A most energetic type Ic supernova: SN 2003L

Abstract

We present extensive radio observations of SN 2003L, the most luminous and energetic Type Ic radio supernova with the exception of SN 1998bw. Using radio data, we are able to constrain the physical parameters of the supernova, including the velocity and energy of the fastest ejecta, the temporal evolution of the magnetic field, and the density profile of the surrounding medium. We highlight the extraordinary properties of the radio emission with respect to the supernova's normal characteristics within optical bands. We find that although the explosion does not show evidence for a significant amount of relativistic ejecta, it produces a radio luminosity which is comparable to that seen in the unusual SN 1998bw. Using SN 2003L as an example, we comment briefly on the broad diversity of type Ic properties and the associated implications for progenitor models.

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arXiv:astro-ph/0310305v1 10 Oct 2003
A most energetic type Ic supernova: SN 2003L
Alicia M. Soderberg1
Palomar Observatory, 105-24, California Institute of Technology, Pasadena, CA
91125 ams@astro.caltech.edu
Summary. We present extensive radio observations of SN 2003L, the most lumi-
nous and energetic Type Ic radio supernova with the exception of SN 1998bw. Using
radio data, we are able to constrain the physical parameters of the supernova, in-
cluding the velocity and energy of the fastest ejecta, the temporal evolution of the
magnetic field, and the density profile of the surrounding medium. We highlight
the extraordinary properties of the radio emission with respect to the supernova’s
normal characteristics within optical bands. We find that although the explosion
does not show evidence for a significant amount of relativistic ejecta, it produces
a radio luminosity which is comparable to that seen in the unusual SN 1998bw.
Using SN 2003L as an example, we comment briefly on the broad diversity of type
Ic properties and the associated implications for progenitor models.
1 Introduction
Despite active campaigns to study radio emission from type Ib/c supernovae,
only a small number of events have been successfully detected. Among the
class of radio bright supernovae is SN 1998bw, an unusually bright type Ic
discovered within the error box of the nearby gamma-ray burst GRB 980425.
Reaching a peak radio luminosity ∼ 100 times higher than all other radio
bright type Ib/c supernovae (SNe), it has been proposed that SN 1998bw
was powered by a central engine, similar to the popular model for gamma-ray
bursts (GRBs) [3].
In this paper we present observations of the first radio bright type Ib/c su-
pernova with energetics comparable to those shown in SN 1998bw. SN 2003L
was optically discovered on 2003 Jan 12.15 UT [2] and spectroscopically iden-
tified on 2003 Jan 25.0 UT [5,8]. The supernova was seen to bear strong
resemblance to the typical type Ic SN 1994I at maximum light, showing low
average expansion velocities of 5900 km/s as derived from the Si II line. The
optical light-curve peaks at mV ≈ 16 which places SN 2003L among the
brightest optical type Ic SNe observed to date.

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2Alicia M. Soderberg
2 Observations with the VLA
On Jan 26.23 2003 UT we detected a radio transient coincident with the op-
tical position of SN 2003L. We subsequently initiated an intense radio moni-
toring campaign at the Very Large Array (VLA) to trace the evolution of the
radio emission from the supernova. Data were taken in standard continuum
observing mode with a bandwidth of 2×50 MHz centered on frequencies 8.5,
15.0 and 22.5 GHz. Flux density measurements were derived using calibra-
tor 3C286 and phase referenced against calibrators J1118+125, J1120+134,
and J1103+119. Data were reduced using standard packages within the As-
tronomical Image Processing System (AIPS). At 8.5 GHz (our most densely
sampled light-curve) typical flux uncertainties were ∼ 60 µJy for an average
integration time of 10 minutes. The results of our radio monitoring campaign
of SN 2003L are summarized as Figure 1. These observations demonstrate a
broad spectrum, similar to that observed for SN 1998bw.
Fig. 1. Radio light-curves for type Ic SN 2003L at 8.5, 15., and 22.5 GHz for the
time period 2003 Jan 26 - 2003 Aug 15 UT.
3 Robust Constraints
Here we discuss the constraints imposed by the radio observations for SN
2003L. As a preliminary constraint on the total energy of the source, we
estimate the brightness temperature (Tb) of the supernova and compare it with
the robust constraints imposed by equipartition arguments and the inverse
Compton catastrophe (ICC). From [6], the brightness temperature is defined
as a function of the observed flux density, the peak frequency, and the angular
size of the source. As an initial estimate for the physical size of the SN ejecta,
we first assume the optical expansion velocity of 5900 km s−1[8] can be used

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A most energetic type Ic supernova: SN 2003L3
as an average speed to describe the motion of the radio bright ejecta. Using
an approximate explosion date of Jan 1 2003 UT based on optical light-curves
[7], we estimate the shock radius to be r ≈ 4.3×1015cm at t ≈ 85 days when
the observed flux density peaked at 8.5 GHz. Using the observed peak flux of
F8.5 GHz≈ 2.8 mJy and adopting a source distance of 91.7 Mpc (ΩM= 0.27,
ΩΛ = 0.73, H0 = 71 km s−1Mpc−1), we find a brightness temperature of
Tb ≈ 1.8 × 1012K which is dangerously near the ICC limit of Tb < 1012
K. This suggests that the radio ejecta expanded with a velocity significantly
higher than that observed at optical frequencies. In fact, an ejecta velocity of
∼ 16,000 km/s (∼ 3 times larger than that derived from optical spectroscopy)
would be necessary to avoid violating the ICC constraint.
Assuming equipartition of energy places a further constraint on the bright-
ness temperature limit and reduces it to Tb< 5 × 1010K. Using the equipar-
tition arguments of [6] and [3], we derive the minimum energy for the radio
supernova. Assuming that the observed radio flux is produced by synchrotron
emission, the total energy of the source (U) can be expressed as the sum of
the energy in relativistic electrons (Ue) and the energy in the magnetic field
(UB). At equipartition, the fraction of total energy in electrons equals the
fraction of total energy in magnetic fields (ǫe = ǫB = 1) and the total en-
ergy is minimized at Ueq[6]. This occurs when the emitting source reaches an
equipartition radius denoted by the angular size, θeq. The minimum energy
of the source can be thus be parameterized in terms of the synchrotron peak
flux and the equipartition size.
Using our most densely sampled light-curve, we fit for the peak flux (Sp)
over the observed ∼ 200 day evolution and find Sp ≈ 2.8 mJy at νp = 8.5
GHz on Mar 27 2003 UT (≈ 85 days since explosion). For this epoch we
estimate an angular size θeq ≈ 19µas (with β ≈ −1.0) which implies an
averageshock velocity of v ≈ 0.1c and an equipartition brightness temperature
of Tbeq≈ 5.0×1010K. By setting U = Ueqwe find the energy is minimized at
the equipartition value of Ueq≈ 4.3 × 1047erg with an associated magnetic
field strength of Bpeq≈ 0.6 G. As shown by [6], synchrotron emission systems
which diverge from equipartition necessitate a huge increase in total energy.
Consequently, it is possible that the total energy contained within the fast
moving ejecta of SN 2003L is in fact much larger than 4.3 × 1047erg.
These preliminary constraints allow us to make two robust conclusions: 1.)
the velocity of the radio bright SN ejecta must be at least 16,000 km s−1to
avoid violating the inverse Compton catastrophe limit and ∼ 30,000 km s−1
assuming equipartition, 2.) the energy of the supernova must be > 4.3 ×
1047erg and could be significantly larger depending on the proximity of the
system to equipartition. These conclusions imply that there was a considerable
amount of energy released at high velocities in the type Ic supernova explosion
of SN 2003L. In fact, these equipartition constraints alone demand that SN
2003L is among the most energetic type Ib/c supernovae observed to date,
second only to the unusual event of SN 1998bw/GRB 980425. Figure 2 is a
compilation of all the radio bright type Ib/c supernovae observed to date.

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4Alicia M. Soderberg
By comparing the peak radio luminosity to the observed time of peak flux,
the diversity in equipartition derived expansion velocities can be examined.
Note that although SN 2003L peaks later, it is among the brightest radio
supernovae.
Fig. 2. The diversity of peak luminosities and observed time of the peak is shown
above for all radio bright type Ib/c supernova. By assuming equipartition, the ex-
pansion velocity for each event can be estimated (dashed lines).Note the radio ejecta
of SN 2003L is relatively slow and luminous.
4 Implications and Physical Parameters
Assuming equipartition values of ǫB = ǫe = 1 and adopting synchrotron
self-absorption as the dominant absorption process, we determine the tem-
poral evolution of the total energy and radius of the ejecta for SN 2003L.
For observations spanning t = 25 − 200 days, the total energy increases from
E ≈ 3.0×1047to 1.1×1048erg. Over the same period, the shock radius scales
as r ∝ t0.67from r ≈ 1.45×1016to 5.0×1016cm. Assuming an explosion date
of Jan 1 2003 UT, the average velocity decreases from v ≈ 0.22c to 0.10c. In
comparison to SN 1998bw where it was observed that v ≈ c, it is clear that SN
2003L does not have a significant amount of material moving at relativistic
speeds. However, the total energy within the radio bright ejecta remains quite
high at ∼ 10% that of SN 1998bw (on similar time-scales) and 10-100 times
greater than other radio supernovae.

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A most energetic type Ic supernova: SN 2003L5
Using the values derived for the total energy and radius, we predict the
magnetic field decreased from B ≈ 0.75 G to 0.23 G over the period t = 25−
200 days. We find an temporal evolution of B ∝ t−0.63, such that B ∝ r−0.93.
Extrapolating, we find B(t) ≈ 10 G atr ≈ 1015cm. For comparison, type IIb
SN1993J exhibited a similar evolution with B ≈ 60 G at r ≈ 1015cm and a
radial scaling of B(r) ∝ r−1.
Environmental properties can also be predicted based on our radio obser-
vations. From 25 days to 200 days, we find that the electron density, ne(t),
drops by a factor of ∼ 10 from ne ≈ 340 cm−3to 36 cm−3. Expressed in
terms of a radial dependence, ne ∝ r−1.8; similar to the density profile ex-
pected from a massive stellar wind, ne∝ r−2. This was also seen in the case of
SN 1998bw/GRB980425 [4], although solid evidence for a wind environment
has yet to be detected for the majority of observed gamma-ray bursts.
Directly coupled to the electron number density is the mass loss rate,˙M of
the progenitor star. For an assumed stellar wind velocity of w = 103km s−1,
we find a roughly constant mass loss rate of ˙ M(t) ≈ 5 × 10−6M⊙yr−1. This
is ∼10 percent larger than values derived for SN 1998bw and SN 2002ap, of
˙M(t) ≈ 2.5 × 10−7and 5 × 10−7M⊙ yr−1, respectively [1,4]. It should be
noted that these rates are consistently smaller than the predicted mass loss
rate for Wolf-Rayet stars (˙ M(t) ≈ 10−4−10−5M⊙yr−1) , which are thought
to be the progenitors of type Ic supernovae.
5 Discussion
Although the constraints provided by equipartition arguments are robust, they
are also preliminary. The extensive radio data set for SN 2003L warrants a full
modeling effort to accommodate the effects of multiple absorption processes
including synchrotron self-absorption and free-free absorption. Results from
our radio modeling study of SN 2003L will be presented along with extensive
broadband data for this event [7]. We will show that the highly energetic
supernovae SN 2003L is becoming one of the best studied radio supernovae
to date, thereby offering new insights on the diversity of cosmic explosions.
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