How Bright in Gravitational Waves are Millisecond Pulsars for the Galactic Center GeV Gamma-Ray Excess? A Systematic Study

TL;DR

The paper tackles whether a bulge MSP population could explain the Galactic Center GeV gamma-ray excess by predicting their gravitational-wave emission in the 200–2000 Hz band. It combines three physically motivated ellipticity mechanisms, two MSP-population frameworks, and two detection strategies (coherent and incoherent) to forecast GW signals and detector prospects for current and future interferometers. The main finding is that while current detectors are unlikely to detect individual MSPs, next-generation observatories like CE and ET could observe a fraction under plausible assumptions, and even optimistic spin-down–to–GW conversion scenarios could bring some signals into LVK O4 reach. This work provides a concrete pathway to empirically test the MSP interpretation of the GCE and to constrain MSP ellipticities and abundances, with significant implications for distinguishing astrophysical MSPs from dark-matter explanations of the GCE.

Abstract

The existence of dark matter (DM) is supported by various macroscopic observations, but its microscopic nature remains elusive. The Galactic Center GeV gamma-ray excess (GCE) has been a leading candidate signal for particle dark matter annihilation. However, an unresolved population of millisecond pulsars (MSPs) in the bulge provides the alternative explanation for the excess. Identifying these MSPs in electromagnetic bands is difficult due to source confusion, pulse broadening, and extinction. Gravitational waves (GWs) provide a complementary probe: a steadily rotating, non-axisymmetric MSP emits a nearly monochromatic GW signal in the sensitive band of ground-based detectors, with amplitude set by its ellipticity. In this work, we systematically investigate the GW emission from the MSP population proposed to explain the GCE and its detectability with current and future detectors. We consider three major scenarios for the origin of ellipticity and model the population properties of these MSPs. We also consider both isolated MSPs and MSPs in binary systems, as well as Doppler effects in the detection. We find that while the signal is below the reach of current interferometers, next-generation detectors such as the Einstein Telescope (ET) and Cosmic Explorer (CE) can detect a fraction of those MSPs, offering a novel test of the MSP interpretation of the GCE. Future directed searches toward the Galactic Center with continued improvements in sensitivities will either uncover this long-sought MSP population or place stringent limits on their ellipticities and abundance, with important implications for both the astrophysical and dark-matter interpretations of the GCE.

Figures (7)

• Figure 1: Distributions of parameters of bulge MSPs responsible for the GCE. Pink: Pop. i@ derived from the filtered ATNF pulsar catalog ATNF_catalog. Green: Pop. ii@ derived from Ploeg et al. Ploeg_2020. Left and Middle: Distributions of the rotational frequency $f_{\rm rot}$ and its derivative $\dot{f}_{\rm rot}$, respectively. Right: Distributions of the surface magnetic field $B_{\rm surf}$, computed using Eq. \ref{['eq_Bsurf']}. In all panels, the curves represent the KDEs derived from the sample for the corresponding parameters.
• Figure 2: Distributions of ellipticities of bulge MSPs from three distinct scenarios. Pink: Pop. i@ derived from the filtered ATNF pulsar catalog ATNF_catalog. Green: Pop. ii@ derived from Ploeg et al. Ploeg_2020. Left: Magnetic-field-induced deformation. Middle: Crust mountains from breaking strain. Right: Model independent spin-down energy fraction with $\eta=1\%$. The curves in the left and right panels represent the KDEs derived from the sample for the corresponding parameters.
• Figure 3: (Main results of the paper.) Our results for the intrinsic strain amplitude $h_0(f_{\rm GW})$ of bulge MSPs responsible for the GCE, shown for different ellipticity origins (vertical panels; Sec. \ref{['sec_ellipticity']}) and MSP population models (horizontal panels; Sec. \ref{['sec_pop_paras']}), along with the sensitivity for continuous wave searches from different GW detectors, as labeled. The scattered points represent our predicted $h_0$ for the individual MSPs, to be compared with the solid sensitivity curves (coherent strategy; Eq. \ref{['eq_h0min_coh']}). The green dashed lines represent the total effective strain amplitude (Eq. \ref{['eq_heff']}) from the MSPs within a $2$-Hz bin, to be compared with the dashed sensitivity lines (incoherent strategy; Eq. \ref{['eq_h0min_incoh']}). Top row: ellipticity originating from magnetic-field-induced deformation (Sec. \ref{['sec_ellipticity_MF']}). Second row: ellipticity originating from crustal mountains from breaking strain (Sec. \ref{['sec_ellipticity_crustal']}). Third row: ellipticity assuming $\eta=1\%$ of spin-down energy converts to GW emission (Sec. \ref{['sec_ellipticity_Eloss']}). Bottom row: theoretical maximum, assuming $\eta=100\%$ of spin-down energy converts to GW emission (Sec. \ref{['sec_ellipticity_Eloss']}). Left column: MSP Population i@ based on the ATNF pulsar catalog ATNF_catalog. Right column: MSP Population ii@ based on Ploeg et al. Ploeg_2020.
• Figure 4: Distribution of maximum Doppler shifts, $(\Delta f)^{\max }_{\mathrm{bin}}$, versus half orbital period for the 199 MSPs in the binary systems from the ATNF pulsar catalog ATNF_catalog. Among the 619 MSPs used in the main text, 289 are confirmed to be in binary systems, of which 199 have measured orbital semi-major axis $a_p$, orbital period $P_{\rm bin}$, and eccentricity $e$, as required in Eq. \ref{['eq_v_binary']}.
• Figure 5: The distribution of MSPs based on the boxy bulge model (left; used in the main text) and the spherical bulge model (right).