**Up:** Abstract

A&A Supplement series, Vol. 129, April I 1998, 195-204

Received July 18; accepted September 29, 1997

## The luminosity function of individually undetectable stars

**R.C. Snel**

Lund Observatory, Box 43, S-221 00 Lund, Sweden

e-mail: Ralph.Snel@astro.lu.se

### Abstract:

A method is presented to derive the faint end of the stellar luminosity
function in crowded fields. The method assumes that two images that
look similar, have similar luminosity functions. A simulated image with
known luminosity function is compared with an observed image, and the
luminosity function is adjusted until the images look sufficiently similar.
A number of tests were performed on simulated and real images, showing
the effects of various error sources. The histogram of the image was used
to determine similarity.
It was possible to derive the luminosity function to a limit of
approximately one source per beam, with the beam defined as
times the square of the half width at half maximum of the point
spread function.
Defining the limit of detection for classical
photometry as the magnitude where the completeness of detection dropped
below 0.5, and for the luminosity function derived with this method at the
magnitude where the uncertainty in the luminosity function exceeded the
derived number of stars at this magnitude,
it was possible to derive the luminosity function up to two magnitudes fainter
than possible with classical photometry. The accuracy was limited by
knowledge of the analog-digital converter effects, read-out noise, and
point spread function.

**keywords:** methods: data analysis -- methods: observational -- methods:
statistical -- techniques: photometric -- stars: luminosity function, mass
function

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