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IC-40 Time Dependent Analysis/Flares/Lightcurve

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[edit] Flares seen with comprehensive coverage

[edit] Method

For these flares, the analysis utilizes 1-day binned lightcurves from the Fermi LAT. We use the Maximum Likelihood Block algorithm to de-noise the lightcurves by finding periods from the lightcurves which are consistent with constant emission. Finally we use the Maximum Likelihood Block algorithm output to search for a best-fit threshold on emission given the data.

A comparison study for different significance levels for the Maximum Likelihood Block method de-noising can be found here. We found that the output of the algorithm is only weakly dependent on the significance parameter.

For this analysis using lightcurves we began from the work studying ASM lightcurves of blazars by ElisaR et al. [1] which uses ten years of X-ray observations of blazars to determine a baseline flux, then moves on to calculate the fraction of time a given source has a flux 1- $σ$ or 3- $σ$ above that baseline. The initial test was to take the block reconstruction of the Fermi lightcurve and to perform the same analysis, to determine a quiescent flux and take the periods with a significance 3- $σ$ or greater above to test for coincidence with neutrinos.

I found that the discovery potential depends quite a bit on the assumed emission threshold. For instance, if I make my flaring states at 3- $σ$ above quiescence, but the flux of neutrinos is directly proportional to the lightcurve without the cut above 3- $σ$ , I need a good deal more events. I likewise also need more events if neutrino emission is proportional to the lightcurve above 4 or 5- $σ$ . On the right we see the comparison between fixing or fitting for the threshold of emission, and the effect of also finding a best-fit time lag.

Fig. 1 (left) and Fig. 2 (right): We compare the impact of fixing the tested threshold of emission to an incorrect value versus leaving it as a best fit parameter.

This choice of how to choose flaring states can be avoided by maximizing to find the best threshold for flaring, to make the choice part of the analysis. Here is a cartoon illustrating the lightcurve with block reconstruction and the threshold parameter to be fit in the analysis (lavender dashed line) on left, the resulting Pdf in time on the right:

Fig. 3 This diagram shows the resulting Pdf from varying the tested threshold of emission.

This leaves us with the expression of the total pdf as the following, where thresh is the threshold, block(t_i) is the flux value of the block at time t_i and N is a normalization factor which depends on the threshold and block reconstruction:

$\mathcal{S}_i(|x_i-x_s|, E_{i}, \gamma, t_i, thresh) = \frac{1}{2\pi\sigma_i^2} exp(-\frac{|x_i-x_s|^2}{2\sigma_i^2}) P_{SigMue}(E_i,\gamma) * \mathcal{T}_i : if \{block(t_{i})>thresh\} ( \mathcal{T}_{i} = (block(t_{i})-thresh)*\frac{1}{N} ) else ( \mathcal{T}_{i} = 0 )$

Due to the one-day binning of the Fermi lightcurves, there is some ambiguity on where a flare will begin or end. To avoid missing signal neutrinos due to this ambiguity, I propose to allow the method to move the lightcurve forward or back in time by up to 0.5 days to find the best signal. The upper limit of 0.5 days being motivated by the lightcurve bin size, as opposed to a difference in the arrival times of messenger particles.

We can compare the discovery potential with this lightcurve using the IC40 ps sample and scrambling times over the entire year, varying the threshold above which signal events are injected. Below is the Poisson average number of injected E^-2 signal events needed for discovery in 50% of trials for 4 cases:

1) a method where we find a best-fit for the threshold, also fit for a potentially long time-lag between neutrinos and photons;
2) a method where we fit for the best threshold given the data and allow a small (up to 0.5 day) time-lag motivated by the binning;
3) a method where the threshold is fixed to the true value of the injected signal events (this is the best case we can expect); and 
4) the example of a time-integrated analysis.

Below left shows the threshold in flux units, below right shows the discovery potential as a function of the number of days passing the cut. Both are for the PKS 1510-089 Fermi LAT lightcurve shown above. The method proposed to use for the analysis is the red line.

Fig. 4 We compare the average number of E^-2 spectrum neutrino events needed for 50% discovery versus (left) the true threshold of emission for injected signal and (right) the number of days above threshold of emission.

The lightcurves are made by using the Fermi public data release photon-by-photon data and released Fermi tools. All Fermi "diffuse-class" events [2] within 2° of the source position are taken, and the flux errors are statistical only. There are two deviations from this procedure, they and their justifications are listed below:

3C454.3 has a significant published flare before science data runs began. For this source we would take the published lightcurve from their paper and the website here.

PKS 1502+106 has a flare which was reported by Fermi to begin on August 6 2008 (MJD 54684), five days before science operations begin on August 11 2008 (MJD 54689). I would like to extend the Pdf back for these 5 days, at the level of the second daily bin (4.43e-06 photons/s/cm^2).

[edit] List and Discovery Potentials of IC-40 Flares seen with comprehensive coverage

This is a list of sources and periods of interest from the IC-40 data-taking period. Light-curves and publications are linked below.

Source (link to MWL Lightcurves)	LC with Block Reconstruction	Discovery Potentials (click for larger image)	Flaring time	Papers	comments
PKS 1510-089	[3]		MJD 54840-54850		Fermi atel: [4]
			MJD ~54910-20		Atels: [5], [6], [7], [8]
			MJD ~54950		Peak visible in Fermi LC
3C66A/B [9]	[10]		MJD ~54743	ICRC0637	Veritas [11], [12], 1759
3C66A/B [9]	[10]		MJD 54963-54970		Peak visible in Fermi LC
3C 454.3 More GeV	[13]		MJD ~54669-54674	[14]	Atel: [15], 1628, [16], [17]
			MJD ~54643	[18]	Atel [19]
			MJD ~54613		Atel [20]
PKS 1454-354 [21]	[22]		MJD 54712-54715	[23]	Atel: [24]
3C279	[25]		MJD 54790-54802		Atel: [26] KANATA optical data
3C279	[25]		MJD ~54880		Fermi peak
PKS 0454-234	[27]		MJD ~54843		Atel:[28]
PKS 1502+106	[29]		MJD ~54686		Atel: [30], [31], [32], Fermi cites a paper in preparation in the Bright Sources paper.
PKS 1502+106	[29]		MJD ~54853		Atel: [33]
J123939+044409	[34]		MJD 54827-54831		Atel: [35], [36]