Stars Stars up to Chapter 9.3, page 194up to Chapter 9.3, page 194

“The stars are distant and unobtrusive, but bright and enduring as our fairest and most memorable experiences.”

Henry David Thoreau (1849)

Are Stars similar to our Sun?How far away are they?Where did they come from?What do they do?Do they live forever?

Panorama view of the sky Panorama view of the sky

The Four Basic Parameters of Stars

LuminositySizeMassSurface Temperature

However…However…

To measure Luminosity I need To measure Luminosity I need DISTANCEDISTANCE

All I can really measure is All I can really measure is FLUXFLUX FLUXFLUX is the amount of energy that is the amount of energy that

hits my detector. It is not the amount hits my detector. It is not the amount of energy that is emitted by the of energy that is emitted by the source.source.

Luckily:Luckily: Flux = L / 4Flux = L / 4DD22

Questions to be addressedQuestions to be addressed

How may a star’s luminosity be How may a star’s luminosity be inferred?inferred?

How may a star’s Temperature be How may a star’s Temperature be inferred?inferred?

How may a stsar’s distance be inferredHow may a stsar’s distance be inferred Parallax as a measure of distance: how Parallax as a measure of distance: how

does the parallax of a star depend on does the parallax of a star depend on its distance?its distance?

How may a star’s radius be inferred?How may a star’s radius be inferred?

LuminosityLuminosity

Luminosity is the total amount of power given off by a star.

-Since it’s a power, Luminosity is measured in Watts Lsun=3.0x1026 Watt

-For convenience, we often refer to the luminosity ofa star in terms of the luminosity of the Sun.

-Eg, -“That star has a luminosity of 22LSun”-“That galaxy has a luminosity of 2x1014LSun ”

Brightness, Distance, and Brightness, Distance, and LuminosityLuminosity

L=4D2 B

luminosity distance

apparent brightnessor flux

B=L/(4D2 )

Magnitudes and Distance Magnitudes and Distance ModulusModulus

Apparent magnitude:Apparent magnitude: m = -2.5 x Log(B) + constm = -2.5 x Log(B) + const

Absolute magnitude: MAbsolute magnitude: M the magnitude you would observe, were the the magnitude you would observe, were the

source placed at 10 pcsource placed at 10 pc m – M = -5 + 5 x Log (d)m – M = -5 + 5 x Log (d)

d = 10d = 10(m-M+5)/5(m-M+5)/5

Bolometric magnitude:Bolometric magnitude: From the flux that includes all wavelengths From the flux that includes all wavelengths

(not only those in a given band)(not only those in a given band)

There is a Big Range of There is a Big Range of Stellar Luminosities Out Stellar Luminosities Out

there!there!

StarStar Luminosity (in Luminosity (in units of solar units of solar Luminosity)Luminosity)

SunSun 11

Proxima Proxima CentauriCentauri

0.00060.0006

Rigel (Orion)Rigel (Orion) 70,00070,000

Deneb Deneb (Cygnus)(Cygnus)

170,000170,000

Stellar Parallax

The measurements are taken six months apart.The baseline is the diameter of the Earth’s orbit.

What is seen

What is seen

The ½ of the angle between the current location and the 6-month location is called the stellar parallax = P.

Parallax Distance

D (in Parsecs) = 1 (AU)

P (in arcseconds)

The larger P, the smaller DThe smaller P, the larger D

P, the parallax angle, is measured in arcseconds

60 arcseconds = 1 arcminute 60 arcminutes = 1 degreeThere are 3600 arcseconds in a degree

1 parsec = 3.26 light years= 3.086x1016 meter

Parallax would be easier to measure if

3) Earth moved backwards along its orbit.

4) none of these.

1) the stars were further away.

2) Earth's orbit were larger.

Star A has a parallax angle that is twice that of Star B. What is the relationship between their distances?

Star A is closer than Star B Star B is closer than Star A The stars are at the same

distance Not enough information is given

How to measure the surface How to measure the surface temperature of a star?temperature of a star?

1.1. Overall spectral shape (the peak of the Overall spectral shape (the peak of the blackbody continuous spectrum)blackbody continuous spectrum)

2.2. More accurately, spectroscopicallyMore accurately, spectroscopically

Spectral TypesSpectral Types

The sun has a spectral type: G2

For historical reasons, astronomers classify the temperatures of stars on a scale defined by spectral types, called O B A F G K M, ranging from the hottest (type O) to the coolest (type M) stars.

Stellar SizeStellar Size

Stars are very spherical so we Stars are very spherical so we characterize a star’s size by its characterize a star’s size by its radius.radius.

R

Stellar Radii vary in sizefrom ~1500xRSun for a large Red Giant to 0.008xRSun for a WhiteDwarf.

How do we determine the radius of a star?

Temperature, Luminosity, Temperature, Luminosity, and Size – pulling them all and Size – pulling them all

togethertogether

Stefan-Boltzmann Law

Luminosity Stellarradius

Surfacetemperature

L=4πR2 σT4

A star’s luminosity, surface temperature, and size are all related by the Stefan-Boltzmann Law:

In terms of Solar quantities:L/LSun = (R/RSun)2 x (T/TSun)4

1) 10 times more luminous

2) 100 times more luminous

3) 1000 times more luminous

4) 1/10th as luminous

5) 1/100th as luminous

Two stars have the same surface temperature, butthe radius of one is 10 times the radius of the other.The larger star is

L=4πR2 σT4

1) 1/2 as great

2) 1/4 as great

3) the same

4) 4 times

5) 16 times as great

Suppose two stars are at equal distance and have the sameradius, but one has a temperature that is twice as great as theother. The apparent brightness of the hotter star is ____ as the other.

L=4πR2 σT4L=4πD2 B

In ReviewIn Review There are four principal There are four principal

characteristics of a star:characteristics of a star: LuminosityLuminosity Surface TemperatureSurface Temperature SizeSize MassMass

How can we put all this together so that we can classify stars?We can take a census of stars and see what’s out there.

Measurements of Star PropertiesMeasurements of Star Properties

Apparent brightness DistanceLuminosity

TemperatureRadius

Direct measurentParallaxDistance + apparent brightness( L=4D2 B)Spectral type (or color)Luminosity + temperature(L=4R2 T4)

Luminosity and temperature are the two independent intrinsic parameters of stars.