1	Chapter 11 Surveying the Stars Key Concepts Properties of Stars: -Luminosity -Temperature -Masses The Hertzsrung-Russell Diagram Star Clusters
2	Stars of Different Colors
3	Luminosity for Stars Luminosity - amount of electromagnetic radiation over all wavelengths emitted by star’s entire photosphere per unit of time Measure in watts ( = joule/s) or erg/s L = (4pR²)(sT⁴) Luminosities known for several hundred stars Examples: L_sun = 3.8 x 10²⁶ watts, L_{Proxima Centauri} = 0.0006L_sun, L_Betelgeuse = 38,000L_sun Apparent brightness (luminosity-distance formula) b_star = L_star/ (4p*distance²)
4	Inverse-Square Law Must know true brightness of class of stars, membership can be based on Spectral type Luminosity type Variability Association, etc. Calculate distance from observed apparent brightness by inverse-square law
5	Is knowing the distance to stars important in understanding stars? If so, why? Yes, the distance permits us to determine the intrinsic properties of stars, such as luminosity, radius, and mass. Otherwise, we are restricted to relative values, which is a much weaker understanding of stars.
6	Stellar Parallax
7	Distance Units Light Year - distance light travels in one year at the rate of 300,000 km/s (186,000 miles/s) 1 ly = 9.46 x 10¹² km Example - Proxima Centauri, nearest star, is 4.2 ly Parsec - (parallax of one second of arc) the distance at which one AU subtends an angle of one second of arc 1 pc = 3.26 ly = 3.09 x 10¹³ km Example - Proxima Centauri is 1.3 pc from Solar System Formula: d (in parsecs) = 1 / p (in arcseconds)
8	Magnitude System of Brightness Hipparchus (2^nd century BC) measured (naked eye) apparent brightness of stars assigning them to 1 of 6 magnitude categories Bright stars - 1st magnitude Faintest stars - 6th magnitude Apparent magnitude - logarithmic measure of apparent brightness Ratio of apparent brightness of 1st to 6th magnitude defined to be 100:1 Formula: b_1st/b_6th = 100 = 2.512⁵ = 2.512^(6-1)
9	Magnitude Scale Formula: b₁/b₂ = 2.512^(m2-m1) Apparent scale is an inverted scale Bright stars are algebraically small numbers (m<0) Faint stars are algebraically large numbers (m>0)
10	Apparent Magnitude Scale for Selected Objects
11	Apparent Magnitudes for Bright Stars in Orion
12	Absolute Magnitude Absolute magnitude - apparent magnitude star would have at distance of 10 pc or 32.6 ly Formula: B/b = (d/10 pc)² = 2.512^(m-M)
13	Some Nearby Stars (<12 ly)
14	Some Bright Stars
15	Luminosity Function for Stars Numbers of stars for a given luminosity lying within 1000 pc³ Faint stars far more numerous than bright stars Steep decline toward high luminosities Shows that extremely luminous stars are rare
16	Does a star’s color depend on temperature? If so, the temperature of what? Yes Temperature of its photosphere. Stars are thermal sources of radiation.
17	Color Indices - Temperature Slope of thermal radiation curve through the visual depends on temperature Ratio of brightness in one part of spectrum, such as blue, to that in another part, such as green, depends on temperature Ratio of brightness is called a color index or just a color
18	Can temperature be determined in the photospheric absorption spectrum of a star? Yes, the ability of any atom or ion to absorb radiation at selected wavelengths depends on the temperature and density of the matter in which the atom or ion is located (the photosphere of the star).
19	Hydrogen verses Temperature
20	How hot are stars?
21	Spectral Classification Spectral classification - grouping stars according to similarities in violet, blue, and green portions of visible spectrum Seven spectral classes - O, B, A, F, G, K, M Each spectral class subdivided into 10 spectral types Spectral class A subdivided into spectral types A0, A1, A2, A3, A4, A5, A6, A7, A8, A9 Spectral class O is exception, subdivided into O4, O5, O6, O7, O8, O9
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23	Stellar Spectral Sequence
24	Stellar Spectral Sequence
25	Elements, Spectral Type and Temperature
26	Meaning of Spectral Classification Terminology for direction along spectral sequence Early-type stars - toward spectral classes O, B, A Late-type stars - toward spectral classes G, K, M Spectral classification grades stars according to photospheric temperature (66 bins) and not chemical composition Spectral appearance of star depends on temperature and density of the photosphere
27	Some Nearby Stars (<12 ly)
28	Some Bright Stars
29	How massive are stars? The overall range of stellar masses runs from 0.08 to about 100 times the mass of the Sun. We can measure the masses of stars in binary star systems using Newton’s version of Kepler’s third law, if we can measure the orbital period and separation of the two stars.
30	Why is a star’s mass it’s most important property? A star's mass at birth determines virtually everything that happens to it throughout its life. While a star is a main-sequence star, its mass determines its luminosity, surface temperature, radius, and hydrogen-burning lifetime—which is shorter for more massive stars. Once a star exhausts its core hydrogen, its mass determines how and when it grows into a giant or super-giant, and also determines what happens to it when it finally dies.
31	How is the mass of a star determined? Are there any restrictions in determining mass? The primary method for determining mass is through the motion in which stars exert significant gravitational influence on other stars, such as in a binary system. Restrictions Most be able to determine orbits or path. Sum of the masses of both stars in a binary are determined.
32	Binary Stars Binary system - two (or more) stars held by mutual gravitational attraction
33	Binary Star Orbits
34	Binary Star Classification Visual binaries - two or more stars observed Widely separated in general Fairly close to Solar System in general Spectroscopic binaries - appears as single star, Doppler shifts reveal binary nature Double-line systems - absorption spectrum of both stars visible In general, not widely separated pair of stars Single-line systems - absorption spectrum of only brighter star visible and undergoing Doppler shifts; second star too faint Eclipsing binaries - systems in which one star passes in front of other star Orbit plane contains line of sight Relative few systems, but important for amount of information obtainable on star properties
35	Orbit of 70 Ophiuchi Visual binary Orbit is that of fainter star relative to brighter Kepler’s third law yields sum of masses for system
36	Spectroscopic Binary Systems
37	Eclipsing Binary Systems
38	Frequency of Binary Systems Percentage of all stars that are part of binary system is at least 50%, probably higher Probable that all stars form in companion relation with and/or Other stars Brown dwarfs Jovian-like planets Terrestrial-like planets Even smaller bodies
39	How do we classify stars? We classify stars according to their spectral type and luminosity class. The spectral type tells us the star’s surface temperature and color. The luminosity class tells us how much light the star puts out. Giant and super-giant stars put out far more light than main-sequence stars like our Sun, even though their surface temperatures are generally lower, meaning that their radii must be much larger. All stars become giants or super-giants near the ends of their lives, and many end up as hot but dim white dwarfs.
40	Luminosity Classes Luminosity class - luminosity obtained from spectra of stars More subtle than temperature effects I very luminous supergiants II bright giants III giants (red giants) IV subgiants V main-sequence (dwarf stars) VI subdwarfs VII white dwarfs
41	Mass-Luminosity Relation for Main-Sequence Stars Observation - masses increase from spectral class M to O for main-sequence stars Mass-luminosity relation - plot of mass against luminosity (where possible) Luminosity proportional to approximately fourth power of mass Equation: L µ M⁴ Fundamental property upon which distinguishes star is mass
42	What is a Hertzsprung-Russell diagram? An H–R diagram plots stars according to their surface temperatures and luminosities. Hydrogen-burning stars occupy a narrow band in the diagram known as the main sequence. Giants and super-giants are to the upper right of the main sequence and white dwarfs are to the lower left.
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44	Luminosity Classes on the H-R Diagram Examples Sun - G2 V Sirius - A1 V Procyon - F5 IV-V Betelguese - M2 I Rigel - B8 I Names more than poetic Supergiants possess large radii Main-sequence stars possess small radii 90% of all stars are main-sequence stars
45	The correlation in the H-R diagram between luminosity and temperature is due to what physical law? Stars radiate like blackbodies. L = 4pR²sT⁴ µ R²T⁴ R = radius T = photospheric temperature (K)
46	Main Sequence Lifetime Main sequence is defined by hydrogen burning; all stars on the main sequence derive energy through hydrogen burning Time star spends on main sequence is proportional to mass divided by luminosity Equation: t_{main sequence} µ M/L Substituting mass-luminosity relation for main-sequence stars; t_{main sequence} µ M/(M⁴) µ 1/M³ How long H-burning lasts depends on star’s mass High-mass stars Þ short main-sequence life Low-mass stars Þ long main-sequence life
47	Main-Sequence Lifetime Estimates
48	Main Sequence Masses and Lifetimes
49	Stellar Clusters Stellar cluster - many stars, greater than about 100, held together by mutual gravitational attraction Star orbits in cluster unstable Motion like a random walk Categories Open (galactic) clusters Globular clusters OB Associations
50	Open Clusters Typical separation - » 2-3 ly Field stars (Sun) - » 5-6 ly Typical size - 10’s of ly Roughly spherical shape Typical numbers of stars - 10’s to 1000’s Brightest stars Either blue main sequence, giants, and supergiants Or, red giants and supergiants Number of clusters > 20,000 Located in spiral arms and disk
51	Pleiades HR Diagram Number of stars - about 500 Diameter - about 5 ly Age - about 100 million years Main sequence stars No red giant stars
52	How might one track the course of stellar evolution using star clusters? Stellar evolution proceeds according to the mass of the star. According to our theoretical understanding of stellar evolution, massive stars evolve faster than low mass stars. Star clusters are collections of different mass stars, but they formed at the same time and from the same material.
53	Main Sequence Turnoff Point Turnoff point - most massive main sequence star that has not reached hydrogen exhaustion line Indicates age of cluster from model calculations
54	How do we measure the age of a star cluster?
55	Globular Cluster M13 in Hercules
56	Globular Clusters Typical separation - » 0.2 ly Typical size - 100’s ly Nearly spherical shape Typical number of stars - 10,000’s to 100,000’s Brightest stars Always red giants and red supergiants No bright blue stars Number of globular clusters - » 150 Located in halo and near nucleus Are among the oldest stars in our Galaxy (10-13 billion years)
57	Range of Stellar Properties
58	The Big Picture Mass and age determine differences among stars; stars are hydrogen and helium structures at birth. Hertzsprung-Russell (H-R) diagram summarizes properties of stars and their evolution. Stars spend most of their lives as main-sequence stars replacing the luminosity by converting hydrogen to helium; masses of stars increases up the main sequence; the more massive the star the shorter its main-sequence lifetime will be. Star clusters provide a validation of our theoretical studies of stellar structure and evolution.