Re: stellar density as a function of magnitude

[Andrew Bennett <andrew.bennett@ns.sympatico.ca>]

On Fri, 2 Jun 2000 09:41:33 -0400, Stupendous Man 
<richmond@a188-l009.rit.edu> wrote:

>...
>                      number of stars in field of Mark IV
> magnitude         galactic equator            galactic poles
>    m             mag = m    mag <= m         mag = m    mag <= m
>--------------------------------------------------------------------
>   13             3,800       6,700            330          830
>   14             9,800      18,000            630        1,700
>   15            24,000      44,700          1,100        3,200
>   16            49,000     100,000          2,000        5,900
>   17           120,000     230,000          3,200       10,000
>   18           270,000     540,000          5,400       18,000
Ah! It's good to have some real numbers. The sums I
posted on confusion errors assumed a uniform distribution
to infinity (apart from a cutoff to avoid melting our CCD's).
This distribution has many more faint stars. My estimated error
of 15% rms (times "a factor of order unity") is therefore too 
high.

Unfortunately, it is not too high by very much. Putting in
power law exponents fitting the Stupendous data above instead
of the -2.5, -1.5 appropriate for the uniform distribution, I
get rms errors around 11% instead of 15% at the 6000 stars per 
image level. The error is dominated by the stars close to the 
analysis limit so taking away a lot of fainter ones does not 
make much difference.

With the more realistic distribution, while there are fewer
faint confusing sources, when one comes to analyse the brighter
sources, there are more bright confusing sources ... things do
not get better as fast as one might expect for bright sources.
And, while I did my analysis to account for position errors
between the MK IV and the catalog positions, the confusion
errors do affect the photometry too. As Arne pointed out, even
if the PSF is stable, stars do move, giving changes in the
confusion error for the same source seen at different times.

Andrew Bennett, Avondale Vineyard, Nova Scotia, Canada.