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Class Discussion Date: April 15, 2009
Physics 511.
NOTE: Come prepared! We’ll call on students at random to lead the discussion on each
of the questions below.
Questions to ponder regarding the Barish and Weiss (LIGO) paper:
Physics Today, Oct. 1999, p44.
1. Why is it so difficult to observe low-frequency gravity-wave signals (10-4 to 10-1
Hz) with a ground based measurement?
2. Why is the noise described in terms of a spectral density with units of m Hz-1/2?
3. The “free” masses in LIGO are actually suspended as pendulums. In what sense
do they behave as if they are free?
4. Why does a hoped for 15-fold increase in LIGO’s sensitivity translate into an
almost 3000-fold increase in the expected rate of detectable events?
5. How do laser frequency variations produce spurious signals?
6. How can adding a properly-chosen partially-reflecting mirror on the laser input
line increase “the effective laser power by a factor of 30”? What limits this
increase to the factor of 30?
7. Why is the shot noise contribution in Fig. 4 rising above 100 Hz rather than flat?
What does this say about the effective number of bounces in the cavities?
8. What are some advantages of Dicke’s scheme of feeding back a force onto a
mirror to keep the interference fringe constant?
9. How do laser intensity variations produce spurious signals? After all, don’t the
radiation pressure forces act equally on the two end mirrors and therefore cancel?
10. Suppose identical two stars rotate about their common center of mass at a
frequency f. What is the frequency of their gravitational radiation and does the
energy lost to gravitational radiation decrease or increase the frequency as a
function of time? How does your answer change if one star is much more massive
than the other?
11. The radiated field from a fluctuating dipole falls off as 1/r. What is the radial
dependence of the radiated field from a fluctuating quadrupole?
Note: See http://www.ligo.org/results/ for some recent papers and talks from LIGO.