Download Lecture 19 Brightness Units

Lecture 19
Stellar Luminosity;
Surface Temperature
Luminosity from brightness and distance
Temperature from color
Temperature from lines: spectral type
The H-R classification diagram:
Main Sequence, Giants, and Dwarfs
Mar 3, 2006
Astro 100 Lecture 19
1
Brightness Units
• Magnitude: a measurement of relative intensity where a
ratio of 10 gives a difference in magnitude of 2.5 (called a
"logarithmic" scale). Greek origin, based on human eye.
m(star 1) - m(star 2) = -2.5 log10 (brt(star 1) / brt(star 2))
or
brt(star 1) / brt(star 2) = 10 -(m(star 1) - m(star 2))/2.5
• Apparent magnitude: magnitudes "relative to the
brightness of Vega" (α Lyrae, one of the stars in the
Summer Triangle).
– So for apparent magnitude, star 2 in the formula is Vega.
– This means Vega’s apparent magnitude is 0
– Apparent magnitude is usually written (lower case) "m".
• Some Examples
Mar 3, 2006
Astro 100 Lecture 19
2
1
Luminosity
• Luminosity measured in solar units: "Lsun"
Lsun = 3.9x1026 W
• Recall relation between Brightness and Luminosity
Lum = 4π distance2 Brightness
• By combining brightnesses and distances from parallax of nearby stars,
find stellar luminosities
• L(Vega)/Lsun
= b(Vega)/bsun × (d(Vega)/dsun)2
= 10-11 × (7.8/5.5x10-6 )2 = 24
• Bottom Line: By combining brightnesses and distances from parallax
of nearby stars, find stellar luminosities have huge range:
L(star) = 10-5 - 106 Lsun
• This means a star can have a large brightness (low magnitude) if it is
close, or if it is intrinsically luminous
Mar 3, 2006
Astro 100 Lecture 19
3
Stellar Surface Temperature
• One of the easier things to measure is a star’s
surface temperature
• Like the Sun, stars show absorption line
spectra: continuum plus absorption lines. Each
depend mainly on the surface temperature.
Mar 3, 2006
Astro 100 Lecture 19
4
2
Stellar Continuum Color
• The continuous spectrum is approximately a blackbody
radiator from opaque gas.
• Color => approximate surface Temperature from Wien’s law:
Surface Temp = constant/wavelength(maximum)
• Range of surface temperatures seen: 3500 - 30,000. The Sun
is in the middle.
Star
Wavelength (maximum)
(color)
Sun
520 nm (yellow)
Rigel (β Ori)
250 nm (ultraviolet-blue)
Betelgeuse (α Ori)
800 nm (red-infrared)
Mar 3, 2006
Surface
Temperature
5800 K
12,000 K
3750 K
Astro 100 Lecture 19
5
Stellar Absorption lines - Spectral "Type"
• The absorption lines are due to absorption by
atoms in its transparent, slightly cooler, overlying
atmosphere. Different stars show different
absorption lines. Why?
– Which spectral lines appear depends mainly on the
temperature of the atmosphere.
– The elemental composition of stars does not (usually)
vary enough to make a big effect.
• Example, the hydrogen Balmer Lines.
– (Recall these are from photons absorbed by Hydrogen
atoms in their second energy state).
Mar 3, 2006
Astro 100 Lecture 19
6
3
Balmer Lines
• most prominent in stars between 8000 and 15000 K
• > 15,000K:
– It is so hot that collisions between H atoms knock the
electrons off the atoms, leaving them ionized (bare
protons).
– A bare proton has no lines at all. Balmer lines are
weak.
• < 8000 K:
– The H Balmer absorption lines at visible wavelengths
are all due to absorption by atoms starting from the
second energy state.
– The only way an atom gets into this state is by being hit
by a neighbor, and the neighbors at these temperatures
are not moving fast enough. Balmer lines are weak.
Mar 3, 2006
Astro 100 Lecture 19
7
Spectral Type
• Similar (more complex) story for other elements, at other
temperatures. Which lines are prominent is quantified by (in
order of decreasing temperature)
• spectral type letters: O B A F G K M, and
• subtype numbers G0,G1...G9.
• This turns out to be the easiest way to get the surface
temperature of even very faint stars- this has been done for
almost a million stars!
• Try this applet! It combines the continuum color and lines.
http://www.jb.man.ac.uk/distance/life/sample/java/spectype/specplot.htm
Star
Rigel
Surface Temp
Spectral Type
Lines
12,000
B8
H Balmer lines
Sun
5800
G2
Ca+, Fe+
Betelgeuse
3750
M2
TiO molecule
Mar 3, 2006
Astro 100 Lecture 19
8
4
Classification Diagram
• We now have all the data we need to make a
famous diagram which shows what kind of stars
there are:
• "H-R (Hertzsprung-Russell) Diagram"
Luminosity vs Temperature
• For historical reasons, luminosity is plotted up and
temperature towards left.
• Each star is one point on the diagram
Mar 3, 2006
Astro 100 Lecture 19
9
Stellar Classes
•
•
•
•
Find there are only certain kinds of stars
Supergiants Very rare. eg Betelgeuse (alpha Ori)
Giants Pretty rare. eg Aldebaran (alpha Tau)
Main Sequence 90% of stars. eg the Sun . The least
luminous (coolest) main sequence stars are by far the most
common (albeit the most inconspicuous)
• White Dwarfs (a different typing scheme). Probably very
common, but so faint that not many are known. eg Sirius B
(faint companion to Sirius)
Next time: how size comes into it..
Mar 3, 2006
Astro 100 Lecture 19
10
5
Brightness & Luminosity of Some Stars
m
brtness parallax dist Lum
(mag) b(Vega)) (arcsec) (pc) (Lsun)
Sun
Vega (α Lyr)
“Proxima” Cen
α Cen
Betelgeuse (α Ori)
Mar 3, 2006
-27.5 1027.5/2.5
=1011
0.0
1.00
10.7 5.3×10-5
0.1
0.91
0.5
0.63
5x10-6 1
0.128
0.775
0.775
0.011
7.8
1.3
1.3
95
24
6x10-5
1
20,000
Astro 100 Lecture 19
11
Orion Star Colors
Betelgeuse
3750 K
Rigel
12,000 K
Mar 3, 2006
Astro 100 Lecture 19
12
6
Spectral Types
Hγ
He Hβ
Hα
Temperature
>25,000
11 -25,000
8 -11,000
Ca+
6 -8,000
5 -6,000
4 -5,000
3 -4,000
CH
Mar 3, 2006
TiO
Astro 100 Lecture 19
13
H-R Diagram
Mar 3, 2006
Astro 100 Lecture 19
14
7