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in early 2001 , the hubble space telescope obtained the deepest data set ever observed for a globular cluster , an exposure of 123 orbits centered on a field 5@xmath1 from the center of the globular cluster m4 .
we reported analysis of the lower main sequence of m4 ( richer et al .
2002 ) and a determination of the white dwarf cooling age of m4 ( hansen et al .
the latter is derived from a @xmath2 fit of models to the entire white dwarf luminosity function .
the derived age of 12.7@xmath3 ( @xmath4 statistical error only ) is consistent with other age determinations for old star clusters , and with the _ wmap _ concordance cosmology age ( spergel et al . 2003 ) .    in a recent contribution
, de marchi , paresce , straniero and moroni ( 2003 ) performed a reanalysis of the long exposure data from our hst project go-8679 ( richer et al .
2002 , hansen et al . 2002 ) and were unable to reproduce results similar to ours .
in particular their photometry failed to reach as faint as ours by almost a full magnitude .
this can be seen quite dramatically in figure 1 where we plot our cmd in the white dwarf region from this data set and that of de marchi et al .
taken from their paper .
continuing , the authors claim that the only possible age constraint for m4 is that the lower limit for the white dwarf cooling age is 9 gyr , whereas we ( hansen et al .
2002 ) derive a cooling age of 12.7 gyr .
the analysis of de marchi et al . raises distressing questions about our competence both in data analysis and in interpretation . as they have already been cited by others in the literature ( e.g. , moehler et al .
2003 ) we believe that it becomes crucial for us to respond .
the conflict raises two questions .
first , why do two independent teams approaching the same data set get such different results ?
second , what is the correct approach to fitting a measured white dwarf luminosity function ?
we answer the first question in this contribution and the second in detail in hansen et al .
( 2004 , in preparation ) and illustrate how the de marchi et al .
analysis fails on both counts .
the reason de marchi et al .
are unable to reproduce the depth and quality of our cmd is purely one of data treatment .
the hst data set under consideration , go-8679 , contains 98 f606w and 148 f814w images each of exposure 1300 sec .
a first - epoch set of images taken in f555w and f814w ( go-5461 ) were obtained by us in 1995 ( richer et al .
1995 , 1997 ) and were not nearly as deep .
some care is required in getting the most out of this large and impressive data set .    in our case , after accounting for dithers , those frames corresponding to a particular epoch and filter were averaged together with pixel rejection 
the @xmath5 highest pixels being rejected to eliminate cosmic ray contamination . from the hst wfpc2 manual the mean number of pixels on a given chip affected by a cosmic ray hit in an 1800 sec exposure is about 20,000 .
hence in a stack of @xmath6 sec exposures we expect @xmath7 pixels at a given position to have suffered a hit .
taking the dispersion to be @xmath8 and using @xmath9 rejection we find that in combining the 98 f606w images the highest 7 pixels should be rejected while for the 148 f814w images we should eliminate the highest 9 .
our procedure thus used 93% of the available pixels in constructing the mean .
by contrast , de marchi et al .
used image - association stacks produced by the pipeline software developed by the canadian astronomy data centre and the eso space - telescope coordinating facility ( micol & durand 2002 ) .
this pipeline software essentially takes the median of the available pixel values , and is therefore less efficient in a statistical sense than the scheme we employed as described above . according to zwillinger & kokoska ( 2000 ) the efficiency of the median ranges from 1.000 for @xmath10 , 0.743 for @xmath11 , ... 0.681 for @xmath12 , to 0.637 for @xmath13 .
hence de marchi et al . effectively used less than 2/3 of the information available in the images .
we requested from the canadian astronomy data centre the image association stacks that were used by de marchi et al . and compared them to the combined images resulting from our analysis . after allowing for the change in image scale ( we expanded our images by a factor of three in each dimension )
, the main difference is that images of faint stellar objects appear perceptibly more diffuse in the pipeline generated associations .
this has the effect of making the faintest stars difficult to detect in the images de marchi et al
. used , exactly what is seen in figure 1 .
we illustrate this by employing the same 2 stars de marchi et al . used to claim that objects fainter than f814w = 27.0 could not be measured on our first - epoch frames
recall that all we seek from the first - epoch images is a position so that proper motions can be measured .
all the photometry is carried out on the longer - exposure frames .
for this reason most of our positional matching comes from the f606w @xmath14 f555w pair as the first - epoch exposures in f555w are actually quite long31.5 ksec .
figure 2 displays these two images as we produced them with the stars discussed by de marchi et al .
clearly the lower of the two is easily visible in both frames while the upper of the two is not seen in the shorter exposure first epoch .
there is , however , a simple reason for this - it is in fact not a star at all , as our deep images clearly show it to be extended .
this faint galaxy is thus lost in the noisier first - epoch image . some specific numbers for these two objects
are that each is detected at a @xmath15 of about 8 on the long exposure f606w image , the upper one is not detected on the shorter f555w frame while the lower is detected at @xmath15 of about 5 .
the lower star has a proper motion completely consistent with cluster membership and its measured magnitudes are f606w = 28.48 , f814w = 27.25 .
it is a cluster white dwarf and as can be seen in figure 1 we are able to measure stars almost 0.5 magnitudes fainter than this one .
one crucial point is that our experiment matches long exposures in f606w ( 127.4 ksec ) and f814w ( 192.4 ksec ) with much shorter exposures in f555w ( 31.5 ksec ) and f814w ( 7.2 ksec ) .
the question thus arises as to how we could measure positions in the earlier epoch data for the faintest stars where the @xmath15 is obviously poor . for a star at f606w = 29.0 the expected @xmath15 ( from the hst etc ) in our deep f606w frames
is 6.7 while a star at this magnitude on the shorter exposure f555w frames has @xmath15 = 2.5 .
this is just about what we measured on our frames .
the reason we can successfully measure positions of such faint objects in the first epoch are twofold .    first , we applied the finding list from the deep frames to the shallower frames .
if the background noise in an image is gaussian , then a @xmath16 positive deviation will occur in about 6 pixels out of every 1000 .
if , in a @xmath17 image ( neglecting the vignetted areas at the low - x and low - y sides of the wfpc2 ccds ) , we were to mark all of the @xmath16 peaks as detected astronomical objects , we would expect more than 3,000 false detections .
however , if we consider only the area within 0.5 pixels radius of an object confidently detected in the long second - epoch exposure , we expect a probability @xmath18 of finding a positive 2.5@xmath19 deviation which is purely the result of random noise in the first - epoch image . that is to say ,
we expect of order 5 false cross - identifications for every 1000 correct re - detections .
even at @xmath20 , presumed re - identifications will be correct 19 times out of 20 . for this reason ,
the knowledge that an actual astronomical object is present somewhere nearby based upon the long - exposure second - epoch images allows us to be confident that most of the claimed re - detections on the short - exposure first epoch images correspond to true re - detections .
the first - epoch astrometric positions , then , while poorer than those of the second epoch , are nevertheless good enough to distinguish stars that are moving with the cluster from stars and galaxies that are not . by contrast ,
de marchi et al . made no use of this technique and hence the shorter first - epoch frames effectively set their limiting magnitude .
we checked the above by rerunning the photometry programs on the wf3 chip using a finding list with star positions generated randomly .
this list contained the same number of stars as the original finding list .
we then selected the objects whose photometry had converged on all frames . the resulting proper motion displacement diagram and cmd
is shown in figure 3 and compared with the one when the true finding list is used in figure 4 .
there are numerous spurious faint matches in figure 3 , but almost all disappear when the match radius of 0.5 pixels is invoked .
those objects that lie outside 0.5 pixels are likely random noise spikes which have no correlated positions between frames .
figures 3 and 4 taken together show that false detections of noise spikes are not a serious source of contamination in our cmds and that the suggestion to the contrary by de marchi et al .
is incorrect .
secondly , the proper motions of the m4 stars are actually quite large ( about 1 hst pixel with respect to an extragalactic background over the 6 year time baseline ( kalirai et al . 2003 ) ) .
while the lower @xmath15 image would not produce good enough photometry , the @xmath15 is sufficient to give the centroid , which is crucial for astrometry . in figure 5
we illustrate the quality of the proper motion separation between cluster and field from the long and short images .
some of the brightest stars do not exhibit clean separation due to their near saturation .
however , what is clear from this diagram is that most of the field objects can be easily eliminated down to very faint magnitudes ( f606w = 29.0 ) by making the generous proper motion cut within a total value of 0.5 pixel ( @xmath21 mas / yr ) of that of the mean cluster motion over the 6 year baseline of the observations . a disturbing aspect of the de marchi et al .
paper is that nowhere do they illustrate their displacement measurements .    the analysis techniques of de marchi et al .
compounded the effect of their somewhat lower quality images .
their approach uses aperture photometry to measure the stellar magnitudes .
we employ point spread function fitting , which clearly has the advantage of just using the pixels with the largest signal  thus reducing the sky contribution  a critical issue when attempting to measure faint stars .
the effect of this is obvious even along the brighter portion of the white dwarf cooling sequence where the de marchi et al .
diagram exhibits significantly larger scatter ( see figure 1 ) .
further , as we mentioned above , we use the positional information from the deepest frames in carrying out the photometry on the shorter exposure frames .
by contrast de marchi et al . made no use of this information .
_ this has the effect of allowing the depth of the first - epoch images alone to set their limiting magnitude . _
in a paper currently in press ( hansen et al . 2004 ) we consider in some detail the host of systematic effects in the white dwarf cooling age determination . in that contribution we will comment in detail on some of the points raised by de marchi et al . such as distance modulus , reddening and mass function . here
we have only considered reduction and analysis of the data . with regards to this data
we offer our stacked images and finding lists to anyone wanting to use them and in richer et al .
2004 we have published the complete photometry lists .    on one point we agree with de marchi et al . 
the pursuit of globular cluster white dwarfs is an important and interesting scientific goal .
however , it is also an extremely expensive project in terms of telescope time , and we have a responsibility to take the time to give the analysis significant thought and effort to come up with the best possible analysis
. we would be delighted if we could detect the truncation of the white dwarf luminosity function , and hope to do so in future work , but until such time we reiterate the point that there is abundant age information in the white dwarf luminosity function and it can be modelled .
the authors would like to thank i. king and j. anderson for reading an early version of this paper and making useful comments .
the research of hbr is supported in part by the natural sciences and engineering research council of canada .
hbr extends his appreciation to the killam foundation and the canada council for the award of a canada council killam fellowship .
rmr and ms acknowledge support from proposal go-8679 and bh from a hubble fellowship hf-01120.01 both of which were provided by nasa through a grant from the space telescope science institute which is operated by aura under nasa contract nas5 - 26555 .
bkg acknowledges the support of the australian research council through its large research grant program a00105171 .
kalirai , j.s .
, richer , h.b . ,
hansen , b.m . ,
stetson , p.b . ,
shara , m.m . , saviane , i. , rich , r.m . ,
limongi , m. , ibata , r. , gibson , b.k . ,
fahlman , g.g . & brewer , j. 2003 , accepted for publication in apj , astro - ph/0304036 .
spergel , d. n. , verde , l. , peiris , h. v. , komatsu , e. , nolta , m. r. , bennett , c. l. , halpern , m. , hinshaw , g. , jarosik , n. , kogut , a. , limon , m. , meyer , s. s. , page , l. , tucker , g. s. , weiland , j. l. , wollack , e. & wright , e. l. 2003 apjs , 148 , 175 .
we respond to the paper by de marchi , paresce , straniero and moroni ( 2003 ) on the white dwarf cooling age of m4 . 
 the authors question the data analysis and interpretation that led to the conclusions in hansen et al . 
 ( 2002 ) . in their paper , de marchi et al . 
 are unable to obtain photometry as deep as ours from the same data set and therefore assert that only a lower limit to the white dwarf cooling age for this cluster of @xmath0 gyr can be obtained .    in this short contribution 
 we show that shortcomings in the data analysis and reduction techniques of de marchi et al . 
 are responsible for their inability to reach the photometry limits that our study reports . in a forthcoming paper in which the complete techniques for age determination with white dwarfs are laid out , 
 we demonstrate that their method of fitting the luminosity function gives a spuriously low white dwarf cooling age .    
 richer/jbrewer/jkalirai@astro.ubc.ca , greg.fahlman@nrc-cnrc.gc.ca    peter.stetson@nrc-cnrc.gc.ca    hansen/rmr@astro.ucla.edu    ibata@newb6.u-strasbg.fr    bgibson@astro.swin.edu.au    mshara@amnh.org