1

Lecture 2

• Long-term solar variability

– Grant minima/maxima

– Total solar irradiance

• Spectral irradiance

– Black body, gray body

• Internal structure of the Sun

– Y-dependence

– Intensity & radiation transport

2

Summary of previous lecture

• Previous space weather events

– Halloween storm, Carrington flare, etc

• Effect on aviation, GPS, radiation, GICs, etc

– GPS stories: climbers on Mt Everest, Heathrow…

– Biol. impact measured in

(A) Grey, (B) Curie, © Sieverts, (D) rem?

• Kp index

• Sun’s position in HR diagram (L=3.8x1026W)

3

Long-term variability

J. Eddy E. Maunder S. Schwaber

4

Past sunspot predictions

5

6

7

htt

p:/

/sp

ace

wea

ther

.com

8

htt

p:/

/sp

ace

wea

ther

.com

9

Low, but not as low as 1913

10

Little Ice Age

11

Cycle progression as of now

12

Total solar

irrradiance

FrL 24

Integrated flux

Over all l

AU1r

13

Pyrheliometer

14

Conversion of spectral

distribution function

dTITF ),()(

ll

c)(

or

lll dTITF ),()(

Hint: compute l

d

d

Dimensional analysis

Hzm

W),(

2TI

dcba kcTvTI B),(

K

J1038.1 23

B

k

16

Planck

spectrum

1

12),(

B/2

3

Tkhec

hTI

Tkhe

c

hB/

2

32

Tkch

Tk

c

hB2

2

B

2

3 22

Rayleigh-Jeans law

Tkc

TI B2

22),(

Tkc

c

cTITI B22

2

2

2),(),(

l

ll l

Tkc

B4

2

l

18

Visible spectrum: most of energy

19

Infrared: l-4 law

20

Radio:

interesting

break

• Clue about hot corona

• Brightness temperature

21

“Gray body” at short wavelengths

Page 78 of

Knipp (2011)

22

Internal structure of the Sun

• Seeing deeper – Different wavelengths

– Ca, Fe lines (slightly higher up)

– infrared (slightly deeper)

• Helioseismology

• Neutrinos

• Theory (depends on Y and mixing length) – X+Y+Z=1

23

Dependence on Y

• Solve time-dependent stellar structure eqns

• Produce more Y

R and L grow (faint sun paradox)

More on intensity

),ˆ,( tI nx

SI

ds

dI

SI

d

dI dsd

SII n̂

depends also

on direction

for each ray path…

or

with

optical depth

Related to homework