Lecture 12 Stars
Brightness depends on
amount of light it actually emits
e.g. Betelgeuse emits 5000x as much light as Procyon because it’s much
Brightness vs. luminosity
• When we talk about how bright stars look in our sky, we are talking about
apparent brightness. More specifically, we define the appar- ent
brightness of any star in our sky as the amount of power (energy per
second) reaching us per unit area.
Depends on distance
• inverse square law leads to a very simple and important formula re
lating the apparent brightness, lumnosity, and distance of any light
We will call it the inverse square law for light:
apparent brightness=luminosity/4pi * (distance)
Because the standard units of luminosity are watts, the units of apparent
brightness are watts per square meter.
• When we talk about how bright stars are in an absolute sense, re- gardless of
their distance, we are talking about luminosity—the total amount of
power that a star emits into space.
Magnitude and brightness examples:
1. a group of 20 identical stars are so close together that they appear to be one
star. If each star has a brightness of 5.0 mag what is the brightness in
magnitudes that is observed for the group?
"m 20ag) - m (ma1) = -2.5 log (20 stars / 1 star) "
m 20ag) - 5.0 = -2.5 log(20) = -2.5 " 1.30 = -3.25 "
m 20ag) = 5.0 - 3.25 = 1.75 mag
2. stars A and B are identical except that B is three times further away than A. If mA= 2.5
mag what is m ?Bm - A = -B.5 log (b / bA)
"Be are told that A and B are
identical... but isAb =B ?
"Yes, if the stars were at the same distance, but in this caseBd = 3A ... so... NO.
"Remembering that brightness as d we then have b = 1/32 b = 1/9 b (or b
2 B A A A
= 9b B and...
m -m = -2.5 log (9) = -2.38 and finally, m = 2.38 + 2.5 = 4.88 mag
A B B
3. absolute visual (V) magnitude of the Sun is 4.8.What is the
absolute magnitude of a galaxy with 2x10 stars identical to the Sun? If it is at a
distance of 760 kiloparsecs (7.6x10 pc =760 kpc) what is its apparent
Mgal – Msun = -2.5 log (2x10 /1) = -20.8
Mgal = Msun – 20.7 = -15.9
mgal- Mgal = 5 log (d/10) = 5 log (7.6x104) = 24.4
mgal = Mgal + 24.4 = 8.4
Hertzsprung-Russell (H-R) diagrams
• The horizontal axis represents stellar surface temperature, which, as
we’ve discussed, corresponds to spectral type. Temperature decreases
from left to right because Hertzsprung and Russell based their dia-
grams on the spectral sequence OBAFGKM.
• The vertical axis represents stellar luminosity, in units of the Sun’s
luminosity (LSun). Stellar luminosities span a wide range, so we keep
the graph compact by making each tick mark represent a luminosity 10
times as large as the prior tick mark.
• stars near the upper left are hot and luminous. Similarly, stars near the
upper right are cool and luminous, stars near the lower right are cool and
dim, and stars near the lower left are hot and dim.
• star’s luminosity depends on both its surface temperature and its surface
area or radius. If two stars have the same surface temperature, one can
be more luminous than the other only if it is larger in size. Stellar radii
therefore must increase as we go from the high-temperature, low- luminosity corner on the lower