# The NANOGrav 11-Year Data Set: Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

## TL;DR

This study used 11 years of NANOGrav data to search for gravitational waves from individual supermassive black hole binaries, setting upper limits on their strain and ruling out certain sources within specific distances.

## Contribution

The paper presents the first limits on gravitational waves from individual SMBHBs using the 11-year NANOGrav data set and introduces a new technique to assess signal significance in pulsar timing data.

## Key findings

- No strong evidence for GWs was found in the data.
- Placed a sky-averaged upper limit on GW strain of 7.3 x 10^{-15} at 8 nHz.
- Ruled out SMBHBs with certain masses within specific distances.

## Abstract

Observations indicate that nearly all galaxies contain supermassive black holes (SMBHs) at their centers. When galaxies merge, their component black holes form SMBH binaries (SMBHBs), which emit low-frequency gravitational waves (GWs) that can be detected by pulsar timing arrays (PTAs). We have searched the recently-released North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 11-year data set for GWs from individual SMBHBs in circular orbits. As we did not find strong evidence for GWs in our data, we placed 95\% upper limits on the strength of GWs from such sources as a function of GW frequency and sky location. We placed a sky-averaged upper limit on the GW strain of $h_0 < 7.3(3) \times 10^{-15}$ at $f_\mathrm{gw}= 8$ nHz. We also developed a technique to determine the significance of a particular signal in each pulsar using ``dropout' parameters as a way of identifying spurious signals in measurements from individual pulsars. We used our upper limits on the GW strain to place lower limits on the distances to individual SMBHBs. At the most-sensitive sky location, we ruled out SMBHBs emitting GWs with $f_\mathrm{gw}= 8$ nHz within 120 Mpc for $\mathcal{M} = 10^9 \, M_\odot$, and within 5.5 Gpc for $\mathcal{M} = 10^{10} \, M_\odot$. We also determined that there are no SMBHBs with $\mathcal{M} > 1.6 \times 10^9 \, M_\odot$ emitting GWs in the Virgo Cluster. Finally, we estimated the number of potentially detectable sources given our current strain upper limits based on galaxies in Two Micron All-Sky Survey (2MASS) and merger rates from the Illustris cosmological simulation project. Only 34 out of 75,000 realizations of the local Universe contained a detectable source, from which we concluded it was unsurprising that we did not detect any individual sources given our current sensitivity to GWs.