[Paper Review] Modeling the Galactic Neutron Star Population for Use in Continuous Gravitational Wave Searches

Brendan T. Reed, Alex Deibel+1 more|arXiv (Cornell University)|Apr 1, 2021

Pulsars and Gravitational Waves Research47 references24 citations

TL;DR

This paper develops a simple population model for Galactic neutron stars to estimate how many are probed by continuous gravitational wave (CGW) searches based on strain sensitivity limits. Using spatial and spin distributions, it shows that third-generation detectors could probe 100–1000 times more neutron stars than current detectors, especially for moderate ellipticities (ϵ ≲ 10⁻⁶), with high-frequency sensitivity being the most impactful factor for increasing detection reach.

ABSTRACT

Searches for continuous gravitational waves from extit{unknown} Galactic neutron stars provide limits on the shapes of neutron stars. A rotating neutron star will produce gravitational waves if asymmetric deformations exist in its structure that are characterized by the star's ellipticity. In this study, we use a simple model of the spatial and spin distribution of Galactic neutron stars to estimate the total number of neutron stars probed, using gravitational waves, to a given upper limit on the ellipticity. This may help optimize future searches with improved sensitivity. The improved sensitivity of third-generation gravitational wave detectors may increase the number of neutron stars probed, to a given ellipticity, by factors of 100 to 1000.

Motivation & Objective

• To estimate the number of Galactic neutron stars (NSs) probed by continuous gravitational wave (CGW) searches using current sensitivity limits.
• To quantify how improvements in gravitational wave strain sensitivity, particularly at high frequencies, increase the number of detectable NSs.
• To assess the impact of NS disk thickness (z₀) and spin-frequency distribution on the number of probed NSs.
• To evaluate the implications of future third-generation detectors for probing the full population of neutron stars with moderate ellipticity.
• To guide future CGW searches by identifying optimal search parameters, such as spin-down rate limits (|ḟ|), for detecting NSs with different ellipticities.

Proposed method

• Uses a 3D spatial density model for Galactic NSs: ρc(rc, z) = N₀/(4πσ²rz₀) × exp(−r²c/(2σ²r)) × exp(−|z|/z₀), with N₀ = 10⁸, σr = 5 kpc, and z₀ varied to test disk thickness effects.
• Applies the CGW strain amplitude formula h₀ = (4π²G/c⁴) × (Izzf²GWϵ)/d to compute the maximum distance d(fGW, ϵ) excluded for a given ellipticity ϵ and frequency fGW.
• Combines strain sensitivity limits from Abbott et al. (2019a) across three pipelines (SkyHough, Frequency-Hough, TDFstat), taking the 95% confidence lower limit on h₀ at each frequency.
• Integrates over the spatial and spin distributions to compute the total number of NSs probed, N⋆, using Equation 12, which accounts for the overlap of detection volume and NS density.
• Varying the spin-down rate limit |ḟ| to assess its impact on the number of detectable NSs, especially for low-ellipticity sources.
• Projects future sensitivity improvements using the blue dash-dot curve in Figure 6, assuming a 10× improvement in h₀ sensitivity, to estimate N⋆ for third-generation detectors.

Experimental results

Research questions

• RQ1 How many Galactic neutron stars are probed by current continuous gravitational wave searches for a given upper limit on ellipticity?
• RQ2 How does the assumed thickness of the Galactic neutron star disk (z₀) affect the number of detectable neutron stars?
• RQ3 What is the impact of improving gravitational wave strain sensitivity at high frequencies (fGW ≥ 1000 Hz) on the number of neutron stars probed?
• RQ4 How do different assumptions about the spin-down rate (|ḟ|) influence the detectable population of neutron stars with low ellipticity?
• RQ5 To what extent could third-generation gravitational wave detectors increase the number of neutron stars probed compared to current instruments?

Key findings

• Current CGW searches probe fewer than about one in ten thousand neutron stars with ellipticity ϵ ≳ 10⁻⁶.
• Improving strain sensitivity by a factor of 10 at high frequencies (fGW ≥ 1000 Hz) could increase the number of probed neutron stars by a factor of 100 to 1000 with third-generation detectors.
• The number of probed neutron stars (N⋆) is highly sensitive to the assumed disk thickness z₀ for low ellipticities (ϵ ≲ 10⁻⁵.⁵), with an order-of-magnitude difference in estimates depending on z₀.
• High-frequency sensitivity has a greater impact than low-frequency sensitivity for moderate ellipticities, with low-frequency improvements being roughly four orders of magnitude less effective.
• Using a stricter |ḟ| limit of 2.5×10⁻¹² Hz s⁻¹ reduces the search parameter space and improves h₀ sensitivity, but also limits the detection of fast-spinning, highly elliptical NSs (e.g., ϵ ≳ 10⁻⁶), reducing the number of probed NSs for high-ellipticity sources.
• For ϵ ≈ 10⁻⁶, third-generation detectors could probe nearly 40% of all Galactic neutron stars, assuming a 10× improvement in strain sensitivity and |ḟ| = 2×10⁻⁹ Hz s⁻¹.