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J. W. T. Hessels

Publications and source records attributed to J. W. T. Hessels.

At least 19 recordsLinked to original sources

Timing and statistical analysis of single-pulse search pulsar discoveries from the PALFA survey

Almost two decades after their discovery, pulsars discoverable only through their single, dispersed radio pulses, known as rotating radio transients (RRATS), remain a poorly-understood class of objects. Compared to the overall pulsar population, few have timing solutions, limiting our ability to understand the mechanisms underlying their sporadic emission. Here, we present a single-pulse analysis of twelve sources from the PALFA survey, consisting of eleven objects initially identified as RRATs and one candidate fast radio burst. We present timing solutions for five of the sources with detections at a sufficient number of epochs and spin periods for two more. For all sources, we use a Bayesian framework to fit distributions of single-pulse energies, finding support for log-normal energy distributions and pulse-to-pulse wait times that are consistent with Poisson processes. Finally, we provide updates on the previously-published candidate fast radio burst J0613+18, with new indications that it is in fact extragalactic.

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Pulsars in Globular Clusters With the SKAO

Globular clusters (GCs) are highly efficient factories of radio pulsars: per unit of stellar mass, they contain about 1000 times more pulsars than in the Galactic field. Thus far, 345 radio pulsars have been found in GCs. These can be used as precision probes of the structure, gas content, magnetic field, and dynamic history of their host clusters; some of them are also highly interesting in their own right because they probe exotic stellar evolution scenarios, the physics of dense matter, accretion, gravity, etc. One of them (PSR~J0514$-$4002E) might even be the first pulsar - black hole system known. Deep searches with SKA telescopes will only require one to a few tied-array beams, and can be done during early commissioning of the telescopes, before an all-sky pulsar survey using hundreds to thousands of tied-array beams is feasible. Even a conservative approach predicts discoveries only with the core of SKA-MID AA*. Eventually, SKA-MID AA4 is expected to increase the number of discoveries even more, leading to more than doubling the current known population. Thus, a dedicated search for pulsars in GCs will fully utilise the best possible natural laboratories to study various branches of physics and astrophysics, including the properties of dense matter, stellar evolution, and the dynamical history of these GCs.

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Searching for links between energetic millisecond pulsars and repeating fast radio bursts

The unexpected localization of the repeating FRB 20200120E to a globular cluster challenges conventional FRB models based on magnetars formed via core collapse. One alternative model suggests that FRB 20200120E is a millisecond pulsar (MSP) producing giant pulses (GPs). To test this hypothesis, we compared the characteristics of FRB 20200120E bursts with the GPs of the most energetic Galactic MSP known, M28A (PSR B1821$-$24A), using observations with the Parkes (Murriyang) telescope's Ultra Wideband Low-frequency (UWL) receiver. Our analysis provides insight into the spectral structure and frequency extent of M28A's GPs, revealing broad-band spectra spanning $700-4000$ MHz (in some cases) with complex spectral peaks. We find that known M28A GP characteristics persist at this bandwidth, such as durations, luminosities, periodicity, wait-time, and energy distribution. A sub-band search for narrow-band GPs yielded no detection of genuinely narrow-band GPs. However, we do find narrow-band spectral peaks of $\sim100$ MHz bandwidth, a similar scale observed for FRB 20200120E's bursts. Compared to FRB 20200120E's bursts, M28A's GPs have $50\times$ shorter durations, $10^5\times$ lower spectral luminosities, clear periodicity (vs. no periodicity), a purely Poissonian wait-time distribution (vs. quasi-Poissonian), and generally broad-band spectra with narrow-band peaks (vs. only narrow-band bursts). Both sources show a steep energy distribution and minor dispersion measure variability. Our study finds no strong links between M28A and FRB 20200120E. However, we cannot rule out the possibility that FRB 20200120E is a rare and unique type of MSP with no Galactic analogue. Furthermore, higher-cadence monitoring of M28A, for hundreds to thousands of hours, might reveal rare but extremely luminous pulses.

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A 4200-hour HyperFlash and ÉCLAT campaign on the hyperactive FRB 20240114A: constraining energetics with the most brilliant bursts

Hyperactive repeaters provide a unique window into the evolving environments and energy budgets of fast radio burst (FRB) sources, though they may not be representative of the FRB population in general. High-cadence observations are key to capturing the rarest and most energetic bursts, which occur only once per hundreds to thousands of hours. Here we present an unprecedented $4{,}200$-hour observing campaign targeting FRB 20240114A as part of the HyperFlash and ÉCLAT FRB monitoring programs. Over $806$ days, we detected $178$ high-energy ($\sim$$10^{40-42}$ erg) bursts with HyperFlash, which together amount to $4.4 \times 10^{42}$ erg of released radio energy (assuming isotropic emission and 1-GHz emission bandwidth). The cumulative energy of the HyperFlash bursts is about twice that of $\sim$$11{,}000$ lower-energy bursts detected with FAST, emphasising the significant role that the highest-energy bursts play in depleting the central engine's stored energy. In fact, the single most brilliant burst from our sample, which we term the STROOP, contributes roughly $1/3$ of all the energy we measure, and is at the maximum energy seen in studies of both repeating and apparently one-off FRBs alike. We also find a break in the burst energy distribution at $\sim$$2\times10^{40}$ erg and a linear dispersion measure (DM) increase of $+0.96 \pm 0.06$ pc cm$^{-3}$ over a period of $318$ days. We discuss these findings in the context of a magnetar source model and highlight comparisons with the energetics of intermediate and giant X-ray/$γ$-ray flares from Galactic sources.

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A HyperFlash and ÉCLAT view of the local environment and energetics of the repeating FRB 20240619D

Time-variable propagation effects provide a window into the local plasma environments of repeating fast radio burst (FRB) sources. Here we report high-cadence observations of FRB 20240619D, as part of the HyperFlash and ÉCLAT programs. We observed for $500$h and detected $217$ bursts, including $10$ bursts with high fluence ($>25$ Jy ms) and implied energy. We track burst-to-burst variations in dispersion measure (DM) and rotation measure (RM), from which we constrain the parallel magnetic field strength in the source's local environment: $0.27\pm0.13$ mG. Apparent DM variations between sub-bursts in a single bright event are interpreted as coming from plasma lensing or variable emission height. We also identify two distinct scintillation screens along the line of sight, one associated with the Milky Way and the other likely located in the FRB's host galaxy or local environment. Together, these (time-variable) propagation effects reveal that FRB 20240619D is embedded in a dense, turbulent and highly magnetised plasma. The source's environment is more dynamic than that measured for many other (repeating) FRB sources, but less extreme compared to several repeaters that are associated with a compact, persistent radio source. FRB 20240619D's cumulative burst fluence distribution shows a power-law break, with a flat tail at high energies. Along with previous studies, this emphasises a common feature in the burst energy distribution of hyperactive repeaters. Using the break in the burst fluence distribution, we estimate a source redshift of $z=0.042$-$0.240$. We discuss FRB 20240619D's nature in the context of similar studies of other repeating FRBs.

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Multi-Method Timing of Transient Radio Pulsars with the GBT350 and GBNCC Surveys

We present the timing solutions for three radio pulsars discovered with the Green Bank North Celestial Cap (GBNCC) and 350-MHz Green Bank Telescope drift-scan surveys. These pulsars were initially discovered through their single-pulse emission and therefore designated as rotating radio transients (RRATs). Follow-up timing campaigns yielded a number of higher signal-to-noise summed pulse profiles for each pulsar, allowing us to obtain timing solutions both through single pulses as well as the standard method of time-integrating the pulsar's emission. We find that the two methods return timing parameters which are usually in agreement within two standard deviations, and have similar sized error bars. The single-pulse timing solutions have significantly higher RMS errors and reduced chi-squared values, likely due to pulse jitter. The distribution of wait times between detected single pulses indicates a significant amount of pulse clustering in time on short timescales from all three sources. For all sources, the presence of low-level emission outside of the sparse bright pulses and lack of giant pulses is more reminiscent of highly nulling canonical radio pulsars than extremely transient RRATs, highlighting the diversity of emission behavior observed from sources published as RRATs.

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A probe of the maximum energetics of fast radio bursts through a prolific repeating source

Fast radio bursts (FRBs) are sufficiently energetic to be detectable from luminosity distances up to at least seven billion parsecs (redshift $z > 1$). Probing the maximum energies and luminosities of FRBs constrains their emission mechanism and cosmological population. Here we investigate the maximum energetics of a highly active repeater, FRB 20220912A, using 1,500 h of observations. We detect $130$ high-energy bursts and find a break in the burst energy distribution, with a flattening of the power-law slope at higher energy -- consistent with the behaviour of another highly active repeater, FRB 20201124A. There is a roughly equal split of integrated burst energy between the low- and high-energy regimes. Furthermore, we model the rate of the highest-energy bursts and find a turnover at a characteristic spectral energy density of $E^{\textrm{char}}_ν = 2.09^{+3.78}_{-1.04}\times10^{32}$ erg/Hz. This characteristic maximum energy agrees well with observations of apparently one-off FRBs, suggesting a common physical mechanism for their emission. The extreme burst energies push radiation and source models to their limit: at this burst rate a typical magnetar ($B = 10^{15}$ G) would deplete the energy stored in its magnetosphere in $\sim$ 2150 h, assuming a radio efficiency $ε_\mathrm{radio} = 10^{-5}$. We find that the high-energy bursts ($E_ν> 3 \times 10^{30}$ erg Hz$^{-1}$) play an important role in exhausting the energy budget of the source.

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A Hyperactive FRB Pinpointed in an SMC-Like Satellite Host Galaxy

Precise localizations of fast radio bursts (FRBs) are essential for uncovering their host galaxies and immediate environments. We present the milliarcsecond-precision European VLBI Network localization of FRB 20240114A, a hyperactive repeating FRB, achieving <90x30 mas (1-sigma) accuracy. This precision places the burst 0.5 kpc from the nucleus of its low-metallicity star-forming dwarf host at a spectroscopic redshift of z = 0.130287. Our Gran Telescopio CANARIAS spectroscopic follow-up reveals that the dwarf FRB host is gravitationally bound to a more massive, star-forming spiral galaxy. This establishes the first known instance of an FRB residing in a satellite galaxy within a larger galactic system. This configuration, analogous to the Small Magellanic Cloud orbiting the Milky Way (but at a lower overall mass scale), expands the known diversity of FRB host environments and offers important insights for interpreting seemingly "hostless" or highly offset FRBs. Furthermore, our detailed dispersion measure (DM) budget analysis indicates that the dominant contribution to FRB 20240114A's DM likely originates from the foreground galaxy halos. This finding addresses the anomalously high DM observed for this FRB and underscores the significant role of intervening foreground structures in shaping observed FRB DMs, which is important for accurate FRB-based cosmological measurements. Our results highlight the importance of deep, high-resolution optical/infrared observations (e.g., with the Hubble or James Webb Space Telescopes) to fully leverage our precise radio localization and probe the immediate astrophysical birthplaces of FRB progenitors within these complex galactic systems.

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Revisiting FRB 20121102A: milliarcsecond localisation and a decreasing dispersion measure

FRB 20121102A is the original repeating fast radio burst (FRB) source and also the first to be localised to milliarcsecond precision using very-long-baseline interferometry (VLBI). It has been active for over 13 years and resides in an extreme magneto-ionic environment in a dwarf host galaxy at a distance of ~1 Gpc. In this work, we use the European VLBI Network (EVN) to (re-)localise FRB 20121102A and its associated persistent radio source (PRS). We confirm that the two are co-located -- improving on previous results by a factor of ~4 and constraining the FRB and PRS co-location to ~12 pc transverse offset. Over a decade, the PRS luminosity on milliarcsecond scales remains consistent with measurements on larger angular scales, showing that the PRS is still compact. We also present the detection of 18 bursts with the Nancay Radio Telescope (NRT) as part of our ÉCLAT monitoring program. These bursts, together with previously published results, show that the observed dispersion measure (DM) of FRB 20121102A has dropped by ~25 pc/cc in the past five years, highlighting a fractional decrease in the local DM contribution of >15%. We discuss potential physical scenarios and highlight possible future observations that will help reveal the nature of FRB 20121102A, which is one of only a few known FRBs with a luminous PRS.

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Sporadic radio pulses from a white dwarf binary at the orbital period

Recent observations have revealed rare, previously unknown flashes of cosmic radio waves lasting from milliseconds to minutes, and with periodicity of minutes to an hour. These transient radio signals must originate from sources in the Milky Way, and from coherent emission processes in astrophysical plasma. They are theorized to be produced in the extreme and highly magnetised environments around white dwarfs or neutron stars. However, the astrophysical origin of these signals remains contested, and multiple progenitor models may be needed to explain their diverse properties. Here we present the discovery of a transient radio source, ILT J1101+5521, whose roughly minute-long pulses arrive with a periodicity of 125.5 minutes. We find that ILT J1101+5521 is an M dwarf -- white dwarf binary system with an orbital period that matches the period of the radio pulses, which are observed when the two stars are in conjunction. The binary nature of ILT J1101+5521 establishes that some long-period radio transients originate from orbital motion modulating the observed emission, as opposed to an isolated rotating star. We conclude that ILT J1101+5521 is likely a polar system where magnetic interaction has synchronised the rotational and orbital periods of the white dwarf. Magnetic interaction and plasma exchange between two stars has been theorized to generate sporadic radio emission, making ILT J1101+5521 a potential low-mass analogue to such mechanisms.

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The Massive and Quiescent Elliptical Host Galaxy of the Repeating Fast Radio Burst FRB20240209A

The discovery and localization of FRB20240209A by the Canadian Hydrogen Intensity Mapping Fast Radio Burst (CHIME/FRB) experiment marks the first repeating FRB localized with the CHIME/FRB Outriggers and adds to the small sample of repeating FRBs with associated host galaxies. Here we present Keck and Gemini observations of the host that reveal a redshift $z=0.1384\pm0.0004$. We perform stellar population modeling to jointly fit the optical through mid-infrared data of the host and infer a median stellar mass log$(M_*/{\rm M_{\odot}})=11.34\pm0.01$ and a mass-weighted stellar population age $\sim11$Gyr, corresponding to the most massive and oldest FRB host discovered to date. Coupled with a star formation rate $<0.36\,{\rm M_{\odot}\ yr^{-1}}$, the specific star formation rate $<10^{-11.8}\rm\ yr^{-1}$ classifies the host as quiescent. Through surface brightness profile modeling, we determine an elliptical galaxy morphology, marking the host as the first confirmed elliptical FRB host. The discovery of a quiescent early-type host galaxy within a transient class predominantly characterized by late-type star-forming hosts is reminiscent of short-duration gamma-ray bursts, Type Ia supernovae, and ultraluminous X-ray sources. Based on these shared host demographics, coupled with a large offset as demonstrated in our companion paper, we conclude that preferred progenitors for FRB20240209A include magnetars formed through merging binary neutron stars/white dwarfs or the accretion-induced collapse of a white dwarf, or a luminous X-ray binary. Together with FRB20200120E localized to a globular cluster in M81, our findings provide strong evidence that some fraction of FRBs may arise from a process distinct from the core collapse of massive stars.

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A repeating fast radio burst source in the outskirts of a quiescent galaxy

We report the discovery of the repeating fast radio burst source FRB 20240209A using the CHIME/FRB telescope. We have detected 22 bursts from this repeater between February and July 2024, six of which were also recorded at the Outrigger station KKO. The 66-km long CHIME-KKO baseline can provide single-pulse FRB localizations along one dimension with $2^{\prime\prime}$ accuracy. The high declination of $\sim$86 degrees for this repeater allowed its detection with a rotating range of baseline vectors, enabling the combined localization region size to be constrained to $1^{\prime\prime}\times2^{\prime\prime}$. We present deep Gemini observations that, combined with the FRB localization, enabled a robust association of FRB 20240209A to the outskirts of a luminous galaxy (P(O|x) = 0.99; $L \approx 5.3 \times 10^{10}\,L_{\odot}$). FRB 20240209A has a projected physical offset of $40 \pm 5$ kpc from the center of its host galaxy, making it the FRB with the largest host galaxy offset to date. When normalized by the host galaxy size, the offset of FRB 20240209A is comparable to that of FRB 20200120E, the only FRB source known to originate in a globular cluster. We consider several explanations for the large offset, including a progenitor that was kicked from the host galaxy or in situ formation in a low-luminosity satellite galaxy of the putative host, but find the most plausible scenario to be a globular cluster origin. This, coupled with the quiescent, elliptical nature of the host as demonstrated in our companion paper, provide strong evidence for a delayed formation channel for the progenitor of the FRB source.

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A Radio Study of Persistent Radio Sources in Nearby Dwarf Galaxies: Implications for Fast Radio Bursts

We present 1 - 12 GHz Karl G. Jansky Very Large Array observations of 9 off-nuclear persistent radio sources (PRSs) in nearby (z < 0.055) dwarf galaxies, along with high-resolution European very-long baseline interferometry (VLBI) Network (EVN) observations for one of them at 1.7GHz. We explore the plausibility that these PRSs are associated with fast radio burst (FRB) sources by examining their properties, physical sizes, host-normalized offsets, spectral energy distributions (SEDs), radio luminosities, and light curves, and compare them to those of the PRSs associated with FRBs 20121102A and 20190520B, two known active galactic nuclei (AGN), and one likely AGN in our sample with comparable data, as well as other radio transients exhibiting characteristics analogous to FRB-PRSs. We identify a single source in our sample, J1136+2643, as the most promising FRB- PRS, based on its compact physical size and host-normalized offset. We further identify two sources, J0019+1507 and J0909+5955, with physical sizes comparable to FRB-PRSs, but which exhibit large offsets and flat spectral indices potentially indicative of a background AGN origin. We test the viability of neutron star wind nebulae and hypernebulae models for J1136+2643, and find that the physical size, luminosity, and SED of J1136+2643 are broadly consistent with these models. Finally, we discuss the alternative interpretation that the radio sources are instead powered by accreting massive black holes and outline future prospects and follow-up observations for differentiating between these scenarios.

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An emission state switching radio transient with a 54 minute period

Long-period radio transients are an emerging class of extreme astrophysical events of which only three are known. These objects emit highly polarised, coherent pulses of typically a few tens of seconds duration and minutes to hour-long periods. While magnetic white dwarfs and magnetars, either isolated or in binary systems, have been invoked to explain these objects, a consensus has not emerged. Here we report on the discovery of ASKAP J193505.1+214841.0 (henceforth ASKAPJ1935+2148) with a period of 53.8 minutes exhibiting three distinct emission states - a bright pulse state with highly linearly polarised pulses with widths of 10-50 seconds; a weak pulse state which is about 26 times fainter than the bright state with highly circularly polarised pulses of widths of approximately 370 milliseconds; and a quiescent or quenched state with no pulses. The first two states have been observed to progressively evolve over the course of 8 months with the quenched state interspersed between them suggesting physical changes in the region producing the emission. A constraint on the radius of the source for the observed period rules out a magnetic white dwarf origin. Unlike other long-period sources, ASKAPJ1935+2148 is the first to exhibit drastic variations in emission modes reminiscent of neutron stars. However, its radio properties challenge our current understanding of neutron star emission and evolution.

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Discovery and timing of ten new millisecond pulsars in the globular cluster Terzan 5

We report the discovery of ten new pulsars in the globular cluster Terzan 5 as part of the Transients and Pulsars with MeerKAT (TRAPUM) Large Survey Project. We observed Terzan 5 at L-band (856--1712 MHz) with the MeerKAT radio telescope for four hours on two epochs, and performed acceleration searches of 45 out of 288 tied-array beams covering the core of the cluster. We obtained phase-connected timing solutions for nine discoveries, covering nearly two decades of archival observations from the Green Bank Telescope for all but one. Highlights include PSR J1748$-$2446ao which is an eccentric ($e = 0.32$) wide-orbit (orbital period $P_{\rm b} = 57.55$ d) system. We were able to measure the rate of advance of periastron ($\dotω$) for this system allowing us to determine a total mass of $3.17 \pm \, 0.02\, \rm M_{\odot}$. With a minimum companion mass ($M_{\rm c}$) of $\sim 0.8\, \rm M_{\odot}$, PSR J1748$-$2446ao is a candidate double neutron star (DNS) system. If confirmed to be a DNS, it would be the fastest spinning pulsar ($P = 2.27$ ms) and the longest orbital period measured for any known DNS system. PSR J1748$-$2446ap has the second highest eccentricity for any recycled pulsar ($e \sim 0.905$) and for this system we can measure the total mass ($1.997 \pm 0.006\, \rm M_{\odot}$) and also estimate the individual pulsar and companion masses. PSR J1748$-$2446ar is an eclipsing redback (minimum $M_{\rm c} \sim 0.34\, \rm M_{\odot}$) system whose properties confirm it to be the counterpart to a previously published source identified in radio and X-ray imaging. With these discoveries, the total number of confirmed pulsars in Terzan 5 is 49, the highest for any globular cluster so far. These discoveries further enhance the rich set of pulsars known in Terzan 5 and provide scope for a deeper understanding of binary stellar evolution, cluster dynamics and ensemble population studies.

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A 350-MHz Green Bank Telescope Survey of Unassociated Fermi LAT Sources: Discovery and Timing of Ten Millisecond Pulsars

We have searched for radio pulsations towards 49 Fermi Large Area Telescope (LAT) 1FGL Catalog $γ$-ray sources using the Green Bank Telescope at 350 MHz. We detected 18 millisecond pulsars (MSPs) in blind searches of the data; 10 of these were discoveries unique to our survey. Sixteen are binaries, with eight having short orbital periods $P_B < 1$ day. No radio pulsations from young pulsars were detected, although three targets are coincident with apparently radio-quiet $γ$-ray pulsars discovered in LAT data. Here, we give an overview of the survey and present radio and $γ$-ray timing results for the 10 MSPs discovered. These include the only isolated MSP discovered in our survey and six short-$P_B$ binary MSPs. Of these, three have very low-mass companions ($M_c$ $\ll$ 0.1M$_{\odot}$) and hence belong to the class of black widow pulsars. Two have more massive, non-degenerate companions with extensive radio eclipses and orbitally modulated X-ray emission consistent with the redback class. Significant $γ$-ray pulsations have been detected from nine of the discoveries. This survey and similar efforts suggest that the majority of Galactic $γ$-ray sources at high Galactic latitudes are either MSPs or relatively nearby non-recycled pulsars, with the latter having on average a much smaller radio/$γ$-ray beaming ratio as compared to MSPs. It also confirms that past surveys suffered from an observational bias against finding short-$P_B$ MSP systems.

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An X-ray and radio view of the 2022 reactivation of the magnetar SGRJ1935+2154

Recently, the Galactic magnetar SGR J1935+2154 has garnered attention due to its emission of an extremely luminous radio burst, reminiscent of Fast Radio Bursts (FRBs). SGR J1935+2154 is one of the most active magnetars, displaying flaring events nearly every year, including outbursts as well as short and intermediate bursts. Here, we present our results on the properties of the persistent and bursting X-ray emission from SGR J1935+2154, during the initial weeks following its outburst on October 10, 2022. The source was observed with XMM-Newton and NuSTAR (quasi-)simultaneously during two epochs, separated by $\sim$5 days. The persistent emission spectrum is well described by an absorbed blackbody plus power-law model up to an energy of $\sim$25 keV. No significant changes were observed in the blackbody temperature ($kT_{\rm BB}\sim$ 0.4 keV) and emitting radius ($R_{\rm BB}\sim$ 1.9 km) between the two epochs. However, we observed a slight variation in the power-law parameters. Moreover, we detected X-ray pulsations in all the datasets and derived a spin period derivative of $\dot{P} = 5.52(5) \times 10^{-11}$ ss. This is 3.8 times larger than the value measured after the first recorded outburst in 2014. Additionally, we performed quasi-simultaneous radio observations using three 25--32-m class radio telescopes for a total of 92.5 hr to search for FRB-like radio bursts and pulsed emission. However, our analysis did not reveal any radio bursts or periodic emission.

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Detection of ultra-fast radio bursts from FRB 20121102A

Fast radio bursts (FRBs) are extragalactic transients with typical durations of milliseconds. FRBs have been shown, however, to fluctuate on a wide range of timescales: some show sub-microsecond sub-bursts while others last up to a few seconds in total. Probing FRBs on a range of timescales is crucial for understanding their emission physics, how to detect them effectively, and how to maximize their utility as astrophysical probes. FRB 20121102A is the first-known repeating FRB source. Here we show that FRB 20121102A is able to produce isolated microsecond-duration bursts whose total durations are more than ten times shorter than all other known FRBs to date. The polarimetric properties of these micro-bursts resemble those of the longer-lasting bursts, suggesting a common emission mechanism producing FRBs spanning a factor of 1,000 in duration. Furthermore, this work shows that there exists a population of ultra-fast radio bursts that current wide-field FRB searches are missing due to insufficient time-resolution. These results indicate that FRBs occur more frequently and with greater diversity than initially thought. This could also influence our understanding of energy, wait time, and burst rate distributions.

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