242
11 The Kapteyn Universe
with the change of the color of the stars with distance. He actually found
an effect that, according to current insights, is not so bad at all. However,
Shapley’s study of a globular cluster (see Sect. 9.5) had shown that there could
be no so large an effect of reddening, so Kapteyn’s result would be the result
of systematic changes in color, for example as a function of the luminosity
or absolute magnitude of the stars. Either way, absorption (or extinction) was
believed by everyone in the astronomical community as being very small and
could therefore safely be neglected.
The third assumption was that everywhere in space the stars are distributed
in the same way over different sorts of stars, especially that the distribution of
absolute magnitude or luminosity would be the same everywhere. But what
that distribution, the luminosity curve as Kapteyn called it, looked like, still
had to be determined. Pieter van Rhijn’s dissertation consisted for half of a
determination of the background light of faint stars, as described already. The
second part was an accurate determination, with the latest data, of the average
parallax of stars as a function of apparent magnitude and proper motion. If for
a star one knew both properties, one could statistically estimate its distance.
And to refine this, van Rhijn had determined this separately for stars of spectral
class B (i.e., helium stars and the like) and for stars of types F, G, and K , i.e.,
stars roughly like the Sun (which is of type G). This then should lead to the
determination of the luminosity function.
Of course, it was necessary to determine the star counts as accurately as
possible and to the faintest brightness possible in the sky. By ‘star count’ is
meant the number of stars as a function of their apparent magnitude. And
that also, at least as a first exercise, as a function of Galactic latitude, i.e. of the
angle above or below the plane of the Milky Way. Kapteyn had been working
on this problem for much longer, first with Herman Weersma and, after he
had left, with Pieter van Rhijn. A number of articles on this subject appeared
in the Publications of the Astronomical Laboratory at Groningen, with finally in
1920 the, as far as Kapteyn was concerned, for that moment definitive tables of
numbers of stars between certain limits of magnitude, proper motion, Galactic
latitude and spectral type. This result was partly based on measurements of
proper motions of large numbers of stars on plates recorded at Helsingfors,
Cape of Good Hoop and Potsdam. This would then have to be expanded and
improved as the work on the Plan of Selected Areas progressed.
And then there was the theoretical work. How do you get from all those
data the distribution of the density (number of stars per unit volume)? That
after all was the ultimate goal. This presents a mathematical problem that is
rather difficult. I give a brief summary of the mathematics involved can be
found in the online version of Appendix (A.8) for those interested. For this
11 The Kapteyn Universe
with the change of the color of the stars with distance. He actually found
an effect that, according to current insights, is not so bad at all. However,
Shapley’s study of a globular cluster (see Sect. 9.5) had shown that there could
be no so large an effect of reddening, so Kapteyn’s result would be the result
of systematic changes in color, for example as a function of the luminosity
or absolute magnitude of the stars. Either way, absorption (or extinction) was
believed by everyone in the astronomical community as being very small and
could therefore safely be neglected.
The third assumption was that everywhere in space the stars are distributed
in the same way over different sorts of stars, especially that the distribution of
absolute magnitude or luminosity would be the same everywhere. But what
that distribution, the luminosity curve as Kapteyn called it, looked like, still
had to be determined. Pieter van Rhijn’s dissertation consisted for half of a
determination of the background light of faint stars, as described already. The
second part was an accurate determination, with the latest data, of the average
parallax of stars as a function of apparent magnitude and proper motion. If for
a star one knew both properties, one could statistically estimate its distance.
And to refine this, van Rhijn had determined this separately for stars of spectral
class B (i.e., helium stars and the like) and for stars of types F, G, and K , i.e.,
stars roughly like the Sun (which is of type G). This then should lead to the
determination of the luminosity function.
Of course, it was necessary to determine the star counts as accurately as
possible and to the faintest brightness possible in the sky. By ‘star count’ is
meant the number of stars as a function of their apparent magnitude. And
that also, at least as a first exercise, as a function of Galactic latitude, i.e. of the
angle above or below the plane of the Milky Way. Kapteyn had been working
on this problem for much longer, first with Herman Weersma and, after he
had left, with Pieter van Rhijn. A number of articles on this subject appeared
in the Publications of the Astronomical Laboratory at Groningen, with finally in
1920 the, as far as Kapteyn was concerned, for that moment definitive tables of
numbers of stars between certain limits of magnitude, proper motion, Galactic
latitude and spectral type. This result was partly based on measurements of
proper motions of large numbers of stars on plates recorded at Helsingfors,
Cape of Good Hoop and Potsdam. This would then have to be expanded and
improved as the work on the Plan of Selected Areas progressed.
And then there was the theoretical work. How do you get from all those
data the distribution of the density (number of stars per unit volume)? That
after all was the ultimate goal. This presents a mathematical problem that is
rather difficult. I give a brief summary of the mathematics involved can be
found in the online version of Appendix (A.8) for those interested. For this