Fast and Fewrious: Stochastic binary perturbations from fast compact objects

Abstract

Massive compact objects soften binaries. This process has been used for decades to constrain the population of such objects, particularly as a component of dark matter (DM). The effects of light compact objects, such as those in the unconstrained asteroid-mass range, have generally been neglected. In principle, low-energy perturbers can harden binaries instead of softening them, but the standard lore is that this effect vanishes when the perturber velocities are large compared to the binary's orbital velocity, as is typical for DM constituents. Here, we revisit the computation of the hardening rate induced by light perturbers. We show that although the perturbations average to zero over many encounters, many scenarios of interest for DM constraints are in the regime where the variance cannot be neglected. We show that a few fast-moving perturbers can leave stochastic perturbations in systems that are measured with great precision, and we use this framework to revisit the constraint potential of systems such as binary pulsars and the Solar System. This opens a new class of dynamical probes with potential applications to asteroid-mass DM candidates.

Figures (8)

• Figure 1: Schematic description of the regimes in which different processes are relevant. These regimes are shown in the plane of perturber mass and velocity, on logarithmic axes. The boundaries between regions are only illustrative: realistically, several of these processes can occur in overlapping regions. Note that "evaporation" and "ionization" are terms used in the three-body scattering literature to refer to softening and disruption, respectively, and are unrelated to Hawking evaporation and atomic ionization. The dashed black lines indicate the mass and velocity of the binary. In this work, we study the light blue region, where velocities are high (fast), but number densities are still low (few) compared to the dynamical friction regime.
• Figure 2: Hardening rate as a function of velocity. Orange points are computed from an ensemble of simulations. The blue curve shows the fit from Ref. Quinlan:1996vp. Error bars indicate $1\sigma$ uncertainties on the mean values. Insets show the full distribution of energy transferred in a single encounter for selected velocities, and are shown to scale. For high perturber velocities $v_3 \gg v_{12}$, while the mean energy transfer goes to zero, the width of the distribution remains nonzero.
• Figure 3: Fits to simulation ensembles.Left: Energy transfer distributions in an ensemble of simulations for several values of $v_3/v_{12}$. Dotted curves show the fitted $t$ distribution (see text). Top right: dependence of the variance $\sigma_E$ on the impact parameter of the encounter. The dashed curve shows the behavior implied by our approximation $T(a, b)$ (\ref{['eq:energy-scaling']}). Bottom right: dependence of $\sigma_E$ on the perturber velocity. The dashed line shows a fit to the $1/v_3$ scaling assumed in \ref{['eq:energy-scaling']}.
• Figure 4: Components of \ref{['eq:p-tot', 'eq:p-hat']} for an equal-mass circular binary with component masses $m_1=m_2=\qty{1}{M_\odot}$ and semimajor axis $a=\qty{1}{\au}$. An observing time of 1 is assumed, with all of the DM in the form of compact objects at mass $m_3$, and the minimal energy transfer for detection is taken to be a 2.0e-14 fraction of the mechanical energy of the binary, chosen to make the curves distinct for illustrative purposes. Blue, orange, and green curves show the values of individual estimators $p_{\mathrm{many}}$, $p_{\mathrm{ann}}$, and $p_{\mathrm{orb}}$, respectively. Each of these curves is solid where it is the greatest of the three, and dashed elsewhere. The dashed black curve shows the value of the estimator $\hat{p}$. Crosses show results from Monte Carlo sampling of the $t$ distribution (see text).
• Figure 5: Detection probability as a function of minimum detectable energy for several perturber masses. In the limit of a low detection threshold, the detection probability is limited by the rate of encounters, and increases to 1 at low masses.