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Astonomy 62 Lecture #9

Liouville's TheoremBlackbody Radiation

Plank FunctionWien's Displacement LawStefan-Boltzmann Law

Plank Function

I T=B T =2 hc2/ 5

eh c/ kT −1

I T =B T =2 h 3 / c2

eh / kT−1

Stefan-Boltzmann Law

L=4 R2T 4

Wien's Displacement Law

peak=0.29 cm

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Astonomy 62 Lecture #9

Applications of Stefan-Boltzmann LawColor MagnitudeColor Index

Reading for today: 3.6

Reading for next lecture: 5.1-5.4

Topics for TodayTopics for TodayAstonomy 62 Lecture #9

Problem: Problem: Estimate the effective temperature of the Solar surface if L = 3.8x10

26 J/s R = 7.0x10

8 m

Astonomy 62 Lecture #9

T = 5740 KT = 5740 K

Astonomy 62 Lecture #9

Sirius B:Sirius B:T = 27,000 KT = 27,000 KR = 5400 kmR = 5400 km

Earth:Earth:RR++ == 6400 km 6400 km

A

B

Sirius B

Earth

Problem: Sirius BProblem: Sirius BEstimate the radius of Sirius B if its luminosity is L = 0.03 L = 1.1 x 1025 J/s and its spectrum peaks at 107nm.

Astonomy 62 Lecture #9

T c=T∗ R∗

Rc=260 K

Problem: Embedded Star Problem: Embedded Star A young star with surface temperature T* = 10,000K

and radius R* = 1010m is hidden inside a completely

opaque cloud of radius Rc = 100AU. What is the equilibrium temperature of the cloud?

Albedo = percentage of incident radiation Albedo = percentage of incident radiation that is refected. that is refected.

Kirchhoff's RuleKirchhoff's Rule

Good absorbers (low albedo) are also good emitters and vice versa.

Astonomy 62 Lecture #9

Spitzer Space Telescope

Credit: NASA

Astonomy 62 Lecture #9

B T =2 hc2 /5

ehc /kT−1

Astonomy 62 Lecture #9

Visible LightVisible Light

Color Magnitudes

Color Magnitude is measured the same way as a regular (bolometric) magnitude, but through a flter which restricts photon detection to a certain wavelength range.

Astonomy 62 Lecture #9

Astonomy 62 Lecture #9

U B V R IStandard

Visual BandFilters

U B V R I � x(A) 3650 4400 5500 7000 9000

Wx(A) 680 980 890 2200 2400

1 Å=0.1nm=10−10 m

Fx=∫0

∞F Sx d

F x≃F xW x

mx ,1−m x ,2=2.5 logFx ,2F x ,1

mx ,1−mx ,2≃2.5 logF , 2 x

F ,1 x

Flux through filter X:

Apparent Color Magnitude:

B−V=2.5 log [ F V

F B ]CB−V

Color Index:

Astonomy 62 Lecture #9

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From C&O (Fig. 3.10)

Astonomy 62 Lecture #9

Color–Color Diagram for Normal Stars Color–Color Diagram for Normal Stars

Credit & Copyright: KPNO 0.9m Telescope, AURA, NOAO, NSF APOD

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Stellar SpectraStellar Spectra