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Slide 2 How to classify a star and to place it on the H-R diagram correctly?? Need to know its luminosity, but it is difficult, because distance is unknown If you can estimate a star’s diameter and/or mass, you can figure out its luminosity Then you can also find the distance to this star

Slide 3 The Radii of Stars in the Hertzsprung-Russell Diagram 10,000 times the sun’s radius 100 times the sun’s radius As large as the sun Rigel Betelgeuse Sun Polaris

Slide 4 The Relative Sizes of Stars in the Hertzsprung-Russell Diagram

Slide 5 Is there any spectral signature of giants? The width of spectral lines! How to distinguish between main-sequence stars and giants?

Slide 6 Spectral Lines of Giants => Absorption lines in spectra of giants and supergiants are narrower than in main sequence stars Pressure and density in the atmospheres of giants are lower than in main sequence stars. => From the line widths, we can estimate the size and therefore, the luminosity of a star.  Distance estimate (spectroscopic parallax)

Slide 7 Luminosity Classes Ia Bright Supergiants Ib Supergiants II Bright Giants III Giants IV Subgiants V Main-Sequence Stars Ia Ib II III IV V

Slide 8 Luminosity classes Ia bright supergiant Ib Supergiant II bright giant III giant IV subgiant V main-sequence star

Slide 9 Example Luminosity Classes Our Sun: G2 star on the Main Sequence: G2V Polaris: G2 star with Supergiant luminosity: G2Ib

Slide 10 Mass is the most important parameter. Knowing masses of stars would allow us to calculate their luminosities, lifetime and all other properties. But how to measure masses?? Measuring masses

Slide 11 Binary Stars More than 50 % of all stars in our Milky Way are not single stars, but belong to binaries: Pairs or multiple systems of stars which orbit their common center of mass. If we can measure and understand their orbital motion, we can estimate the stellar masses. Measuring masses

Slide 12 The Center of Mass center of mass = balance point of the system. Both masses equal => center of mass is in the middle, r A = r B. The more unequal the masses are, the more it shifts toward the more massive star.

Slide 13 Center of Mass (SLIDESHOW MODE ONLY)

Slide 14 m1m1 m2m2

Slide 15 Estimating Stellar Masses Recall Kepler’s 3rd Law: P y 2 = a AU 3 Valid for the Solar system: star with 1 solar mass in the center. We find almost the same law for binary stars with masses M A and M B different from 1 solar mass: M A + M B = a AU 3 ____ Py2Py2 (M A and M B in units of solar masses)

Slide 16 Examples: Estimating Mass Binary system with period of P = 32 years and separation of a = 16 AU: M A + M B = = 4 solar masses ____ 32 2 How to measure period and separation? Arbitrary units:

Slide 17 Visual Binaries The ideal case: Both stars can be seen directly, and their separation and relative motion can be followed directly.

Slide 18 Visual binaries The Castor systemThe Sirius system The two stars are separately visible in the telescope

Slide 19 Detecting the presence of a companion by its gravitational influence on the primary star. Wobbling motion of Sirius A

Slide 20 Spectroscopic Binaries Usually, binary separation a can not be measured directly because the stars are too close to each other. However: 1) their SPECTRA are different, like different fingerprints; 2) Their spectral lines shift periodically because of Doppler effect. This allows us to measure their orbital velocities Stars are seen as a single point

Slide 21 The Doppler Effect The light of a moving source is blue/red shifted by  / 0 = v r /c 0 = actual wavelength emitted by the source  Wavelength change due to Doppler effect v r = radial velocity( along the line of sight) Blue Shift (to higher frequencies) Red Shift (to lower frequencies) vrvr

Slide 22 Shift z = (Observed wavelength - Rest wavelength) (Rest wavelength) Doppler effect: The Doppler effect: apparent change in the wavelength of radiation caused by the motion of the source

Slide 23 Doppler effect The Doppler effect: apparent change in the wavelength of radiation caused by the motion of the source RADIAL velocity!!

Slide 24 The Doppler Effect The Doppler effect allows us to measure the source’s radial velocity. vrvr  / 0 = v r /c

Slide 25 Spectroscopic Binaries The approaching star produces blue shifted lines; the receding star produces red shifted lines in the spectrum. Doppler shift  Measurement of radial velocities  Estimate of separation a  Estimate of masses

Slide 26 Spectroscopic binaries Stars are seen as a single point Spectra of both stars are distinguishable Sometimes spectrum of only one star is seen

Slide 27 Spectroscopic Binaries (3) Time Typical sequence of spectra from a spectroscopic binary system

Slide 28 Determining the orbital period

Slide 29 Measure the orbital period Measure the radial component of the orbital velocities Can estimate the orbit size Can determine masses!

Slide Below is a radial velocity curve for a spectroscopic binary. Estimate the mass of each star if the mass of the binary system is 6 solar masses. M A d A = M B d B V ~ 2  d/P

Slide 31 Only the function of masses and inclination angle can be measured

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Slide 33...BUT THE PLANET CANNOT BE SEEN MOTIONS OF THE STAR BETRAY ITS PRESENCE !

Slide 34 X EARTH X JUPITER km 30 km/s 450 km 9 cm/s km 13 km/s km 13 m/s

Slide ” MOTIONS OF THE SUN VIEWED FROM A STAR 30 LIGHT YEARS AWAY 0.002’’ IS THE ANGULAR SIZE OF A MAN ON THE MOON OR A STANDARD NEWSPAPER FONT 300 KM AWAY Unobservable!

Slide 36 STELLAR WOBBLE RECEDING: REDDER APPROACHING: BLUER

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Slide 38 Over 100 planets discovered

Slide 39 EXPECTED: NEARLY CIRCULAR ORBITS BIG PLANETS FAR AWAY FROM THE STAR NO PLANETS BIGGER THAN JUPITER DISCOVERED: STRONGLY ELONGATED ORBITS BIG PLANETS VERY CLOSE TO THE STAR MANY PLANETS BIGGER THAN JUPITER

Slide 40 Planetary system of  And Solar system 0.06 AU 4.5 days 0.75 M J 2.5 AU 3.5 years 4 M J 0.85 AU 242 days 2 M J 0.39 AU 89 days 0.73 AU 228 days 1 AU 1 year 1.54 AU 1.9 years Source: Harvard-Smithsonian CfA

Slide 41 Habitable zones

Slide 42 Signs of life in the spectrum:

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Slide 44 The Puzzle of Algol

Slide 45 John Goodricke Explained Algol puzzle in 1783

Slide 46 Eclipsing binaries

Slide 47 Eclipsing Binaries Usually, inclination angle of binary systems is unknown  uncertainty in mass estimates. Special case: Eclipsing Binaries Here, we know that we are looking at the system edge-on!

Slide 48 The light curve of Algol

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Slide 50 Measuring orbital period and diameters

Slide 51 Measuring diameters D = V orb (t 2 – t 1 )

Slide 52 Specific segments of the main sequence are occupied by stars of a specific mass L~ M 3.5 dependence, but Cutoff at masses > 100 M  and < 0.08 M 

Slide 53 Puzzles of H-R diagram Why > 90% of stars are on the main sequence? Reason for mass- luminosity dependence and mass cutoff Same stars at different stages of life or just different stars?

Slide 54 How can we learn about the life of stars?? Our life span is ~ 80 years Human civilization exists ~ 5000 years Our Sun exists at least 4.6 billion years!

Slide 55 Star Clusters – “School Classes” for Stars They consist of stars of the same age ! Open clusters 100’s of stars Globular clusters 100,000 of stars

Slide 56p. 188 Pleiades

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Slide 58 Age of the cluster from turnoff point Turnoff point: stars of that mass are going to die and move away from the main sequence

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Slide 62 Stars spent most of their lives on the Main Sequence. That is why it is so populated! At the end of its life the star moves away from the Main Sequence More massive and more luminous stars die faster Hypothesis: Stars on the Main Sequence live due to nuclear fusion of hydrogen! Stars stay on the main sequence until all hydrogen in the core is consumed Then something should happen

Slide 63 H-R diagram 90% of stars are on the main sequence and obey the mass- luminosity dependence L ~ M 3.5 Stars on the main sequence generate energy due to nuclear fusion of hydrogen In the end of their lives stars move to the upper right corner of the H-R diagram

Slide 64 Check this hypothesis Mass should be most important parameter It determines the pressure in the star center and the central temperature It determines the surface temperature How to get this dependence?

Slide 65 Gravity Holds a Star Together Stars are held together by gravity. Gravity tries to compress everything to the center. What holds an ordinary star up and prevents total collapse is thermal and radiation pressure. The thermal and radiation pressure tries to expand the star layers outward to infinity. 1.Newton’s gravitation law 2.Hydrostatic equilibrium 3.Equation of state 4.Energy transport Mass determines all star’s properties

Slide 66 star mass (solar masses)time (years)Spectral type 603 millionO millionO millionB millionA billionF5 110 billionG2 (Sun) 's billionsM7 Lifetime T ~ M/L ~ 1/M = 1/M 2.5 ; p ~ 3.5 M = 4M  ; Lifetime = Amount of hydrogen fuel Rate of energy loss T ~ 3x10 8 years

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Slide 68 How to explain the cutoff at masses > 100 M  and < 0.08 M 

Slide 69 Maximum Masses of Main-Sequence Stars  Carinae M max ~ solar masses a) More massive clouds fragment into smaller pieces during star formation. b) Very massive stars lose mass in strong stellar winds Example:  Carinae: Binary system of a 60 M sun and 70 M sun star. Dramatic mass loss; major eruption in 1843 created double lobes.

Slide 70 Too massive and luminous stars throw off their outer layers due to radiation pressure Eta Carinae High-mass cutoff at M ~ 100 M sun

Slide 71 Minimum Mass of Main-Sequence Stars M min = 0.08 M sun At masses below 0.08 M sun, stellar progenitors do not get hot enough to ignite thermonuclear fusion.  Brown Dwarfs Gliese 229B

Slide 72 Low-mass cutoff of the main sequence: M ~ 0.08 M sun Gliese 229B: only 0.02 M  Brown dwarfs: temperature is too low to ignite nuclear fusion

Slide 73 Conclusion Based on this evidence, we conclude: Stars spend most of their lives as main sequence stars. During its lifetime, the surface temperature and luminosity stays almost constant. Something else could happen in the star birth process. Something else could happen in the star death process. The star's mass determines what the temperature and luminosity is during the star's main sequence lifetime. More mass -> hotter. More mass -> more luminous. Also, more mass -> bigger.