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 radii Mass:333,000 Earth masses Mean density:1.41 g/cm 3 Composition: 74% hydrogen 25% helium Luminosity:3.86  Watts

The Sun as a big cosmic light bulb Suppose every human being on Earth turned on watt light bulbs. With about 6 billion people this would only be 6  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 c 2 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  kg 1 helium atom has a mass of  kg Thus,  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

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

Temperature Distance Mass Composition Velocity Luminosity Radius Age

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 – ultravioletI – infrared B – blueR – 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 3 rd law The square of the sidereal period is proportional to the cube of the semimajor axis of the orbit: p 2  a 3 Newton’s laws require:

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 2 nd 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 and HD 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?