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Lecture 14: Studying the stars Astronomy 111 Monday October 17, 2016 Reminders • Homework #7 due Monday ASTR111 Lecture 14 Studying the stars • • • • • How far? How bright? How massive? How big? How hot? ASTR111 Lecture 14 Why are distances important? Distances are necessary for estimating: • Total energy released by an object (Luminosity) • Masses of objects from orbital motions (Kepler’s third law) • Physical sizes of objects ASTR111 Lecture 14 The problem of measuring distances Q: What do you do when an object is out of reach of your measuring instruments? Examples: • Surveying & mapping • Architecture • Any astronomical object A: You resort to using GEOMETRY. ASTR111 Lecture 14 Method of trigonometric parallaxes June p December Foreground Star Distant Stars ASTR111 Lecture 14 Parallax decreases with distance Closer stars have larger parallaxes: Distant stars have smaller parallaxes: ASTR111 Lecture 14 Stellar parallaxes All stellar parallaxes are less than 1 arcsecond Nearest star, a Centauri, has p=0.76-arcsec Cannot measure parallaxes with naked eye. First parallax observed in 1837 (Bessel) for the star 61 Cygni. Use photography or digital imaging today. ASTR111 Lecture 14 Parallax formula 1 d p p = parallax angle in arcseconds d = distance in “Parsecs” ASTR111 Lecture 14 Parallax Second = Parsec (pc) Fundamental unit of distance in astronomy “A star with a parallax of 1 arcsecond has a distance of 1 Parsec.” Relation to other units: 1 parsec (pc) is equivalent to 206,265 AU 3.26 Light Years 3.085x1013 km ASTR111 Lecture 14 Light year (ly) Alternative unit of distance “1 Light Year is the distance traveled by light in one year.” Relation to other units: 1 light year (ly) is equivalent to 0.31 pc 63,270 AU Used mostly by journalists, Star Trek, etc. —not generally used by astronomers! ASTR111 Lecture 14 Examples a Centauri has a parallax of p=0.76 arcsec: A distant star has a parallax of p=0.02 arcsec: ASTR111 Lecture 14 Limitations If stars are too far away, the parallax can be too small to measure accurately. The smallest parallax measurable from the ground is about 0.01 arcsec • Measure distances out to ~100 pc • But, only a few hundred stars are this close to the Sun ASTR111 Lecture 14 Hipparcos satellite European Space Agency Launched in 1989 Designed to measure precision parallaxes to about ±0.001 arcseconds! • Gets distances good out to 1000 pc • Measured parallaxes for ~100,000 stars! ASTR111 Lecture 14 GAIA satellite • ESA’s new GAIA mission is way better: • Parallax precision p ~ 10-5 arcsec for 1 billion stars – 100x better parallaxes – 10,000x more stars – Stars that are ~100 times fainter than Hipparcos The position of a billion stars will be measured by GAIA; this image shows the first preliminary data release. From sci.esa.int/gaia ASTR111 Lecture 14 How “bright” is an object? • We must define “brightness” quantitatively. • Two ways to quantify brightness: – Intrinsic Luminosity: Total energy output. – Apparent Brightness: How bright it looks from a distance. ASTR111 Lecture 14 Appearances can be deceiving... • Does a star look “bright” because – it is intrinsically very luminous? – it is intrinsically faint but located nearby? • To know for sure you must know: – the distance to the star, or – some other, distance-independent property of the star that clues you in. ASTR111 Lecture 14 Luminosity • Luminosity is the total energy output from an object. – Measured in power units: Energy/second emitted by the object (e.g., Watts) – Independent of distance • Important for understanding the energy production of a star. ASTR111 Lecture 14 Apparent brightness • Measures how bright an object appears to be to a distant observer. • What we measure on earth (“observable”) • Measured in flux units: Energy/second/area from the source. • Depends on the distance to the object. ASTR111 Lecture 14 Inverse Square Law of Brightness The apparent brightness of a source is inversely proportional to the square of its distance: 1 B 2 d 2-times Closer = 4-times Brighter 2-times Farther = 4-times Fainter ASTR111 Lecture 14 d=1 B=1 d=2 B=1/4 d=3 B=1/9 Flux-luminosity relationship Relates apparent brightness (Flux) and intrinsic brightness (Luminosity) through the Inverse Square Law of Brightness: Luminosity Flux = 2 4 d ASTR111 Lecture 14 Measuring apparent brightness • The process of measuring the apparent brightnesses of objects is called Photometry. • Two ways to express apparent brightness: – as Stellar Magnitudes – as Absolute Fluxes (energy per second per area) ASTR111 Lecture 14 Magnitude system • Traditional system dating to classical times (Hipparchus of Rhodes, c. 300 BC) • Rank stars according to apparent brightness – 1st magnitude are brightest stars – 2nd magnitude are the next brightest – and so on... • Faintest naked-eye stars are 6th magnitude. • Modern version quantifies this system – 5 steps of magnitude = factor of 100 in Flux. • Computationally convenient, but somewhat obtuse. ASTR111 Lecture 14 Flux photometry • Measure the flux of photons from a star using a light-sensitive detector: – Photographic Plate – Photoelectric Photometer (photomultiplier tube) – Solid State Detector (e.g., CCD) • Calibrate the detector by observing a set of “Standard Stars” of known brightness. ASTR111 Lecture 14 Measuring luminosity • In principle you just combine – the brightness (flux) measured via photometry – and the distance to the star • using the inverse-square law. • The biggest problem is finding the distance. ASTR111 Lecture 14 Measuring masses of stars: Binary stars • Apparent Binaries – Chance projection of two distinct stars along the line of sight. – Often at very different distances. • True Binary Stars: – A pair of stars bound by gravity. – Orbit each other about their center of mass. – Between 20% and 80% of all stars are binaries. ASTR111 Lecture 14 Types of binaries • Visual Binary: Can see both stars & follow their orbits over time. • Spectroscopic Binary: Cannot resolve the two stars, but can see their orbit motions as Doppler shifts in their spectra. • Eclipsing Binary: Cannot resolve the two stars, but can see the total brightness drop when they periodically eclipse each other. ASTR111 Lecture 14 Visual Binary 1890 1940 1990 ASTR111 Lecture 14 Center of mass • Two stars orbit about their center of mass: a a 1 2 M2 a M1 • Measure semi-major axis, a, from projected orbit and the distance. • Relative positions give: M1 / M2 = a2 / a1 ASTR111 Lecture 14 Measuring masses Newton’s Form of Kepler’s Third Law: P 2 4 a = G(M1 + M 2) 2 3 • Measure period, P, by following the orbit. • Measure semi-major axis, a, and mass ratio (M1/M2) from projected orbit. ASTR111 Lecture 14 Problems • We need to follow the orbits long enough to trace them out in detail. – This can take decades. – Need to work out the projection on the sky. • Everything depends critically on the distance: – semi-major axis depends on d – derived mass depends on d3 !! ASTR111 Lecture 14 Spectroscopic binaries • Most binaries are too far away to see both stars separately. • But, you can detect their orbital motions by the periodic Doppler shifts of their spectral lines. – Determine the orbital period & size from velocities. ASTR111 Lecture 14 Spectroscopic binaries B A B B A A A ASTR111 Lecture 14 B Problems • Cannot see the two stars separately: – Semi-major axis must be guessed from orbit – Can’t tell how the orbit is tilted on the sky • Everything depends critically on knowing the distance. ASTR111 Lecture 14 Eclipsing binaries • Two stars orbiting nearly edge-on. – See a periodic drop in brightness as one star eclipses the other. – Combine with spectra which measure orbital speeds. • With the best data, one can find the masses without having to know the distance! ASTR111 Lecture 14 Eclipsing binaries 4 Brightness 3 1 2 1 3 2 Time ASTR111 Lecture 14 4 Problems • Eclipsing Binaries are very rare – Orbital plane must line up just right • Measurement of the eclipse light curves complicated by details: – Partial eclipses yield less accurate numbers. – Atmospheres of the stars soften edges. – Close binaries can be tidally distorted. ASTR111 Lecture 14 Stellar masses • Masses are known for only ~200 stars. – Range: ~0.1 to 50 Solar masses • Stellar masses can only be measured for binary stars. ASTR111 Lecture 14 Stellar radii • Very difficult to measure because stars are so far away. • Methods: – Eclipsing binaries (need distance) – Interferometry (single stars) – Lunar occultation (single stars) • Radii are only measured for about 500 stars ASTR111 Lecture 14 Colors of stars • Stars are made of hot, dense gas – Continuous spectrum from the lowest visible layers (“photosphere”). – Approximates a blackbody spectrum. • From Wien’s Law, we expect: – hotter stars appear BLUE (T=10,00050,000 K) – middle stars appear YELLOW (T~6000K) – cool stars appear RED (T~3000K) ASTR111 Lecture 14 ASTR111 Lecture 14 Spectra of stars • Hot, dense lower photosphere of a star is surrounded by thinner (but still fairly hot) atmosphere. – Produces an Absorption Line spectrum. – Lines come from the elements in the stellar atmosphere. ASTR111 Lecture 14 ASTR111 Lecture 14 Spectral classification of stars • Astronomers noticed that stellar spectra showed many similarities. • Can stars be classified or grouped according to similarities in their spectra? • Draper Survey at Harvard (1886-1897): – Objective prism photography – Obtained spectra of >100,000 stars – Hired women as “computers” to analyze spectra ASTR111 Lecture 14 Harvard “Computers” (c. 1900) ASTR111 Lecture 14 Objective prism spectra ASTR111 Lecture 14 Harvard classification Edward Pickering • Edward Pickering’s first attempt at a systematic spectral classification: – Sort by Hydrogen absorption-line strength – Spectral Type “A” = strongest Hydrogen lines – followed by types B, C, D, etc. (weaker) • Problem: Other lines followed no discernible patterns. ASTR111 Lecture 14 Annie Jump Cannon • Leader of Pickering’s “computers”, she noticed subtle patterns among metal lines. • Re-arranged Pickering’s ABC spectral types, throwing out most as redundant. • Left 7 primary and 3 secondary classes: • O B A F G K M (R N S) • Unifying factor: Temperature ASTR111 Lecture 14 Annie Jump Cannon ASTR111 Lecture 14 The spectral sequence O B A F G K MLT Hotter 50,000K Cooler 2000K Bluer Redder Spectral sequence is a Temperature sequence ASTR111 Lecture 14 Spectral types ASTR111 Lecture 14 Stellar spectra in order from the hottest (top) to coolest (bottom). ASTR111 Lecture 14 The spectral sequence is a Temperature sequence • Gross differences among the spectral types are due to differences in Temperature. • Composition differences are minor at best. – Demonstrated by Cecilia Payne-Gaposhkin in 1920’s • Why? What lines you see depends on the state of excitation and ionization of the gas. ASTR111 Lecture 14 Example: Hydrogen Lines • Visible Hydrogen absorption lines come from the second excited state. • B Stars (15-30,000 K): Most of H is ionized, so only very weak H lines. • A Stars (10,000 K): Ideal excitation conditions, strongest H lines. • G Stars (6000 K): Too cool, little excited H, so only weak H lines. ASTR111 Lecture 14 ASTR111 Lecture 14 O Stars • Hottest Stars: T>30,000 K • Strong lines of He+ • No lines of H ASTR111 Lecture 14 B Stars • T=15,000 - 30,000 K • Strong lines of He • Very weak lines of H ASTR111 Lecture 14 A Stars • T = 10,000 - 7500 K • Strong lines of H • Weak lines of Ca+ ASTR111 Lecture 14 F Stars • • • • T = 7500 - 6000 K weaker lines of H Ca+ lines growing stronger first weak metal lines appear ASTR111 Lecture 14 G Stars • T = 6000 - 5000 K • Strong lines of Ca+, Fe+, & other metals • much weaker H lines • The Sun is a G-type Star ASTR111 Lecture 14 K Stars • • • • Cool Stars: T = 5000 - 3500 K Strongest metal lines H lines practically gone first weak CH & CN molecular bands ASTR111 Lecture 14 M Stars • Very cool stars: T 2000-3500 K • Strong molecular bands (especially TiO) • No lines of H ASTR111 Lecture 14 L & T Stars • Coolest stars: T < 2000 K • Discovered in 1999 • Strong molecular bands • Metal-hydride (CrH & FeH) • Methane (CH4) in T stars • Probably not stars at all ASTR111 Lecture 14 Modern synthesis: The M-K System • An understanding of atomic physics and better techniques permit finer distinctions. • Morgan-Keenan (M-K) Classification System: Start with Harvard classes: • O B A F G K M L T Subdivide each class into numbered subclasses: • A0 A1 A2 A3 ... A9 ASTR111 Lecture 14 Examples • The Sun: G2 star • Other bright stars: Betelgeuse: M2 star (Orion) Rigel: B8 star (Orion) Sirius: A1 star (Canis Major) Aldebaran: K5 star (Taurus) ASTR111 Lecture 14 Summary of stellar properties • Large range of Stellar Luminosities: – 10-4 to 106 Lsun • Large range of Stellar Radii: – 10-2 to 103 Rsun • Modest range of Stellar Temperatures: – 3000 to >50,000 K • Wide Range of Stellar Masses: – 0.1 to ~50 Msun ASTR111 Lecture 14 Luminosity-Radius-Temperature Relation • Stars are approximately black bodies. Stefan-Boltzmann Law: energy/sec/area = sT4 The area of a spherical star: area = 4R2 • Predicted Stellar Luminosity (energy/sec): L = 4R2 sT4 ASTR111 Lecture 14 Example 1: 2 stars are the same size, (RA=RB), but star A is 2 hotter than star B (TA=2TB): LA (2TB ) LA 4R sT 4 L B 4R sT LB TB LA 4 2 LA 16 LB LB 2 A 2 B 4 A 4 B 4 Therefore: star A is 16 brighter than star B ASTR111 Lecture 14 Example 2: 2 stars are the same temperature, (TA=TB), but star A is 2 bigger than star B (RA=2RB): LA (2R B ) LA 4R sT 2 L B 4R sT LB RB LA 2 2 LA 4 L B LB 2 A 2 B 4 A 4 B 2 Therefore: star A is 4 brighter than star B ASTR111 Lecture 14 Hertzsprung-Russell Diagram • Plot of Luminosity versus Temperature: – estimate T from Spectral Type – estimate L from apparent brightness & distance • Done independently by: – Eljnar Hertzsprung (1911) for star clusters – Henry Norris Russell (1913) for nearby stars ASTR111 Lecture 14 Eljnar Hertzsprung ASTR111 Lecture 14 Henry Norris Russell H-R Diagram Luminosity (Lsun) 106 Supergiants 104 102 Giants 1 10-2 10-4 40,000 White Dwarfs 20,000 10,000 5,000 Temperature (K) ASTR111 Lecture 14 2,500 Main Sequence • Most nearby stars (85%), including the Sun, lie along a diagonal band called the Main Sequence • Ranges of properties: – L=10-2 to 106 Lsun – T=3000 to >50,0000 K – R=0.1 to 10 Rsun ASTR111 Lecture 14 Giants & Supergiants • Two bands of stars brighter than Main Sequence stars of the same Temperature. – Means they must be larger in radius. • Giants R=10 -100 Rsun L=103 - 105 Lsun T<5000 K • Supergiants R>103 Rsun L=105 - 106 Lsun T=3000 50,000 K ASTR111 Lecture 14 White Dwarfs • Stars on the lower left of the H-R Diagram are fainter than Main Sequence stars of the same Temperature. – Means they must be smaller in radius. – L-R-T Relation predicts: R ~ 0.01 Rsun (~ size of Earth!) ASTR111 Lecture 14 Hipparcos H-R Diagram 4902 single stars with distance errors of <5% ASTR111 Lecture 14 Luminosity classification • Absorption lines are Pressure-sensitive: – Lines get broader as the pressure increases. – Larger stars are puffier, which means lower pressure, so that • Larger Stars have Narrower Lines. • This gives us a way to assign a Luminosity Class to a star based solely on its spectrum! ASTR111 Lecture 14 Luminosity Effects in Spectra ASTR111 Lecture 14 Luminosity Classes: Ia = Bright Supergiants Ib = Supergiants II = Bright Giants III = Giants IV = Subgiants V = Dwarfs = Main-Sequence Stars ASTR111 Lecture 14 Spectral + Luminosity Classification of Stars: • Sun: G2v (G2 Main-Sequence star) • Winter Sky: Betelgeuse: M2 Ib (M2 Supergiant star) Rigel: B8 Ia (B8 Bright Supergiant star) Sirius: A1v (A1 Main-Sequence star) Aldebaran: K5 III (K5 Giant star) ASTR111 Lecture 14 From Stellar Properties to Stellar Structure • Any theory of stellar structure must explain the observed properties of stars. • Seek clues in correlations among the observed properties, in particular: – Mass – Luminosity – Radius – Temperature ASTR111 Lecture 14 H-R Diagram Luminosity (Lsun) 106 Supergiants 104 102 Giants 1 10 -2 10 -4 40,000 White Dwarfs 20,000 10,000 5,000 Temperature (K) ASTR111 Lecture 14 2,500 • Main Sequence: – Strong correlation between Luminosity and Temperature. – Holds for 85% of nearby stars including the sun • All other stars differ in size: – Giants & Supergiants: Very large radius, but same masses as M-S stars – White Dwarfs: Very compact stars: ~Rearth but with ~Msun! ASTR111 Lecture 14 Mass-Luminosity Relationship • For Main-Sequence stars: L M Lsun M sun 3.5 In words: “More massive M-S stars are more luminous.” Not true of Giants, Supergiants, or White Dwarfs. ASTR111 Lecture 14 Luminosity (Lsun) 104 102 LM3.5 1 10-2 0.01 0.1 1 10 Mass (Msun) ASTR111 Lecture 14 100 Stellar Density • Density = Mass Volume • Main Sequence: small range of density – Sun: ~1.6 g/cc – O5v Star: ~0.005 g/cc – M0v Star: ~5 g/cc • Giants: 10 -7 g/cc • White Dwarfs: 105 g/cc ASTR111 Lecture 14 Interpreting the Observations: • Main-Sequence Stars: – Strong L-T Relationship on H-R Diagram – Strong M-L Relationship Implies they have similar internal structures & governing laws. • Giants & White Dwarfs: – Must have very different internal structures than Main-Sequence stars of similar mass. ASTR111 Lecture 14 Summary • Distance is important but hard to measure • Trigonometric parallaxes – direct geometric method – only good for the nearest stars (~500pc) • Units of distance in Astronomy: – Parsec (Parallax second) – Light Year ASTR111 Lecture 14 Summary • Luminosity of a star: – total energy output – independent of distance • Apparent brightness of a star: – depends on the distance by the inversesquare law of brightness. – measured quantity from photometry. ASTR111 Lecture 14 Summary • Types of binary stars – Visual – Spectroscopic – Eclipsing • Only way to measure stellar masses: – Only ~150 stars • Radii are measured for very few stars. ASTR111 Lecture 14 Summary • Color of a star depends on its Temperature – Red Stars are Cooler – Blue Stars are Hotter • Spectral Classification – Classify stars by their spectral lines – Spectral differences mostly due to Temperature • Spectral Sequence (Temperature Sequence) • O B A F G K M L T ASTR111 Lecture 14 Summary • The Hertzsprung-Russell (H-R) Diagram – Plot of Luminosity vs. Temperature for stars. • Features: – Main Sequence (most stars) – Giant & Supergiant Branches – White Dwarfs • Luminosity Classification • Mass-Luminosity Relationship ASTR111 Lecture 14 Summary • Observational Clues to Stellar Structure: – H-R Diagram – Mass-Luminosity Relationship – The Main Sequence is a sequence of Mass • Equation of State for Stellar Interiors – Perfect Gas Law – Pressure = density temperature ASTR111 Lecture 14 Questions • What makes it necessary to launch satellites into space to measure very precise parallax? • Would it be easier to measure parallax from Jupiter? From Venus? ASTR111 Lecture 14 Questions • How much does the apparent brightness of stars we see in the sky vary? Why? • Stars have different colors? So is the amount of light at different wavelengths the same? • Can we tell the difference between a very luminous star that is far away and an intrinsically low luminosity star that is nearby? ASTR111 Lecture 14 Questions • What star do we know the mass of very precisely? • Why is it so unlikely that binaries are in eclipsing systems? • Most binaries are seen as spectroscopic. Why? • How can we know the sizes of more stars than masses? ASTR111 Lecture 14 Questions • What does the temperature of a star mean? • Are there stars with temperatures higher than 50000K? • Are hotter stars brighter than cooler stars? Are they more luminous? • Why did it take so long to find L & T stars? ASTR111 Lecture 14 Questions • Why don’t stars have just any Luminosity and Temperature? • Why is there a distinct Main Sequence? ASTR111 Lecture 14