Constraints of relic gravitational waves by pulsar timing arrays: Forecasts for the FAST and SKA projects

Wen Zhao, Yang Zhang, Xiao-Peng You, and Zong-Hong Zhu

Phys. Rev. D 87, 124012 – Published 13 June 2013

Abstract

Measurement of pulsar timing residuals provides a direct way to detect relic gravitational waves at the frequency $f \sim 1 / yr$ . In this paper, we investigate the constraints on the inflationary parameters, the tensor-to-scalar ratio $r$ , and the tensor spectral index $n_{t}$ , by the current and future pulsar timing arrays. We find that the Five-hundred-meter Aperture Spherical Radio Telescope in China and the planned Square Kilometre Array projects have fairly strong abilities to test the phantomlike inflationary models. If $r = 0.1$ , then Five-hundred-meter Aperture Spherical Radio Telescope could give the constraint on the spectral index $n_{t} < 0.56$ and Square Kilometre Array could give $n_{t} < 0.32$ , while an observation with total time $T = 20 yr$ , pulsar noise level $σ_{w} = 30 ns$ , and monitored pulsar number $n = 200$ could even constrain $n_{t} < 0.07$ . These are much tighter than those inferred from the current results of the Parkes Pulsar Timing Array, European Pulsar Timing Array, and North American Nanohertz Observatory for Gravitational Waves. By studying the effects of various observational factors on the sensitivities of pulsar timing arrays, we find that compared with $σ_{w}$ and $n$ , the total observation time $T$ has the most significant effect.

Received 19 March 2013

DOI:https://doi.org/10.1103/PhysRevD.87.124012

Authors & Affiliations

Wen Zhao^1,2, Yang Zhang^1,2, Xiao-Peng You³, and Zong-Hong Zhu⁴

¹Department of Astronomy, University of Science and Technology of China, Hefei 230026, China
²Key Laboratory for Researches in Galaxies and Cosmology, University of Science and Technology of China, Hefei 230026, China
³School of Physical Science and Technology, Southwest University, Chongqing 400715, China
⁴Department of Astronomy, Beijing Normal University, Beijing 100875, China

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Vol. 87, Iss. 12 — 15 June 2013

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Images

Figure 1
Left panel: The upper limit of $A$ as a function of the spectral slope $α$ . Right panel: The upper limit of $r$ for any given $n_{t}$ , where the shaded region is excluded by the current Planck observations. In each panel, the black solid line (L1) is the current PPTA $2 σ$ result [34], the blue dashed line (L2) is the current EPTA $2 σ$ result [35], the green dash-dotted line (L3) is the current NANOGrav $2 σ$ result [36], and the red dotted line (L4) is the future PPTA $2 σ$ result [34].Reuse & Permissions
Figure 2
The detection significance of RGWs for FAST (black lines or dark lines) and SKA (red lines or gray lines) projects. For FAST, we have assumed $T = 5 yr$ , $σ_{w} = 30 ns$ , and $n = 20$ , and for SKA we have assumed $T = 10 yr$ , $σ_{w} = 50 ns$ , and $n = 100$ . For both cases, solid lines are for the models with $r = 0.1$ , dashed lines are for $r = 0.01$ , and dotted lines are for $r = 0.001$ .Reuse & Permissions
Figure 3
The upper limits of $r$ and $n_{t}$ based on the potential FAST observations (black line, i.e., L1) and SKA observations (red line, i.e., L2). Note that the shaded region is excluded by current Planck observations. The dashed blue line (Lb) is the current tightest constraint coming from the EPTA observations, which is identical to that in the right panel of Fig. 1. The solid blue line (La) indicates the result in the optimal case considered in this paper, where $T = 20 yr$ , $σ_{w} = 30 ns$ , and $n = 200$ are assumed.Reuse & Permissions
Figure 4
The upper limits of $r$ and $n_{t}$ depend on the total observation time $T$ . The solid black line (L2) is the case with $T = 5 yr$ , the dashed black line (L1) is $T = 10 yr$ , and the dotted black line (L3) is $T = 20 yr$ . In all cases, $σ_{w} = 50 ns$ and $n = 100$ are assumed. The solid blue line (La) and dashed blue line (Lb) are identical to those in Fig. 3. The dashed black line (L1) is identical to that for SKA.Reuse & Permissions
Figure 5
The upper limits of $r$ and $n_{t}$ depend on the noise level $σ_{w}$ . The solid black line (L2) is the case with $σ_{w} = 100 ns$ , the dashed black line (L1) is $σ_{w} = 50 ns$ , and the dotted black line (L3) is $σ_{w} = 30 ns$ . In all cases, $T = 10 yr$ and $n = 100$ are assumed. The solid blue line (La) and dashed blue line (Lb) are identical to those in Fig. 3. The dashed black line (L1) is identical to that for SKA.Reuse & Permissions
Figure 6
The upper limits of $r$ and $n_{t}$ depend on the monitored pulsar number $n$ . The solid black line (L2) is the case with $n = 50$ , the dashed black line is $n = 100$ (L1), and the dotted black line is $n = 200$ (L3). In all cases, $σ_{w} = 50 ns$ and $T = 10 yr$ are assumed. The solid blue line (La) and dashed blue line (Lb) are identical to those in Fig. 3. The dashed black line (L1) is identical to that for SKA.Reuse & Permissions

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