# FRB emission mechanisms vs. observations

Popov S.B.1,2 1Sternberg Astronomical Institute, 119234, Universitetski pr.
13, Moscow, Russia
2Department of Physics, Lomonosov Moscow State University, 119991, Moscow,
Russia

(2022)

###### Abstract

Presently, it is broadly assumed that fast radio bursts (FRBs) are sources of
coherent emission powered by the magnetic energy release in magnetars.
However, the exact emission mechanism is not known, yet. Two main frameworks
exist: magnetospheric emission and radiation from external relativistic
shocks. In this brief review, I describe basics of both approaches and discuss
how they are probed in modern observations.

###### keywords:

radiation mechanisms: nonthermal, stars: neutron

††volume: 369††journal: The Dawn of Cosmology & Multi-Messenger Studies with
Fast Radio Bursts††editors: E. Keane, K. Rajwade, A. Fialkov & C. Walker, eds.

##  1 Introduction. Where do we stand?

After 15 years of studies, we know quite a lot about FRBs (see e.g., a recent
broad review by Caleb & Keane 2021). Regarding the topic of this brief review,
I want to underline three main items which can be considered as the base of
the present day ’standard’ FRB model:

  * •

Coherent emission;

  * •

Magnetic energy release;

  * •

Magnetars as the sources.

In the following three paragraphs I briefly comment on each of them.

Already in the discovery paper (Lorimer et al., 2007) the authors demonstrated
that the brightness temperature might be $\sim 10^{34}$ K and thus, a coherent
emission mechanism is necessary. All later observations only supported this
conclusion. So, from the very beginning development of all reliable mechanisms
is focused on a coherent emission generation.

Since 2007 dozens of various types of sources and emission mechanisms have
been proposed (see Xiao, Wang & Dai 2021 and references therein). Still,
relatively quickly two of them started to attract the main attention:
magnetars and ’pulsars on steroids’. In the former, magnetic energy
$E_{\mathrm{mag}}$ is released, in the latter – rotational energy,
$E_{\mathrm{rot}}$. Potentially,
$E_{\mathrm{rot}}=\frac{1}{2}I\omega^{2}\sim\mathrm{few}\times
10^{52}p_{-3}^{-2}$ erg is significantly larger than
$E_{\mathrm{mag}}\sim\mathrm{few}\times 10^{47}B_{15}^{2}$ erg. Still, step by
step pulsar-like mechanisms started to face difficulties. In particular,
rotation powered mechanisms hardly can produce very energetic bursts, or
revealed parameters imply a rapid evolution of the source, which is not
observed (Lyutikov, 2017). Presently, most of prominent approaches involve
just magnetic energy release.

Finally, after the celebrated discovery in April 2020 of simultaneous radio
and high energy bursts from the Galactic source SGR 1935+2154 (see a brief
review in Sec. 6 of Nicastro et al. 2021, references to the original papers
are given below), the original proposal that FRBs are related to flashes of
magnetars (Popov & Postnov, 2007) got a strong support. Recently (October
2022), a few more coincident radio and high energy events were detected from
the same source (Dong et al., 2022; Wang et al., 2022; Frederiks et al., 2022;
Huang et al., 2022; Li et al., 2022). Although this does not prove that all
FRBs are due to a magnetar activity, magnetars seem to be the best site to
produce FRBs.

Below, I shall discuss only the mechanisms related to a coherent emission
generation powered by the magnetic energy release in magnetars.

##  2 Emission mechanisms

The most popular approaches to describe radio emission of FRBs can be divided
in the two families of models (see an excellent brief review by Zhang 2020).
The first one deals just with magnetospheric processes. In the second
approach, pioneered by Lyubarsky (2014), radio emission is generated in
relativistic shocks outside the magnetosphere. Both scenarios (below I dub
them as magnetospheric and external, correspondingly) include an initial
perturbation in the magnetosphere accompanied by significant energy release
most of which might be emitted at high energies. The radio emission is
generated either in the magnetosphere and then propagates through it outwards,
or a part of the energy of the flare is reprocessed in an external medium
producing radio waves.

It is not for granted that all FRBs are caused by a single emission mechanism.
Still, different authors mostly try to explain in one model the whole set of
the main parameters observed in various sources (repeating or not). The entire
list of these parameters can be very long, just to name a few:

  * •

Range of luminosities;

  * •

Various morphological types;

  * •

Duration;

  * •

Rapid variations of the flux;

  * •

Brightness temperature;

  * •

Repetitions (sometimes with a very high rate);

  * •

Very high degree of polarization in many cases;

  * •

Variations of polarization from burst to burst in repeaters;

  * •

Relatively narrow spectra (sometimes variable from burst to burst in the case
of repeating sources);

  * •

Frequency drift (’sad trombone’ effect, etc.).

In the following two subsections I present a sketch of both scenarios, and
then in Sec. 3 briefly discuss correspondence between theoretical predictions
and observational data.

###  2.1 Synchrotron maser models

The idea of a coherent emission generated at relativistic shocks has been
discussed in relation to astrophysical applications long before the discovery
of FRBs (Hoshino & Arons, 1991). During the last $\sim 8$ years this model
(including a synchrotron maser emission) is actively developed by many groups
all over the world to explain properties of FRBs (see a comprehensive review
by Lyubarsky 2021).

In this framework an ejecta (or a ’magnetic piston’ – an electromagnetic pulse
dominated by the magnetic field) formed in the magnetar’s magnetosphere
propagates outwards with an ultra-relativistic speed and interacts with the
surrounding medium forming a relativistic shock. For example, in the model by
Beloborodov (2020) a magnetar via reconnection produces a plasmoid which moves
with a Lorentz factor $\Gamma_{\mathrm{pl}}\gtrsim 10^{5}$. It starts to
interact with the magnetar’s cold relativistic wind with
$\Gamma_{\mathrm{w}}\sim(10-20)$. This results in the formation of a shock
wave with $\Gamma\gtrsim 10^{3}$. In the shock wave downstream the conditions
corresponding to a synchrotron maser can be fulfilled. Then, at a typical
distance $\sim 10^{14}$ cm from the magnetar a millisecond-long radio burst
with a typical frequency $\sim$GHz is produced.

In order to demonstrate a different approach in the same framework, we can
look at the model by Khangulyan, Barkov & Popov (2022). These authors
presented a scenario where a radio burst is generated at the reverse shock
which appears after interaction of a powerful magnetar flare with a magnetar’s
wind termination shock. For the terminal shock distance $\lesssim 10^{15}$ cm
the characteristic frequency of emission is about 1 GHz. In this model only
$\sim$10% of magnetars are in the evolutionary phase suitable for the
production of FRBs and just a small fraction ($\sim 10^{-4}$) of their flares
produce FRBs. This helps to resolve several issues known from observations.

###  2.2 Magnetospheric emission models

Some early models of FRBs utilised magnetospheric processes to generate
emission due to rotational energy losses (e.g., Katz 2014). However, in this
subsection I discuss only scenarios based on magnetic energy dissipation.
Three scenarios will be mentioned, however there are many more magnetospheric
models. There detailed discussion requires a special review.

In the first one proposed by Lu, Kumar & Zhang (2020), disturbances are
propagating along opened field lines, which finally results in generation of
radio emission (while a high energy flare is generated by plasma trapped in
the closed lines part of the magnetosphere). Conversion of Alfven waves into
radio waves happens at the charge starvation region at $\sim 10^{8}$ cm.

Quite a different scenario was proposed by Lyubarsky (2020). In this model a
magnetic pulse is generated after a magnetar flare. It propagates outside the
light cylinder till it hits the current sheet. This results in reconnection of
field lines, which finally leads to radio emission. In some sense, this is a
’hybrid’ model (in some respect similar to the external scenario), but I
prefer to put it together with the magnetospherics ones, as it involves just
the structure which is intrinsic for a magnetosphere of a rotating neutron
star.

Finally, Lyutikov (2021) used a free electron laser concept in application to
radio emission of highly magnetized neutron stars. In this case a relativistic
beam of electrons, generated due to a reconnection event, must propagate
through periodically varying magnetic field. In the case of neutron stars such
a field structure can appear e.g., due to the firehose instability in the
magnetosphere. Then, bunches of particles are formed in the beam, and
particles in a bunch emit coherently producing a FRB.

Notice, that in these three models energy is carried towards the site of radio
emission by three different subjects: MHD waves, a magnetic pulse pushing
plasma, and a particle beam.

In the next section I summarize how successful are the two main frameworks –
magnetospheric and external, – in fitting the present observational data.

##  3 Observations and theory

Despite a very rich phenomenology, the exact emission mechanism for FBRs
remains unknown, yet. In many respects, this situation resembles the one with
radio pulsars (e.g., Beskin 2018). Although, thousands of pulsars are known
and many of them are observed in all wavelengths – from radio to gamma, –
there is no consensus about important issues regarding generation of their
radiation (again, from radio to gamma), despite 55 years of studies.
Hopefully, for the FRBs we can find a solution faster.

Here I select just eight points, which are briefly reviewed below:

  * •

Polarization;

  * •

Periodicity;

  * •

Narrow spectra;

  * •

Frequency drift;

  * •

Rapid variability;

  * •

Repeaters vs. non-repeaters;

  * •

Burst rate and total energetics;

  * •

Bursts from SGR 1935+2154.

A review of polarization properties of FRBs can be found e.g., in Sec 5.9 of
Caleb & Keane (2021). Polarization is measured for more than 20 FRBs
(including several repeaters). In a few cases (again, including repeaters) the
measured degree of linear polarization is compatible with 100%.

An important result was presented by Luo et al. (2020). Analysing 15 bursts
from FRB 180301 these authors discovered significant changes in polarization
properties from burst to burst. This feature does not easily fit external
models, but can be explained in the magnetospheric scenario, naturally.

Oppositely, observations of FRB 121102 (Michilli et al., 2018) demonstrated a
very stable polarization angle and nearly 100% linear polarization for all
bursts. Such stability is not expected for magnetospheric emission. However,
Lyubarsky (2020) noticed, that it is non-trivial to explain 100% polarization
in the framework of relativistic shock emission.

A unique result was obtained by CHIME/FRB collaboration (2022). A non-
repeating source FRB 20191221A demonstrated a 3-second long burst with a
complicated pulse structure. Analysis allowed to derive a periodicity with the
period $\sim 217$ msec at a $\sim 6.5\,\sigma$ level. As it was noted by the
authors, such periodicity can be easier explained in magnetospheric models
than in the external framework.

Much effort has been expended to detect FRBs simultaneously at different radio
frequencies (from $\sim 100$ MHz up to several GHz) in order to measure
spectral parameters in a wide range. However, all such attempts (especially
intensive for repeaters, like FRB 121102 and R3) were so far unsuccessful. For
example, Pastor-Marazuela et al. (2021) observed FRB 20180916B with LOFAR
(110-190 MHz) and Apertif/Westerbork (1.2-1.5 GHz). Many detections have been
made by each instrument, but not a single one simultaneously at high and low
frequencies. Similar results were obtained for several sources by different
authors. Simultaneous detections are done only at close frequencies, e.g. like
in the case of FRB 121102 at 1.4 and 3 GHz (but without detections at 4.85 and
15 GHz), see Law et al. (2017). This points to narrow spectra of FRBs.

An extreme example is given by Kumar et al. (2021). Using the 64-meter Parkes
telescope these authors detected a very short (1 msec) burst from the repeater
FRB 20190711A. The peculiarity of the result is related to an extremely narrow
band in which the source was detected: just 65 MHz at $\sim 1.4$ GHz. It is
not clear, if this feature is directly related to the emission mechanism, but
if it does – then it can be a challenge for many models. Specifically
accounting for the fact, that this repeating source shows different spectral
properties for different bursts.

Generally, explanation of the variety of spectral properties (including recent
detection of a radio burst from SGR 1935+2154 at 400 MHz and 5.6 GHz
simultaneously with high-energy detection, see Maan et al. 2022) and their
variability in repeating sources might be a good tool to probe theoretical
models, especially if the aim is to explain all sources in one framework.

FRBs can also have unusual dynamical spectra: spectral properties can change
during a burst or from one sub-burst no another. The most known is so-called
’sad trombone’ effect, when the frequency of emission is decreasing during a
burst (Gajjar et al., 2018).

The ’sad trombone’ effect can be naturally explained in the magnetospheric
approach (e.g., Lyutikov 2020). As emitting particles move in the
magnetosphere outwards, the frequency of their radiation goes down because the
emission site is situated at larger and larger distance (i.e., in lower
magnetic field) for later moments of time. In the external framework the
frequency down drift can be explained, too, e.g., via a deceleration of the
shock (see Metzger et al. 2022 and references therein).

Often, subsequent sub-bursts have frequencies shifted down, somehow similar to
the ’sad trombone’ effect (see examples in Gajjar et al. 2018). However,
sometimes opposite behavior is observed: sub-bursts demonstrate frequency
increase (Zhou et al., 2022). Explanation of such behavior in one framework
together with ’sad trombone’ and other peculiarities can be difficult for both
concurrent approaches.

Another important observational feature is related to the shortest time scale
of variability found in FRBs. At the moment, the record probably belongs to
FRB 20180916B. Nimmo et al. (2021) reported observations of sub-pulses at the
time scale about few $\mu$s. Such short time scales are more naturally
explained in the magnetospheric scenario. However, small scale inhomogeneities
in the external medium, where the shock propagates, can help to obtain
$\sim\mu$s variability also in synchrotron maser models. Larger statistics of
short flux variations in repeating sources potentially can help to distinguish
between predictions of the two frameworks.

One of the most disputable questions in phenomenology of FRBs is related to a
possible dichotomy between repeaters and non-repeaters. Extensive comparison
was made by Pleunis et al. (2021). These authors used 61 bursts from 18
repeaters plus 474 events from non-repeaters, all detected by CHIME. Clearly,
two groups of bursts are well-separated in terms of spectral and temporal
parameters (with a possible addition of the third group of one-off events from
not-yet-identified repeaters). Repeaters have larger bursts duration and more
narrow band width.

Note that many (indirect) arguments in favour of the magnetospheric framework
mentioned above come from observations of repeaters. Then, it is tempting to
hypothesize that non-repeaters (or one-off events) are due to the competitive
mechanism – synchroton maser radiation of relativistic shocks. However, this
idea can be criticized. One-off events have very narrow distributions in
duration and band width (see Pleunis et al. 2021). This is not naturally
expected in the external framework due to either different properties of the
external medium in different sources, or due to different parameters of the
magnetar wind, if its properties are important.

Some problems for the ’standard’ model of FRBs can appear due to observations
of ’burst storms’ from several sources (Xu et al., 2022; Nimmo et al., 2022;
Zhou et al., 2022). If we assume that the ratio of radio luminosity to the
total energy release in a flare is $\sim 10^{-5}$, as it is suggested from
observations of the Galactic source (see below), then the total magnetic
energy losses can be $\gtrsim 10^{46}$ erg just in few days. Total magnetic
energy available for powering a magnetar’s flares hardly can exceed $10^{48}$
ergs. Thus, such a strong activity might be a very short, $\sim 10$ yrs,
episode in a life of the magnetar. Appearance of this short evolutionary stage
requires a satisfactory explanation.

In addition, the huge energy release during such active periods might
significantly modify properties of the external medium. This can be important
for some external models. So, it is promising to look for systematic
differences between bursts emitted during periods of strong activity and
bursts from more quiet sources.

For several years one of the key arguments against the hypothesis that
magnetars are the sources of FRBs was a simple question: why we do not see
flares from Galactic objects? Finally, on April 28, 2020 simultaneous bursts
in radio and in X/$\gamma$-rays were detected from the Galactic source SGR
1935+2154 (CHIME/FRB Collaboration et al., 2020; Bochenek et al., 2020;
Mereghetti et al., 2020; Ridnaia et al., 2021; Tavani et al., 2021; Li et al.,
2021).

As this is the very first detection of a high-energy counterpart of an FRB,
now we have the first estimate of the fraction of the total energy of a flare
emitted in radio: $E_{\mathrm{radio}}/E_{\mathrm{total}}\sim 10^{-5}$. This
value can be explained in both frameworks (Lyutikov, 2021; Yang & Zhang, 2021;
Yuan et al., 2020).

An intriguing feature of FRB 200428 is related to the delay between radio and
high energy emission: at low frequencies peaks of the bursts are emitted a few
millisecond earlier than in the opposite part of the electromagnetic spectrum
(Mereghetti et al., 2020; Li et al., 2021). Curiously, this peculiarity also
can be explained in both frameworks (Lyutikov, 2021; Yuan et al., 2020). New
detections of simultaneous bursts from this source in October 2022 (see Dong
et al. 2022; Wang et al. 2022; Frederiks et al. 2022; Huang et al. 2022; Li et
al. 2022) can provide new information on this issue, but at the time of
writing of this review details are not published, yet.

In addition to the importance of observations of simultaneous bursts, there is
a question why among hundreds of high energy and radio bursts detected from
SGR 1935+2154 just a few come together (see e.g., Lin et al. 2020; Younes et
al. 2020). The first FRB-like event (coincident with an X-ray flare) from this
source had peculiar properties in the high energy range (Mereghetti et al.,
2020; Ridnaia et al., 2021; Tavani et al., 2021; Li et al., 2021). But at
least the first of the October bursts observed simultaneously by radio
telescopes and gamma-ray detectors has properties much closer to the rest of
high energy events (Frederiks et al., 2022). This variety of properties must
be explained in a successful model.

##  4 Future outlook

To conclude, magnetars seem to be the sources of (at least, most of) FRBs. The
exact mechanism of emission is unknown, but two main frameworks are
formulated: magnetospheric processes and coherent (e.g., maser) emission from
external relativistic shocks. Up to now, plethora of observational data cannot
exclude either of the main scenarios.

Some progress in disentangling between different models of FRB emission may be
achieved due to variety of properties of medium in vicinity of the sources. If
we accept the magnetar model, then there is a question regarding the origin of
these magnetars. Already now, we can formulate some ideas about it, as FRBs
are detected at very different sites. For $\sim 20$ sources host galaxies are
identified (Heintz et al., 2020). The prolific repeater FRB 121102 is known to
be situated in a starforming region in a dwarf galaxy (Kokubo et al., 2017).
Similar situations are realized for several other sources. On other hand, some
sources are localized in galaxies with low starformation rate. An extreme
example of such situation is the source FRB 20200120E which is located in a
globular cluster of the M81 galaxy (Kirsten et al., 2022). It is natural to
assume that magnetars in these cases have different origin. In regions of
active starformation they might mostly come from a normal core collapse. In
globular clusters and early type galaxies they, most probably, originate from
coalescence of compact objects or accretion induced collapse. Thus, we can
expect quite different environment in these cases. Finally, if periodicity of
FRB 121102 (Rajwade et al., 2020) and FRB 180916 (R3) (CHIME/FRB
collaboration, Amiri et al., 2020) is due to the orbital motion in a binary,
then magnetars there are embedded in a dense stellar wind of the massive
companion (see e.g., Barkov & Popov 2022 and references therein). Which again
suggests a specific type of surrounding medium.

Properties of the environment are important in several models involving
external shocks, mentioned above. If parameters of the surrounding medium are
not determined solely by the magnetar wind, then we can expect significant
differences in the conditions at the shock, which might manifest themselves in
properties of FRB emission. For example, pressure in the external medium is
important in models by Lyubarsky (2014) and Khangulyan, Barkov & Popov (2022).
Then we can expect that in significantly different environments properties of
the observed FRBs are also systematically different.

Many hopes are bind to observations of Galactic magnetars. While perspectives
to detect counterparts of extragalactic FRBs are very vague, in our own Galaxy
we have now three detections of simultaneous high-energy and radio bursts from
SGR 1935+2154.111On October 14, 2022 the second simultaneous event was
detected, see Dong et al. 2022; Wang et al. 2022; Frederiks et al. 2022; Maan
et al. 2022. And then, the third event, see Huang et al. 2022; Li et al. 2022.
Detailed observations of relatively near-by sources might provide insight into
the emission mechanism. It is particularly interesting to measure precisely if
there is a time delay between radio and high-energy signals in all cases.
E.g., this feature was discussed by Lyutikov (2021) in his free electron laser
approach.

Another feature, which can help to shed light on the emission mechanism, is
spin periodicity, especially in a series of consecutive bursts, like in the
case of FRB 20191221A (CHIME/FRB collaboration, 2022). A solid proof of spin
period origin of such events can be a strong argument in favour of the
magnetospheric origin of radio emission.

And, of course, it well can be that some serendipitous discoveries (e.g., high
energy counterparts of extragalactic FRBs) will finally uncover the emission
mechanism of FRBs.

###### Acknowledgements.

I acknowledge support from the Russian Science Foundation (grant 21-12-00141).
Also I thank dr. D. Khangulyan for many useful comments on the manuscript.

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