An updated version of the results on this webpage may be found here

This is the page describing the main results for various dependences of the GWSim simulations on parameters.

Description of behaviour of scatter - see "summary of GWsim results" on venice.

Describe what parameters were used e.g. value of alpha

Important!

It appears that even though ensemble averaging over anywhere from 1-50 Universes drastically reduces the amount of scatter in the plot, it does not change the significance by a large amount (Sig = 13.1 for 1 Universe, 13.75 for 50). This is probably due mainly to machine errors (erf(3) = 0.999978 and we are attempting to calculate erf(>13)) and also the fact that the largest correlation we can have is 1, hence the largest significance we can have for 20 pulsars is 1*sqrt(190) = 13.784. This also explains why in the plots in Part 3 (and the other sections also) the scatter in the plot reduces but the significance does not reduce very much - this is because the significance is approaching it's maximum value, whereas the scatter can decrease uniformly to 0.

Part 1: no rms noise, even sampling in RA

Statement of the issue: In this first part, we are simulating an isotropic background of gravitational wave sources with perferct timing residual measurements (i.e. rms = 0). Particularly when the pulsar term is off, should we therefore see 0 scatter in the plot of correlation-vs-angle between pulsars? However, the simulated correlations exhibit some scatter about the expected function (as mentioned in Jenet et al, 2005 and derived in Hellings and Downs, 1983).

Uses contrived uiverse with all on same declination of -45 degrees, evenly distributed in RA across sky.

Part 2: 100ns rms noise, even sampling in RA

Part 3: 100ns rms noise, use of real .par files for the pulsars

1. Num GWs vs. Significance

2. Num GWs vs. Scatter

3. Scatter vs. Significance as you change Num GWs

4. MJD range (observing length) vs. Sig

5. MJD range vs. Scatter

6. Scatter vs. Sig as MJD is varied

Averaging over many universes

We can easily reduce the amount of scatter in plots such as:

\[Removed GWplot.png because it incorrectly labelled the HD curve a "Dipole" signature instead of a "Quadrupole" signature\]

7. Ensemble average over 50 Universes

\[Removed ens_avg.png because it incorrectly labelled the HD curve a "Dipole" signature instead of a "Quadrupole" signature\]

Observe dramatic increase in significance (by eye), showing that the scatter is ultimately due to the noise term (a result of there only being one universe, whereas the theoretical curve carries out an ensemble average over an infinite number of universes.

8. Any other random properties George wants me to simulate. Other dependences.

My other file pre-editing