1. 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

2. 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

3. 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
= × (5.5x106)2 = 52
Bottom Line: By combining brightnesses and distances from parallax of nearby stars, find stellar luminosities have huge range:
L(star) = 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

4. 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

5. 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: ,000. The Sun is in the middle.
Star
Wavelength (maximum)
(color)
Surface
Temperature
Sun
520 nm (yellow)
5800 K
Rigel (β Ori)
250 nm (ultraviolet-blue)
12,000 K
Betelgeuse (α Ori)
800 nm (red-infrared)
3750 K
Mar 3, 2006
Astro 100 Lecture 19

6. 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

7. Balmer Lines most prominent in stars between 8000 and 15000 K
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

8. 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.
Star
Surface Temp
Spectral Type
Lines
Rigel
12,000 B8
H Balmer lines
Sun
5800 G2
Ca+, Fe+
Betelgeuse
3750 M2
TiO molecule
Mar 3, 2006
Astro 100 Lecture 19

9. 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

10. 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

11. Brightness & Luminosity of Some Stars
m brtness
(mag) b(Vega))
Sun /2.5
=1011
Vega (α Lyr)
“Proxima” Cen ×10-5
α Cen
Betelgeuse (α Ori)
Lum
(Lsun) 1 52
6x10-5
20,000
parallax dist
(arcsec) (pc)
5x10-6
Mar 3, 2006
Astro 100 Lecture 19

12. Orion Star Colors Betelgeuse 3750 K Rigel 12,000 K Mar 3, 2006
Astro 100 Lecture 19

13. Spectral Types He >25,000 11 -25,000 8 -11,000 6 -8,000 5 -6,000Ha Hb Hg He
>25,000
11 -25,000
8 -11,000
6 -8,000
5 -6,000
4 -5,000
3 -4,000
Temperature
Ca+
TiO CH
Mar 3, 2006
Astro 100 Lecture 19

14. H-R Diagram
Mar 3, 2006
Astro 100 Lecture 19