Astro 1050 Mon. Apr. 3, 017 Today: Chapter 15, Surveying the Stars Reading in Bennett: For Monday: Ch. 15 Surveying the Stars Reminders: HW CH. 14, 14 due next monday. 1
Chapter 1: Properties of Stars How much energy do stars produce? How large are stars? How massive are stars? We will find a large range in properties but we need to measure distances.
How to get distances to stars: Parallax The angular diameter here is p the parallax in arcsec. The linear diameter is 1 AU. d = 0665/p in AUs d = 1/p in units of parsecs 1 parsec or 1pc = 0665 AU 1 pc = 3.6 light years From Horizons by Seeds 3
Intrinsic Brightness of Stars Apparent Brightness: How bright star appears to us Intrinsic Brightness: Inherent corrected for distance How does brightness change with distance? Flux = energy per unit time per unit area: joule/sec/m = watts/m Example: 100 watt light bulb (assume this is 100 W of light energy) spread over 5 m desk gives 0 Watts/m Sun s flux at the Earth Luminosity = 3.8 10 6 Watts It has spread out over sphere of radius 1 AU = 1.5 10 11 m Surface area of sphere = 4 π R =.8 10 3 m F Sun = 3.8 10 6 Watts /.8 10 3 m = 1357 W/m Inverse Square Law: Flux falls of as 1/distance 4
Inverse-square law for light: Inverse Square Law: Flux falls of as 1/distance Double distance flux drops by 4 Triple distance flux drops by 9 5
Correcting Magnitudes for Distance To correct intensity or flux for distance, use Inverse Square Law Fdistance A L /(4π r ) A rb = = distance B /(4 ) F L πr r B A Up to now we have used apparent magnitudes m v Define absolute magnitude M v as magnitude star would have if it were at a distance of 10 pc. m A m M m B = m =.5log( I / I ) A = true distanced, B= 10pc d m 10 pc B A I =.5log I 10 pc distance d This gives us a way to correct Magnitude for distance, or find distance if we know absolute magnitude. Note: the book writes m v and M v : The V stands for Visual -- Later we ll consider magnitudes in other colors like B=Blue U=Ultraviolet d =.5log 10 pc d m M = 5 + 5 log d = 10 ( m M + 5) / 5 1pc d = 5 + 5 log 1pc 6
Some Examples: Fill in the Table: m V M V d (pc) P (arcsec) 7 10 11 1000-0.05 4 0.040 7
Some Examples: Filling in the Table: m M V d (pc) P (arcsec) 7 7 10 0.1 11 1 1000 0.001 1-40 0.05 4 5 0.040 8
How to recognize patterns in data What patterns matter for people and how do we recognize them? Weight and Height are easy to measure Knowing how they are related gives insight into health A given weight tends to go with a given height Weight either very high or very low compared to trend ARE important Plot weight vs. height and look for deviations from simple line Example of cars from the book Note main sequence of cars Weight plotted backwards Just make main sequence a line which goes down rather than up Points off main sequence are unusual cars From our text: Horizons, by Seeds 9
Stars: Patterns of Lum., Temp., Rad. The Hertzsprung-Russsell (H-R) diagram Plot L vs. Decreasing T. (We can find R given L and T) From Horizons, by Seeds 10
How are L, T, and R related? L = area σt 4 = 4 π R σt 4 Stars can be intrinsically bright because of either large R or large T Use ratio equations to simplify above equation (Note book s symbol for Sun is circle with dot inside) L L Sun = 4πR 4πR Sun σt σt 4 Sun Example: Assume T is different but size is same A star is ~ as hot as sun, expect L is 4 = 16 times as bright M star is ~1/ as hot as sun, expect L is -4 = 1/16 as bright 4 = B star is ~ 4 as hot as sun, expect L is 4 4 = 56 times as bright Example: Assume T same but size is different If a G star 4 as large as sun, expect L would be 4 =16 times as bright R R Sun T T Sun 4 11
L, T, R, and the H-R diagram L = 4 π R σt 4 The main sequence consists very roughly of similar size stars The giants, supergiants, and white dwarfs are much larger or smaller From our text: Horizons, by Seeds 1
Lines of constant R in the H-R diagram Main sequence not quite constant R B stars: R ~10 R Sun M stars: R ~0.1 R Sun Betelgeuse: R~ 1,000 R Sun Larger than 1 AU White dwarfs: R~ 0.01 R Sun A few Earth radii From our text: Horizons, by Seeds What causes the main sequence? Why similar size, with precise R related to T? Why range of T? Why are a few stars (giants, 13 white dwarfs) not on main sequence?
14
Different types of H-R diagrams Hertzsprung-Russell diagram will appear over and over again in class Deviations from patterns useful for understanding evolution of stars Equivalent kinds of plots: Luminosity vs. Temperature (what we ve been showing) Absolute Magnitude vs. Spectral Type (the original H-R diagram) Apparent Magnitude vs. Spectral Type Patterns still the same if all stars are at same difference All stars will be shifted vertically by the same amount: m-m= -5 + 5 log(d) Magnitude vs. Color (called color-magnitude diagrams ) 15
Luminosity Classes Ia Bright supergiant Ib Supergiant II Bright giant III Giant IV Subgiant V Main sequence star white dwarfs not given Roman numeral Sun: G V Rigel: B8 Ia Betelgeuse: M Iab From our text: Horizons, by Seeds 16
Spectra of Different Luminosity Classes Presence of different lines determined by Spectral Class (temperature) Width of individual lines determined by Luminosity Class Pressure broadening : High density (so high pressure) frequent atomic collisions Energy levels shifted by nd nearby atom broad lines Main sequence stars are high density and pressure Supergiants are low density and pressure Something can cause a main sequence star to expand to a large size to form a giant or supergiant From our text: Horizons, by Seeds 17
What fundamental property of a star varies along the main sequence? T and R vary smoothly (and together) along the main sequence B stars are ~4 times hotter and ~10 times bigger than sun M stars are ~ times cooler and ~10 times smaller than sun Presence of a line implies that a single fundamental property is varying to make some stars B stars and some stars M stars That fundamental property then controls T, R A second property controls whether we get a giant or dwarfs Fundamental properties we could measure Location: Doesn t seem to be of major importance Composition: Outside composition of stars similar (H, He,...) Age: Will be important but put off till Chapter 9 Mass: Turns out to be the most important parameter 18
Masses From Binary stars From our text: Horizons, by Seeds Newton s form of Kepler s 3 rd law for planets: 4π P = GM a Modified form when mass of planet gets very large P = G( M 3 4π 3 + a A M B ) 3 4π a M A + M B = G P Dividing by same equation for Earth-Sun and canceling constants gives: M + M M A B = Sun ( a /1AU) ( P /1yr) 3 19
Masses of Binary stars M + M M A B = Sun ( a /1AU) ( P /1yr) 3 An example. Suppose we measured the period in a spectroscopic binary and knew the spectral types (and hence the masses, as we shall see) of the component stars. The period is years (P = years) and the stars are a G star (1 solar mass) and a M star (0.5 solar masses). What is the separation? From our text: Horizons, by Seeds 0
Masses of Binary stars M + M M A B = Sun ( a /1AU) ( P /1yr) 3 An example. Suppose we measured the period in a spectroscopic binary and knew the spectral types (and hence the masses, as we shall see) of the component stars. The period is years (P = years) and the stars are a G star (1 solar mass) and a M star (0.5 solar masses). What is the separation? M A +M B = 1.5 M Sun 1.5 x () = (a/1 AU) 3 6 = (a/1 AU) 3 From our text: Horizons, by Seeds 1.8 AU = a 1
Measuring a and P of binaries Two types of binary stars Visual binaries: See separate stars a large, P long Can t directly measure component of a along line of sight Spectroscopic binaries: See Doppler shifts in spectra a small, P short Can t directly measure component of a in plane of sky If star is visual and spectroscopic binary get get full set of information and then get M
Masses and the HR Diagram Main Sequence position: M: 0.5 M Sun G: 1 M Sun B: 40 M sun Luminosity Class Must be controlled by something else From our text: Horizons, by Seeds 3
The Mass-Luminosity Relationship L = M 3.5 Implications for lifetimes: 10 M Sun star Has 10 mass Uses it 10,000 faster Lifetime 1,000 shorter From our text: Horizons, by Seeds 4
Eclipsing Binary Stars System seen edge-on Stars pass in front of each other Brightness drops when either is hidden Used to measure: size of stars (relative to orbit) relative surface brightness area hidden is same for both eclipses drop bigger when hotter star hidden tells us system is edge on useful for spectroscopic binaries From our text: Horizons, by Sees 5