The NANOGrav 15-year Data Set: Search for Gravitational Scattering of Pulsars by Free-Floating Objects in Interstellar Space

TL;DR

This work leverages the NANOGrav 15-year pulsar-timing data set to search for gravitational scattering of millisecond pulsars by free-floating objects on hyperbolic trajectories. It develops a closed-form, seven-parameter Bayesian signal model for the pulse-arrival-time perturbation $R(t)$, with independent orbit parameters $(p, v_{ abla})$ and a mass proxy $m ext{sin} i$, and fits this model to 68 MSPs while accounting for white and red noise. No detections are found, enabling upper limits on the local FFO number density as a function of mass, including Jupiter-mass objects, where a combined limit of $6.03 imes 10^{5}~ ext{pc}^{-3}$ is reported; individual pulsars set looser limits in the range $5.25 imes 10^{6}$–$5.37 imes 10^{9}~ ext{pc}^{-3}$. These results provide the first pulsar-timing constraints on FFO populations and offer a complementary probe to microlensing and interstellar-object surveys for understanding the prevalence of free-floating bodies and their potential connection to primordial black holes.

Abstract

Free-floating objects (FFOs) in interstellar space$-$rogue planets, brown dwarfs, and large asteroids that are not gravitationally bound to any star$-$are expected to be ubiquitous throughout the Milky Way. Recent microlensing surveys have discovered several free-floating planets that are not bound to any known stellar systems. Additionally, three interstellar objects, namely 1I/'Oumuamua, 2I/Borisov, and 3I/ATLAS, have been detected passing through our solar system on hyperbolic trajectories. In this work, we search for FFOs on hyperbolic orbits that pass near millisecond pulsars (MSPs), where their gravitational influence can induce detectable perturbations in pulse arrival times. Using the NANOGrav 15-year narrowband dataset, which contains high-precision timing data for 68 MSPs, we conduct a search for such hyperbolic scattering events between FFOs and pulsars. Although no statistically significant events were detected, this non-detection enables us to place upper limits on the number density of FFOs as a function of their mass within our local region of the Galaxy. For example, the upper limit on the number density for Jupiter-mass FFOs ($\sim 10^{-2.5} - 10^{-3.5}~M_{\odot}$) obtained from different pulsars ranges from $5.25\times10^{6}~\text{pc}^{-3}$ to $5.37\times10^{9}~\text{pc}^{-3}$, while the upper limit calculated by combining results from all the pulsars is $6.03\times10^{5}~\text{pc}^{-3}$. These results represent the first constraints on FFO population derived from pulsar timing data.

Figures (1)

• Figure 1: Pulse arrival time perturbations induced by a hyperbolic gravitational scattering of an FFO with projected mass $m\sin{i} = 10^{-8}\,M_{\odot}$, periapsis distance $p = 10$ AU, asymptotic velocity relative to the pulsar $v_{\infty} = 20$ km/s, and time of periapsis $t_0 = 55000$ MJD, for a pulsar with mass $M = 1.4 \,M_{\odot}$. The left panel displays the total induced time delay due to the reflex motion of the pulsar and the right panel shows these time perturbations after subtracting a second-order polynomial fit, for three different orientations of the orbit.