Stars All 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

The Four Basic Parameters of Stars Luminosity Size Mass Surface Temperature To understand the physics of stars, we need to measures these four parameters and compare them with the predictions of the theory

However… To measure Luminosity I need DISTANCE To measure Luminosity I need DISTANCE All I can really measure is FLUX All I can really measure is FLUX FLUX is the amount of energy that hits my detector. It is not the amount of energy that is emitted by the source. FLUX is the amount of energy that hits my detector. It is not the amount of energy that is emitted by the source. Luckily: Luckily: Flux = L / 4  D 2 Flux = L / 4  D 2

Questions to be addressed How may a star’s luminosity be inferred? How may a star’s luminosity be inferred? How may a star’s Temperature be inferred? How may a star’s Temperature be inferred? How may a star’s distance be inferred How may a star’s distance be inferred Parallax as a measure of distance: how does the parallax of a star depend on its distance? Parallax as a measure of distance: how does the parallax of a star depend on its distance? How may a star’s radius be inferred? How may a star’s radius be inferred?

Luminosity Luminosity is the total amount of power given off by a star. -Since it’s a power, Luminosity is measured in Watts Lsun=3.0x10 26 Watt -For convenience, we often refer to the luminosity of a star in terms of the luminosity of the Sun. -Eg, -“That star has a luminosity of 22L Sun ” -“That galaxy has a luminosity of 2x10 14 L Sun ”

Brightness, Distance, and Luminosity L=4  D 2 B luminositydistance apparent brightness or flux B=L/(4  D 2 )

Magnitudes and Distance Modulus Apparent magnitude: Apparent magnitude: m = -2.5 x Log(B) + const m = -2.5 x Log(B) + const Absolute magnitude: M Absolute magnitude: M the magnitude you would observe, were the source placed at 10 pc the magnitude you would observe, were the source placed at 10 pc m – M = x Log (d) m – M = x Log (d) d = 10 (m-M+5)/5 d = 10 (m-M+5)/5 Bolometric magnitude: Bolometric magnitude: From the flux that includes all wavelengths (not only those in a given band) From the flux that includes all wavelengths (not only those in a given band)

There is a Big Range of Stellar Luminosities Out there! Star Luminosity (in units of solar Luminosity) Sun1 Proxima Centauri Rigel (Orion) 70,000 Deneb (Cygnus) 170,000

Back to the distance: how do we measure it? Parallax (a.k.a. triangulation) For getting distances Using 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 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 D The smaller P, the larger D P, the parallax angle, is measured in arcseconds 60 arcseconds = 1 arcminute 60 arcminutes = 1 degree There are 3600 arcseconds in a degree 1 parsec = 3.26 light years = 3.086x10 16 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 temperature of a star? 1. Overall spectral shape (the peak of the blackbody continuous spectrum) 2. More accurately, spectroscopically

Spectral 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 Size Stars are very spherical so we characterize a star’s size by its radius. Stars are very spherical so we characterize a star’s size by its radius. R Stellar Radii vary in size from ~1500xR Sun for a large Red Giant to 0.008xR Sun for a White Dwarf. How do we measure the radius of a star? Except for the Sun, we don’t! We infer it!

The Size (Radius) of a Star We already know: flux increases with surface temperature (~ T 4 ); hotter stars are brighter. But brightness also increases with size: A B Star B will be brighter than star A. Absolute brightness is proportional to radius squared, L ~ R 2 Quantitatively: L = 4  R 2  T 4 Surface area of the star Surface flux due to a blackbody spectrum

Example: 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 = 10,000 times more than our sun’s.

Temperature, Luminosity, and Size – pulling them all together Stefan-Boltzmann Law Luminosity Stellar radius Surface temperature L=4 π R 2 σ T 4 A star’s luminosity, surface temperature, and size are all related by the Stefan-Boltzmann Law: In terms of Solar quantities: L/L Sun = ( R/R Sun ) 2 x ( T/T Sun ) 4

1) 10 times more luminous 2) 100 times more luminous 3) 1000 times more luminous 4) 1/10 th as luminous 5) 1/100 th as luminous Two stars have the same surface temperature, but the radius of one is 10 times the radius of the other. The larger star is L=4 π R 2 σ T 4

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 same radius, but one has a temperature that is twice as great as the other. The apparent brightness of the hotter star is ____ as the other. L=4 π R 2 σ T 4 L=4 π D 2 B

In Review There are four principal characteristics of a star: There are four principal characteristics of a star: Luminosity Luminosity Surface Temperature Surface Temperature Size Size Mass Mass 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 Properties Apparent brightness Distance Luminosity Temperature Radius Direct measurent Parallax Distance + apparent brightness ( L=4  D 2 B) Spectral type (or color) Luminosity + temperature (L=4  R 2  T 4 ) Luminosity and temperature are the two independent intrinsic parameters of stars.

Classificagtion of Stars: The 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 evolution of stars, their phases of life? One approach is to collect a large number of stars (statistical approach). One approach is to collect a large number of stars (statistical approach). The idea is that a large sample of stars will contain examples of all life stages (newborn, adult, moribund) and of all types of stars. The idea is that a large sample of stars will contain examples of all life stages (newborn, adult, moribund) and of all types of stars. The hope is that by looking at some carefully selected observable properties of the stars, we will see trends that are the telltale of stellar evolution The hope is that by looking at some carefully selected observable properties of the stars, we will see trends that are the telltale of stellar evolution A large sample is also expected to contain all the star types that exist, except, maybe, the most rare ones A large sample is also expected to contain all the star types that exist, except, maybe, the most rare ones But which observables to look at? And how? But which observables to look at? And how?

Discussion Question How can I understand the performance of CARS P = P(Weight; Power; Overall Built) Make a plot that shows the general relationship between Weight and Horsepower of cars. -now add to your plot sports cars… -… racing cars… -… and economy models This kind of plots summarizes in a powerful way general features of most cars

Classification of Stars: Statistical Study 1)Collect information on a 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: The 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) Luminosity Temperature Spectral type: O B A F G K M Hertzsprung-Russell Diagram or Absolute mag.

The Hertzsprung-Russell Diagram Most stars are found along the Main Sequence

The Hertzsprung-Russell Diagram Stars spend most of their active life time on the Main Sequence (MS). Same temperature, but much brighter than Main Sequence stars

The Hertzsprung-Russell Diagram Size of Star Mass of Star

The Radii of Stars in the Hertzsprung-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 in the HR Diagram

The Hertzsprung-Russell Diagram

The Main Sequence - all main sequence stars have nuclear fusion of H into He in their cores - this is the defining characteristic of a main sequence star.

The Hertzsprung-Russell Diagram Red Giants - Red Giant stars are very large, cool and quite bright. Ex. Betelgeuse is 100,000 times more luminous than the Sun but is only 3,500K on the surface. It’s radius is 1,000 times that of the Sun.

The Hertzsprung-Russell Diagram

White Dwarfs - White Dwarfs are hot but since they are so small, they are not very luminous.

The Hertzsprung-Russell Diagram Lifetime of 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? Think SUV vs a Honda Civic

The 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 sun < M < 8 M sun ) in common?  What about red dwarfs (0.08 M sun < M < 0.4 M sun ) ?  Where do stars spend most of their time? O What is the order of stellar evolution of a star like the Sun?

Mass-Luminosity relation Most stars appear on the Main Sequence, where stars appear to obey a Mass-Luminosity relation: L  M 3.5 For example, if the mass of a star is doubled, its luminosity increases by a factor ~ 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=4 π R 2 σ T 4

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=4 π R 2 σ T 4

What is burning in stars? Gasoline Gasoline Nuclear fission Nuclear fission Nuclear fusion Nuclear fusion Natural gas Natural gas

Review Questions 1. What is the Hertzsprung-Russell Diagram? 2. Why are most stars seen along the so-called main sequence? 3. What makes more massive stars hotter and brighter?