11.7 The Spatial Distribution of the Stars
245
In 1920 Kapteyn (see Fig. 11.8) was finally ready to make a ‘first attempt’ to
deduce the spatial distribution of stars. The article, written together with van
Rhijn, was published via the Mount Wilson Observatory in the Astrophysical
Journal. The first paragraph reads:
The investigation contained in G.P. [Groningen Publications] 27, 29 and 30
were carried out for the purpose of making possible an elaborate treatment of the
arrangement of the stars in space. At least two more publications will be necessary
to complete this investigation. Now that, after so many years of preparation, our
data seem at last to be sufficient for the purpose, we have been unable to restrain
our curiosity and have resolved to carry through completely a small part of the
work, even though, by doing so, the rules for strict economy of labor cannot be
altogether adhered to.
Kapteyn and van Rhijn started by recalibrating the parallax of stars as a function
of apparent magnitude and proper motion. In doing so they made use of the
latest parallax measurements, both directly as a result of the motion of the Earth
around the Sun and via the method of secular parallax, based on the velocity of
the Sun through space. Then they had to make an assumption about how those
parallaxes would be distributed around that average, but that—as Kapteyn had
already shown—was not too critical. And from that they deduced what the
luminosity curve was.
There’s an interesting sideline. We already saw that the absolute magnitude,
a measure for the luminosity of a star, is defined as the apparent magnitude
if the distance would be 10 parsec. This definition comes from Kapteyn. He
was one of the first researchers in this field and initially chose as the unit of
distance that of a star with parallax of 0 .1. When Herbert Turner introduced
the term parsec, Kapteyn first refused to use it, saying it was ‘ugly’. In this article
with Pieter van Rhijn, he finally accepted the term (although he kept calling
it ‘ugly’), but as a result felt compelled to redefine the absolute magnitude
to a distance of 1 pc. At the first meeting of the International Astronomical
Union in 1922 in Rome, the 10 pc was formally chosen for the definition of the
absolute magnitude, taking over Kapteyn’s decades of use (without mentioning
Kapteyn by the way).
With methods that Kapteyn had already designed in principle in 1902, it was
now possible to determine the luminosity curve using the available material. It
resembled a Gaussian curve, as in the probability distribution, and that made
the further mathematical procedures easier to perform. This luminosity curve
is quite adequate for the bright stars compared to modern insights, but not so
for the fainter stars. The curve of Kapteyn & van Rhijn rises for fainter absolute
magnitude (the fainter intrinsically, the more stars there are in each volume of
245
In 1920 Kapteyn (see Fig. 11.8) was finally ready to make a ‘first attempt’ to
deduce the spatial distribution of stars. The article, written together with van
Rhijn, was published via the Mount Wilson Observatory in the Astrophysical
Journal. The first paragraph reads:
The investigation contained in G.P. [Groningen Publications] 27, 29 and 30
were carried out for the purpose of making possible an elaborate treatment of the
arrangement of the stars in space. At least two more publications will be necessary
to complete this investigation. Now that, after so many years of preparation, our
data seem at last to be sufficient for the purpose, we have been unable to restrain
our curiosity and have resolved to carry through completely a small part of the
work, even though, by doing so, the rules for strict economy of labor cannot be
altogether adhered to.
Kapteyn and van Rhijn started by recalibrating the parallax of stars as a function
of apparent magnitude and proper motion. In doing so they made use of the
latest parallax measurements, both directly as a result of the motion of the Earth
around the Sun and via the method of secular parallax, based on the velocity of
the Sun through space. Then they had to make an assumption about how those
parallaxes would be distributed around that average, but that—as Kapteyn had
already shown—was not too critical. And from that they deduced what the
luminosity curve was.
There’s an interesting sideline. We already saw that the absolute magnitude,
a measure for the luminosity of a star, is defined as the apparent magnitude
if the distance would be 10 parsec. This definition comes from Kapteyn. He
was one of the first researchers in this field and initially chose as the unit of
distance that of a star with parallax of 0 .1. When Herbert Turner introduced
the term parsec, Kapteyn first refused to use it, saying it was ‘ugly’. In this article
with Pieter van Rhijn, he finally accepted the term (although he kept calling
it ‘ugly’), but as a result felt compelled to redefine the absolute magnitude
to a distance of 1 pc. At the first meeting of the International Astronomical
Union in 1922 in Rome, the 10 pc was formally chosen for the definition of the
absolute magnitude, taking over Kapteyn’s decades of use (without mentioning
Kapteyn by the way).
With methods that Kapteyn had already designed in principle in 1902, it was
now possible to determine the luminosity curve using the available material. It
resembled a Gaussian curve, as in the probability distribution, and that made
the further mathematical procedures easier to perform. This luminosity curve
is quite adequate for the bright stars compared to modern insights, but not so
for the fainter stars. The curve of Kapteyn & van Rhijn rises for fainter absolute
magnitude (the fainter intrinsically, the more stars there are in each volume of