Gravitational memory meets astrophysical environments: exploring a new frontier through osculations

Abstract

We study how dark matter environments influence nonlinear gravitational memory from intermediate-mass-ratio binaries. Incorporating environmental effects from the dark matter gravitational potential, dynamical friction, and accretion, we compute the leading-order nonlinear memory for both bound and unbound orbits under dark matter minispikes and Navarro-Frenk-White haloes. For quasi-circular inspirals in a minispike, we additionally include an empirical prescription for the time-dependent evolution of the dark matter profile, which gradually evolves along the inspiral and captures the cumulative environmental response. We find that dark matter can modify the time evolution and mode content of the memory relative to the vacuum case, with the cumulative effect depending sensitively on the density profile and on how the environment accelerates the inspiral. We use these waveforms to assess signal-to-noise ratios and mismatches in representative space-based detector configurations, highlighting where memory-driven differences may be large enough to warrant targeted parameter-estimation studies. Our results emphasize that astrophysical environments can leave a hereditary imprint on gravitational memory and provide a framework for connecting memory observables with dark matter dynamics.

Figures (9)

• Figure 1: Schematic of the orbital motion described in the fundamental reference frame in the presence of a surrounding DM distribution (in orange colour).
• Figure 2: The above plots show the $h_{20}^{\textup{(mem)}}$ and $h_{40}^{\textup{(mem)}}$ as functions of eccentricity with different values of initial eccentricities $e_0$, initial semi-latus rectum $p_0$ and DM spike exponent $\alpha$ in panels (a), (b), and (c), respectively, for elliptical binaries. We also consider $R=10$Mpc.
• Figure 3: Comparison of nonlinear memory modes from elliptical binaries as functions of eccentricity in vacuum and in DM environments. The $(2,0)$ and $(4,0)$ modes are shown for a spike profile ($\alpha=2.25$) and an NFW halo for binaries with $e_0=0.9$ and $p_0=100$.
• Figure 4: SNR of GW signal from elliptical binaries as a function of the DM spike exponent $\alpha$. Panel (a) shows the SNR computed for the LISA detector, while panel (b) shows the corresponding results for GWSat. In each panel, four cases are considered: binaries evolving in a vacuum, binaries in a vacuum with nonlinear memory, binaries embedded in a DM environment, and DM binaries with nonlinear memory. The initial orbital parameters are fixed to $e_0=0.1$ and $p_0=70$ with $R=10$Mpc.
• Figure 5: SNR of the nonlinear memory response from elliptical binaries as a function of the DM spike exponent $\alpha$, computed using the $(2,0)$ and $(4,0)$ memory modes, which are combined to construct the memory polarizations and projected onto the detector response. Results are shown for LISA (a) and GWSat (b), assuming $e_0=0.1$ and $p_0=50$, for vacuum and DM spike environment.