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J. W. T. Hessels

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

At least 73 records · Page 4Linked to original sources

A LOFAR census of non-recycled pulsars: extending below 80 MHz

We present the results from the low-frequency (40--78 MHz) extension of the first LOFAR pulsar census of non-recycled pulsars. We have used the Low-Band Antennas of the LOFAR core stations to observe 87 pulsars out of 158 that have been detected previously with the High-Band Antennas. Forty-three pulsars have been detected and we present here their flux densities and flux-calibrated profiles. Seventeen of these pulsars have not been, to our knowledge, detected before at such low frequencies. We re-calculate the spectral indices using the new low-frequency flux density measurements from the LOFAR census and discuss the prospects of studying pulsars at the very low frequencies with the current and upcoming facilities, such as NenuFAR.

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Eight Millisecond Pulsars Discovered in the Arecibo PALFA Survey

We report on eight millisecond pulsars (MSPs) in binary systems discovered with the Arecibo PALFA survey. Phase-coherent timing solutions derived from 2.5 to 5 years of observations carried out at Arecibo and Jodrell Bank observatories are provided. PSR J1921+1929 is a 2.65-ms pulsar in a 39.6-day orbit for which we detect $γ$-ray pulsations in archival Fermi data. PSR J1928+1245 is a very low-mass-function system with an orbital period of 3.3 hours that belongs to the non-eclipsing black widow population. We also present PSR J1932+1756, the longest-orbital-period (41.5 days) intermediate-mass binary pulsar known to date. In light of the numerous discoveries of binary MSPs over the past years, we characterize the Galactic distribution of known MSP binaries in terms of binary class. Our results support and strengthen previous claims that the scatter in the Galactic scale height distribution correlates inversely with the binary mass function. We provide evidence of observational biases against detecting the most recycled pulsars near the Galactic plane, which overestimates the scale height of lighter systems. A possible bimodality in the mass function of MSPs with massive white dwarfs is also reported.

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Mass measurements for two binary pulsars discovered in the PALFA survey

In this paper, we present the results of timing observations of PSRs J1949+3106 and J1950+2414, two binary millisecond pulsars discovered in data from the Arecibo ALFA pulsar survey (PALFA). The timing parameters include precise measurements of the proper motions of both pulsars, which show that PSR J1949+3106 has a transversal motion very similar to that of an object in the local standard of rest. The timing also includes measurements of the Shapiro delay and the rate of advance of periastron for both systems. Assuming general relativity, these allow estimates of the masses of the components of the two systems; for PSR J1949+3106, the pulsar mass is $M_p \, = \, 1.34^{+0.17}_{-0.15} \, M_{\odot}$ and the companion mass $M_c \, = \, 0.81^{+0.06}_{-0.05}\, M_{\odot}$; for PSR J1950+2414 $M_p \, = \, 1.496 \, \pm \, 0.023\, M_{\odot}$ and $M_c \, = \, 0.280^{+0.005}_{-0.004}\, M_{\odot}$ (all values 68.3 % confidence limits). We use these masses and proper motions to investigate the evolutionary history of both systems: PSR J1949+3106 is likely the product of a low-kick supernova; PSR J1950+2414 is a member of a new class of eccentric millisecond pulsar binaries with an unknown formation mechanism. We discuss the proposed hypotheses for the formations of these systems in light of our new mass measurements.

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A sample of low energy bursts from FRB 121102

We present 41 bursts from the first repeating fast radio burst discovered (FRB 121102). A deep search has allowed us to probe unprecedentedly low burst energies during two consecutive observations (separated by one day) using the Arecibo telescope at 1.4 GHz. The bursts are generally detected in less than a third of the 580-MHz observing bandwidth, demonstrating that narrow-band FRB signals may be more common than previously thought. We show that the bursts are likely faint versions of previously reported multi-component bursts. There is a striking lack of bursts detected below 1.35 GHz and simultaneous VLA observations at 3 GHz did not detect any of the 41 bursts, but did detect one that was not seen with Arecibo, suggesting preferred radio emission frequencies that vary with epoch. A power law approximation of the cumulative distribution of burst energies yields an index $-1.8\pm0.3$ that is much steeper than the previously reported value of $\sim-0.7$. The discrepancy may be evidence for a more complex energy distribution. We place constraints on the possibility that the associated persistent radio source is generated by the emission of many faint bursts ($\sim700$ ms$^{-1}$). We do not see a connection between burst fluence and wait time. The distribution of wait times follows a log-normal distribution centered around $\sim200$ s; however, some bursts have wait times below 1 s and as short as 26 ms, which is consistent with previous reports of a bimodal distribution. We caution against exclusively integrating over the full observing band during FRB searches, because this can lower signal-to-noise.

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The LOFAR Tied-Array All-Sky Survey (LOTAAS): Survey overview and initial pulsar discoveries

We present an overview of the LOFAR Tied-Array All-Sky Survey (LOTAAS) for radio pulsars and fast transients. The survey uses the high-band antennas of the LOFAR Superterp, the dense inner part of the LOFAR core, to survey the northern sky (dec > 0 deg) at a central observing frequency of 135 MHz. A total of 219 tied-array beams (coherent summation of station signals, covering 12 square degrees), as well as three incoherent beams (covering 67 square degrees) are formed in each survey pointing. For each ofthe 222 beams, total intensity is recorded at 491.52 us time resolution. Each observation integrates for 1 hr and covers 2592 channels from 119 to 151 MHz. This instrumental setup allows LOTAAS to reach a detection threshold of 1 to 5 mJy for periodic emission. Thus far, the LOTAAS survey has resulted in the discovery of 73 radio pulsars. Among these are two mildly recycled binary millisecond pulsars (P = 13 and 33 ms), as well as the slowest-spinning radio pulsar currently known (P = 23.5 s). The survey has thus far detected 311 known pulsars, with spin periods ranging from 4 ms to 5.0 s and dispersion measures from 3.0 to 217 pc/cc. Known pulsars are detected at flux densities consistent with literature values. We find that the LOTAAS pulsar discoveries have, on average, longer spin periods than the known pulsar population. This may reflect different selection biases between LOTAAS and previous surveys, though it is also possible that slower-spinning pulsars preferentially have steeper radio spectra. LOTAAS is the deepest all-sky pulsar survey using a digital aperture array; we discuss some of the lessons learned that can inform the approach for similar surveys using future radio telescopes such as the Square Kilometre Array.

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Resolving the decades-long transient FIRST J141918.9+394036: an orphan long gamma-ray burst or a young magnetar nebula?

Ofek (2017) identified FIRST J141918.9+394036 (hereafter FIRST J1419+3940) as a radio source sharing similar properties and host galaxy type to the compact, persistent radio source associated with the first known repeating fast radio burst, FRB 121102. Law et al. (2018) showed that FIRST J1419+3940 is a transient source decaying in brightness over the last few decades. One possible interpretation is that FIRST J1419+3940 is a nearby analogue to FRB 121102 and that the radio emission represents a young magnetar nebula (as several scenarios assume for FRB 121102). Another interpretation is that FIRST J1419+3940 is the afterglow of an `orphan' long gamma-ray burst (GRB). The environment is similar to where most such events are produced. To distinguish between these hypotheses, we conducted radio observations using the European VLBI Network at 1.6 GHz to spatially resolve the emission and to search for millisecond-duration radio bursts. We detect FIRST J1419+3940 as a compact radio source with a flux density of $620 \pm 20\ \mathrm{μJy}$ (on 2018 September 18) and a source size of $3.9 \pm 0.7\ \mathrm{mas}$ (i.e. $1.6 \pm 0.3\ \mathrm{pc}$ given the angular diameter distance of $83\ \mathrm{Mpc}$). These results confirm that the radio emission is non-thermal and imply an average expansion velocity of $(0.10 \pm 0.02)c$. Contemporaneous high-time-resolution observations using the 100-m Effelsberg telescope detected no millisecond-duration bursts of astrophysical origin. The source properties and lack of short-duration bursts are consistent with a GRB jet expansion, whereas they disfavor a magnetar birth nebula.

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Fast Radio Bursts

The discovery of radio pulsars over a half century ago was a seminal moment in astronomy. It demonstrated the existence of neutron stars, gave a powerful observational tool to study them, and has allowed us to probe strong gravity, dense matter, and the interstellar medium. More recently, pulsar surveys have led to the serendipitous discovery of fast radio bursts (FRBs). While FRBs appear similar to the individual pulses from pulsars, their large dispersive delays suggest that they originate from far outside the Milky Way and hence are many orders-of-magnitude more luminous. While most FRBs appear to be one-off, perhaps cataclysmic events, two sources are now known to repeat and thus clearly have a longer-lived central engine. Beyond understanding how they are created, there is also the prospect of using FRBs -- as with pulsars -- to probe the extremes of the Universe as well as the otherwise invisible intervening medium. Such studies will be aided by the high implied all-sky event rate: there is a detectable FRB roughly once every minute occurring somewhere on the sky. The fact that less than a hundred FRB sources have been discovered in the last decade is largely due to the small fields-of-view of current radio telescopes. A new generation of wide-field instruments is now coming online, however, and these will be capable of detecting multiple FRBs per day. We are thus on the brink of further breakthroughs in the short-duration radio transient phase space, which will be critical for differentiating between the many proposed theories for the origin of FRBs. In this review, we give an observational and theoretical introduction at a level that is accessible to astronomers entering the field.

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The Green Bank North Celestial Cap Pulsar Survey. IV: Four New Timing Solutions

We present timing solutions for four pulsars discovered in the Green Bank Northern Celestial Cap (GBNCC) survey. All four pulsars are isolated with spin periods between 0.26$\,$s and 1.84$\,$s. PSR J0038$-$2501 has a 0.26$\,$s period and a period derivative of ${7.6} \times {10}^{-19}\,{\rm s\,s}^{-1}$, which is unusually low for isolated pulsars with similar periods. This low period derivative may be simply an extreme value for an isolated pulsar or it could indicate an unusual evolution path for PSR J0038$-$2501, such as a disrupted recycled pulsar (DRP) from a binary system or an orphaned central compact object (CCO). Correcting the observed spin-down rate for the Shklovskii effect suggests that this pulsar may have an unusually low space velocity, which is consistent with expectations for DRPs. There is no X-ray emission detected from PSR J0038$-$2501 in an archival swift observation, which suggests that it is not a young orphaned CCO. The high dispersion measure of PSR J1949+3426 suggests a distance of 12.3$\,$kpc. This distance indicates that PSR J1949+3426 is among the most distant 7% of Galactic field pulsars, and is one of the most luminous pulsars.

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First detection of frequency-dependent, time-variable dispersion measures

Context. High-precision pulsar-timing experiments are affected by temporal variations of the Dispersion Measure (DM), which are related to spatial variations in the interstellar electron content. Correcting for DM variations relies on the cold-plasma dispersion law which states that the dispersive delay varies with the squared inverse of the observing frequency. This may however give incorrect measurements if the probed electron content (and therefore the DM) varies with observing frequency, as is predicted theoretically. Aims. We study small-scale density variations in the ionised interstellar medium. These structures may lead to frequency-dependent DMs in pulsar signals and could inhibit the use of lower-frequency pulsar observations to correct time-variable interstellar dispersion in higher-frequency pulsar-timing data. Methods. We used high-cadence, low-frequency observations with three stations from the German LOng-Wavelength (GLOW) consortium, which are part of the LOw Frequency ARray (LOFAR). Specifically, 3.5 years of weekly observations of PSR J2219+4754 are presented. Results. We present the first detection of frequency-dependent DMs towards any interstellar object and a precise multi-year time-series of the time- and frequency-dependence of the measured DMs. The observed DM variability is significant and may be caused by extreme scattering events. Potential causes for frequency-dependent DMs are quantified and evaluated. Conclusions. We conclude that frequency-dependence of DMs has been reliably detected and is caused by small-scale (up to 10s of AUs) but steep density variations in the interstellar electron content. We find that long-term trends in DM variability equally affect DMs measured at both ends of our frequency band and hence the negative impact on long-term high-precision timing projects is expected to be limited.

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Low-frequency Faraday rotation measures towards pulsars using LOFAR: probing the 3-D Galactic halo magnetic field

We determined Faraday rotation measures (RMs) towards 137 pulsars in the northern sky, using Low-Frequency Array (LOFAR) observations at 110-190 MHz. This low-frequency RM catalogue, the largest to date, improves the precision of existing RM measurements on average by a factor of 20 - due to the low frequency and wide bandwidth of the data, aided by the RM synthesis method. We report RMs towards 25 pulsars for the first time. The RMs were corrected for ionospheric Faraday rotation to increase the accuracy of our catalogue to approximately 0.1 rad m$^{\rm -2}$. The ionospheric RM correction is currently the largest contributor to the measurement uncertainty. In addition, we find that the Faraday dispersion functions towards pulsars are extremely Faraday thin - mostly less than 0.001 rad m$^{\rm -2}$. We use these new precise RM measurements (in combination with existing RMs, dispersion measures, and distance estimates) to estimate the scale height of the Galactic halo magnetic field: 2.0$\pm$0.3 kpc for Galactic quadrants I and II above and below the Galactic plane (we also evaluate the scale height for these regions individually). Overall, our initial low-frequency catalogue provides valuable information about the 3-D structure of the Galactic magnetic field.

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The radio-bright accreting millisecond X-ray pulsar IGR J17591-2342

IGR J17591$-$2342 is a 527-Hz accreting millisecond X-ray pulsar that was discovered in outburst in 2018 August. In this paper, we present quasi-simultaneous radio and X-ray monitoring of this source during the early part of the outburst. IGR J17591$-$2342 is highly absorbed in X-rays, with an equivalent hydrogen absorption along the line of sight, $N_{\rm H}$, of $\approx$4.4$\times$10$^{22}$\,cm$^{-2}$, where the Galactic column density is expected to be $\approx$1 -- 2$\times$10$^{22}$\,cm$^{-2}$. The high absorption suggests that the source is either relatively distant ($>$6\,kpc), or the X-ray emission is strongly absorbed by material local to the system. Radio emission detected by the Australia Telescope Compact Array shows that, for a given X-ray luminosity and for distances greater than 3\,kpc, this source was exceptionally radio loud when compared to other accreting neutron stars in outburst ($L_{\rm X} > 10^{33}$\,erg\,s$^{-1}$). For most reasonable distances, IGR J17591$-$2342 appeared as radio luminous as actively accreting, stellar-mass black hole X-ray binaries.

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FRB 121102 Bursts Show Complex Time-Frequency Structure

FRB 121102 is the only known repeating fast radio burst source. Here we analyze a wide-frequency-range (1-8 GHz) sample of high-signal-to-noise, coherently dedispersed bursts detected using the Arecibo and Green Bank telescopes. These bursts reveal complex time-frequency structures that include sub-bursts with finite bandwidths. The frequency-dependent burst structure complicates the determination of a dispersion measure (DM); we argue that it is appropriate to use a DM metric that maximizes frequency-averaged pulse structure, as opposed to peak signal-to-noise, and find DM = 560.57 +/- 0.07 pc/cc at MJD 57644. After correcting for dispersive delay, we find that the sub-bursts have characteristic frequencies that typically drift lower at later times in the total burst envelope. In the 1.1-1.7 GHz band, the ~ 0.5-1-ms sub-bursts have typical bandwidths ranging from 100-400 MHz, and a characteristic drift rate of ~ 200 MHz/ms towards lower frequencies. At higher radio frequencies, the sub-burst bandwidths and drift rate are larger, on average. While these features could be intrinsic to the burst emission mechanism, they could also be imparted by propagation effects in the medium local to the source. Comparison of the burst DMs with previous values in the literature suggests an increase of Delta(DM) ~ 1-3 pc/cc in 4 years, though this could be a stochastic variation as opposed to a secular trend. This implies changes in the local medium or an additional source of frequency-dependent delay. Overall, the results are consistent with previously proposed scenarios in which FRB 121102 is embedded in a dense nebula.

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LOFAR discovery of a 23.5-second radio pulsar

We present the discovery of PSR J0250+5854, a radio pulsar with a spin period of 23.5 s. This is the slowest-spinning radio pulsar known. PSR J0250+5854 was discovered by the LOFAR Tied-Array All-Sky Survey (LOTAAS), an all-Northern-sky survey for pulsars and fast transients at a central observing frequency of 135 MHz. We subsequently detected pulsations from the pulsar in the interferometric images of the LOFAR Two-metre Sky Survey, allowing for sub-arcsecond localization. This, along with a pre-discovery detection 2 years prior, allowed us to measure the spin-period derivative to be $\dot{P}=2.7 \times 10^{-14}$ s s$^{-1}$. The observed spin period derivative of PSR J0250+5854 indicates a surface magnetic field strength, characteristic age and spin-down luminosity of $2.6 \times 10^{13}$G, $13.7$ Myr and $8.2 \times 10^{28}$ erg s$^{-1}$ respectively, for a dipolar magnetic field configuration. This also places the pulsar beyond the conventional pulsar death line, where radio emission is expected to cease. The spin period of PSR J0250+5854 is similar to those of the high-energy-emitting magnetars and X-ray dim isolated neutron stars (XDINSs). However, the pulsar was not detected by the Swift/XRT in the energy band of 0.3-10 keV, placing a bolometric luminosity limit of $1.5 \times 10^{32}$ erg s$^{-1}$ for an assumed $N_{\rm H}=1.35\times10^{21}$ cm$^{-2}$ and a temperature of 85 eV (typical of XDINSs). We discuss the implications of the discovery for models of the pulsar death line as well as the prospect of finding more similarly long-period pulsars, including the advantages provided by LOTAAS for this.

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Single-pulse classifier for the LOFAR Tied-Array All-sky Survey

Searches for millisecond-duration, dispersed single pulses have become a standard tool used during radio pulsar surveys in the last decade. They have enabled the discovery of two new classes of sources: rotating radio transients and fast radio bursts. However, we are now in a regime where the sensitivity to single pulses in radio surveys is often limited more by the strong background of radio frequency interference (RFI, which can greatly increase the false-positive rate) than by the sensitivity of the telescope itself. To mitigate this problem, we introduce the Single-pulse Searcher (SpS). This is a new machine-learning classifier designed to identify astrophysical signals in a strong RFI environment, and optimized to process the large data volumes produced by the new generation of aperture array telescopes. It has been specifically developed for the LOFAR Tied-Array All-Sky Survey (LOTAAS), an ongoing survey for pulsars and fast radio transients in the northern hemisphere. During its development, SpS discovered 7 new pulsars and blindly identified ~80 known sources. The modular design of the software offers the possibility to easily adapt it to other studies with different instruments and characteristics. Indeed, SpS has already been used in other projects, e.g. to identify pulses from the fast radio burst source FRB 121102. The software development is complete and SpS is now being used to re-process all LOTAAS data collected to date.

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PALFA Single-Pulse Pipeline: New Pulsars, Rotating Radio Transients and a Candidate Fast Radio Burst

We present a newly implemented single-pulse pipeline for the PALFA survey to efficiently identify single radio pulses from pulsars, Rotating Radio Transients (RRATs) and Fast Radio Bursts (FRBs). We have conducted a sensitivity analysis of this new pipeline in which multiple single pulses with a wide range of parameters were injected into PALFA data sets and run through the pipeline. Based on the recovered pulses, we find that for pulse widths $\rm < 5\ ms$ the sensitivity of the PALFA pipeline is at most a factor of $\rm \sim 2$ less sensitive to single pulses than our theoretical predictions. For pulse widths $\rm > 10\ ms$, as the $\rm DM$ decreases, the degradation in sensitivity gets worse and can increase up to a factor of $\rm \sim 4.5$. Using this pipeline, we have thus far discovered 7 pulsars and 2 RRATs and identified 3 candidate RRATs and 1 candidate FRB. The confirmed pulsars and RRATs have DMs ranging from 133 to 386 pc cm$^{-3}$ and flux densities ranging from 20 to 160 mJy. The pulsar periods range from 0.4 to 2.1 s. We report on candidate FRB 141113, which we argue is likely astrophysical and extragalactic, having $\rm DM \simeq 400\ pc~cm^{-3}$, which represents an excess over the Galactic maximum along this line of sight of $\rm \sim$ 100 - 200 pc cm$^{-3}$. We consider implications for the FRB population and show via simulations that if FRB 141113 is real and extragalactic, the slope $α$ of the distribution of integral source counts as a function of flux density ($N (>S) \propto S^{-α}$) is $1.4 \pm 0.5$ (95% confidence range). However this conclusion is dependent on several assumptions that require verification.

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Discovery of synchronous X-ray and radio moding of PSR B0823+26

Simultaneous observations of PSR B0823+26 with ESA's XMM-Newton, the Giant Metrewave Radio Telescope and international stations of the Low Frequency Array revealed synchronous X-ray/radio switching between a radio-bright (B) mode and a radio-quiet (Q) mode. During the B mode we detected PSR B0823+26 in 0.2$-$2 keV X-rays and discovered pulsed emission with a broad sinusoidal pulse, lagging the radio main pulse by 0.208 $\pm$ 0.012 in phase, with high pulsed fraction of 70$-$80%. During the Q mode PSR B0823+26 was not detected in X-rays (2 $σ$ upper limit a factor ~9 below the B-mode flux). The total X-ray spectrum, pulse profile and pulsed fraction can globally be reproduced with a magnetized partially ionized hydrogen atmosphere model with three emission components: a primary small hot spot ($T$$\sim$3.6$\times10^6$ K, $R$$\sim$17 m), a larger cooler concentric ring ($T$$\sim$1.1$\times10^6$ K, $R$$\sim$280 m) and an antipodal hot spot ($T$$\sim$1.1$\times10^6 $ K, $R$$\sim$100 m), for the angle between the rotation axis and line of sight direction $\sim66^\circ$. The latter is in conflict with the radio derived value of $(84\pm0.7)^\circ$. The average X-ray flux within hours-long B-mode intervals varied by a factor $\pm$20%, possibly correlated with variations in the frequency and lengths of short radio nulls or short durations of weak emission. The correlated X-ray/radio moding of PSR B0823+26 is compared with the anti-correlated moding of PSR B0943+10, and the lack of X-ray moding of PSR B1822-09. We speculate that the X-ray/radio switches of PSR B0823+26 are due to variations in the rate of accretion of material from the interstellar medium through which it is passing.

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The implementation of a Fast-Folding pipeline for long-period pulsar searching in the PALFA survey

The Pulsar Arecibo L-Band Feed Array (PALFA) survey, the most sensitive blind search for radio pulsars yet conducted, is ongoing at the Arecibo Observatory in Puerto Rico. The vast majority of the 180 pulsars discovered by PALFA have spin periods shorter than 2 seconds. Pulsar surveys may miss long-period radio pulsars due to the summing of a finite number of harmonic components in conventional Fourier analyses (typically $\sim$16), or due to the strong effect of red noise at low modulation frequencies. We address this reduction in sensitivity by using a time-domain search technique: the Fast-Folding Algorithm (FFA). We designed a program that implements a FFA-based search in the PALFA processing pipeline, and tested the efficiency of the algorithm by performing tests under both ideal, white noise conditions, as well as with real PALFA observational data. In the two scenarios, we show that the time-domain algorithm has the ability to outperform the FFT-based periodicity search implemented in the survey. We perform simulations to compare the previously reported PALFA sensitivity with that obtained using our new FFA implementation. These simulations show that for a pulsar having a pulse duty cycle of roughly 3%, the performance of our FFA pipeline exceeds that of our FFT pipeline for pulses with DM $\lesssim$ 40 pc cm$^{-3}$ and for periods as short as $\sim$500 ms, and that the survey sensitivity is improved by at least a factor of two for periods $\gtrsim$ 6 sec. Discoveries from the implementation of the algorithm in PALFA are also presented in this paper.

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Fast Radio Bursts and their Possible Neutron Star Origins

The discovery of the `Lorimer Burst', a little over a decade ago, ignited renewed interest in searching for short-duration radio transients. This event is now considered to be the first established Fast Radio Burst (FRB), which is a class of millisecond-duration radio transients. The large dispersive delays observed in FRBs distinguish them from the individual bright pulses from Galactic pulsars, and suggests that they originate deep in extragalactic space. Amazingly, FRBs are not rare: the implied event rate ranges up to many thousands of events per sky, per day. The fact that only two dozen FRBs have been discovered to date is a consequence of the limited sensitivity and field of view of current radio telescopes. The precise localization of FRB 121102, the first and currently only FRB observed to repeat, has led to the unambiguous identification of its host galaxy and thus proven its extragalactic origin and large energy scale. It remains unclear, however, whether all FRBs are capable of repeating (many appear far less active) or whether FRB 121102 implies that there are multiple sub-classes. Regardless, the repetitive nature of FRB 121102 and its localization to within a star-forming region in the host galaxy imply that the bursts might originate from an exceptionally powerful neutron star - one necessarily quite unlike any we have observed in the Milky Way. In these proceedings, I give a very brief introduction to the FRB phenomenon and focus primarily on the insights that FRB 121102 has provided thus far.

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