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One advantage of this approach is to use other globular clusters to probe the halo. what about pulsars? They're only 20 km or so in diameter! That's 2e4 m or 2e6 cm! yup, found a good paper on that....
Wave optics
If diffraction becomes important on Schwarzchild radius rather than Einstein radius scale, what is that? GM/c^2 for M=10^20 gm = 10^17 kg = 6.67E-11*1E17/(3e8)^2 = 7 E-11 m
Sure enough, that's way less than a micron. This might be because the entire Einstein radius does not make a thin lens, light only arrives from the marginal rays.
For 100 km Eistein radius at 10 kpc = 3e17 km, angle is 100/3e17 = 30 e-15 = 3e-14. Path length difference is (1-cos(theta))*L ~
pulsars
what about pulsars? They're only 20 km or so in diameter! That's 2e4 m or 2e6 cm! yup, found a good paper on that....
collision rate
How many hit the Earth? If R_E for LMC distance is 100 km, surface area of the microlensing sausage is 2piR*L = 600km * 1.5E18 km ~ 10^21 km^2. We get about one PBH per year
through that, at 10^12 solar masses. Cross section of the Earth is pi*(6500km)^2 = 1.3e8 km^2. So we get hit once in every 10^21/10^8 = 10^13 years, or >> a Hubble time. rats.
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