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Paper text:
fitting the ultra high energy cosmic ray ( uhecr ) spectrum is a common way to attempt to gain understanding of the sources of these particles .
these fits often neglect the galactic component of cosmic rays , which is expected to be small at the very highest energies .
however , the energy at which at which this becomes true is not known .    rather than assume a negligible galactic component
, we employ a toy model in which composition determines source . in this model , we use the recent composition measurements of the hires prototype / mia experiment@xcite and of hires in stereo mode@xcite .
these are shown in figure  [ fig : comp ] . the light component in these measurements , assumed to be protons , is identified with the extragalactic component of uhecrs ; the heavy component , assumed to be iron , is identified with the galactic component .
having identified the extragalactic component of the uhecr spectrum , we fit this component using the assumption that the protons have lost energy between their acceleration and our observation , and that the sources are distributed uniformly throughout the universe , with a density that is smoothly varying in time .
the fits assume a simple power law spectrum , @xmath3 , with a spectral index @xmath4 identical for all sources .
we use the average energy loss model of berezinsky _
et al._@xcite to find the observed spectrum from a source a given redshift .
in addition , we use a monte carlo ( mc ) simulation@xcite for the discrete energy losses associated with pion production .
the mc is only important for propagating particles from small redshifts , @xmath5 , where the proton interacts only a few times . for propagation from larger redshifts ,
the distribution of observed energies for a given input energy is a gaussian of ever narrowing width .
the mc is run to create an @xmath6-@xmath7 matrix with two million entries for propagation from each redshift , @xmath8 , to our observation .
the @xmath6-@xmath7 matrix is calculated every 0.01 step in @xmath8 for @xmath9 to @xmath10 .
smaller steps , as small as 0.0001 , are used below 0.05 .
sources are assumed to be uniformly distributed at any given redshift , and with a density with which varies as @xmath11 .
the mc results at individual redshifts are added together to form an @xmath6-@xmath7 matrix for uniformly distributed sources evolving according given value of @xmath12 .
these @xmath8-integrated matrices were formed for @xmath130 to @xmath135 in steps of 0.5 .
the fits are performed by varying the normalization , the spectral slope ( @xmath4 ) , and the evolution parameter ( @xmath12 ) .
the goodness - of - fit is evaluated using the binned - maximum - likelihood method .
the comparison spectra for fitting are calculated by multiplying a vector containing the input spectrum by the @xmath6-@xmath7 matrix using matrix multiplication .
the input spectrum vectors are calculated every 0.05 in the spectral index @xmath4 .
the comparison spectra for intermediate values of @xmath4 and @xmath12 are found by interpolation .
the result of the fit to the most recent hires - i@xcite and hires - ii@xcite monocular spectra is @xmath0 and @xmath1 .
this fit is shown in figure  [ fig : bestfit ] .
the quoted uncertainties include the effect of the correlation between @xmath4 and @xmath12 .
this correlation is shown in figure  [ fig : ch2plot ] .
not included in this fit are any systematic uncertainties . the largest systematic uncertainty is expected to be due to the details of composition used in the aperture calculation for the hires - ii spectrum .
changes in the composition tend to move the best fit point along the trough of figure  [ fig : ch2plot ] , changing the @xmath12 vs. @xmath4 relationship little .
upper limit on the flux in two more bins for each measurement are shown above the highest energy actually observed .
the black fit line is the sum of the galactic ( green ) and extragalactic ( red ) components .
the parameters of the extragalactic component are @xmath14 and @xmath15 .
there are 42 data points , giving 39 degrees of freedom in the fit . ]
( @xmath16 ) in @xmath12-@xmath4 space .
the first four @xmath17 contours are shown . ]
because the uncertainty in composition is a large part of the uncertainty in the parameters in the fit to the spectrum , we were motivated to try to improve on the existing composition measurements , especially below @xmath18 ev . to go to low energies with hires
requires using the monocular data sets , and we chose the hires - ii monocular data set for this analysis .
unfortunately , the limited elevation coverage of the hires - ii aperture biases our @xmath19 acceptance , with the bias increasing at lower energies .
the bias stems from the requirement that we find @xmath19 within that extent of the shower observed in the detector .
events that are closer to the detector are more likely to have @xmath19 above the visible range , and thus be cut .
furthermore , because lower energies can only be observed close to the detector , events at these energies will have a larger acceptance bias than those at higher energies .
this bias precludes performing an elongation rate analysis at energies below @xmath18 ev .    instead
, we have chosen to fit the @xmath20  distribution in energy bins to a combination of mc generated @xmath20  distributions from proton primaries and from iron primaries .
the @xmath20  distribution in each energy bin is stored in a histogram , and the data histogram is then compared to a mixture of the proton and iron mc histograms to find the best fit proportion of each .
the fit is performed using the binned maximum likelihood technique as implemented in the hbook@xcite routine hmclnl .
the uncertainty of the fit in each energy bin is taken from the width of @xmath16 as fit to a quadratic in the region about the maximum .
an example of this procedure for the bin at @xmath18 ev is shown in figure  [ fig : compfit18 ] .
the result of these fits for the data at all energies is shown in figure  [ fig : rawdata ] .    at an energy of @xmath18 ev .
the top panel shows @xmath16 as a function of the proton fraction in 1% steps ( black histogram ) , and a polynomial fit to the same ( red line ) . the bottom panel shows the @xmath20   distribution that results from the fit , with the data shown as filled circles with error bars , the proton distribution in blue , the iron distribution in red and the sum in black ]        this fit gives only the proportion of proton and iron in the final , accepted sample ; as such , it is not intrinsically interesting , but must be corrected to find the proton - iron ratio of uhecrs entering the atmosphere .
however , one can test this procedure on an independent mc sample where one knows _ a priori _ which events are protons and which are iron .
the result of this analysis on the mc sample used to calculate the aperture used in the spectrum analysis is shown in figure  [ fig : rawmc ] .
the fits agree very well with what is actually in the sample .
the raw composition measurements are corrected using the relative acceptances in the proton and iron mc samples .
these are the same mc samples used to provide the comparison @xmath20  distributions used in the fit .
the fit proton - iron proportion is interpreted as given numbers of proton events and iron events .
these numbers then are separately corrected for the relative acceptance appropriate to each .
finally , the proton - iron ratio is recalculated using the corrected numbers of events of each type .    for a mc sample
, we can again compare the corrected proton - iron proportion to the input to the mc simulation .
this is shown in figure  [ fig : cormc ] . in this case , the input is just the hires prototype / mia and hires stereo composition measurements , where the mean @xmath20  of the data is interpreted as representing a proton - iron proportion given by the distance between the corsika / qgsjet proton and iron lines .
the input is in fact given by linear fits to the mean @xmath20  above and below @xmath21 ev .
again , the corrected results of the fits agree very well with the inputs to the mc .        finally , we show as a very preliminary result , the corrected proton - iron ratio for the data . see figure  [ fig : cordata ] .
this result shows a very light composition ( 90% protons ) above @xmath2 ev . below this energy
we measure a sharply lower composition , but with large uncertainties because of few events and a large acceptance correction .
the measured composition at high energies is in agreement with the hires stereo measurement , but closer to being all protons .
the data used in the fits comes from the same data set used in the hires - ii spectrum analysis which was fit above
. a considerable amount of data , about a factor of three more , was collected after this data set .
this later data was collected with lower light thresholds , and as such , will have a lower energy threshold .
in addition , the aperture at each energy will be increased , reducing the size of @xmath20   biases .
performing this analysis on this expanded data set should give us much tighter constraints on the composition in the middle of the @xmath22 ev energy decade .
the telescope array ( ta ) , which has already received japanese funding , and the ta low energy extension ( tale ) will be able to push this analysis even further .
tale will use the hires phototubes with larger mirrors to push the thresholds even lower .
the mirrors will be arranged in a tower rather than a ring to avoid biases in @xmath20 .
geometrical resolution at the level of hires stereo will be provided by coincidences with the ta ground array .
this paper consists of two sections . in the first section 
 , we discuss our fits to the latest hires monocular spectra . 
 we find that the best fit for the extragalactic component has a spectral index of @xmath0 with a distribution of sources varying with a evolution parameter @xmath1 . in the second section , 
 we discuss preliminary results from a new composition measurement using hires monocular data . 
 we find a predominantly light spectrum above @xmath2 ev .