Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 1 Workshop HEND Procedures of HEND data convolution for mapping of neutron Martian emission Workshop “The First year of HEND operations on the NASA Odyssey Mars Orbiter” Procedures of HEND data convolution for mapping of neutron Martian emission Workshop “The First year of HEND operations on the NASA Odyssey Mars Orbiter” Moscow, Russia May 20-22, 2002

Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 2 Workshop HEND The signal detected by HEND consists of: Flux of neutrons from Mars (this we need to know to build maps of Martian neutron flux) Flux of secondary neutrons generated in Odyssey by isotropic galactic cosmic rays (this we know and subtract from detected signal to determine 1) Flux of secondary neutrons generated in Odyssey by radiation from Mars (this we need to know, but at present stage this isn’t determined value)

Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 3 Workshop HEND The flux of secondary neutrons generated in Odyssey by isotropic galactic cosmic rays is determined during aerobraking phase of mission. This value was defined as signal obtained at big (> 10 4 km) distances from Mars.

Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 4 Workshop HEND where N i – measured counts during i -th frame, B i – counts of isotropic galactic cosmic rays in i -th frame,  Mars – angular radius of Mars as seen from Odyssey C i – signal from Mars in i -th frame. The HEND have time resolution is 19.2 sec. During this interval instrument accumulate counts for all detectors, and only after end of interval measured counts are write in spacecraft memory and transmitted on Earth. This interval is called frame. Accordingly, the signal from Mars in i -th frame we define as:

Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 5 Workshop HEND Due to HEND placed on spacecraft with very complex shape, some constructive elements and instruments are between HEND and Mars. Here shown a projection of HEND’s field of view, geometrical visible part of Mars (orange area), spacecraft At present stage this effect not takes in to account. But in future analyses it must be done. shadow (violet area) and area limited by physical neutron collimation in soil and atmosphere (blue area). The Martian neutrons only from blue area can be detected by HEND.

Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 6 Workshop HEND Building the Map 1.On the surface of planet we make a mesh with selected size of pixels. In each pixel we will independently accumulate counts and exposure time. 2.We select a time interval, detector and set of channels to create map.

Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 7 Workshop HEND To minimize computing time we assume the trajectory projection during i -th time bin is well fitted by line. 4.Moving through selected time interval we going from one frame to another. For each frame we determine the fractions ( k 1, k 2, …, k n ) of the trajectory projection on Martian surface length corresponded this pixel: where l i - length of a part of trajectory projection which lay in i -th pixel, L – total length of trajectory projection for current frame.

Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 8 Workshop HEND According this fractions k i for selected frames we accumulate counts and exposure time in all pixels on map: where C j – count in j -th frame, t j – duration of j -th frame, k ij – fraction of j -th frame length in i -th pixel, n – number of frames in selected time interval, E i – total counts accumulated in i -th pixel, T i exposure – total exposure time for i -th pixel, F i – average flux in i -th pixel.

Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 9 Workshop HEND The map of fluxes is produces by ratio F i. This ratio is well determined, if T i exposure enough large (for example, T i exposure > 60 sec). The maps for exposure time accumulated during Mapping stage of the Mission from February 18 to May 16 (~ frames).

Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 10 Workshop HEND Due to orbit of the 2001 Mars Odyssey have inclination ~86° where are two areas around North and South poles with ~250 km radii which spacecraft don’t cross. Therefore, using this maps building procedure we will never fill polar pixels of map if theirs size < 4°. So, in future we need to develop new procedure, based on “reverse scattering” of measured counts on visible from spacecraft Martian surface.

Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 11 Workshop HEND

Russian Aviation and Space Agency Institute for Space Research NASA 2001 Mars Odyssey page 12 Workshop HEND