Three methods to transport energy. Convection – wholesale streaming of a fluid from hot to cool regions. Conduction – energy is transported by free electrons.

Three methods to transport energy.

Convection – wholesale streaming of a fluid from hot to cool regions.

Conduction – energy is transported by free electrons in a metal.

Radiation – Energy is transported by EM radiation.

Granulated appearance on the Sun’s surface (photosphere)

Stream of hot gas rises in the center, gives off energy and sinks at the edges

Sun has a core, radiative zone and a convective zone. Convection is a very efficient method of

energy transport

Radiation not an efficient way to transport energy.

There is little mixing of material in the radiative zone of the Sun. So hydrogen is not mixed down into the core of the Sun.

When the core runs out of hydrogen, the rest of the Sun will still be mostly hydrogen, but there is no way for the hydrogen to get down into the core.

How do we know that the convection zone doesn’t go all the way to the core?

Theoretical modeling of the Sun’s temperature and pressure shows that convection will break down in the inner portions of the Sun.

In the past decade these models have been verified using helioseismic measures. Just like on the Earth, where earthquakes passing through the Earth show use that the inside has a crust, mantle, outer core and inner core.

Earth’s interior

Probing the Sun’s interior using Sun Quakes

How can we be sure that the p-p chain is responsible for the energy generation in the core

of the Sun?

How can we be sure that the p-p chain is responsible for the energy generation in the core

of the Sun? The neutrinos that are produced in every

reaction of the p-p chain, barely interact with matter. They can pass right from the core out into space. Unlike light which can take a million years of absorption and re-emission to finally make it out of the Sun.

The detected rates of neutrinos leaving the Sun is the same rate that is predicted using the p-p chain to make the internal energy.

A solar neutrino image of the Sun’s core

A hypothetical question The reaction rates in the core of the Sun

depend on two parameters. 1) temperature (high enough kinetic energy to

make protons stick together. 2) the density of the particles (particles close

enough together so that collisions are frequent) One other point: Because of the slow rate of

energy transfer in the radiative zone, any changes in the nuclear reaction rate will first effect the core, before any effect to the outer part of the Sun.

The Sun does not have exactly the same number of reactions from day-to-day. It is close to the same but on any given day there can be fewer or more than the day before. It is just based on chance collisions.

Let’s suppose this is a very unlucky day in the core of the Sun and there are much fewer reactions today than normal.

What will happen to the core of the Sun?

What would happen to the core of the Sun?

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1. The core would shrink down to a very small size and the Sun would collapse inward and disappear

2. The core would expand outward since it would now be out of balance with gravity. The Sun would explode

3. The core would shrink increasing the reaction rates and then re-expand.

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Sun is in a state of stable equilibrium. It is a self regulating process.

IF reaction rates go down in the core, gravity will cause the core to begin to shrink. (gravity wins)

As the core shrinks the density and temperature of the core begins to rise.

When these two parameters increase so does the nuclear reaction rate. (internal pressure wins)

The core re-expands.

Ultimately, it is the mass of the star that controls the reaction rate in the core. More mass, more reactions. Less mass, fewer reactions

This means there is a direct relation between the star’s luminosity and its mass, IF the star is in equilibrium.

We need to see if this theoretical idea is correct or not. We need stellar masses and stellar

luminosities. Remember how the apparent brightness of a star is

related to its luminosity.

B = L/4πd2

B, the apparent brightness, we can find by hooking detectors to telescopes and making an observation of the star.

We can get L, the luminosity of the star, if we know the distance to the star.

L = B(4πd2)

So we need to find the distance to the stars!

For stars that are near by we can use a triangulation technique to measure distance.

This technique is called trigonometric parallax. This is the exact technique that surveyors use

to measure the height of mountains or the widths of canyons, etc.

It is based on no assumptions other then trigonometry.

Quiz #5

Wednesday we learned that the Sun has a total lifetime of 10 billion years (1 x 1010 years). Suppose that there is a star elsewhere that has 10 times the mass of the Sun (10 times the fuel supply) but a luminosity which is 100,000 times that of the Sun. (rate of consumption is 100,000 times the Sun’s rate).

What is the lifetime for this star in years? Show your work and/or explain your reasoning. There will be partial credit for correct reasoning.

Who discovered that the Earth was round?

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25% 25%25%25%1. Cortez

2. Einstein

3. Columbus

4. Ancient Greeks

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Erasothene Determines size of Earth (240 BC)

A well in Cyrene and an obelisk in Alexandria separated by 440 miles

How do you compute Earth’s circumference?

Ratio and proportion.

C/440 miles = 360o/7o

C = 22,628 miles.

Today’s value: C = 24,901.46 miles

How can you find the distance to the Comet?

I estimate the change in angle to be 6 arcseconds and the distance from

Denmark to Portugal to be 1,700 miles.

How can you find the distance to the Comet?

I estimate the change in angle to be 6 arcseconds and the distance from

Denmark to Portugal to be 1,700 miles.

Answer: about 58 million miles

What about distance to the stars? The stars are too far away to see a shift in position just

using locations on the Earth. We need a bigger baseline. So we use the entire orbit

of the Earth to do the measurements.

This technique works for nearby stars but eventually the distance is to great to measure a shift.

Calculating the distance to the stars

To find the distance to the stars we introduce a new distance unit called the parsec (pc). For a parallax angle p = 1 arcsecond, then d = 1 pc.

The equation is:

d = 1/p where p is in arcseconds.

You can see that when p = 1 arcsecond, d =1 parsec.

1 parsec = 3.26 light years. The closest star besides the Sun is α Centuari at a distance of 4.5 light years.

If a star has a parallax angle of p = 0.1 arcseconds, how distant is it?

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25% 25%25%25%1. 0.1 parsecs away

2. 2 parsecs away

3. 10 parsecs away

4. 0.5 parsecs away

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α Centuari is 4.5 light years away. 1 parsec = 3.26 light years. What can you predict about its parallax angle?

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50%50%1. It is less than 1

arcsecond

2. It is greater than 1 arcsecond

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The Hipparcos Satelite

Hipparcos is a Earth orbiting satellite which is able to make extremely accurate measurements of parallax.

Hipparcos can measure parallax angles as small as 0.001 arcseconds, but not as accurately as bigger shifts.

It mapped the distance to 7,000 stars within about 500 light years of the Earth with very high accuracy.

With this information a Hertzsprung-Russell diagram can be made. An H-R diagram.

H-R Diagram parameters

An H-R Diagram plots a star’s luminosity on the y-axis and the surface temperature on the x-axis.

Surface temperature is found using the stars color, or using Wein’s Law. T = 3,000,000/λmax

Luminosity is found using the apparent brightness (B) and the distance (d). L = B(4πd2)

On the Main-sequence we can see there is a direct relationship between the surface temperature and the luminosity, in the sense that as the temperature goes up so does the luminosity.

Characteristics of the H-R Diagram

Main-sequence stars are stars in equilibrium. They are converting Hydrogen to Helium in their cores.

The Main-sequence is really a mass sequence. On the Main-sequence the stars that have the highest luminosity are the most massive. The stars with the lowest luminosity are the least massive.

Stars not on the Main-sequence have different energy sources and do not follow the mass-luminosity relation. The giant stars are dying.

Two star clusters – An open cluster and a globular cluster

Two H-R diagrams

Which cluster is older?

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1. The open cluster (#1) because the high mass stars are still on the main sequence and they live the longest.

2. The globular cluster (#2) because there are no high mass stars on the main sequence and they live the shortest.

3. They are the same age because both clusters have main sequences

4. There is no way to tell from the plots.

Age of the clusters

The open cluster still has enormously massive stars on the main-sequence. They are on the order of 10 times the Sun’s mass and emitting 100,000 times the Sun’s Luminosity.

The globular cluster has many stars that are no longer on the main-sequence. The most massive stars on the main sequence are slightly less massive than the Sun.

The Open cluster is ~1 million years old, and the globular is > 10 billion years old.

How do we find stellar masses?

We look at binary stars and measure their orbital parameters. Then make use of Kepler’s 3rd law.

(M1 + M2)P2 = (4π2/G)a3

Where P is the orbital period, a is the distance to the center of mass of the system.

Nearly 50% of all stars are in a binary system. Two stars orbiting about a common center of mass

Three types of binary stars. Visual binaries – Stars that are far enough

apart that they can be seen as separate stars through a telescope. They typically have orbital periods that are hundreds of years long.

Stars orbit a common center of mass. More massive star has smaller orbit.

Spectroscopic Binaries – Much shorter orbital periods because stars are so close to each other that they aren’t separable. But the spectral lines show that there are two stars.

A Delema

Spectroscopic binaries often show double the absorption lines of a regular spectrum. But the wavelength at which a line forms does not depend on the type of star. It is set by the element that is giving off the light. Why don’t the two absorption lines fall right on top of each other?

A Delema

Spectroscopic binaries often show double the absorption lines of a regular spectrum. But the wavelength at which a line forms does not depend on the type of star. It is set by the element that is giving off the light. Why don’t the two absorption lines fall right on top of each other?

The reason is the Doppler Shift.

The Doppler shift is a wave phenomenon

When an object emits a wave, the wave moves out in all directions with its center at the source.

This is true of water waves, sound waves, and light waves.

What if the source is moving?

If a source of the wave is moving, then as the source emits the wave, the center is continuously moving.

Here is a real picture of Doppler shift

When a star is moving toward or away from us Doppler shift is blue-ward (toward) or red-

ward (away) of what it would be if the star was not moving.

We can see this as a shift in the absorption or emission lines in a spectrum. The wavelength that absorption

occurs at depends only on the type of atom. But the shift depends on the motion

Using the Doppler shift of light from a star we can not only tell if the star is coming toward us or going away from us, but we can also measure the speed at which it is moving toward or away.

How is the velocity related to the amount of Doppler shift?

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1. The faster the object is moving toward or away from us the bigger the shift should be.

2. The faster the object moves toward or away from us the smaller the shift will be.

3. If an object is moving rapidly towards us we get a large speed, but if it is moving rapidly away we get a small speed.

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Relation of velocity to Doppler shift

The bigger the shift the fast the velocity because the center of the wave is moving rapidly causing greater compression or expansion.

v/c = Δλ/λo where v is the velocity, c is the speed of light,

λo is the rest wavelength and Δλ is the doppler shift. Δλ = (λobserved – λo)

What about stars orbiting each other?

The result is two absorption lines that have slightly different wavelengths from what they have in the lab.