Chapter 15 15.1 Properties of Stars Surveying the Stars Our goals - PDF document

Chapter 15 15.1 Properties of Stars Surveying the Stars • Our goals for learning • How do we measure stellar luminosities? • How do we measure stellar temperatures? • How do we measure stellar masses? How do we measure stellar luminosities? The brightness of a star depends on both distance and luminosity Luminosity: Luminosity passing through each sphere is the Amount of power a star same radiates (energy per second = Watts) Area of sphere: 4 π (radius) 2 Apparent brightness: Amount of starlight that Divide luminosity by area reaches Earth to get brightness (energy per second per square meter) 1

The relationship between apparent brightness and luminosity depends on distance: Luminosity Brightness = 4 π (distance) 2 We can determine a star’s luminosity if we can measure its distance and apparent brightness: Luminosity = 4 π (distance) 2 x (Brightness) So how far are these stars? Parallax Apparent is the apparent positions of shift in nearest stars position of a nearby object shift by against a about an background of arcsecond more distant as Earth objects orbits Sun Parallax angle Parallax is depends on measured by distance comparing snapshots taken at different times and measuring the shift in angle to star 2

Parallax and Distance p = parallax angle 1 d (in parsecs) = p (in arcseconds) 1 d (in light - years) = 3.26 × p (in arcseconds) Most luminous stars: The Magnitude Scale 10 6 L Sun m = apparent magnitude , M = absolute magnitude Least luminous stars: apparent brightness of Star 1 apparent brightness of Star 2 = (100 1/ 5 ) m 1 − m 2 10 -4 L Sun (L Sun is luminosity luminosity of Star 1 luminosity of Star 2 = (100 1/5 ) M 1 − M 2 of Sun) How do we measure stellar temperatures? Every object emits thermal radiation with a spectrum that depends on its temperature 3

Properties of Thermal Radiation An object of fixed size grows more 1. Hotter objects emit more light per unit area at all luminous as its frequencies. temperature rises 2. Hotter objects emit photons with a higher average energy. Hottest stars: 10 6 K Level of ionization also reveals a star’s 50,000 K 10 5 K Ionized temperature Gas Coolest stars: 10 4 K (Plasma) 3,000 K 10 3 K Neutral Gas (Sun’s surface 10 2 K Molecules is 5,800 K) 10 K Solid Lines in a star’s spectrum correspond to a spectral type that reveals its temperature Absorption lines in star’s spectrum tell us ionization level (Hottest) O B A F G K M (Coolest) 4

Pioneers of Stellar Classification Remembering Spectral Types (Hottest) O B A F G K M (Coolest) • Annie Jump Cannon and the • Oh, Be A Fine Girl, Kiss Me “calculators” at Harvard laid the • Only Boys Accepting Feminism Get Kissed foundation of Meaningfully modern stellar classification How do we measure stellar masses? The orbit of a binary star system depends on strength of gravity Visual Binary Types of Binary Star Systems • Visual Binary • Eclipsing Binary • Spectroscopic Binary We can directly observe the orbital motions of these stars About half of all stars are in binary systems 5

Eclipsing Binary Spectroscopic Binary We can measure periodic eclipses We determine the orbit by measuring Doppler shifts We measure mass using gravity Need 2 out of 3 observables to measure mass: Direct mass measurements are possible only for stars in binary star systems 1) Orbital Period ( p ) 4 π 2 2) Orbital Separation ( a or r = radius) p 2 = a 3 v G (M 1 + M 2 ) 3) Orbital Velocity ( v ) p = period r a = average separation M For circular orbits, v = 2 π r / p Isaac Newton Most massive What have we learned? stars: • How do we measure stellar luminosities? 100 M Sun – If we measure a star’s apparent brightness and distance, we can compute its luminosity with the inverse square law for light Least massive – Parallax tells us distances to the nearest stars stars: • How do we measure stellar temperatures? 0.08 M Sun – A star’s color and spectral type both reflect its temperature ( M Sun is the mass of the Sun) 6

What have we learned? 15.2 Patterns among Stars • How do we measure stellar masses? – Newton’s version of Kepler’s third law tells us • Our goals for learning the total mass of a binary system, if we can measure the orbital period ( p ) and average • What is a Hertzsprung-Russell diagram? orbital separation of the system ( a ) • What is the significance of the main sequence? • What are giants, supergiants, and white dwarfs? • Why do the properties of some stars vary? An H-R What is a Hertzsprung-Russell diagram plots the diagram? luminosity and Luminosity temperature of stars Temperature Most stars fall somewhere on the main sequence of the H-R diagram 7

Large radius Stars with lower Stars with higher T and higher L T and lower L than main- than main- sequence stars sequence stars must have larger must have radii: smaller radii: giants and white dwarfs supergiants Small radius H-R diagram A star’s full classification includes spectral type depicts: (line identities) and luminosity class (line shapes, related to the size of the star): Temperature I - supergiant Color II - bright giant Luminosity Spectral Type III - giant Luminosity IV - subgiant V - main sequence Radius Examples: Sun - G2 V Sirius - A1 V Proxima Centauri - M5.5 V Betelgeuse - M2 I Temperature Main-sequence stars are fusing What is the significance of the hydrogen into main sequence? helium in their cores like the Sun Luminous main- sequence stars are hot (blue) Less luminous ones are cooler (yellow or red) 8

Mass The mass of a High-mass stars measurements of High-mass stars normal, hydrogen- main-sequence burning star stars show that the determines its hot, blue stars are luminosity and much more spectral type! massive than the cool, red ones Low-mass stars Low-mass stars Core pressure and Stellar Properties Review temperature of a higher-mass star Luminosity: from brightness and distance need to be larger in order to balance 10 -4 L Sun - 10 6 L Sun gravity Temperature: from color and spectral type Higher core 3,000 K - 50,000 K temperature boosts fusion rate, Mass: from period (p) and average separation (a) leading to larger of binary-star orbit luminosity 0.08 M Sun - 100 M Sun Stellar Properties Review Mass & Lifetime Luminosity: from brightness and distance Sun’s life expectancy: 10 billion years 10 -4 L Sun - 10 6 L Sun (0.08 M Sun ) (100 M Sun ) Temperature: from color and spectral type (0.08 M Sun ) (100 M Sun ) 3,000 K - 50,000 K Mass: from period (p) and average separation (a) of binary-star orbit 0.08 M Sun - 100 M Sun 9

Mass & Lifetime Mass & Lifetime Until core hydrogen Until core hydrogen (10% of total) is (10% of total) is used up used up Sun’s life expectancy: 10 billion years Sun’s life expectancy: 10 billion years Life expectancy of 10 M Sun star: 10 times as much fuel, uses it 10 4 times as fast 10 million years ~ 10 billion years x 10 / 10 4 Main-Sequence Star Summary Mass & Lifetime Until core hydrogen High Mass: (10% of total) is used up High Luminosity Sun’s life expectancy: 10 billion years Short-Lived Life expectancy of 10 M Sun star: Large Radius Blue 10 times as much fuel, uses it 10 4 times as fast 10 million years ~ 10 billion years x 10 / 10 4 Low Mass: Life expectancy of 0.1 M Sun star: Low Luminosity Long-Lived 0.1 times as much fuel, uses it 0.01 times as fast Small Radius Red 100 billion years ~ 10 billion years x 0.1 / 0.01 What are giants, supergiants, and Off the Main Sequence white dwarfs? • Stellar properties depend on both mass and age: those that have finished fusing H to He in their cores are no longer on the main sequence • All stars become larger and redder after exhausting their core hydrogen: giants and supergiants • Most stars end up small and white after fusion has ceased: white dwarfs 10

Why do the properties of some stars vary? Variable Stars Pulsating Variable Stars • Any star that varies significantly in brightness with time is called a variable star • Some stars vary in brightness because they cannot achieve proper balance between power welling up from the core and power radiated from the surface • Such a star alternately expands and contracts, • The light curve of this pulsating variable star shows varying in brightness as it tries to find a balance that its brightness alternately rises and falls over a 50-day period What have we learned? Cepheid Variable Stars • What is a Hertzsprung-Russell diagram? • Most pulsating – An H-R diagram plots stellar luminosity of variable stars inhabit stars versus surface temperature (or color or an instability strip spectral type) on the H-R diagram • What is the significance of the main sequence? • The most luminous ones are known as – Normal stars that fuse H to He in their cores Cepheid variables fall on the main sequence of an H-R diagram – A star’s mass determines its position along the main sequence (high-mass: luminous and blue; low-mass: faint and red) 11