Project Cyclops, A Design... - Department of Earth and Planetary ...

distantgalaxies (oraninertialreference frame)wouldbe
proportional to the cosineof thegalacticlatitude,
andwouldbeindependent of range.Sincetheperiodof
starsincreases with theirdistancefrom the galactic
center,their velocitiesare not proportional to this
centraldistance; in fact,in thesolarneighborhood,
velocitydecreases slightlywithdistance fromthegalactic
center.Thedifferencebetweenthesetwo functions is
proportional to radial distance from the Sun's orbit and
hence causes a proper motion that is a function of
galactic longitude, but is independent of distance from
the Sun.
Thus, the only class of stellar motions that can be of
any use to us are those caused by random velocities. If
we base our distance estimates on these:
1. We will fail to include a large number of valid
target stars whose velocities are either low or
along our line of sight. This fraction will increase
with range.
2. We will include a substantial number of stars
beyond range whose velocities are higher than
normal.
3. Unless some additional technique is used, no
selection by spectral or luminosity class is provided.
Clearly, proper motion studies, by themselves, are
inadequate to prepare a good target list.
has been used to find the distances of a great many stars.
Since in any case we wish to know the spectral class
of each star and to know that it is a main sequence star,
the determination of its distance is a trivial additional
step involving only the apparent magnitude. The crux of
our problem is therefore to select or develop a rapid
(and preferably automated) method of spectral classification
that will exclude from consideration stars that
are not on the main sequence. For our purposes, we do
not need to determine the luminosity class of stars not
on the main sequence, but this information would be of
interest to astronomers in refining their statistics of
stellar distributions.
UBV PHOTOMETRY
A widely used method of star classification involves
the measurement of the apparent magnitudes of the star
in three wavelength ranges, one in the ultraviolet, one in
the blue, and one in the "visible" part of the spectrum,
as listed in Table 13-1. These measurements have been
made photoelectrically on single stars and, more recently,
by densitometric measurement of star images on
plates taken in the three spectral regions of fields of
stars. The ultraviolet, blue, and visible magnitudes are
designated U, B, and V, respectively.
TABLE 13-1
DISTANCE DETERMINATION FROM ABSOLUTE
MAGNITUDE
As we saw in Chapter 2, the vast majority of stars fall
into well-defined groups, called luminosity classes, _ on
the H-R diagram. The luminosity class of a star can be
determined from certain features of its spectrum such as
the strength of the Balmer absorption band in the
ultraviolet, the strength and number of the absorption
lines of metals and heavy elements, and the relative
heights of emission lines (core reversals) particularly of
the calcium line. Once the luminosity class is known,
along with the spectral class, the luminosity and therefore
the absolute magnitude of the star can be determined
within rather narrow limits. This is particularly
true for main sequence stars.
Since the absolute magnitude M is the magnitude the
star would have at a distance of 10 parsecs, we can
determine the distance from the inverse square law,
knowing the apparent magnitude m:
pcs (3)
This method of distance determination is reliable and
Measurement X (center) /XX
of (nanometers) (nanometers)
U 365 70
B 440 90
V 548 70
With care, U, B, and V can be measured from
photographic plates to -+0.05 magnitude. If the magnitude
difference U-B is plotted against the difference B-V
for a large number of stars including both supergiants
and main sequence stars, the points fall into two loci as
shown in Figure 13-2. Such a plot is known as a two-color
diagram. The bands are drawn with a width of 0.1
magnitude to show the effects of measurement error.
Because the shape of the black-body radiation curve
is temperature dependent, both U-B and B-V will change
with stellar surface temperature, but U-B is additionally
affected by the amount of ultraviolet (Balmer) absorption,
which is related to the luminosity. Thus B-V is
primarily a measure of spectral class, and the spectral
I The_ are commonly designated by roman numerals: I,
supergiant; II, bright giant; III, giant; IV, subgiant; V, main sequence
(dwarf); VI, sub or white dwarf.
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