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The observed spectral shapes variation and tentative bimodal burst energy distribution (E-distribution) of fast radio burst (FRB) 20121102A with the FAST telescope are great puzzles. Adopting the published multifrequency data observed with the FAST and Arecibo telescopes at $L$ band and the GBT telescope at $C$ band, we investigate these puzzles through Monte Carlo simulations. The intrinsic energy function (E-function) is modeled as $dp/dE\propto E^{-\alpha_{\rm E}}$, and the spectral profile is described as a Gaussian function. A fringe pattern of its spectral peak frequency ($\nu_{\rm p}$) in 0.5-8 GHz is inferred from the $\nu_{\rm p}$ distribution of the GBT sample. We estimate the likelihood of $\alpha_{\rm E}$ and the standard deviation of the spectral profile ($\sigma_{\rm s}$) by utilizing the Kolmogorov--Smirnov (K-S) test probability for the observed and simulated specific E-distributions. Our simulations yields $\alpha_{\rm E}=1.82^{+0.10}_{-0.30}$ and $\sigma_{\rm s}=0.18^{+0.28}_{-0.06}$ ($3\sigma$ confidence level) with the FAST sample. These results suggest that a single power-law function is adequate to model the E-function of FRB 20121102A. The variations of its observed spectral indices and E-distributions with telescopes in different frequency ranges are due to both physical and observational reasons, i.e. narrow spectral width for a single burst and discrete $\nu_{p}$ fringe pattern in a broad frequency range among bursts, and the selection effects of the telescope bandpass and sensitivity. The putative $\nu_{p}$ fringe pattern cannot be explained with the current radiation physics models of FRBs. Some caveats of possible artificial effects that may introduce such a feature are discussed., Comment: Published in ApJ,13 pages, 5 figures

Assuming that the shallow-decaying phase in the early X-ray lightcurves of gamma-ray bursts (GRBs) is attributed to the dipole radiations (DRs) of a newborn magnetar, we present a comparative analysis for the magnetars born in death of massive stars and merger of compact binaries with long and short GRB (lGRB and sGRB) data observed with the {\em Swift} mission. We show that the typical braking index ($n$) of the magnetars is $\sim 3$ in the sGRB sample, and it is $\sim 4$ for the magnetars in the lGRB sample. Selecting a sub-sample of the magnetars whose spin-down is dominated by DRs ($n\lesssim 3$) and adopting a universal radiation efficiency of $0.3$, we find that the typical magnetic field strength ($B_p$) is $10^{16}$ G {\em vs.} $10^{15}$ G and the typical initial period ($P_0$) is $\sim 20$ ms {\em vs.} $2$ ms for the magnetars in the sGRBs {\em vs.} lGRBs. They follow the same relation between $P_0$ and the isotropic GRB energy as $ P_0\propto E_{\rm jet}^{-0.4}$. We also extend our comparison analysis to superluminous supernovae (SLSNe) and stable pulsars. Our results show that a magnetar born in merger of compact stars tends to have a stronger $B_p$ and a longer $P_0$ by about one order of magnitude than that born in collapse of massive stars. Its spin-down is dominated by the magnetic DRs as old pulsars, being due to its strong magnetic field strength, whereas the early spin-down of magnetars born in massive star collapse is governed by both the DRs and gravitational wave (GW) emission. A magnetar with a faster rotation speed should power a more energetic jet, being independent of its formation approach., 10 pages, 2 tables, 7 figures. Published in MNRAS

Fast radio bursts (FRBs) are mysterious astronomical radio transients with extremely short intrinsic duration. Until now, the physical origins of them still remain elusive, especially for the nonrepeating FRBs. Strongly inspired by recent progress on possible evidence of Earth-mass primordial black holes, we revisit the model of Earth-mass primordial black holes mergers as sources for nonrepeating FRBs. Under the null hypothesis that the observed nonrepeating FRBs originate from the mergers of Earth-mass primordial black holes, we analyzed four independent samples of nonrepeating FRBs to study the model parameters, i.e., the typical charge value ${q}_{\mathrm{c}}$ and the power index $\ensuremath{\alpha}$ of the charge distribution function of the primordial black hole population $\ensuremath{\phi}(q)\ensuremath{\propto}(q/{q}_{\mathrm{c}}{)}^{\ensuremath{-}\ensuremath{\alpha}}$, which describe how the charge was distributed in the population. $q$ is the charge of the hole in the unit of $\sqrt{G}M$, where $M$ is the mass of the hole. It turns out that this model can explain the observed data well. Assuming the monochromatic mass spectrum for primordial black holes, we get the average value of typical charge ${\overline{q}}_{\mathrm{c}}/{10}^{\ensuremath{-}5}=1.5{9}_{\ensuremath{-}0.18}^{+0.08}$ and the power index $\overline{\ensuremath{\alpha}}=4.5{3}_{\ensuremath{-}0.14}^{+0.21}$ by combining the fitting results given by four nonrepeating FRB samples. The event rate of the nonrepeating FRBs can be explained in the context of this model if the abundance of the primordial black hole populations with charge $q\ensuremath{\gtrsim}{10}^{\ensuremath{-}6}$ is larger than ${10}^{\ensuremath{-}5}$, which is far below the upper limit given by current observations for the abundance of Earth-mass primordial black holes. In the future, simultaneous detection of FRBs and high frequency gravitational waves produced by mergers of Earth-mass primordial black holes may directly confirm or deny this model.

Fast radio bursts (FRBs) are intense radio transients whose physical origin remains unknown. Therefore, it is of crucial importance to use a model-independent method to obtain the energy function and cosmic formation rate directly from the observational data. Based on current samples from the Parkes and ASKAP telecsopes, we determine, for the first time, the energy function and formation rate of FRBs by using the Lynden-Bell C − method. The energy function derived from the Parkes sample is a broken power law, however it is a simple power law for the ASKAP sample. For Parkes sample, we derive the formation rate which is roughly consistent with the star formation rate up to z ∼ 1.7 , with a local formation rate of ρ ˙ ( 0 ) ≃ ( 3.2 ± 0.3 ) × 10 4 Gp c − 3 y r − 1 above a detection threshold of 2 Jyms . For ASKAP sample, we find that the formation rate evolves much faster than the star formation rate up to z ∼ 0.7 , namely ρ ˙ ( z ) ∝ ( 1 + z ) 6.9 ± 1.9 , with a local formation rate of ρ ˙ ( 0 ) ≃ ( 4.6 ± 0.8 ) × 10 3 Gp c − 3 y r − 1 above a detection threshold of 51 Jyms . This might be a important clue for the physical origin of FRBs.

There are some similarities between bursts of repeating fast radio bursts (FRBs) and giant pulses (GPs) of pulsars. To explore possible relations between them, we study the cumulative energy distributions of these two phenomena using the observations of repeating FRB 121102 and the GPs of Crab pulsar. We find that the power-law slope of GPs (with fluence ≥130 Jy·ms) is 2.85±0.10. The energy distribution of FRB 121102 can be well fitted by a smooth broken power-law function. For the bursts of FRB 121102 above the break energy (1.22 · 1037 erg), the best-fitting slope is 2.90 −0.44 +0.55 , similar to the index of GPs at the same observing frequency (

Owing to the detection of an extremely bright fast radio burst (FRB) 200428 associated with a hard X-ray counterpart from the magnetar soft gamma-ray repeater (SGR) 1935+2154, the distance of SGR 1935+2154 potentially hosted in the supernova remnant (SNR) G57.2+0.8 can be revisited. Under the assumption that the SGR and the SNR are physically related, in this Letter, by investigating the dispersion measure (DM) of the FRB contributed by the foreground medium of our Galaxy and the local environments and combining with other observational constraints, we find that the distance of SGR 1935+2154 turns out to be $9.0\pm2.5\,$kpc and the SNR radius falls into $10$ to $18\,$pc since the local DM contribution is as low as $0-18\,$pc cm$^{-3}$. These results are basically consistent with the previous studies. In addition, an estimate for the Faraday rotation measure of the SGR and SNR is also carried out., Comment: 7 pages, 3 figures (replotted), an uncertainty analysis of the distance estimate has been added, accepted for publication in ApJ Letters

In this work, we propose an accreting stellar binary model for understanding the active periodic fast radio bursts (FRBs). The system consists of a stellar compact object (CO) and a donor star (DS) companion in an eccentric orbit, where the DS fills its own Roche lobe near the periastron. The CO accretes the material from the DS and then drive relativistic magnetic blobs. The interaction between the magnetic blobs and the stellar wind of the DS produces a pair of shocks. We find that both of the reverse shock and the forward shock are likely to produce FRBs via synchrotron maser mechanism. We show that this system can in principle sufficiently produce highly active FRBs with a long lifetime, and also can naturally explain the periodicity and the duty cycle of the activity as appeared in FRBs 180916 and 121102. The radio nebula excited by the long-term injection of magnetic blobs into the surrounding environment may account for the associated persistent radio source. In addiction, we discuss the possible multi-wavelength counterparts of FRB 180916 in the context of this model. Finally, we encourage the search for FRBs in the ultraluminous X-ray sources., 11 pages, 2 figures; accepted to APJ

For a binary composed of a spinning black hole (BH) (with mass $\gtrsim 7M_\odot$) and a strongly magnetized neutron star (NS) (with surface magnetic field strength $B_{\rm S,NS}\gtrsim10^{12}$\,G and mass $\sim 1.4M_\odot$), the NS as a whole will possibly eventually plunge into the BH. During the inspiral phase, the spinning BH could be charged to the Wald charge quantity $Q_{\rm W}$ until merger in an electro-vacuum approximation. During the merger, if the spinning charged BH creates its own magnetosphere due to an electric field strong enough for pair cascades to spark, the charged BH would transit from electro-vacuum to force-free cases and could discharge in a time $\gtrsim1~{\rm ms}$. As the force-free magnetosphere is full of a highly conducting plasma, the magnetic flux over the NS's caps would be retained outside the BH's event horizon under the frozen-in condition. Based on this scenario, we here investigate three possible energy-dissipation mechanisms that could produce electromagnetic (EM) counterparts in a time interval of the BH's discharge post a BH-NS merger-induced gravitational wave event: (1) magnetic reconnection at the BH's poles would occur, leading to a millisecond bright EM signal, (2) a magnetic shock in the zone of closed magnetic field lines due to the detachment and reconnection of the entire BH magnetic field would probably produce a bright radio emission, e.g., a fast radio burst, and (3) the Blandford-Znajek mechanism would extract the BH's rotational energy, giving rise to a millisecond-duration luminous high-energy burst. We also calculate the luminosities due to these mechanisms as a function of BH's spin for different values of $B_{\rm S,NS}$., 8 pages, 4 figures, accepted for publication in ApJ Letters

In this paper we propose the model that the coalescence of primordial black holes (PBHs) binaries with equal mass $M \sim 10^{28}$g can emit luminous gigahertz (GHz) radio transient, which may be candidate sources for the observed fast radio bursts (FRBs), if at least one black hole holds appropriate amount of net electric charge $Q$. Using a dimensionless quantity for the charge $q = Q/\sqrt{G}M$, our analyses infer that $q\sim O(10^{-4.5})$ can explain the FRBs with released energy of order $O(10^{40}) {\rm ergs}$. With the current sample of FRBs and assuming a distribution of charge $\phi(q)$ for all PBHs, we can deduce that its form is proportional to $q^{-3.0\pm0.1}$ for $q\geq 7.2\times10^{-5}$ if PBHs are sources of the observed FRBs. Furthermore, with the proposed hypothetical scenario and by estimating the local event rate of FRBs $\sim 2.6 \times 10^3 {\rm Gpc}^{-3} {\rm yr}^{-1}$, one derives a lower bound for the fraction of PBHs (at the mass of $10^{28}$g) against that of matter $f_{\rm PBH}(10^{28}{\rm g})$ $\gtrsim 10^{-5}$ needed to explain the rate. With this inspiring estimate, we expect that future observations of FRBs can help to falsify their physical origins from the PBH binaries coalescences. In the future, the gravitational waves produced by mergers of small black holes can be detected by high frequency gravitational wave detectors. We believe that this work would be a useful addition to the current literature on multimessenger astronomy and cosmology., Comment: 7 pages, 1 figure, published in PRD

We report our very early optical observations of GRB 110530A and investigate its jet properties together with its X-ray afterglow data. A peculiar broad onset bump followed by a plateau is observed in its early R band afterglow lightcurve. The optical data in the other bands and the X-ray data are well consistent with the temporal feature of the R band lightcurve. Our joint spectral fits of the optical and X-ray data show that they are in the same regime, with a photon index of $\sim 1.70$. The optical and X-ray afterglow lightcurves are well fitted with the standard external shock model by considering a delayed energy injection component. Based on our modeling results, we find that the radiative efficiency of the GRB jet is $\sim 1\%$ and the magnetization parameter of the afterglow jet is $, Comment: 24 pages, 5 figures, 3 tables, accpeted for publication in ApJ

The external forward shock (EFS) models have been the standard paradigm to interpret the broad-band afterglow data of gamma-ray bursts (GRBs). One prediction of the models is that some afterglow temporal breaks at different energy bands should be achromatic. Observations in the Swift era have revealed chromatic afterglow behaviors at least in some GRBs, casting doubts on the EFS origin of GRB afterglows. In this paper, we perform a systematic study to address the question: how bad/good are the external forward shock models? Our sample includes 85 GRBs well-monitored X-ray and optical lightcurves. Based on how well the data abide by the EFS models, we categorize them as: Gold sample: (Grade I and II) include 45/85 GRBs. They show evidence of, or are consistent with having, an achromatic break. The temporal/spectral behaviors in each afterglow segment are consistent with the predictions (closure relations) of the EFS models. Silver sample: (Grade III and IV) include 37/85 GRBs. They are also consistent with having an achromatic break, even though one or more afterglow segments do not comply with the closure relations. Bad sample: (Grade V), 3/85 shows direct evidence of chromatic behaviors, suggesting that the EFS models are inconsistent with the data. These are included in the Bad sample. We further perform statistical analyses of various observational properties ($\alpha$, $\beta$, $t_b$ and model parameters (energy injection index q, p, $\theta_j$, $\eta_\gamma$, etc) of the GRBs in the Gold Sample, and derive constraints on the magnetization parameter $\epsilon_B$ in the EFS. Overall, we conclude that the simplest EFS models can account for the multi-wavelength afterglow data of at least half of the GRBs. When more advanced modeling (e.g., long-lasting reverse shock, structured jets) is invoked, up to $>90 \%$ of the afterglows may be interpreted within the framework of the ESF models., Comment: 69 pages,134 figures, 7 tables, ApJS, in press

The cosmic evolution of gamma-ray burst (GRB) luminosity is essential for revealing the GRB physics and for using GRBs as cosmological probes. We investigate the luminosity evolution of long GRBs with a large sample of 258 {\em Swift}/BAT GRBs. Parameterized the peak luminosity of individual GRBs evolves as $L_{\rm p}\propto{\rm }(1+z)^{k}$, we get $k=1.49\pm0.19$ using the non-parametric $\tau$ statistics method without considering observational biases of GRB trigger and redshift measurement. By modeling these biases with the observed peak flux and characterizing the peak luminosity function of long GRBs as a smoothly broken power-law with a break that evolves as $L_{\rm b}\propto (1+z)^{k_{\rm b}}$, we obtain $k_{\rm b}=1.14^{+0.99}_{-0.47}$ through simulations based on assumption that the long GRB rate follows the star formation rate (SFR) incorporating with cosmic metallicity history. The derived $k$ and $k_b$ values are systematically smaller than that reported in previous papers. By removing the observational biases of the GRB trigger and redshift measurement based on our simulation analysis, we generate mock {\em complete} samples of 258 and 1000 GRBs to examine how these biases affects on the $\tau$ statistics method. We get $k=0.94\pm 0.14$ and $k=0.80\pm 0.09$ for the two samples, indicating that these observational biases may lead to overestimate the $k$ value. With the large uncertain of $k_b$ derived from our simulation analysis, one even cannot convincingly argue a robust evolution feature of the GRB luminosity., Comment: 37 pages, 6 figures, accepted for publication in ApJ