A multi-messenger window into galactic magnetic fields and black hole mergers with LISA

TL;DR

This work introduces a novel multi-messenger framework linking galactic large-scale magnetic fields with LISA-detectable massive black hole mergers through hierarchical galaxy mergers. It combines a semi-analytic SMBH binary evolution pipeline (via holodeck) with a modified galmag dynamo model to map the binary mass dependence onto the host galaxy's magnetic field and EM observables (PI, RM), and then couples this to the LISA response using balrog and IMRPhenomXHM. The study finds correlations between GW observables (e.g., SNR $\rho$) and EM signatures such as the maximum field strength $|\mathbf{B}|$, $PI$, and $RM$, with $|\mathbf{B}|$ and $PI$ generally decreasing with increasing total mass $M$ while $RM$ can rise, revealing a rich, nontrivial multi-messenger parameter space. These results suggest that LISA will enable probing galactic magnetism at high redshift and motivate joint EM–GW analyses to constrain the evolution of magnetic-field structure in merging galaxies, albeit with caveats about morphology, time evolution, and line-of-sight RM contributions. Overall, the paper lays out a framework for integrating GW data with galactic dynamo theory to study cosmic magnetism across cosmic time.

Abstract

Large-scale (i.e., $\gtrsim {\rm kpc}$) and micro-Gauss scale magnetic fields have been observed throughout the Milky Way and nearby galaxies. These fields depend on the geometry and matter-energy composition, can display complicated behavior such as direction reversals, and are intimately related to the evolution of the source galaxy. Simultaneously, gravitational-wave astronomy offers a new probe into astrophysical systems, for example the Laser Interferometer Space Antenna (LISA) will observe the mergers of massive (i.e., $M ~> 10^6$ M$_{\odot}$) black-hole binaries and provide extraordinary constraints on the evolution of their galactic hosts. In this work, we show how galactic, large-scale magnetic fields and their electromagnetic signatures are connected with LISA gravitational-wave observations via their common dependence on the massive black-hole binary formation scenario of hierarchical galaxy mergers. Combining existing codes, we astrophysically evolve a population of massive binaries from formation to merger and find that they are detectable by LISA with signal-to-noise ratio $\sim 10^3$ which is correlated with quantities from the progenitors' phase of circumbinary disk migration such as the maximum magnetic field magnitude $|\mathbf{B}| \approx 7 \,μ$G, polarized intensity, and Faraday rotation measure. Interesting correlations result between these observables arising from their dependencies on the black-hole binary total mass, suggesting a need for further analyses of the full parameter space. We conclude with a discussion on this new multi-messenger window into galactic magnetic fields.

Figures (6)

• Figure 1: Dependence on the SMBH binary total mass $M$ of the GW-driven SMBH binary merger timescale $t_{\rm m}$ (assuming equal masses), shown by the blue lines for two values of binary separation, and of two timescales relevant for the large-scale galactic magnetic field: the dynamo timescale $t_{dyn}$ (dot-dashed red line) is the time over which the magnitude of a large-scale field is amplified from the dynamo action, and the ordering timescale $t_{ord}$ (dashed red line) is the time over which the spatial ordering of the field is obtained. The gray patch shows an example region of interest: SMBH binaries with $13.8\,{\rm Gyr} > t_{\rm merge} > t_{\rm dyn}$ allowing dynamo amplification in the host galaxy before the merger of the SMBH binary, which is ultimately limited by the age of the Universe (dotted black line) for observable GWs with LISA.
• Figure 2: The rotation measure ($RM$) computed from galmag, i.e., see Eq. (\ref{['E:RM']}), in the $y$--$z$ plane of a galaxy composed only of a thin disk [spherical halo] in the left panel [right panel]. We emphasize that this is the rotation of the polarization due to the source galaxy's media, and discuss other possible sources of rotation in Sec \ref{['sec:MultiMess']}. In the left panel with the flared disk source, we assume one field reversal at $r = 7$ kpc.
• Figure 3: Angular velocity profiles versus the galactic radius $r$. The solid black line is the default profile for a rigidly rotating disk. Our SMBH-mass dependent profiles for the spherical halo in dotted lines (i.e., Eq. (\ref{['E:vel_gas']})) and the thin disk in dashed lines (i.e., Eq. (\ref{['E:Vdisk2']})) are shown for two values of the SMBH mass, $M = 10^6 \rm \,M_{\odot}$ in red and $M = 10^8 \rm \,M_{\odot}$ in blue. We assume the SMBH binary resides in the (unresolved) galactic center.
• Figure 4: The dependence of the magnitude of the galactic magnetic field in the galactic plane as a function of galactic radius assuming one field reversal at $r = 7$ kpc. The black solid line is the mass-independent output of galmag, i.e. using the default velocity profiles, whereas the dashed lines result from our SMBH mass-dependent velocity profiles for $M = 10^6,\ 10^7,\ 10^8$ and $10^9 \rm \,M_{\odot}$ shown by dashed blue, red, orange, and cyan lines, respectively. Here (and in the remainder of this article) we assume the galaxy is composed of both thin disk and spherical halo sources of the magnetic field.
• Figure 5: An example of the correlations between the SMBH binary total mass $M$, the maximum magnitude of the total galactic magnetic field $\mathbf{B}$, and the maximum of the $\lambda = 5$ cm polarized intensity $PI$ in the colorbar.