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B-V Color Index and Temperature Hot stars appear bluer than cooler stars - cooler stars are redder than hotter stars. • B-V color index way of quantifying this - determining spectral class using two different filters Ø one a blue (B) filter that only lets a narrow range of colors or wavelengths through centered on the blue colors, Ø and a “visual” (V) filter that only lets the wavelengths close to the green-yellow band through. Hot star has a B-V color index close to 0 or negative, Cool star has a B-V color index close to 2.0. Other stars are somewhere in between. ⇒ 1. Measure the apparent brightness (flux) with two different filters (B, V). ⇒ 2. The flux of energy passing through the filter tells you the magnitude (brightness) at the wavelength of the filter. ⇒ 3. Compute the magnitude difference of the two filters, B - V. Hipparcos satellite measured 105 bright stars with δp>0.001" ⇒ confident distances for stars with d<100 pc Hertzsprung-Russell diagram for the 41704 single stars from the Hipparcos Catalogue with relative distance precision better than 20% and σ (B-V) less than or equal to 0.05 mag. Colors indicate number of stars in a cell of 0.01 mag in (B-V) and 0.05 mag in absolute magnitude (MV). Notice the spread in stars on main sequence. First H-R diagram from the Gaia mission A model atmospheric transmission for the mean conditions at Mt. Hopkins - ~8500 ft (location of one of the PHYS-3380 2MASS telescopes) Gaia asteroid detections Ecliptic Gaia asteroid detections compared with the positions on the sky of a sample of 50,000 known asteroids. The color indicates accuracy of the detection - the separation on the sky between the observed position of Gaia's detection and the expected position of PHYS-3380 each asteroid.The regions showing lower accuracy (red) of Milky Way Ecliptic PHYS-3380 The Milky Way on the Celestial Sphere Yes, the ecliptic plane (and earth’s) equator are tilted with respect to each other – about 60 degrees. PHYS-3380 Mass–Luminosity Relation All main sequence stars fuse H into He in their cores. Luminosity depends directly on mass because: - more mass means more weight from the star’s outer layers - nuclear fusion rates must be higher in order to maintain gravitational equilibrium L ∝ m3.5 So mass is the single most important property of any star. - at each stage of a star’s life, mass determines… - what its luminosity will be - what its spectral type will be Its lifetime on the main sequence is dependent on its mass PHYS 3380 Lifetime on the Main Sequence How long will it be before MS stars run out of fuel? i.e. Hydrogen? How much fuel is there? How fast is it consumed? M (solar mass) L ∝ M3.5 How long before it is used up? M/L = M/M3.5 = M-2.5 MS Lifetime τ = 1010 yrs / M2.5 Our Sun will last 1010 years on the Main Sequence PHYS 3380 Masses of Stars in the Hertzsprung-Russell Diagram The higher a star’s mass, the more luminous (brighter) it is: L ~ M3.5 High-mass stars have much shorter lives than low-mass stars: tlife ~ M-2.5 Sun: ~ 10 billion yr. 10 Msun: ~ 30 million yr. 0.1 Msun: ~ 3 trillion yr. Masses in units of solar masses 40 18 6 3 1.7 1.0 0.8 0.5 PHYS 3380 Lifetime on the Main Sequence So for example: B2 (10 M¤) lasts 3.2 x 107 yr F0 (2 M¤) lasts 1.8 x 109 yr M0 dwarf (.5 M¤) lasts 5.6 x 1010 yr But the Universe is 1.37 x 1010 yr old! Every M dwarf that was ever created is still on the main sequence!! PHYS 3380 Spectroscopic Parallax 1. Determine star’s spectral class/color index. 2. Determine luminosity class from spectral line width. 3. Use photometry to measure the apparent magnitude of the star. 4. Knowing spectral class/color index allows placement of the star on a vertical line or band along a Hertzsprung-Russell Diagram. 5. Knowing its luminosity class further constrains its position along this line, i.e. we can distinguish between a red supergiant, giant or main sequence 6. Once we know its position on the HR diagram we can infer what its absolute magnitude should be by either reading off across to the vertical scale of the HR diagram or looking it up from a reference table. A main sequence (luminosity class V) star with a color index of 0.0 (i.e. A0 V) has an absolute magnitude of +0.9 for example. 7. Now knowing mV from measurement and inferring MV we can use the distance modulus equation to find the distance to the star, d, in parsecs: mV – MV = -5 + 5 log10(d [pc]) PHYS 3380 Spectroscopic Parallax In practice not very precise Uncertainties in absolute magnitude of stars of specific spectral and luminosity class range from about 0.7 up to 1.25 magnitudes. • give a factor of 1.4 to 1.8 × variation in the resultant distance. • increases as the stellar distance increases only accurate enough to measure stellar distances of up to about 10 Mpc. • star has to be sufficiently bright to be able to measure the spectrum • can be obscured by matter between the star and the observer. PHYS 3380 Binary Stars About 1/3 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. The Center of Mass Newton showed that two objects attracted to each other by gravity actually orbit about their center of mass = balance point of the system. Both masses equal => center of mass is in the middle, rA = rB. The more unequal the masses are, the more it shifts toward the more massive star. Using this formulation, we can determine the total mass of a binary star system if we can determine the orbital characteristics of the system. Examples: Estimating Mass a) Binary system with period of P = 32 years and separation of a = 16 AU: MA + MB = 163 ____ = 4 solar masses. 2 32 b) Any binary system with a combination of period P=1 year and separation a=1 AU that obeys Kepler’s 3rd Law must have a total mass of 1 solar mass. Binary Star Systems Three types: - Visual - stars separately visible in telescope - Spectrographic - not separately visible - evidence of binary system determined spectroscopically - Eclipsing - orbital plane nearly edge on from Earth - one star periodically eclipses other. Visual Binaries The ideal case: Both stars can be seen directly, and their separation and relative motion can be followed directly. Can take years or decades to work out - depends on period. - Orbital period of is 50 years - Top photo taken in 1960 Sirius Spectroscopic Binaries Usually, binary separation a can not be measured directly because the stars are too close to each other. A limit on the separation and thus the masses can be inferred in the most common case: Spectroscopic Binaries In a spectroscopic binary system, the approaching star produces blue shifted lines; the receding star produces red shifted lines in the spectrum. Spectral lines shifting apart and then merging sign of spectroscopic binary Doppler shift → Measurement of radial velocities →Estimate of separation a →→ Estimate of masses Spectroscopic Binaries Typical sequence of spectra from a spectroscopic binary system Time Problems With a Spectroscopic Binary Cannot see the two stars separately: • Distance/semimajor axes must be guessed from the orbit motions. • Can't tell how the orbit is tilted on the sky Eclipsing Binaries Usually, inclination angle of binary systems is unknown → uncertainty in mass estimates. Special case: Eclipsing Binaries In the case of an eclipsing binary, we know that we are looking at the system edge-on. Eclipsing Binary In this case, a small hot star orbits a large, cool star. - we see total light when no eclipse occurs - as the hot star passes in front of the of the cool star, there is a decrease in the brightness. - when the hot star is eclipsed behind the cool start, the brightness again drops. The depth of the eclipses depends on the surface temperatures of the stars Eclipsing Binaries Example: Algol in the constellation of Perseus From the light curve of Algol, we can infer that the system contains two stars of very different surface temperature, orbiting in a slightly inclined plane. VW Cephei - an eclipsing binary star system in constellation Cepheus. - contains a red supergiant (A) which fills its Roche lobe when closest to its companion blue star, which appears to be on the main sequence Peculiar “double-dip” light curve of VW Cephei - lower curve shows observations - indicate so close together that gravity distorts their shape - evidence of dark spots on surface - upper curve shows what light curve would look like if there were no spots VV Cephei A's mass estimated from orbital motion - about 100 solar masses. Mass estimated from its luminosity is about 25-40 solar masses. Problems With Eclipsing Binaries Eclipsing Binary stars are very rare. Measurement of the light curves is complicated by details: • Partial eclipses yield less accurate numbers. • The atmospheres of the stars soften the edges. • Close binaries can be tidally distorted. However, the best masses are from eclipsing binaries. From a combination of visual and eclipsing binaries, masses are known for about 150 stars. Maximum Masses of Main-Sequence Stars Mmax ~ 50 - 100 solar masses a) More massive clouds fragment into smaller pieces during star formation. b) Very massive stars lose mass in strong stellar winds Eta Carinae Example: Eta Carinae: Estimated to be over 100 Msun. Dramatic mass loss; major eruption in 1843 created double lobes. Minimum Mass of Main-Sequence Stars Mmin = 0.08 Msun Gliese 229B At masses below 0.08 Msun, stellar progenitors do not get hot enough to ignite thermonuclear fusion. → Brown Dwarfs The Life Cycle of Stars Aging supergiant Young stars, still in their birth nebulae Dense, dark clouds, possibly forming stars in the future Stars are produced in dense nebulae in which much of the hydrogen is in the molecular (H2) form, so these nebulae are called molecular clouds. The largest such formations are called giant molecular clouds. Giant Molecular Clouds Barnard 68 Infrared Visible Star formation collapse of the cores of giant molecular clouds: Dark, cold, dense clouds obscuring the light of stars behind them. ← (More transparent in infrared light.) Parameters of Giant Molecular Clouds Size: r ~ 50 pc Mass: > 100,000 Msun Temp.: a few 0K Dense cores: R ~ 0.1 pc M ~ 1 Msun Much too cold and too low density to ignite thermonuclear processes Clouds need to contract and heat up in order to form stars. Contraction of Giant Molecular Cloud Cores Horse Head Nebula • Thermal Energy (pressure) • Magnetic Fields • Rotation (angular momentum) • Turbulence → External trigger required to initiate the collapse of clouds to form stars. Three Kinds of Such Nebulae 1) Emission Nebulae Hot star illuminates a gas cloud; excites and/or ionizes the gas (electrons kicked into higher energy states); electrons recombining, falling back to ground state produce emission lines. The Trifid The Fox Fur Nebula NGC 2246 Nebula Three Kinds of Nebulae Star illuminates a gas and dust cloud; star light is reflected by the dust; reflection nebulae appear blue because blue light is scattered by larger angles than red light; the same phenomenon makes the day sky appear blue (if it’s not cloudy). 2) Reflection Nebulae Three Kinds of Nebulae Dense clouds of gas and dust absorb the light from the stars behind; 3) Dark Nebulae appear dark in front of the brighter background; Barnard 86 Horsehead Nebula