2000-2006 AMANDA Point Source Analysis

Data and Simulation
Event Selection
Methodology
Sensitivity & Discovery Potential
Unblinding Proposal
Results
Questions and Answers
Systematics, Publication, and Figures
LS I +61 303 Periodic Analysis
Solar WIMP Analysis

NASA/ESA Hubble

Methodology

Fixed Point and All Sky Search

The proposed point source search method for the 2000-2006 combined analysis is identical to the unbinned search used in 2006. Since the method is capable of measuring spectral index, we will place constraints on the spectral index of any spot in the all-sky search with significance > 5σ. See our point source search methodology internal report for more details on the search method.

Stacked Search for Milagro Galactic Sources

Introduction

The high energy galactic sources observed by Milagro [1] are some of the best candidates for neutrino emission which can be detected with AMANDA/IceCube [2]. We wish to combine observations from the direction of several Milagro sources to enhance the probability of detection in a manner similar to the AMANDA AGN stacking search [3]. We include all sources with >5σ pre-trial significance which do not have known PWN counterparts (i.e. exclude the Crab, Geminga, and C4). Several of these sources are known to be extended; however, the extent radius estimated by Milagro [1] is generally smaller than our point spread function, poorly measured, or both, so we treat the sources as true point-like sources. We adapt a method developed by HiRes [4] to perform our likelihood search simultaneously for all Milagro source locations.

Milagro Galactic Sources (>=5σ pretrial significance)

The sources are shown below along with AMANDA E^-2 point source simulation:

Source	l	b	δ	α
MGRO J2019+37	75.0	0.2	36.72^o	305.03^o
MGRO J1908+06	40.4	-1.0	6.18^o	287.18^o
MGRO J2034+41	80.3	1.1	41.57^o	308.04^o
C1 (MGRO J2043+36)	77.5	-3.9	36.3^o	310.98^o
C2 (MGRO J2032+37)	76.1	-1.9	36.52^o	307.75^o
MGRO J1852+01	33.5	0.0	0.51^o	283.12^o

Method

The single source likelihood

described in the unbinned search internal report is modified to use a multiple source hypothesis according to [4]. The new multiple-source pdf, assuming M sources, is given by

where S^j_i is the source PDF for the j^th source s_j and i^th event. The source relative efficiencies R(s_j) are approximated as unity, since detector efficiency over the declination ranges spanned by the Milagro sources varies only by ~15%. The new likelihood expression is now

The total number of signal events from all sources, n_s, and the combined spectral index of all sources, γ, remain free parameters in the likelihood formulation and are fit to best values when -log(likelihood) is minimized. γ is restricted to the range 2.0 < γ < 2.7 as in the fixed point search. Since the Milagro sources span a significant declination range and the AMANDA background is declination dependent, the background PDF is computed individually for each event rather than calculating a single background PDF for all events, which is possible in the single-source case since we limit the search to a small declination range around the source.

A Monte Carlo point source sample is prepared by combining point source simulation for each Milagro source. Each source is assumed to have the same neutrino flux. Discovery potential is then calculated by the same method discussed in the internal report by randomly selecting E^-2 events from the simulation without respect to any particular source, adding them to the data, and analyzing distributions of the test statistic.

Sensitivity & MDP

For the entire sample containing 6 sources:

90% CL Sensitivity	P=0.9 MDP (5σ)
3.74 * 10^-11 TeV cm^-2 s^-1	1.51 * 10^-10 TeV cm^-2 s^-1

The more interesting per-source sensitivity and MDP are obtained by dividing by the number of sources:

90% CL Sensitivity	P=0.9 MDP (5σ)
*6.23 10^-12 TeV cm^-2 s^-1**	*2.51 10^-11 TeV cm^-2 s^-1**

i.e. if all 6 sources emit a flux of 2.51 * 10^-11 TeV cm^-2 s^-1 (approximately the sensitivity level of our search based on a list of source candidates), we would have a 90% chance of 5σ detection. This is a factor of 4 improvement over a fixed-point search for any individual source (P=0.9 ~1e-10 TeV cm^-2 s^-1 for 5σ). In the case of high statistics, significance improves with signal/sqrt(background), so combining 6 sources would yield 6/sqrt(6) ~ 2.6x improvement. However, already low statistics and the use of energy to effectively further reduce the atmospheric neutrino background allow a larger improvement.

Search for Event Clustering

The nature of the signal we expect determines which method we use to search for that signal. If the data contains a small number of strong sources, the sources will be most likely be first discovered with standard point source techniques. At the other extreme, if the data contains a small number of events from many sources, diffuse techniques are more sensitive. A search for event clustering examines signal scenarios which are not as extreme as the above two cases, where events are spatially correlated but do not come from a small number of sources. A search for clustering was done by Jan-Patrick [5] for 2000-2003 AMANDA data.

In this method, we evaluate the two-point correlation function, i.e. we count the number of event pairs with angular separation smaller than some critical separation. Such searches are common in EHE cosmic ray physics [6]. We optimize the search to produce the best model discovery factor to a set of E^-2 signal events. We use both angular separation and Nch as an energy parameter to separate signal from atmospheric neutrino background. We plan to produce a plot of significance vs. angular separation and energy (Nch cut) similar to fig. 3 in [6]. P-values are shown below for randomized data and randomized data with 18 signal clusters added. The number of events in the Nth cluster are given by a power law distribution 18*N^-α, with α=-0.7, similar to distributions in [3], corresponding to to (18, 11, 8, 6, 5, 5, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2) E^-2 events added.

Randomized Data	Data + 18 Clusters of events

We only take events with declination > 5^o to avoid high Nch atmospheric muon background near the horizon. A final significance can be calculated by comparing the lowest p-value against the lowest p-value obtained from randomized data.

References

[1] A.A. Abdo et al. TeV Gamma-Ray Sources from a Survey of the Galactic Plane with Milagro. arXiv:0705.0707 [astro-ph].

[2] Francis Halzen, Alexander Kappes, and Aongus O'Murchadha. Identifying the Sources of the Galactic Cosmic Rays with IceCube. arXiv:0803.0314v1 [astro-ph].

[3] A. Achterberg et al. On the selection of AGN neutrino source candidates for a source stacking analysis with neutrino telescopes. Astropart. Physics 26 282 (2006).

[4] R. U. Abbasi et. al. Search for Cross-Correlations of Ultra--High-Energy Cosmic Rays with BL Lacertae Objects. Astrophys. J., 636 680 (2006).

[5] J.-P. Hulss , Ch. Wiebusch (With the IceCube collaboration). Search for Signatures of Extra-Terrestrial Neutrinos with a Multipole Analysis of the AMANDA-II Sky-map. Proceedings of the 30^th International Cosmic Ray Conference, Merida, Mexico, 111 (2007).

[6] R. U. Abbasi et. al. Study of Small-Scale Anisotropy of Ultra-High-Energy Cosmic Rays Observed in Stereo by the High Resolution Fly's Eye Detector. Astrophys. J., 610 L73 (2004)