Our Star and Other Stars Lots of material to cover in this one week!

A Closer Look at the Sun Our Goals for Learning: Why does the Sun shine? What is the Sun’s structure? LUMINOSITY = TOTAL ENERGY EMITTED PER SECOND Our star

Is it on FIRE? … Luminosity ~ 10,000 years Chemical Energy Content NO!

Luminosity Gravitational Potential Energy Is it CONTRACTING? … ~ 25 million years NO!

Is it powered by NUCLEAR ENERGY? … Luminosity ~ 10 billion years Nuclear Potential Energy (core) E = mc 2 - Einstein, 1905 YES!

Gravitational equilibrium: The Sun is a huge ball of hydrogen and helium gas held together by gravity. The outward push or pressure from very hot expanding gases is balanced by the strong inward pull of gravity. Note: Any gaseous cloud that is a little bit denser in the inside will pull in the outer particles.

Like a stack of pillows, t Like a stack of pillows, the weight of the upper layers compresses lower layers. This is exactly what happens to the layers of hydrogen gas. Compressed gas becomes hot

Gravitational equilibrium: Energy provided by nuclear fusion of hydrogen to helium in the Sun’s hot core maintains the very high temperature and creates a pressure balance against gravity. Gravitational contraction: Provided the energy that heated the core as the Sun was forming and thus slowed contraction. Contraction stopped when fusion began. This was the moment that the proto-Sun became a “star”. The Role of Gravity in the Sun

The Solar wind: A flow of charged particles, protons and electrons, from the opaque “surface” of the Sun. (This “wind” causes the aurora when it hits Earth.) Corona: Outermost gaseous layer of the solar “atmosphere”. Very thin; fast moving particles. Temperature ~1 million K.

Chromosphere: Middle layer of the solar atmosphere; can be seen as pinkish in eclipse due to hydrogen emission – hence the “chromo” in the name. ~ K

Photosphere: Visible “surface” of Sun. Not really a surface in the normal sense. This is just as far into the Sun as we can see. The gas becomes dense and opaque below this level. ~ 6,000 K

Convection Zone: Hot, dense, very turbulent gas. Energy transported upward by rising hot gas. Breaks through photosphere to cause a granulation appearance that reminds one of boiling water.

Radiation Zone: A much hotter and denser region. Energy transported upward by photons, not by the mass motion of gas. Core: Extremely dense region, but still gaseous!! Energy generated by nuclear fusion. Temperature: ~ 15 million K

Nuclear Fusion in the Sun Our Goals for Learning: How does nuclear fusion occur in the Sun? How does the energy from fusion get out of the Sun? How do we know what is happening inside the Sun?

Fission Big nucleus (e.g. uranium) splits into smaller pieces (Nuclear power plants) Fusion Small nuclei stick together to make a bigger one (Sun, stars) Two kinds of nuclear reactions

The very high temperature enables nuclear fusion to happen in the core. Electrostatic repulsion between positively charged protons can be overcome if the nuclei get close enough for the STRONG force – a nuclear binding force – to take over. TWO POWERFULL FORCES

The Sun releases energy by fusing four hydrogen nuclei (protons) into one helium nucleus (2 protons and 2 neutrons). Let’s look at details. THE BASIC NUCLEAR FUSION PROCESS

Proton-proton chain is how hydrogen fuses into helium in Sun

IN 4 protons OUT 4 He nucleus 2 gamma rays 2 positrons 2 neutrinos Total mass is 0.7% lower! This mass goes to ENERGY because of E = mc 2 The process may seem complicated at first, but it is in fact very simple, and it can be reproduced by Man in a Hydrogen bomb!

Energy gradually leaks out of the radiation zone in the form of randomly bouncing photons. The photons bounce off electrons and make a “random walk”. It can take over 100,000 years for a photon to reach the surface. HOW DOES THE ENERGY GET OUT?

At the top of the radiation zone the temperature has dropped to ~2 million K. Here, photons are absorbed, not scattered. This creates rising plumes of hot gas (convection) that takes energy to the surface.

Bright blobs on the photosphere are where hot gas is reaching the surface. Granulation

We learn about the inside of the Sun by Making mathematical models –To predict the radius, temperature, luminosity and age of the Sun from its mass and chemical composition Observing “sun quakes” Observing solar neutrinos

Patterns of vibration on the surface tell us about what the Sun is like inside. This is a mathematical model predicting one such pattern. Doppler shifts in the spectrum from different parts of the surface can be measured. Results agree very well with mathematical models of the solar interior. Helio-seismology uses “quaking” of the Sun.

Neutrinos are very tiny nuclear particles with no electric charge created during fusion. They fly directly through the Sun and escape! Observations of these solar neutrinos can tell us what’s happening in the core. Neutrinos are remarkable! They are exceedingly small and have almost no interaction with anything. NEUTRINOS

Early searches for solar neutrinos failed to find the predicted number but, More recent observations find the right number of neutrinos, but some have changed form  new physics! The Solar neutrino problem: These pictures show 2 huge underground neutrino “observatories” Homestake Mine, South Dakota Sudbury Mine, Canada

What have we learned? How does nuclear fusion occur in the Sun? Fusion of hydrogen into helium, which occurs via the proton–proton chain. Gravitational equilibrium acts as a thermostat that keeps the fusion rate steady.

Properties of Stars Our Goals for Learning How luminous are stars? How hot are stars? How massive are stars?  Not all stars are exactly like the Sun! Surveying the Stars

Luminosity: Amount of power a star radiates (energy per second) The units of power is: 1 Joule per second = 1 Watt Apparent brightness: Amount of starlight that reaches Earth - the energy per second per square meter. So, apparent brightness of a star depends on LUMINOSITY & DISTANCE Everything we know is deduced from the light we receive

Luminosity (energy per second) passing through each sphere in the diagram is the same – this is conservation of energy. Area of sphere: = 4π (radius) 2 So, divide Luminosity by Area to get Brightness. How are Luminosity and Brightness related?

The relationship between apparent brightness and luminosity depends on distance: Luminosity Brightness = 4π (distance) 2 We can determine a star’s luminosity if we can measure its distance and apparent brightness: Luminosity = 4π (distance) 2 x (Brightness) Brightness is easy to measure with a photo-meter. How do we measure distance?

PARALLAX d (parsecs) =1/p (arcsec) p can be as small as 0.01 arcsec 1 parsec is the distance that gives a parallax angle of 1 second of arc = 3.26 light years = AU This works out to 100pc or 326 ly

1) Hotter objects emit more light at all wavelengths (~σT 4 ) 2) Hotter objects emit light at shorter wavelengths ( ~3000/T) If we measure the spectrum we can get the temperature. Laws of Thermal Radiation How hot are stars? Shape of curve depends only on T

Dark lines in a star’s spectrum correspond to a spectral type that reveals its temperature. Spectral type (letter/number) is shorthand for T (Hottest) O B A F G K M (Coolest) STELLAR SPECTRA Hottest stars Coolest stars Letters (A-O) assigned over 100 years ago before temperatures were known. Had to be re-ordered to make sense. Still a useful aid to memory. 50,000 K 3,500 K

(Hottest) O B A F G K M (Coolest) Remembering Spectral Types Oh, Be A Fine Girl/Guy, Kiss Me We have distance, luminosity and temperature. What else can we get?

GRAVITATIONALLY BOUND STARS Two stars orbiting each other = BINARY Binary Stars yield Stellar Masses Types of Binary Star Systems Visual Binary Eclipsing Binary Spectroscopic Binary NOTE: About half of all stars are in binary systems

Visual Binary We can directly observe the orbital motions of these stars. We can determine the orbital period and projected size of the orbit (on the sky) directly. We don’t know the inclination of the plane of the orbit (so the orbital size is the “projected” size).

Eclipsing Binary Inclination of the orbit is essentially zero (edge-on), causing eclipses. Periodic eclipses implies orbital period. Duration gives RADIUS. This Light Curve is observed even if the two stars are blended together by distance.

Spectroscopic Binary Again, seen as one object because of large distance but, We find the orbit (period and velocity) by measuring Doppler shifts

Isaac Newton We measure mass using gravity Newton’s Form of Kepler’s 3 rd Law Direct mass measurements are possible only for stars in binary star systems p = period a = average separation p 2 = a 3 4π 2 G (M 1 + M 2 ) If you only have p and a then you get M 1 +M 2, but if you have the separate orbits then you can get M 1 and M 2 separately.

How massive are stars? The overall range of stellar masses runs from 0.08 times the mass of the Sun to about 150 times the mass of the Sun. Masses are only known for stars that form binary systems, but about half of all stars are in fact in binary systems! –0.08 M Sun is approximately 80 M Jupiter Objects less massive than 0.08 M Sun exist; discovered 1995 – called Brown Dwarfs

What have we learned? How luminous are stars? The apparent brightness of a star in our sky depends on both its luminosity — the total amount of light it emits into space—and its distance from Earth, as expressed by the inverse square law for light.

What have we learned? How hot are stars? The surface temperatures of the hottest stars exceed 40,000 K and those of the coolest stars are less than 3,000 K. We measure a star’s surface temperature from its COLOR or SPECTRUM, and we classify spectra according to the sequence of spectral types OBAFGKM, which runs from hottest (O) to the coolest (M).

Classifying Stars Our Goals for Learning How do we classify stars? Why is a star’s mass its most important property? What is a Hertzsprung–Russell diagram?

Mass & Lifetime Sun’s life expectancy: 10 billion years Life expectancy of 10 M Sun star: 10 times as much fuel, but uses it 10 4 times as fast 10 million years ~ 10 billion years x 10 / 10 4 Life expectancy of 0.1 M Sun star: 0.1 times as much fuel, uses it 0.01 times as fast 100 billion years ~ 10 billion years x 0.1 / 0.01 Until core hydrogen (10% of total) is used up.

Normal Star Summary High Mass: High Luminosity Short-Lived Large Radius Blue Low Mass: Low Luminosity Long-Lived Small Radius Red The Sun is “low mass”.

Temperature Luminosity This diagram plots the Luminosity (y) as a function of Temperature (x) of many different kinds of stars. It is called a Hertzsprung- Russell Diagram. It tells us everything in one picture!

Normal hydrogen- burning stars reside on the main sequence of the H-R diagram. Mass increases from lower right to upper left. Gravitational equilibrium for each mass.

Temperature Luminosity Which of these stars must be physically larger in radius than main sequence stars of the same temperature? A B C D D Relative to the size of the Sun, stars in the upper right are “giants”, those in the lower left are “dwarfs”

Two types of star clusters Open clusters contain up to several thousand stars and are found in the disk of the Milky Way galaxy. Globular clusters contain hundreds of thousands of stars, all closely packed together. They are found mainly in a “halo” around our galaxy.

Measuring the age of a star cluster Because all of a cluster’s stars we born at the same time, we can measure a cluster’s age by finding the main sequence turnoff point on an H–R diagram of its stars. The cluster’s age is equal to the hydrogen-burning lifetime of the hottest, most luminous stars that remain on the main sequence. That is, those that have not “evolved” in red giants.

What have we learned? How do we classify stars? We classify stars according to their spectral type and luminosity class. The spectral type tells us the star’s surface temperature The luminosity class tells us how much light it puts out (surface area). Why is a star’s mass its most important property? A star’s mass at birth determines virtually everything that happens to it throughout its life.