|
|
|||||||
| Mv | φ(Mv) | Mv | φ(Mv) | Mv | φ(Mv) | ||
| -8.0 | - | -3.5 | 0.0006 62 | 1.0 | 0.345 | ||
| -7.5 | 0.0000 0074 | -3.0 | 0.0011 62 | 1.5 | 0.291 | ||
| -7.0 | 0.0000 0294 | -2.5 | 0.0020 0 | 2.0 | 0.423 | ||
| -6.5 | 0.0000 0502 | -2.0 | 0.0031 5 | 2.5 | 0.422 | ||
| -6.0 | 0.0000 0504 | -1.5 | 0.0042 0 | 3.0 | 0.421 | ||
| -5.5 | 0.0000 0501 | -1.0 | 0.0201 | 3.5 | - | ||
| -5.0 | 0.0000 733 | -0.5 | 0.0702 | 4.0 | 1.67 | ||
| -4.5 | 0.0001 86* | 0.0 | 0.130 | 4.5 | 3.34** | ||
| -4.0 | 0.0002 65 | 0.5 | 0.246 | 5.0 | - | ||
Notable Conclusions from the above Table
(1) This sample is representative of the "naked-eye" stars
(or even the stars seen in a telescope brighter than mL).
(2)
This approach gives one the bright
end of the luminosity function compared with the faint end for the previous
approach.
(3) In principle this approach is easier than the previous
one. However the absorption correction makes things difficult. Such
a correction
makes
φ(Mv)
larger since it reduces the volume searched.
(4) The variation in effective volume with Mv
is extreme, e.g., even though there are 14 stars in the sample with Mv
between -4 and -5 and only
one with Mv
between +4 and +5, φ(4.5) »
18,000 φ(-4.5)
because the volume searched is nearly 250 000 times smaller (r is
~63 times
smaller). It is this decreasing volume
with increasing Mv which causes the sample to be statistically
inadequate for determining the faint
end of
φ(Mv)
for any sort of reasonable
limiting magnitude mL.
(5) Because of the huge volume surveyed at bright Mv,
the extremely rare stars with Mv = -6 or -7 make up a
substantial fraction (10%-20%) of
the stars in the catalog.
(6) Because very bright stars are rare and therefore
generally very distant, they are often affected by significant absorption.
(7) ò-¥
φ(Mv)
dMv »
0.0037 stars pc-3.
(8) Only 7 stars are common to both the lists of 100 nearest
stars and 100 brightest stars.
