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# A hyper flare of a weeks-old magnetar born from a binary-neutron-star merger

B.-B. Zhang1,2∗ Z. J. Zhang1,2 J.-H. Zou1,2,3 X. I. Wang1,2 Y.-H. Yang1,2
J.-S. Wang4 J. Yang1,2 Z.-K. Liu1,2 Z.-K. Peng1,2 Y.-S. Yang1,2 Z.-H. Li1,2
Y.-C. Ma5 B. Zhang6

1School of Astronomy and Space Science, Nanjing University, Nanjing 210093,
China
2Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University),
Ministry of Education, China
3College of Physics, Hebei Normal University, Shijiazhuang 050024, China
4Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg,
Germany
5School of Artificial Intelligence, Nanjing University, Nanjing 210093, China
6Department of Physics and Astronomy, University of Nevada Las Vegas, NV
89154, USA

∗Corresponding author; E-mail<EMAIL_ADDRESS>

###### Abstract

MagnetarsDuncan:1992ApJ.392L, a population of isolated neutron stars with
ultra-strong magnetic fields of $\sim 10^{14}-10^{15}$ G, have been
increasingly accepted to explain a variety of astrophysical transients. A
nascent millisecond-period magnetar can release its spin-down energy and power
bright sources such as Gamma-ray BurstsUsov1992Natur (GRBs) and their
subsequent X-ray plateaus2006ApJ...642..354Z, Super Luminous Supernovae
(SLSNe) Kasen10, Woosley10, and the fast X-ray transients such as CDF-S
XT-22019Natur.568..198X. Magnetars with ages of $10^{3}-10^{4}$ years have
been observed within the Milky Way Galaxy, which are found to power diverse
transients with the expense of their magnetic energy, in the form of giant
flares and repeated soft-$\gamma$-ray or hard X-ray bursts Thompson:1995MNRAS,
Kaspi:2017ARA and occasionally fast radio bursts (FRBs) CHIME/FRB:2020Natur,
Bochenek2020. Magnetar giant flares were also detected as disguised short GRBs
from nearby galaxies Roberts2021Natur, 2021Natur.589..211S, YangJun:2020ApJ.
Here we report the identification of a GRB as a hyper flare of magnetar in a
nearby galaxy. The magnitude of the hyper flare is about one thousand times
brighter than that of a typical magnetar giant flare. A significant $\sim 80$
millisecond period is detected in the decaying light curve. Interpreting this
period as the rotation period and given a magnetic field strength typical for
a young magnetar, the age of the magnetar is constrained to be only a few
weeks. The non-detection of a (superluminous) supernova nor a GRB weeks before
the event further constrains that the magnetar is likely born from an off-axis
merger event of two neutron stars. Our finding bridges the gap between the
hypothetical millisecond magnetars and the observed Galactic magnetars, and
points toward a broader channel of magnetar-powered gamma-ray transients.

Figure 1:  Light curve and periodic signal detection of the hyper flare event,
GRB 130310A. Figure 2:  The $E_{\rm p}$ versus $E_{\rm iso}$ correlation
diagram. The upper left purple, middle blue and lower right black solid lines
show the best-fit correlations for the MGF, short and long GRB populations,
respectively. Dashed borderlines show the 3$\rm\sigma$ regions for each
correlation. The red dashed line represents the locations of the sharp peak of
GRB 130310A at different redshift values. The red square marks its location at
a redshift of z = 0.0155, which is determined by its candidate host galaxy,
g0927191-170053. The two red circles mark the allowed edge if the MGF folows
the MGF-GRB track. All error bars represent 1$\sigma$ uncertainties.

Recent observations of the extragalactic magnetar giant flare
(MGF)Roberts2021Natur, 2021Natur.589..211S, YangJun:2020ApJ, GRB 200415A,
suggested that MGF GRBs follow the third track (other than long and short
GRBs) in the rest-frame peak energy vs. isotropic energy ($E_{\rm p}-E_{\rm
iso}$) planeYangJun:2020ApJ. Motivated by this new track, we performed a
systematic search in the Fermi/GBM GRB archives2020ApJ...893...46V, aiming at
finding additional MGF GRB cases. Our search started from looking for those
GRBs with relatively high $E_{\rm p}$ and low $E_{\rm iso}$ (or low fluence if
the redshift is not available), so they can be outliers of the short and long
GRB populations in the $E_{\rm p}-E_{\rm iso}$ diagram. Our search quickly
returned a strong candidate, GRB 130310A (Figure 1). The burst consists of two
main emission episodes: a precursor and a main burst, lasting a total of
$\sim$ 4.2 seconds (see Methods and Extended Figure 1). The precursor
triggered Fermi/GBM2013GCN.14283....1X at 20:09:41.503 on March $10^{th}$ 2013
UTC (hereafter $T_{0}$) and lasted for approximately 0.8 s. It is
characterized by a thermal spectrum with $kT=45.06^{+13.57}_{-5.69}$ keV
(Methods). The main burst occurred at about $T_{0}+3.8$ s and presented a
sharp peak followed by a series of erratic overlapping pulses and lasted for
approximately 1.3 s (Methods). Such a profile broadly resembles the previous
observations of magnetar giant flaresMereghetti2005ApJ...628..938M, which are
characterized by a hard, sharp spike followed by a soft, long-lasting tail.
The time-integrated spectrum of the main burst is characterized by a Cutoff
Power Law (CPL) model with $E_{\rm p}=2732.60_{-197.80}^{+229.75}$ keV and
$\alpha=-1.10_{-0.01}^{+0.01}$. Such an $E_{p}$ value is already significantly
higher than most GRBs, making GRB 130310A, even with any assumed redshift
between 0.0001 and 10, a distinct outlier from the long collapsar-type GRB
track in the $E_{\rm p}-E_{\rm iso}$ diagram (Figure 2). In consideration of
its strong spectral evolution (Methods) as well as its spike+tail feature, we
treat the 27-ms sharp peak (SP) (ranging from $4.108$ to $4.135$ s; as
indicated in Extended Data Figure 1) as the characteristic emission of the
event, and the following emission as its extended radiation. The time-
integrated spectrum of the SP is best fitted by a CPL model parameterized by
$\alpha=-1.19\pm 0.02$ and $E_{\rm p}=9.8_{-1.2}^{+2.2}$ MeV, with a fluence
of $9.88_{-0.82}^{+0.90}\times 10^{-6}$ erg cm-2 (Methods). This suggests that
the bulk Lorentz factor should be at least $\sim 430$ (Methods), being the
highest among all observed MGFs observed so far Roberts2021Natur.

Since there is no reportedly redshift measurement of GRB 130310A, we assigned
$z$ as a free parameter ranging from $10^{-4}$ to $10$, and overplotted the
corresponding values of the rest-frame $E_{\rm p}$ and $E_{\rm iso}$ of the SP
onto the $E_{\rm p}$-$E_{\rm iso}$ diagram, as shown in Figure 2.
Interestingly, due to its high $E_{\rm p}$, the event lies far away from
typical long and short GRBs tracks. Instead, it is consistent with the third
track for the MGF-GRB population. The redshift of the GRB is constrained in
the range of [0.0079, 0.0595], assuming that the burst follows the MGF track.
We further searched for the host galaxy (Methods) of the burst in the 6df
Galaxy Survey (6dfgs) database2004MNRAS.355..747J, 2009MNRAS.399..683J within
such a redshift range inside the overlapped region between the LAT error
circle (Methods) and the IPN error box2013GCN.14284....1G. Our search yields
only one galaxy within that redshift range and error box, which is
g0927191-170053 located at RA = $+09^{h}27^{m}19.70^{s}$ and DEC =
$-17^{\circ}00^{\prime}53.0^{\prime\prime}$ with a redshift of 0.0155. At such
a redshift, the isotropic energy (peak luminosity) of SP is
$5.61_{-0.46}^{+0.51}\times 10^{48}$ erg ($2.30_{-0.25}^{+0.25}\times 10^{50}$
erg s-1). With such a low energy and a high spectral peak, GRB 130310A
consistently lies at the high-end of the MGF GRB population track (Figure 2).
The total isotropic energy of the main burst is $2.37_{-0.18}^{+0.18}\times
10^{49}$ erg, which is around a thousand times higher than that of GRB
200415A. We hence consider it as a “hyper” flare of a magnetar in this study.

The magnetar nature of GRB 130310A is further manifested by the period
detection in the light curve. We employed the Lomb-Scargle (LS)
methodLomb:1976, Scargle1982 to search for periodic signals in different time
windows with different time scales in different energy ranges (Methods). As
shown in Figure 1, we performed the LS calculation on the original light
curves as well as the detrended light curves resulted from three different
detrending methods. Our analysis yielded a significant periodic signal of 12.4
Hz with a confidence $>5\sigma$ found in the 8-1000 keV light curve in the
time region between 4.4 s and 4.9 s (Methods). Such a period is unprecedented
in the magnetar observations and has never been observed in GRB events.

The period of $\sim$ 80 ms can be directly connected to the neutron star
rotation. Assuming magnetic dipole radiation, the spin-down rate, $\dot{P}$,
can be estimated from the spin period, $P$, and its estimated surface magnetic
field strength, $B_{*}$, asShapiro1983:

$\displaystyle\dot{P}$ $\displaystyle\simeq\frac{2\pi^{2}R_{\rm
s}^{6}B_{*}^{2}}{3c^{3}IP}$ $\displaystyle={1.94}\times 10^{-8}\
\mathrm{s\leavevmode\nobreak\ s^{-1}}\bigg{(}\frac{P}{80\ \rm
ms}\bigg{)}^{-1}\bigg{(}\frac{M}{2M_{\odot}}\bigg{)}^{-1}\bigg{(}\frac{B_{*}}{10^{15.5}\leavevmode\nobreak\
\rm G}\bigg{)}^{2}\bigg{(}\frac{R_{s}}{10^{6}\leavevmode\nobreak\ \rm
cm}\bigg{)}^{6},$ (1)

where $c$ is the speed of light, $M_{\odot}$ is the solar mass, $I\simeq
2MR_{s}^{2}/5$ is the moment of inertia, $M$ and $R_{\rm s}$ are the mass and
surface radius of the magnetar, respectively. We normalize $M$ to be
$2M_{\odot}$ considering that the magnetar is likely born from a binary
neutron star merger, as explained below. Here we have adopted $Q=10^{n}Q_{n}$
in cgs units. The magnetic field of a young megnetar can be as high as$\sim
10^{16}$ GGourgou2016 and is normalized to $10^{15.5}$ (or 3.2$\times
10^{15}$) G in this study. The characteristic age of the magnetrar can be
estimated asShapiro1983:

$\tau_{c}\simeq\frac{P}{2\dot{P}}={23.9}\leavevmode\nobreak\ \mathrm{\
days}\bigg{(}\frac{B_{*}}{10^{15.5}\rm\ G}\bigg{)}^{-2}\bigg{(}\frac{P}{80\rm\
ms}\bigg{)},$ (2)

which is about three weeks for nominal parameters. For simplicity, we further
assume that there is about 50% uncertainty in assigning the $B_{*}$ value, so
the minimal and maximum age of the magnetar can be calculated as
$\tau_{c,min}=11$ days and $\tau_{c,max}=56$ days respectively.

At age $\tau_{c}$, the spin-down luminosity is

$\displaystyle L_{\rm sd}=-\dot{E}_{\rm rot}$
$\displaystyle=-I\Omega\dot{\Omega}=4\pi^{2}I\frac{\dot{P}}{P^{3}}=\frac{B_{*}^{2}R_{\rm
s}^{6}\Omega^{4}}{6c^{3}}$ $\displaystyle\simeq 2.35\times 10^{42}\mathrm{erg\
s}^{-1}\bigg{(}\frac{P}{80\ \rm
ms}\bigg{)}^{-4}\bigg{(}\frac{B_{*}}{10^{15.5}\leavevmode\nobreak\ \rm
G}\bigg{)}^{2}\bigg{(}\frac{R_{s}}{10^{6}\leavevmode\nobreak\ \rm
cm}\bigg{)}^{6}.$ (3)

We note that such an $L_{\rm sd}$ is much smaller than the observed peak
luminosity of GRB 130310A, suggesting that the hyper flare is not powered by
the spindown of the magnetar, but is rather powered by significant magnetic
energy dissipation in this early phase of a magnetar’s life.

One may compare the GRB energy with the total energy available from the
source. Considering a beaming factor of $f\sim 0.01$, the total energy of GRB
130310A may be estimated as $E_{\rm\gamma}=fE_{\rm
iso}=2.37_{-0.18}^{+0.18}\times 10^{47}f_{-2}$ erg. The total spin energy of
the magnetar at the epoch is

$\displaystyle E_{\rm rot}\simeq\frac{1}{2}I\Omega^{2}\simeq{4.85}\times
10^{48}\leavevmode\nobreak\ \mathrm{erg}\
\bigg{(}\frac{M}{2M_{\odot}}\bigg{)}\bigg{(}\frac{P}{80\rm\
ms}\bigg{)}^{-2}\bigg{(}\frac{R_{s}}{10^{6}\leavevmode\nobreak\ \rm
cm}\bigg{)}^{6},$ (4)

and the total magnetic energy of the magnetar can be estimated as

$\displaystyle E_{B}\simeq\frac{1}{6}B_{*}^{2}R_{s}^{3}\simeq 1.67\times
10^{48}\leavevmode\nobreak\ {\rm erg}\
\bigg{(}\frac{B_{*}}{10^{15.5}\leavevmode\nobreak\ \rm
G}\bigg{)}^{2}\bigg{(}\frac{R_{s}}{10^{6}\leavevmode\nobreak\ \rm
cm}\bigg{)}^{3}.$ (5)

One can see that the GRB energy is within the energy budget of the magnetar if
$f\ll 1$. The hyper flare likely originates from the instantaneous release of
the magnetic energy due to the dissipation of magnetic energy. The emission is
likely highly beamed so that magnetar rotation can leave a periodic signal in
the light curve.

Figure 3:  ${\rm P}-\dot{{\rm P}}$ diagram. All known neutron stars collected
in different categories in the ATNF Pulsar CatalogueATNF are plotted with
different symbols as indicated in the top-right corner. The weeks-old magnetar
in this study is overplotted with a red star. The hypothetical newborn
millisecond magnetars with B$\sim 10^{15-16}$ G are located in the diamond
region. The arrow indicates the evolution path from a newborn magentar to a
weeks-old magnetar, assuming that $B$ does not decay significantly.

The estimated position of the magnetar powering GRB 130310A in the $P-\dot{P}$
diagram is presented in Figure 3. One can see that it bridges the hypothetical
millisecond magnetars born in GRBs/SLSNe and Galactic magnetars.

We searched for potential GRBs from the archival data as the possible
progenitor of the magnetar. Our search window covers the time range between
$T_{\rm 0}-\tau_{c,max}$ and $T_{\rm 0}-\tau_{c,min}$. We followed the burst
search method described in Ref. Zou212021ApJ...923L..30Z. The search yielded
no significant signal in either triggered or untriggered GRBs samples around
the location of GRB 130310A. The duty cycle, calculated by counting the time-
span during which the GRB 130310A was in a good field of view (FOV) of
Fermi/GBM, is 64.6%, suggesting that we had about 35.4% probability to miss
the progenitor GRB event if there was any. Assuming a typical GRB spectrum
parameterized by a CPL model with $\alpha=-1$ and $E_{\rm p}$ = 300 keV, the
10-s flux upper limit in 10-1000 keV at $T_{\rm 0}$-23.9 day is $7.01\times
10^{-8}\rm\,erg\,cm^{-2}\,s^{-1}$, corresponding to a luminosity upper limit
of $3.98\times 10^{46}\rm\,erg\,s^{-1}$, which is $\sim 6000$ times fainter
than the peak luminosity of GRB 130310A. Our search suggests that a progenitor
GRB must be significantly off-axis if it was not missed during the 35.4% off
time.

We further utilize the archival data in the optical band to constrain the
progenitor type of the magnetar. No supernova discovery was reported from the
host galaxy within $T_{0}\pm$ 6 months. The Panoramic Survey Telescope and
Rapid Response System (Pan-STARRS)Panstarr_survey2016 largely covered the
region of the magnetar from 2012-06 to 2014-07. We searched the PAN-STARRS
data archiveFlewelling2020_Panstarr and found that there were 15 observations,
from November 04, 2012 to November 18, 2013, with a total exposure time of
$\sim$ 912 seconds, covering the host galaxy region, which can place a series
of $3\sigma$ non-detection upper limit for a point source around $T_{0}$
(Methods), as plotted in Figure 4. Such upper limits can rule out the
existence of a Type-Ic supernova associated with a long GRB or an SLSN at any
time later than $T_{0}-\tau_{c,max}$ days (Methods). On the other hand, a
kilonova or an off-axis afterglow of a GRB 170817A-like event at $\sim 70$
Mpc, can survive these constraints. Even for an on-beam short GRB, the
afterglow emission may also avoid detection if it occurred in the gaps between
PAN-STARRS observations. All these suggest that the progenitor of the magnetar
is likely a neutron star merger event, with the off-axis viewing angle
preferred because of its much higher probability. We note that the merger
origin is also consistent with the fact that its host, g0927191-170053, is an
old-type elliptical galaxyCampbell2014.

Figure 4:  Optical upper limits from the archival data and their constraints
on optical emissions from the magnetar progenitor. The arrows show the multi-
band 3$\sigma$ upper limits for the non-detection of a point source transient
in the skirt of the galaxy g0927191-170053 constrained from the PANN-STARR
archival data (Methods). The solid green line shows a typical superluminous
supernova light curve, assuming that it occurred at $T_{0}$ \- 23.9 day at
$\sim$ 70 Mpc. The brown solid line shows a typical type Ic supernova light
curve assuming that it occurred at $T_{0}$ \- 23.9 day at $\sim$ 70 Mpc. The
orange, purple and navy curves stand for the kilonova, on-axis and off-axis
optical afterglow light curves, respectively, for a GRB 170817A-like event
located at $70$ Mpc.

To date, the age of the magnetar is approximately $8.5$ years old. Using the
total energy of $2.37\times 10^{49}$ erg derived above and the standard
afterglow parameters (Methods), we calculate the afterglow flux as $\sim$
$1.02\times 10^{-12}$ / $3.04\times 10^{-6}$ mJy in the X-ray/optical bands
(Methods), which are way below the detection thresholds of the current
missions/telescopes in operation. One possible way of detecting emission from
the system may be fast radio bursts if the magnetar can survive until now. At
$\sim$ 70 Mpc, an FRB with a typical luminosity of $10^{42}$ erg s-1 should be
readily detectable with most radio telescopes.

## Fermi data analyses

The hyper flare event, GRB 130310A, was a bright burst detected by several
high-energy missions including Fermi/GBM 2013GCN.14283....1X, Fermi/LAT
GCN14282, Konus-Wind GCN14285, and Suzaku WAM GCN14310. We performed our
analysis based on the time-tagged events (TTE) data collected by the Gamma-ray
Monitor (GBM) onboard the Fermi satellite. The data were obtained from the
Fermi Public Data Archive (https://heasarc.gsfc.nasa.gov/FTP/fermi/data/). We
use the data of sodium iodide (NaI) detectors n9 & na and germanium oxide
(BGO) detector b1, which have the smallest angular separations with respect to
the location of GRB 130310A and the highest brightness. We also utilized the
Large Area Telescope (LAT) data covering 30 MeV to 100 MeV (LLE) and 100
MeV$-$300 GeV energy ranges. The standard data reduction procedure was
described in Zhang:2011ApJ730, Zhang:2016ApJ816, Zhang:2018NatAs. The key
results of our analysis are outlined below.

Light curves and duration: Light curves in different energy ranges are
extracted from the TTE data following the procedures described in
RefZhang:2018NatAs. Those light curves are searched for possible periodic
signals. The multi-wavelength light curves with typical energy ranges are
presented in Extended Data Figure 2. The burst duration ($T_{\rm 90}$) is
calculated in the standard range of 8 keV- 1 MeV. As shown in Extended Data
Figure 1 and listed in Extended Data Table 1, the $T_{\rm 90}$, defined by the
time interval during which 90% of total counts are detected, is $\approx$ 1.3
s for the precursor and is $\approx$ $2.93\leavevmode\nobreak\ \rm s$ for the
main burst.

Time lag: Time lag measures the difference of photon arrival time in different
energies2000ApJ...534..248N and is often used as a probe to infer the emission
size. We utilized the cross-correlation function (CCF)2000ApJ...534..248N,
2010ApJ...711.1073U to calculate the time lags of light curves among different
energy bands between $T_{0}$ \+ $4.1\rm$ s and $T_{0}$ \+ $4.6\rm s$,
following the method described in ref.2012ApJ...748..132Z. As shown in
Extended Data Figure 2, no significant lag is detected for the light curves in
different energy bands. The zero-lag result suggests that the emission region
of GRB 130310A is small, consistent with the speculation that it is an MGF
GRB.

Amplitude parameter: The amplitude parameter $f\equiv\frac{F_{\rm P}}{F_{\rm
B}}$ is defined as the ratio between the peak flux $F_{\rm p}$ and background
flux $F_{\rm B}$ (Ref. Lv14). A small $f$ often suggests that the signal is
more likely affected by the ”tip-of-iceberg” effect. The $f$ parameter of the
sharp peak of GRB 130310A is $11.22\pm 1.32$, which is the highest among all
the GRBs (Extended Data Figure 4).

Spectral analysis: For the main burst ranging from $T_{0}+3.85s$ to
$T_{0}+5.25s$, we performed both time-integrated and time-resolved spectral
analyses using the data from the two NaI and one BGO detectors as mentioned
ahead. The time slices for time-resolved analyses are obtained according to
the light curve brightness profile in such a way that the photon count of each
spectral channel is greater than twenty. All those intervals are listed in
Extended Data Table 2. The spectral files, including the total observed count
spectra, the background spectra, and the detector response matrices (DRMs),
are extracted from the event files using the same method as described in Ref.
Yang:2020ApJ...899...60Y. Four frequently used spectral models, namely Band
function (Band), Black body (BB), simple power-law (PL), and cutoff power-law
(CPL), are employed to fit the observed spectra. In particular, the CPL model
is defined as Yu:2016A&A588

$N(E)=AE^{\alpha}{\rm exp}[-(\alpha+2)E/E_{p}],$ (6)

where $\alpha$ is the power-law photon index, $E_{p}$ is the peak energy of
the fitted spectrum in units of keV, and A is the normalization factor.

The time-integrated spectrum of the main burst is characterized by a CPL model
with $E_{p}=2454.34_{-189.19}^{+199.78}$ keV and
$\alpha=-1.05_{-0.01}^{+0.01}$. We noticed that such an $E_{p}$ value is
already significantly higher than that of most typical GRBs.

The time-integrated spectrum of the shart peak alone is characterized by a CPL
model with $E_{p}=9802.23_{-1220.55}^{+2234.88}$ keV and $\alpha=-1.19\pm
0.02$. We noticed that such an $E_{p}$ value is already significantly higher
than that of most typical GRBs. The total fluence of the first peak is
$9.88_{-0.82}^{+0.90}\times 10^{-6}$ erg cm-2.

By comparing the goodness of the fits in each time slice of the main burst, we
found that the CPL model is the best model that adequately describes the
observed data with the lowest Bayesian Information Criteria
(BIC)111BICSchwarz:1978 is defined as ${\rm BIC}=-2{\rm ln}\mathcal{L}+k\ln
n$, where $\mathcal{L}$ is the maximum likelihood, k is the number of
parameters of the model, and N is the number of data points used in the fit.,
we thus only employ the CPL model to perform the time-resolved spectral
fitting.

Interestingly, the time-resolved spectral analysis suggests even more extreme
values of $E_{\rm p}$. With significant spectral evolution within the $T_{\rm
90}$ interval, Ep reaches at $\sim 10^{+1.5}_{-3.2}$ MeV around the peak
region of the light curve. As shown in Extended Data Figure 3, we note that
$\alpha$ and $E_{\rm p}$ evolution shows an intensity tracking behavior as
suggested by Wheaton1973, Golenetskii1983, Lu2012.

High-energy photons: We extracted the LAT data in the energy range of 100
MeV$-$300 GeV from $T_{0}$ to $T_{0}+800$ s. The region of interest (ROI) is a
square with the width of $10^{\circ}$ and the center at the position RA, Dec =
142.34, -17.23 (J2000). Using the standard Fermitools 2020ApJS..247...33A, and
with a cut on zenith angle at $100^{\circ}$ and the instrument response
function set P8R3_SOURCE_V3, an unbinned likelihood point source analysis is
performed. The GRB spectral model is assumed to be Powerlaw2
222https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/source_models.html
with $E_{min}=20$ and $E_{max}=20000$. Consequently, the spectral index is
fitted to be $-1.9\pm 0.1$. Finally, we obtained 20 photons with different
probabilities originating from GRB 130310A. Those high-energy photon events
are plotted in Extended Data Figure 2a & 2b.

## Amati relation

The correlation between the GRB isotropic energy $E_{\rm\gamma,iso}$ and the
rest-frame peak energy $E_{\rm p,z}=(1+z)E_{\rm p}$ is commonly refereed to as
Amati relationAmati:2002, and can be written as ${\rm log\leavevmode\nobreak\
}E_{\rm p,z}=a+b{\rm log\leavevmode\nobreak\ }E_{\rm\gamma,iso}$. Typically,
long and short GRBs, as well as MGF GRBs follow different tracks in the
diagramYang:2020ApJ...899...60Y. We plotted the $E_{\rm
p,z}-E_{\rm\gamma,iso}$ diagram (Figure 2a) using GRB samples with known
redshift from Ref.Amati:2002 and Ref.Zhang:2009ApJ. Utilizing the MCMC method,
the optimal fitting parameters and 3$\sigma$ uncertainties are constrained. We
obtain $a=-25.01^{+3.91}_{-4.25}$ and $b=0.52^{+0.08}_{-0.07}$ for long GRBs,
$a=-19.92^{+9.18}_{-7.60}$ and $b=0.45^{+0.15}_{-0.18}$ for short GRBs, and
$a=-13.20^{+7.82}_{-5.62}$ and $b=0.35^{+0.12}_{-0.17}$ for MGF GRBs. The
hyper flare event, GRB 130310A, is a significant outlier from both the short
and long GRB tracks, but is consistent with being an MGF GRB. Assuming that it
follows the MGF track, the redshift of GRB 130310A can be constrained within
the range from 0.0079 to 0.0595.

## Periodicity Measurement

To maximize the signal detection, we combined all the photon events from the
three detectors n9, na, and nb to search for periodic signals. The light
curves in different energy bands are all binned with 0.0005s, which ensure
sufficient resolution for the periodicity search. We searched possible
periodic signals in the light curve of the main burst by using the Lomb-
Scargle (LS) periodograms method. In addition to the original light curves,
our search also considers the detrended light curves, with the latter aiming
to remove the effect of global temporal evolution of the event. The following
three detrending models are employed and fitted to the search phase of the
light curve:

  1. 1.

Exponential model $f(t)=ae^{-b(t)^{d}}+c$, indicated as yellow solid line in
Figure 1.

  2. 2.

Whittaker SmoothWhittaker1922, Eilers2003 (WS) model, indicated as blue solid
line in Figure 1. WS is a fast and wildly used smooth approach, which can well
fit the trend of the light curve and retain the periodic signal by giving an
appropriate smoothing parameter.

  3. 3.

A model using the multivariate adaptive regression splines
algorithmfriedman1991, coded as py-earth model and indicated as the purple
solid line in Figure 1. The multivariate adaptive regression splines algorithm
is a non-parametric regression method that builds multiple linear regression
models on each different partition, which can efficiently catch the global
temporal features of the light curve.

The LS periodogram calculated based on the original light curve as well as the
de-trended light curves by the above three methods are shown in the right
column of Figure 1. A significant periodic signal of 12.4 Hz, corresponding to
a period of 0.08s, is detected in all four situations. The strongest detection
of the signal lies in a energy range of 50-300 KeV, and time range of 4.4-4.9
s. The confidence level of the detection in all cases exceeds 5$\sigma$, with
a false alarm probability (FAP)2008MNRAS.385.1279B, VanderPlas2018 of $\leq
5.7\times 10^{-7}$.

The periodic signal as well as its detectable range are also verified by
applying the weighted wavelet Z-transform) to the detrended data, as shown and
Extended Data Figure 7.

The lack of detection of the periodic signal after 4.9 s in the extended tail
is not unexpected as the observed flux can become less modulated by the
underlying periodic signal when it decreases exponentially and emerges to the
background level. This can be illustrated in Extended Data Figure 8, where we
generated a series of Fast-Rising-Exponential-Decaying (FRED) shape light
curves with injected noise similar to that of GRB 130310A, as well as a
periodic $f=12$ Hz signal, $S_{\rm p}$, characterized by different amplitude
$A$, time scale $\tau$, which is formulated by

$S_{\rm p}(t)=\frac{A}{{\rm exp}\big{[}(t-4.4)/\tau\big{]}}{\rm sin}(2\pi ft)$
(7)

.

As shown in Extended Data Figure 8, our simulations indicate that the periodic
signal can become undetectable after 4.9 s in the extended tail under certain
configurations of the $S_{\rm p}(t)$.

## Implication on the bulk Lorentz factor

Following the derivation from Ref.2001ApJ...555..540L, for a photon spectrum
modelled as $fe^{-\alpha_{+}}$, in which $f$ is the normalization factor in
unit of ph cm-2 s-1 keV-1 and $\alpha_{+}$ is the inverse number of the photon
index, $\alpha$, in correspondence with the definition in Eq. 6, the lower
limit of the bulk Lorentz factor can be constrained by:

$\gamma>\gamma_{\rm min}=\hat{\tau}^{1\over 2\alpha_{+}+2}({E_{\rm max}\over
m_{e}c^{2}})^{\alpha_{+}-1\over 2\alpha_{+}+2}$ (8)

$\hat{\tau}\equiv{\eta(\alpha_{+})\sigma_{T}d^{2}(m_{e}c^{2})^{-\alpha_{+}+1}f\over
c^{2}\delta T(\alpha_{+}-1)},$ (9)

where $E_{\rm max}$ is the photon with the highest energy, $\delta T$ is the
minimal variability time scale constrained through the Bayesian block method,
d is the distance of the burst, $\sigma_{T}$ is the Thomson cross-section and
$\eta(\alpha_{+})$ is the correction factor which reflects the averaging
effect of the pair production cross section. The form of $\eta(\alpha_{+})$
varies in the literatureSvensson1987MNRAS.227..403S, Gupta2008MNRAS.384L..11G
and we adopt $\eta(\alpha_{+})=(3/8)(1+\alpha_{+})^{-1}$ as discussed in
Ref.Gupta2008MNRAS.384L..11G.

Observationally, the minimal variability time scale of GRB 130310A is 7.5 ms.
The sharp peak whose spectrum is fitted as a CPL model parameterized by
f=98.57, $\alpha_{+}$ = 1.19, and $E_{\rm max}\simeq E_{\rm p}=9.8$ MeV. By
putting those numbers in Eq. 7, we can calculate the lower limit of the bulk
Lorentz factor as $\gamma_{\rm min}\simeq$ 430.

## Localization with Fermi/LAT and IPN

By removing the source model of GRB 130310A from the fitted model, we
construct the Test Statistics (TS) map by gttsmap, and we localize GRB 130310A
at RA = 142.52 and DEC = -17.16 with the maximum TS value. To obtain the
confidence interval, we subtract the ${\rm TS}_{\rm max}$ from the TS map to
build a Localization Test Statistics (LTS) map in Extended Data Figure 5. The
white, orange, green, and black ellipses denote the 68.3%, 95.5%, 99.7%, and
99.9% confidence areas, respectively. The LAT counterpart of the peak of the
GBM light curve is located with RA = 144.50 and DEC = -19.02.

The InterPlanetary Network (IPN) reports a constraint of the burst location
from a group of spacecraft equipped with gamma-ray burst (GRB)
detectors2013GCN.14284....1G. The overlapping region between the IPN error box
and the $99$% confidence of the LAT box is regarded as the most probable
location region of the hyper flare event and is used for the host galaxy
search.

## Host galaxy search

Within the redshift range constrained by the Amati relation and spatial range
of the overlapping IPN & LAT error boxes, we performed a host galaxy search in
the 6df Galaxy Survey (6dfgs) database2004MNRAS.355..747J,
2009MNRAS.399..683J, which records more than 100,000 galaxies in the nearby
universe. Only one host galaxy, g0927191-170053 with RA =
$+09^{h}27^{m}19.07^{s}$ and DEC = $-17^{\circ}00^{\prime}53.0^{\prime\prime}$
and redshift = 0.015492, was found. The galaxy is also cross-matched in the
Two Micron All Sky Survey Extended Source (2MASS), as
09271905-17005282011ApJ...737..103S. The location of the galaxy is marked in
Extended Data Figure 5.

## Optical upper limits of the magnetar emission around T0

We search for all available archival optical sky-survey data in the hope of
finding observations that can cover several months around T0. Those
observations can provide upper limits, if not detection, of a point source
associated with the magnetar’s optical counterpart.

Our investigation yields one set of archival data obtained from the Panoramic
Survey Telescope and Rapid Response System (Pan-STARRS). Around T0, Pan-STARRS
covered the host galaxy of the magnetar for a total period of about one year,
from November 04, 2012 to November 18, 2013, with a total observational time
of 912 secondsPanstarr_survey2016. Those observations are listed in Extended
Data Table 3, and are available as single-epoch “warp” images in Pan-STARRS1
data archive, which are astrometrically and photometrically
calibrated333https://outerspace.stsci.edu/display/PANSTARRS/PS1+Warp+images.
No variable point source was found within a circular region of 3′ radius from
the galaxy center in those observations. For each warp image, we calculate the
3$\sigma$ upper limit of a merger-type point source detection using the
following procedure:

  1. 1.

For each pixel in the warp image, we calculate its A-B magnitude following the
guide as listed in Pan-STARRS
document444https://outerspace.stsci.edu/display/PANSTARRS/PS1+Stack+images and
Ref2020ApJS..251....4W, 2020ApJS..251....5M as

$m_{AB}=A-2.5\times\mathrm{log}C+2.5\times\mathrm{log}t_{exp},$ (10)

where A is the magnitude zero point, C is the photon counts in each pixel,
$t_{exp}$ is the exposure time in units of second.

  2. 2.

The K half-light radius is $R_{50}$ = 4.94′′2006AJ....131.1163S. Since the
magnetar is likely a merger event, we assume it occurred at the outskirt of
the galaxy with the normalized offset $r_{\rm off}$ with a similar value as in
the case of GRB 0507242010ApJ...708....9F, namely $r_{\rm off}$ =
$\frac{R_{\rm off}}{R_{\rm gal}}$ = 0.68. This allows us to place the magnetar
at a distance of $R_{\rm off}$ = 3.36′′ from the galaxy center.

  3. 3.

With an same inclination angle of the host galaxy, we selecte a region of an
ellipse annulus with the outer semi-major axis of 4.30′′ and the inner semi-
major axis of 3.19′′, as shown in Extended Data Figure 6. We then calculate
the magnitude of each pixel within the annulus and plot their probability
density distribution, as shown in Extended Data Figure 6. The 3$\sigma$ value
of such distribution is used to determine the 3$\sigma$ upper limit of a point
source at radius $R_{\rm off}$.

Through the above steps, we obtained the 3$\sigma$ upper limit of a point
source at $r$ for a total of 15 warp images, as listed in Extended Data Table
3 and plotted in Figure 4. We note that 8 warp images in Extended Data Table 3
are considered “bad” (e.g., the magnitude value of each pixel is marked as
“nan” due to gaps between detectors, bad pixel regions,
etc555https://outerspace.stsci.edu/display/PANSTARRS/PS1+Image+Cutout+Service.)
so their upper limits are unavailable.

## Possible optical light curves of the progenitor

The progenitor of the magnetar can be either a collapsar-type GRB/SN, a
superluminous supernova (SLSN), or a neutron star merger event. All those
cases are associated with significant optical emission. Moreover, if the
progenitor is an off-axis GRB, the off-axis afterglow could last for weeks.
Below we test if any of the expected optical emission is consistent with the
upper limits obtained from the Pan-STARR data.

For the case of SLSN, we choose SN2015bn as a representative and assume that
it could serve as the progenitor of the magnetar in this study. SN 2015bn was
located in a faint host galaxy at D${}_{L}\simeq$ 544.8 MpcModjaz2016A_2015bn.
The optical data are available at the Open Supernova
Catalog666https://sne.space. We first fit the multi-wavelength optical light
curves using the magnetar-powered model described in Ref.Nicholl2015b and
obtain the physical parameters to describe the observational data of SN
2015bn. As listed in Extended Data Table 4, after being updated on the
luminosity distance and the magnetic field using those values of the hyper
flare GRB 130310A, the parameter set is utilized to calculate the $r$-band
magnitude using the same model. The resulted light curve is plotted as a solid
green line in Figure 4. One can see the SLSN magnitude is way above the PAN-
STARR upper limit. The weeks-scale coverage of PAN-STARR observations around
$T_{0}$ can rule out the existence of an SLSN,

For the case of a collapsar-type GRB/SN, We choose SN 1998bw as an
representative. SN 1998bw was located in a barred spiral galaxy (ESO 184-G82)
at D${}_{L}\simeq$ 37 MpcGuillochon2017_SNCatlog. The data are also available
in the Open Supernova Catalog. After fitting the multi-wavelength optical
light curves using the 56Ni-decay modelNadyozhin1994_Ic, the best-fit physical
parameters expect for the luminosity distance (as listed in Extended Data
Table 4) are used to calculate the $r$-band Type Ic SN light curve at $70$
Mpc. The resulting light curve, as shown in Figure 4, is well above the PAN-
STARR upper limit. We can thus also rule out the classical collapsar-type
supernova origin of the magentar.

For the case of a neutron star merger, one should consider the existence of a
kilonova (KN). A comparable case is the observed AT2017gfo with GRB 170817A.
AT2017gfo was located in an elliptical galaxy (NGC 4993) at $D_{L}\simeq$ 40
MpcAndreoni2017. The optical data are available at the Open Kilonova
Catalog777https://kilonova.space. We apply the model employed in
RefMetzger2019_kilonova and fit the multi-wavelength optical light curves to
obtain the best-fit physical parameters as listed in Extended Data Table 4.
After updating the luminosity distance, we plot the $r$-band kilonova light
curve at 70 Mpc in Figure 4. Our results suggest that the peak magnitude of
the kilonova could be above the upper limit of point-source detection. On the
other hand, the theoretical KN light curve fell in the observational gap of
PAN-STARR. So the neutron star merger origin of the magnetar is allowed.

Giving the fact that no GRB was found between $\sim$ $T_{0}-\tau_{c,max}$ and
$T_{0}$ and that a kilonova could not be ruled out, the putative short GRB
associated with the merger event was likely off-axis with respect to the
observer, unless it was missed during the 35.4% off-FOV-time of Fermi/GBM. We
compared the off-axis afterglow of GRB 170817A with the upper limit
constrained from PAN-STARR observations. To do so, we first fit the $r$-band
afterglow light curve of GRB 170817A using the structured jet model in
Ref.Troja2020_off_axis_afterglow, which gave us a set of best-fit physical
parameters, as listed in Extended Data Table 4. After replacing the luminosity
distance with $70$ Mpc, we calculated the predicted off-axis afterglow in our
case. Such a light curve is plotted in Figure 4. One can see that the off-axis
afterglow of the short GRB is undetectable by PAN-STARR. We also calculated
the on-axis short GRB afterglow for the same set of parameters at $70$ Mpc and
found that such an afterglow can also survive the observational constraints if
it occurred in the observational gaps. Considering the 35.4% off time for GRB,
this suggests that an on-axis short GRB and afterglow as the magnetat
progenitor is not ruled out. However, in view that the event rate density of
off-axis neutron star merger events is much higher than that of the on-axis
events, we regard an off-beam neutron star merger as a more likely progenitor
of the magnetar.

## Late-time afterglow and multiwavelength counterparts

The late-time afterglow of the event should undergo the slow-cooling phase.
The flux density $F_{\nu}$ at frequency $\nu$ follows
$F_{\nu}\propto\nu^{-p/2}t^{(2-3p)/4}$. Using the following typical parameters
in a standard forward shock model:

  1. 1.

electron distribution power law index, $p$ = 2.2

  2. 2.

energy fraction in electrons, $\epsilon_{e}$ = 0.1

  3. 3.

energy fraction in magnetic fields, $\epsilon_{B}$ =0.01

  4. 4.

accelerated electron fraction, $\xi_{N}$ =1.0

  5. 5.

ISM density $n_{0}$ = 1.0 $\rm cm^{-3}$

we can calculate the flux densities in X-ray at
$10^{18}\rm\leavevmode\nobreak\ Hz$ and optical band at
$10^{14}\rm\leavevmode\nobreak\ Hz$ at $t\sim$ 8.5 years as
2002ApJ...568..820G:

$\displaystyle f_{\nu}(X)\simeq 1.21\times 10^{-10}{\rm
mJy}\leavevmode\nobreak\ \epsilon_{\rm e,0.1}^{p-1}\epsilon_{\rm
B,0.01}^{(p-2)/4}E_{\rm iso,49}^{(2+p)/4}t_{8.5\rm
yrs}^{(2-3p)/4}d_{27}^{-2}\nu_{18}^{-p/2},$ (11)

and

$\displaystyle f_{\nu}(\rm O)\simeq 3.04\times 10^{-6}{\rm
mJy}\leavevmode\nobreak\ \epsilon_{\rm e,0.1}^{p-1}\epsilon_{\rm
B,0.01}^{(p-2)/4}E_{\rm iso,49}^{(2+p)/4}t_{8.5\rm
yrs}^{(2-3p)/4}d_{27}^{-2}\nu_{14}^{-p/2}.$ (12)

Magentasrs are also believed to be the energy source of Fast Radio Bursts
(FRBs). For a typical FRB with luminosity of $10^{42}$ erg/s, its observed
flux density at 70 Mpc is about $50$ Jy in typical raido bands, which is
detected by the ground-based radio telescopes, such as CHIME, MeeKat, FaST and
VLA.

The luminosity of the X-ray bursts of the Galactic SGRs are typically $\sim
10^{35}$ erg/s. Putting it at 70 Mpc, we found that it too faint for current
X-ray missions including Chandra and Swift.

## Data Availability

Processed data are presented in the tables and figures in the paper. Source
and optical observational data are available upon reasonable requests to the
corresponding authors. The Fermi/GBM data are publicly available at
https://heasarc.gsfc.nasa.gov/FTP/fermi/data.

## Code Availability

Upon reasonable request, the code (mostly in Python) used to produce the
results and figures will be provided.

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B.B.Z acknowledges support by the National Key Research and Development
Programs of China (2018YFA0404204), the National Natural Science Foundation of
China (Grant Nos. 11833003, U2038105, 12121003), the science research grants
from the China Manned Space Project with NO.CMS-CSST-2021-B11, and the Program
for Innovative Talents, Entrepreneur in Jiangsu. We also acknowledge the use
of public data from the Fermi Science Support Center (FSSC). BBZ thank
Rongfeng Shen for helpful discussions. ZJZ acknowledges the helpful
discussions and constructive comments from Ken Chen, Jianbin Weng, Ke Xu,
Shengyu Yan and Prof. Lang Shao.

BBZ and YSY initiated the study. BBZ, ZJZ, JSW and BZ coordinated the
scientific investigations of the event. BBZ, ZKL, YHY, JHZ, XIW, and JY
processed and analyzed the data. YCM helped on independently verifying the
periodic signal identification. BBZ wrote the paper with the contributions
from all coauthors.

The authors declare that they have no competing financial interests.

Correspondence and requests for materials should be addressed to B.-B. Z.

Table 1: Observational properties of the hyper flare event GRB 130310A. The total fluence and peak flux are calculated in 10–10,000 keV energy band. All errors correspond to the 1$\sigma$ credible intervals. Observed Properties | GRB 130310A
---|---
Abrupt rise time |  $\sim 20$ ms
Steep decay time |  $\sim 900$ ms
$T_{\rm 90}$ (burst) |  $2.90_{-0.22}^{+0.31}$ s
$T_{\rm 90}$ (precursor) |  $1.30_{-0.44}^{+0.57}$ s
Duration of the “sharp peak” |  $\sim$ 27 ms
Waiting time between precursor and main burst |  $\sim 3.79$s
$\alpha$ at peak | $-1.15_{-0.02}^{+0.26}$
$E_{\rm p}$ at peak |  $10.75_{-1.52}^{+3.25}$ MeV
Time-integrated $\alpha$ (main burst ) | $-1.10_{-0.01}^{+0.01}$
Time-integrated $E_{\rm p}$(main burst) |  $2.73_{-0.20}^{+0.23}$ MeV
Time-integrated $\alpha$ (sharp peak ) | $-1.19\pm 0.02$
Time-integrated $E_{\rm p}$(sharp peak) |  $9.80_{-1.22}^{+2.23}$ MeV
Total fluence |  $4.12_{-0.32}^{+0.32}\times 10^{-5}$ $\rm erg\ cm^{-2}$
Peak flux | $4.06_{-0.44}^{+0.44}\times 10^{-4}\ \rm{erg\ cm^{-2}\ s^{-1}}$
Possible host galaxy | g0927191-170053
Luminosity distance | 69.41 Mpc (z=0.0155)
Isotropic energy (precursor) $E_{\rm\gamma,iso}$ | $6.30_{-3.75}^{+7.49}\times 10^{46}\rm\ erg$
Isotropic energy (sharp peak) $E_{\rm\gamma,iso}$ | $5.61_{-0.46}^{+0.51}\times 10^{48}\rm\ erg$
Isotropic energy (main burst) $E_{\rm\gamma,iso}$ | $2.37_{-0.18}^{+0.18}\times 10^{49}\rm\ erg$
Peak luminosity $L_{\rm\gamma,p,iso}$ | $2.30_{-0.25}^{+0.25}\times 10^{50}\rm\ erg\ s^{-1}$
Average tail luminosity $L_{\rm tail}$ | $5.63\times 10^{48}\rm\ erg\ s^{-1}$
Spectral lag |  $\sim$ 0 s
Minimal variability time scale $\delta t$ | 0.0075 s
f parameter | $11.22\pm 1.32$
Table 2: Spectral properties of GRB 130310A Component | $t_{1}$ | $t_{2}$ | Model | Parameter(s) | PGSTAT/dof |
---|---|---|---|---|---|---
$\alpha$ |  $E_{\rm p}$ or KT (keV) |
Precursor | -0.57 | 0.35 | BB | … | $45.06_{-5.69}^{+13.57}$ | 307.2/349 |
Sharp Peak | 4.108 | 4.135 | CPL | $-1.19_{-0.02}^{+0.02}$ | $9802.23_{-1220.55}^{+2234.88}$ | 354.3/349 |
Main Burst | 3.85 | 4.05 | CPL | $-2.09_{-0.40}^{+2.31}$ | $858.50_{-438.85}^{+1668.71}$ | 163.3/349 |
4.05 | 4.118 | $-1.29_{-0.06}^{+0.04}$ | $3943.29_{-801.26}^{+2681.62}$ | 270.2/349 |
4.118 | 4.135 | $-1.15_{-0.03}^{+0.02}$ | $10749.48_{-1522.56}^{+3247.12}$ | 356.3/349 |
4.135 | 4.155 | $-1.04_{-0.04}^{+0.03}$ | $4964.09_{-807.51}^{+1233.92}$ | 306.5/349 |
4.155 | 4.185 | $-0.73_{-0.08}^{+0.06}$ | $1153.87_{-155.79}^{+262.58}$ | 275.7/349 |
4.185 | 4.215 | $-0.79_{-0.09}^{+0.06}$ | $940.61_{-111.29}^{+279.29}$ | 251.1/349 |
4.215 | 4.265 | $-0.49_{-0.10}^{+0.10}$ | $593.03_{-58.23}^{+106.63}$ | 279.2/349 |
4.265 | 4.485 | $-0.69_{-0.06}^{+0.05}$ | $706.63_{-63.63}^{+104.73}$ | 355.6/349 |
4.485 | 5.25 | $-1.07_{-0.05}^{+0.04}$ | $885.18_{-127.37}^{+247.26}$ | 316.8/349 |
| 4.05 | 5.25 |  | $-1.10_{-0.01}^{+0.01}$ | $2732.60_{-197.80}^{+229.75}$ | 421.2/349 |
Date | Number of observations | Observation time | Exposure time (s) | Filters | Upper limit for a point source detection (mAB)
---|---|---|---|---|---
2012-11-04 | 1 | 14:46:23.563 | 30 | y | 18.72
2012-11-25 | 2 | 15:28:02.527 | 30 | z | Unconstrained
|  | 15:43:20.493 | 30 | z | Unconstrained
2012-12-28 | 2 | 13:36:32.675 | 45 | i | 18.98
|  | 13:54:38.657 | 45 | i | 18.94
2012-12-29 | 2 | 14:09:08.155 | 40 | r | 19.49
|  | 14:26:01.300 | 40 | r | 19.48
2013-01-25 | 4 | 10:54:12.288 | 40 | r | Unconstrained
|  | 10:55:56.784 | 40 | r | 19.38
|  | 11:11:00.673 | 40 | r | Unconstrained
|  | 11:12:44.948 | 40 | r | 19.38
2013-01-26 | 2 | 11:30:33.887 | 45 | i | 19.06
|  | 11:49:06.794 | 45 | i | 19.11
2013-04-01 | 4 | 06:44:26.925 | 43 | g | Unconstrained
|  | 06:51:45.444 | 43 | g | 20.87
|  | 07:02:04.029 | 43 | g | Unconstrained
|  | 07:09:21.358 | 43 | g | 20.75
2013-04-24 | 5 | 05:32:38.923 | 30 | y | Unconstrained
|  | 05:47:32.901 | 30 | y | Unconstrained
|  | 05:54:35.440 | 30 | y | 18.91
|  | 06:11:14.971 | 30 | z | 18.97
|  | 06:26:05.774 | 30 | z | 18.91
2013-11-18 | 1 | 15:52:03.043 | 80 | y | 18.45
Table 3: List of PAN-STARR observations that covered the host galaxy around $T_{0}$.  The up-limit calculation is detailed in Methods. SLSN | Value | Ic-SN | Value | Kilonova | Value | Off-axis afterglow | Value
---|---|---|---|---|---|---|---
Surface field |  $B_{s}$ $\sim 10^{15.5}$ G | Nickel fraction |  $f_{\rm Ni}$ = 0.023 | Blue ejecta mass |  $M_{\rm ej}^{\rm blue}$ = 0.023 $M_{\odot}$ | fraction of magnetic energy |  $\varepsilon_{B}$ = $10^{-4}$
NS mass |  $M_{\rm NS}$ = 1.79 $M_{\odot}$ |  Opacity to $\gamma$-rays |  $\kappa_{\gamma}$ = 0.11 ${\rm cm}^{2}{\rm g}^{-1}$ | Blue ejecta velocity |  $v_{\rm ej}^{\rm blue}\sim$ 78000 $\rm km\ s^{-1}$ | fraction of electron population energy |  $\varepsilon_{e}$ = 0.04
Spin period |  $P_{\rm spin}$ = 1.60 $\rm ms$ | Ejecta mass |  $M_{\rm ej}$ = 1.78 $M_{\odot}$ | Blue opacity |  $\kappa_{\rm ej}^{\rm blue}$ = 0.5 ${\rm cm}^{2}{\rm g}^{-1}$ | power-law slope of the electron population |  $p$ = 2.17
Optical opacity |  $\kappa$ = 0.20 ${\rm cm}^{2}{\rm g}^{-1}$ | Host H number density |  $n_{\rm H,host}$ $\sim$ $10^{17.8}{\rm cm}^{-3}$ | Blue temperature |  $T^{\rm blue}$ = 3983 K | ISM density |  $n_{0}$ = 0.002 $\rm cm^{-3}$
Opacity to $\gamma$-rays |  $\kappa_{\gamma}$ = 0.01 ${\rm cm}^{2}{\rm g}^{-1}$ | Photosphere temperature |  $T_{\rm min}$ = 6607 K | Red ejecta mass |  $M_{\rm ej}^{\rm red}$ = 0.050 $M_{\odot}$ | jet orientation |  $\theta_{V}$ = 0.40 rad
Ejecta mass |  $M_{\rm ej}$ = 0.1 $M_{\odot}$ | Explosion time |  $t_{\rm exp}$ = -54.52 days | Red ejecta velocity | $v_{\rm ej}^{\rm red}\sim 44700\ \rm km\ s^{-1}$ | jet core width |  $\theta_{c}$ = 0.07 rad
Ejecta velocity |  $v_{\rm ej}$ $\sim 5460\ \rm km\ s^{-1}$ | Variance |  $\sigma$ = 0.38 mag | Red temperature |  $T^{\rm red}$ = 3745 K | jet total width |  $\theta_{w}$ = 0.47 rad
Host galaxy Extinction |  $A_{V}=0.08$ mag | Ejecta velocity |  $v_{\rm ej}$ $\sim$ 77625 $\rm km\ s^{-1}$ | Red opacity |  $\kappa_{\rm ej}^{\rm red}$ = 10 ${\rm cm}^{2}{\rm g}^{-1}$ |  |
Temperature |  T = $8.32\times 10^{13}$ K | Luminosity distance |  $\simeq$ 70 Mpc | Variance |  $\sigma$ = 0.24 mag |  |
Variance |  $\sigma$ = 0.18 mag |  |  | Luminosity distance |  $\simeq$ 70 Mpc |  |
Luminosity distance |  $\simeq$ 70 Mpc |  |  |  |  |  |
Table 4: Model parameters of the SLSN, Ic-SN, kilonova and off-axis afterglow.
Figure 1:  Light curve and duration of GRB 130310A. a, the black solid lines
show the light curve obtained by the GBM-na data in energy range of 8-1000
KeV. The red solid line represents the level of background. The sharp spike
(SP) is at $\sim 4s$. and marked with purple shaded area. The inset brackets
the precursor region. b, black line represents the accumulated count light
curve. The blue horizontal dashed (solid) lines are plotted at 5$\%$ (0$\%$)
and 95$\%$ (100$\%$) of the total accumulated counts, respectively. The two
regions marked by the green vertical dashed lines are the $T_{90}$ intervals
of the precursor and the main burst. Figure 2: Multi-wavelength light curves,
high-energy photon detection and time . a, Multi-wavelength light curves
detected with GBM and LAT. The filled blue circle is an event detected by LAT
around the peak time of the GBM light curve. b, LAT events with energy above
100 MeV in $0-800$ s. Different colors represent different ranges of
probabilities that the photon count may originate from this event. c,
Comparison between LAT-LLE and GBM light curves. d, Energy dependent lags
between the lowest energy(10-20 keV) band and any higher energy bands. All
error bars represent 1$\sigma$ uncertainties. Figure 3: Spectral evolution of
the GRB 130310A.  The time-resolved spectra are fitted with a CPL model for
the main burst and a black body model for the precursor. The top panel shows
the evolution of the low-energy photon index, $\alpha$ for the main burst. The
bottom panel shows the evolution spectral peak, $E_{\rm p}$, for both the
precursor and the main burst, where an equivalent $E_{\rm p}\sim 2.82$ kT
(Ref. Lu2012ApJ...758L..34Z) is adapted for the precursor. All error bars
represent 1-$\sigma$ uncertainties Figure 4: $T_{90}-f(f_{\rm eff})$ plot. The
blue circles represent the $f$ value of short GRBs, and black circles
represent the $f_{\rm eff}$ of long GRBs. The effective amplitude parameter
$f_{\rm eff}=\frac{F_{\rm p^{\prime}}}{F_{\rm b}}$ for a long GRB is measured
by scaling down the burst until “pseudo GRB” is shorter than 2 s (Ref.Lv14)
.The green vertical dashed line is the boundary of 2 s. The green diamond
represents the MGF GRB 200415A. The red-star-marker highlights the sharp peak
of GRB 130310A . Figure 5: Localization Test Statistics (LTS) map of the hyper
flare GRB 130310A obtained with LAT data in the time range of 0$-$800 s. The
white, orange, green and black counters are the 68.3%, 99.5%, 99.7% and 99.9%
confidence regions, respectively. $3\sigma$ IPN error box2013GCN.14284....1G
(blue parallelogram) and the potential host galaxy g0927191-170053 (red star)
are over-plotted on top of the LAT error circles.

a

b

Figure 6: An example illustrating the method of the up-limit calculation. a, A warp image of the host galaxy, g0927191-170053, obtained from the PAN-STARR archive for the observation performed on 2012-12-28T13:36:32.675. The green ellipse annuli is the region to measure the up-limit of the point-source transient. b, The magnitude distribution of each pixel within the annuli. The black solid line is the probability density function, and the black dashed line marks the 3$\sigma$ level. Figure 7: The wavelet plot of the detrended data. A significant signal is shown at 12 HZ between 4.4 and 5.0 s. The left plot is derived from WWZ (Weighted Wavelet Z-Transform) transform of the detrended data. The right panel shows the mean wwz power for different frequencies. a | b
---|---
|
c | d
|
e | f
|
Figure 8: An illustration shows that the periodic signal can become
undetectable depending on its modulation strength to the observed flux. In
each plot, the simulated light curve is composed of a FRED-shaped pulse (solid
red line on the top panel), a random noise signal (blue in the middle panel),
and a 12.4-Hz periodic signal applied between 4.4 s and 7.0 s (solid red line
in middle panel). With the strength of the periodic signal decreasing from a
to f (see Methods), one can see the detectable range of the 12-Hz period
becomes more concentrated to its maximum-strength region. The detecting range
of the periodic signal in d is similar to that of GRB 130310A.