Search

The interstellar medium of the Milky Way contains turbulent plasma with structures driven by energetic processes that fuel star formation and shape the evolution of our Galaxy. Radio waves from pulsars are scattered off the small (au-scale and below) structures, resulting in frequency-dependent interference patterns that are modulated in time because of the relative motions of the pulsar, Earth, and plasma. Power spectral analyses of these patterns show parabolic arcs with curvatures that encode the locations and kinematics of individual structures. Here we report the discovery of at least 25 distinct plasma structures in the direction of the brilliant millisecond pulsar, PSR J0437$-$4715, in observations obtained with the MeerKAT radio telescope. Four arcs reveal structures within 5000 au of the pulsar, from a series of shocks induced as the pulsar and its wind interact with the ambient insterstellar medium. The measured radial distance and velocity of the main shock allows us to solve the shock geometry and space velocity of the pulsar in three dimensions, while the velocity of another structure unexpectedly indicates a back flow from the direction of the shock or pulsar-wind tail. The remaining 21 arcs represent a surprising abundance of structures sustained by turbulence within the Local Bubble -- a region of the interstellar medium thought to be depleted of gas by a series of supernova explosions about 14 Myr ago., Comment: 46 pages, 10 figures, 1 table, submitted to Nature Astronomy

We report Bayesian inference of the mass, radius and hot X-ray emitting region properties - using data from the Neutron Star Interior Composition ExploreR (NICER) - for the brightest rotation-powered millisecond X-ray pulsar PSR J0437$\unicode{x2013}$4715. Our modeling is conditional on informative tight priors on mass, distance and binary inclination obtained from radio pulsar timing using the Parkes Pulsar Timing Array (PPTA) (Reardon et al. 2024), and we use NICER background models to constrain the non-source background, cross-checking with data from XMM-Newton. We assume two distinct hot emitting regions, and various parameterized hot region geometries that are defined in terms of overlapping circles; while simplified, these capture many of the possibilities suggested by detailed modeling of return current heating. For the preferred model identified by our analysis we infer a mass of $M = 1.418 \pm 0.037$ M$_\odot$ (largely informed by the PPTA mass prior) and an equatorial radius of $R = 11.36^{+0.95}_{-0.63}$ km, each reported as the posterior credible interval bounded by the 16% and 84% quantiles. This radius favors softer dense matter equations of state and is highly consistent with constraints derived from gravitational wave measurements of neutron star binary mergers. The hot regions are inferred to be non-antipodal, and hence inconsistent with a pure centered dipole magnetic field., Comment: 27 pages, 16 figures, + appendices. Accepted in ApJL. Data files and reproduction package available in Zenodo

The observation of neutron stars enables the otherwise impossible study of fundamental physical processes. The timing of binary radio pulsars is particularly powerful, as it enables precise characterization of their (three-dimensional) positions and orbits. PSR~J0437$-$4715 is an important millisecond pulsar for timing array experiments and is also a primary target for the Neutron Star Interior Composition Explorer (NICER). The main aim of the NICER mission is to constrain the neutron star equation of state by inferring the compactness ($M_p/R$) of the star. Direct measurements of the mass $M_p$ from pulsar timing therefore substantially improve constraints on the radius $R$ and the equation of state. Here we use observations spanning 26 years from Murriyang, the 64-m Parkes radio telescope, to improve the timing model for this pulsar. Among the new precise measurements are the pulsar mass $M_p=1.418\pm 0.044$ $M_{\odot}$, distance $D=156.96 \pm 0.11$ pc, and orbital inclination angle $i=137.506 \pm 0.016^\circ$, which can be used to inform the X-ray pulse profile models inferred from NICER observations. We demonstrate that these results are consistent between multiple data sets from the Parkes Pulsar Timing Array (PPTA), each modeled with different noise assumptions. Using the longest available PPTA data set, we measure an apparent second derivative of the pulsar spin frequency and discuss how this can be explained either by kinematic effects due to the proper motion and radial velocity of the pulsar or excess low-frequency noise such as a gravitational-wave background., Comment: 13 pages, 3 figures, accepted for publication in Astrophysical Journal Letters

The stability of the spin of pulsars and the precision with which these spins can be determined, allows many unique tests of interest to physics and astrophysics. Perhaps the most challenging and revolutionary of these, is the detection of nanohertz gravitational waves. An increasing number of efforts to detect and study long-period gravitational waves by timing an array of pulsars have been ongoing for several decades and the field is moving ever closer to actual gravitational-wave science. In this review article, we summarise the state of this field by presenting the current sensitivity to gravitational waves and by reviewing recent progress along the multiple lines of research that are part of the continuous push towards greater sensitivity. We also briefly review some of the most recent efforts at astrophysical interpretation of the most recent GW estimates derived from pulsar timing., Comment: 37 pages, 4 figures, 4 tables. Accepted for publication in "Results in Physics" special issue

It is currently unknown how matter behaves at the extreme densities found within the cores of neutron stars. Measurements of the neutron star equation of state probe nuclear physics that is otherwise inaccessible in a laboratory setting. Gravitational waves from binary neutron star mergers encode details about this physics, allowing the equation of state to be inferred. Planned third-generation gravitational-wave observatories, having vastly improved sensitivity, are expected to provide tight constraints on the neutron star equation of state. We combine simulated observations of binary neutron star mergers by the third-generation observatories Cosmic Explorer and Einstein Telescope to determine future constraints on the equation of state across a plausible neutron star mass range. In one year of operation, a network consisting of one Cosmic Explorer and the Einstein Telescope is expected to detect $\gtrsim 3\times 10^5$ binary neutron star mergers. By considering only the 75 loudest events, we show that such a network will be able to constrain the neutron star radius to at least $\lesssim 200$ m (90% credibility) in the mass range $1-1.97$ $M_{\odot}$ -- about ten times better than current constraints from LIGO-Virgo-KAGRA and NICER. The constraint is $\lesssim 75$ m (90% credibility) near $1.4-1.6$ $M_{\odot}$ where we assume the the binary neutron star mass distribution is peaked. This constraint is driven primarily from the loudest $\sim 20$ events., Comment: 6 pages, 3 figures. Submitted to Physical Review Letters

The noise in millisecond pulsar (MSP) timing data can include contributions from observing instruments, the interstellar medium, the solar wind, solar system ephemeris errors, and the pulsars themselves. The noise environment must be accurately characterized in order to form the null hypothesis from which signal models can be compared, including the signature induced by nanohertz-frequency gravitational waves (GWs). Here we describe the noise models developed for each of the MSPs in the Parkes Pulsar Timing Array (PPTA) third data release, which have been used as the basis of a search for the isotropic stochastic GW background. We model pulsar spin noise, dispersion measure variations, scattering variations, events in the pulsar magnetospheres, solar wind variability, and instrumental effects. We also search for new timing model parameters and detected Shapiro delays in PSR~J0614$-$3329 and PSR~J1902$-$5105. The noise and timing models are validated by testing the normalized and whitened timing residuals for Gaussianity and residual correlations with time. We demonstrate that the choice of noise models significantly affects the inferred properties of a common-spectrum process. Using our detailed models, the recovered common-spectrum noise in the PPTA is consistent with a power law with a spectral index of $\gamma=13/3$, the value predicted for a stochastic GW background from a population of supermassive black hole binaries driven solely by GW emission., Comment: 18 pages, 10 figures. Accepted for publication in ApJL

We present the third data release from the Parkes Pulsar Timing Array (PPTA) project. The release contains observations of 32 pulsars obtained using the 64-m Parkes "Murriyang" radio telescope. The data span is up to 18 years with a typical cadence of 3 weeks. This data release is formed by combining an updated version of our second data release with $\sim 3$ years of more recent data primarily obtained using an ultra-wide-bandwidth receiver system that operates between 704 and 4032 MHz. We provide calibrated pulse profiles, flux-density dynamic spectra, pulse times of arrival, and initial pulsar timing models. We describe methods for processing such wide-bandwidth observations, and compare this data release with our previous release., Comment: 15 pages, 6 figures. Accepted for publication in PASA

Pulsar timing arrays aim to detect nanohertz-frequency gravitational waves (GWs). A background of GWs modulates pulsar arrival times and manifests as a stochastic process, common to all pulsars, with a signature spatial correlation. Here we describe a search for an isotropic stochastic gravitational-wave background (GWB) using observations of 30 millisecond pulsars from the third data release of the Parkes Pulsar Timing Array (PPTA), which spans 18 years. Using current Bayesian inference techniques we recover and characterize a common-spectrum noise process. Represented as a strain spectrum $h_c = A(f/1 {\rm yr}^{-1})^{\alpha}$, we measure $A=3.1^{+1.3}_{-0.9} \times 10^{-15}$ and $\alpha=-0.45 \pm 0.20$ respectively (median and 68% credible interval). For a spectral index of $\alpha=-2/3$, corresponding to an isotropic background of GWs radiated by inspiraling supermassive black hole binaries, we recover an amplitude of $A=2.04^{+0.25}_{-0.22} \times 10^{-15}$. However, we demonstrate that the apparent signal strength is time-dependent, as the first half of our data set can be used to place an upper limit on $A$ that is in tension with the inferred common-spectrum amplitude using the complete data set. We search for spatial correlations in the observations by hierarchically analyzing individual pulsar pairs, which also allows for significance validation through randomizing pulsar positions on the sky. For a process with $\alpha=-2/3$, we measure spatial correlations consistent with a GWB, with an estimated false-alarm probability of $p \lesssim 0.02$ (approx. $2\sigma$). The long timing baselines of the PPTA and the access to southern pulsars will continue to play an important role in the International Pulsar Timing Array., Comment: 19 pages, 10 figures, Accepted for publication in ApJL

The recent observation of a common red-noise process in pulsar timing arrays (PTAs) suggests that the detection of nanohertz gravitational waves might be around the corner. However, in order to confidently attribute this red process to gravitational waves, one must observe the Hellings-Downs curve -- the telltale angular correlation function associated with a gravitational-wave background. This effort is complicated by the complex modelling of pulsar noise. Without proper care, mis-specified noise models can lead to false-positive detections. Background estimation using bootstrap methods such as sky scrambles and phase shifts, which use the data to characterize the noise, are therefore important tools for assessing significance. We investigate the ability of current PTA experiments to estimate their background with "quasi-independent" scrambles -- characterized by a statistical "match" below the fiducial value: $|M|<0.1$. We show that sky scrambling is affected by "saturation" after $O(10)$ quasi-independent realizations; subsequent scrambles are no longer quasi-independent. We show phase scrambling saturates after $O(100)$ quasi-independent realizations. With so few independent scrambles, it is difficult to make reliable statements about the $\gtrsim 5 \sigma$ tail of the null distribution of the detection statistic. We discuss various methods by which one may increase the number of independent scrambles. We also consider an alternative approach wherein one re-frames the background estimation problem so that the significance is calculated using statistically dependent scrambles. The resulting $p$-value is in principle well-defined but may be susceptible to failure if assumptions about the data are incorrect., Comment: Paper accepted for publication on ApJ on the 7th of August 2023

Precision pulsar timing is integral to the detection of the nanohertz stochastic gravitational-wave background as well as understanding the physics of neutron stars. Conventional pulsar timing often uses fixed time and frequency-averaged templates to determine the pulse times of arrival, which can lead to reduced accuracy when the pulse profile evolves over time. We illustrate a dynamic timing method that fits each observing epoch using basis functions. By fitting each epoch separately, we allow for the evolution of the pulse shape epoch to epoch. We apply our method to PSR J1103$-$5403 and demonstrate that it undergoes mode changing, making it the fourth millisecond pulsar to exhibit such behaviour. Our method, which is able to identify and time a single mode, yields a timing solution with a root-mean-square error of 1.343 $\mu \mathrm{s}$, a factor of 1.78 improvement over template fitting on both modes. In addition, the white-noise amplitude is reduced 4.3 times, suggesting that fitting the full data set causes the mode changing to be incorrectly classified as white noise. This reduction in white noise boosts the signal-to-noise ratio of a gravitational-wave background signal for this particular pulsar by 32%. We discuss the possible applications for this method of timing to study pulsar magnetospheres and further improve the sensitivity of searches for nanohertz gravitational waves., Comment: Accepted in MNRAS, 8 pages, 8 figures

Density fluctuations in the ionised interstellar medium have a profound effect on radio pulsar observations, through angular scattering, intensity scintillations, and small changes in time delays from dispersion. Here we show that it is possible to recover the variations in dispersive delays that originate from a dominant scattering region using measurements of the dynamic spectrum of intensity scintillations, provided that the pulsar velocity and scattering region location are known. We provide a theoretical framework for the technique, which involves estimating the phase gradient from the dynamic spectra and integrating that gradient to obtain phase variations. It can be used to search for "extreme scattering events" (ESEs) in pulsars for which precision dispersion delay measurements are not otherwise possible, or to separate true dispersion variations from apparent variability caused by frequency-dependent pulse shape changes. We demonstrate that it works in practice by recovering an ESE in PSR J1603$-$7202, which is known from precision dispersion delay measurements from pulsar timing. For this pulsar, we find that the phase gradients also track the long-term variations in electron column density observed by pulsar timing, indicating that the column density variations and the scattering are dominated by the same thin scattering screen. We identify a sudden increase in the scintillation strength and magnitude of phase gradients over $\sim$days in 2010, indicating a compact structure. A decrease in the electron density in 2012 was associated with persistent phase gradients and preceded a period of decreased scintillation strength and an absence of scintillation arcs., Comment: 9 pages, 7 figures, Accepted for publication in MNRAS

We present the first 2.5 years of data from the MeerKAT Pulsar Timing Array (MPTA), part of MeerTime, a MeerKAT Large Survey Project. The MPTA aims to precisely measure pulse arrival times from an ensemble of 88 pulsars visible from the Southern Hemisphere, with the goal of contributing to the search, detection and study of nanohertz-frequency gravitational waves as part of the International Pulsar Timing Array. This project makes use of the MeerKAT telescope, and operates with a typical observing cadence of two weeks using the L-band receiver that records data from 856-1712 MHz. We provide a comprehensive description of the observing system, software, and pipelines used and developed for the MeerTime project. The data products made available as part of this data release are from the 78 pulsars that had at least $30$ observations between the start of the MeerTime programme in February 2019 and October 2021. These include both sub-banded and band-averaged arrival times, as well as the initial timing ephemerides, noise models, and the frequency-dependent standard templates (portraits) used to derive pulse arrival times. After accounting for detected noise processes in the data, the frequency-averaged residuals of $67$ of the pulsars achieved a root-mean-square residual precision of $< 1 \mu \rm{s}$. We also present a novel recovery of the clock correction waveform solely from pulsar timing residuals, and an exploration into preliminary findings of interest to the international pulsar timing community. The arrival times, standards and full Stokes parameter calibrated pulsar timing archives are publicly available., Comment: 18 pages, 6 figures

Precision timing of millisecond pulsars in binary systems enables observers to detect the relativistic Shapiro delay induced by space time curvature. When favourably aligned, this enables constraints to be placed on the component masses and system orientation. Here we present the results of timing campaigns on seven binary millisecond pulsars observed with the 64-antenna MeerKAT radio telescope that show evidence of Shapiro delay: PSRs~J0101$-$6422, J1101$-$6424, J1125$-$6014, J1514$-$4946, J1614$-$2230, J1732$-$5049, and J1909$-$3744. Evidence for Shapiro delay was found in all of the systems, and for three the orientations and data quality enabled strong constraints on their orbital inclinations and component masses. For PSRs~J1125$-$6014, J1614$-$2230 and J1909$-$3744, we determined pulsar masses to be $M_{\rm p} = 1.68\pm 0.17 \, {\rm M_{\odot}} $, $1.94\pm 0.03 \, {\rm M_{\odot}} $ and $1.45 \pm 0.03 \, {\rm M_{\odot}}$, and companion masses to be $M_{\rm c} = 0.33\pm 0.02 \, {\rm M_{\odot}} $, $0.495\pm 0.005 \, {\rm M_{\odot}} $ and $0.205 \pm 0.003 \, {\rm M_{\odot}}$, respectively. This provides the first independent confirmation of PSR~J1614$-$2230's mass, one of the highest known. The Shapiro delays measured for PSRs~J0101$-$6422, J1101$-$6424, J1514$-$4946, and J1732$-$5049 were only weak, and could not provide interesting component mass limits. Despite a large number of millisecond pulsars being routinely timed, relatively few have accurate masses via Shapiro delays. We use simulations to show that this is expected, and provide a formula for observers to assess how accurately a pulsar mass can be determined. We also discuss the observed correlation between pulsar companion masses and spin period, and the anti-correlation between recycled pulsar mass and their companion masses., Comment: 19 pages, 8 figures

In 2018 an ultra-wide-bandwidth low-frequency (UWL) receiver was installed on the 64-m Parkes Radio Telescope enabling observations with an instantaneous frequency coverage from 704 to 4032 MHz. Here, we present the analysis of a three-year data set of 35 millisecond pulsars observed with the UWL by the Parkes Pulsar Timing Array (PPTA), using wideband timing methods. The two key differences compared to typical narrow-band methods are, firstly, generation of two-dimensional templates accounting for pulse shape evolution with frequency and, secondly, simultaneous measurements of the pulse time-of-arrival (ToA) and dispersion measure (DM). This is the first time that wideband timing has been applied to a uniform data set collected with a single large-fractional bandwidth receiver, for which such techniques were originally developed. As a result of our study, we present a set of profile evolution models and new timing solutions including initial noise analysis. Precision of our ToA and DM measurements is in the range of 0.005 $-$ 2.08 $\mu$s and (0.043$-$14.24)$\times10^{-4}$ cm$^{-3}$ pc, respectively, with 94% of the pulsars achieving a median ToA uncertainty of less than 1 $\mu$s., Comment: 29 pages, 12 figures, Accepted for publication in ApJ

Pulsar timing array experiments have recently reported strong evidence for a common-spectrum stochastic process with a strain spectral index consistent with that expected of a nanohertz-frequency gravitational-wave background, but with negligible yet non-zero evidence for spatial correlations required for a definitive detection. However, it was pointed out by the Parkes Pulsar Timing Array (PPTA) collaboration that the same models used in recent analyses resulted in strong evidence for a common-spectrum process in simulations where none is present. In this work, we introduce a methodology to distinguish pulsar power spectra with the same amplitude from noise power spectra of similar but distinct amplitudes. The former is the signature of a spatially uncorrelated pulsar term of a nanohertz gravitational-wave background, whereas the latter could represent ensemble pulsar noise properties. We test the methodology on simulated data sets. We find that the reported common process in PPTA pulsars is indeed consistent with the spectral feature of a pulsar term. We recommend this methodology as one of the validity tests that the real astrophysical and cosmological backgrounds should pass, as well as for inferences about the spatially uncorrelated component of the background., Comment: 9 pages, 2 figures

We model long-term variations in the scintillation of binary pulsar PSR J1603$-$7202, observed by the 64 m Parkes radio telescope (Murriyang) between 2004 and 2016. We find that the time variation in the scintillation arc curvature is well-modelled by scattering from an anisotropic thin screen of plasma between the Earth and the pulsar. Using our scintillation model, we measure the inclination angle and longitude of ascending node of the orbit, yielding a significant improvement over the constraints from pulsar timing. From our measurement of the inclination angle, we place a lower bound on the mass of J1603$-$7202's companion of $\gtrsim 0.5\,\text{M}_\odot$ assuming a pulsar mass of $\gtrsim1.2\,\text{M}_\odot$. We find that the scintillation arcs are most pronounced when the electron column density along the line of sight is increased, and that arcs are present during a known extreme scattering event. We measure the distance to the interstellar plasma and its velocity, and we discuss some structures seen in individual scintillation arcs within the context of our model., Comment: 18 pages, 13 figures, 3 tables, accepted for publication in ApJ

The nature of dark matter remains obscure in spite of decades of experimental efforts. The mass of dark matter candidates can span a wide range, and its coupling with the Standard Model sector remains uncertain. All these unknowns make the etection of dark matter extremely challenging. Ultralight dark matter, with $m \sim10^{-22}$ eV, is proposed to reconcile the disagreements between observations and predictions from simulations of small-scale structures in the cold dark matter paradigm, while remaining consistent with other observations. Because of its large de Broglie wavelength and large local occupation number within galaxies, ultralight dark matter behaves like a coherently oscillating background field with an oscillating frequency dependent on its mass. If the dark matter particle is a spin-1 dark photon, such as the $U(1)_B$ or $U(1)_{B-L}$ gauge boson, it can induce an external oscillating force and lead to displacements of test masses. Such an effect would be observable in the form of periodic variations in the arrival times of radio pulses from highly stable millisecond pulsars. In this study, we search for evidence of ultralight dark photon dark matter (DPDM) using 14-year high-precision observations of 26 pulsars collected with the Parkes Pulsar Timing Array. While no statistically significant signal is found, we place constraints on coupling constants for the $U(1)_B$ and $U(1)_{B-L}$ DPDM. Compared with other experiments, the limits on the dimensionless coupling constant $\epsilon$ achieved in our study are improved by up to two orders of magnitude when the dark photon mass is smaller than $3\times10^{-22}$~eV ($10^{-22}$~eV) for the $U(1)_{B}$ ($U(1)_{B-L}$) scenario., Comment: 12 pages, 4 figures

We present baseband radio observations of the millisecond pulsar J1909$-$3744, the most precisely timed pulsar, using the MeerKAT telescope as part of the MeerTime pulsar timing array campaign. During a particularly bright scintillation event the pulsar showed strong evidence of pulse mode changing, among the first millisecond pulsars and the shortest duty cycle millisecond pulsar to do so. Two modes appear to be present, with the weak (lower signal-to-noise ratio) mode arriving $9.26$ $\pm 3.94$ $\mu$s earlier than the strong counterpart. Further, we present a new value of the jitter noise for this pulsar of $8.20 \pm 0.14$ ns in one hour, finding it to be consistent with previous measurements taken with the MeerKAT ($9 \pm 3$ ns) and Parkes ($8.6 \pm 0.8$ ns) telescopes, but inconsistent with the previously most precise measurement taken with the Green Bank telescope ($14 \pm 0.5$ ns). Timing analysis on the individual modes is carried out for this pulsar, and we find an approximate $10\%$ improvement in the timing precision is achievable through timing the strong mode only as opposed to the full sample of pulses. By forming a model of the average pulse from templates of the two modes, we time them simultaneously and demonstrate that this timing improvement can also be achieved in regular timing observations. We discuss the impact an improvement of this degree on this pulsar would have on searches for the stochastic gravitational wave background, as well as the impact of a similar improvement on all MeerTime PTA pulsars.

A cosmological first-order phase transition is expected to produce a stochastic gravitational wave background. If the phase transition temperature is on the MeV scale, the power spectrum of the induced stochastic gravitational waves peaks around nanohertz frequencies, and can thus be probed with high-precision pulsar timing observations. We search for such a stochastic gravitational wave background with the latest data set of the Parkes Pulsar Timing Array. We find no evidence for a Hellings-Downs spatial correlation as expected for a stochastic gravitational wave background. Therefore, we present constraints on first-order phase transition model parameters. Our analysis shows that pulsar timing is particularly sensitive to the low-temperature ($T \sim 1 - 100$ MeV) phase transition with a duration $(\beta/H_*)^{-1}\sim 10^{-2}-10^{-1}$ and therefore can be used to constrain the dark and QCD phase transitions., Comment: 9 pages, 4 figures, 2 tables

Intensity scintillations of radio pulsars are known to originate from interference between waves scattered by the electron density irregularities of interstellar plasma, often leading to parabolic arcs in the two-dimensional power spectrum of the recorded dynamic spectrum. The degree of arc curvature depends on the distance to the scattering plasma and its transverse velocity with respect to the line-of-sight. We report the observation of annual and orbital variations in the curvature of scintillation arcs over a period of 16 years for the bright millisecond pulsar, PSR J0437-4715. These variations are the signature of the relative transverse motions of the Earth, pulsar, and scattering medium, which we model to obtain precise measurements of parameters of the pulsar's binary orbit and the scattering medium itself. We observe two clear scintillation arcs in most of our $>$5000 observations and we show that they originate from scattering by thin screens located at distances $D_1 = 89.8 \pm 0.4$ pc and $D_2 = 124 \pm 3$ pc from Earth. The best-fit scattering model we derive for the brightest arc yields the pulsar's orbital inclination angle $i = 137.1 \pm 0.3^\circ$, and longitude of ascending node, $\Omega=206.3\pm0.4^\circ$. Using scintillation arcs for precise astrometry and orbital dynamics can be superior to modelling variations in the diffractive scintillation timescale, because the arc curvature is independent of variations in the level of turbulence of interstellar plasma. This technique can be used in combination with pulsar timing to determine the full three-dimensional orbital geometries of binary pulsars, and provides parameters essential for testing theories of gravity and constraining neutron star masses., Comment: 19 pages, 10 figures. Accepted for publication in ApJ

It is widely accepted that dark matter contributes about a quarter of the critical mass-energy density in our Universe. The nature of dark matter is currently unknown, with the mass of possible constituents spanning nearly one hundred orders of magnitude. The ultralight scalar field dark matter, consisting of extremely light bosons with $m \sim 10^{-22}$ eV and often called "fuzzy" dark matter, provides intriguing solutions to some challenges at sub-Galactic scales for the standard cold dark matter model. As shown by Khmelnitsky and Rubakov, such a scalar field in the Galaxy would produce an oscillating gravitational potential with nanohertz frequencies, resulting in periodic variations in the times of arrival of radio pulses from pulsars. The Parkes Pulsar Timing Array (PPTA) has been monitoring 20 millisecond pulsars at two to three weeks intervals for more than a decade. In addition to the detection of nanohertz gravitational waves, PPTA offers the opportunity for direct searches for fuzzy dark matter in an astrophysically feasible range of masses. We analyze the latest PPTA data set which includes timing observations for 26 pulsars made between 2004 and 2016. We perform a search in this data set for evidence of ultralight dark matter in the Galaxy using Bayesian and Frequentist methods. No statistically significant detection has been made. We therefore place upper limits on the local dark matter density. Our limits, improving on previous searches by a factor of two to five, constrain the dark matter density of ultralight bosons with $m \leq 10^{-23}$ eV to be below $6\,\text{GeV}\,\text{cm}^{-3}$ with 95\% confidence in the Earth neighborhood. Finally, we discuss the prospect of probing the astrophysically favored mass range $m \gtrsim 10^{-22}$ eV with next-generation pulsar timing facilities., Comment: Fixed a typo in Fig. 5; Published in Phys. Rev. D as Editor's Suggestion article, 17 pages, 7 figures, 4 tables

Quantum fluctuations of the gravitational field in the early Universe, amplified by inflation, produce a primordial gravitational-wave background across a broad frequency band. We derive constraints on the spectrum of this gravitational radiation, and hence on theories of the early Universe, by combining experiments that cover 29 orders of magnitude in frequency. These include Planck observations of cosmic microwave background temperature and polarization power spectra and lensing, together with baryon acoustic oscillations and big bang nucleosynthesis measurements, as well as new pulsar timing array and ground-based interferometer limits. While individual experiments constrain the gravitational-wave energy density in specific frequency bands, the combination of experiments allows us to constrain cosmological parameters, including the inflationary spectral index, $n_t$, and the tensor-to-scalar ratio, $r$. Results from individual experiments include the most stringent nanohertz limit of the primordial background to date from the Parkes Pulsar Timing Array, $\Omega_{\rm gw}(f)<2.3\times10^{-10}$. Observations of the cosmic microwave background alone limit the gravitational-wave spectral index at 95\% confidence to $n_t\lesssim5$ for a tensor-to-scalar ratio of $r = 0.11$. However, the combination of all the above experiments limits $n_t<0.36$. Future Advanced LIGO observations are expected to further constrain $n_t<0.34$ by 2020. When cosmic microwave background experiments detect a non-zero $r$, our results will imply even more stringent constraints on $n_t$ and hence theories of the early Universe., Comment: accepted for publication in Physical Review X