Re: stellar density as a function of magnitude

[hjohnson@pluto.njcc.com (Herbert R Johnson)]

On Fri, 2 Jun 2000 09:41:33 -0400, Stupendous Man <richmond@a188-l009.rit.edu> wrote:
*>
*>  On the other hand, it appears from the table above that fields
*>far from the galactic equator will not have a significant fraction
*>of bright stars blended with other bright stars.  For example,
*>near the poles, we may expect 3,200 stars in the field down to
*>M = 15.  Tech Note 66 shows that about 8 percent of those stars
*>would have companions within 5 pixels, and about 4 percent
*>would have companions within 3 pixels.  Hmmmm.  Actually, even 
*>8 percent seems like it could be annoying ...
*>
*>                                               Michael Richmond

Tom Droege in his recent comments suggested a width of 7 pixels,
at least for retaining raw data, so there would be even more companions
by that measure.

One "annoying" aspect is the tradeoff with photometry, as I think Tom
was getting at. Variations due to on or off-pixel centering, plus
variations due to companions as seen through optical abberations and
seeing conditions will limit the level of variability we will be able
to detect. I've urged Tom to give some actual results on companions if he
can: statistics and catalogs can tell us what we "should" see, but
only the instrument can tell us what it "actually' sees.

Again, as Tom suggested, we can take N samples and get root
N improvement, but I think all these variations will degrade that improvement
for those stars that are just "too close" for us to resolve well.
Also, it seems to me that with variables, we trade that "root N" improvement
for resolving the variability over *time* by N/2 (unequal sampling
intervals degrades that value). Yes?

Meanwhile, the trick would seem to be how to determine what "too close" is.
I think statistics or star charts will set a "floor" or minimal value of
close: I suspect in practice overall performance will be worse, particularly
if we set a single value of "too close" for the entire field of view.
Seeing and optical abberations will likely raise the value of "too close".
If we follow the Mark III model of essentially one observation equals one
data point, with perhaps one error bar (?), then "too close" will need to
be set by the WORST condition and not the average. Tom suggested the other
extreme, save ALL the data for each observation, and presumably some
set of error information, then process all the obs' as needed.

My feeling at this point is that information derived directly from
the images will be very informative, so I continue to encourage that
kind of analysis and reportage.

Herb JOhnson



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