Small-scale shear: Peeling off diffuse subhalos with gravitational waves - INSPIRE

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Small-scale shear: Peeling off diffuse subhalos with gravitational waves

Mar 15, 2021

24 pages

Published in:

Phys.Rev.D 104 (2021) 6, 063001

Published: Sep 2, 2021

e-Print:

2103.08618 [astro-ph.CO]

DOI:

10.1103/PhysRevD.104.063001 (publication)

View in:

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Abstract: (APS)

Subhalos at subgalactic scales (

M ≲ 10^{7} M_{⊙}

or

k ≳ 10^{3} {Mpc}^{- 1}

) are pristine test beds of dark matter (DM). However, they are too small, diffuse and dark to be visible, in any existing observations. In this paper, we develop a complete formalism for weak and strong diffractive lensing, which can be used to probe such subhalos with chirping gravitational waves (GWs). Also, we show that Navarro-Frenk-White (NFW) subhalos in this mass range can indeed be detected individually, albeit at a rate of

O (10)

or less per year at Big Bang Observer and others—limited by small merger rates and large required

SNR ≳ 1 / γ (r_{0}) \sim 10^{3}

. It becomes possible as NFW scale radii

r_{0}

are of the right size comparable to the GW Fresnel length

r_{F}

, and unlike all existing probes, their lensing is more sensitive to lighter subhalos. Remarkably, our formalism further reveals that the frequency dependence of weak lensing (which is actually the detectable effect) is due to shear

γ

at

r_{F}

. Not only is it consistent with an approximate scaling invariance, but it also offers a new way to measure the mass profile at a successively smaller scale of chirping

r_{F} \propto f^{- 1 / 2}

. Meanwhile, strong diffraction that produces a blurred Einstein ring has a universal frequency dependence, allowing only detections. These are further demonstrated through semianalytic discussions of power-law profiles. Our developments for a single lens can be generalized and will promote diffractive lensing to a more concrete and promising physics in probing DM and small-scale structures.

Note:

21 pages, 15 figures

frequency: dependence
black hole: binary
gravitation: lens
dark matter
diffraction
gravitational radiation
cosmological model
LISA
galaxy
galaxy: halo

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