58 research outputs found
The effect of small inter-pulsar distance variations in stochastic gravitational wave background searches with Pulsar Timing Arrays
One of the primary objectives for Pulsar Timing Arrays (PTAs) is to detect a
stochastic background generated by the incoherent superposition of
gravitational waves (GWs), in particular from the cosmic population of
supermassive black hole binaries. Current stochastic background searches assume
that pulsars in a PTA are separated from each other and the Earth by many GW
wavelengths. As more millisecond pulsars are discovered and added to PTAs, some
may be separated by only a few radiation wavelengths or less, resulting in
correlated GW phase changes between close pulsars in the array. Here we
investigate how PTA overlap reduction functions (ORFs), up to quadrupole order,
are affected by these additional correlated phase changes, and how they are in
turn affected by relaxing the assumption that all pulsars are equidistant from
the solar system barycenter. We find that in the low frequency GW background
limit of ~Hz, and for pulsars at varying distances from the
Earth, that these additional correlations only affect the ORFs by a few percent
for pulsar pairs at large angular separations, as expected. However when nearby
(order 100 pc) pulsars are separated by less than a few degrees, the correlated
phase changes can introduce variations of a few tens of percent in the
magnitude of the isotropic ORF, and much larger fractional differences in the
anisotropic ORFs-- up to 188 in the , ORF for equidistant pulsars
separated by 3 degrees. In fact, the magnitude of most of the anisotropic ORFs
is largest at small, but non-zero, pulsar separations. Finally, we write down a
small angle approximation for the correlated phase changes which can easily be
implemented in search pipelines, and for completeness, examine the behavior of
the ORFs for pulsars which lie at a radiation wavelength from the Earth.Comment: 16 pages, 8 figures, submitted to PR
Characterising gravitational wave stochastic background anisotropy with Pulsar Timing Arrays
Detecting a stochastic gravitational wave background, particularly radiation
from individually unresolvable super-massive black hole binary systems, is one
of the primary targets for Pulsar Timing Arrays. Increasingly more stringent
upper limits are being set on these signals under the assumption that the
background radiation is isotropic. However, some level of anisotropy may be
present and the characterisation of the power at different angular scales
carries important information. We show that the standard analysis for isotropic
backgrounds can be generalised in a conceptually straightforward way to the
case of generic anisotropic background radiation by decomposing the angular
distribution of the gravitational wave power on the sky into multipole moments.
We introduce the concept of generalised overlap reduction functions which
characterise the effect of the anisotropy multipoles on the correlation of the
timing residuals from the pulsars timed by a Pulsar Timing Array. In a search
for a signal characterised by a generic anisotropy, the generalised overlap
reduction functions play the role of the so-called Hellings and Downs curve
used for isotropic radiation. We compute the generalised overlap reduction
functions for a generic level of anisotropy and Pulsar Timing Array
configuration. We also provide an order of magnitude estimate of the level of
anisotropy that can be expected in the background generated by super-massive
black hole binary systems.Comment: 12 pages plus 5 page Appendix. Accepted to PR
Analysis of the first IPTA Mock Data Challenge by the EPTA timing data analysis working group
This is a summary of the methods we used to analyse the first IPTA Mock Data
Challenge (MDC), and the obtained results. We have used a Bayesian analysis in
the time domain, accelerated using the recently developed ABC-method which
consists of a form of lossy linear data compression. The TOAs were first
processed with Tempo2, where the design matrix was extracted for use in a
subsequent Bayesian analysis. We used different noise models to analyse the
datasets: no red noise, red noise the same for all pulsars, and individual red
noise per pulsar. We sampled from the likelihood with four different samplers:
"emcee", "t-walk", "Metropolis-Hastings", and "pyMultiNest". All but emcee
agreed on the final result, with emcee failing due to artefacts of the
high-dimensionality of the problem. An interesting issue we ran into was that
the prior of all the 36 (red) noise amplitudes strongly affects the results. A
flat prior in the noise amplitude biases the inferred GWB amplitude, whereas a
flat prior in log-amplitude seems to work well. This issue is only apparent
when using a noise model with individually modelled red noise for all pulsars.
Our results for the blind challenges are in good agreement with the injected
values. For the GWB amplitudes we found h_c = 1.03 +/- 0.11 [10^{-14}], h_c =
5.70 +/- 0.35 [10^{-14}], and h_c = 6.91 +/- 1.72 [10^{-15}], and for the GWB
spectral index we found gamma = 4.28 +/- 0.20, gamma = 4.35 +/- 0.09, and gamma
= 3.75 +/- 0.40. We note that for closed challenge 3 there was quite some
covariance between the signal and the red noise: if we constrain the GWB
spectral index to the usual choice of gamma = 13/3, we obtain the estimates:
h_c = 10.0 +/- 0.64 [10^{-15}], h_c = 56.3 +/- 2.42 [10^{-15}], and h_c = 4.83
+/- 0.50 [10^{-15}], with one-sided 2 sigma upper-limits of: h_c <= 10.98
[10^{-15}], h_c <= 60.29 [10^{-15}], and h_c <= 5.65 [10^{-15}].Comment: 10 pages, 5 figure
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