Pulsar Timing Array Based Search for Supermassive Black Hole Binaries in the Square Kilometer Array Era

The advent of next generation radio telescope facilities, such as the Square Kilometer Array (SKA), will usher in an era where a pulsar timing array (PTA) based search for gravitational waves (GWs) will be able to use hundreds of well timed millisecond pulsars rather than the few dozens in existing PTAs. A realistic assessment of the performance of such an extremely large PTA must take into account the data analysis challenge posed by an exponential increase in the parameter space volume due to the large number of so-called pulsar phase parameters. We address this problem and present such an assessment for isolated supermassive black hole binary (SMBHB) searches using a SKA era PTA containing $10^3$ pulsars. We find that an all-sky search will be able to confidently detect nonevolving sources with a redshifted chirp mass of $10^{10}{M}_{\odot }$ out to a redshift of about 28 (corresponding to a rest-frame chirp mass of $3.4\times 10^8{M}_{\odot }$). We discuss the important implications that the large distance reach of a SKA era PTA has on GW observations from optically identified SMBHB candidates. If no SMBHB detections occur, a highly unlikely scenario in the light of our results, the sky-averaged upper limit on strain amplitude will be improved by about 3 orders of magnitude over existing limits.

Figure 1

The condition number of the response matrix $\mathbf{A}$ as a function of RA ($\alpha$) and DEC ($\delta$), both expressed in radians. The dots show the locations of the MSPs constituting the simulated SKA era PTA used in this Letter. The stars show the Galactic poles (North Galactic Pole on top) and the squares show the Galactic center (right) and anticenter (left). From top to bottom, the triangles denote the four source locations $A$, $B$, $C$, and $D$, respectively, that are used in the simulations. The condition numbers corresponding to these locations in the same order are 1.0139, 1.0486, 1.1832, and 1.3159.

Figure 2

Cumulative network SNR for a uniformly spaced $6\times 6$ grid of source locations (gray) and the four locations, $A$ (blue), $B$ (black), $C$ (red), and $D$ (magenta), used in the simulations. The total network SNR $\rho$ is 30 for this plot. The curve for any other $\rho$ can be obtained by using an overall scale factor of $\rho /30$.

Figure 3

Maximum likelihood estimates (blue dots) of the GW source location in equatorial coordinates with 50 data realizations for the network SNR $\rho \ne 0$ and 200 for $\rho =0$ (noise only). The subpanels for each $\rho \ne 0$ panel correspond to the true locations a (top left), b (top right), c (bottom left), and d (bottom right), respectively. The true and estimated mean locations are marked by red triangles and magenta crosses, respectively. The solid black lines show regions in which the probability of getting an estimated location is 68% and 95% (estimated using kernel density estimation [36]). In the $\rho =0$ panel, the center and anticenter of the Galaxy and its poles are marked by red squares and green stars, respectively.