Lecture 14: Studying the stars. Astronomy 111 Monday October 16, 2017

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1 Lecture 14: Studying the stars Astronomy 111 Monday October 16, 2017

2 Reminders Homework #7 due Monday I will give a lecture on DES and LIGO tomorrow at 4pm in the Mitchell Institute

3 Studying the stars 1. How far? 2. How bright? 3. How massive? 4. How big? 5. How hot?

4 1. How far? 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

5 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 An astronomical object A: You resort to using GEOMETRY.

6 Method of trigonometric parallaxes June p December Foreground Star Distant Stars

7 Parallax decreases with distance Closer stars have larger parallaxes: Distant stars have smaller parallaxes:

8 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.

9 Parallax formula d 1 p p = parallax angle in arcseconds d = distance in Parsecs

10 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 3.085x10 13 km

11 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!

12 Examples a Centauri has a parallax of p=0.76 arcsec: A distant star has a parallax of p=0.02 arcsec:

13 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

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!

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

15 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

16 2. 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.

17 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.

18 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.

19 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.

20 Inverse Square Law of Brightness The apparent brightness of a source is inversely proportional to the square of its distance: B 1 d 2 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

21 Flux-luminosity relationship Relates apparent brightness (Flux) and intrinsic brightness (Luminosity) through the Inverse Square Law of Brightness: Flux = Luminosity 4 d 2

22 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)

23 Magnitude system Traditional system dating to classical times (Hipparchus of Rhodes, c. 300 BC) Rank stars according to apparent brightness 1 st magnitude are brightest stars 2 nd magnitude are the next brightest and so on... Faintest naked-eye stars are 6 th magnitude. Modern version quantifies this system 5 steps of magnitude = factor of 100 in Flux. Computationally convenient, but somewhat obtuse.

24 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.

25 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.

26 3. How massive? Binary stars as a way to measure mass 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.

27 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.

28 Visual Binary Observations of the 70 Ophiuchi binary system. Period=88 years

29 Center of mass Two stars orbit about their center of mass: a 2 a 1 M 2 a M 1 Measure semi-major axis, a, from projected orbit and the distance. Relative positions give: M 1 / M 2 = a 2 / a 1

30 Measuring masses Newton s Form of Kepler s Third Law: P 2 = a G( M + M ) 1 2 Measure period, P, by following the orbit. Measure semi-major axis, a, and mass ratio (M 1 /M 2 ) from projected orbit.

31 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 d 3!!

32 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.

33 Spectroscopic binaries B A B B A A A ASTR111 Lecture 14 B

34 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.

35 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!

36 Brightness ASTR111 Lecture 14 Eclipsing binaries Time

37 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.

38 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.

39 4. How big? Measuring 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

40 5. How hot? Studying the 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=10,000-50,000 K) middle stars appear YELLOW (T~6000K) cool stars appear RED (T~3000K)

42 5. How hot? Continued Studying the 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.

44 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 ( ): Objective prism photography Obtained spectra of >100,000 stars Hired women as computers to analyze spectra ASTR111 Lecture 14

45 Harvard Computers (c. 1900) ASTR111 Lecture 14

46 Objective prism spectra ASTR111 Lecture 14

Harvard classification Edward Pickering s first attempt at a systematic spectral classification: Sort by Hydrogen absorption-line strength

47 Harvard classification 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: Edward Pickering Other lines followed no discernible patterns.

48 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

49 The spectral sequence O B A F G K M L T Hotter Cooler 50,000K 2000K Bluer Redder Spectral sequence is a Temperature sequence

50 Spectral types ASTR111 Lecture 14

51 Stellar spectra in order from the hottest (top) to coolest (bottom).

52 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.

53 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.

55 O Stars Hottest Stars: T>30,000 K Strong lines of He + No lines of H

56 B Stars T=15,000-30,000 K Strong lines of He Very weak lines of H

57 A Stars T = 10, K Strong lines of H Weak lines of Ca+

58 F Stars T = K weaker lines of H Ca + lines growing stronger first weak metal lines appear

59 G Stars T = K Strong lines of Ca +, Fe +, & other metals much weaker H lines The Sun is a G-type Star

60 K Stars Cool Stars: T = K Strongest metal lines H lines practically gone first weak CH & CN molecular bands

61 M Stars Very cool stars: T K Strong molecular bands (especially TiO) No lines of H

62 L & T Stars Coolest stars: T < 2000 K Discovered in 1999 Strong molecular bands Metal-hydride (CrH & FeH) Methane (CH 4 ) in T stars Probably not stars at all

63 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

64 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)

65 Summary of stellar properties Large range of Stellar Luminosities: 10-4 to 10 6 L sun Large range of Stellar Radii: 10-2 to 10 3 R sun Modest range of Stellar Temperatures: 3000 to >50,000 K Wide Range of Stellar Masses: 0.1 to ~50 M sun

66 Luminosity-Radius-Temperature Relation Stars are approximately black bodies. Stefan-Boltzmann Law: energy/sec/area = st 4 The area of a spherical star: area = 4 R 2 Predicted Stellar Luminosity (energy/sec): L = 4 R 2 st 4

67 In class assignment: 2 stars are the same size, (R A =R B ), but star A is 2 hotter than star B (T A =2T B ) How much brighter is star A than star B? 2 stars are the same temperature, (T C =T D ), but star A is 2 bigger than star B (R C =2R D ) How much brighter is star C than star D?

68 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

69 Eljnar Hertzsprung Henry Norris Russell

70 Luminosity (L sun ) H-R Diagram 10 6 Supergiants Giants White Dwarfs 40,000 20,000 10,000 5,000 2,500 Temperature (K) ASTR111 Lecture 14

71 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 10 6 L sun T=3000 to >50,0000 K R=0.1 to 10 R sun

72 Giants & Supergiants Two bands of stars brighter than Main Sequence stars of the same Temperature. Means they must be larger in radius. Giants R= R sun L= L sun T<5000 K Supergiants R>10 3 R sun L= L sun T= ,000 K ASTR111 Lecture 14

73 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 R sun (~ size of Earth!)

74 Hipparcos H-R Diagram 4902 single stars with distance errors of <5%

75 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!

76 Luminosity Effects in Spectra ASTR111 Lecture 14

77 Luminosity Classes: Ia = Bright Supergiants Ib = Supergiants II = Bright Giants III = Giants IV = Subgiants V = Dwarfs = Main-Sequence Stars

78 Spectral + Luminosity Classification of Stars: Sun: G2V (G2 Main-Sequence star) Stars that can be seen in the 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)

79 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

80 Luminosity (L sun ) ASTR111 Lecture 14 H-R Diagram 10 6 Supergiants Giants White Dwarfs 40,000 20,000 10,000 5,000 2,500 Temperature (K)

81 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: ~R earth but with ~M sun!

82 Mass-Luminosity Relationship For Main-Sequence stars: L L M sun M sun In words: More massive M-S stars are more luminous. Not true of Giants, Supergiants, or White Dwarfs. 3.5

83 Luminosity (L sun ) ASTR111 Lecture L M Mass (M sun )

84 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: 10 5 g/cc

85 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.

86 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

87 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.

88 Summary Types of binary stars Visual Spectroscopic Eclipsing Only way to measure stellar masses: Only ~150 stars Radii are measured for very few stars.

89 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

90 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

91 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

92 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?

93 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?

94 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?

95 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?

96 Questions Why don t stars have just any Luminosity and Temperature? Why is there a distinct Main Sequence?

Lecture 12: Distances to stars. Astronomy 111

Lecture 12: Distances to stars Astronomy 111 Why are distances important? Distances are necessary for estimating: Total energy released by an object (Luminosity) Masses of objects from orbital motions