Stars up 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

The Four Basic Parameters of Stars Luminosity Size Mass Surface Temperature

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 stsar’s distance be inferred How may a stsar’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

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 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 determine the radius of a star?

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? We can take a census of stars and see what’s 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.