DISTANCES

Parallax is an object's apparent shift relative to some more distant background as the observer's point of view changesParallax 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.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.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?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.We get an answer of 206,265 A.U.

Astronomers call this distance 1 parsec (1 pc), from "parallax in arc seconds."Astronomers call this distance 1 parsec (1 pc), from "parallax in arc seconds."

Calculating Parallax:Calculating Parallax: Sirius displays a large known stellar parallax, 0.377”. Calculate its distance in parsecs and in light yearsSirius 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 years1 pc = 3.26 light years, so d = 8.65 light years

Astronomers measure the apparent brightnessAstronomers measure the apparent brightness This is compared to the star’s luminosity (actual brightness)This is compared to the star’s luminosity (actual brightness) Distance is calculated by comparing the two valuesDistance is calculated by comparing the two values

Distances to galaxies can be measured via:Distances to galaxies can be measured via: RedshiftRedshift Brightness of supernovaeBrightness of supernovae

Temperature The color of a star indicates its relative temperature – blue stars are hotter than red starsThe 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 lawMore precisely, a star’s surface temperature is given by Wien’s law 3x10 6 3x10 6 λ m λ m T = star’s surface temperature in Kelvin λ m = strongest wavelength in nanometers (nm) 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)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 wattA typical unit of measurement for luminosity is the watt Compare a 100-watt bulb to the Sun’s luminosity, 4x10 26 wattsCompare a 100-watt bulb to the Sun’s luminosity, 4x10 26 watts

Luminosity Luminosity is a measure of a star’s energy production (or hydrogen fuel consumption)Luminosity is a measure of a star’s energy production (or hydrogen fuel consumption) Luminosity is determined by diameter and temperatureLuminosity is determined by diameter and temperature

The inverse–square law relates an object’s luminosity to its distance (apparent brightness)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 distanceAs 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 magnitudesAbout 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 6Brightest stars had magnitude 1 and dimmest had magnitude 6 A star’s apparent magnitude depends on the star’s luminosity and distance.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 magnitude difference = brightness ratio of 100 1/5 =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 wavelengthA 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 radiusA 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 NHistorically, 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 classesAnnie 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

Measuring a Star’s Motion A star’s radial motion is determined from the Doppler shift of its spectral linesA star’s radial motion is determined from the Doppler shift of its spectral lines The amount of shift depends on the star’s radial velocityThe amount of shift depends on the star’s radial velocity Δλ = the shift in wavelength of an absorption lineΔλ = the shift in wavelength of an absorption line λ = resting wavelength, the radial speed v is given by:λ = resting wavelength, the radial speed v is given by: V = Δλ/ λ c where c is the speed of light

Hertzsprung-Russell DiagramSurface 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

main sequenceThe 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.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 elseStars that are not on the main sequence are doing something else

The Mass-Luminosity RelationThe Mass-Luminosity Relation –Main-sequence stars obey a mass- luminosity relation, approximately given by: L = M 3 where L and M are measured in solar units –Consequence: Stars at top of main- sequence are more massive than stars lower down

Another look

Dwarf starsDwarf stars are comparable in size (or smaller) to the Sun GiantsGiants range from 10 to 100 times the radius of the Sun SupergiantsSupergiants 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 EarthWhite dwarfs stars are around the size of the Earth

Visual binariesVisual binaries –actually see the stars moving around each other Spectroscopic binariesSpectroscopic binaries –make use of the Doppler shift of the spectral lines of the stars Eclipsing binariesEclipsing binaries –binaries may be orbiting in such a way that one star moves in front of the other as in an eclipse

u Shape: Irregular, no specific shape u Where: Galactic disk u Types of Stars: Population I u Age of Stars: Young!

u Shape: Spherical u Where found: Galactic Halo u Types of Stars: Population II u Age of Stars: Old

Stellar motion has two components: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 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 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.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 velocityIt describes the transverse component of a star's velocity