The Sun

Discussion

Why does the Sun emit light?

Discussion

How do you know the Sun is hot?

The setting Sun is red because

a)The Earth is rotating away from the Sun, so it is redshifted. b)The setting Sun is cooler at sunset, so Wien’s law says the frequency of maximum emission shifts to lower frequencies thus appears redder.c)At sunset the light has to travel through more of the Earth’s atmosphere, which has lots of absorption lines in the blue portion of the spectrum. d)None of the above

Solar Data

Radius: 109 Earth radiiMass: 333,000 Earth massesMean density: 1.41 g/cm3

Composition: 74% hydrogen 25% helium

Luminosity: 3.86 1026 Watts

The Sun as a big cosmic light bulb

Suppose every human being on Earth turned on 1000 100-watt light bulbs. With about 6 billion people this would only be 6 1014 watts. We would need 670 billion more Earth’s doing the same thing to equal the energy output of the Sun.

Discussion

Why is there less solar intensity at sea level than there is at the top of Earth’s atmosphere?

Discussion

Where do you think that energy goes?

Discussion

Why isn’t the Sun a perfect blackbody?

Line blanketing

More heavy elements in a star’s atmosphere means more absorption lines, the redder a star will appear as higher frequency light is absorbed and re-emitted at lower frequencies.

Discussion

The Sun releases lots of energy each second, what if it were cooling down over time. How could we tell?

Thermal equilibrium

The Sun is not measurably heating up or cooling down.

Discussion

Given the composition of the Sun, why is it unlikely that it could be heated by the burning of wood or coal?

Kelvin-Helmoltz contraction

As things contract gravitationally, they become hotter.

Discussion

Why do you think gravitational contraction leads to a temperature increase?

Discussion

If the Sun is getting its energy from Kelvin-Helmoltz contraction, how could you prove this? Do you think this is an easy thing to do? Explain.

Hydrostatic Equilibrium

The Sun is not measurably expanding or contracting

E = m c2

Matter is a form of frozen energy.

From Einstein’s Special theory of relativity, energy equals the mass times the speed of light squared.

H and He

H – one proton

He – two protons and two neutrons

Neutrons are electrically neutral protons with slightly more mass

Fusion converts the Sun’s Mass into Energy

4 hydrogen atoms have a mass of 6.693 10-27 kg

1 helium atom has a mass of 6.645 10-27 kg

Thus, 0.048 10-27 kg are converted into energy.

Free neutrons are unstable

A neutron, left by itself will decay into a proton, an electron and a neutrino.

Likewise a proton can change into a neutron by emitting a positron and a neutrino.

You can think of a neutron as a proton/electron pair.

Discussion

Why must matter be so hot, 10 million K, for H to fuse into He?

Discussion

How can atoms with more than one proton in the nucleus stay together? Why don’t they just fly apart?

Discussion

Fusion keeps the Sun hot, but fusion requires the Sun to be hot. How did the Sun ever get hot enough to start fusion?

Modeling the Sun

1. Hydrostatic equilibrium

2. Thermal equilibrium

Pressure increases toward the center of the Sun

To maintain equilibrium, the pressure below each layer of the Sun must be greater than the pressure above that layer.

Discussion

What does this tell you about how the density changes with depth in the Sun?

Discussion

What does this tell you about how the temperature changes with depth in the Sun?

Discussion

According to the previous graphs, where is fusion taking place in the Sun? Explain.

Discussion

What would happen if the Sun started to contract? What would happen if the Sun started to expand?

Discussion

What would happen if all fusion ended in the Sun?

Heat Transport in the Sun

• Conduction – particles transfer energy via collisions

• Convection – energy transferred by movement of material from hotter to cooler regions

• Radiative Diffusion – energy transferred via photons

Discussion

Which would you rather do, put your hand in an oven at 450 degrees F or put you hand on a 450 degree F stove top?

Radiative Diffusion

Radiative zone – inner 71 percent of the Sun’s Interior were all atoms are ionized.

Takes a photon 170,000 years to reach the convective zone. Each time a photon is absorbed it loses energy.

Convection

Convective Zone – outer 29 percent of Sun’s interior. Bottom of convective zone is cool enough for heavy atoms to regain electrons and absorb light.

Discussion

What happens to the bottom layer of the convection zone as it absorbs light from the radiative zone.

Solar Granulation

Solar Granulation

Discussion

Can all the hydrogen in the Sun be converted to helium? Why or why not?

Discussion

Will observations of the properties of the photons emitted by the Sun reveal much information about the interior of the Sun? Why or why not?

Physical properties

Physical properties

TemperatureDistanceMassCompositionVelocityLuminosityRadiusAge

Surface temperatures

We can determine a star’s surface temperature from its color using Wien’s law, the temperature of a blackbody is proportional to the peak frequency of the blackbody radiation.

Stellar spectra

Spectrograph’s spread out the star light

Getting a star’s spectrum is time consuming

How do we measure a star’s color?

UBVIR photometry

We measure the stars apparent brightness through a number of colored filters.

U – ultraviolet I – infrared B – blue R – red V – visual

Band pass filters

Color index

The ratio of the brightness through various filters can be compared to blackbody curves of different temperatures.

Discussion

We’ve discussed two potential problems with measuring a stars temperature using its color. What are they?

Distances to the Stars

The most accurate method of determining stellar distances is geometric parallax.

The parsec

With a baseline of 1 AU, a star that has a parallax of 1 arcsec has a distance of 1 parsec.

Thus distance in parsecs is given by

d = 1/p

where p is the parallax in arcsec.

Discussion

From Earth we can only measure a star’s parallax to about 100 pc. The distance to the center of the galaxy is 8 kpc or 80 times this distance.

Why are parallax measurements so limited?

Discussion

From Earth we can only measure a star’s parallax to about 100 pc. The distance to the center of the galaxy is 8 kpc or 80 times this distance.

Why are parallax measurements so limited? What could you do to get parallax measurements for more distant stars?

Hipparcos

Measured the parallax of the brighter stars (118,000 of them) from Earth orbit out to about 1000 pc or 1 kpc.

Discussion

How do you think astronomers determine the masses of stars?

Hint: Most stars are binaries.

Kepler’s 3rd law

The square of the sidereal period is proportional to the cube of the semimajor axis of the orbit: p2 a3

Newton’s laws require:

3

21

22

)(

4a

MMGp

Discussion

After observing this binary system for an entire orbit, what else do we need to know to determine the star’s mass?

Discussion

What are some of the things stellar spectra can tell us?

Stellar spectroscopy

Discussion

The strength of the hydrogen absorption lines does not correlate well with the amount of hydrogen present. Almost all stars have about 75% hydrogen, 24% helium and 1% metals.

Why do stars have absorption lines in their spectra?

Discussion

The hydrogen Balmer lines are produced by electrons absorbing a photon and jumping from the 2nd energy level to a higher energy level. How can this not take place with hydrogen still present the stellar atmosphere?

Discussion

Classification of stars using spectral line strengths tells you what about a star?

OBAFGKM

Oh Be A Fine Girl (Guy) Kiss Me. Oh Brother, Astronomers Frequently Give Killer Midterms.

O stars are the hottest M stars are the coolest

The Sun is a G2 star.

Discussion

I have two stars

HD 1378326 and HD 1177892

Both are B8 stars. What do they have in common?

Discussion

Describe the three ways astronomers have of determining a stars surface temperature.

Discussion

How is the surface temperature of a star related to its brightness?

Another inverse square law

The apparent brightness of a star falls as the square of its distance from you.

Luminosity

Luminosity is an object’s intrinsic brightness, the total amount of energy given off in a second.

This is different from an object’s apparent brightness

Discussion

What are some things that change the apparent brightness of a star, how bright that star appears in the sky?

Absolute magnitude

Luminosity is the same as apparent brightness, without considering the distance.

Absolute magnitude is magnitude a star would have if it were 10 parsecs away.

Apparent and absolute magnitudes

Apparent magnitude measures brightness in the sky.

Absolute magnitude measures luminosity.

Discussion

I have two light bulbs, one is 25 watts and the other is 100 watts. If the 25-watt light bulb is 1 mile away, how far would I need to place the 100-watt light bulb to have the same apparent brightness?

Luminosity and Distance

If we know the luminosity of a star or galaxy, we can figure out how far away it is by comparing it to its apparent brightness.

Discussion

But, what if there is a lot of dust between us and the object we are observing. That would make the object appear fainter and we would be misled into thinking the object was much farther away than it really is. How can astronomers determine if dust is making things fainter?