stars all chapter 9 “the stars are distant and unobtrusive, but bright and enduring as our fairest...

Stars Stars All Chapter 9All Chapter 9

“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

To understand the physics of stars, we need to measures these four parameters and compare them with the predictions of the theory

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 star’s distance be inferredHow may a star’s distance be inferred Parallax as a measure of distance: Parallax as a measure of distance:

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

Back to the distance: how do we measure it?Parallax (a.k.a. triangulation)

For getting distancesUsing triangulation; requires

1. A baseline (distance over which observer moves).

2. Measurement of angles to the object from each end of the baseline.

3. Mathematical relationships between angles and lengths of sides of triangle. This is called trigonometry.

Stellar Parallax:Takes advantage of the fact that Earth orbits the Sun

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 measure the radius of a star? Except for the Sun, we don’t! We infer it!

The Size (Radius) of a StarThe Size (Radius) of a StarWe already know: flux increases with surface temperature (~ T4); hotter stars are brighter.

But brightness also increases with size:

A BStar B will be brighter than

star A.

Absolute brightness is proportional to radius squared, L ~ R2

Quantitatively: L = 4 R2 T4

Surface area of the starSurface flux due to a blackbody spectrum

Example: Star RadiiExample: Star Radii

Polaris has just about the same spectral type (and thus surface temperature) as our sun, but it is 10,000 times brighter than our

sun.

Thus, Polaris is 100 times larger than the sun.

This causes its luminosity to be 1002 = 10,000 times more than our sun’s.

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



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 and understand how they evolve?We can take a census of stars and see what is 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.

Classificagtion of Stars:Classificagtion of Stars:The H-R diagramThe H-R diagram

“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?

How can we study the How can we study the evolution of stars, their evolution of stars, their

phases of life?phases of life? One approach is to collect a large number of stars One approach is to collect a large number of stars

(statistical approach).(statistical approach). The idea is that a large sample of stars will contain The idea is that a large sample of stars will contain

examples of all life stages (newborn, adult, examples of all life stages (newborn, adult, moribund) and of all types of stars.moribund) and of all types of stars.

The hope is that by looking at some carefully The hope is that by looking at some carefully selected observable properties of the stars, we will selected observable properties of the stars, we will see trends that are the telltale of stellar evolutionsee trends that are the telltale of stellar evolution

A large sample is also expected to contain all the A large sample is also expected to contain all the star types that exist, except, maybe, the most rare star types that exist, except, maybe, the most rare onesones

But which observables to look at? And how?But which observables to look at? And how?

Discussion QuestionDiscussion QuestionHow can I understand the How can I understand the

performance of CARSperformance of CARS

P = P(Weight; Power; Overall P = P(Weight; Power; Overall Built)Built)

Make a plot that shows the general Make a plot that shows the general relationship between Weight and relationship between Weight and Horsepower of cars.Horsepower of cars.

-now add to your plot sports cars…-… racing cars…-… and economy models

This kind of plots summarizes in a powerful waygeneral features of most cars

Classification of Stars:Classification of Stars:Statistical StudyStatistical Study

1) Collect information ona large sample of stars: surveys of stars.

2) Measure their luminosities(need the distance!)

3) Measure their surface temperatures(need their spectra or at least their color)

Organizing the Family of Stars: Organizing the Family of Stars: The Hertzsprung-Russell DiagramThe Hertzsprung-Russell Diagram

We know:

Stars have different temperatures, different luminosities, and different sizes.

To bring some order into that zoo of different types of stars: organize them in a diagram of

Luminosity versus Temperature (or spectral type)

Lum

inos

ity

Temperature

Spectral type: O B A F G K M

Hertzsprung-Russell Diagram

orA

bsol

ute

mag

.

The Hertzsprung-Russell DiagramThe Hertzsprung-Russell Diagram

Most stars are found along the

Main Sequence

The Hertzsprung-Russell DiagramThe Hertzsprung-Russell Diagram

Stars spend most of their

active life time on the M

ain

Sequence (MS).

Same temperature,

but much brighter than

Main Sequence

stars

The Hertzsprung-Russell The Hertzsprung-Russell DiagramDiagram

Size of Star

Mass ofStar

The Radii of Stars in the The Radii of Stars in the Hertzsprung-Russell DiagramHertzsprung-Russell Diagram

10,000 times the

sun’s radius

100 times the

sun’s radius

As large as the sun

Rigel Betelgeuse

Sun

Polaris

The Relative Sizes of Stars The Relative Sizes of Stars in the HR Diagramin the HR Diagram


The Main Sequence

- all main sequencestars have nuclear fusion of H into Hein their cores

- this is the definingcharacteristic of a main sequence star.


Red Giants

- Red Giant starsare very large, cooland quite bright.

Ex. Betelgeuse is100,000 times moreluminous than the Sunbut is only 3,500K onthe surface. It’s radiusis 1,000 times that of theSun.


White Dwarfs

- White Dwarfsare hot but sincethey are so small,they are not veryluminous.


Lifetimeof Star

Shorter

Longer

More mass,more fuel,very fast burning.

Less mass,less fuel,slow, steady burning.

How do we know the age of a star?

ThinkThinkSUV vs a Honda CivicSUV vs a Honda Civic

The H-R diagramThe H-R diagram

Which is the faintest? the sun, an O star, a white dwarf, or a red giant?Which of these star is the hottest?What are Sun-like stars (0.4 M < M < 8 M) in

common?What about red dwarfs (0.08 M < M < 0.4 M) ?Where do stars spend most of their time?

O

What is the order of stellar evolution of a star like the Sun?

Mass-Luminosity relationMass-Luminosity relation Most stars appear on the Main Sequence, where

stars appear to obey a Mass-Luminosity relation: L M3.5

For example, if the mass of a star is doubled, its luminosity increases by a factor 23.5 ~ 11.

Thus, stars like Sirius that are about twice as massive as the Sun are about 11 times as luminous.

The more massive a Main Sequence star is, the hotter (bluer), and more luminous.

The Main Sequence is a mass sequence!

To calculate a star's radius, you must know its

1) temperature and luminosity.

2) chemical composition and temperature.

3) color and chemical composition.

4) luminosity and surface gravity.

L=4πR2 σT4

3) 4 times larger

4) the same

1) ½ times as large

2) ¼ times as large

If a star is half as hot as our Sun, but has the same luminosity, how large is its radius compared to the Sun?

L=4πR2 σT4

What is burning in stars?What is burning in stars?

Gasoline Gasoline Nuclear fissionNuclear fission Nuclear fusionNuclear fusion Natural gas Natural gas

Review QuestionsReview Questions

1.1. What is the Hertzsprung-Russell What is the Hertzsprung-Russell Diagram?Diagram?

2.2. Why are most stars seen along the Why are most stars seen along the so-called main sequence?so-called main sequence?

3.3. What makes more massive stars What makes more massive stars hotter and brighter?hotter and brighter?

stars all chapter 9 “the stars are distant and unobtrusive, but bright and enduring as our fairest...

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