190
9 Mount Wilson
What Kapteyn had at his disposal were measurements of the apparent brightness of stars at photographic and at visual wavelengths. Photographic refers to
the wavelength sensitivity of the first photographic emulsions. It is relatively
blue light with a central wavelength of around 4300 Å, but more than 1000
Å wide. Visually refers to the wavelength sensitivity of the human eye, whose
central wavelength is close to 5400 Å. By comparing these two magnitudes,
he could get an impression of the color of the light of a star. Kapteyn found
that the color of stars depends on its spectral type. But if he included the effect
of distances he also found an effect, so according to his analysis there were
indeed effects of extinction. However, the change of color in itself does not yet
tell us what the total amount of absorption is. For that, Kapteyn assumed that
it was Rayleigh scattering and that it depended on the wavelength with the
fourth power. He concluded that the ‘loss of light’ over his unit of distance of
32.6 light-years (10 pc) was 0.01 magnitude in the photographic, and 0.005
magnitude in the visual. Not a bad result, because the modern values are on
average 0.013 and 0.010, respectively. He quickly published this result in the
Astrophysical Journal.
However, Kapteyn discovered very quickly that he had made a fundamental
mistake. Instead of calculating average distances, he had taken average parallaxes. Of course, a distance r is the inverse of the parallax p. So the distance
is proportional to 1/ p. But it is a property of numbers that the average of a
number of values of p is not the same as the inverse of the average of the values
1/ p. He therefore quickly sent an erratum to the editors of the journal. This
changed his conclusion: the extinction turned out to be twice as small than he
had previously concluded.
In 1914 Kapteyn returned to the question of extinction. In an article he
published that year, he did not present a new analysis, but discussed the available literature. In the meantime, more was known about the nature of stars;
in particular, it was now known that the intrinsically brightest stars were intrinsically bluer, and the intrinsically fainter were redder. So apparently fainter
stars would on average be redder. This complicated the analysis. It boils down
to the fact that the effects of a relationship between the color of a star and its
absolute magnitude or luminosity, and reddening by dust in space were difficult to separate. Pieter van Rhijn studied this subject again in his dissertation
of 1915. He showed that change in color of a star if it were due to extinction
was 0.00195 ± 0.0003 magnitudes per 10 pc, about half of Kapteyn’s value.
Kapteyn and his colleagues still did not know whether this was really a matter
of interstellar extinction.
This changed in 1916 with the publication of a study of the globular cluster
Messier 13 (M13, see Fig. 9.15). Globular clusters belong to the halo of our
9 Mount Wilson
What Kapteyn had at his disposal were measurements of the apparent brightness of stars at photographic and at visual wavelengths. Photographic refers to
the wavelength sensitivity of the first photographic emulsions. It is relatively
blue light with a central wavelength of around 4300 Å, but more than 1000
Å wide. Visually refers to the wavelength sensitivity of the human eye, whose
central wavelength is close to 5400 Å. By comparing these two magnitudes,
he could get an impression of the color of the light of a star. Kapteyn found
that the color of stars depends on its spectral type. But if he included the effect
of distances he also found an effect, so according to his analysis there were
indeed effects of extinction. However, the change of color in itself does not yet
tell us what the total amount of absorption is. For that, Kapteyn assumed that
it was Rayleigh scattering and that it depended on the wavelength with the
fourth power. He concluded that the ‘loss of light’ over his unit of distance of
32.6 light-years (10 pc) was 0.01 magnitude in the photographic, and 0.005
magnitude in the visual. Not a bad result, because the modern values are on
average 0.013 and 0.010, respectively. He quickly published this result in the
Astrophysical Journal.
However, Kapteyn discovered very quickly that he had made a fundamental
mistake. Instead of calculating average distances, he had taken average parallaxes. Of course, a distance r is the inverse of the parallax p. So the distance
is proportional to 1/ p. But it is a property of numbers that the average of a
number of values of p is not the same as the inverse of the average of the values
1/ p. He therefore quickly sent an erratum to the editors of the journal. This
changed his conclusion: the extinction turned out to be twice as small than he
had previously concluded.
In 1914 Kapteyn returned to the question of extinction. In an article he
published that year, he did not present a new analysis, but discussed the available literature. In the meantime, more was known about the nature of stars;
in particular, it was now known that the intrinsically brightest stars were intrinsically bluer, and the intrinsically fainter were redder. So apparently fainter
stars would on average be redder. This complicated the analysis. It boils down
to the fact that the effects of a relationship between the color of a star and its
absolute magnitude or luminosity, and reddening by dust in space were difficult to separate. Pieter van Rhijn studied this subject again in his dissertation
of 1915. He showed that change in color of a star if it were due to extinction
was 0.00195 ± 0.0003 magnitudes per 10 pc, about half of Kapteyn’s value.
Kapteyn and his colleagues still did not know whether this was really a matter
of interstellar extinction.
This changed in 1916 with the publication of a study of the globular cluster
Messier 13 (M13, see Fig. 9.15). Globular clusters belong to the halo of our