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Register a new userPrimordial Black Hole Microlensing: The Einstein Crossing Time Distribution
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Gravitational microlensing is one of the few means of finding primordial black holes (PBHs), if they exist. Recent LIGO detections of 30 Msun black holes have re-invigorated the search for PBHs in the 10-100 Msun mass regime. Unfortunately, individual PBH microlensing events cannot easily be distinguished from stellar lensing events from photometry alone. However, the distribution of microlensing timescales (tE, the Einstein radius crossing time) can be analyzed in a statistical sense using models of the Milky Way with and without PBHs. While previous works have presented both theoretical models and observational constrains for PBHs (e.g. Calcino et al. 2018; Niikura et al. 2019), surprisingly, they rarely show the observed quantity -- the tE distribution -- for different abundances of PBHs relative to the total dark matter mass (fPBH). We present a simple calculation of how the tE distribution changes between models with and without PBHs.
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Microlensing of stars, e.g. in the Galactic bulge and Andromeda galaxy (M31), is among the most robust, powerful method to constrain primordial black holes (PBHs) that are a viable candidate of dark matter. If PBHs are in the mass range $M_{rm PBH} lower.5exhbox{$; buildrel < over sim ;$} 10^{-10}M_odot$, its Schwarzschild radius ($r_{rm Sch}$) becomes comparable with or shorter than optical wavelength ($lambda)$ used in a microlensing search, and in this regime the wave optics effect on microlensing needs to be taken into account. For a lensing PBH with mass satisfying $r_{rm Sch}sim lambda$, it causes a characteristic oscillatory feature in the microlensing light curve, and it will give a smoking gun evidence of PBH if detected, because any astrophysical object cannot have such a tiny Schwarzschild radius. Even in a statistical study, e.g. constraining the abundance of PBHs from a systematic search of microlensing events for a sample of many source stars, the wave effect needs to be taken into account. We examine the impact of wave effect on the PBH constraints obtained from the $r$-band (6210AA) monitoring observation of M31 stars in Niikura et al. (2019), and find that a finite source size effect is dominant over the wave effect for PBHs in the mass range $M_{rm PBH}simeq[10^{-11},10^{-10}]M_odot$. We also discuss that, if a denser-cadence (10~sec), $g$-band monitoring observation for a sample of white dwarfs over a year timescale is available, it would allow one to explore the wave optics effect on microlensing light curve, if it occurs, or improve the PBH constraints in $M_{rm PBH}lower.5exhbox{$; buildrel < over sim ;$} 10^{-11}M_odot$ even from a null detection.
We consider gravitational radiation and electromagnetic radiation from point mass binary with electric charges in a Keplerian orbit, and calculate the merger rate distribution of primordial black hole binaries with charges and a general mass function by taking into account gravitational torque and electromagnetic torque by the nearest primordial black hole. We apply the formalism to the extremal charged case and find that $alpha=-(m_i+m_j)^2partial^2 ln {cal R}(m_i,m_j)/partial m_i partial m_j=12/11$, which is independent of the mass function.
If the Dark Matter consists of primordial black holes (PBHs), we show that gravitational lensing of stars being monitored by NASAs Kepler search for extra-solar planets can cause significant numbers of detectable microlensing events. A search through the roughly 150,000 lightcurves would result in large numbers of detectable events for PBHs in the mass range $5 ten{-10}msun$ to $aten{-4}msun$. Non-detection of these events would close almost two orders of magnitude of the mass window for PBH dark matter. The microlensing rate is higher than previously noticed due to a combination of the exceptional photometric precision of the Kepler mission and the increase in cross section due to the large angular sizes of the relatively nearby Kepler field stars. We also present a new formalism for calculating optical depth and microlensing rates in the presence of large finite-source effects.
In light of our previous work cite{Liu:2019xhn}, we investigate the possibility of formation for primordial black-hole during preheating period, in which we have implemented the instability of the Mathieu equation. For generating sufficient enough enhanced power spectrum, we choose some proper parameters belonging to the narrow resonance. To characterize the full power spectrum, the enhanced part of the power spectrum is depicted by the $delta$ function at some specific scales, which is highly relevant with the mass of inflaton due to the explicit coupling between the curvaton and inflaton. After the inflationary period (including the preheating period), there is only one condition satisfying with the COBE normalization upper limit. Thanks to the huge choices for this mass parameter, we can simulate the value of abundance of primordial black holes nearly covering all of the mass ranges, in which we have given three special cases. One case could account for the dark matter in some sense since the abundance of a primordial black hole is about $75%$. At late times, the relic of exponential potential could be approximated to a constant of the order of cosmological constant dubbed as a role of dark energy. Thus, our model could unify dark energy and dark matter from the perspective of phenomenology. Finally, it sheds new light for exploring Higgs physics.
It has recently been proposed that massive primordial black holes (PBH) could constitute all of the dark matter, providing a novel scenario of structure formation, with early reionization and a rapid growth of the massive black holes at the center of galaxies and dark matter halos. The scenario arises from broad peaks in the primordial power spectrum that give both a spatially clustered and an extended mass distribution of PBH. The constraints from the observed microlensing events on the extended mass function have already been addressed. Here we study the impact of spatial clustering on the microlensing constraints. We find that the bounds can be relaxed significantly for relatively broad mass distributions if the number of primordial black holes within each cluster is typically above one hundred. On the other hand, even if they arise from individual black holes within the cluster, the bounds from CMB anisotropies are less stringent due to the enhanced black hole velocity in such dense clusters. This way, the window between a few and ten solar masses has opened up for PBH to comprise the totality of the dark matter.
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