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HellDown below is a very rough draft (including DY's notes to himself) For some further information, check out the Projects/IntProjects/GWsim page Questions about curve Remember it's not gravity, it's gravitational waves, so you CAN have positives and negatives. TEST if my residuals from expected curve form a zero-mean Gaussian random variable ("for practical purposes" - Jenet et al 2005, near bottom of 1st page). Result: They probably are over many runs of the code. 0.(i) Why does the Hellings-and-Downs curve not go down to -0.5? 0.(ii) Why is the minimum not at 90 degrees? 1. Why does the curve only go to 0.5 at angle = 0? (okay I know the answer to this one, but let's start easy!) An isotropic background of gravitational waves perturbs space time at the Earth, at every pulsar and throughout all space in between in a stochastic way. However, the perturbations of the Earth should be observable by looking for correlations in the timing data. The "pulsar term" for each pulsar will have a correlation of zero with every other pulsar, since their GW perturbations are uncorrelated. However, the "Earth term" will be correlated as described by the H&D curve. When the angle between two pulsars is zero (either they are directly behind each other or we could use the double pulsar system 0737), they still occupy different points in space time, so are subjected to different regions of the GW background, and every region has to be uncorrelated with every other region. 2. What determines the angle of the minimum of the curve? If the different polarisations have different amplitudes of effect, then shouldn't we be able to tell them apart? there's something a bit strange about that... 3. What determines the minimum correlation in the curve? (i.e. what determines the greatest anti-correlation present in the curve?) Ans: 4. What determines the amount of scatter in the plot? Ans: 5. Why can't we detect a background with less than ~20 pulsars? Ans: We can, is just 6. What is the effect of turning on/off the pulsar term? Ans: does everything double? significance doesn't, but how does it change? 7. What happens as we add more GWs into our simulated background? Ans: The significance increases and the scatter reduces. 8. Why is there scatter in the curve? Ans: because we cannot perform the ensemble average over many universes. it is the "noise term" spoken of at the bottom of page 1 of Jenet et al 2005. Can we simulate many universes with a selection of seeds? then take the mean of all the points and they should lie exactly along the theoretical curve. This performs the ensemble average. COULD TRY doing a weighted average where the weighting is by the significance, so that universes with less significance appear less strongly in the ensemble average. HOW DO I TELL IF SOMETHING IS NOT A GAUSSIAN RANDOM VARIABLE?? ASIDE FROM PLOTTING ITS DISTRIBUTION AND LOOKING AT IT... |