Effects of Timing Noise on Square-Wave Optoelectronic Oscillators

Optoelectronic oscillators produce microwave-modulated optical beams without external modulation. The most commonly studied types produces narrow-band output, i.e., optical output modulated by a sinusoid, in which case phase noise determines key figures of merit that limit device performance. Nonetheless, other types of modulated signals have been exhibited by optoelectronic oscillators, including square waves. In this work we provide a theoretical treatment of the power spectral density of a microwave self-modulated optical periodic, but non-sinusoidal, oscillator in the presence of timing noise (as phase noise is only defined for a single sinusoid) and focus on the case of square waves. We consider the effects of timing noise on the power spectral density and autocorrelation function of the modulation signal.

Parameter estimation of a two-component neutron star model with spin wandering

ABSTRACT It is an open challenge to estimate systematically the physical parameters of neutron star interiors from pulsar timing data while separating spin wandering intrinsic to the pulsar (achromatic timing noise) from measurement noise and chromatic timing noise (due to propagation effects). In this paper, we formulate the classic two-component, crust-superfluid model of neutron star interiors as a noise-driven, linear dynamical system and use a state-space-based expectation–maximization method to estimate the system parameters using gravitational-wave and electromagnetic timing data. Monte Carlo simulations show that we can accurately estimate all six parameters of the two-component model provided that electromagnetic measurements of the crust angular velocity and gravitational-wave measurements of the core angular velocity are both available. When only electromagnetic data are available, we can recover the overall relaxation time-scale, the ensemble-averaged spin-down rate, and the strength of the white-noise torque on the crust. However, the estimates of the secular torques on the two components and white-noise torque on the superfluid are biased significantly.

Timing of young radio pulsars – II. Braking indices and their interpretation

ABSTRACT In Paper I of this series, we detected a significant value of the braking index (n) for 19 young, high-$\dot{E}$ radio pulsars using ∼10 yr of timing observations from the 64-m Parkes radio telescope. Here, we investigate this result in more detail using a Bayesian pulsar timing framework to model timing noise and to perform selection to distinguish between models containing exponential glitch recovery and braking index signatures. We show that consistent values of n are maintained with the addition of substantial archival data, even in the presence of glitches. We provide strong arguments that our measurements are unlikely due to exponential recovery signals from unseen glitches even though glitches play a key role in the evolution of a pulsar’s spin frequency. We conclude that, at least over decadal time-scales, the value of n can be significantly larger than the canonical 3 and discuss the implications for the evolution of pulsars.

The UTMOST pulsar timing programme – II. Timing noise across the pulsar population

ABSTRACT While pulsars possess exceptional rotational stability, large-scale timing studies have revealed at least two distinct types of irregularities in their rotation: red timing noise and glitches. Using modern Bayesian techniques, we investigated the timing noise properties of 300 bright southern-sky radio pulsars that have been observed over 1.0–4.8 yr by the upgraded Molonglo Observatory Synthesis Telescope (MOST). We reanalysed the spin and spin-down changes associated with nine previously reported pulsar glitches, report the discovery of three new glitches and four unusual glitch-like events in the rotational evolution of PSR J1825−0935. We develop a refined Bayesian framework for determining how red noise strength scales with pulsar spin frequency (ν) and spin-down frequency ($\dot{\nu }$), which we apply to a sample of 280 non-recycled pulsars. With this new method and a simple power-law scaling relation, we show that red noise strength scales across the non-recycled pulsar population as $\nu ^{a} |\dot{\nu }|^{b}$, where $a = -0.84^{+0.47}_{-0.49}$ and $b = 0.97^{+0.16}_{-0.19}$. This method can be easily adapted to utilize more complex, astrophysically motivated red noise models. Lastly, we highlight our timing of the double neutron star PSR J0737−3039, and the rediscovery of a bright radio pulsar originally found during the first Molonglo pulsar surveys with an incorrectly catalogued position.

NICER observations of the Crab pulsar glitch of 2017 November

Context. The Crab pulsar underwent its largest timing glitch on 2017 Nov. 8. The event was discovered at radio wavelengths, and was followed at soft X-ray energies by observatories, such as XPNAV and NICER. Aims. This work aims to compare the glitch behavior at the two wavelengths mentioned above. Preliminary work in this regard has been done by the X-ray satellite XPNAV. NICER with its far superior sensitivity is expected to reveal much more detailed behavior. Methods. NICER has accumulated more than 301 kilo seconds of data on the Crab pulsar, equivalent to more than 3.3 billion soft X-ray photons. These data were first processed using the standard NICER analysis pipeline. Then the arrival times of the X-ray photons were referred to the solar system’s barycenter. Then specific analysis was done to study the specific behavior outlined in the following sections, while taking dead time into account. Results. The variation of the rotation frequency of the Crab pulsar and its time derivative during the glitch is almost exactly similar at the radio and X-ray energies. The following properties of the Crab pulsar remain essentially constant before and after the glitch: the total X-ray flux; the flux, widths, and peaks of the two components of its integrated profile; and the soft X-ray spectrum. There is no evidence for giant pulses at X-ray energies. However, the timing noise of the Crab pulsar shows quasi sinusoidal variation before the glitch, with increasing amplitude, which is absent after the glitch. Conclusions. Even the strongest glitch in the Crab pulsar appears not to affect all but one of the properties mentioned above, at either frequency. The fact that the timing noise appears to change due to the glitch is an important clue to unravel as this is still an unexplained phenomenon.

Timing of young radio pulsars – I. Timing noise, periodic modulation, and proper motion

ABSTRACT The smooth spin-down of young pulsars is perturbed by two non-deterministic phenomenon, glitches, and timing noise. Although the timing noise provides insights into nuclear and plasma physics at extreme densities, it acts as a barrier to high-precision pulsar timing experiments. An improved methodology based on the Bayesian inference is developed to simultaneously model the stochastic and deterministic parameters for a sample of 85 high-$\dot{E}$ radio pulsars observed for ∼10 yr with the 64-m Parkes radio telescope. Timing noise is known to be a red process and we develop a parametrization based on the red-noise amplitude (Ared) and spectral index (β). We measure the median Ared to be $-10.4^{+1.8}_{-1.7}$ yr3/2 and β to be $-5.2^{+3.0}_{-3.8}$ and show that the strength of timing noise scales proportionally to $\nu ^{1}|\dot{\nu }|^{-0.6\pm 0.1}$, where ν is the spin frequency of the pulsar and $\dot{\nu }$ is its spin-down rate. Finally, we measure significant braking indices for 19 pulsars and proper motions for 2 pulsars, and discuss the presence of periodic modulation in the arrival times of 5 pulsars.

Correlated timing noise and high-precision pulsar timing: measuring frequency second derivatives as an example

We investigate the impact of noise processes on high-precision pulsar timing. Our analysis focuses on the measurability of the second spin frequency derivative $\ddot{\nu }$. This $\ddot{\nu }$ 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 $\ddot{\nu }$ values, we find that we are able to recover the injected $\ddot{\nu }$, even when the noise model used to inject and recover the input parameters are different. Using simulations, we show that the measurement uncertainty on $\ddot{\nu }$ decreases with the timing baseline T as Tγ, where γ = −7/2 + α/2 for power-law noise models with shallow power-law indices α (0 < α < 4). For steep power-law indices (α > 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 $\ddot{\nu }$ probability density functions for 49 millisecond pulsars. We find a statistically significant $\ddot{\nu }$ value for PSR B1937+21 and consider possible options for its origin. Significant (95 per cent C.L.) values for $\ddot{\nu }$ 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, such as 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.

Diagnostics of timing noise in middle-aged pulsars

ABSTRACT Radio pulsars are often used as clocks in a wide variety of experiments. Imperfections in the clock, known as timing noise, have the potential to reduce the significance of, or even thwart e.g. the attempt to find a stochastic gravitational wave (GW) background. We measure the timing noise in a group of 129 mostly middle-aged pulsars (i.e. characteristic ages near 1 Myr) observed with the Parkes radio telescope on a monthly basis since 2014. We examine four different metrics for timing noise, but it remains unclear which, if any, provides the best determination. In spite of this, it is evident that these pulsars have significantly less timing noise than their younger counterparts, but significantly more than the (much older) millisecond pulsars (MSPs). As with previous authors, we find a strong correlation between timing noise and the pulsar spin-down rate, $\dot{\nu}$. However, for a given $\dot{\nu}$ there is a spread of about a factor of 30 in the strength of the timing noise likely indicating that nuclear conditions in the interior of the stars differ between objects. We briefly comment on the implications for GW detection through pulsar timing arrays as the level of timing noise in MSPs may be less than predicted.

Timing offset calibration of CZTI instrument aboard ASTROSAT

Aim: Both the radio and the high-energy emission mechanism in pulsars is not yet properly understood. A multiwavelength study is likely to help better understand of such processes. ASTROSAT, the first Indian space-based observatory, has five instruments aboard that cover the electromagnetic spectrum from infra-red (1300 Å) to hard X-ray (380 keV). The instrument relevant to our study is the Cadmium Zinc Telluride Imager (CZTI). CZTI is a hard X-ray telescope functional over an energy range of 20–380 keV. We aim to estimate the timing offset introduced in the data acquisition pipeline of the instrument, which will help in time alignment of high energy time-series with those from two other ground based observatories, viz. the Giant Meterwave Radio Telescope (GMRT) and the Ooty Radio Telescope (ORT). Method: PSR B0531+21 is a well studied bright pulsar with closely aligned radio and hard X-ray pulse profiles. We used simultaneous observations of this pulsar with the ASTROSAT, the ORT, and the GMRT. As the pulsar resides in a very turbulent environment and shows significant timing noise, it was specially observed using the ORT with almost daily cadence to obtain good timing solutions. We also supplemented the ORT data with archival Fermi data for estimation of timing noise. We obtained the phase connected timing solution of the pulsar by estimating its dispersion measure variations and the timing noise. The timing offset of ASTROSAT instruments was estimated from fits to pulse arrival time data at the ASTROSAT and the radio observatories. Results: We estimate the relative offset of ASTROSAT-CZTI with respect to GMRT to be −4716 ± 50 μs. The corresponding offset with the ORT was −29639 ± 50 μs and Fermi-LAT was −5368 ± 56 μs respectively.