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Ke-Jia Lee

Publications and source records attributed to Ke-Jia Lee.

At least 19 recordsLinked to original sources

FAST Polarization Catalog of FRB 20240114A

Polarization measurements of fast radio bursts (FRBs) probe the magnetized plasma surrounding their central engines. FRB~20240114A is an exceptionally active repeating source, with 17,356 bursts detected between 2024 January 28 and 2025 May 30 by FAST, enabling time-resolved polarimetric studies. In this work, we present a polarimetric catalog of 6,131 bright bursts (with a signal-to-noise ratio S/N $\geq$ 20, 35.3% of the total sample), including arrival time (MJD$_{\text{topo}}$), dispersion measure (DM), burst width (W$_{\text{eff}}$), bandwidth, Faraday rotation measure (RM), linear and circular polarization degrees (DOL, DOC), and intrinsic polarization angle (PA$_0$). We detect a clear temporal evolution of RM: after an initial stable phase, it decreases linearly by $\sim$200 $\rm rad\ m^{-2}$ over 200 days, forming a bimodal distribution, whereas DM remains stable at 528.9 $\rm pc\ cm^{-3}$. The linear polarization fraction is generally high, with the 3$σ$ lower bound around 76%, while circular polarization is low, with 1,157 of 17,356 bursts (6.67%) having DOC $\geq$10%. We perform a power-law fit between $|\textrm{V}|$/I and $|\textrm{RM}|$, which yields an index of $-2.98 \pm 0.80$. It is found that the combined 2D distribution of L/I versus V/I remains stable, implying that the emission mechanism is largely invariant. Our PA$_0$ measurements show a broad, non-uniform distribution, implying a complex emission geometry. These results suggest that FRB~20240114A resides in a dynamically evolving magneto-ionic environment. This catalog provides a foundation for studies of repeating FRB progenitors and their environments.

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Joint Observation of SGR J1935+2154 with \textit{Insight}-HXMT and KM40m during the active episode of October 2022

SGR J1935+2154 is the unique magnetar so far from which fast radio bursts have been detected. In October 2022, it resumed its burst activity, and we implemented a dedicated target-of-opportunity (ToO) observation on it from Oct. 13th to Nov. 1st, 2022 (about 940 ks in total) with \textit{Insight}-HXMT, while the KM40m radio telescope observed this source for about 1400 hours since Oct. 15th. We searched the LE, ME, and HE data of \textit{Insight}-HXMT in the overlapping observation time windows with the KM40m radio telescope and revealed 60 magnetar X-ray bursts (MXBs), while KM40m only detected 1 radio burst. In particular, we find that there is an X-ray burst on October 21 (denoted as MXB 221021) temporally associated with this radio burst. Interestingly, this association event shows very different morphology from those X-ray and radio association events from this source reported before (e.g., MXB/FRB 200428). Moreover, we systematically analyzed the temporal and spectral properties of the sample of MXBs during this observation and found that % the (radio-associated) MXB 221021 shows some different properties from other MXBs without associated radio bursts. These findings shed new light on the physical mechanisms of X-ray bursts and radio burst emission in magnetars.

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Resolving the 2024 Outburst of Magnetar 1E 1841-045 from its host Supernova Remnant with EP-FXT

The magnetar 1E 1841-045 exhibited a new active episode starting on August 20, 2024, marked by X-ray bursts and enhanced persistent emission. Using data from the Einstein Probe (EP), we report on the timing and spectral results following the onset of this outburst. The pulse profile displays a multi-peaked structure, with notable phase shifts in the secondary peak. Energy-resolved pulse profile analysis indicates a transition in the dominant peak of the pulse profile above 5.8 keV. The 0.5-10 keV X-ray spectrum is well-modeled by a combined blackbody and power-law (BB+PL) model, showing a $\sim 20\%$ flux increase following the outburst. Phase-resolved spectroscopy indicates a correlation between BB temperature and pulse profile intensity, along with spectral hardening at a specific pulse phase. The high spatial resolution of EP enables effective separation of the supernova remnant emission, which is crucial for measuring the intrinsic pulse emission of the source. These findings underscore the intricate relationship between magnetar outbursts, pulse profile evolution, and spectral characteristics.

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GECAM discovery of a peculiar magnetar X-ray burst (MXB 221120) from SGR J1935+2154 associated with a fast radio burst

Fast radio bursts (FRBs) are enigmatic cosmic transients of millisecond duration observed in the radio band. The identification of FRB-associated magnetar X-ray bursts (MXBs) from galactic magnetar SGR J1935+2154 suggests that at least a fraction of FRBs can be produced from magnetar activity. However, the sample size of FRB-associated MXBs is still very small. Here we report a bright and peculiar FRB-associated MXB from SGR J1935+2154 detected by GECAM on November 20, 2022, dubbed MXB 221120. We find that both temporal and spectral properties of MXB 221120 exhibit distinctive features. Its light curve could be generally described by a single FRED function with superposition of several narrow pulses. Interestingly, we identify a possible QPO feature with center frequency of ~18 Hz in this MXB. The time-integrated spectrum is best fitted by a blackbody model with temperature (kT ) of 18.6 keV, rendering it the first thermal spectrum FRB-associated MXB from SGR J1935+2154. Compared to other MXBs with single emission episode, MXB 221120 has longer duration and higher blackbody temperature, making it an outlier in the burst sample. These results indicate that MXB 221120 may be produced by a special mechanism with extreme physical conditions.

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Investigating FRB 20240114A with FAST: Morphological Classification and Drifting Rate Measurements in a Burst-Cluster Framework

This study investigates the morphological classification and drifting rate measurement of the repeating fast radio burst (FRB) source FRB 20240114A using the Five-hundred-meter Aperture Spherical Telescope (FAST). Detected on January 14, 2024, FRB 20240114A exhibited an exceptionally high burst rate, revealing unique properties. Through observational campaigns over several months, we selected a dataset comprising 3,203 bursts (2,109 burst-clusters) during a continuous monitoring session (15,780 seconds) on March 12, 2024. Improving upon previous work, we clarify the definitions of sub-bursts, bursts and burst-clusters. Using an average dispersion measures (DM) of 529.2 pc cm$^{-3}$, we classified the burst-clusters into Downward Drifting, Upward Drifting, No Drifting, No Evidence for Drifting, Not-Clear, and Complex burst-clusters. Among the 978 burst-clusters that exhibit drifting behavior, 233 (23.82%) show upward drifting. Additionally, if 142 upward drifting single-component burst-clusters are excluded, upward drifting double- and multi-component burst-clusters still account for 10.89% of the 836 burst-clusters exhibiting drifting behavior, equating to 91 burst-clusters. Furthermore, if only upward drifting burst-clusters with consecutive time intervals (or upward drifting bursts) are considered, only 9 bursts remain. Drifting rate comparisons with other physical quantities reveal that the drifting rate increases with peak frequency for single-component burst-clusters with drifting behavior. Moreover, in single-component burst-clusters, those with upward drifting exhibit smaller effective widths, bandwidths, and fluxes than their downward drifting counterparts. A Kolmogorov-Smirnov test further indicates that upward drifting burst-clusters possess longer consecutive time intervals than downward drifting ones, suggesting distinct underlying physical mechanisms.

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A comprehensive search for Long and Short Periodic Features from an Extremely Active Cycle of FRB 20240114A

Possible periodic features in fast radio bursts (FRBs) may provide insights into their astrophysical origins. Using extensive observations from the Five-hundred-meter Aperture Spherical radio Telescope (FAST), we conduct a multi-timescale periodicity search for the exceptionally active repeater FRB~20240114A. Our analysis is based on different datasets for different timescales: for short-timescale periodicity in Time of Arrivals (TOAs), we use 57 observations from January to August 2024; for long-timescale periodicity, we employ an extended TOA dataset comprising 111 observations spanning from January 2024 to October 2025; and for burst time series analysis, we utilize individual burst data from the 57 FAST observations. We identify three candidate short-timescale periodic signals (0.673~s, 0.635~s, and 0.536~s) with significances of $3.2σ$--$6σ$, each detected in two independent observations. On longer timescales, we detect a significant $143.40\pm7.19$-day periodicity with $5.2σ$ significance, establishing FRB~20240114A as a periodic repeater. In burst time series, we find quasi-periodic oscillations in the few hundred Hz range ($3.4σ$ and $3.7σ$) and periodic burst trains with periods of several to tens of milliseconds ($3σ$--$3.9σ$), though these periodic features appear transient and short-lived. The detection of periodic signals at these different time scales indicates that FRB 20240114A exhibits intriguing periodic self-similar characteristics. Despite the comprehensive dataset, no definitive periodicity linked to the source's rotation is confirmed, placing stringent constraints on the intrinsic source properties and the modulation mechanisms. All data are available via the Science Data Bank.

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The magnetar model's energy crisis for a prolific repeating fast radio burst source

Fast radio bursts (FRBs) are widely considered to originate from magnetars that power the explosion through releasing magnetic energy. Active repeating FRBs have been seen to produce hundreds of bursts per hour and can stay active for months, thus may provide stringent constraints on the energy budget of FRBs' central engine. Within a time span of 214 days, we detected 11,553 bursts from the hyper-active FRB 20240114A that reached a peak burst rate of 729 hr$^{-1}$. This is the largest burst sample from any single FRB source, exceeding the cumulative total of all published bursts from all known FRBs to date. Assuming typical values of radio efficiency and beaming factor, the estimated total isotropic burst energy of this source exceeds 86% of the dipolar magnetic energy of a typical magnetar. The total released energy from this source exceeds that of other known repeaters by about one and a half orders of magnitude, yielding the most stringent lower limit of $4.7\times10^{32}$ G cm$^3$ for the magnetar's magnetic moment. The source remained active at the end of this observation campaign. Our findings thus require either the FRB's central magnetar engine's possessing exceptionally high emission efficiency or a more powerful compact object than a typical magnetar.

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Long-term simultaneous 2.25/8.60~GHz monitoring of the newly-discovered repeating FRB~20240114A

We report on the simultaneous monitoring of the repeating fast radio burst (FRB) 20240114A at 2.25 and 8.60~GHz, conducted 66 times between 2024 January 29 and 2025 February 15 with the Shanghai Tianma Radio Telescope (TMRT). In about 180 hours of observation, we detected 155 bursts at 2.25~GHz above a fluence threshold of 0.72~Jy~ms, but none at 8.60~GHz above a fluence threshold of 0.27~Jy~ms. FRB~20240114A exhibited frequency-dependent activity, as evidenced by the non-detections in 14.3 hours of observations at 2.25~GHz prior to 2024 February 24, despite its reported activity below 2~GHz. In contrast to its low-activity state reported below 1.4~GHz between 2024 June and December, FRB~20240114A exhibited high activity at 2.25~GHz in 2024 July with a mean burst rate of $1.72^{+0.18}_{-0.16}~\rm{hr}^{-1}$, followed by a low-activity state. We also detected a short-term reactivation at 2.25~GHz around 2025 January 20, about two weeks after renewed activity was reported below 1.4~GHz by other telescopes. The median burst width at 2.25~GHz is 3~ms, which is narrower than that at lower frequencies. The waiting time distribution peaks at 1019~s, and burst arrivals on hourly timescales consistent with a Poisson process. The isotropic-equivalent energy of bursts spans $10^{37} -10^{39}$~erg. The distribution of burst energy above the completeness threshold ($7.5\times10^{37}$~erg) follows a power-law relation with an index of $γ=-1.20\pm0.03\pm0.02$. Finally, we find that FRB~20240114A is at least two orders of magnitude less active at 8.60~GHz than at 2.25~GHz, and we constrain the broadband spectra of the detected bursts.

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Hyper-active repeating fast radio bursts from rotation modulated starquakes on magnetars

The non-detection of periodicity related to rotation challenges magnetar models for fast radio bursts (FRBs) with FRB emission from close to the magnetar surface. Moreover, a bimodal distribution of the burst waiting times is widely observed in hyper-active FRBs, a significant deviation from the exponential distribution expected from stationary Poisson processes. By combining the epidemic-type aftershock sequence (ETAS) earthquake model and the rotating vector model (RVM) involving the rotation of the magnetar and orientations of the spin and magnetic axes, we find that starquake events modulated by the rotation of FRB-emitting magnetar can explain the bimodal distribution of FRB waiting times, as well as the non-detection of periodicity in hyper-active repeating FRBs. We analyze data from multiple FRB sources, demonstrating that differences in waiting time distributions and, to some extent, observed energies can be explained by varying parameters related to geometric properties of the magnetar FRB emission and starquake dynamics. Our results show that the assumption that all FRBs are repeaters is compatible with our model. Notably, we find that hyper-active repeaters tend to have small magnetic inclination angles in order to hide their periodicity. We also show that our model can reproduce the waiting time distribution of a pulsar phase of the galactic magnetar SGR J1935+2154 with a larger inclination angle than the hyper-active repeaters, which could explain the detection of spin period and the relatively low observed energy for FRBs from the magnetar. The spin periods of hyper-active repeaters are not well constrained, but most likely fall in the valley region between the two peaks of the waiting time distributions.

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The flat tail in the burst energy distribution of FRB 20240114A

Fast Radio Bursts (FRBs) are enigmatic millisecond-duration radio transients of extra-galactic origin, whose underlying mechanisms and progenitors remain poorly understood. FRBs are broadly classified into two categories: repeating FRBs, which emit multiple bursts over time, and one-off FRBs, which are detected as single events. A central question in FRB research is whether these two classes share a common origin. In this study, we present observations of FRB 20240114A, a repeating FRB that entered a hyperactive phase in January 2024. We conducted a 318-hour monitoring campaign using the Kunming 40-Meter Radio Telescope (KM40M) in the S-band (2.187-2.311 GHz), during which we detected eight radio bursts. We analyzed their properties, including dispersion measure (DM), bandwidth, pulse width, flux, fluence, and energy. Additionally, we searched for counterparts in overlapping data from the Five-hundred-meter Aperture Spherical Telescope (FAST) in the L-band (1.0-1.5 GHz). While no bursts were temporally aligned between the two telescopes, we identified one FAST burst that arrived approximately 6 ms after one of the KM40M bursts. The absence of FAST counterparts for the KM40M bursts suggests that individual bursts from FRB 20240114A are likely narrow-band, with fractional bandwidths less than 10%. By comparing the cumulative event rates from KM40M and FAST observations, we found that the two measurements are compatible, indicating a possible flattening of the event rate at higher energies. This feature aligns with observations of one-off FRBs, supporting the hypothesis that repeating and one-off FRBs may share a common origin.

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Scintillation Arc from FRB 20220912A

We present the interstellar scintillation analysis of fast radio burst (FRB) 20220912A during its extremely active episode in 2022 using data from the Five-hundred-meter Aperture Spherical Radio Telescope (FAST). We detect a scintillation arc in the FRB's secondary spectrum, which describes the power in terms of the scattered FRB signals' time delay and Doppler shift. The arc indicates that the scintillation is caused by a highly localized region of the ionized interstellar medium (IISM). Our analysis favors a Milky Way origin for the localized scattering medium but cannot rule out a host galaxy origin. We present our method for detecting the scintillation arc, which can be applied generally to sources with irregularly spaced bursts or pulses. These methods could help shed light on the complex interstellar environment surrounding the FRBs and in our Galaxy.

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FAST Observations of FRB 20220912A: Burst Properties and Polarization Characteristics

We report the observations of FRB 20220912A using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). We conducted 17 observations totaling 8.67 hours and detected a total of 1076 bursts with an event rate up to 390 hr$^{-1}$. The cumulative energy distribution can be well described using a broken power-law function with the lower and higher-energy slopes of $-0.38\pm0.02$ and $-2.07\pm0.07$, respectively. We also report the L band ($1-1.5$ GHz) spectral index of the synthetic spectrum of FRB~20220912A bursts, which is $-2.6\pm0.21$. The average rotation measure (RM) value of the bursts from FRB~20220912A is $-0.08\pm5.39\ \rm rad\,m^{-2}$, close to 0 $\rm rad\,m^{-2}$ and maintain relatively stable over two months. Most bursts have nearly 100\% linear polarization. About 45\% of the bursts have circular polarization with SNR $>$ 3, and the highest circular polarization degree can reach 70\%. Our observations suggest that FRB~20220912A is located in a relatively clean local environment with complex circular polarization characteristics. These various behaviors imply that the mechanism of circular polarization of FRBs likely originates from an intrinsic radiation mechanism, such as coherent curvature radiation or inverse Compton scattering inside the magnetosphere of the FRB engine source (e.g. a magnetar).

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Atlas of dynamic spectra of fast radio burst FRB 20201124A

Fast radio bursts (FRBs) are highly dispersed millisecond-duration radio bursts, of which the physical origin is still not fully understood. FRB 20201124A is one of the most actively repeating FRBs. In this paper, we present the collection of 1863 burst dynamic spectra of FRB 20201124A measured with the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The current collection, taken from the observation during the FRB active phase from April to June 2021, is the largest burst sample detected in any FRB so far. The standard PSRFITs format is adopted, including dynamic spectra of the burst, and the time information of the dynamic spectra, in addition, mask files help readers to identify the pulse positions are also provided.

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FAST observations of an extremely active episode of FRB 20201124A: III. Polarimetry

As the third paper in the multiple-part series, we report the statistical properties of radio bursts detected from the repeating fast radio burst (FRB) source FRB 20201124A with the Five-hundred-meter Aperture Spherical radio telescope (FAST) during an extremely active episode between the 25th and the 28th of September 2021 (UT). We focus on the polarisation properties of 536 bright bursts with $\mathrm{S/N}>50$. We found that the Faraday rotation measures (RMs) monotonically dropped from $-579 \ {\rm rad \ m^{-2}}$ to $-605 \ {\rm rad \ m^{-2}}$ in the 4-day window. The RM values were compatible with the values ($-300$ to $-900\ {\rm rad \ m^{-2}}$ ) reported 4 month ago (Xu et al. 2022). However, the RM evolution rate in the current observation window was at least an order of magnitude smaller than the one ($\sim 500\ {\rm rad \ m^{-2}\, day^{-1}}$) previously reported during the rapid RM-variation phase, but is still higher than the one ($\le 1\ {\rm rad \ m^{-2} day^{-1}}$ ) during the later RM no-evolution phase. The bursts of FRB 20201124A were highly polarised with the total degree of polarisation (circular plus linear) greater than 90% for more than 90\% of all bursts. The distribution of linear polarisation position angles (PAs), degree of linear polarisation ($L/I$), and degree of circular polarisation ($V/I$) can be characterised with unimodal distribution functions. During the observation window, the distributions became wider with time, i.e. with larger scatter, but the centroids of the distribution functions remained nearly constant. For individual bursts, significant PA variations (confidence level 5-$σ$) were observed in 33% of all bursts. The polarisation of single pulses seems to follow certain complex trajectories on the Poincaré sphere, which may shed light on the radiation mechanism at the source or the plasma properties along the path of FRB propagation.

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FAST observations of an extremely active episode of FRB 20201124A: II. Energy Distribution

We report the properties of more than 800 bursts detected from the repeating fast radio burst (FRB) source FRB 20201124A with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) during an extremely active episode on UTC September 25-28, 2021 in a series of four papers. In this second paper of the series, we mainly focus on the energy distribution of the detected bursts. The event rate initially increased exponentially but the source activity stopped within 24 hours after the 4th day. The detection of 542 bursts in one hour during the fourth day marked the highest event rate detected from one single FRB source so far. The bursts have complex structures in the time-frequency space. We find a double-peak distribution of the waiting time, which can be modeled with two log-normal functions peaking at 51.22 ms and 10.05 s, respectively. Compared with the emission from a previous active episode of the source detected with FAST, the second distribution peak time is smaller, suggesting that this peak is defined by the activity level of the source. We calculate the isotropic energy of the bursts using both a partial bandwidth and a full bandwidth and find that the energy distribution is not significantly changed. We find that an exponentially connected broken-power-law function can fit the cumulative burst energy distribution well, with the lower and higher-energy indices being $-1.22\pm0.01$ and $-4.27\pm0.23$, respectively. Assuming a radio radiative efficiency of $η_r = 10^{-4}$, the total isotropic energy of the bursts released during the four days when the source was active is already $3.9\times10^{46}$ erg, exceeding $\sim 23\%$ of the available magnetar dipolar magnetic energy. This challenges the magnetar models invoking an inefficient radio emission (e.g. synchrotron maser models).

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FAST observations of an extremely active episode of FRB 20201124A: IV. Spin Period Search

We report the properties of more than 800 bursts detected from the repeating fast radio burst (FRB) source FRB 20201124A with the Five-hundred-meter Aperture Spherical radio telescope (FAST) during an extremely active episode on UTC September 25th-28th, 2021 in a series of four papers. In this fourth paper of the series, we present a systematic search of the spin period and linear acceleration of the source object from both 996 individual pulse peaks and the dedispersed time series. No credible spin period was found from this data set. We rule out the presence of significant periodicity in the range between 1 ms to 100 s with a pulse duty cycle $< 0.49\pm0.08$ (when the profile is defined by a von-Mises function, not a boxcar function) and linear acceleration up to $300$ m s$^{-2}$ in each of the four one-hour observing sessions, and up to $0.6$ m s$^{-2}$ in all 4 days. These searches contest theoretical scenarios involving a 1 ms to 100 s isolated magnetar/pulsar with surface magnetic field $<10^{15}$ G and a small duty cycle (such as in a polar-cap emission mode) or a pulsar with a companion star or black hole up to 100 M$_{\rm \odot}$ and $P_b>10$ hours. We also perform a periodicity search of the fine structures and identify 53 unrelated millisecond-timescale "periods" in multi-components with the highest significance of 3.9 $σ$. The "periods" recovered from the fine structures are neither consistent nor harmonically related. Thus they are not likely to come from a spin period. We caution against claiming spin periodicity with significance below $\sim$ 4 $σ$ with multi-components from one-off FRBs. We discuss the implications of our results and the possible connections between FRB multi-components and pulsar micro-structures.

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Simultaneous view of the FRB~180301 with FAST and NICER during a bursting phase

FRB180301 is one of the most actively repeating fast radio bursts (FRBs) which has shown polarization angle changes in its radio burst emission, an indication for their likely origin in the magnetosphere of a highly-magnetized neutron star. We carried out a multi-wavelength campaign with the FAST radio telescope and NICER X-ray observatory to investigate any possible X-ray emission temporally coincident with the bright radio bursts. The observations took place on 2021 March 4, 9 and 19. We detected five bright radio bursts with FAST, four of which were strictly simultaneous with the NICER observations. The peak flux-density of the radio bursts ranged between $28-105$ mJy, the burst fluence between $27-170$ mJy-ms, and the burst durations between $1.7-12.3$ ms. The radio bursts from FRB~180301 exhibited complex time domain structure, and sub-pulses were detected in individual bursts, with no significant circular polarisation. The linear degree of polarisation in L-band reduced significantly compared to the 2019 observations. We do not detect any X-ray emission in excess of the background during the 5ms, 10ms, 100ms, 1sec and 100sec time intervals at/around the radio-burst barycenter-corrected arrival times, at a $>5σ$ confidence level. The $5σ$ upper limits on the X-ray a) persistent flux is $<7.64\times 10^{-12}\, \rm erg\, cm^{-2}\, s^{-1}$ , equivalent to $L_{\rm X}<2.50 \times 10^{45} \rm erg\, s^{-1}$ and b) 5 ms fluence is $<2\times 10^{-11} \rm erg\, cm^{-2}$, at the radio burst regions. Using the $5$ ms X-ray fluence upper limit, we can estimate the radio efficiency $η_{R/X} \equiv L_{\rm Radio}/L_{\rm X-ray} \gtrsim 10^{-8}$. The derived upper limit on $η_{R/X}$ is consistent with both magnetospheric models and synchrotron maser models involving relativistic shocks.

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5 GHz TMRT observations of 71 pulsars

We present integrated pulse profiles at 5~GHz for 71 pulsars, including eight millisecond pulsars (MSPs), obtained using the Shanghai Tian Ma Radio Telescope (TMRT). Mean flux densities and pulse widths are measured. For 19 normal pulsars and one MSP, these are the first detections at 5~GHz and for a further 19, including five MPSs, the profiles have a better signal-to-noise ratio than previous observations. Mean flux density spectra between 400~MHz and 9~GHz are presented for 27 pulsars and correlations of power-law spectral index are found with characteristic age, radio pseudo-luminosity and spin-down luminosity. Mode changing was detected in five pulsars. The separation between the main pulse and interpulse is shown to be frequency independent for six pulsars but a frequency dependence of the relative intensity of the main pulse and interpulse is found. The frequency dependence of component separations is investigated for 20 pulsars and three groups are found: in seven cases the separation between the outmost leading and trailing components decreases with frequency, roughly in agreement with radius-to-frequency mapping; in eleven cases the separation is nearly constant; in the remain two cases the separation between the outmost components increases with frequency. We obtain the correlations of pulse widths with pulsar period and estimate the core widths of 23 multi-component profiles and conal widths of 17 multi-component profiles at 5.0~GHz using Gaussian fitting and discuss the width-period relationship at 5~GHz compared with the results at at 1.0~GHz and 8.6~GHz.

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