Galactic sources

It is generally assumed that the number of neutrinos emitted by a galactic source per time unit and per energy unit is given by:

#displaymath524#

The spectral index is #tex2html_wrap_inline538# as measured in gamma-ray observations in the region below 10GeV. The normalization factor A is related to the luminosity of the source by:

#displaymath525#

where #tex2html_wrap_inline542# and #tex2html_wrap_inline544# are respectively the luminosities for neutrino and proton emissions for the whole energy spectrum between the minimal value #tex2html_wrap_inline546# and the cut-off energy value #tex2html_wrap_inline548# and where #tex2html_wrap_inline550# is the ratio of the total neutrino luminosity to the total proton luminosity. It is then easy to derive the neutrino flux at the detector for a source which is at a given distance D:

#displaymath526#

In order to estimate the sensitivity of the detector to the total luminosity #tex2html_wrap_inline554# it is necessary to calculate the number of expected muons with energies above the energy threshold during the exposure time for any given value of #tex2html_wrap_inline556# and to compare it to the expected background due to atmospheric neutrinos. The expected number of muons is given by:

#displaymath527#

The values of #tex2html_wrap_inline558# are given in table~#lmtbtab1#103> for two different values of the differential spectral index #tex2html_wrap_inline560# and for different muon energy thresholds. The detector exposure ST is a covolution of the effective area, which is supposed to be independent of the muon direction, with the running time, calculated by taking into account the on source duty factor. The fluxes of muons induced by atmospheric neutrinos, averaged over the detectable hemisphere, have been calculated by using the neutrino flux given in ref.~[#volkova##1#] and are also given in the last column of table~#lmtbtab1#105>. This flux allows us to calculate the background which contaminates the signal:

#displaymath528#

where #tex2html_wrap_inline564# is the angular cut used to define the direction of the source.

#table119#
Table: Values of #tex2html_wrap_inline566# (see the text) for different energy thresholds and for two different spectral index, #tex2html_wrap_inline568# and #tex2html_wrap_inline570#, and flux of muons induced by atmospheric neutrinos averaged over the whole #tex2html_wrap_inline572# downward hemisphere for the same thresholds.

The luminosity that can be detected as a signal (of at least 10 events) exceding 5 standard deviations from the atmospheric neutrinos background is:

#displaymath529#

with:

#displaymath530#

As an example the detectable luminosities for sources located at 5kpc are given in table~#lmtbtab2#179> for two different spectral index values and for different energy thresholds. This table clearly shows that better sensitivities can be obtained for the highest values of the muon energy threshold.

#table180#
Table: Example of minimum detectable proton luminosities for #tex2html_wrap_inline616#.

For individual known sources the calculation of the detectable luminosity can be performed by taking into account of the distance of each individual source, the fraction of time #tex2html_wrap_inline644# during which the source is below the horizon, the latitude of the detector and the flux of the background atmospheric neutrinos averaged along the apparent path of the source. As an example these values are given in table~#lmtbtab3#203> for detectors of 1km#tex2html_wrap_inline646# located at #tex2html_wrap_inline648#N and #tex2html_wrap_inline650#S running for one year and for a threshold energy of 1TeV.

#table206#
Table: Detectable luminosities for several known sources. #tex2html_wrap_inline652#.

This table clearly shows that there are more sources visible for a detector located at #tex2html_wrap_inline710#N of latitude than for a detector located at #tex2html_wrap_inline712#S. This is because, due to the Earth rotation, the solid angle seen by the first one is greater than that of the second one. But the value of #tex2html_wrap_inline714# is always 1 or 0 for the detector located at the South Pole because, if a source is below the horizon of the South Pole it decribe an apparent circle around the Earth axis and its elevation remains always equal to its declination. So, the source remains always detectable or undetectable. This also explain why for sources that may be detected at both latitudes the sensitivity of the detector located at #tex2html_wrap_inline716#S is better than the sensitivity of the detector located at #tex2html_wrap_inline718#N.