1. IC40 Flares analysis update Mike Baker PS call, Jan 11 2010

2. Brief outline:
I start out with a brief study of an untriggered flare search using a Gaussian time, and some of the developments that have been made there.
Then I have an update on the triggered flare analysis using Fermi lightcurves, which uses some of the ideas from the untriggered search.

3. In an untriggered search, we find some flare (red, top), but getting the same strength flare at any time is equivalent (bottom).

4. The issue with this is that it pushes the null test statistics to higher values than a chi-square with 4 degrees of freedom, which we would expect with 4 free parameters.
Due to the effective trials being higher for shorter flares, shorter flares are found more often.(Which could be fine, depending on what you're looking for...)

5. The idea Jim Braun came up with is to marginalizate, to take out the dependence on the mean. We start out with our log likelihood ratio, which depends on the best-fit # source events, spectrum, and the mean and sigma of the flare.
we integrate over the Pdf in the likelihood and T_L is the uniform prior, the total time of data taking. The formula becomes:
Maximizing this formula gives us a null test statistic distribution that is a chi square distribution with 3 dof.

6. This example is at the same declination as 3C 454.3.
Marginalizing improves sensitivity to longer flares, the discovery potential becomes better around 0.2 days, or flares with a FWHM of half a day.
This example is at the same declination as 3C

7. I've also made an approximation of this marginalization for the case for the Fermi flares where I let the lightcurve slide forward and back in time:
Where I use the total time as the prior and T_Above is the duration of the lightcurve above the flux threshold, the log likelihood ratio becoming:

8. When applying the marginalization to the lightcurve for PKS 1510-089
The dashed black curve is the too optimistic line I presented previously, the solid black line is using the marginalization.

9. I've also checked the distribution of null test statistics for instances where I allow for a small time lag. Previously I had looked for at time lag with the motivation of finding a difference in the arrival time of messenger particles, however using a small limit on the lag is better described as interpolating the Pdf.
Allowing for ±0.5 or ±1 days of lag ( % of the IC40 year) gives a null test statistic distribution identical to not allowing a lag. This means the discovery potential curve will be the same as using no time interpolation.
I would like to use the ±0.5 day as a maximum lag, or one full day spread. That is identical to the size of the binning I used making the Fermi lightcurves.
There is a summary page of checks of these investigations at: