The supernova/gamma-ray burst/jet connection
Jens Hjorth
The observed association between supernovae and gamma-ray bursts represents a cornerstone in our understanding of the nature of gamma-ray bursts. The collapsar model \citep{1999ApJ...524..262M} provides a theoretical framework for this connection. A key element is the launch of a bi-polar jet (seen as a gamma-ray burst). The resulting hot cocoon disrupts the star while the $^{56}$Ni produced gives rise to radioactive heating of the ejecta, seen as a supernova. In this discussion paper I summarise the observational status of the supernova/gamma-ray burst connection in the context of the `engine' picture of jet-driven supernovae and highlight SN 2012bz/GRB 120422A -- with its luminous supernova but intermediate high-energy luminosity -- as a possible transition object between low-luminosity and jet gamma-ray bursts. The jet channel for supernova explosions may provide new insight into supernova explosions in general.
hjorth_revised.tex
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\jname{Phil. Trans. R. Soc. A}
\markboth{SN/GRB/jet connection}{SN/GRB/jet connection}
\begin{document}

\title[SN/GRB connection]{The supernova/gamma-ray burst/jet connection}

\author{Jens Hjorth}

\address{Dark Cosmology Centre, Niels Bohr Institute, University of
Copenhagen, \\
Juliane Maries Vej 30, DK-2100 Copenhagen \O, Denmark}

\keywords{supernovae; gamma-ray bursts; jets}
%\classification{supernovae; gamma-ray bursts}

\label{firstpage}


\abstract{
The observed association between supernovae and gamma-ray bursts represents a 
cornerstone in our understanding of the nature of gamma-ray bursts. The 
collapsar model \citep{1999ApJ...524..262M} provides a theoretical framework 
for this connection. A key element is the launch of a bi-polar jet (seen as 
a gamma-ray burst). The resulting hot cocoon disrupts the star while the
$^{56}$Ni produced gives rise to radioactive heating of the ejecta, seen as 
a supernova. In this discussion paper I summarise the observational status of 
the supernova/gamma-ray burst connection in the context of the `engine' 
picture of jet-driven supernovae and highlight SN 2012bz/GRB 120422A --
with its luminous supernova but intermediate high-energy luminosity -- 
as a possible transition object between low-luminosity and jet gamma-ray 
bursts. The jet channel for supernova explosions may provide new insight 
into supernova explosions in general.
}

\maketitle


\section{Introduction}


SN 1998bw \citep{1998Natur.395..670G,1998Natur.395..663K}, coincident in 
space and time with GRB 980425, remains the prototype radio-bright, 
broad-lined (BL) Type Ic supernova, against which other supernova/gamma-ray 
bursts are measured up. GRB 980425, however, was peculiar, 
with an isotropic equivalent energy release in $\gamma$-rays of only 
$E_{\rm \gamma,iso}\sim 10^{48}$ erg.  The optical lightcurve of SN 1998bw,
depicted in Fig.~1, exhibited a characteristic rise to peak of about 
$M_V=-19.2$ mag in about 16 days, similar to a Ia supernova. 
\citet{1999ApJ...524..262M} 
predicted that ``{\it all gamma-ray bursts produced by the collapsar model 
will also make supernovae like SN 1998bw}''. In this model, the progenitor
star is a Wolf--Rayet star \citep{2007ARA&A..45..177C,2012ARA&A..50..107L}, 
i.e., a massive star which has shed its envelope of hydrogen and helium, 
possibly through eruptions \citep{2006ApJ...645L..45S}.

%The first indication of such a SN 1998bw-like lightcurve from a GRB
%was observed in 
%GRB 980326 (at about the time SN 1998bw/GRB 980425 was detected!) as 
%an excess flux (a lightcurve `bump') relative to the extrapolated afterglow 
%decay \citep{1999A&AS..138..449C,1999Natur.401..453B}. The redshift 
%unfortunately was not determined, although consistent with $z\approx1$ under
%the assumption that the bump was caused by a supernova similar to SN 1998bw.

\begin{figure}
 \includegraphics[width=1.00\columnwidth]{grbsn_all.ps}
 \caption{Optical lightcurves for the grade A \citep{2011arXiv1104.2274H}
 spectroscopic supernovae
 associated with gamma-ray bursts (excluding SN 2012bz). 
 The olive points are supernovae from
 low-luminosity gamma-ray bursts while the orchid data
 points are for SN 2003dh, associated with the jet 
 gamma-ray burst GRB 030329. There is considerable diversity in the light
 curves, regarding time to peak and peak magnitude. The $^{56}$Co decay
 slope is shown for reference (dashed line). Also shown are upper
 limits on supernova emission from long gamma-ray bursts (blue) and short
 gamma-ray bursts (red)
 \citep[adapted from][]{2011arXiv1104.2274H}.
A recent compilation of lightcurves of other supernovae associated with 
gamma-ray bursts is available in \citet{2011ApJ...740...41C}. 
          }
 \label{fig:lightcurves}
\end{figure}

The ultimate proof of a SN 1998bw-like supernova associated with a `normal'
cosmological gamma-ray burst with $E_{\rm \gamma,iso}\sim 10^{52}$ erg
came with the spectroscopic 
identification of SN 2003dh associated with GRB 030329, as a supernova 
spatially and temporally coincident with the gamma-ray burst, and with 
lightcurve properties and spectroscopic broad-line evolution very similar to
that of SN 1998bw \citep{2003ApJ...591L..17S,2003Natur.423..847H}.

The night before the Royal Society Discussion Meeting on ``New
windows on transients across the universe'', GRB 120422A was observed by
{\it Swift} and subsequently by ground-based telescopes at a redshift of 0.28.
An accompanying supernova was predicted at the meeting and indeed 
reported soon after as SN 2012bz 
\citep{2012GCN..13276...1W,2012GCN..13277...1M}.

In this paper I focus on `jet-driven' supernovae and their relation 
(or lack thereof) to the different classes of gamma-ray bursts and
highlight the importance of SN 2012bz/GRB 120422A. More comprehensive 
(and less speculative) reviews of the supernova/gamma-ray burst connection 
can be found in \citet{2006ARA&A..44..507W} and \citet{2011arXiv1104.2274H}.



\section{Supernovae associated with long-duration gamma-ray bursts}

There seem to be two types of long-duration gamma-ray bursts. The
exact division is unclear but we will discuss them in turn below.

\subsection{Low-luminosity gamma-ray bursts}

Low-luminosity gamma-ray bursts (also termed `sub-energetic' or
`nearby' bursts) seem
to be about 100 times as common as the other class discussed
below \citep{2006Natur.442.1011P}, but because of their low 
luminosities they are primarily found at low redshifts as
rare events (one every $\sim 3$ years). They typically 
have single-peak high-energy prompt lightcurves, soft high-energy 
spectra, and are often found to be X-ray flashes, i.e.,
gamma-ray bursts with peak energies below $\sim 50$ keV.
Observational evidence suggests that the radio and high-energy
emission is due to the breakout of a relativistic shock
from the surrounding massive wind of the progenitor star
\citep{1968CaJPh..46..476C,1998Natur.395..663K,2006Natur.442.1008C,
2006Natur.442.1014S,2012ApJ...747...88N}. Apart from SN 2003dh (and 
possibly SN 2012bz), the best studied supernovae related to gamma-ray bursts 
are all members of this class. Their lightcurves are shown in Fig.~1.

\subsection{Jet gamma-ray bursts}

\begin{figure}
 \includegraphics[width=1.00\columnwidth,clip=]{compare.ps}
 \caption{Schematic diagram illustrating the challenges in detecting supernova 
 light on the background of the gamma-ray burst afterglow and the host galaxy. 
 The supernova region
 (olive) reflects the range in lightcurves shown in Fig.~1. The 
 afterglow is assumed to decay as $t^{-1.5}$; the afterglow region 
 reflects the range in 
 afterglow brightness reported by \citet{2010ApJ...720.1513K}. The range in 
 host galaxy magnitudes reflect those
 detected in the TOUGH survey \citep{2012ApJ...756..187H}. 
 The diagram shows that observed lightcurves 
 may either be supernova, afterglow or host galaxy dominated. All situations
 are encountered in nature.
 }
 \label{fig:compare}
\end{figure}

These are also known as `normal' or `cosmological' gamma-ray bursts 
(or `collapsar' bursts, although this is a somewhat theory-laden term) 
and are characterised by more complex prompt emission lightcurves and
higher energies, luminosities and peak energies. They are believed to arise 
from emission from a relativistic jet at large distances from the progenitor 
star.

Observing a supernova related to a gamma-ray burst at higher redshift
is challenging because of possible contamination by the host galaxy
(which often appears unresolved in ground-based observations) and 
the afterglow. This is illustrated
in Fig.~2. Indeed, as shown by \citet{2004ApJ...606..381L}, the
lightcurve of GRB 0303029 did not exhibit a conspicuous lightcurve
bump from SN 2003dh because it was afterglow dominated. 
%
Besides 2003dh
(shown in Fig.~1), the best example of a supernova related to a gamma-ray 
burst in this class is SN 2010ma \citep{2011ApJ...735L..24S}
(and possibly SN 2012bz).
\subsection{Statistical properties of supernovae associated with 
gamma-ray bursts}

Inferring statistical properties of supernovae associated with
gamma-ray bursts requires a well-defined sample.
For this purpose \citet{2011arXiv1104.2274H} devised a grading
scheme for each supernova claimed in the literature to be related 
to a gamma-ray burst. The evidence for a supernova was graded A--E.%
\footnote{We have created a website (http://www.dark-cosmology.dk/GRBSN) 
dedicated to providing updates to the list of supernovae related to gamma-ray 
bursts, the grading of the observational evidence for a supernova, and 
supplementary 
information on the supernovae and the associated gamma-ray bursts.}
Based on supernovae with grades A,B,C we plot in Fig.~3 the
distribution of peak supernova magnitudes as a function of
isotropic equivalent luminosity in $\gamma$-rays. Defining
$L_{\rm \gamma,iso} = E_{\rm \gamma,iso} T_{90} ^{-1} (1+z)$
we have tentatively identified low-luminosity gamma-ray bursts as having
$L_{\rm \gamma,iso} < 10^{48.5}$ erg s$^{-1}$ and jet gamma-ray bursts as
having $L_{\rm \gamma,iso} > 10^{49.5}$ erg s$^{-1}$. 
There is a real dispersion in the peak magnitudes; supernovae related
to gamma-ray bursts are evidently not standard candles. It remains an 
open question whether they are standardizable similar to Type Ia supernovae
\citep{2005ApJ...626L...5S,2011ApJ...740...41C}. It is evident that the
lightcurves of the subsample of supernovae shown in Fig.~1 exhibit a clear 
correlation between the peak magnitude and the width of the peak.

We note that beaming and viewing angle can significantly affect the 
inferred high-energy luminosity \citep{2010arXiv1012.5101G}. For example,
GRB 091127, which appears in the high-luminosity (jet) part of 
Fig.~3, has been suggested to be a sub-energetic burst 
\citep{2012ApJ...761...50T} due to a beaming correction. 
Nevertheless, it is evident that there appears to be a
parabola-shaped upper envelope to the brightness of supernovae
as a function of high-energy luminosity. By the time of 
the meeting there were no gamma-ray bursts with convincing supernovae in 
the range $10^{48.5}$ erg $<E_{\rm \gamma,iso} < 10^{49.5}$ erg.
This changed with SN 2012bz/GRB 120422A which fills this gap in
high-energy luminosity as one of the brightest supernovae associated
with a gamma-ray burst ever detected \citep{2012A&A...547A..82M}.
%$E_{\rm \gamma,iso} < 10^{50}$ erg and jet gamma-ray bursts as
%$E_{\rm \gamma,iso} > 10^{51}$ erg. Curiously, there are no
%gamma-ray bursts with convincing supernovae in the range
%$10^{50}$ erg $<E_{\rm \gamma,iso} < 10^{51}$ erg.


\begin{figure}
 \includegraphics[width=1.00\columnwidth,clip=]{lmv.ps}
 \caption{Supernova optical peak brightness versus gamma-ray burst isotropic
 luminosity \citep{2008MNRAS.391..577A,2009A&A...508..173A} for grade A,B,C 
 systems \citep{2011arXiv1104.2274H}. Low-luminosity gamma-ray burst supernovae 
 ($E_{\rm \gamma,iso} < 10^{48.5}$ erg, olive) and supernovae from 
 jet gamma-ray bursts ($E_{\rm \gamma,iso} > 10^{49.5}$ erg, orchid) have 
 similar distributions of peak brightness. SN 2012bz/GRB 120422A is 
 highlighted (orange) as a possible transition object in the grey area
 $10^{48.5}$ erg $<E_{\rm \gamma,iso} < 10^{49.5}$ erg
 \citep{2012ApJ...756..190Z}.
 }
 \label{fig:emv}
\end{figure}


How do these peak magnitudes compare to other similar supernovae,
i.e., Type Ic supernovae, with no hydrogen or helium in their
spectra? Using the well-defined sample of normal Ic supernovae
from \citet{2011ApJ...741...97D} and a more heterogeneous sample of 
broad-lined Ic supernovae from a variety of sources, we plot in
Fig.~4 cumulative histograms of their peak magnitudes. Type Ic supernovae
seem to be fainter than supernovae related to gamma-ray bursts
while the situation is less clear-cut for Ic-BL supernovae with
no GRBs. We note
that strong observational evidence (grade A--C) quite naturally
will bias our sample against fainter supernovae.

\begin{figure}
 \includegraphics[width=1.00\columnwidth,clip=]{grbic.ps}
 \caption{Cumulative distributions of the brightness of different
 kinds of Ic supernovae. The supernovae associated with gamma-ray
 bursts graded A, B, or C are from \citet{2011arXiv1104.2274H}. 
 The normal Ic supernovae are from \citet{2011ApJ...741...97D}.
 The Ic-BL distribution comes from a variety of sources and as such
 represents a more ill-defined sample. The gamma-ray burst supernovae
 generally appear brighter than normal Ic supernovae, although it 
 should be noted that they are likely biased against faint systems.
 The brightness distribution of Ic-BL is probably consistent with that 
 of gamma-ray burst supernovae although there may be a lack of very 
 bright gamma-ray burst supernovae. 
 }
 \label{fig:histogram}
\end{figure}

The comparison to Ic-BL is 
interesting because the rates of low-luminosity gamma-ray bursts and 
Ic-BL are comparable, suggesting perhaps a common origin and indicates
that low-luminosity gamma-ray bursts, as expected, may not be strongly 
beamed \citep{2004ApJ...607L..17P}. 

\section{Supernova-less gamma-ray bursts}

Two classes of gamma-ray bursts are not accompanied by bright supernovae.

\subsection{Short gamma-ray bursts}

Short-duration, hard-spectrum gamma-ray bursts \citep{1993ApJ...413L.101K},
with durations $T_{90} < 2$~s, are known not to lead to supernovae. In Fig.~1 
we have plotted the upper limits on the existence of supernovae 
accompanying GRBs 050509B \citep{2005ApJ...630L.117H} and 050709 
\citep{2005Natur.437..859H}. These constrain any supernova to be about 
100 times fainter than SN 1998bw at peak. This is consistent with short 
gamma-ray bursts being the results of compact object mergers.

The data also rule out the existence of an early rebrightning in GRB 050509B 
\citep{2005ApJ...630L.117H} at 1.5 days in the restframe. Bright transient 
emission, dubbed a `mini SN' \citep{1998ApJ...507L..59L,2002MNRAS.336L...7R},
`kilonova' \citep{2010MNRAS.406.2650M} or `macronova' 
\citep{2005astro.ph.10256K}, is expected to peak around the optical-UV range 
within a day or so with a semi-thermal spectrum \citep{1998ApJ...507L..59L}. 
GRB 050509B sets very strong contraints on such emission
\citep{2005ApJ...630L.117H,2010MNRAS.404..963K,2011ApJ...736L..21R}.


\subsection{Long supernova-less gamma-ray bursts}

Perhaps surprisingly, some long-duration gamma-ray bursts are not
accompanied by bright supernovae. As shown in Fig.~1, the constraints
on GRBs 060505 and 060614 are about as constraining as the those 
related to the short gamma-ray bursts discussed above. These puzzling 
systems may be related to non-$^{56}$Ni producing supernovae or they may be
merger gamma-ray bursts with longer durations than usually found
\citep{2006Natur.444.1044G, 2006Natur.444.1047F, 2006Natur.444.1050D,
2006Natur.444.1053G, 2007ApJ...662.1129O}.

\subsection{Mind the gap}

It is quite remarkable that current observations reveal a clear gap 
between the brightnesses of gamma-ray burst supernovae, at around absolute 
magnitude $-17$ to $-19$, and the upper limits on long supernova-less
gamma-ray bursts at around $-12$ to $-14$ mag. Finding faint supernovae is of
course difficult and fainter supernovae will likely be detected but the 
current factor of 100 may indicate that there is not a simple continuum
of events.

\section{Engine-driven supernovae}

The collapsar model \citep{1999ApJ...524..262M} 
operates with two time scales, the duration of the
active `engine' (jet), $t_E$, and the time for shock breakout, $t_S$. 
A successful gamma-ray burst requires the engine to be active for longer 
than the shock-breakout time. 
%
\citet{2011ApJ...739L..55B} and \citet{2012ApJ...750...68L} have used
this picture to explore the consequences of the relative durations for
the resulting supernovae and gamma-ray bursts
\citep[an alternative jet scenario is presented by][]{2011MNRAS.416.1697P}:

\begin{itemize}
\item
$t_E > t_S$: a normal jet gamma-ray burst accompanied by a Ic-BL is produced
\item
$t_E \approx t_S$: a low-luminosity gamma-ray burst accompanied by a Ic-BL 
or a relativistic Ic-BL with no gamma-ray burst is produced
\item
$t_E < t_S$: a non-relativistic supernova but no gamma-ray burst is produced
\end{itemize}
%
In this picture, relativistic supernovae, like SN 2009bb
\citep{2010Natur.463..513S,2011ApJ...728...14P} are jet-driven supernovae,
similar to low-luminosity gamma-ray bursts. It is worth noting
that a low luminosity is not necessarily synomynous with a short
engine duration, i.e., it may be possible to have low-luminosity
jet gamma-ray bursts, such as possibly GRB 120422A.

In the collapsar model, one could also imagine that the engine does not 
occur in a stripped-envelope core-supernova but in a Type II supernova with a 
hydrogen and/or helium layer which would prevent the escape of the jet 
\citep[see also][]{2003ApJ...591..288H}. Such massive stars 
may have a dense circumstellar medium which would make them appear as 
Type IIn supernovae, as suggested by e.g., \citet{2003astro.ph..8136N} and
\citet{2012ApJ...752L...2C}. Recently a possible jet-powered IIn (SN 2010jp)
was reported \citep{2012MNRAS.420.1135S}, albeit not a relativistic one.

The picture regarding jet-driven supernovae and gamma-ray bursts that emerges 
from the discussion in this paper is summarised in Table~1. 
SN 2012bz/GRB 120422A, which may be a transition object between the 
low-luminosity and jet gamma-ray bursts, reminds us that this fairly simple
picture could easily be more complex.


 \begin{table}[h]
  \caption{The supernova/gamma-ray burst/jet connection}
    %\begin{tabular}{l|ccccl}
    \begin{tabular}{lll}
     \hline \hline
Core-collapse supernovae & Supernova/gamma-ray bursts    & Gamma-ray bursts \\
     \hline
Relativistic Ic-BL  & Low-luminosity GRBs     & Fall-back supernovae? \\
(SN 2009bb)         & (SN 1998bw/GRB 980425)  & (GRB 060505)          \\
                    &                         &                       \\
Type IIn?           & Jet GRBs                & Mergers               \\
(SN 2010jp)         & (SN 2003dh/GRB 030329)  & (GRB 050509B)         \\
     \hline \hline
    \end{tabular}
  \label{t:table}
\end{table}


\ack{
I acknowledge discussions with Andrew MacFadyen, Paul Crowther, 
Davide Lazzati, Enrico Ramirez-Ruiz, Darach Watson and Tsvi Piran.
I thank the anonymous referees for helpful comments.
The Dark Cosmology Centre is funded by the Danish National Research
Foundation. 
}

\bibliography{hjorth}
\end{document}

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