Constraining primordial black holes using fast radio burst gravitational-lens interferometry with CHIME/FRB

Calvin Leung et al.

Phys. Rev. D 106, 043017 – Published 15 August 2022

Abstract

Fast radio bursts (FRBs) represent an exciting frontier in the study of gravitational lensing, due to their brightness, extragalactic nature, and the compact, coherent characteristics of their emission. In a companion work [Z. Kader and C. Leung, Phys. Rev. D 106, 043016 (2022).], we use a novel interferometric method to search for gravitationally lensed FRBs in the time domain using bursts detected by CHIME/FRB. There, we dechannelize and autocorrelate electric field data at a time resolution of 1.25 ns. This enables a search for FRBs whose emission is coherently deflected by gravitational lensing around a foreground compact object such as a primordial black hole (PBH). Here, we use our nondetection of lensed FRBs to place novel constraints on the PBH abundance outside the Local Group. We use a novel two-screen model to take into account decoherence from scattering screens in our constraints. Our constraints are subject to a single astrophysical model parameter—the effective distance between an FRB source and the scattering screen, for which we adopt a fiducial distance of 1 pc. We find that coherent FRB lensing is a sensitive probe of sub-solar mass compact objects. Having observed no lenses in 172 bursts from 114 independent sightlines through the cosmic web, we constrain the fraction of dark matter made of compact objects, such as PBHs, to be $f ≲ 0.8$ , if their masses are $\sim 10^{- 3} M_{⊙}$ .

Received 18 April 2022
Accepted 12 July 2022

DOI:https://doi.org/10.1103/PhysRevD.106.043017

Physics Subject Headings (PhySH)

Gravitational lenses Massive compact halo objects Radio, microwave, & sub-mm astronomy Transient & explosive astronomical phenomena

Gravitation, Cosmology & Astrophysics

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High-time resolution search for compact objects using fast radio burst gravitational lens interferometry with CHIME/FRB

Zarif Kader et al. (CHIME/FRB Collaboration)

Phys. Rev. D 106, 043016 (2022)

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Vol. 106, Iss. 4 — 15 August 2022

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Images

Figure 1
Our schematic depiction of the lens plane, with coordinates centered on the source’s unlensed position, and transverse distances measured in units of Einstein radii. We shade the delay between images as a function of lens’s transverse position in the lens plane (colored disk). A time-delay based detection search space constrains possible lens positions to an annulus within the plane. A flux-based detection threshold, parametrized by $ϵ_{\min}^{2}$ , further constrains the annulus’s outer boundary via Eq. (5) (dotted boundaries). The lensing cross section $σ$ can be understood as the area of the annulus that satisfies both the flux- and time-delay based detection thresholds [Eq. (8)].
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Figure 2
The expected lensing rate as a function of the lens mass for the sightline toward FRB 20191219F. The height of the curve can be interpreted as the Poisson rate of lensing events (i.e., the probability that the FRB is lensed) assuming that all dark matter is made up of compact lenses with mass $M_{c}$ . For example, the probability of seeing a statistically significant lensing signal if all the dark matter is composed of $\sim 10^{- 1} M_{⊙}$ black holes is $\approx 0.6$ . We calculate this rate via two methods, shown by the solid and dotted curves. Solid curve: sensitivity given by the ACF $ϵ^{2} (τ)$ measured by our correlation algorithm. Dashed curve: sensitivity given by a constant fiducial value of $ϵ^{2} = 10^{- 4}$ , shown to illustrate the difference with the approach taken by earlier work such as [22]. Color shading denotes the additive contributions to the total probability from different time-delay scales. Relative to the constant- $ϵ^{2}$ case, the reduced event rate at short lags/low lens masses is because instrumental systematics in the delay spectrum at short delay scales ( $\approx 100 ns$ ) degrade sensitivity. A similar reduction happens at long lags because of the large trials factor at large delay values (see text).
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Figure 3
The expected lensing event rate for our full sample of 114 FRB events assuming that all dark matter is composed of PBHs with mass $M_{c}$ (i.e., that $f = 1$ ). Left: in the absence of plasma scattering screens which cause decoherence, the predicted lensing event rate extends over a wide range of PBH masses. Right: in the presence of plasma screens, the level of decoherence is sensitive to the screen’s effective distance from the FRB source (different traces). This shows the impact of plasma scattering on coherent FRB lensing constraints.
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Figure 4
A two-screen model for a coherently lensed FRB observed at some central frequency $ν_{obs}$ . The plasma lens is responsible for the observed temporal broadening ( $τ_{scatt, obs}$ ), produced by a scattering screen of apparent size $r_{ref}$ . The gravitational lens, modeled as a point mass with mass $M$ and impact parameter $b$ , can be thought of as a very long baseline interferometer with baseline $\sim R_{E} \propto \sqrt{M}$ observing at a frequency of $ν_{obs} (1 + z_{L})$ from the lens plane. When the scattering screen looks like a point source [Eq. (20)] to the gravitational lens, coherence is maintained, and the observer can see an interference fringe.
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Figure 5
Left: 95% constraints on PBHs as a function of scattering screen distance corresponding to the optical depth calculated in Fig. 3. We plot our fiducial (1 pc screen) model in red and suppress curves for screen distances of 10 and 100 pc because $λ < 3$ under those assumptions. Right: a collection of microlensing constraints on the fraction of dark matter composed of compact objects (such as PBHs), $f (M_{c})$ , assuming a monochromatic mass function peaked around $M_{c}$ . We have shown Local Group PBH constraints in blue (M: MACHO [108], EROS [109], OGLE [30], Long: long-duration optical microlensing [110], Icarus [111]), and Local Universe constraints in red (SNe [11], CHIME/FRB, this work). CHIME/FRB lensing constraints depend on our two-screen scattering model, in which we have assumed that the average FRB is scattered by a screen at an effective distance of $1 p c$ , and our model for how DM correlates with distance. In these constraints, we have used Eq. (22) to define the exclusion limit as a function of $M_{c}$ . Wave optics effects suppress our signal at $M ≲ 1.5 \times 10^{- 4} M_{⊙}$ and finite source size suppresses our signal at $M ≳ 3 \times 10^{4} M_{⊙}$ . This shows that coherent FRB lensing has the potential to search new parameter space for exotic compact objects such as PBHs.
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