Download ASTR2050 Spring 2005 •

ASTR2050 Spring 2005
Lecture 11am 18 January 2005
In this class we will cover:
• The brightness of stars
• Electromagnetic radiation
• The color of stars: “Blackbody radiation”
• The Planck Radiation Formula
Brightness and Magnitude
The ancients looked at the stars and saw that some of
them appeared brighter than others. They divided them
into (about) five different so-called “magnitudes”:
“First magnitude” meant the brightest star observed
“Sixth magnitude” meant the faintest star observed
Today, we know better how to measure “brightness”
but we are stuck with the ancients’ convention!
This leaves us with two minor complications:
Smaller magnitude means larger brightness
Converting magnitude to brightness uses logarithms
•
•
For now, we consider only ratios of brightness,
which correspond to differences in magnitude.
b1
(m2 −m1 )/5
(m2 −m1 )/2.5
= 100
= 10
b2
b1
m2 − m1(= !m) = 2.5 log10
b2
Examples
How much brighter is a third magnitude
star than a fourth magnitude star?
b1/b2 = 100(4−3)/5 = 1000.2 = 2.51
A certain telescope allows you to see a million times more
light than your naked eye. What is the faintest magnitude
star that you can see now?
!m = 2.5 log10 10 = 2.5 × 6 = 15
6
m2 = 6 + !m = 21
Electromagnetic Radiation
White light breaks up into colors, but
that’s only a small part of the story.
Depending on circumstances, it may be more or
less convenient to express the type of radiation in
terms of either its frequency or its wavelength.
Frequency
! = c/"
Wavelength
For astronomers, a very important issue is to what
extent various types of electromagnetic radiation can
penetrate the Earth’s atmosphere!
See also Figure 2.3 in your textbook!
Why do stars have colors?
This is Figure 2.4 in your textbook
Color = Temperature
Think about a light bulb. As the current through the
filament increases, the color turns from red to blue/white.
This is called “Black Body Radiation”.
!max = 2.90 × 10 nm · K/T
6
Energy per unit area = !T
4
Note: Radiated energy goes like fourth power of T
Planck’s Radiation Law
Photons!
2
5
!c"
2hc /!
I(!, T ) = hc/!kT
= 2 I(", T )
!
e
−1
This is the radiated energy intensity per unit area
and per unit wavlength (or frequency) interval.
It is now understood that this formula was the first early
evidence that electromagnetic radiation came in “bundles”.
E = h!
Stars look like black body radiators!
So, we connect
“brightness” to
the total energy
radiated by a star:
L = (4!R2)("T 4)
“Luminosity”