Introduction to Astronomy !AST0111-3 (Astronomía)

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Semester 2014B

Prof. Thomas H. Puzia

The large mass of H and He gas has remained in stable equilibrium for about 4,500,000,000 years. This is because at every point inside the Sun is in hydrostatic and thermal equilibrium.

Hydrostatic (gravitational+pressure) equilibrium: at each point inside there is a balance of forces: the force of gravity pulls material inward, while the pressure pushes outward. Without buoyancy, gravity would dominate (blue arrows), and the Sun would shrink. Alternatively, if gas and radiation pressure dominate (green arrows), the Sun would expand.

Thermal equilibrium: the amount of energy flowing into and out of a point is equal. So the temperature at each point remains constant.

Internal Structure of the Sun

Photosphere Conv. Rad. Nucleus

Zones

15000000 --

10000000 --

5000000 --

degree K

TP150000 --

100000 --

50000 --

Kg/m3

The interior of the Sun• The temperatures, densities and

pressures grow inside the sun, reaching their peak in the core.

• In the Sun's core densities, temperatures and pressures are so high that atoms collide. For example, in the Sun's core temperature reaches T = 16,000,000 K, and the pressure reaches P = 160,000 kg/m3.

• All the energy (light) from the Sun is produced in a core out to a radius of 0.2 R⊙.

Model of the SunModels of the internal structure of the Sun must specify the temperature, pressure, density, chemical composition and luminosity as a function of radius. !To build these models we use five (5) "structural equations": 1. Hydrostatic Equilibrium 2. Mass Conservation 3. Thermal Equilibrium 4. Energy Transport 5. Equation of State !We also require that certain boundary conditions are met at the core and surface. !Modern astronomers have two ways to check their internal structure models of the Sun: Helioseismology and Neutrinos.

Neutrino ExperimentsFusion (e.g. proton-proton chain) produces a large number of neutrinos in the core of the Sun

The "neutrino telescopes" use large tanks of billions of liters of Gallium or Chloride located in abandoned mines or Antarctic ice, along with 1000s of photomultipliers to look for very low probability interactions.

For example, the Kamiokande or ICECUBE experiments (very delicate).

Found a big problem: a deficit of neutrinos observed with respect to solar theoretical models, as it was expected to detect 3-times the flux of neutrinos observed (as of 2003).

Besides the Sun, the only other source of cosmic neutrinos observed in the Universe was the explosion of SN1987A.

We now know that there are three different kinds of neutrinos, and that detectors are only sensitive to certain types.

Ga

neutrinos

Three Neutrino Flavours

Seismology of the SunAlthough it is a ball of gas, the Sun also has earthquakes (sunquakes). These movements can be observed by measuring very precise velocities in the outer layers using the Doppler shift of spectral lines. In this model, the gas moving inward (away from us) is red and outward is blue (toward us). !This solar-seismology is very important because it allows us to test models of internal structure of the Sun, just as terrestrial seismology reveals information about the internal structure of our planet. !

Sun αCen βHya

So why does the Sun shine?

What is the source of energy from the sun?

Alternative 1: chemical burning.

If the Sun were made of gasoline, it exhaust itself in ~1000 years to produce energy.

Alternative 2: gravitational collapse

The contraction of the Sun by gravity would heat the interior and generate radiation (blackbody).

Lord Kelvin calculated that the gravitational energy available would only last for about 107 years.

But we know that the Sun has remained in hydrostatic equilibrium by more than 109 years.

Alternative 3: Thermonuclear Fusion (=>Solar Nucleosynthesis)

What happens to material at 16000000 K and 150 times the density of water?

Atoms and molecules cannot survive, only nuclei of H, He and free electrons.

high energy = high speeds ⇒ fusion (two particles collide and merge into one)

normal repulsive forces overcome by high speeds, allow fusion (do not confuse with fission)

Thermonuclear Fusion

Energy Production in the Sun

Proton-proton chain in the SunThe most common type of fusion in the Sun's core is the proton-proton chain (below), which requires 4 H nuclei to fuse, producing a helium nucleus and releasing energy as γ-ray photons and neutrinos (ν). Part of the material is converted to energy following Einstein's equation: e=mc2

CNO CycleOther types of fusion produce heavier elements than Helium. The CNO cycle is very important at higher temperatures than currently

exist in the Sun (e.g., more massive stars). !!!!!!!!!The net result: 4 protons fuse to form a helium nucleus. Note that 12C is

regenerated at the end, but this allows heavier elements to be made as byproducts.

Temperature DependenceThe types of fusion processes sensitively depend on the temperature of

the stellar interior. The pp-chain and CNO cycle can occur at the same time, but at very

different rates that deliver very different energy outputs.

1.5 M⊙ 120-200 M⊙!

radiatively unstable

0.08 M⊙

relative energy output

stellar core temperature

Propagation of photons to the surface:• A photon emitted in the nucleus has a very short “half-life”, meaning it is

immediately absorbed and re-emitted (it’s “optical depth”/opacity is high).• On their way out, photons lose energy as they interact with the gas. It can take

between 10,000-200,000 yrs for the energy of a photon originally emitted in the nucleus to escape from the surface (note: a non-interactive neutrino emitted in the same process takes 2 sec.)

• The energy declines with increasing radius, so re-issued photons have less energy.• If we had eyes sensitive to neutrinos then would see the

nucleus directly, because neutrinos escape the Sun without interacting.

• Energy conservation: each layer has the same amount of energy. But the surface area of layers increases as we move out. Thus, if we consider each layer to be a black body, then its surface temperature decreases as its radius increases.

Internal Structure of the SunWhy do we not see the direct γ-ray radiation produced in the center?

Transport of Energy• Conduction:

– Energy is transported via thermal interactions between atoms – Some materials are better than others for this type of transport – Example: propagation of heat in a metal

• Convection: – Large circulating fluid masses transport the energy – Example: water heating in a teapot

• Radiation: – Electromagnetic radiation (photons). – Example: Blackbody. !

These competing processes depend on the physical conditions within a star.

Turbulence and ConvectionTransport of energy by convection:

The Sun's surface is turbulent, with gas bubbles that rise and fall, as if the material was boiling water, but obviously at a much higher temperatures.

Granulation shows the typical “boiling” scale (convection zones) of the material on the solar surface . The hotter gas produces brighter granules.

Turbulence and ConvectionTransport of energy by convection:

The Sun's surface is turbulent, with gas bubbles that rise and fall, as if the material was boiling water, but obviously at a much higher temperatures.

Granulation shows the typical “boiling” scale (convection zones) of the material on the solar surface . The hotter gas produces brighter granules.

The Solar AtmosphereThe atmosphere is the outer layer of the Sun, and is only about 700 km thick. It is divided into photosphere, chromosphere, transition region and the corona.

!The photosphere is the innermost layer, from which the photons are emitted. It is a blackbody.

The chromosphere is the official surface of the Sun (T = 5,800 degrees, and 100 km thick). The chromosphere emits most of its energy in the optical, and that is where the Sun is observed with our naked eye.

The transition region is a relatively small area outside the solar surface where the temperature rises rapidly.

The corona is a very tenuous and hot outer region which is thought to be a heated by pressure and reconnections from the Sun’s external magnetic field.

The Photosphere

• The photosphere is R ≈ 1/1000 Ro thick • Its density is ≈ 1 / 10000 that of air in our

atmosphere. • Granular surface (due to convection) • The granule size is about 1000 km, and

its center is about 100K hotter than its edge (remember TBB = 5800K).

• The effect of limb (edge) darkening: – The center of the disk of the sun is

brighter than the edges. – In the center we see deeper into

warmer internal layers. – At the edges we only see the

outermost layers which are cooler.

The corona is very extended and diffuse, w/ T = 1,000,000 K, emits UV/X-rays.!

The corona appearance is variable, and depends strongly on solar activity cycle.!

Without an active heating source, the corona would cool to 6000 K in a few hours!

The CoronaThe corona can only be seen at optical wavelengths during total solar eclipses when the moon completely covers the bright optical disk of the Sun.!

The Sun at distinct wavelengthsLooking at different wavelengths (optical, IR, UV, X-ray) the Sun shows different aspects. For example, the sunspots are dark in the optical, but bright in X-rays.

CaK

IR UV

Radio

Neutrinos!

If the Sun stopped fusing material this instant, what would happen?

A. Without any new radiation, the Sun would collapse quite rapidly B. The core would begin to slowly contract, but collapse of the outer layers

would be delayed by at least 10,000 yrs C. The Sun would immediately appear cooler D. The Sun would start appearing cooler after ~8 min E. Both B & D