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Register a new userHigh signal-to-noise ratio observations and the ultimate limits of precision pulsar timing
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We demonstrate that the sensitivity of high-precision pulsar timing experiments will be ultimately limited by the broadband intensity modulation that is intrinsic to the pulsars stochastic radio signal. That is, as the peak flux of the pulsar approaches that of the system equivalent flux density, neither greater antenna gain nor increased instrumental bandwidth will improve timing precision. These conclusions proceed from an analysis of the covariance matrix used to characterise residual pulse profile fluctuations following the template matching procedure for arrival time estimation. We perform such an analysis on 25 hours of high-precision timing observations of the closest and brightest millisecond pulsar, PSR J0437-4715. In these data, the standard deviation of the post-fit arrival time residuals is approximately four times greater than that predicted by considering the system equivalent flux density, mean pulsar flux and the effective width of the pulsed emission. We develop a technique based on principal component analysis to mitigate the effects of shape variations on arrival time estimation and demonstrate its validity using a number of illustrative simulations. When applied to our observations, the method reduces arrival time residual noise by approximately 20%. We conclude that, owing primarily to the intrinsic variability of the radio emission from PSR J0437-4715 at 20 cm, timing precision in this observing band better than 30 - 40 ns in one hour is highly unlikely, regardless of future improvements in antenna gain or instrumental bandwidth. We describe the intrinsic variability of the pulsar signal as stochastic wideband impulse modulated self-noise (SWIMS) and argue that SWIMS will likely limit the timing precision of every millisecond pulsar currently observed by Pulsar Timing Array projects as larger and more sensitive antennae are built in the coming decades.
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Signals from radio pulsars show a wavelength-dependent delay due to dispersion in the interstellar plasma. At a typical observing wavelength, this delay can vary by tens of microseconds on five-year time scales, far in excess of signals of interest to pulsar timing arrays, such as that induced by a gravitational-wave background. Measurement of these delay variations is not only crucial for the detection of such signals, but also provides an unparallelled measurement of the turbulent interstellar plasma at au scales. In this paper we demonstrate that without consideration of wavelength- independent red-noise, simple algorithms to correct for interstellar dispersion can attenuate signals of interest to pulsar timing arrays. We present a robust method for this correction, which we validate through simulations, and apply it to observations from the Parkes Pulsar Timing Array. Correction for dispersion variations comes at a cost of increased band-limited white noise. We discuss scheduling to minimise this additional noise, and factors, such as scintillation, that can exacerbate the problem. Comparison with scintillation measurements confirms previous results that the spectral exponent of electron density variations in the interstellar medium often appears steeper than expected. We also find a discrete change in dispersion measure of PSR J1603-7202 of ~2x10^{-3} cm^{-3}pc for about 250 days. We speculate that this has a similar origin to the extreme scattering events seen in other sources. In addition, we find that four pulsars show a wavelength-dependent annual variation, indicating a persistent gradient of electron density on an au spatial scale, which has not been reported previously.
Pulsar timing array projects measure the pulse arrival times of millisecond pulsars for the primary purpose of detecting nanohertz-frequency gravitational waves. The measurements include contributions from a number of astrophysical and instrumental processes, which can either be deterministic or stochastic. It is necessary to develop robust statistical and physical models for these noise processes because incorrect models diminish sensitivity and may cause a spurious gravitational wave detection. Here we characterise noise processes for the 26 pulsars in the second data release of the Parkes Pulsar Timing Array using Bayesian inference. In addition to well-studied noise sources found previously in pulsar timing array data sets such as achromatic timing noise and dispersion measure variations, we identify new noise sources including time-correlated chromatic noise that we attribute to variations in pulse scattering. We also identify exponential dip events in four pulsars, which we attribute to magnetospheric effects as evidenced by pulse profile shape changes observed for three of the pulsars. This includes an event in PSR J1713$+$0747, which had previously been attributed to interstellar propagation. We present noise models to be used in searches for gravitational waves. We outline a robust methodology to evaluate the performance of noise models and identify unknown signals in the data. The detection of variations in pulse profiles highlights the need to develop efficient profile domain timing methods.
We report on the high-precision timing of 42 radio millisecond pulsars (MSPs) observed by the European Pulsar Timing Array (EPTA). This EPTA Data Release 1.0 extends up to mid-2014 and baselines range from 7-18 years. It forms the basis for the stochastic gravitational-wave background, anisotropic background, and continuous-wave limits recently presented by the EPTA elsewhere. The Bayesian timing analysis performed with TempoNest yields the detection of several new parameters: seven parallaxes, nine proper motions and, in the case of six binary pulsars, an apparent change of the semi-major axis. We find the NE2001 Galactic electron density model to be a better match to our parallax distances (after correction from the Lutz-Kelker bias) than the M2 and M3 models by Schnitzeler (2012). However, we measure an average uncertainty of 80% (fractional) for NE2001, three times larger than what is typically assumed in the literature. We revisit the transverse velocity distribution for a set of 19 isolated and 57 binary MSPs and find no statistical difference between these two populations. We detect Shapiro delay in the timing residuals of PSRs J1600$-$3053 and J1918$-$0642, implying pulsar and companion masses $m_p=1.22_{-0.35}^{+0.5} text{M}_{odot}$, $m_c = 0.21_{-0.04}^{+0.06} text{M}_{odot }$ and $m_p=1.25_{-0.4}^{+0.6} text{M}_{odot}$, $m_c = 0.23_{-0.05}^{+0.07} text{M}_{odot }$, respectively. Finally, we use the measurement of the orbital period derivative to set a stringent constraint on the distance to PSRs J1012$+$5307 and J1909$-$3744, and set limits on the longitude of ascending node through the search of the annual-orbital parallax for PSRs J1600$-$3053 and J1909$-$3744.
We investigate the impact of noise processes on high-precision pulsar timing. Our analysis focuses on the measurability of the second spin frequency derivative $ddot{ u}$. This $ddot{ u}$ can be induced by several factors including the radial velocity of a pulsar. We use Bayesian methods to model the pulsar times-of-arrival in the presence of red timing noise and dispersion measure variations, modelling the noise processes as power laws. Using simulated times-of-arrival that both include red noise, dispersion measure variations and non-zero $ddot{ u}$ values, we find that we are able to recover the injected $ddot{ u}$, even when the noise model used to inject and recover the input parameters are different. Using simulations, we show that the measurement uncertainty on $ddot{ u}$ decreases with the timing baseline $T$ as $T^gamma$, where $gamma=-7/2+alpha/2$ for power law noise models with shallow power law indices $alpha$ ($0<alpha<4$). For steep power law indices ($alpha>8$), the measurement uncertainty reduces with $T^{-1/2}$. We applied this method to times-of-arrival from the European Pulsar Timing Array and the Parkes Pulsar Timing Array and determined $ddot{ u}$ probability density functions for 49 millisecond pulsars. We find a statistically significant $ddot{ u}$ value for PSR,B1937+21 and consider possible options for its origin. Significant (95 per cent C.L.) values for $ddot{ u}$ are also measured for PSRs,J0621+1002 and J1022+1001, thus future studies should consider including it in their ephemerides. For binary pulsars with small orbital eccentricities, like PSR,J1909$-$3744, extended ELL1 models should be used to overcome computational issues. The impacts of our results on the detection of gravitational waves are also discussed.
This paper is the third part of a trilogy dealing with the principles, performance and limitations of what I named Telescope-Interferometers (TIs). The basic idea consists in transforming one telescope into a Wavefront Error (WFE) sensing device. This can be achieved in two different ways, namely the off axis and phase-shifting TIs. In both cases the Point-Spread Function (PSF) measured in the focal plane of the telescope carries information about the transmitted WFE, which is retrieved by fast and simple algorithms suitable to an Adaptive Optics (AO) regime. Herein are evaluated the uncertainties of both types of TIs, in terms of noise and systematic errors. Numerical models are developed in order to establish the dependence of driving parameters such as useful spectral range, angular size of the observed star, or detector noise on the total WFE measurement error. The latter is found particularly sensitive to photon noise, which rapidly governs the achieved accuracy for telescope diameters higher than 10 m. We study a few practical examples, showing that TI method is applicable to AO systems on telescope diameters ranging from 10 to 50 m, depending on seeing conditions and magnitude of the observed stars. We also discuss the case of a space-borne coronagraph where TI technique provides high sampling of the input WFE map.
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