DISTANCESDISTANCES

•Parallax is an object's apparent Parallax is an object's apparent shift relative to some more shift relative to some more distant background as the distant background as the observer's point of view observer's point of view changeschanges

•As the distance to the As the distance to the object increases, the object increases, the parallax becomes parallax becomes smaller and therefore smaller and therefore harderharder to measure. to measure.

• Astronomers measure parallax in Astronomers measure parallax in arc seconds arc seconds rather than in degreesrather than in degrees..

• At what distance must a star lie in At what distance must a star lie in order for its observed parallax to be order for its observed parallax to be exactly 1 arc-sec?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 Astronomers call this distance 1 parsec (1 pc), from "parsec (1 pc), from "parparallax in arc allax in arc secseconds."onds."

• Calculating Parallax:Calculating Parallax:• Sirius displays a large known Sirius displays a large known

stellar parallax, 0.377”. Calculate stellar parallax, 0.377”. Calculate its distance in parsecs and in light its distance in parsecs and in light yearsyears

d = 1/pd = 1/pd = 1/0.377d = 1/0.377

d = 2.65 pc awayd = 2.65 pc away• 1 pc = 3.26 light years, so d = 1 pc = 3.26 light years, so d =

8.65 light years8.65 light years

• Astronomers measure the apparent Astronomers measure the apparent brightnessbrightness

• This is compared to the star’s This is compared to the star’s luminosity (actual brightness)luminosity (actual brightness)

• Distance is calculated by comparing Distance is calculated by comparing the two valuesthe two values

• Distances to galaxies can be Distances to galaxies can be measured via:measured via:

• RedshiftRedshift• Brightness of supernovaeBrightness of supernovae

TemperatureTemperature• The color of a star indicates its relative The color of a star indicates its relative

temperature – blue stars are hotter than red starstemperature – blue stars are hotter than red stars• More precisely, a star’s surface temperature is More precisely, a star’s surface temperature is

given by Wien’s law given by Wien’s law

3x103x1066

λλmm

T = star’s surface temperature in KelvinT = star’s surface temperature in Kelvin

λλ mm = strongest wavelength in nanometers (nm) = strongest wavelength in nanometers (nm)

LUMINOSITY & LUMINOSITY & APPARENT BRIGHTNESSAPPARENT BRIGHTNESS

LuminosityLuminosity

• The amount of energy a star emits The amount of energy a star emits each second is its luminosity each second is its luminosity (usually abbreviated as (usually abbreviated as LL))

• A typical unit of measurement for A typical unit of measurement for luminosity is the wattluminosity is the watt

• Compare a 100-watt bulb to the Compare a 100-watt bulb to the Sun’s luminosity, 4x10Sun’s luminosity, 4x102626 watts watts

LuminosityLuminosity

• Luminosity is a measure of a star’s Luminosity is a measure of a star’s energy production (or hydrogen energy production (or hydrogen fuel consumption)fuel consumption)

• Luminosity is determined by Luminosity is determined by diameter and temperaturediameter and temperature

• The The inverse–square lawinverse–square law relates an relates an object’s luminosity to its distance object’s luminosity to its distance (apparent brightness)(apparent brightness)

• As the distance to a star increases, the As the distance to a star increases, the apparent brightness decrease with the apparent brightness decrease with the SQUARE of the distanceSQUARE of the distance

• About 150 B.C., the Greek astronomer About 150 B.C., the Greek astronomer Hipparchus measured apparent Hipparchus measured apparent brightness of stars using units calledbrightness of stars using units called magnitudesmagnitudes

• Brightest stars had magnitude 1 and Brightest stars had magnitude 1 and dimmest had magnitude 6dimmest had magnitude 6

• A star’s apparent magnitude depends A star’s apparent magnitude depends on the star’s luminosity and distanceon 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 Absolute magnitude” is a measure a star’s star’s luminosityluminosity

–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¤

http://www.youtube.com/watch?v=8DC5D2jU_L4

Spectral Spectral TypesTypes

Spectra of StarsSpectra of StarsIntroductionIntroduction• A star’s spectrum typically depicts A star’s spectrum typically depicts

the energy it emits at each the energy it emits at each wavelengthwavelength

• A spectrum also can reveal a star’s A spectrum also can reveal a star’s composition, temperature, composition, temperature, luminosity, velocity in space, rotation luminosity, velocity in space, rotation speed, and it may reveal mass and speed, and it may reveal mass and radiusradius

Spectra of StarsSpectra of StarsMeasuring a Star’s CompositionMeasuring a Star’s Composition

–A star’s spectrum = absorption A star’s spectrum = absorption spectrumspectrum

–Every atom creates its own unique Every atom creates its own unique set of absorption linesset of absorption lines

–Match a star’s absorption lines with Match a star’s absorption lines with known spectra to determine surface known spectra to determine surface compositioncomposition

Classification of Stellar SpectraClassification of Stellar Spectra

• HistoricallyHistorically, stars were first classified into , stars were first classified into four groups based on color (white, yellow, four groups based on color (white, yellow, red, and deep red), then into classes using red, and deep red), then into classes using the letters A through N the letters A through N

• Annie Jump CannonAnnie Jump Cannon: classes were more : classes were more orderly if arranged by temperature – Her orderly if arranged by temperature – Her new sequence became O, B, A, F, G, K, M (O new sequence became O, B, A, F, G, K, M (O being the hottest and M the coolest) and are being the hottest and M the coolest) and are today known as spectral classestoday known as spectral classes

SpectralClass

SurfaceTemp

AbsorptionLines

Example

O 30,000 KIonized He

Weak H

B 20,000 KHe, H

moderate Rigel

A 10,000 K Strong HVegaSirius

SpectralClass

SurfaceTemp

AbsorptionLines

Example

F 7,000 KMod. H,Metals

Canopus

G 6,000 KMod. H,Metals

Sun

K 4,000 KMetalsstrong

Arcturus

M 3,000 KMetalsstrong

Betelgeuse

Measuring aMeasuring a Star’s MotionStar’s Motion

• A star’s radial motion is determined from A star’s radial motion is determined from the Doppler shift of its spectral linesthe Doppler shift of its spectral lines

• The amount of shift depends on the star’s The amount of shift depends on the star’s radial velocityradial velocity

• ΔλΔλ = = the shift in wavelength of an the shift in wavelength of an absorption line absorption line

• λλ = resting wavelength, the radial speed = resting wavelength, the radial speed vv is is given by:given by:

V = V = ΔλΔλ// λ λ • c • c

where c is the speed of lightwhere 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-Hertzsprung-Russell DiagramRussell 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 sequencemain 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 We now know that the main sequence comprises all the sequence comprises all the stars that are converting stars that are converting hydrogen to helium in their hydrogen to helium in their cores. cores.

•Stars that are not on the Stars that are not on the main sequence are doing main sequence are doing something elsesomething else

• The Mass-Luminosity RelationThe Mass-Luminosity Relation– Main-sequence stars obey a mass-Main-sequence stars obey a mass-

luminosity relation, approximately given luminosity relation, approximately given by:by:

LL = = MM33

where where LL and and MM are measured in solar units are measured in solar units– Consequence: Stars at top of main-Consequence: Stars at top of main-

sequence are more massive than stars sequence are more massive than stars lower downlower 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 The range in sizes of Main Main SequenceSequence stars is about 0.1 to stars is about 0.1 to 100 solar radii. 100 solar radii.

SupergiantsSupergiants can be enormous. can be enormous. Betelgeuse would reach out to Betelgeuse would reach out to the orbit of Mars. the orbit of Mars.

• White dwarfsWhite dwarfs stars are around stars are around the size of the Earththe size of the Earth

• Visual binariesVisual binaries – actually see the stars moving around each otheractually see the stars moving around each other

• Spectroscopic binariesSpectroscopic binaries

– make use of the Doppler shift of the spectral make use of the Doppler shift of the spectral lines of the starslines of the stars

• Eclipsing binariesEclipsing binaries

– binaries may be orbiting in such a way that binaries may be orbiting in such a way that one star moves in front of the other as in an one star moves in front of the other as in an eclipseeclipse

Shape: Irregular, no specific shape

Where: Galactic disk

Types 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: Stellar motion has two components:

• The The transversetransverse component measures a component measures a star's motion perpendicular to our line star's motion perpendicular to our line of sight—in other words, its motion of sight—in other words, its motion across the sky. across the sky.

• The The radialradial component measures a star's component measures a star's movement along our line of sight—movement along our line of sight—toward us or away from us.toward us or away from us.

•The annual movement of a The annual movement of a star across the sky, as star across the sky, as seen from Earth (and seen from Earth (and corrected for parallax), is corrected for parallax), is called called proper motionproper motion. .

• It describes the transverse It describes the transverse component of a star's component of a star's velocityvelocity