Constraints on a dark matter sub-halo near the Sun from pulsar timing

Abstract

Using pulsar accelerations, we identify and constrain the properties of a dark matter sub-halo in the Galaxy for the first time from analyzing the acceleration field of binary and solitary pulsars. Our MCMC calculations show that this sub-halo has a mass of $2.45^{+1.07}_{-0.96} \times 10^{7}~M_{\odot}$ and is located at Galactocentric coordinates $X = 7.43^{+0.2}_{-0.12}~\rm$ kpc, $Y = 0.38^{+0.11}_{-0.16} ~\rm kpc$, $Z = 0.21^{+0.06}_{-0.11} ~\rm kpc$, using flat, uninformative priors, where we have modeled the sub-halo as a compact object. The Bayes factors for the models are in the range of $\sim$ 20-40, which indicates tentative evidence (though not yet decisive) for the sub-halo. Modeling the sub-halo with a NFW profile gives a sub-halo mass within the scale radius (0.1 kpc) of $0.48^{0.15}_{-0.16} \times 10^{7} M_{\odot}$, located at $X = 7.47^{+0.21}_{-0.14}$, $Y=0.38^{+0.11}_{-0.16}$, $Z=0.21^{+0.06}_{-0.11}$. We examine \textit{Gaia} data and the atomic and molecular hydrogen data of our Galaxy and show that the measured deviation from a smooth potential cannot arise from the gas or the stars in our Galaxy. By analyzing the full sample of binary pulsars with available acceleration measurements, we find that massive (with mass $>10^{8}~M_{\odot}~$) sub-halos are disfavored for the Milky Way within several kiloparsec of the Sun. Smaller sub-halos are beyond the reach of current direct acceleration measurements. The presence of a $\sim 10^{7}~M_{\odot}$ sub-halo within a few kpc of the Sun is potentially consistent with the expected number counts of sub-halos in the prevailing $Λ$CDM paradigm, for a substantial sub-halo mass fraction. This work now provides a proof of principle for probing nearby, low-mass sub-halos, and has implications across many fields of astrophysics - from understanding the nature of dark matter to galaxy formation.

Figures (2)

• Figure 1: Posterior distribution showing derived properties of a dark matter sub-halo The panels show the PDFs that display our constraint for the mass of the sub-halo (in solar masses), and its Galactocentric X,Y,Z coordinates using the set of high $S/N$ binary pulsars that are centered near the binary pulsar set PSR J1640+2224, PSR J1713+0747, along with high $S/N$ spin period pulsars. Here we have modeled the sub-halo as a compact object. The derived parameters of the mid-plane density and scale height for the exponential disk are also shown. Here, we show the results for the Galactic potential that includes both the exponential disk and spiral potential (the latter is adopted from Antoja2011).
• Figure 2: The top panel shows the fractional difference in the observed LOS acceleration relative to the model considering an exponential disk in Galactocentric coordinates R,z; the bottom panel shows the same considering an exponential disk and a sub-halo with a NFW profile. The colorbar shows the fractional difference in the observed and model LOS acceleration, normalized to the error in the observed LOS acceleration; the lighter colors for the sub-halo model suggest that it may be favored by the data. However, more precise measurements of pulsars (that are clearly above the noise) are needed to confirm this tentative result.