# X-RAY AND RADIO BURSTS FROM THE MAGNETAR

G. L. Israel INAF–Osservatorio Astronomico di Roma, via Frascati 33, I-00078
Monteporzio Catone, Italy<EMAIL_ADDRESS>M. Burgay INAF–Osservatorio
Astronomico di Cagliari, Via della Scienza 5, I-09047 Selargius, Italy  N. Rea
Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans
s/n, 08193, Barcelona, Spain  Institut d’Estudis Espacials de Catalunya
(IEEC), Carrer Gran Capità 2–4, 08034 Barcelona, Spain  P. Esposito Scuola
Universitaria Superiore IUSS Pavia, Palazzo del Broletto, piazza della
Vittoria 15, I-27100 Pavia, Italy  INAF–Istituto di Astrofisica Spaziale e
Fisica Cosmica di Milano, via A. Corti 12, I-20133 Milano, Italy  A. Possenti
INAF–Osservatorio Astronomico di Cagliari, Via della Scienza 5, I-09047
Selargius, Italy  S. Dall’Osso  Gran Sasso Science Institute, viale F. Crispi
7, I-67100, L’Aquila, Italy  INFN - Laboratori Nazionali del Gran Sasso,
I-67100, L’Aquila, Italy  L. Stella INAF–Osservatorio Astronomico di Roma, via
Frascati 33, I-00078 Monteporzio Catone, Italy  M. Pilia INAF–Osservatorio
Astronomico di Cagliari, Via della Scienza 5, I-09047 Selargius, Italy  A.
Tiengo Scuola Universitaria Superiore IUSS Pavia, Palazzo del Broletto, piazza
della Vittoria 15, I-27100 Pavia, Italy  INAF–Istituto di Astrofisica Spaziale
e Fisica Cosmica di Milano, via A. Corti 12, 20133 Milano, Italy  Istituto
Nazionale di Fisica Nucleare (INFN), Sezione di Pavia, via A. Bassi 6, I-27100
Pavia, Italy  A. Ridnaia Ioffe Institute, 26 Politekhnicheskaya, St
Petersburg, 194021, Russia  A. Y. Lien Center for Research and Exploration in
Space Science and Technology, NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA  Department of Physics, University of Maryland, Baltimore County,
1000 Hilltop Circle, Baltimore, MD 21250, USA  D. D. Frederiks Ioffe
Institute, 26 Politekhnicheskaya, St Petersburg, 194021, Russia  F. Bernardini
INAF–Osservatorio Astronomico di Roma, via Frascati 33, I-00078 Monteporzio
Catone, Italy  INAF $-$ Osservatorio Astronomico di Capodimonte, Salita
Moiariello 16, I-80131 Napoli, Italy  New York University Abu Dhabi, Saadiyat
Island, Abu Dhabi, 129188, United Arab Emirates

(Received 20 July 2020; Revised 22 October 2020; Accepted 12 November 2020)

###### Abstract

We report on simultaneous radio and X-ray observations of the radio-emitting
magnetar 1E 1547.0–5408 on 2009 January 25 and February 3, with the 64-m
Parkes radio telescope and the _Chandra_ and _XMM-Newton_ X-ray observatories.
The magnetar was observed in a period of intense X-ray bursting activity and
enhanced X-ray emission. We report here on the detection of two radio bursts
from 1E 1547.0–5408 reminiscent of Fast Radio Bursts (FRBs). One of the radio
bursts was anticipated by $\sim$1 s (about half a rotation period of the
pulsar) by a bright SGR-like X-ray burst, resulting in a $F_{\rm radio}/F_{\rm
X}\sim 10^{-9}$. Radio pulsations were not detected during the observation
showing the FRB-like radio bursts, while they were detected in the previous
radio observation. We also found that the two radio bursts are neither aligned
with the latter radio pulsations nor with the peak of the X-ray pulse profile
(phase shift of $\sim$0.2). Comparing the luminosity of these FRB-like bursts
and those reported from SGR 1935+2154, we find that the wide range in radio
efficiency and/or luminosity of magnetar bursts in the Galaxy may bridge the
gap between “ordinary” pulsar radio bursts and the extragalactic FRB
phenomenon.

Magnetars(992) — Neutron stars(1108) — Radio pulsars(1353) — Transient
sources(1851) — X-ray bursts(1814)

††facilities: _XMM-Newton_ , Parkes, Chandra, _Swift_ , Konus-Wind††software:
FTOOLS (Blackburn, 1995), XSPEC (Arnaud, 1996), XMM-SAS (Gabriel et al., 2004)

… Accepted to ApJ

##  1 Introduction

Among the isolated neutron stars, there is a sub-class of bright X-ray pulsars
believed to be powered by their large magnetic fields, of the order of $\sim
10^{13-15}$ G (see Kaspi & Beloborodov 2017; Esposito et al. 2018 for recent
reviews). Among their hallmarks, there are: i) slow rotation periods in the
0.3–12 s range, ii) X-ray persistent emission modelled by the thermal (0.3–1
keV) emission of a surface hot spot plus a non-thermal magnetospheric
component (power law with $\Gamma\sim$2–4), iii) the emission of X-ray bursts
on a wide range of luminosities and timescales ($\approx 10^{38-45}$erg s-1;
ms to minutes), and iv) large X-ray outbursts lasting years.

The discovery of transient pulsed radio emission following intense X-ray
outbursts of five members of the class (Halpern et al., 2005; Camilo et al.,
2006; Esposito et al., 2020) was a bolt in the field. The pulsed radio
emission from magnetars is characterised by a flat radio spectral index
($S_{\nu}\propto\nu^{0.5}$) and large variabilities both in flux density and
pulse profile (Camilo et al., 2006; Kramer et al., 2007, e.g.). To further
blur the line between magnetars and ‘ordinary’ pulsars, magnetar-like X-ray
activity was found in objects with dipolar B fields as low as $6\times
10^{12}$ G (Rea et al., 2010, 2013), and in pulsars with powerful rotational
energy loss rate, such as the radio-quiet PSR J1846$-$0258 (Gavriil et al.,
2008) and the radio-loud PSR J1119$-$6127 (Archibald et al., 2016).

Table 1: Main parameters of the X-ray and radio observations of 1E
1547.0–5408.

Date | Start Time (UT) | Overlap | $T_{\rm X}/T_{\rm Radio}$ | Flux${}_{\rm X}^{a}$ | Radio band | X-ray $P$
---|---|---|---|---|---|---
(mm/dd/yy) | Radio | X-ray | (hr) | (hr) | (erg/cm2/s) |  $\nu$ (MHz) |  $\Delta\nu$ (MHz) | (s)
01/23/2009 | 23:10:11 | – | – | –/1.17 | – | 3094.0b | 1024.0b | –
01/25/2009 | 16:48:22 | 15:44:01c | 1.17 | 3.37/1.17 | 5.74$\pm^{0.02}_{0.41}$ | 2935.5/3094.0b | 576.0/1024.0b | 2.07213(2)
02/03/2009 | 18:28:58 | 18:23:50d | 1.51 | 15.68/1.51 | 4.52$\pm^{0.01}_{0.04}$ | 6592.5/6380.5b | 576.0/256.0b | 2.072151(2)

a X-ray flux in units of $10^{-11}$ and in the 0.5–10 keV energy range. Values
are from Bernardini et al. (2011).

b DFB observations. c _Chandra_ observation. d _XMM-Newton_ observation.

A renewed interest for magnetar radio emission comes from its possible
connection to Fast Radio Bursts (FRBs). FRBs are bright ($\sim$ Jy) ms-
duration transients whose impulsive nature and extreme brightness temperatures
imply coherent emission and connect them to compact objects. When the first
repeating FRB was observed (Spitler et al., 2014, 2016) it became clear that
at least a selection of FRBs could not be powered by a single explosive event.
All these characteristics pointed to a connection with magnetar bursts,
possible from very young extra-Galactic magnetars (Metzger et al., 2017;
Beloborodov, 2017). Recently, the detection of a double-peaked radio burst
simultaneous with a bright SGR-like burst from SGR 1935+2154 (The CHIME/FRB
Collaboration et al., 2020; Bochenek et al., 2020; Mereghetti et al., 2020; Li
et al., 2020; Ridnaia et al., 2020) showed for the first time that magnetar
bursts can indeed have bright radio counterparts.

1E 1547.0–5408 has a $\sim$ 2.07 s spin period and a surface dipolar magnetic
field of $B_{\rm{p}}\sim 6.4\times 10^{19}(P\dot{P})^{1/2}\sim 6.4\times
10^{14}$ G (Dib et al., 2012). Since its discovery (Lamb & Markert, 1981;
Gelfand & Gaensler, 2007), 1E 1547.0–5408 has experienced at least three
outbursts (in 2007, 2008 and 2009) during which emitted several energetic
short bursts (Israel et al., 2010; Bernardini et al., 2011; Scholz & Kaspi,
2011; Coti Zelati et al., 2020). Multiple expanding X-ray rings were detected
around the source during the 2009 outburst decay, allowing an estimate of the
source distance of $\sim$4.5 kpc (Tiengo et al. 2010; in the following, we
adopt this distance value).

In this work, we present simultaneous X-ray and radio observations of 1E
1547.0–5408 performed in 2009, while it was undergoing its brightest outburst.
Summary of the results and discussion are presented in §3 and §4.

##  2 Observations and analysis

###  2.1 X-ray datasets

On 2009 January 25, 1E 1547.0–5408 was observed with the S3 CCD of the ACIS
camera on board _Chandra_ (Table 1). The observations were performed in
Continuos Clocking mode (time resolution of 2.85 ms) and standard data
processing and reduction were performed with the CIAO software package (v.
4.10) and the calibration files in CALDB (v. 4.8). We extracted the source
events in the 0.3–10 keV energy range from a 3.5 arcsec region around the
source position (RA = 15:50:54.12, Dec = -54:18:24.05, J2000), and the
background from a region of the same size.

On 2009 February 3–4, 1E 1547.0–5408 was observed with _XMM-Newton_ with all
EPIC cameras operating in Full Frame mode (frame time of 73.4 ms and 2.6 s,
for the pn and MOS, respectively). The data were processed and reduced with
standard procedures using the SAS software package. The source photons were
accumulated from a circular region with radius of 36$\arcsec$, while the
background was estimated from a circle of the same size in the same chip as
the source. To search for bursts, we extracted the EPIC-pn events from the
full detector because bright magnetar bursts can cause heavy pile-up and other
saturation effects that substantially reduce the number of valid events at the
source position. To study the properties of the persistent emission of the
source, the time intervals of the detected bursts (see Figure 1) were excluded
from the analysis by applying an intensity filter (with a negligible reduction
of the net exposure time; see Table 1).

1E 1547.0–5408 also triggered Konus-Wind (KW; Aptekar et al. 1995) during our
simultaneous radio/X-ray campaign on 2009 February 3. KW consists of two
identical NaI(Tl) scintillation detectors with a 2$\pi$ steradians field of
view, operating from 20 keV to 16 MeV. In the triggered mode, activated when
the count rate in the 80-320 keV band exceeds a $\approx$9$\sigma$ threshold
above background, lightcurves with a time resolution up to 2 ms are recorded
in three energy bands, starting from 0.512 s before the trigger time T0.

At the same epoch also the Burst Alert Telescope (BAT) on board _Swift_
(Gehrels et al., 2004), detected a significant count rate increase coincident
in time (and shape) with the KW trigger. BAT is a coded-mask instrument
operating in the 15-150 keV band with a field of view (FoV) of about 1.4
steradians (half-coded). At the time of the trigger 1E 1547.0–5408 was outside
the BAT FoV, and no source was found in the BAT image. However, high-energy
photons can reach the BAT detector from different directions, and even an out-
of-FoV source can sometimes cause a count-rate increase in the BAT
detectors111See https://swift.gsfc.nasa.gov/analysis/bat_swguide_v6_3.pdf.. No
spectral information can be obtained in such cases and only timing information
are recorded.

For the timing analysis, the _Chandra_ , _XMM-Newton_ , KW and _Swift_ photon
arrival times were referred to the barycenter of the Solar System using the
JPL-DE405 ephemeris. The epochs of the bursts discussed in the following are
in barycentric dynamical time (TDB).

###  2.2 Radio datasets

We observed 1E 1547.0–5408 with the Parkes 64-m telescope three times during
its 2009 outburst: on 2009 January 23 and 25, and on February 3. On January 23
data were recorded at a central frequency of 3.1 GHz with the digital
filterbank backend DFB3,222See
http://www.srt.inaf.it/media/uploads/astronomers/dfb.pdf. over a 1024 MHz
bandwidth split into 1-MHz wide channels and were on-line folded with constant
period to form 1024 phase bins and 30 s long subintegrations, for a total of
1.2 hr. On January 25, in parallel with the DFB3, we also acquired data with
the analogue filterbank AFB in search mode, over a total bandwidth of 576 MHz
(centered at 2.9 GHz) split in 3-MHz wide channels. AFB data were 1-bit
digitized every 1 ms, while DFB3 data were folded on-line with the same
parameters and duration as the previous observation, providing total overlap
with X-ray data. For the third observation on February 3, we collected data at
a central frequency of 6.6 GHz for 1.5 hr beginning at 18:28:58, i.e. about 5
minutes after the start of the X-ray observation. Data were collected
simultaneously with the AFB using 3-MHz-wide channels covering a total
bandwidth of 576 MHz and with the DFB3 using 0.5-MHz-wide channels and a total
bandwidth of 256 MHz centered at 6.4 GHz. AFB data were 1-bit sampled every 1
ms, while DFB3 data were folded on-line with the same parameters adopted for
the previous observations (1024 phase-bins, 30-s subintegrations).

Figure 1:  _XMM-Newton_ EPIC-pn 2–10 keV light curve binned at 0.5 s, where
the gray area marks the time interval covered by Parkes observations. The
detected X-ray bursts within the radio overlap interval are marked as “1” and
“2”. The inset shows burst “2” as observed by EPIC-pn in the 2–10 keV band
(black line; time resolution 73.4 ms), _Swift_ /BAT in the 15–100 keV band
(red line; time resolution of 3 ms) and KW in the 20–1400 keV band (blue line;
time resolution of 2 ms).

##  3 Results

###  3.1 X-ray results

By means of a phase-coherent timing analysis, we measured a spin period of
$P=2.07213(2)$ s in the _Chandra_ data set, and $P=2.072151(2)$ s in the _XMM-
Newton_ one (1$\sigma$ confidence level). We checked that these values are in
agreement with the long-term phase-coherent timing solution presented in
Bernardini et al. (2011). Both the pulse shape and the pulsed fraction (PF,
defined as the semi-amplitude of a sinusoidal function divided by the source
average count rate) changed significantly between the two X-ray observations:
from an almost sinusoidal to a double-peaked pulse profile, and from $\rm
PF=10\pm 1$ % to $15\pm 1$% (in the 0.5–10 keV interval).

The search for bursts was performed on the 2–10 keV light curve of the full
EPIC-pn detector, with bin time of 0.5 s. We label as a burst every bin with a
probability $<$0.001 of being a Poissonian fluctuation of the average count-
rate, considering the number of time bins of the light curve as the number of
independent trials. Based on this definition, we detected 11 bursts in the
_XMM-Newton_ X-ray lightcurve and only two in the interval covered also by the
Parkes observation. The TDB time of the latter two bursts (“1” and “2” in Fig.
1) are 19:17:10.5 and 19:31:28.5. The 0.5 s time bin associated to the two
bursts contain 90 and 374 pn events, respectively.

During the peak of burst “2”, some of the pn quadrants, consisting of three
CCDs sharing the same electronics, were fully saturated and registered no
valid events, making it impossible to evaluate the burst fluence. On the other
hand, burst “2” was detected in a single 2.6 s frame in both the MOS cameras.
In this case, the burst is heavily piled-up, with no events detected in the
PSF core, but a reliable spectrum could be extracted from a 2–5 arcmin annular
region, containing 120 and 122 counts in MOS1 and MOS2, respectively, in the
2–10 keV energy range.

Burst “2” was also seen by _Swift_ BAT (TDRSS ObsID 00341964000) even though
the source was out of the nominal FoV at the time of the event. No spectral
information are available but it provided us with an accurate peak barycentred
time of 19:31:28.66 TDB.

Furthermore, burst “2” triggered KW at $T_{0,\,\mathrm{KW}}$ = 19:31:28.646
TDB (with an accuracy of few ms). The EPIC-pn, BAT and KW light curves are
shown in Fig. 1.

Spectral information could be derived from the KW data, from 16 to 80 ms after
the rise of the burst. This spectrum contains 400 background-subtracted counts
in the 20–300 keV energy band. The lightcurves in the 20–80 keV and 80–350 keV
bands show no evidence of spectral changes along the burst evolution. We
therefore performed a joint analysis of the KW and MOS spectra by applying to
the model of the KW spectrum a cross-normalization factor accounting for the
instrumental dead-time and the fraction of burst background-subtracted counts
detected in this 64 ms time interval. We obtained a good fit
($\chi^{2}_{\nu}=1.6$ for 16 d.o.f.) with a double blackbody model, with
photoelectric absorption fixed at $N_{\rm H}$= $4.2\times 10^{22}$ cm-2
(Pintore et al., 2017), obtaining the following best-fit parameters:333To
evaluate the blackbody radii, a burst duration of 20 ms was assumed.
$kT_{1}=4.1\pm 0.2$ keV and $R_{1}=65\pm 4$ km, $kT_{2}=14.3\pm 0.8$ keV and
$R_{2}=5.5\pm 0.8$ km. From this model, we derive a bolometric fluence of
2.6$\times$10-6 erg cm-2. The observed fluence in the 2–10 keV and 20–100 keV
is $3.1\times 10^{-7}$ erg cm-2 and $1.5\times 10^{-6}$ erg cm-2,
respectively. A much worse fit ($\chi^{2}_{\nu}=2.2$ for 17 d.o.f.) was
obtained by adopting an absorbed cutoff power-law model.

Also burst “1” was detected by the MOS cameras. Due to its lower fluence, we
could safely extract its spectrum from an annulus with a smaller inner radius
(20 arcsec), containing 35 counts in MOS1 and 37 counts in MOS2. Assuming the
same best-fit spectral model as burst “2”, its fluence in the 2–10 keV energy
band is only 4.5$\times$10-9 erg cm-2.

Figure 2:  X-ray and radio pulse profiles of 1E 1547.0–5408 from the _Chandra_
ACIS-S (0.5–10 keV) and 3.1 GHz Parkes light curves obtained on 2009 January
25. Superimposed to the X-ray folded light curve is the best fit obtained with
the sum of sinusoidal functions.

Figure 3:  X-ray and radio simultaneous observations of 1E 1547.0–5408
performed on 2009 February 3, around the time of the brightest X-ray burst
(burst “2” in Fig. 1) and the two radio pulses (pulse A and B). The blue line
is the burst lightcurve, while the grey line is the X-ray folded light curve
using the _XMM-Newton_ dataset. The Parkes simultaneous radio light curve is
shown in red. The grey shaded areas are the phase intervals of the expected
peak of the radio pulse profiles extrapolated from the 2009 January 25 Parkes
observation (see also Figure 2). Note that the flat top of the first radio
peak (pulse A), and the drop of the intensity of the radio signal below the
average noise level following both pulses, are artifacts caused by the
saturation of the backend.

###  3.2 Radio results

We first searched for radio pulsations during the three Parkes observations.
No radio pulsations were detected from 1E 1547.0–5408 in our first
observation, taken on January 23rd, down to a flux density limit of $\sim
0.06$ mJy. The source was again visible as a radio pulsar on January 25th
(Burgay et al., 2009). As expected, the rotational ephemeris available in the
literature did not satisfactorily phase align the radio data. A local timing
solution obtained from the X-ray data (Bernardini et al., 2011) was used to
correctly fold off-line the radio data. In the third observation on February
3rd, no pulsations were detected, but only two single pulses/bursts were
observed, at epochs 19:31:29.82 (pulse A) and 19:31:34.05 (pulse B) TDB. The
reported times are also corrected for the dispersion delay (using the
dispersion measure DM = $830\pm 50\,pc/cm^{3}$, from Camilo et al. 2007a) at
the observing frequency. The error on the DM results in an uncertainty in the
bursts arrival times of 4.4 ms. All times are reported at infinite frequency.

Pulse A was so strong to saturate for about 0.2 seconds the AFB backend. This
can be clearly seen from the red curve in Fig 3, where pulse A shows a flat
top and the baseline following it shows a significant distortion. Pulse B was
also likely very close to the saturation level, as can be inferred from the
value of its highest point and from the (smaller than for pulse A) distortion
of the baseline. For pulse A the time of arrival reported above refers to the
mid-point of the saturated portion, while for pulse B to the highest point in
the profile.

Taking into account the 1-bit sampling, the 1-ms sampling time, and the
frequency width of the channels in use, we can place a lower limit for the
flux density necessary to saturate the backend. Using the receiver’s system
temperature and gain (55 K and 0.71 K/Jy
respectively444https://www.parkes.atnf.csiro.au/observing/documentation/), we
obtain a peak flux density lower limit for the pulse A of $\gtrsim 1$ Jy.
Given the 0.2 s duration of the saturation, this corresponds to a lower limit
in the pulse fluence of $\gtrsim 200$ Jy ms.

Thanks to the simultaneous observations obtained with the DFB3, we can also
give an approximate estimate of the actual peak flux density of the saturated
pulse. Even though the data were folded on-line, in fact, the two pulses fall
in two separate, consecutive, 30-s long sub-integrations. The signal-to-noise
ratio of pulse A (averaged with $\sim 15$ ‘silent’ rotations) is, in the DFB3
data, three times larger than that of pulse B, also smoothed by the noise
resulting from $\sim 15$ ‘silent’ rotations. Since the pulse B is very close
to saturate the AFB, we can tentatively conclude that pulse A must be
approximately three times stronger than the saturation limit for the AFB. We
can hence estimate a fluence of $\sim 0.6$ kJy ms.

To align in phase the X-ray and radio observations of the bursts, we first
measured the times of arrival (ToAs) of a fiducial point of the radio profiles
(the peak or, in the case of the saturated pulse, the mid point of the
saturation plateau). For the two single pulses the times were obtained
directly from the time series, barycentered and corrected for the dispersion
delay at the observed radio frequency using prepdata, from the presto
package555https://www.cv.nrao.edu/~sransom/presto/. On the other hand, the ToA
of the peak of the folded profile of the pulsations observed on January 25,
was measured by cross-correlation with a synthetic profile template using pat
from the psrchive package(van Straten et al., 2012), and then barycentered and
corrected for the dispersion delay using the general2 plugin in
tempo2666https://bitbucket.org/psrsoft/tempo2/src/master/ (Hobbs et al.,
2006). A local set of ephemerides obtained from the simultaneous X-ray
observations was used in the process. The same ephemerides were used to
determine the fractional part of the absolute phase of the radio pulses, from
which we obtained the phase offset between the selected bin in the radio
profiles and the beginning of the first bin of the X-ray light curve.

The results are shown in Fig. 2 and Fig. 3 where the total X-ray folded light-
curve is almost aligned with the radio pulses. This result is at variance with
that obtained by Halpern et al. (2008), who found $\sim$0.2 cycles phase shift
between the X-ray and radio profiles (with the X-rays peak preceding the radio
one). This is not surprising because the source is known to vary its profile
shape and hence also the exact position of its main peak (Bernardini et al.,
2011; Camilo et al., 2007a). Moreover, the single pulses (even for otherwise
ordinary pulsars) are often seen to wander around the integrated peak profile
with notable exceptions (as an example see the case of XTE J1810-197; Camilo
et al. 2007b).

###  3.3 Radio/X chance coincidence probability

We estimated the probability of having two radio pulses occurring by chance
within $\sim 1.2$ s (about half a rotation cycle) of the two X-ray bursts
detected in the window of radio/X-ray simultaneity on February 3. The 0.5 s
bin time of the X-ray light curve corresponds to the zero height width of the
saturated radio pulse and yields to ${\cal N}\approx$ 10 800 bins in the time
interval of interest. As a conservative approximation, we assume the
probability of chance coincidence as the ratio between $N_{\rm c}$, the total
number of configurations in which one random radio pulse may follow one X-ray
burst by $\leq 3$ bins, and ${\cal N}$, the total number of bins. We obtain
$N_{\rm c}=12$ as the number of trials (2 radio pulses) times the number of
targets (2 X-ray bursts) times the number of valid bins per trial (3), which
implies a (maximum) chance coincidence probability of 1.1$\times$10-3
(3.3$\sigma$). Similarly, we obtain a probability of 7.3$\times$10-4
(3.5$\sigma$) by considering the two-bin delay ($\lesssim$1 s) between the
X-ray burst peak and the start of the radio pulse.

##  4 Discussion

We performed two X-ray and three radio observations of 1E 1547.0–5408 during
its 2009 burst active phase. In our 1.5 hr-long 2009 February 3rd observing
campaign we detected two bright radio pulses/bursts. In particular, the first
event (pulse A), with fluence $F\sim 0.6$ kJy ms and width $\sim 200$ ms,
occurred about 1 s (half a rotation cycle) after a very bright X-ray burst
(burst “2”) showing a profile with two peaks separated by 10 ms. The X-ray
burst had a bolometric fluence of 1.3$\times$10-6 erg cm-2 and width of $\sim
50$ ms. The radio bursts are neither aligned with the radio pulsations
detected six days before in a previous radio observation, nor with the X-ray
pulsations, presenting a $\sim$ 0.2 phase shift with respect to both. These
findings, along with the lack of “normal” radio pulsations during our 1.5 hr-
long observation, strongly suggest a close connection of the X-ray and radio
bursts. This new and peculiar magnetar phenomenology assumes additional
relevance in the context of the recently detected FRB-like bursts from SGR
J1935+2154 (The CHIME/FRB Collaboration et al., 2020; Bochenek et al., 2020;
Mereghetti et al., 2020; Ridnaia et al., 2020; Tavani et al., 2020a; Li et
al., 2020). Two bright radio bursts were detected from SGR J1935+2154, with a
total fluence of $\sim 700$ kJy ms at 600 MHz. The second of them was also
independently observed by STARE2 at 1.5 GHz, with an estimated fluence above
1.5 MJy ms (Bochenek et al., 2020). Furthermore, the reported radio bursts
show a steep spectral index, as do FRBs. In our case, the spectral properties
of the radio bursts cannot be constrained as we only observed at 6.6 GHz.

In the case of SGR J1935+2154, despite a slight misalignment of the X-ray
peaks as observed by different instruments (Mereghetti et al., 2020; Ridnaia
et al., 2020; Li et al., 2020), the radio burst appears to lead the SGR-like
X-ray burst by no more than $\sim$ 8 ms, while in 1E 1547.0–5408 it is the
X-ray burst that leads the first radio burst by $\sim 1$ s.

Comparing the SGR-like X-ray bursts of SGR J1935+ 2154 and 1E 1547.0–5408, as
detected by KW data, both were in line in terms of energy and duration with
what usually observed from their respective sources. The spectrum, in the case
of SGR J1935+2154, was harder than in typical bursts from that source and was
indeed among the top 2% hardest magnetar bursts ever detected by KW (Ridnaia
et al., 2020). On the other hand, the softer spectrum of 1E 1547.0–5408’s
burst was very typical within the magnetar population.

No further simultaneous X-ray and radio bursts were detected despite the
continued X-ray activity of SGR J1935+2154, while several fainter radio bursts
were reported (Zhang et al., 2020; Kirsten et al., 2020). The source entered a
new radio active phase in early October 2020, characterized by one bright
burst of fluence $\sim 900$ Jy ms observed by CHIME, followed by many fainter
bursts below 50 Jy ms observed by both CHIME and FAST (Good & Chime/Frb
Collaboration, 2020; Pleunis & Chime/Frb Collaboration, 2020; Zhu & FAST,
2020). FAST pulses were aligned in phase with the detected radio pulsation of
the source.

The energy released in the brightest radio bursts of SGR J1935+2154 and 1E
1547.0–5408 is $3\times 10^{34}$ erg and $8.4\times 10^{30}$ erg, with a
radio-to-X-ray ratio $E_{r}/E_{X}\sim 10^{-5}$ and $\sim 10^{-9}$,
respectively. In both cases these were brighter than standard magnetar radio
single peaks (below a few Jy; e.g. Camilo et al. 2006), yet “mild” compared to
FRBs, although the latter are known to span a wide range of energies (The
CHIME/FRB Collaboration et al., 2020; Bochenek et al., 2020). For the giant
flare of SGR 1806–20 (Palmer et al., 2005) the most stringent limits to the
ratio of radio versus X-ray emitted energy were set down to $\lesssim 10^{-8}$
(Tendulkar et al., 2016). On the other hand, in the case of the better
constrained FRB repeaters with simultaneous X/radio observations (Scholz et
al., 2017; Pilia et al., 2020) these limits are of the order of $\geq
10^{-9}-10^{-8}$. According to Chen et al. (2020), who derive constraints on
$E_{r}/E_{X}$ in FRBs from past surveys, $E_{r}$ should be of order $\sim
10^{-5}E_{X}$, larger than our detection for 1E 1547.0–5408.

The wide range in radio efficiency and/or luminosity of magnetar bursts
suggests that these sources may bridge the gap between “ordinary” pulsar radio
bursts and the extragalactic FRB phenomenon (as also suggested in The
CHIME/FRB Collaboration et al. 2020; Bochenek et al. 2020; Kirsten et al.
2020). The detection of energetic radio bursts simultaneous with regular X-ray
bursts is indicative of what already pointed by previous studies (Cunningham
et al., 2019; Casentini et al., 2020; Guidorzi et al., 2020; Scholz et al.,
2020), i.e. that non-detections of high-energy emission from FRBs can be
attributed to limiting telescopes sensitivities rather than intrinsic
inhibition of the phenomenon .

The bursts reported in this work appear to be magnetospheric in origin, given
their relatively good phase alignment with the rotation of the magnetar.
Lyutikov & Popov (2020) propose that magnetospheric reconnection events can
explain the energetics and the apparent simultaneity of the X-ray and radio
bursts of SGR J1935+2154. In the case of 1E 1547.0–5408, however, the total
energy in the radio burst may still be consistent with rotation-powered
emission, given its $\sim 0.5$ s duration and the estimated spin-down
luminosity of the source, $\sim 10^{35}$ erg s-1. (Rea et al., 2012; Lyutikov
et al., 2016; Esposito et al., 2020).

On the other hand, according to Lu et al. (2020), an explosion at the surface
of the neutron star would produce both the X-ray burst and the radio burst, by
propagating through the crust towards the polar cap in the form of Alfven
waves. In this scenario the emission is magnetospheric and it arises naturally
that not all X-ray bursts generate an FRB-like radio burst, as it is observed
for both SGR J1935+2154 (Borghese et al., 2020) and 1E 1547.0–5408. However,
the radio emission is expected to lag the X-ray burst, albeit slightly,
contrary to the observations in 1E 1547.0–5408.

Moreover, both this and the external models (Margalit et al., 2020) require a
ratio $L_{r}/L_{X}>10^{-5}-10^{-4}$, which is in tension with our findings and
with observations of the SGR 1806-20 giant flare.

The picture emerging from our detection of radio and X-ray bursts from 1E
1547.0–5408, as well as from the most recently observed bright and faint radio
and X-ray bursts from SGR J1935+2154 (The CHIME/FRB Collaboration et al.,
2020; Bochenek et al., 2020; Zhang et al., 2020; Kirsten et al., 2020), is
that there exists a continuum of magnetar radio burst energies, which might at
times look like FRBs and at others be much closer to typical radio pulsar
single pulse phenomenology (such as Rotating Radio Transients or Giant Pulses,
McLaughlin et al. 2004; Lyutikov & Popov 2020). On the other hand, the X-ray
counterparts of such radio bursts are not yet easily predictable, and may
depend on specific parameters of the burst, most of which are still not fully
understood.

GLI and LS acknowledge funding from ASI-INAF agreements I/037/12/0 and
2017-14-H.O. GLI and AT acknowledge financial support from the Italian MIUR
PRIN grant 2017LJ39LM. MB, AP, and LS acknowledge funding from the grant
“iPeska” (INAF PRIN-SKA/CTA; PI Possenti). NR is supported by the ERC
Consolidator Grant “MAGNESIA” (nr.817661), and by grants SGR2017-1383 and
PGC2018-095512-BI00. We acknowledge the support of the PHAROS COST Action
(CA16214).

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