Download Baker_pscallJan102010

IC40 Flares analysis update
Mike Baker
PS call, Jan 11 2010
Brief outline:
-Untriggered flare search using Gaussian emission
(still under development)
-Introduce marginalization over flare time
-Introduce discovery potentials
-Triggered flare search using Fermi Lightcurves
(ready for final review before analysis call)
-Introduce time marginalization
-Introduce interpolation
-Update discovery potentials
http://wiki.icecube.wisc.edu/index.php/IC-40_Time_Dependent_Analysis
In an untriggered search, we find some flare (red, top), but
getting the same strength flare at any time is equivalent.
There's a certian 'trials factor' inside the analysis, for how
many independent ways we could find a flare of the same
duration (for example, one of the black curves on the bottom
instead of the red).
A simple maximization of the likelihood doesn't account
for this trials factor, and we get higher values for the null
test statistic than we'd expect given that we have 4 free
parameters.
Also, 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...)
The idea Jim Braun came up with is to marginalize. We start out
with our log likelihood ratio, which depends on the best-fit # of
source events, spectrum, and the mean and sigma of the flare.
we integrate over time in 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 follows a chi square distribution with 3 dof.
Marginalizing improves
detection probability
for longer flares, the
discovery potential
becomes better above
0.2 days, or flares with
a FWHM of half a day.
This example is at the
same declination as
3C 454.3.
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 by many days:
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:
Graphically, T_Above is the number of days we have a
non-zero entry in the Pdf (right) given the threshold on
the blocks lightcurve (left).
Here I apply the marginalization to the lightcurve of PKS
1510-089 (seen on previous slide).
The dashed black curve is the too optimistic line I presented
previously, the solid black line is using the marginalization.
The red and blue lines are not marginalized, since they don't
search over broad lengths of time.
I've just explained what I've done with searching for some long time lag (up
to ±70 days) to detect some difference between the arrival time between
messenger particles.
I've also checked the distribution of null test statistics for instances where I
allow for only a small time lag. This has a statistical motivation, since I use
1-day binned lightcurves and can choose where the bin starts. Essentially
I'm using this to interpolate the Pdf.
Allowing for ±0.5 or ±1 days of lag (0.1-0.2% 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 in
the analysis.
There is a summary page of checks of these investigations at:
http://www.icecube.wisc.edu/~mfbaker/IC40/lc_teststats.
The work with untriggered flare searches is ongoing, but I'm
still working on more checks for applications of the method
beyond one point. The goal is an all-sky search for flares.
For triggered flares, the lightcurve method is outlined here
and I think it's ready to go.
There are also several flares from times without Fermi data
which use the same box method as used for IC22 MWL flares
which is also ready.
I'd like to have another round with the PS referees and move
to the analysis call as soon as possible with these triggered
flares.