problemset1

Problemset1

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Unformatted text preview: y distributed in direction) has a uniform (flat) probability distribution in cos i. Using the measured distribution of mass functions for the systems in the table, determine if these systems are consistent with being a randomly chosen ensemble of symbiotic binaries with typical component masses. To do this, first plot the cumulative distribution function (CDF) for the set of f1 measurements. [Recall that for an ensemble of measurements {xi }, the function CDF(xi ) is equal to the fraction of ensemble values for which x < xi . The CDF thus increases monotonically between zero and unity.] For comparison, also plot the expected CDF of mass functions for a randomly oriented ensemble of binaries with M1 = 1.5M and M2 = 0.56M . What can you say about whether the collection of binaries in the table is “typical” of symbiotic binaries in terms of masses? If there are any individual systems that seem to stand out as different, identify them and indicate what you can deduce about them is you assume only that M1 = 1.5M is correct. 10. Magnitudes (optical intensity). Because photon counting detectors are governed by Poisson statistics, when we expect to observe N photons from an astrophysical source in a given time interval, the √ actual number detected will fluctuate by an amount ± N . (a) How many photons need to be collected if the apparent magnitude of a star has to be measured to an accuracy of ±0.02? How long an exposure would be required with a 1-m (diameter) telescope to measure the B magnitude of an mB = 20 star to this accuracy? You may assume that the telescope+detector combination have 100% detection efficiency. You may also neglect the noise background from the sky. (b) Now consider an attempt to measure the magnitude of a fainter star (mB = 24) with the same accuracy. Assume that the sky background light has brightness 22.5 mag arcsec−2 in B , and that atmospheric effects cause the starlight to be spread over a circle with 1 arcsec diameter. How many photons are required to achieve this measurement? How long would this take with a 1-m telescope? What about with a 4-m telescope? Note that MIT is a consortium partner for the two 6.5-m Magellan telescopes in Chile.....
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This note was uploaded on 01/24/2014 for the course PHYS 8.901 taught by Professor Deeptochakrabarty during the Spring '06 term at MIT.

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