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DISTANCES • Parallax is an object's apparent shift relative to some more distant background as the observer's point of view changes • As the distance to the object increases, the parallax becomes smaller and therefore harder to measure. • Astronomers measure parallax in arc seconds rather than in degrees. • At what distance must a star lie in order for its observed parallax to be exactly 1 arc-sec? • We get an answer of 206,265 A.U. • Astronomers call this distance 1 parsec (1 pc), from "parallax in arc seconds." • Calculating Parallax: • Sirius displays a large known stellar parallax, 0.377”. Calculate its distance in parsecs and in light years d = 1/p d = 1/0.377 d = 2.65 pc away • 1 pc = 3.26 light years, so d = 8.65 light years • Astronomers measure the apparent brightness • This is compared to the star’s luminosity (actual brightness) • Distance is calculated by comparing the two values • Distances to galaxies can be measured via: • Redshift • Brightness of supernovae Temperature • The color of a star indicates its relative temperature – blue stars are hotter than red stars • More precisely, a star’s surface temperature is given by Wien’s law 3x106 λm T = star’s surface temperature in Kelvin λ m = strongest wavelength in nanometers (nm) LUMINOSITY & APPARENT BRIGHTNESS Luminosity • The amount of energy a star emits each second is its luminosity (usually abbreviated as L) • A typical unit of measurement for luminosity is the watt • Compare a 100-watt bulb to the Sun’s luminosity, 4x1026 watts Luminosity • Luminosity is a measure of a star’s energy production (or hydrogen fuel consumption) • Luminosity is determined by diameter and temperature • The inverse–square law relates an object’s luminosity to its distance (apparent brightness) • As the distance to a star increases, the apparent brightness decrease with the SQUARE of the distance • About 150 B.C., the Greek astronomer Hipparchus measured apparent brightness of stars using units called magnitudes • Brightest stars had magnitude 1 and dimmest had magnitude 6 • A star’s apparent magnitude depends on the star’s luminosity and distance. Magnitude differences equate to brightness ratios: • A difference of 5 magnitudes = a brightness ratio of 100 • 1 magnitude difference = brightness ratio of 1001/5=2.512 “Absolute magnitude” is a measure a star’s luminosity –The absolute magnitude of a star is the apparent magnitude that same star would have at 10 parsecs –An absolute magnitude of 0 approximately equates to a luminosity of 100L¤ Spectral Types Spectra of Stars Introduction • A star’s spectrum typically depicts the energy it emits at each wavelength • A spectrum also can reveal a star’s composition, temperature, luminosity, velocity in space, rotation speed, and it may reveal mass and radius Spectra of Stars Measuring a Star’s Composition –A star’s spectrum = absorption spectrum –Every atom creates its own unique set of absorption lines –Match a star’s absorption lines with known spectra to determine surface composition Classification of Stellar Spectra • Historically, stars were first classified into four groups based on color (white, yellow, red, and deep red), then into classes using the letters A through N • Annie Jump Cannon: classes were more orderly if arranged by temperature – Her new sequence became O, B, A, F, G, K, M (O being the hottest and M the coolest) and are today known as spectral classes Spectral Class O B A Surface Temp Absorption Example Lines Ionized He 30,000 K Weak H He, H 20,000 K moderate Rigel Vega 10,000 K Strong H Sirius Spectral Surface Class Temp F 7,000 K G 6,000 K K 4,000 K M 3,000 K Absorption Example Lines Mod. H, Canopus Metals Mod. H, Sun Metals Metals Arcturus strong Metals Betelgeuse strong Measuring a Star’s Motion • A star’s radial motion is determined from the Doppler shift of its spectral lines • The amount of shift depends on the star’s radial velocity • Δλ = the shift in wavelength of an absorption line • λ = resting wavelength, the radial speed v is given by: V = Δλ/ λ • c where c is the speed of light • Surface temperature and luminosity can be plotted to make the single most important graph for the study of stars, the Hertzsprung-Russell Diagram • Luminosity (y-axis) increases upwards, and temperature (x-axis) increases to the left • The majority of stars lie along a band (not a sharp line) from top left to bottom right called the main sequence. • On the main sequence, hot stars are the most luminous, (top left) and cool stars are the least luminous (bottom right). • We now know that the main sequence comprises all the stars that are converting hydrogen to helium in their cores. • Stars that are not on the main sequence are doing something else • The Mass-Luminosity Relation – Main-sequence stars obey a massluminosity relation, approximately given by: L = M3 where L and M are measured in solar units – Consequence: Stars at top of mainsequence are more massive than stars lower down Another look • Dwarf stars are comparable in size (or smaller) to the Sun • Giants range from 10 to 100 times the radius of the Sun • Supergiants range from 100 to 1000 solar radii The range in sizes of Main Sequence stars is about 0.1 to 100 solar radii. Supergiants can be enormous. Betelgeuse would reach out to the orbit of Mars. • White dwarfs stars are around the size of the Earth • Visual binaries – actually see the stars moving around each other • Spectroscopic binaries – make use of the Doppler shift of the spectral lines of the stars • Eclipsing binaries – binaries may be orbiting in such a way that one star moves in front of the other as in an eclipse Shape: Irregular, no specific shape Where: Types Galactic disk of Stars: Population I Age of Stars: Young! Shape: Spherical Where found: Galactic Halo Types of Stars: Population II Age of Stars: Old http://www.astrographics.com/GalleryPrints/Display/GP0046.jpg http://images.astronet.ru/pubd/2008/05/07/0001227653/OmegaCen_spitzer_c800.jpg • Stellar motion has two components: • The transverse component measures a star's motion perpendicular to our line of sight—in other words, its motion across the sky. • The radial component measures a star's movement along our line of sight— toward us or away from us. • The annual movement of a star across the sky, as seen from Earth (and corrected for parallax), is called proper motion. • It describes the transverse component of a star's velocity