A). We apply this analytic model to SN2011fe 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. 2011.
Observations are described in Sec. 2; limits to the SN pro-
genitor system from X-ray observations are derived and dis-
cussedinSec. 3usingtheICformalismfromAppendixA.We
combine our radio (Chomiuk et al. 2012) and X-ray limits to
constrain the post-shock energy density in magnetic fields in
Sec. 4, while the results from the search of a burst of gamma-
rayradiationfromthe SN shock break-outis presentedin Sec.
5. Conclusions are drawn in Sec. 6.
Next we dis-
2. OBSERVATIONS
SN 2011fe was discovered by the Palomar Transient Fac-
tory (PTF) on 2011 August 24.167 UT and soon identified

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X-ray limits on SN 2011fe3
as a very young type Ia explosion in the Pinwheel galaxy
(M101) (Nugent et al. 2011a). From early time optical obser-
vations Nugent et al. (2011b) were able to constrain the SN
explosion date to August 23, 16 : 29±20min (UT). The SN
site was fortuitouslyobservedboth by the Hubble Space Tele-
scope(HST) andbyChandraon severaloccasionspriorto the
explosionin the optical and X-ray band, giving the possibility
to constrain the progenitor system (Li et al. 2011a; Liu et al.
2011). Very early optical and UV photometry has been used
by Brown et al. (2011) and Bloom et al. (2011) to infer the
progenitor and companion radius and nature, while multi-
epoch high-resolution spectroscopy taken during the evolu-
tionoftheSNhas beenemployedasa probeofthecircumstel-
lar environment (Patat et al. 2011b). Limits to the circumstel-
lar density have been derived from deep radio observations in
our companion paper (Chomiuk et al. 2012), where we con-
sistently treat the shock parameters and evolution. Here we
study SN 2011fe from a complementary perspective, bridg-
ing 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 HEA-
SOFT package at the time of writing (v11). Standard fil-
tering 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.
2011; Margutti & Soderberg 2011b) or in the combined 142
ks exposure covering the time interval 1−65 days (see Fig.
1). In particular, using the first 4.5 ks obtained on August
24th, we find a PSF (Point Spread Function) and exposure
map corrected243σ count-rate limit on the undetected SN
? 4×10−3cs−1. For a simple power-law spectrum with pho-
tonindexΓ∼2andGalacticneutralhydrogencolumndensity
NH=1.8×1020cm−2(Kalberla et al.2005)thistranslatesinto
an unabsorbed 0.3-10 keV flux F = 1.5×10−13ergs−1cm−2
corresponding to a luminosity L = 7×1038ergs−1at a dis-
tance 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 2×10−4cs−1(F =
7.4×10−15ergs−1cm−2, L = 3.6×1037ergs−1). Finally, ex-
tracting data around maximum light (the time interval 8-
38 days), the X-rays are found to contribute less than 3×
10−4cs−1(3σ limit, total exposure of 61 ks) corresponding
to F = 1.1×10−14ergs−1cm−2, L = 5.9×1037ergs−1.
We observed SN 2011fe with the Chandra X-ray Obser-
vatory on Aug 27.44 UT (day 4 since the explosion) under an
approvedDDTproposal(PIHughes). Datahavebeenreduced
with the CIAO software package (version 4.3), with cali-
bration database CALDB (version 4.4.2). We applied stan-
dard filtering using CIAO threads for ACIS data. No X-ray
sourceisdetectedat theSN positionduringthe50ksexposure
(Hughes et al. 2011), with a 3σ upper limit of 1.1×10−4cs−1
in the 0.5-8 keV band, from which we derive a flux limit of
7.7×10−16ergs−1cm−2correspondingto L = 3.8×1036ergs−1
(assuming a simple power-law model with spectral photon in-
dex Γ = 2). 3σ upper limits from Swift and Chandra observa-
tions are shown in Fig. 2.
The SN was clearly detected in Swift-UVOT observations.
Photometry was extracted from a 5′′aperture, closely follow-
24Note that correcting for both the PSF and the exposure map is here
of primary importance to compute the upper limits. If the exposure map is
neglected, deeper but unrealistic limits would be computed.
ing the prescriptions by Brown et al. (2009) (see Fig. 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 uncertain-
ties) with the results of Brown et al. (2011). With respect
to Brown et al. (2011) we extend the UVOT photometry of
SN 2011feto day ∼60 since the explosion. Due to the bright-
ness of SN 2011fe, u, b and v observations strongly suffer
from coincidence losses (Breeveld et al. 2010) around maxi-
mum light (see Brown et al. 2011for details): supernovatem-
plates from Nugent et al. (2002) were used to fit the u and b
light-curvesand infer the SN luminosity during those time in-
tervals in the u and b bands. For the v-band, it was possible to
(partially) recover the original light-curve applying standard
coincidence losses corrections: however, due to the extreme
coincidence losses, our v-band light-curve may still provide a
lowerlimit to thereal SN luminosityin the time interval8−37
days since explosion. In Fig. 2 we present the Swift-UVOT
6-filter light-curves,and note that the re-constructedv-bandis
broadly consistent with the Nugent template25. 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 Lv∼ 1041ergs−1, corre-
sponding to Lbol≈ 5×1041erg s−1and note that at this time
the luminosity in the v, b, u, w1 and w2 bands account for
≈ 0.5Lbol. We therefore assumed that the v, b, u, w1 and w2
bands represent26≈ 0.5Lbol. In the following we explicitly
providethe dependenceof our density limits on Lbol, so that it
iseasilypossibletore-scaleourlimitstoanyLbolvalue. Given
that the optical properties point to a normal SN Ia (Parrent at
al. in prep.) we adopt fiducial parameters Mej= 1.4M⊙and
E = 1051erg for the ejecta mass and SN energy, respectively,
throughout this paper.
3. LIMITS ON THE AMBIENT DENSITY FROM X-RAYS
X-ray emission from SNe may be attributed to a number
of emission processes including (i) synchrotron, (ii) thermal,
(iii) Inverse Compton (IC), or (iv) a long-lived central engine
(see Chevalier & Fransson 2006 for a review). It has been
shown that the X-ray emission from stripped supernovae ex-
ploding into low density environments is dominated by IC on
a timescale of weeks to a month since explosion, correspond-
ing to the peak of the optical emission (Björnsson & Fransson
2004, Chevalier & Fransson 2006).
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 up-scattering of optical photons from the SN pho-
tosphere by a population of relativistic electrons (e.g.
Björnsson & Fransson 2004). The IC X-ray luminosity de-
pends on the density structure of the SN ejecta, the struc-
ture of the circumstellar medium (CSM) and the details of
the relativistic electron distribution responsible for the up-
scattering. Here we assume the SN outer density structure
In specific cases, this
25Note that, as it will be clear from the next section, this possible underes-
timation of the v-band luminosity around maximum light only leads to more
conservative limits to the ambient density derived from Swift observations.
Our main conclusions are however based on the Chandra observation taken
at day 4, when coincidence losses do not play a role.
26Nearly 80% of the bolometric luminosity of a typical SN Ia is emitted
in the range from 3000 to 10000 Å(Contardo et al. 2000).

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4Margutti et al.
FIG. 2.— Limits on the X-ray luminosity of SN 2011fe: 0.5-8 keV luminosity expected from inverse comptonization of optical photons in the case of a wind
ρCSM∝ R−2(green solid line) and an ISM ρCMS∝ const (blue solid line) environment. Deep limits from Swift and Chandra are marked with red bullets and
squares, respectively. In the case of Swift observations we report the combined limit (at the linear midpoint of the time intervals), produced stacking the entire
Swift-XRT data set together with a limit calculated around the SN maximum light. The colored areas span A = (0.8−7)×10−9M⊙yr−1/(100kms−1) (wind,
green) and A = (55−500)cm−3(ISM, blue). The Chandra observation constrains˙M/vw< 2×10−9M⊙yr−1/(100kms−1) (wind); nCSM< 166cm−3(ISM). The
blue and green x-axes report the ISM and wind radius of the shock calculated using these values. Black dotted line: scaled SN bolometric luminosity. Grey filled
circles: scaled Swift-UVOT light-curves. Dashed lines: best-fitting Nugent et al. (2002) templates to the u b and v band. We assume E = 1051erg, Mej= 1.4M⊙,
ǫe= 0.1, p = 3.
ρSN∝R−nwith n∼10(Chevalier & Fransson2006), as found
for SNe arising from compact progenitors (as a comparison,
Matzner & McKee 1999 found the outermost profile of the
ejecta to scale as ρSN∝ R−10.2. See Chomiuk et al. 2012,
Soderberg in prep. for a discussion)27; the SN shock prop-
agates into the circumstellar medium and is assumed to accel-
erate the electrons in a power-law distribution ne(γ) = n0γ−p
for γ > γmin. Radio observations of type Ib/c SNe indicate
p∼3 (Chevalier & Fransson2006). However,noradiodetec-
tion 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 (Fig. 3) as seen for mildly rel-
ativistic and relativistic explosions (e.g., gamma-ray bursts,
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 bolo-
metric luminosity of the SN (LIC(t) ∝ Lbol(t)): the environ-
ment directly determines the ratio of the optical to the X-ray
27Note that the adopted density profile is similar to the W7 model by
Nomoto et al. (1984) with the addition of a power-law profile at high veloc-
ities. A pure W7 profile would give rise to somewhat slower shockwave
velocity (Dwarkadas & Chevalier 1998).
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 parame-
ters.
For a population of optical photons with effective tempera-
tureTeff, theICluminosityatfrequencyν reads(seeAppendix
A):
dLIC
dν
∼0.2
?h
3.6k
?3−p
2 (p−2)σTǫeρCMSv2
sγ(p−2)
mec2
minT
p−3
2
effν
1−p
2 ∆R
Lbol(t)
(1)
where ∆R is the extension of the region containing fast elec-
trons; ρCSMis the circumstellar medium density the SN shock
is impacting on, which we parametrize as a power-law in
shock radius ρCSM∝ R−s; together with ρSN, ρCSMdetermines
the shock dynamics, directly regulating the evolution of the
shock velocity vs≡ vs(t,n,s), shock radius R ≡ R(t,n,s) and
γmin≡ γmin(t,n,s) as derived in Appendix A. For the special
case p = 3,dLIC
it is straightforward to verify that Eq. 1 matches the predic-
tions from Chevalier & Fransson (2006), their Eq. (31) for
s = 2 (wind medium). In the following we use Eq. 1 and the
dν∝ ν−1, its dependence on Teffcancels out and

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X-ray limits on SN 2011fe5
FIG. 3.— Limits on the CSM density around SN 2011fe as derived from the
X-ray non-detection at 4 days after the explosion, assuming inverse comp-
tonization of optical photons in the case of a wind (upper panel) or ISM
(lower panel) scenario. Black solid line: 3σ upper limit as a function of the
power-law index of the electron distribution p assuming T = 10000K. Upper
limit contours in the cases T = 5000 K and T = 20000 K are also shown for
comparison (black dashed lines). Yellow bullets: upper limit to the CSM den-
sity as derived from radio observations for ǫBin the range 0.1−0.01. ǫB= 0.1
gives the tightest constraint (Chomiuk et al. 2012). We assume E = 1051erg,
Mej= 1.4M⊙, ǫe= 0.1.
Lbol(t) evolution calculated from Swift-UVOT observations of
SN 2011fe (Sec. 2) to derive limits on the SN environment
assuming different density profiles. We assume ǫe= 0.1, as
indicated by well studied SN shocks (Chevalier & Fransson
2006). Each limit on the environment density we report be-
low has to be re-scaled of a multiplicative factor (0.1/ǫe)(p−1)
for other ǫevalues.
3.1. Wind scenario
A star which has been losing material at constant rate ˙M
gives rise to a "wind medium": ρCSM=˙M/(4πR2vw). Eq. A8
and the Chandra non-detection constrain the wind density to
˙M/vw< 2×10−9(M⊙y−1/100kms−1) (where vwis the wind
velocity). This is a 3σ limit obtained integrating Eq. A8
over the 0.5-8 keV Chandra pass band and assuming p = 3,
ǫe= 0.1, E = 1051erg and Mej= 1.4M⊙. The observation
was performed on day 4 after the explosion: at this time
Lbol∼ 5×1041ergs−1while the shock wave probes the en-
vironment density at a radius R ∼ 4×1015cm (Eq. A3 and
A7) for˙M/vw=2×10−9(M⊙y−1/100kms−1) (see Fig. 2). For
the wind scenario˙M/vw∝ (1/Lbol)(1/0.64)(see Appendix A).
While giving less deep constraints, Swift observations have
the advantage of being spread over a long time interval giving
us the possibility to probe the CSM density over a wide range
of radii. Integrating Eq. A8 in the time interval 1-65 days
to match the Swift coverage (and using the 0.3-10 keV band)
leads to˙M/vw< 7×10−8(M⊙y−1/100kms−1) for 2×1015?
R ? 6×1016cm from the progenitor site28. A similar value is
obtained using the X-ray limit around maximum optical light,
when the X-ray emission from IC is also expected to peak
(Fig. 229).
3.2. ISM scenario
SN 2011fe might have exploded in a uniform density en-
vironment (ISM, s = 0). In this case, integrating Eq. A6
over the 0.5-8 keV energy range, the Chandra limit implies
a CSM density nCSM< 166cm−3at 3σ confidence level for
fiducial parameter values p = 3, ǫe= 0.1, E = 1051erg and
Mej= 1.4M⊙. This limit applies to day 4 after the explo-
sion (or, alternatively to a distance R ∼ 4×1015cm, see Fig.
2).Integrating Eq.A6 over the time interval 1-65 days
(and in the energy window 0.3-10 keV) the Swift upper limit
implies nCSM< 800cm−3(3σ level), over a distance range
2× 1015− 3 ×1016cm from the progenitor site30. Around
maximum light (days 8-38), we constrain nCSM< 770cm−3
for distances (1 ? R ? 3)×1016cm. For an ISM scenario our
constraints on the particle density ∝ (1/Lbol)(1/0.5)(see Ap-
pendix A).
Figure 3 (lower panel) shows how our Chandra limit com-
pares to deep radio observations of SN 2011fe. We explore a
wideparameterspacetounderstandhowadifferentphotonef-
fective temperature and/or electron power-law index p would
affect the inferred density limit: we find nCSM? 150cm−3for
Teff< 20000 K and 2.2 ? p ? 3. X-ray observations are less
constraining than radio observations in the ISM case when
compared to the wind case: this basically reflects the higher
sensitivity of the synchrotron radio emission to the blastwave
velocity,which is faster for anISM-like ambient(forthe same
density at a given radius).
3.3. Implications
From the Chandra non detection we derive ˙M/vw< 2×
10−9(M⊙y−1/100kms−1). This is the deepest limit obtained
from X-ray observations to date and directly follows from
(i) unprecedented deep Chandra observations, (ii) proximity
of SN 2011fe coupled to (iii) a consistent treatment of the
dynamics of the SN shock interaction with the environment
(Appendix A). Before SN 2011fe, the deepest X-ray non-
detection was reported for Type Ia SN 2002bo at a level of ∼
28Given the gentle scaling of the shock radius with wind density (R ∝
A−0.12, Eq. A7), these values are accurate within a factor 10 of˙M/vwvaria-
tion.
29Note that in Fig. 2 the Swift limits are arbitrarily assigned to the linear
midpoint of the temporal intervals. The limit on the ambient density is how-
ever calculated integrated the model over the entire time interval so that the
arbitrary assignment of the “central” bin time has no impact on our conclu-
sions.
30R has a very gentle (∝ A−0.1, see Eq. A5) dependence on the environ-
ment density. The R values we list are representative of an ISM medium with
a wide range of density values: 80 ? nCSM? 8000cm−3.

Page 6

6 Margutti et al.
2×1038ergs−1(distance of 22 Mpc): using 20 ks of Chandra
observations obtained 9.3days after explosion, Hughes et al.
(2007) constrained ˙M/vw? 10−4(M⊙y−1/100kms−1). This
limit was computed conservatively assuming thermal emis-
sion as the leading radiative mechanism in the X-rays. Us-
ing a less conservative approach, other studies were able to
constrain the X-ray luminosity from type Ia SNe observed
by Swift to be ? 1039ergs−1(Immler et al. 2006), leading to
˙M/vw? 10−7(M⊙y−1/100kms−1) (a factor ∼ 100 above our
result).
Our limit on SN 2011fe strongly argues against a symbi-
otic binary progenitor for this supernova. According to this
scenario the WD accretes material from the wind of a giant
star carrying away material at a level of˙M > 10−8M⊙yr−1for
vw? 100kms−1(see e.g. Seaquist & Taylor 1990; Patat et al.
2011a; Chen et al. 2011). We reached the same conclusion
in our companion paper (Chomiuk et al. 2012) starting from
deep radio observations of SN 2011fe. The radio limit is
shown in Fig. 3 for the range of values 0.01 < ǫB< 0.1,
with ǫB= 0.1 leading to the most constraining limit (where ǫB
is the post shock energy density fraction in magnetic fields).
Historical imaging at the SN site rules out red-giant stars and
the majority of the parameter space associated with He star
companions (Li et al. 2011a, their Fig. 2): however, pre-
explosion images could not constrain the Roche-lobe over-
flow (RLOF) scenario, where the WD accretes material ei-
ther from a subgiant or a main-sequence star. In this case,
winds or transferred material lost at the outer Lagrangian
points of the system are expected to contribute at a level
? 3×10−9(˙M/M⊙yr−1)(vw/100kms−1)−1if a fraction ? 1%
of the transferred mass is lost at the Lagrangian points and
the WD is steadily burning (see e.g. Chomiuk et al. 2012 et
al and references therein). The real fraction value is how-
ever highly uncertain, so that it seems premature to rule out
the entire class of models based on the present evidence. X-
ray limits would be compatible with RLOF scenarios where
the fraction of lost material is < 1% (for any 2.1 ? p ? 3 and
5000K?Teff?20000K, Fig. 3). However,fromthe analysis
of early UV/optical data, Bloom et al. (2011) found the com-
panion radius to be Rc< 0.1R⊙, thus excluding Roche-lobe
overflowing red-giants and main sequence secondary stars
(see also Brown et al. 2011).
X-ray non-detections are instead consistent with (but can
hardly be considered a proof of) the class of double degener-
ate (DD) models for type Ia SNe, where two WDs in a close
binary system eventually merge due to the emission of grav-
itational waves. No X-ray emission is predicted (apart from
the shock break out at t ≪ 1day, see Sec. 5) and SN 2011fe
might be embedded in a constant and low-density environ-
ment (at least for R > 1014cm). Pre-explosion radio HI imag-
ing indicates an ambient density of ≈ 1cm−3(Chomiuk et al.
2012) (on scales R >> 1014cm), while our tightest limits in
thecaseofanISMenvironmentarenCSM<166cm−3. Ourob-
servations cannot however constrain the presence of material
atdistancesintherange1013−1014cmfromtheSNexplosion:
recent studies suggest that significant material from the sec-
ondary (disrupted) WD may indeed reside at those distances
either as a direct result of the DD-merger (Shen et al. 2011)
or as an outcome of the subsequent evolution of the system
(Fryer et al. 2010).
Whatever the density profile of the environment, our find-
ings are suggestive of a clean environmentaround SN 2011fe
fordistances 2×1015<R<5×1016cm. The presenceofsig-
nificant material at larger distances (R ? 5×1016cm) cannot
be excluded,so that our observationscannotconstrain models
thatpredictalargedelay(?105yr)betweenmass loss andthe
SN explosion (see e.g. Justham 2011, Di Stefano et al. 2011
and references therein). Finally, it is interesting to note that
the high-resolution spectroscopy study by Patat et al. (2011b)
lead to a similar, clean environment conclusion: at variance
with SN 2006X (Patat et al. 2007), SN 1999cl (Blondin et al.
2009) and SN 2007le (Simon et al. 2009), SN 2011fe shows
no evidence for variable sodium absorption in the time period
8−86 days since explosion. In this context, a recent study by
Sternberg et al. (2011) found evidence for gas outflows from
Type Ia progenitor systems in at least 20% of cases.
Independent constraints on the circumstellar medium den-
sity around Type Ia SNe come from Galactic Type Ia super-
novaremnants(SNR): thestudyofTycho’sSNR in theX-rays
lead Katsuda et al. (2010) to determine a pre-shock ambient
density of less than ∼ 0.2cm−3; the ambient density is likely
<1cm−3both in the case of Kepler’s SNR (Vink 2008) and in
the case of SNR 0509-67.5(Kosenko et al. 2008).
We emphasize that different type Ia SNe might have dif-
ferent progenitor systems as suggested by the increasing ev-
idence of diversity among this class: we know that 30% of
local SNe Ia have peculiar optical properties (Li et al. 2011b,
Li et al. 2001). The above discussion directly addresses the
progenitor system of SN 2011fe: our conclusions cannot be
extended to the entire class of type Ia SNe.
4. LIMITS ON THE POST-SHOCK ENERGY DENSITY
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 ǫB(post
shock energy density in magnetic fields).
quence, when combined with radio observations of syn-
chrotron self-absorbed SNe, deep X-ray limits can be used
to constrain the ǫB vs.ambient density parameter space
(Chevalier & Fransson 2006; Katz 2012). This is shown in
Fig. 4 for a wind (upper panel) and ISM (lower panel) en-
vironment around SN 2011fe: the use of the same formalism
(andassumptions)allowsustodirectlycombinetheradiolim-
its from Chomiuk et al. (2012) with our results. We exclude
the values of ǫB< 0.02 coupled to˙M > 2×10−9M⊙y−1for a
wind medium, while ǫB< 0.1 for any˙M > 5×10−10M⊙y−1.
In the case of an ISM profile, X-ray limits rule out the ǫB<
2×10−3nCSM> 150cm−3parameter space.
The exact value of the microphysical parameters ǫB and
ǫe is highly debated both in the case of non-relativistic
(e.g. SNe) and relativistic (e.g.
GRBs) shocks: equipartition (ǫB/ǫe∼ 1) was obtained for
SN 2002ap from a detailed modeling of the X-ray and ra-
dio emission (Björnsson & Fransson 2004) while significant
departure from equipartition (ǫe/ǫB≈ 30) has recently been
suggested by Soderberg et al. (2011) to model SN 2011dh.
The same is true for SN 1993J, for which ǫB/ǫe ≫ 1
(Fransson & Björnsson 1998).
tic shocks, GRB afterglows seem to exhibit a large range
of ǫB and ǫe values (e.g. Panaitescu & Kumar 2001); fur-
thermore, values as low as ǫB∼ 10−5have 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, start-
As a conse-
Gamma-Ray Bursts,
In the context of relativis-

Page 7

X-ray limits on SN 2011fe7
FIG. 4.— Constraints on the post-shock energy density in magnetic fields
vs. ambient density parameter space as obtained combining the X-ray to
the radio limits from Chomiuk et al. (2012). Upper panel: wind scenario.
Lower panel: ISM environment. In both panels the grey area marks the
pre-explosion density as measured from radio observations at the SN site
(Chomiuk et al. 2012). A distance of 4×1015cm has been used in the case
of a wind medium. The horizontal dashed line marks equipartition (ǫB= ǫe)
for the assumed ǫe= 0.1. THINGS stands for “The HI Nearby Galaxy Sur-
vey" (Walter et al. 2008).
ing from relativistic MHD simulations Zhang et al. (2009)
concluded ǫB∼ 5×10−3: this result applies to GRB inter-
nal shocks, the late stage of GRB afterglows, transrelativis-
tic 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 mag-
netic field generation and particle acceleration might be be-
tween relativistic and non-relativistic shocks.
Figure 4 constitutes the first attempt to infer the ǫBvalue
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.
5. GAMMA AND X-RAY EMISSION FROM SHOCK BREAK OUT
Shock break out from WD explosions is expected to
produce a short (≈ 1 − 30ms) pulse with typical ∼ MeV
photon energy, luminosity ∼ 1044ergs−1and energy in the
range 1040−1042erg (Nakar & Sari 2011). 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 break-out using data collected by the nine
spacecrafts of the interplanetarynetwork (IPN Mars Odyssey,
Konus-Wind, RHESSI, INTEGRAL (SPI-ACS), Swift-BAT,
Suzaku, AGILE, MESSENGER, and Fermi-GBM).
The IPN is full sky with temporalduty cycle ∼100%and is
sensitive to radiation in the range 20−104keV (Hurley2010).
Within a 2-day window centered on Aug 23rd a total of 3
bursts were detected and localized by multiple instruments of
the IPN. Out of these 3 confirmed bursts, one has localiza-
tion consistent with SN 2011fe. Interestingly, this burst was
detected by KONUS, Suzaku and INTEGRAL (SPI-ACS) on
August23rd13:28:25UT: forcomparison,the inferredexplo-
sion 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
poorlocalizationofthiseventdoesnotallowustofirmlyasso-
ciate this burst with SN 2011fe: from poissonian statistics we
calculate a ∼ 10% chance probability for this burst to be spa-
tially consistent with SN 2011fe. A more detailed analysis re-
veals that SN 2011fe lies inside the KONUS-INTEGRAL tri-
angulationannulusbut outsidetheKONUS-Suzakutriangula-
tion annulus. Furthermore, at the inferred time of explosion,
SN 2011fe was slightly above the Fermi-GBM horizon, but
no burst was detected (in spite of the stable GBM background
around this time). We therefore conclude that there is no sta-
tistically significant evidence for a SN-associated burst down
to the Fermi-GBM threshold (fluence ∼ 4×10−8ergcm−2in
the 8-1000 keV band)31.
The early photometry of SN 2011fe constrains the progen-
itor radius to be Rp? 0.02R⊙(Bloom et al. 2011). Using the
fiducial values E = 1051erg, Mej= 1.4M⊙, the shock break
out associated with SN 2011fe is therefore expected to have
released EBO? 3×1041erg over a time-scale tBO? 2ms with
luminosity LBO? 7×1043ergs−1at typical TBO? 250keV
(see Nakar & Sari 2011, their Eq.
of SN 2011fe, the expected fluence is as low as ∼ 5 ×
10−11ergcm−2which 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 ∼ 6×10−9ergcm−2).
For comparison, the KONUS-Suzaku-INTEGRAL burst for-
mally consistent with the position of SN 2011fe was detected
with fluence ∼ 3×10−6ergcm−2and duration of a few sec-
onds (peak flux of ∼ 4×10−7ergs−1cm−2). If it were to be
connected with the SN, the associated 3−sec peak luminos-
ity would be L ∼ 2×1045ergs−1and total energy E ∼ 1046erg
(quantities computed in the 20-1400 keV energy band) which
are orders of magnitudes above expectations.
For t > tBO, the temperature and luminosity drop quickly
(see Nakar & Sari 2011 for details): in particular, for t > tNW
the emitting shell enters the Newtonian phase. For SN 2011fe
we estimate tNW∼ 0.3s (Nakar & Sari 2011, their Eq. 30);
29).At the distance
31Swift is sensitive to fainter bursts: however it has a limited temporal
coverage. We note that Swift-BAT was active and no burst was detected dur-
ing the time window extending from 16:03:54 UT to 16:30:53 UT, implying
a probability > 50% for a SN-associated burst with fluence above the Swift
threshold and below the Fermi-GBM one to occur without being detected.

Page 8

8Margutti et al.
for Rp? 0.02R⊙the luminosity at t = 10×tNWis L(tNW) ?
1 × 1041ergs−1with typical emission in the soft X-rays:
T(tNW) ? 0.2keV. At later times L ∝ t−0.35(Nakar & Sari
2011) while T rapidly drops below the Swift-XRT energy
band (0.3-10 keV). Swift-XRT observations were unfortu-
nately not acquired early enough to constrain the shock break
out emission from SN 2011fe. UV observations were not
acquired early enough either: after ∼ 1 hr the UV emis-
sion connected with the shock break out is expected to be
strongly suppressed due to the deviation from pure radiation
domination (e.g. Rabinak et al. 2011). It is however inter-
esting 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
Fig. 2) whose origin is still unclear (see however Piro 2012).
A detailed modeling is required to disentangle the contribu-
tion 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 Ex∼ 1046−1047erg in the hours following the ex-
plosion (a mechanism which has been referred to as the ana-
log of shock break out emission in core collapse SNe, Kasen
2010). According to Kasen (2010), in the most favorable sce-
nario of a red-giant companion of M ∼ 1M⊙ at separation
distance a = 2×1013cm, the interaction time-scale is ∼ 5hr
after the SN explosion and the burst of X-ray radiation lasts
1.9hr (with a typical luminosity ∼ 6×1044ergs−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 de-
tected either: at t ∼ 1.5days, the emission has Teff? 25000K
and peaks at frequency ν ? 3×1015Hz (Eq. 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 a SN
with its companion star.
6. CONCLUSION
IC emission provides solid limits to the environment den-
sity which are not dependenton assumptions about the poorly
constrained magnetic field energy density (i. e. the ǫBparam-
eter; see also Chevalier & Fransson 2006 and Horesh et al.
2011). This is differentfrom the synchrotronemission, which
was used in our companion paper (Chomiuk et al. 2012) to
constrain the environment of the same event from the deep-
est radio observations ever obtained for a SN Ia. The two
perspectives are complementary: the use of the same assump-
tions and of a consistent formalism furthermore allows us to
constrain the post-shock energy density in magnetic fields vs.
ambientdensity parameterspace (see Fig. 4). This plot shows
how deep and contemporaneous radio and X-rays observa-
tions of SNe might be used to infer the shock parameters.
TheIC luminosityis howeverstronglydependentonthe SN
bolometric luminosity: LIC(t) ∝ Lbol(t). Here we presented
the deepest limit on the ambient density around a type Ia SN
obtainedfromX-rayobservations. Our results directlybenefit
from: (i) unprecedenteddeep Chandra observations of one of
the nearest type Ia SNe, coupled to (ii) a consistent treatment
of the dynamics of the SN shock interaction with the environ-
ment (Appendix A and Chomiuk et al. 2012), together with
(iii) the direct computation of the SN bolometric luminosity
from Swift/UVOT data.
In particular we showed that:
• Assuming a wind profile the X-ray non-detections
imply a mass loss
˙M < 2 × 10−9M⊙yr−1for vw=
100kms−1. This is a factor of ∼ 10 deeper than the
limit reported by Horesh et al. 2011. This rules out
symbiotic binary progenitors for SN 2011fe and argues
against Roche-lobe overflowingsubgiants and main se-
quence secondary stars if a fraction ? 1% of the trans-
ferred mass is lost at the Lagrangianpoints and the WD
is steadily burning.
• Were SN 2011fe to be embedded in an ISM environ-
ment, our calculations constrain the density to nCSM<
160cm−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)×1016cm. This is either
consistent with the bulk of material (transferred from the
donor star to the accreting WD or resulting from the merg-
ing of the two WDs) to be confined within the binary sys-
tem or with a significant delay ? 105yr between mass loss
andSN explosion(e.g. Justham 2011, Di Stefano et al. 2011).
Note that in the context of DD mergers, the presence of ma-
terial on distances 1013−1014cm (as recently suggested by
e.g. Fryer et al. 2010 and Shen et al. 2011) 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 associ-
ated with the shock break out from SN 2011fe. We find no
statistically significant evidence for a SN-associated burst for
fluences>6×10−7ergcm−2. However,withprogenitorradius
Rp<0.02R⊙theexpectedSN2011feshockbreakoutfluence
is ≈ 5×10−11ergcm−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 pa-
per difficult to be surpassed in the near future for type Ia SNe.
However, the generalized IC formalism of Appendix A is ap-
plicable to the entire class of hydrogen poor SNe, and will
provide the tightest constraints to the explosion environment
if X-rayobservationsareacquiredaroundmaximumlight(see
Fig. 2) for Type I supernovae (Ia, Ib and Ic).
We thank Harvey Tananbaum and Neil Gehrels for mak-
ing Chandra and Swift observations possible.
Re’em Sari, Bob Kirshner, Sayan Chakraborti, Stephan Imm-
ler, Brosk Russel and Rodolfo Barniol Duran for help-
ful discussions.L.C. is a Jansky Fellow of the National
Radio Astronomy Observatory.
Clay Fellowship.KH is grateful for IPN support un-
der 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. POS acknowledges partial support
from NASA Contract NAS8-03060.
We thank
R.J.F. is supported by a

Page 9

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APPENDIX
INVERSE COMPTON LUMINOSITY
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 Inverse Compton (IC), see e.g. Chevalier et al. (2006), Chevalier & Fransson (2006). Here
we generalize Eq. (31) from Chevalier & Fransson (2006) for a population of relativistic electrons with arbitrary distribution
ne(γ) = n0γ−pfor γ > γmin, both for an ISM (Eq. A6) and a wind (Eq. A8) scenario.
Using the IC emissivity given by Felten & Morrison (1966), their Eq. 27, the IC luminosity reads:
dLIC
dν
= 2.1σTc
?h
3.6k
?3−p
2R2n0∆RρradT
p−3
2
effν
1−p
2
(A1)
where ρrad(t) =Lbol(t)
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 Rc
(Chevalier & Fransson 2006). For ρSN∝ R−nwith n = 10 the forward shock is at 1.239Rc(1.131Rc) while the reverse shock is
at 0.984Rc(0.966Rc) 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 ∆R ∼ 0.8R (∆R ∼ 0.7R) for an assumed wind (ISM)
density profile.
4πR2cis the energy density of photons of effective temperature Teffwhich are upscattered to ∼ 3.6γ2kTeff; ∆R is

Page 10

10Margutti et al.
Ifa fractionǫeofthe post-shockenergydensitygoesinto nonthermalrelativistic electrons,from?∞
we have:
n0=9(p−2)ǫeρCSMv2
γminγ·ne(γ)dγ =9/8ǫeρCSMv2
s
sγ(p−2)
min
8mec2
(A2)
for p > 2. Combining Eq. A1 with Eq. A2, we obtain Eq. 1. The temporal evolution of LICdirectly depends on Lbol(t); Teff(t);
vs(t); R(t) and γmin(t). The properties of the SN and of its progenitor determine Lbol(t), Teff(t) and the profile of the outer ejecta
ρSN∝ R−n. We assume n ∼ 10 through out the paper (e.g. Chevalier & Fransson 2006). The environment sets the ρCSMprofile,
which we parametrize as ρCSM≡ A·R−s. Both the SN explosion properties and the environment determine the shock dynamics:
evolutionofthe shockradius R(t),shockvelocityvs(t)and,as a consequenceγmin(t). Underthoseconditionsthe shockinteraction
region can be described by a self-similar solution (Chevalier 1982) with the shock radius evolving as R ∝t(n−3
?n−3
n−s
The shock velocity directly determines γmin. From Soderberg et al. (2005), assuming that all electrons go into a power-law
spectrum with spectral index p:
γmin(t) =9ǫe
8η
me
c
where η is the shock compression parameter, Ne(Ni) is the electron (ion) number density and µi is the average number of
nucleonsper atom. We furthermoredefine g(Z)≡
?
Ne/Ni
(Chevalier & Fransson 2006), Z = Z⊙.
n−s)which implies:
vs(t) =
?R(t)
t
(A3)
?mp
??vs(t)
?2?
µi
Ne/Ni
??p−2
p−1
?
(A4)
µi
?
. For Solar metallicity g(Z⊙)≈1.22. In the followingwe assume η ≈4
ISM scenario:
The self-similar solutions for the interaction of the SN ejecta with an ISM-like circumstellar medium (s = 0, ρCSM≡ A/Rs= A)
lead to (Chevalier 1982, Soderberg et al., in prep):
?−0.1?
1051erg
vs(t) = 2.4×109?
A
g/cm3
E
?0.35?Mej
1.4M⊙
?−0.25?t
s
?−0.29
cms−1
(A5)
where Mejis the mass of the ejected material and E is the energy of the supernova explosion. Eq. A2, A3, A4 and A5, together
with Eq. A1, predict an IC luminosity:
dLIC
dν
= fISM(p,Z)ǫp−1
e
?Mej
1.4M⊙
?1−2p
4?
A
gcm−3
?(1.1−0.2p)?
E
1051erg
?(0.7p−0.35)?t
s
?(1.29−0.58p)T
p−3
2
effν
1−p
2
?Lbol
ergs−1
?erg
sHz
(A6)
with fISM(p,Z)≈2.0×107(103)(1.1−0.2p)(1.3×10−11)
in (hydrogen)particles per cm3.
3−p
2
?
53.9
2+p
?(p−2)
(p−2)(p−1)g(Z)(p−2). In the bodyof the paperA will be reported
WIND scenario:
For s = 2 (ρCSM≡ A/R2) the self-similar solutions lead to (Chevalier 1982, Soderberg et al., in prep):
A
g/cm
Combining Eq. A2, A3, A4 and A7 with Eq. A1 we obtain:
?(0.93−0.62p)?
gcm−1
vs(t) = 6.6×1011?
?−0.12?
E
1051erg
?0.43?
M
1.4M⊙
?−0.31?t
s
?−0.12
cms−1
(A7)
dLIC
dν
= fWIND(p,Z)ǫp−1
e
?Mej
1.4M⊙
A
?(1.36−0.24p)?
E
1051erg
?(0.86p−1.29)?t
s
?−(0.24p+0.64)
T
p−3
2
effν
1−p
2
?Lbol
ergs−1
?erg
sHz
(A8)
with fISM(p,Z) ≈ 6.7×10−710(0.24p−1.36)(1.3×10−11)
Note that ρCSM≡A/R2≡˙M/(4πvwR2), so that A =˙M/(4πvw), where˙M and vware 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.
3−p
2
?
5.6×105
2+p
?(p−2)
(p−2)(p−1)g(Z)(p−2).