1 microlensing event rates this problem will step you through an order of magnitude calculation

Name: 1 microlensing event rates this problem will step you through an order of magnitude calculation to determine the rate at which microlensing events are expected to be detected for stars withi 92253
Uploaded: 2024-04-20T16:42:48-08:00
Duration: 3 min 33 s
Channel: Numerade
Description: 1 microlensing event rates this problem will step you through an order of magnitude calculation to determine the rate at which microlensing events are expected to be detected for stars withi 92253

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Question

Microlensing Event Rates: This problem will guide you through an order of magnitude calculation to determine the rate at which microlensing events are expected to be detected for stars within our galaxy. (a) To calculate the rate of microlensing events, we first need to estimate the so-called "optical depth" to microlensing events. This value is given by the total fraction of the sky covered by the Einstein rings of all galactic lenses at a given time. Show that this can be expressed as: Ds = 4TGpDLD dDi Dse where p is the galactic mass density. (b) Using the simplifying assumption of a constant galactic mass density and integrating out to the edge of the galaxy (with galactic radius L), evaluate the integral above to produce the following expression: 2r GM T^3 c^2L (c) Evaluate this expression numerically to determine the approximate optical depth to microlensing in our galaxy. (d) With continuous observations of a crowded field in the galactic bulge consisting of approximately 10 million stars and assuming a typical microlensing event timescale of 20 days, approximately how many microlensing events would one expect to observe annually?

          Microlensing Event Rates: This problem will guide you through an order of magnitude calculation to determine the rate at which microlensing events are expected to be detected for stars within our galaxy.

(a) To calculate the rate of microlensing events, we first need to estimate the so-called "optical depth" to microlensing events. This value is given by the total fraction of the sky covered by the Einstein rings of all galactic lenses at a given time. Show that this can be expressed as:
Ds = 4TGpDLD dDi Dse

where p is the galactic mass density.

(b) Using the simplifying assumption of a constant galactic mass density and integrating out to the edge of the galaxy (with galactic radius L), evaluate the integral above to produce the following expression:
2r GM T^3 c^2L

(c) Evaluate this expression numerically to determine the approximate optical depth to microlensing in our galaxy.

(d) With continuous observations of a crowded field in the galactic bulge consisting of approximately 10 million stars and assuming a typical microlensing event timescale of 20 days, approximately how many microlensing events would one expect to observe annually?

1 microlensing event rates this problem will step you through an order of magnitude calculation to determine the rate at which microlensing events are expected to be detected for stars withi 92253

Added by Isaac V.

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