11. The Sun11. The SunGoalsGoals:1. Examine the characteristic features of the Sun ―

photosphere, chromosphere, corona ― and how they change with time.

2. Study the activity cycle of the Sun and learn about its deep interior, where sunlight is generated.

3. Use some hydrodynamics to understand the heating of the solar chromosphere and corona.

A typical view of the Sun: a spherical star that exhibits

limb-darkening (brightness

drops towards the edge) and a

nearly featureless

disk.

The Sun has increased in size and temperature since it first formed 4½ billion years ago.

Predicted temporal variations of the Sun’s parameters from stellar evolutionary models.

Like all stars, the Sun is in hydrostatic

equilibrium (balance), otherwise its size

would change very quickly ! The weight of each layer in the

Sun is balanced by the buoyant force exerted

by the pressure exerted by gas below

it. The pressure comes from radiation (light)

and the high temperature of the gas. The ultimate power source is

nuclear fusion in the Sun’s core.

2

2

)(

or

)(

r

rMG

dr

dP

r

drrMGdP

The core is where hydrogen is converted to helium via the proton-proton chain, Tcritical = 10 million K.

H1 + H1 → D2 + positron + neutrinoD2 + H1 → He3

He3 + He3 → He4 + 2H1

The proton-proton chain in the 15 million K Sun’s core simplified.

The source of energy in the Sun’s core is the same as that which powers an H bomb (hydrogen bomb).

The short-wavelength gamma rays produced in the core of the Sun gradually diffuse outwards, scattered (absorbed and re-emitted at slightly lower energies) to longer wavelengths by interactions with gas atoms and ions until they eventually emerge at the Sun’s surface 10,000-200,000 years later as visible light photons.

Neutrinos, on the other hand, do not interact with gas atoms and ions at all, and reach Earth 8⅓ minutes later, detected only through the occasional interactions they make with atoms of some substances.

The Solar Neutrino Problem

The observed flux of neutrinos at Earth is on the order of ⅓ to ½ the amount predicted by the Standard Solar Model. Current thinking in subatomic physics suggests that the electron

neutrinos generated in the Sun’s core are oscillating between the states of electron, muon, and tau neutrinos on their way to Earth, so that

detectors on Earth, tuned to detect electron neutrinos, are missing two thirds of the neutrinos

actually generated by the Sun.

The variation of hydrogen and helium composition with radius within the Sun.

The heat of the Sun diffuses outwards by simple radiative transfer in the deep interior, but is

helped by convective eddies over the last 28.6%.

Solar granulation: an indication of the outer convective region of the Sun. Shock waves from the convection zone also heat the gas in the solar chromosphere

and corona to very high temperatures.

The active Sun, displaying prominences and flare activity.

The solar granulation and model (lower).

Models of the Sun’s interior make use of mathematical relationships describing the conditions of hydrostatic equilibrium, thermal equilibrium, radiative equilibrium, and the general continuity of mass in the Sun in order to calculate the mass, density, temperature, and pressure at all points in the solar interior.

The “standard solar model” is well verified by observation, including helioseismology, which matches the oscillations seen at the Sun’s surface with the parameters of seismic waves passing through the Sun’s outer regions. Neutrinos detected from the Sun’s core also provide information about the nuclear reactions occurring there.

Helioseismology.

The variation of mass and density with radius within the Sun.

The variation of luminosity and energy generation with radius within the Sun.

The variation of pressure and temperature with radius within the Sun.

The variation of pressure/temperature gradient with radius within the Sun.

Where different portions of spectral lines are formed in the solar photosphere.

The Sun, Earth to scale, and sunspots.

Bright = Hot

Dark = Cool

White light images of the Sun showing sunspots, limb

darkening, and the solar rotation. The orange “surface” is the solar

photosphere = light sphere.

The motion of sunspots across the Sun’s disk indicates that the Sun rotates differentially, that

is the equatorial regions rotate faster than regions near the poles. Observations indicate a

rotational period of 24½ days at the solar equator and 30 days 60° away from the equator,

corresponding to observed rates from Earth (synodic rates) of ~27 days and ~32 days,

respectively.

Differential rotation also occurs in the gaseous planets Jupiter and Saturn. On the Sun it is responsible for twisting up the subsurface

toroidal magnetic field.

Nomenclature for sunspot features.

Sunspots are cool regions (T ~ 4500K) of the photosphere, where strong magnetic fields have restricted normal turbulence. Because they are cooler than the surrounding photosphere (T ~ 5800K) they are less radiative, and appear dark through contrast with the brighter photosphere.

A complex sunspot group.

The limb darkening of the Sun has a similar explanation. Our line of sight at the edge of the solar disk penetrates to shallower, cooler depths

than does the line of sight at disk centre.

The “optical depth” to which we can see into the Sun’s photosphere (“photon” sphere) is about the same no matter where we look, but we can see to deeper, hotter regions near disk centre.

Sunspots, and the sunspot cycle of ~11 years. The number of spots increases rapidly and declines slowly during the 11-year sunspot cycle. (Sunspot number is a curious function that counts 10 for each spot group, and 1 for each individual spot.)

Sunspot numbers.

Recent sunspot numbers

Sunspots are associated with strong magnetic regions of the photosphere, and cycle through different latitude regions during the 11-year cycle, beginning near both poles, ending near the equator (“butterfly” diagram).

The Butterfly Diagram.

Holland in winter during the Maunder Minimum.

The chromosphere as seen in the light of Hα radiation (right) and at the limb, where spicules are visible (below right).

Close-up view of spicules.

In order to understand the heating that occurs in the Sun’s chromosphere and corona, it is necessary to consider the situation in terms of hydrodynamics. Rewrite acceleration as:

The condition for hydrostatic equilibrium is therefore:

where v is the velocity of the flow and ρ is the gas density. The conservation of mass flow across boundaries becomes:

or

dr

dvv

dt

dr

dr

dv

dt

dv

dt

rd

2

2

onaccelerati

2r

MG

dr

dP

dr

dvv r

constant4 2 vr 0

2

dr

vrd

At the top of the Sun’s outer convection zone the upwards motion of the hot, rising gas bubbles and the return flow of cool gas creates longitudinal (pressure) waves that propagate outward through the solar photosphere and into the chromosphere. The wave energy associated with this outwards flux is the product of the wave energy and the speed of sound waves in the medium, namely:

where vs is the local sound speed and vw is the velocity amplitude of the oscillatory wave motion for individual particles being driven by the convection. Since:

for fixed γ and μ, it follows that sound speed must decrease with decreasing temperature in the photosphere.

swE vvF 221

Tm

kT

mkT

PvHH

s

Initially the longitudinal waves generated near the top of the solar convection zone travel at subsonic speeds, but that changes as they near the top of the photosphere where the sound speed is lower. At that point the longitudinal waves generated by convection become supersonic and develop into shock waves. Shock waves are characterized by a very steep density change over a short distance, called the shock front. As a shock front moves through a gas it produces a large amount of localized heating via collisions. That heating is produced at the expense of the mechanical energy of the shock, and is quickly dissipated.

The constant replenishment of rising gas bubbles from the convection zone produces a constant source of shock heating in the gases lying above the solar photosphere, i.e. in the solar chromosphere.

Magnetic fields produce further complications.

Magnetic field lines on the Sun and constraint of ions.

Active (magnetic) regions in the solar chromosphere seen in spectroheliograms taken in the light of Ca K radiation. Bright regions are called plages or faculae.

More views of the chromosphere from Hα spectroheliograms. A solar flare is developing at right.

Active regions on the Sun are associated with sunspot zones, which are 5° to ~30° away from the Sun’s equator.

Prominences associated with sunspots protrude into the solar corona. Their “feet” rest on active sunspots.

Solar prominences seen on the limb.

Features of the solar corona can be seen in X-rays (right) or radio images (below), which isolate hot regions, even when gas density is low.

The Babcock mechanism as a qualitative explanation for the solar cycle of activity.

The Babcock mechanism (part 2) as a qualitative explanation for the solar cycle of activity.

The solar corona. Its extent varies with the sunspot cycle (largest during sunspot maximum).

Solar corona showing coronal holes.

The magnetic Sun.

The active Sun, displaying prominences and a time sequence of a flare developing.

Solar flare debris injected into the solar wind, eventually to reach Earth a few days later.

The auroral zone on Earth lies within 20° to 30° of Earth’s magnetic poles.

Displays of the aurora borealis.

Noctilucent clouds, perhaps an indicator of solar activity but more likely of climate change.

Astronomical TerminologyPhotosphere = light sphere. The region (disk) of the Sun

from which light appears to originate. It also constitutes the solar atmosphere.

Chromosphere = coloured sphere. The region lying above the solar photosphere containing spicules where the temperature increases with height.

Corona = crown. The outermost region of hot gases surrounding the Sun where temperatures reach 1-2 million K, and where the solar wind originates.

Sunspot cycle. The interval of ~11 years over which sunspot numbers increase and wane.

Proton-proton chain. The sequence of nuclear reactions in which hydrogen nuclei (protons) interact and are fused to become helium nuclei (α particles), with the release of energy.

Convection zone. The upper 29% of the Sun where energy is carried by convective bubbles of hot gas.

Astronomical Terminology (continued)Granulation. The mottled structure of the photosphere

caused by hot bubbles of gas at the Sun’s surface.Spicule. A spikey jet of hot gas from the solar

chromosphere erupting into the solar corona.Prominence. Huge gaseous eruptions of arching clouds

of ionized particles streaming between sunspots of opposite polarity through the corona.

Filament. The dark projection of a prominence viewed against the Sun’s surface in monochromatic light.

Sunspot. A region of cool gas (T ≈ 4500K) in the surrounding solar photosphere (T ≈ 5800 K) appearing as a dark penumbral region, often with a surrounding gray penumbra, that is the site of strong magnetic field.

Floculli, Plages. Light and dark markings in the solar chromosphere seen in monochromatic images of the Sun.

Astronomical Terminology (continued)Maunder Minimum. A period of ~60 years in the late

1600s and early 1700s when sunspot numbers were at an unusual low and northern hemisphere winters were unusually cold. Possibly related to Spörer minima at earlier epochs when sunspot activity may also have been low.

Optical Depth. How far into the Sun’s photosphere we can see before the gas becomes completely opaque.

Neutrino. A nearly massless nuclear particle that travels at nearly the speed of light and is produced during the production of a deuteron through a collision of two protons.

Solar Wind. The stream of ionized and neutral gas particles away from the Sun.

Aurora Borealis = Northern Lights. Radiation produced in Earth’s upper atmosphere by the streaming of charged particles towards the magnetic poles.

Sample QuestionsSample Questions10. In the proton-proton chain process, the mass of four protons is slightly greater than the mass of a helium nucleus. Explain what happens to this difference in mass.

Answer. The difference in mass is accounted for by the energy released in the process in the form of gamma rays, neutrinos, and positrons.

14. The Sun has a radius equal to about 2.3 light seconds. Explain why a gamma ray produced in the Sun’s core does not emerge from the Sun’s surface 2.3 seconds later.

Answer. The ionized gas near the Sun’s core is opaque to gamma rays and absorbs the photons before they can travel very far. The light is re-emitted as photons of slightly lower energy in random directions, repeating the absorption and re-emission process a multitude of times before the light eventually emerges at the Sun’s surface.