Download Astronomy 418/518 final practice exam 1. Give short answers to the

Astronomy 418/518
final
practice exam
1.
a.
Give short answers to the following questions.
What limits the size of a corrected field of view in AO?
b.
Describe the visibility vs. baseline for a two element, adjustable baseline
interferometer for the following objects:
i.
A point source
ii.
A uniformly bright disk
iii.
A binary star
c.
How does a coronagraph aid in the detection of faint companions to a star?
2.
Imagine you are trying to decide whether to use HST or an AO-equipped 8 m
telescope to get stellar photometry at R and H band of a crowded stellar cluster. Assume
the cluster is 50” on a side. Further, assume all cameras have the required field-of-view to
image the cluster. Assume the seeing at the ground-based site is 0.6” in the visible. The
mean height of the turbulence for the site you are considering is 5 km. The wind speed is
10 m/s.
a.
Describe, qualitatively, the technical advantages and disadvantages of each
approach.
b.
c.
Calculate the seeing width expected for R band and H band observations.
If the Strehl ratio is dominated by the fitting error, and you decide you need
a value of 35% or higher, how many actuators should the AO system have
to obtain good results at H band? At R band?
d.
Assume the cluster has enough bright stars you can use any of them for a guide star,
and they all create high Strehl ratio images for the guide star.
Could you obtain the results you need by using a single guide star at the center of
the field at H band? At R band? If not, how many pointings do you need?
3.
An astronomer, tired of traveling to a remote mountaintop to acquire his AO
observations, suggests moving the telescope to the Steward Observatory grounds. On the
mountaintop, the telescope had 0.6” seeing in the H band (1.65 microns) under median
conditions, for non-AO observations. The wind speed for the turbulence is estimated to
be 10 m/s. The AO system produced diffraction-limited images, at H ban. It has 100
actuators distributed within the 4 m circular pupil, and operates at a speed of 300 Hz. He
has measured the seeing at Steward Observatory to be 2” under median conditions, and
estimates that the wind speed for the atmospheric turbulence is similar to the mountaintop
location. His goal (and yours) is to understand how to change the AO system to get the
same performance as on the mountaintop.
a. Estimate the size scale for which the wavefront phase errors are 1 radian, RMS,
(the Fried length) for H band, for both the mountaintop and Steward locations.
b. Describe what effects contribute to wavefront residual errors, for a bright (V
magnitude <8), on-axis star and calculate their values. Use these to calculate
the Strehl of the star for the mountaintop, and for the same system at Steward.
c. How would you modify the AO system to obtain the same performance at the
Steward location as on the mountaintop?
4. Determine a simple formula for the probability of two events on a CCD pixel as a function of
the pixel read time and the count rate. For the case of Chandra, with readouts every 3.2 seconds,
above what count rate will the pileup (two or more events) rate exceed 10% of the count rate?
5. Given an X-ray background of 2 counts/cm2 second ster keV over a band from 0.5 to 2 keV,
compute the minimum number of X-rays that need to be detected with Chandra (for a point
source within a field of 12 arcmin radius, for which you can take the circled event radius to be 10
arcsec; take a collecting area of 1000 square cm) to claim a significant detection of a source in
this band at greater than 99% confidence it is not a random confluence of counts. Report the
result both for an integration time of 3000 seconds and one of 300,000 seconds.
6. You bought an equilateral prism of crown glass, designed with three 60o angles (equal sides).
If you put it into a spectrometer with a camera focal length of 1 meter, what is the linear
dispersion at the focal surface (nm mm-1) at a wavelength of 500nm? Assume for this calculation
that the input beam makes the same angle with the prism face as the output at 500nm. How does
the dispersion change if the input and output angles are not constrained to be the same? The
refractive index of crown glass can be taken as
with A = 1.5220 and B = 0.00459 (m)2
7. A student is measuring a star in a spectral band at 1.55 m, where the sky brightness is 1500
photons sec-1 (square arcsec)-1. The instrument aperture on the sky is 3 arcsec in diameter and the
measurement is obtained by integrating for equal times pointed at the source and at a nearby
region of sky and differencing the two readings. The source signal is 100 photons sec -1. The net
instrument efficiency is 10%. How long does it take to measure the source to a ratio of signal to
noise of ten?
8. The total thickness of the atmosphere is equivalent to 1030 g cm-2 and a radiation length is 37 g
cm-2. Assume that the first photons reaching a Cherenkov light detector was emitted at 3 radiation
lengths and the last at 16 radiation lengths, with a separation of 8km between the two depths in
the atmosphere. Take the refractive index of the air in this range to be 1.0002. Estimate the pulse
width of the light reaching the light detector.
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