Astronomy 142 1

Today in Astronomy 142

More on the Sun as a typical star: !  Radiative transport and

optical depth !  The spectrum of the

surface (atmosphere) of the Sun

!  The structure of the sun’s outer layers: convection, rotation, magnetism and sunspots

!  Solar energy

Multicolor ultraviolet image of the Sun, showing several sunspot-rich active regions (TRACE/NASA).

Astronomy 142 2

The solar spectrum

By and large, the spectrum of the Sun resembles closely a blackbody. From the total energy flux at Earth (solar constant):

we get the Sun’s luminosity:

Setting solar luminosity equal to blackbody power gives Sun’s effective temperature:

Astronomy 142 3

The solar spectrum (continued)

In detail: absorption lines are also seen in the solar spectrum; they match up with many known transitions of atoms, ions and molecules. (See Lab #2.)

Figure: the ultimate high-resolution spectrum of the Sun (Nigel Sharp, from data by Bob Kurucz et al. ( NOAO/NSO/Kitt Peak FTS/AURA/NSF)

Astronomy 142 4

Formation of absorption lines in the solar atmosphere

Figu

re: C

hais

son

and

McM

illan

, Ast

rono

my

Tod

ay

Astronomy 142 5

Radiation transport keeping track of energy in radiation

Astronomy 142 6

Radiative transport optical depth dI = �Id⌧

dI

d⌧= �I

I(⌧) = Ie�⌧

light missing integrate

τ is unit less optical depth

⌧ =

Z⇢ds

κopacity units g-1 cm2

κρ units cm-1

amount of light going missing per unit length

Astronomy 142 7

Mean free path

κopacity units g-1 cm2

κρ units cm-1

amount of light going missing per unit length

absorption per unit length

κρ = n σ n particles per unit volume (cm-3) σ cross section (cm2)

l = (n σ)-1 = (κρ)-1 (cm) how far a photon goes before getting absorbed the mean free path

Astronomy 142 8

Relation between extinction and optical depth

Astronomy 142 9

Opacity depends on wavelength because of atomic and molecular transitions If the opacity is higher then we see only in the top layers where it is cooler. When it is cooler the surface brightness is lower

opacity and photosphere

Astronomy 142 10

d⌧ = ⇢drd⌧

dr= ⇢

optical depth with radius

dP

dr= ⇢g hydrostatic equilibrium

dP

d⌧=

dP

dr

dr

d⌧= ⇢g ⇥ 1

⇢=

g

at photosphere τ=1

P at photosphere =g/κ Pressure broadening of spectral lines gives a measurement for g

Astronomy 142 11

The outer layers of the sun

Convection: ! Opacity from

atoms rises as one moves from center to surface (more atoms there; all ionized in the center).

! “Bubbles” can neutralize, cool and sink.

! Hot material rises to take its place.

Figure: Chaisson and McMillan, Astronomy Today

Astronomy 142 12

Solar “granulation:” the tops of convection cells

Figure: Chaisson and McMillan, Astronomy Today

credit: NOAO

Astronomy 142 13

Simulations of convection

credit: Frank Robinson

Astronomy 142 14

Using Adaptive Optics to look at detail

Visible images from The 1m Swedish Solar Telescope at La Palma show filaments near sunspots as well as the granulation. The dark cored filaments were unexpected.

Astronomy 142 15

More detail on Sun spots

Astronomy 142 16

Further out: the corona and chromosphere

Corona: observed to be well over 1000000 K. Theory of corona: heated by acoustic noise from boiling top of convection zone; diffuse enough that it can’t cool very well, so it reaches very high temperatures.

Figure: Chaisson and McMillan, Astronomy Today

Astronomy 142 17

Solar corona and atmosphere X-ray composite (NASA/SPARTAN)

Astronomy 142 18

Sunspots: solar magnetism

! Sunspots appear dark because they’re slightly cooler than the rest of the solar surface.

! Zeeman effect measurements show that they are also maxima of magnetic field.

! Associated with other activity (e.g. prominences)

Figure: Chaisson and McMillan, Astronomy Today

Astronomy 142 19

The multi-wavelength real-time Sun according to SOHO

Pulled off the SOHO website on Jan 24/2003. This is what the sun looked like in X-rays and UV lines, optical continuum and with a magnetogram.

Astronomy 142 20

Sunspot progress, activity during solar cycle

Figure: Chaisson and McMillan, Astronomy Today

The 11-year sunspot cycle

The first sunspots in a cycle form near ±30° latitude, and the last near the equator, producing the “butterfly diagram.”

Astronomy 142 21

Dav

id H

atha

way

, NA

SA/M

SFC

Astronomy 142 22

11-year sunspot cycle, for the last 400 years

Figure: Chaisson and McMillan, Astronomy Today

Astronomy 142 23

Sunspot formation and cycle: interaction of magnetism and differential rotation

The Sun rotates, but not as a solid body; this differential rotation wraps and distorts an initially “poloidal” solar magnetic field. ! Occasionally, the field lines burst out of the surface and

loop through the lower atmosphere, thereby creating a sunspot pair. The underlying pattern of the solar field lines explains the observed pattern of sunspot polarities.

! If the loop happens to occur on the limb of the Sun and is seen against dark space, a prominence is visible.

! The twisting and wrapping of the field lines eventually results in the production of a poloidal field again, but with north and south switched. Then the process repeats.

! 22 years between identical field configurations, 11 years between sunspot-number maxima.

Astronomy 142 24

Sunspot formation and cycle: interaction of magnetism and differential rotation

Figure: Chaisson and McMillan, Astronomy Today

Astronomy 142 25

Energy and the sun

! Hydrostatic equilibrium and ideal-gas behavior ensure that the center of the Sun is very hot, and energy (in the form of light) is radiated from the center.

! The high opacity of the Sun to light determines the rate at which the energy leaks out. As we have seen, it takes a long time for photons to diffuse from center to surface.

! This cannot go on forever, without the Sun cooling down, or replacement for the energy that leaks away.

! We know that the solar system is about 4.5x109 years old (from many radioisotope abundance measurements on meteorites), and that life has existed here for at least 3x109 years. Thus the Sun must have had close to its present luminosity for billions of years.

Astronomy 142 26

Cooling timescale

Astronomy 142 27

How long would the Sun’s present heat last?

Plasma energy density at center of Sun (energy density of electron gas there, considered again to be ideal):

Energy density of light, which is about to leak away:

We showed last lecture that it takes about t = 31000 years for a photon to leak from center to surface, so the heat lasts

Thus some process must be replacing the energy that leaks away.

Astronomy 142 28

Energy sources for the Sun

Chemical energy (burning) doesn’t work. “The Sun is nothing but a burning ember:” Anaxagoras of Clazomenae, ca. 450 BC. Suppose (optimistically) that the Sun were made of anthracite coal, with enough oxygen to burn it completely to CO2: 5.5x1032 gm coal, 1.45x1033 gm O. Burning 1 gm of anthracite coal to CO2 liberates 4.3x1011 erg. Thus the Sun’s initial energy reserve would be ΔE =4.3x1011 x 5.5x1032 erg = 2.4 x 1044 erg which at the Sun’s present luminosity would last

Astronomy 142 29

Energy sources for the Sun (continued)

Collapse and liberation of gravitational potential energy also doesn’t work (Kelvin and Helmholtz, late 19th century):

However, mass energy would work, even if only 0.1% of it could be converted to radiation:

Astronomy 142 30

Energy sources for the Sun (continued)

How could the Sun convert mass-energy to radiation? ! Nuclear fusion: basically the liberation of mass energy

stored as potential energy of the strong nuclear interaction.

Would this work under the conditions known to prevail at the center of the Sun?

! Yes. Requires such conditions, in fact. To demonstrate these answers we need to talk a bit about the fundamental interactions of matter.

Astronomy 142 31

Summary

!  Phenomenology of the Sun: sunspots, active regions, magnetic activity, solar cycle, solar dynamo.

!  Solar structure: radiative core and convection zone, photosphere, chromosphere, corona.

!  Solar energy problem. Only nuclear reactions provide a plausible energy source for the billion year timescale that the Sun has been luminous.

!  Opacity and radiative transport