Wave effects in the microlensing of pulsars and FRBs by point masses. (arXiv:2002.01570v1 [astro-ph.HE])
<a href="http://arxiv.org/find/astro-ph/1/au:+Jow_D/0/1/0/all/0/1">Dylan L. Jow</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Foreman_S/0/1/0/all/0/1">Simon Foreman</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Pen_U/0/1/0/all/0/1">Ue-Li Pen</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Zhu_W/0/1/0/all/0/1">Wei Zhu</a>
Wave effects are often neglected in microlensing studies; however, for
coherent point-like sources, such as pulsars and fast radio bursts (FRBs), wave
effects will become important in their gravitational lensing. In this paper, we
describe the wave optics formalism, its various limits, and the conditions for
which these limits hold. Using the simple point lens as an example, we will
show that the frequency dependence of wave effects breaks degeneracies that are
present in the usual geometric optics limit, and constructive interference
results in larger magnifications further from the lens. This latter fact leads
to a generic increase in cross section for microlensing events in the
wave-optics regime compared to the geometric optics regime. For realistic
percent-level spectral sensitivities, this leads to a relative boost in lensing
cross section of more than an order of magnitude. We apply the point-lens model
to the lensing of FRBs and pulsars and find that these radio sources will be
lensed in the full wave-optics regime by isolated masses in the range of
$0.1-100,M_oplus$, which includes free-floating planets (FFPs), whose
Einstein radius is smaller than the Fresnel scale. More generally, the
interference pattern allows an instantaneous determination of lens masses,
unlike traditional microlensing techniques which only yield a mass inference
from the event timescale.
Wave effects are often neglected in microlensing studies; however, for
coherent point-like sources, such as pulsars and fast radio bursts (FRBs), wave
effects will become important in their gravitational lensing. In this paper, we
describe the wave optics formalism, its various limits, and the conditions for
which these limits hold. Using the simple point lens as an example, we will
show that the frequency dependence of wave effects breaks degeneracies that are
present in the usual geometric optics limit, and constructive interference
results in larger magnifications further from the lens. This latter fact leads
to a generic increase in cross section for microlensing events in the
wave-optics regime compared to the geometric optics regime. For realistic
percent-level spectral sensitivities, this leads to a relative boost in lensing
cross section of more than an order of magnitude. We apply the point-lens model
to the lensing of FRBs and pulsars and find that these radio sources will be
lensed in the full wave-optics regime by isolated masses in the range of
$0.1-100,M_oplus$, which includes free-floating planets (FFPs), whose
Einstein radius is smaller than the Fresnel scale. More generally, the
interference pattern allows an instantaneous determination of lens masses,
unlike traditional microlensing techniques which only yield a mass inference
from the event timescale.
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