arXiv subjects

C. Tiburzi

Publications and source records attributed to C. Tiburzi.

At least 37 records · Page 2Linked to original sources

arXiv2022

The Thousand-Pulsar-Array program on MeerKAT -- IX. The time-averaged properties of the observed pulsar population

We present the largest single survey to date of average profiles of radio pulsars, observed and processed using the same telescope and data reduction software. Specifically, we present measurements for 1170 pulsars, observed by the Thousand Pulsar Array (TPA) programme at the 64-dish SARAO MeerKAT radio telescope, in a frequency band from 856 to 1712 MHz. We provide rotation measures (RM), dispersion measures, flux densities and polarization properties. The catalogue includes 254 new RMs that substantially increase the total number of known pulsar RMs. Our integration times typically span over 1000 individual rotations per source. We show that the radio (pseudo)luminosity has a strong, shallow dependence on the spin-down energy, proportional to $\dot{E}^{0.15\pm0.04}$, that contradicts some previous proposals of population synthesis studies. In addition, we find a significant correlation between the steepness of the observed flux density spectra and $\dot{E}$, and correlations of the fractional linear polarization with $\dot{E}$, the spectral index, and the pulse width, which we discuss in the context of what is known about pulsar radio emission and how pulsars evolve with time. On the whole, we do not see significant correlations with the estimated surface magnetic field strength, and the correlations with $\dot{E}$ are much stronger than those with the characteristic age. This finding lends support to the suggestion that magnetic dipole braking may not be the dominant factor for the evolution of pulsar rotation over the lifetimes of pulsars. A public data release of the high-fidelity time-averaged pulse profiles in full polarization accompanies our catalogue.

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arXiv2022

The LOFAR Tied-Array All-Sky Survey: Timing of 35 radio pulsars and an overview of the properties of the LOFAR pulsar discoveries

The LOFAR Tied-Array All-Sky Survey (LOTAAS) is the most sensitive untargeted radio pulsar survey performed at low radio frequencies (119--151\,MHz) to date and has discovered 76 new radio pulsars, among which the 23.5-s pulsar J0250+5854, up until recently the slowest-spinning radio pulsar known. Here, we report on the timing solutions of 35 pulsars discovered by LOTAAS, which include a nulling pulsar and a mildly recycled pulsar, and thereby complete the full timing analysis of the LOTAAS pulsar discoveries. We give an overview of the findings from the full LOTAAS sample of 76 pulsars, discussing their pulse profiles, radio spectra and timing parameters. We found that the pulse profiles of some of the pulsars show profile variations in time or frequency and while some pulsars show signs of scattering, a large majority display no pulse broadening. The LOTAAS discoveries have on average steeper radio spectra and have longer spin periods ($1.4\times$) as well as lower spin-down rates ($3.1\times$) compared to the known pulsar population. We discuss the cause of these differences, and attribute them to a combination of selection effects of the LOTAAS survey as well as previous pulsar surveys, though can not rule out that older pulsars tend to have steeper radio spectra.

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arXiv2022

The Scintillating Tail of Comet C/2020 F3 (Neowise)

Context. The occultation of a radio source by the plasma tail of a comet can be used to probe structure and dynamics in the tail. Such occultations are rare, and the occurrence of scintillation, due to small-scale density variations in the tail, remains somewhat controversial. Aims. A detailed observation taken with the Low-Frequency Array (LOFAR) of a serendipitous occultation of the compact radio source 3C196 by the plasma tail of comet C/2020 F3 (Neowise) is presented. 3C196 tracked almost perpendicularly behind the tail, providing a unique profile cut only a short distance downstream from the cometary nucleus itself. Methods. Interplanetary scintillation (IPS) is observed as the rapid variation of the intensity received of a compact radio source due to density variations in the solar wind. IPS in the signal received from 3C196 was observed for five hours, covering the full transit behind the plasma tail of comet C/2020 F3 (Neowise) on 16 July 2020, and allowing an assessment of the solar wind in which the comet and its tail are embedded. Results. The results reveal a sudden and strong enhancement in scintillation which is unequivocally attributable to the plasma tail. The strongest scintillation is associated with the tail boundaries, weaker scintillation is seen within the tail, and previously-unreported periodic variations in scintillation are noted, possibly associated with individual filaments of plasma. Furthermore, contributions from the solar wind and comet tail are separated to measure a sharp decrease in the velocity of material within the tail, suggesting a steep velocity shear resulting in strong turbulence along the tail boundary

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arXiv2022

Solar observations with single-dish INAF radio telescopes: continuum imaging in the 18-26 GHz range

We present a new solar radio imaging system implemented through the upgrade of the large single-dish telescopes of the Italian National Institute for Astrophysics (INAF), not originally conceived for solar observations. During the development and early science phase of the project (2018-2020), we obtained about 170 maps of the entire solar disk in the 18-26 GHz band, filling the observational gap in the field of solar imaging at these frequencies. These solar images have typical resolutions in the 0.7-2 arcmin range and a brightness temperature sensitivity <10 K. Accurate calibration adopting the Supernova Remnant Cas A as a flux reference, provided typical errors <3% for the estimation of the quiet-Sun level components and for active regions flux measurements. As a first early science result of the project, we present a catalog of radio continuum solar imaging observations with Medicina 32-m and SRT 64-m radio telescopes including the multi-wavelength identification of active regions, their brightness and spectral characterization. The interpretation of the observed emission as thermal bremsstrahlung components combined with gyro-magnetic variable emission pave the way to the use of our system for long-term monitoring of the Sun. We also discuss useful outcomes both for solar physics (e.g. study of the chromospheric network dynamics) and space weather applications (e.g. flare precursors studies).

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arXiv2022

Searching for pulsars associated with polarised point sources using LOFAR: Initial discoveries from the TULIPP project

Discovering radio pulsars, particularly millisecond pulsars (MSPs), is important for a range of astrophysical applications, such as testing theories of gravity or probing the magneto-ionic interstellar medium. We aim to discover pulsars that may have been missed in previous pulsar searches by leveraging known pulsar observables (primarily polarisation) in the sensitive, low-frequency radio images from the Low-Frequency Array (LOFAR) Two-metre Sky Survey (LoTSS), and have commenced the Targeted search, using LoTSS images, for polarised pulsars (TULIPP) survey. For this survey, we identified linearly and circularly polarised point sources with flux densities brighter than 2 mJy in LoTSS images at a centre frequency of 144 MHz with a 48 MHz bandwidth. Over 40 known pulsars, half of which are MSPs, were detected as polarised sources in the LoTSS images and excluded from the survey. We have obtained beam-formed LOFAR observations of 30 candidates, which were searched for pulsations using coherent de-dispersion. Here, we present the results of the first year of the TULIPP survey. We discovered two pulsars, PSRs J1049+5822 and J1602+3901, with rotational periods of P=0.73 s and 3.7 ms, respectively. We also detected a further five known pulsars (two slowly-rotating pulsars and three MSPs) for which accurate sky positions were not available to allow a unique cross-match with LoTSS sources. This targeted survey presents a relatively efficient method by which pulsars, particularly MSPs, may be discovered using the flexible observing modes of sensitive radio telescopes such as the Square Kilometre Array and its pathfinders/precursors, particularly since wide-area all-sky surveys using coherent de-dispersion are currently computationally infeasible.

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arXiv2021

A comparative analysis of pulse time-of-arrival creation methods

Extracting precise pulse times of arrival (TOAs) and their uncertainties is the first and most fundamental step in high-precision pulsar timing. In the classical method, TOAs are derived from total intensity pulse profiles of pulsars via cross-correlation with an idealised `1D' template of that profile. While a number of results have been presented in the literature relying on the ever increasing sensitivity of such pulsar timing experiments, there is no consensus on the most reliable methods for TOA creation and, more importantly, the associated TOA uncertainties for each scheme. In this article, we present a comprehensive comparison of TOA determination practices, focusing on the creation of timing templates, TOA determination methods and the most useful TOA bandwidth. The aim is both to present a possible approach towards TOA optimisation as well as the (partial) identification of an optimal TOA-creation scheme and the demonstration of optimisation differences between pulsars and data sets. We compare the values of data-derived template profiles as compared to analytic profiles and evaluate the three most commonly used template-matching methods. Finally, we study the relation between timing precision and TOA bandwidth to identify any potential breaks in that relationship. As a practical demonstration, we apply our selected methods to European Pulsar Timing Array data on the three test pulsars PSRs\ J0218+4232, J1713+0747 and J2145$-$0750.

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arXiv2021

Noise analysis in the European Pulsar Timing Array data release 2 and its implications on the gravitational-wave background search

The European Pulsar Timing Array (EPTA) collaboration has recently released an extended data set for six pulsars (DR2) and reported evidence for a common red noise signal. Here we present a noise analysis for each of the six pulsars. We consider several types of noise: (i) radio frequency independent, "achromatic", and time-correlated red noise; (ii) variations of dispersion measure and scattering; (iii) system and band noise; and (iv) deterministic signals (other than gravitational waves) that could be present in the PTA data. We perform Bayesian model selection to find the optimal combination of noise components for each pulsar. Using these custom models we revisit the presence of the common uncorrelated red noise signal previously reported in the EPTA DR2 and show that the data still supports it with a high statistical significance. Next, we confirm that there is no preference for or against the Hellings-Downs spatial correlations expected for the stochastic gravitational-wave background. The main conclusion of the EPTA DR2 paper remains unchanged despite a very significant change in the noise model of each pulsar. However, modelling the noise is essential for the robust detection of gravitational waves and its impact could be significant when analysing the next EPTA data release, which will include a larger number of pulsars and more precise measurements.

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arXiv2021

Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: Inferences in the stochastic gravitational-wave background search

We present results from the search for a stochastic gravitational-wave background (GWB) as predicted by the theory of General Relativity using six radio millisecond pulsars from the Data Release 2 (DR2) of the European Pulsar Timing Array (EPTA) covering a timespan up to 24 years. A GWB manifests itself as a long-term low-frequency stochastic signal common to all pulsars, a common red signal (CRS), with the characteristic Hellings-Downs (HD) spatial correlation. Our analysis is performed with two independent pipelines, \eprise{} and \tn{}+\ftwo{}, which produce consistent results. A search for a CRS with simultaneous estimation of its spatial correlations yields spectral properties compatible with theoretical GWB predictions, but does not result in the required measurement of the HD correlation, as required for GWB detection. Further Bayesian model comparison between different types of CRSs, including a GWB, finds the most favoured model to be the common uncorrelated red noise described by a power-law with $A = 5.13_{-2.73}^{+4.20} \times 10^{-15}$ and $γ= 3.78_{-0.59}^{+0.69}$ (95\% credible regions). Fixing the spectral index to $γ=13/3$ as expected from the GWB by circular, inspiralling supermassive black-hole binaries results in an amplitude of $A =2.95_{-0.72}^{+0.89} \times 10^{-15}$. We implement three different models, BAYESEPHEM, LINIMOSS and EPHEMGP, to address possible Solar-system ephemeris (SSE) systematics and conclude that our results may only marginally depend on these effects. This work builds on the methods and models from the studies on the EPTA DR1. We show that under the same analysis framework the results remain consistent after the data set extension.

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arXiv2021

The polarization of the drifting sub-pulses from PSR B1919+21

Aims. We aim to expand our understanding of radio wave emission and propagation in the pulsar magnetosphere by studying the polarization of drifting sub-pulses in highly sensitive observations of PSR~B1919+21 recorded at the Arecibo Observatory. Methods. We apply and compare several methods of analysis and visualization, including eigenvalue analysis of the longitude-resolved covariances between the Stokes parameters; longitude-resolved scatter plots of the normalised Stokes vectors in the Poincaré sphere; auto- and cross-correlations between the Stokes parameters as a function of offset in pulse longitude and lag in pulse number; and mean drift bands of polarization state, formed by averaging the Stokes parameters and quantities derived from them synchronously with the drifting sub-pulse modulation period. Results. We observe regions of pulse longitude where the superposition of orthogonally polarised modes is best described as incoherent and regions where the superposition appears to be at least partially coherent. Within the region of coherent superposition, over a range of pulse longitudes spanning $\sim 2\circ$, the distribution of the Stokes polarization vectors forms a torus centered near the origin of the Poincaré sphere. Furthermore, the polarization vectors rotate about the axis of revolution of the torus synchronously with the drifting sub-pulse modulation of the total intensity. Conclusions. The nearly uniform circular modulation of polarization state, clearly evident in both the toroidal distribution of the Stokes polarization vectors and the mean drift bands of the Stokes parameters, is not predicted by current theoretical models of pulsar emission. We propose different scenarios to explain the generation of the torus, based on either incoherent or phase-coherent superposition of orthogonally polarised modes.

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arXiv2021

Evidence of intra-binary shock emission from the redback pulsar PSR J1048+2339

We present simultaneous multiwavelength observations of the 4.66 ms redback pulsar PSR J1048+2339. We performed phase-resolved spectroscopy with the Very Large Telescope (VLT) searching for signatures of a residual accretion disk or intra-binary shock emission, constraining the companion radial velocity semi-amplitude ($K_2$), and estimating the neutron star mass ($M_{\rm NS}$). Using the FORS2-VLT intermediate-resolution spectra, we measured a companion velocity of $291 < K_2 < 348$ km s$^{-1}$ and a binary mass ratio of $0.209 < q < 0.250$. Combining our results for $K_2$ and $q$, we constrained the mass of the neutron star and the companion to $(1.0 < M_{\rm NS} < 1.6){\rm sin}^{-3}i\,M_{\odot}$ and $(0.24 < M_2 < 0.33){\rm sin}^{-3}i\,M_{\odot}$, respectively, where $i$ is the system inclination. The Doppler map of the H$α$ emission line exhibits a spot feature at the expected position of the companion star and an extended bright spot close to the inner Lagrangian point. We interpret this extended emission as the effect of an intra-binary shock originating from the interaction between the pulsar relativistic wind and the matter leaving the companion star. The mass loss from the secondary star could be either due to Roche-lobe overflow or to the ablation of its outer layer by the energetic pulsar wind. Contrastingly, we find no evidence for an accretion disk. We report on the results of the SRT and the LOFAR simultaneous radio observations at three different frequencies (150 MHz, 336 MHz, and 1400 MHz). No pulsed radio signal is found in our search. This is probably due to both scintillation and the presence of material expelled from the system which can cause the absorption of the radio signal at low frequencies. Finally, we report on an attempt to search for optical pulsations using IFI+Iqueye mounted at the 1.2 m Galileo telescope at the Asiago Observatory.

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arXiv2020

The impact of Solar wind variability on pulsar timing

High-precision pulsar timing requires accurate corrections for dispersive delays of radio waves, parametrized by the dispersion measure (DM), particularly if these delays are variable in time. In a previous paper we studied the Solar-wind (SW) models used in pulsar timing to mitigate the excess of DM annually induced by the SW, and found these to be insufficient for high-precision pulsar timing. Here we analyze additional pulsar datasets to further investigate which aspects of the SW models currently used in pulsar timing can be readily improved, and at what levels of timing precision SW mitigation is possible. Our goals are to verify: a) whether the data are better described by a spherical model of the SW with a time-variable amplitude rather than a time-invariant one as suggested in literature, b) whether a temporal trend of such a model's amplitudes can be detected. We use the pulsar-timing technique on low-frequency pulsar observations to estimate the DM and quantify how this value changes as the Earth moves around the Sun. Specifically, we monitor the DM in weekly to monthly observations of 14 pulsars taken with LOFAR across time spans of up to 6 years. We develop an informed algorithm to separate the interstellar variations in DM from those caused by the SW and demonstrate the functionality of this algorithm with extensive simulations. Assuming a spherically symmetric model for the SW density, we derive the amplitude of this model for each year of observations. We show that a spherical model with time-variable amplitude models the observations better than a spherical model with constant amplitude, but that both approaches leave significant SW induced delays uncorrected in a number of pulsars in the sample. The amplitude of the spherical model is found to be variable in time, as opposed to what has been previously suggested.

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arXiv2020

Dispersion measure variability for 36 millisecond pulsars at 150MHz with LOFAR

Radio pulses from pulsars are affected by plasma dispersion, which results in a frequency-dependent propagation delay. Variations in the magnitude of this effect lead to an additional source of red noise in pulsar timing experiments, including pulsar timing arrays that aim to detect nanohertz gravitational waves. We aim to quantify the time-variable dispersion with much improved precision and characterise the spectrum of these variations. We use the pulsar timing technique to obtain highly precise dispersion measure (DM) time series. Our dataset consists of observations of 36 millisecond pulsars, which were observed for up to 7.1 years with the LOFAR telescope at a centre frequency of ~150 MHz. Seventeen of these sources were observed with a weekly cadence, while the rest were observed at monthly cadence. We achieve a median DM precision of the order of 10^-5 cm^-3 pc for a significant fraction of our sources. We detect significant variations of the DM in all pulsars with a median DM uncertainty of less than 2x10^-4 cm^-3 pc. The noise contribution to pulsar timing experiments at higher frequencies is calculated to be at a level of 0.1-10 us at 1.4 GHz over a timespan of a few years, which is in many cases larger than the typical timing precision of 1 us or better that PTAs aim for. We found no evidence for a dependence of DM on radio frequency for any of the sources in our sample. The DM time series we obtained using LOFAR could in principle be used to correct higher-frequency data for the variations of the dispersive delay. However, there is currently the practical restriction that pulsars tend to provide either highly precise times of arrival (ToAs) at 1.4 GHz or a high DM precision at low frequencies, but not both, due to spectral properties. Combining the higher-frequency ToAs with those from LOFAR to measure the infinite-frequency ToA and DM would improve the result.

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arXiv2020

Measuring Interstellar Delays of PSR J0613-0200 over 7 years, using the Large European Array for Pulsars

Using data from the Large European Array for Pulsars (LEAP), and the Effelsberg telescope, we study the scintillation parameters of the millisecond pulsar J0613-0200 over a 7 year timespan. The "secondary spectrum" -- the 2D power spectrum of scintillation -- presents the scattered power as a function of time delay, and contains the relative velocities of the pulsar, observer, and scattering material. We detect a persistent parabolic scintillation arc, suggesting scattering is dominated by a thin, anisotropic region. The scattering is poorly described by a simple exponential tail, with excess power at high delays; we measure significant, detectable scattered power at times out to $\sim 5 μs$, and measure the bulk scattering delay to be between 50 to 200\,ns with particularly strong scattering throughout 2013. These delays are too small to detect a change of the pulse profile shape, yet they would change the times-of-arrival as measured through pulsar timing. The arc curvature varies annually, and is well fit by a one-dimensional scattering screen $\sim 40\%$ of the way towards the pulsar, with a changing orientation during the increased scattering in 2013. Effects of uncorrected scattering will introduce time delays correlated over time in individual pulsars, and may need to be considered in gravitational wave analyses. Pulsar timing programs would benefit from simultaneously recording in a way that scintillation can be resolved, in order to monitor the variable time delays caused by multipath propagation.

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arXiv2020

Pulsars with NenuFAR: backend and pipelines

NenuFAR (New extension in Nançay upgrading LoFAR) is a new radio telescope developed and built on the site of the Nançay Radio Observatory. It is designed to observe the largely unexplored frequency window from 10 to 85\,MHz, offering a high sensitivity across its full bandwidth. NenuFAR has started its "early science" operation in July 2019, with 58\% of its final collecting area being available. Pulsars are one of the major topics for the scientific exploitation of this frequency range and represent an important challenge in terms of instrumentation. Designing instrumentation at these frequencies is complicated by the need to compensate for the effects of both the interstellar medium and the ionosphere on the observed signal. Our real-time pipeline LUPPI (Low frequency Ultimate Pulsar Processing Instrumentation) is able to cope with a high data rate and to provide real-time coherent de-dispersion down to the lowest frequencies reached by NenuFAR (10\,MHz). The full backend functionality is described, as well as the main pulsar observing modes (folded, single-pulse, waveform, and dynamic spectrum). This instrumentation allowed us to detect 172 pulsars in our first targeted search below 85\,MHz, including 10 millisecond pulsars (6 of which detected for the first time below 100 MHz). We also present some of the "early science" results of NenuFAR on pulsars: a high frequency resolution mapping of PSR B1919$+$21's emission profile and a detailed observation of single-pulse sub-structures from PSR~B0809$+$74 down to 16\,MHz, the high rate of giant-pulse emission from the Crab pulsar detected at 68.7\,MHz (43 events/min), and the illustration of the very good timing performance of the instrumentation, allowing us to study dispersion measure variations in great detail.

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arXiv2020

The LOFAR Tied-Array All-Sky Survey: Timing of 21 pulsars including the first binary pulsar discovered with LOFAR

We report on the multi-frequency timing observations of 21 pulsars discovered in the LOFAR Tied-Array All-Sky Survey (LOTAAS). The timing data were taken at central frequencies of 149 MHz (LOFAR) as well as 334 and 1532 MHz (Lovell Telecope). The sample of pulsars includes 20 isolated pulsars and the first binary pulsar discovered by the survey, PSR J1658$+$3630. We modelled the timing properties of the pulsars, which showed that they have, on average, larger characteristic ages. We present the pulse profiles of the pulsars across the three observing bands, where PSR J1643$+$1338 showed profile evolution that appears not to be well-described by the radius-to-frequency-mapping model. Furthermore, we modelled the spectra of the pulsars across the same observing bands, using a simple power law, and found an average spectral index of $-1.9 \pm 0.5$. Amongst the pulsars studied here, PSR J1657$+$3304 showed large flux density variations of a factor of 10 over 300 days, as well as mode changing and nulling on timescales of a few minutes. We modelled the rotational and orbital properties of PSR J1658$+$3630, which has a spin period of 33 ms in a binary orbit of 3.0 days with a companion of minimum mass of 0.87$M_{\odot}$, likely a Carbon-Oxygen or Oxygen-Neon-Magnesium type white dwarf. PSR J1658$+$3630 has a dispersion measure of 3.0 pc cm$^{-3}$, making it possibly one of the closest binary pulsars known.

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arXiv2020

The High Time Resolution Universe Pulsar Survey -- XVI. Discovery and timing of 40 pulsars from the southern Galactic plane

We present the results of processing an additional 44% of the High Time Resolution Universe South Low Latitude (HTRU-S LowLat) pulsar survey, the most sensitive blind pulsar survey of the southern Galactic plane to date. Our partially-coherent segmented acceleration search pipeline is designed to enable the discovery of pulsars in short, highly-accelerated orbits, while our 72-min integration lengths will allow us to discover pulsars at the lower end of the pulsar luminosity distribution. We report the discovery of 40 pulsars, including three millisecond pulsar-white dwarf binary systems (PSRs J1537-5312, J1547-5709 and J1618-4624), a black-widow binary system (PSR J1745-23) and a candidate black-widow binary system (PSR J1727-2951), a glitching pulsar (PSR J1706-4434), an eclipsing binary pulsar with a 1.5-yr orbital period (PSR J1653-45), and a pair of long spin-period binary pulsars which display either nulling or intermittent behaviour (PSRs J1812-15 and J1831-04). We show that the total population of 100 pulsars discovered in the HTRU-S LowLat survey to date represents both an older and lower-luminosity population, and indicates that we have yet to reach the bottom of the luminosity distribution function. We present evaluations of the performance of our search technique and of the overall yield of the survey, considering the 94% of the survey which we have processed to date. We show that our pulsar yield falls below earlier predictions by approximately 25% (especially in the case of millisecond pulsars), and discuss explanations for this discrepancy as well as future adaptations in RFI mitigation and searching techniques which may address these shortfalls.

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arXiv2019

The International Pulsar Timing Array: Second data release

In this paper, we describe the International Pulsar Timing Array second data release, which includes recent pulsar timing data obtained by three regional consortia: the European Pulsar Timing Array, the North American Nanohertz Observatory for Gravitational Waves, and the Parkes Pulsar Timing Array. We analyse and where possible combine high-precision timing data for 65 millisecond pulsars which are regularly observed by these groups. A basic noise analysis, including the processes which are both correlated and uncorrelated in time, provides noise models and timing ephemerides for the pulsars. We find that the timing precisions of pulsars are generally improved compared to the previous data release, mainly due to the addition of new data in the combination. The main purpose of this work is to create the most up-to-date IPTA data release. These data are publicly available for searches for low-frequency gravitational waves and other pulsar science.

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arXiv2019

On the usefulness of existing Solar-wind models for pulsar timing corrections

Dispersive delays due to the Solar wind introduce excess noise in high-precision pulsar timing experiments, and must be removed in order to achieve the accuracy needed to detect, e.g., low-frequency gravitational waves. In current pulsar timing experiments, this delay is usually removed by approximating the electron density distribution in the Solar wind either as spherically symmetric, or with a two-phase model that describes the contributions from both high- and low-speed phases of the Solar wind. However, no dataset has previously been available to test the performance and limitations of these models over extended timescales and with sufficient sensitivity. Here we present the results of such a test with an optimal dataset of observations of pulsar J0034-0534, taken with the German stations of LOFAR. We conclude that the spherical approximation performs systematically better than the two-phase model at almost all angular distances, with a residual root-mean-square (rms) given by the two-phase model being up to 28% larger than the result obtained with the spherical approximation. Nevertheless, the spherical approximation remains insufficiently accurate in modelling the Solar-wind delay (especially within 20 degrees of angular distance from the Sun), as it leaves timing residuals with rms values that reach the equivalent of 0.3 microseconds at 1400 MHz. This is because a spherical model ignores the large daily variations in electron density observed in the Solar wind. In the short term, broadband observations or simultaneous observations at low frequencies are the most promising way forward to correct for Solar-wind induced delay variations.

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