physics 320: astronomy and astrophysics – lecture ix

NJIT

Physics 320: Astronomy and Astrophysics – Lecture IX

Carsten Denker

Physics DepartmentCenter for Solar–Terrestrial Research

October 29th, 2003NJIT Center for Solar-Terrestrial Research

Problem 9.1

3 4 11eye eye

2 2

eye eye

eye eye 15bulb bulb2

max

49.88 10 J with 1.5 cm and 310 K

3

/ 4 with 10 J/s

and 2 /

27.96 10 J

4However: 9.35 m (Wien's law and eye n

bb

bb

E r aT r T

F L r L

EFA t r c

tLA r

E E Er c

otsensitive to IR)


Problem 9.2

4 /

3 3 2

3 30 0

3 315

3 3

3

8( )

1

8( ) with /

1

82.404114 2.2 10

with 477 K and 1 m

hc kT

x

a n d u d dhc e

k T xb n n d dx x hc kT

h c e

k TN nV V

h cT V


Problem 9.7

2 3500 nm

500 nm

0.0264 m /kg and 1.2 kg/m

131.6 m

2 2However: 21.0 m

3 3d


Stellar Atmospheres

The Description of the Radiation Field

Stellar OpacityRadiative TransferThe Structure of Spectral Lines


Opacity

2 1( [m kg ] absorption coefficient or opacity) dI I ds

Any process that removes photons from a beam of light will be called absorption.

(optical depth)d ds

, , 0

s

f i ds

,0 0 00

s sds ds


Opacity (cont.)

,0 (pure absorption)I I e

(gas optically thick)

(gas opticall

1

y t1 hin)

The optical depth may be thought of as the number of mean free paths from the original position to the surface, as measured along the ray’s path.


Photon Interactions

Bound–bound transitions Bound–free absorption Free–free absorption

(bremsstrahlung) Electron scattering

free–free absorption of a photon

2229 2

2

86.65 10

(Thompson

scatt n )

m

g

3

eri

Te

e

m c

319 3

5

11.31 10 m

500 nmbf n


Continuum Opacity

Photoionization of H–

ions.1240 eV nm

1640 nm0.754 eV

hc

, , , ,

(total opacity)

bb bf ff es

The total opacity depends not only on the wavelength of the light being absorbed but also on the composition, density, and temperature of the stellar material. Rosseland mean opacity


Emission

Any process that adds photons to a beam of light will be called emission.

1 2 (random walk) Nd l l l

1 1 1 2 1

2 1 2 2 1

1 2

N

N

N N N N

d d l l l l l l

l l l l l l

l l l l l l

2 212 13 1

21 23 2

1 2 ( 1)

[cos cos cos

cos cos cos

cos cos cos ]

N

N

N N N N

d Nl

d l N l


Limb Darkening

Looking into a star at any angle, we always look back to an optical depth of about = 2/3, as measured by a straight line back along the line–of–sight.

0

sds

radrad

(radiative pressure and flux)

dPF

dr c


Radiative Transfer Equation3 1 ( [m s sr ] emission coefficient)d jI j ds

dI I ds j ds

1 dI jI

ds

1 3 1 ([J s m sr ] source function)j

S

(transfer equa1

tion)dI

I Sds


Radiative Transfer Equation (cont.)

0

0 intensity decreases with distance

0 approaches

dII S

dsdI

dsdI

I Sds

The intensity of the light tends to become equal to the local value of the source function.

For the case of thermodynamic equilibrium, the source function is equal to the Planck function S = B.


Solving RTE

dII S

d

0

, ( ) and cosv zz dz dz ds

,,

,

plane parallel atmos

sec coscos

phere

vv

v

dII S

d

0 0 and cos

dII I d S S d I S

d

radcos 4v v

dFdI d Id S d I S

d d


Solving RTE (cont.)2

2

0 0

rad radrad rad

cos cos cos

cos cos sin 0

1 (speherical coordinates)

v

v

dI d I d S d

d

d d d

dP dPF F

d c dr c

4rad surf

rad

rad rad

const.

0

1 ( : constant of integration)

e

v

v

F F T

dFI S

d

P F C Cc


Eddington Approximation

out in

in rad out in

rad out in

1

20 at 0

2 4

3 3

v

I I I

I F I I

P I I Ic c

rad rad

4rad

4 1 2 and

3 34 2 3 2

3 3 4 3

v

v e v

I F C C Fc c c

I F I T

44 43 2

LTE4 3e v

TI S B T T


Structure of Spectral Lines

(equivalent width)c

c

F FW d

F

2

natural broadenin2

1

g1

i fc t t

Doppler broadening2

2

kT

c m

2 2

pressure broadening 1 2n kT

c t c m


Homework Class Project

Continue improving the PPT presentation. Use the abstract from the previous assignment

as a starting point for a PowerPoint presentation.

The PPT presentation should have between 5 and 10 slides.

Bring a print-out of the draft version to the next class as a discussion template for group work

Homework is due Wednesday November 5th, 2003 at the beginning of the lecture!

Exhibition name competition!


Homework

Homework is due Wednesday November 5th, 2003 at the beginning of the lecture!

Homework assignment: Problems 9.9, 9.12, and 9.13!

Late homework receives only half the credit!

The homework is group homework!Homework should be handed in as a

text document!

physics 320: astronomy and astrophysics – lecture ix

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