This preview shows page 1. Sign up to view the full content.
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 1m (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 1m
telescope? What about with a 4m telescope? Note that MIT is a consortium partner for the two
6.5m Magellan telescopes in Chile.....
View
Full
Document
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.
 Spring '06
 DeeptoChakrabarty
 Physics, Mass

Click to edit the document details