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Mar 6, 2006 Astro 100 Lecture 20 1

Lecture 20

The Stefan Boltzmann lawThe most common Star

Visual binary Stars

Stellar Spectra; Stellar Size; Binary Stars

Mar 6, 2006 Astro 100 Lecture 20 2

Reprise: 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

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Mar 6, 2006 Astro 100 Lecture 20 3

Reprise: Spectral Type� Hydrogen Balmer Lines show up only for temperatures 8000

� 15000 K: requires just right temperature for H to be in 2nd

energy state� 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� Try this applet! It combines the continuum color and lines.http://www.jb.man.ac.uk/distance/life/sample/java/spectype/specplot.htm

TiO moleculeM23750Betelgeuse

Ca+, Fe+G25800Sun

H Balmer linesB812,000Rigel

LinesSpectral TypeSurface TempStar

Mar 6, 2006 Astro 100 Lecture 20 4

Size and the HR diagram� Recall main stellar classification diagram one gets by

plotting Luminosity vs Surface Temperature� The names of the groups on the HR diagram come from

the fact that you can associate a size with each point on the HR

� There are actually two Laws for blackbody radiation:� old: Wien's Law, describes color of blackbody radiation:

Wavelength (max) = constant/T� new: Stefan-Boltzmann Law relates luminosity to

temperature and sizeLuminosity = Constant × Surface Area × Temperature4

= Constant × (4 π Radius2) × T4

Useful applet to demonstrate this: http://www.mhhe.com/physsci/astronomy/applets/Blackbody/frame.html

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Mar 6, 2006 Astro 100 Lecture 20 5

Stellar Size� Taking ratios to the sun (surface temp of sun = 5800 K),

(R/Rsun)2 = L/Lsun / (Temp/5800)4

� So if we measure luminosity and surface temperature, we have size, without even resolving star as an image!

� HR diagram groups from top right (cool, luminous) to bottom left (underluminous and hot), are in order of decreasing size.

� Because larger stars have lower surface gravity, so lower atmospheric pressure, can actually see subtle differences in spectrum of large and small stars of same temperature. For rough classification, add "Luminosity class" (I-V) to spectral type, specifying where in HR diagram a star is.

Mar 6, 2006 Astro 100 Lecture 20 6

Summarizing Stellar Classes

Sirius BD0.01White dwarfs

Sun, G2VV0.1 - 5Main Sequence

Aldebaran, K5III

III �IV3 � 100Giants

Betelgeuse, M2I

I �II30 - 1000Supergiants

ExampleLum ClassRadius (Rsun)Name

� Notice that both Main Sequence and White Dwarf stars fall near lines of constant radius. This is major hint for models of stellar structure.

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Mar 6, 2006 Astro 100 Lecture 20 7

Stellar Census� Get a good idea of how common each type of star is in solar

neighborhood, where we can study the faintest stars� Most stars are Main Sequence, fainter than Sun (KV, MV

red dwarfs)

Mar 6, 2006 Astro 100 Lecture 20 8

Spectral Types

>25,000

11 -25,000

8 -11,000

6 -8,000

5 -6,000

4 -5,000

3 -4,000

TemperatureHαHβHγ

TiOCH

Ca+

He

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Mar 6, 2006 Astro 100 Lecture 20 9

H-R Diagram

Mar 6, 2006 Astro 100 Lecture 20 10

Size on the H-R Diagram

Figure 6.18, p201, Arny

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Mar 6, 2006 Astro 100 Lecture 20 11

Size on the H-R Diagram - illustrated

Mar 6, 2006 Astro 100 Lecture 20 12

Size Affects Spectrum

I

II

III

IV

V

Supergiant

Dwarf (Main sequence)

Figure 6.20, p203, Arny

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Mar 6, 2006 Astro 100 Lecture 20 13

Spectral �Luminosity Class�

Figure 6.21, p203, Arny

Mar 6, 2006 Astro 100 Lecture 20 14

Betelgeuse