1. Lecture 3 The Sun
ESS 154/200C

2. Date Day Topic Instructor Due
ESS 200C Space Plasma Physics ESS 154 Solar Terrestrial Physics M/W/F 10:00 – 11:15 AM Geology Instructors: C.T. Russell (Tel. x-53188; Office: Slichter 6869) R.J. Strangeway (Tel. x-66247; Office: Slichter 6869)
Date Day Topic Instructor Due
1/4 M A Brief History of Solar Terrestrial Physics CTR
1/6 W Upper Atmosphere / Ionosphere CTR
1/8 F The Sun: Core to Chromosphere CTR
1/11 M The Corona, Solar Cycle, Solar Activity
Coronal Mass Ejections, and Flares CTR PS1
1/13 W The Solar Wind and Heliosphere, Part 1 CTR
1/15 F The Solar Wind and Heliosphere, Part 2 CTR
1/20 W Physics of Plasmas RJS PS2
1/22 F MHD including Waves RJS
1/25 M Solar Wind Interactions: Magnetized Planets YM PS3
1/27 W Solar Wind Interactions: Unmagnetized Planets YM
1/29 F Collisionless Shocks CTR
2/1 M Mid-Term PS4
2/3 W Solar Wind Magnetosphere Coupling I CTR
2/5 F Solar Wind Magnetosphere Coupling II;
The Inner Magnetosphere I CTR
2/8 M The Inner Magnetosphere II CTR PS5
2/10 W Planetary Magnetospheres CTR
2/12 F The Auroral Ionosphere RJS
2/17 W Waves in Plasmas 1 RJS PS6
2/19 F Waves in Plasmas 2 RJS
2/26 F Review CTR/RJS PS7
2/29 M Final

3. Today’s Lecture The Sun Interior Atmosphere/Ionosphere The Solar Cycle
Properties
Nomenclature
Interior
Atmosphere/Ionosphere
The Solar Cycle
Granulation
Magnetic Field
Flows
Helioseismology
Solar Dynamo
Chromosphere/Transition Region

4. The Sun: Summary of Properties
Ordinary star
Spectral class G2V
Magnitude 4.8
Properties
Age: 4.5 x 109 years
Mass: 1.99 x 1030 kg
Radius: 696,000 km (~109 Re or AU)
Mean density: 1400 kg · m-3
Composition: 90% H, 10% He, 0.1% other
Distance from Earth: 1AU = 1.5x108km =~215 RS
Surface gravity: 274 m · s-2
Escape velocity: 618 km · s-1
Effective blackbody (surface) temperature: 5785 K
Total Energy Output: per sec=3.8x1026J, per year=1.2x1034J
Tilt of rotation axis: 7°
Average Rotation period as seen from Earth=~27.3 days (=1 Carrington Rotation)
Jan. 13, 2016

5. Useful Nomenclature
Solar Longitude is defined from the Central Meridian. The right half is the West. The left half is the East. The edge of the disk is called the limb.
Solar latitude is defined such that the Northern hemisphere is above the ecliptic. The rotation axis of the Sun is inclined 7° with respect to this plane.
Carrington studied sunspots and inferred the Sun was rotating. Carrington longitude is measured from the central meridian at a particular set time established when Carrington Rotations were first adopted. The subsolar Carrington longitude decreases as the Sun rotates and goes through 360° every 27.3 days. The same sunspots may be seen at about the same disk location for several Carrington Rotations.
Central
meridian
Eastern Western
limb
Image of the Sun in visible light, showing a few dark sunspots near the central disk at low latitude.

6. Fusion: Source of Solar Energy
When the temperature is above 10 million K, two hydrogen nuclei or protons deep inside the Sun fuse to create an unstable particle that decays into a deuterium nucleus, a positron, and a neutrino. [T ~ 8Ga]
The positron is annihilated by an electron, giving off two gamma rays.
A hydrogen atom immediately combines with the deuterium creating a He3 nucleus and a gamma ray. [T ~ 1.45s]
Two He3 nuclei eventually combine, creating a helium nucleus (alpha particle) and two protons [T ~240ka]
Overall, six protons interact, producing one helium nucleus, two neutrinos, two positrons, five gamma rays, and two protons.
A small fraction (~ 0.7%) of the mass of the original hydrogen is converted to the mainly radiative (photon) energy. A small fraction of this radiative energy makes it out of the Sun’s core to the surface to create the light we see.
Hydrogen burning

7. Solar Structure: Interior
Core
Contains nuclear reactions
T ~ 1.5 x 107K; P = 1.6 x 105 kg · m-3
Out to 0.25 RS
Radiative Zone
Energy transfer by photons
Out to 0.75 RS
Top is the tachocline; T = 5 x 105K
Convection Zone
Heat transfer by fluid motion
Region of solar dynamo
Top is the photosphere;
T = 5785K
Number density about 1023m-3
Surface of Sun defined by radius at which photons can escape
Cut-away diagram showing solar interior,
and atmospheric regions and features.

8. Solar Structure: Atmosphere
The Photosphere is the visible surface that emits photons with a nearly constant intensity ~6000 K black body spectrum
The Chromosphere is an overlying region that emits mainly in the UV part of the solar spectrum. Its temperature cools then heats to 20,000 K
The Transition Region is at the boundary between the chromosphere and corona where the temperature increases rapidly to 106K
The Corona is the hot T ~ 2 x 106 K , uppermost layer of the solar atmosphere
Cut-away diagram showing solar interior. and atmospheric regions and features

9. Solar Atmosphere: Key Properties
Note the temperature reaches a relatively shallow minimum in the chromosphere. Changes in the composition of the gas (fall-off of heavier elements) produces the H and electron density differences. Great changes in the solar atmosphere occur in the relatively narrow chromosphere-transition region. In the corona temperature rapidly increases while density falls and magnetic field dominates pressure.
Note also the important presence of neutrals in the chromosphere and that the low β region may be narrow in altitude.

10. The Solar Ionosphere
The region above the photosphere is a weakly ionized gas.
There are significant collision frequencies. Thus we must treat this as a collisional ionospheric plasma.

11. Solar Spectrum: Light from the Sun
Stefan-Boltzman law gives R = σT4 where R is the Watts · m-2 and σ is 5.67 x 10-8 W · m-2 · K-4. The nearly 6000 deg. Black Body-like solar spectrum comes mainly from the photosphere and is the main contributor to visible or white light and the Total Solar Irradiance (TSI). TSI is used in climate models
Most UV and shortward emissions (EUV and X-ray) come from above the photosphere (chromosphere, transition region, corona). These are much more intense than the black body contribution and also the most variable.

12. Solar Spectrum: Where Different Emissions Come From
Soft x-rays (<10nm) White light
Photosphere Chromosphere Corona
transition region
FeXX 171nm FeX 193nm HeII 304nm Hα 656.3nm HeII 10830
NaI589.6nm White light
Wavelength: X-ray EUV UV VIS IR

13. The Solar Cycle: Surface Magnetic Fields
Polar field
Active Regions
Quiet
Sun field
Polar field
Babcock and Hale discovered that if the Sun is observed in the wings of certain spectral lines, the phenomenon known as Zeeman splitting allows detection and imaging of the surface magnetic fields.
The gray scale indicates the strength and polarity (direction of the field), with black and white indicating the stronger inward and outward fields, and gray magnetically neutral and/or weak field.
The stronger fields generally occur in ‘bipolar’ patches, and that there are stronger field areas much larger than sunspots called ‘active regions’.
The fields strengths inferred from a typical magnetogram range from ~100s of G in sunspots to a few G in the ‘quiet Sun’ regions.

14. Active Regions vs. Sunspots
Sunspots may occur within active regions. In closeup images they show structure dominated by a dark umbra and a brighter surrounding penumbra. The field is strongest (may be tenths of T) and most vertical in the umbra
Often an active region has only one spot in its leading polarity, and a trailing diffuse region of moderately strong oppositely directed field that only shows up on the magnetogram and not in the visible image.
Sometimes a spot is in a complex ‘group’ that shares penumbras.
Sunspot types are categorized as alpha, beta, gamma, delta, with the above simple spot on the left the alpha case and the right a delta spot.
Spot complexity is often associated with related solar activity (next lecture)

15. Solar Dynamics Observer Magnetogram
Note: Active regions are numbered by NOAA and tracked
because of their possible involvement in solar activity.

16. Surface Magnetic Field Features: Photospheric Granulation
The granulation resulting from the convection near the surface covers the photosphere.
The size of typical granulation cells is ~1000 km and their separation is about 1400 km.
The life time of a granule is ~18 minutes.
They are separated by dark intergranular lanes that are about 400K cooler.
Fluid rises in the center of cells, flows towards edges, and falls in the lanes with a relative velocity of ~2km/s.
Organized into larger cells of supergranulation whose Doppler shifted spectral line wings can be used to make global images (Dopplergrams) of surface motions
Depth of granulation layers is expected to be ~granule dimensions, so that it is like a ‘rind on the solar ‘orange.
Closeup of granulation cells (top) showng scale , horizontal granulation flows (middle), and a full-disk ‘Dopplergram’ where the gray scale black to white) indicates motion toward and away from the observer.

17. Surface Magnetic Field Features: Quiet Sun Fields
The gas controls the field at photospheric levels. The convective motions associated with the granulation redistribute the magnetic fields that thread the solar surface outside of active regions.
These ‘quiet Sun’ fields become concentrated at the boundaries between granules and supergranules. These fields exist in small bundles of both field polarities and can be as strong as ~ 100T. This has been called a ‘magnetic carpet’.
The quiet Sun fields show different degrees of positive and negative field imbalances. In the polar regions, they are imbalanced in a way that is tied to the prevailing solar cycle. These fields determine the axially-aligned solar dipole moment that reverses every ~11 years.
Near active regions, the fields have the dominant polarity of the nearby active region fields or of an active region that is in the process of disappearing.
blowup of
quiet Sun
field

18. Surface Differential Rotation
Observed average differential rotation curve fits:
ω = A + B sin2 φ + C sin4 φ
ω is the angular velocity in degrees per day, φ is the solar latitude
and A, B, and C are constants approximately equal to
A= 14.7 deg/day
B= –2.4 deg/day
C= –1.8 deg/day
Obtained from feature tracking, including sunspots, other magnetic features.
Different features show slightly different rates.

19. Other Surface Motions: Meridional Flows
Feature tracking suggests the presence of a net Northward flow in the Northern Hemisphere and a net Southward flow in the Southern Hemisphere.
These are used to suggest a deep return flow exists beneath the surface. This may be a key part of tying the interior solar dynamics to the solar cycle on the surface. But how do we look inside the Sun?
(Data Analysis by Ulrich, 2010) ?

20. Probing the field origins: Helioseismology
Uses observed Doppler shift in absorption line to monitor vertical velocity of points on Sun’s surface.
Fourier transforms of time series give wave frequencies.
Fourier transforms of spatial profiles give wavelengths.
Different modes penetrate to different depths depending on sound velocity (temperature).
Can infer information concerning the density stratification, composition and dynamics of the interior from the spectrum
Sample ray paths of sound waves
Result of Fourier
Analysis-sample
Time series of surface vertical
velocity at different locations

21. The Rotation of the Convection Zone
Heliosesimology enabled us to determine the Sun’s interior structure and dynamics.
Red indicates fast rotation at the equator and blue shows the slow rotation at the poles. These rotation rates are about the same as the surface differential rotation.
The interior below the convection zone appears to rotate as a solid body at the rate at ~40 deg latitude. The consequence of this is a velocity shear at the dashed surface, called the tachocline.

22. Beneath Sunspots
The field in sunspots is strong (up to ~10 mT) and temperature low (~3000K) compared to the photosphere in the dark center umbra.
Local helioseismology shows that the convection zone flows beneath sunspots exhibit some organization.
Global maps of the subsurface convection on larger scales and at different depths show converging OR diverging flow signatures of active regions as a whole.
SOHO MDI illustration
From Gizon 2009

23. The Solar Dynamo: Simple Model
From observations of the solar magnetic field over the course of a solar cycle, Babcock developed an empirical model of the solar magnetic cycle.
Surprisingly, it can be understood as an α-ω dynamo like the Earth’s dynamo.
The ω-effect is the stretching o the magnetic field azimuthally by the faster rotation near the equator. This is the toroidal field.
The α-effect is the lifting of the field lines by convection or kinking so they provide north-south (poloidal) field.
The net process produces new poloidal field from the toroidal field which was produced from the original poloidal field.
The new flux is opposite that in the pole and the polar field reverses.
This is consistent with the Hale polarity laws for sunspots.

24. The Solar Dynamo: Interior Aspects
From observations of the surface solar magnetic field over the course of solar cycles, combined with helioseismology measurements of the convection zone flows, this basic picture has emerged
The high velocity shear (velocity gradient) at the bottom of the convection zone, in the tachocline stretches the magnetic fields there into azimuthal or toroidal bands or ‘wreaths’ of strong, twisted fields (ω-effect )
The strong fields are buoyant and may make it to the surface where they emerge though the photosphere. As they rise, coriolis forces give the emerging strong fields a north-south (poloidal) component that is systematic in each hemisphere( α-effect )

25. Surface Magnetic Field Features: Active Region Fields
The active region fields emerge into the pre-existing fields, both large and small scale. If they are strong enough, sunspots form.
The emerging fields can have different degrees of twist or ‘helicity’, indicating they contain currents
They usually emerge with their trailing leg poleward of their leading leg. During the rising phase of the solar cycle the leading leg of the active region usually has the polarity of the polar field in its hemisphere. At solar maximum the poles flip but the butterfly wing (Hale cycle) pattern of occurrence is still in effect, and so the leading leg field instead becomes opposite to that in the nearest pole (Joy’s law). The tilt is thought to be due to the effect of the Sun’s rotation on the rising flux tubes (the Coriolis Force).

26. Magnetic Field Generation: The Dynamo Equation
The solar photosphere is a hot, dense, but weakly ionized plasma with a magnetic field organized in ropes.
With altitude, the magnetic field expands to fill space roughly uniformly but in the photosphere much of the surface is “field-free.”
Maxwell’s equations and the MHD approximation allow us to understand much of what we see, but not necessarily all of it.
Ampere’s law becomes j = B , so j ~ B/ , where L is magnetic scale
Ohm’s law becomes E = -u x B + j/σ
Induction equation is obtained by taking the curl and using Faraday’s law
B u B
where is the magnetic diffusivity and
is the magnetic Reynolds number
If Rm « 1 then and irregularities diffuse away on the
diffusion time scale with a speed
If Rm » 1 then the magnetic field is carried with the flow, i.e. frozen into it.

27. Magnetic Field Generation: Kinematic Dynamo Models
From Meisch (2009) and Browning (2006)
Some of the most highly developed dynamo models assume a prescribed
velocity and use the dynamo equation to calculate the magnetic fields. This
defines them as kinematic. Some of these models are even beginning to include
concentrated flux tubes rising from the region of the tachocline to produce ARs.
Weaknesses of these state-of-art models include: 1) Lack of knowledge of
all of the relevant interior dynamics, especially small scales that affect
‘viscosity’ and ‘diffusivity’; 2) Not accounting for feedback of the generated
fields on the flows (MHD simulations are needed and sometimes applied).

28. Recent Numerical Simulations of Solar Field Structure
Sunspot formation
Convection zone dynamics and
related dynamo fields .
Rising
flux
tubes
Magnetic connections subsurface to corona
Brown ApJ 2010 (top R), Abbett, ApJ 2007 (bot.R), Rempel, 2009 (top L),Weber et al., ApJ 2011(bot)

29. Getting into the Atmosphere: Imaging of the Chromosphere/Transition Region
Line emissions coming from the chromosphere and transition region are particularly important for probing features and processes.
(also HeII304nm and
highly ionized Fe lines)

30. Chromospheric Phenomena: Filaments, Prominences, Plage, Faculae
Filaments are dense, relatively cool clouds of material suspended above the surface (Density m-3, temperature 5,000-8,000K). They appear to lie above the neutral lines of some active regions, or above neutral lines on the photosphere from decayed, redistributed active region fields (e.g. ‘polar crown’)
Plage, seen clearly in H-α, seem to coincide with active region fields outside of sunspots
Prominences are filaments seen projecting out above the limb, or edge, of the Sun, while Faculae are bright regions on the photosphere.
H-α image (top) and magnetogram

31. Chromospheric Phenomena: Spicules
Spicules also surround supergranules. They are jets of plasma lasting 5-10m, reaching heights of 10,000 km with diameters of km and speeds of km·s-1 reaching the corona
Convection at the top of supergranule cells carries magnetic field to edges of cells.
Concentrated vertical fields at the edges of the cells provide ‘funnels’ that enable plasma to flow through the chromosphere to the corona.

32. Transition Region: Chromosphere-Corona Interface
The Transition Region is a relatively thin region (~100s of km or less) between the chromosphere and the corona where temperature suddenly rises. It is patchy and nonuniform, so not really a layer in the strict sense of the word.
Heat conducted from the corona fully ionizes hydrogen and multiply ionizes heavy ions here.
This region can be imaged in heavy ion lines such as Carbon IV (green) [C3+] at 100K K and Silicon VI [Si5+] (red) at 200K (from the SUMER instrument on SOHO).

33. Summary The Sun is powered by nuclear fusion.
This heat engine powers the solar processes.
Heat transfer becomes more efficient by convection about 0.25 Rs from photosphere.
The convection layer generates a complex magnetic field.
This complex magnetic field in turn causes dynamic events leading to space weather on Earth.