“The stars are distant and unobtrusive, but bright and enduring as our fairest and most memorable experiences.” Henry David Thoreau (1849) Stars up to Chapter 9.3, page 194 Are Stars similar to our Sun? How far away are they? Where did they come from? What do they do? Do they live forever?
The Four Basic Parameters of Stars • Luminosity • Size • Mass • Surface Temperature
However… • To measure Luminosity I need DISTANCE • 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. • Luckily: • Flux = L / 4pD2
Questions to be addressed • How may a star’s luminosity be inferred? • How may a star’s Temperature 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? • 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=3.0x1026 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 Luminosity L=4D2 B apparent brightness or flux luminosity distance B=L/(4p D2 )
Magnitudes and Distance Modulus • Apparent magnitude: • m = -2.5 x Log(B) + const • Absolute magnitude: M • the magnitude you would observe, were the source placed at 10 pc • m – M = -5 + 5 x Log (d) • d = 10(m-M+5)/5 • Bolometric magnitude: • From the flux that includes all wavelengths (not only those in a given band)
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 1 (AU) D (in Parsecs) = P (in arcseconds) P, the parallax angle, is measured in arcseconds 60 arcseconds = 1 arcminute 60 arcminutes = 1 degree There are 3600 arcseconds in a degree The larger P, the smaller D The smaller P, the larger D 1 parsec = 3.26 light years = 3.086x1016 meter
Parallax would be easier to measure if 1) the stars were further away. 2) Earth's orbit were larger. 3) Earth moved backwards along its orbit. 4) none of these.
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? • Overall spectral shape (the peak of the blackbody continuous spectrum) • More accurately, spectroscopically
Spectral Types 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. The sun has a spectral type: G2
Stellar Size • Stars are very spherical so we characterize a star’s size by its radius. Stellar Radii vary in sizefrom ~1500xRSun for a large Red Giant to 0.008xRSun for a WhiteDwarf. R How do we determine the radius of a star?
Temperature, Luminosity, and Size – pulling them all together A star’s luminosity, surface temperature, and size are all related by the Stefan-Boltzmann Law: Stefan-Boltzmann Law L=4πR2 σT4 Surfacetemperature Stellarradius Luminosity In terms of Solar quantities: L/LSun = (R/RSun)2 x (T/TSun)4
L=4πR2 σT4 Two stars have the same surface temperature, butthe radius of one is 10 times the radius of the other.The larger star is 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
L=4πR2 σT4 L=4πD2 B 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. 1) 1/2 as great 2) 1/4 as great 3) the same 4) 4 times 5) 16 times as great
In Review • There are four principal characteristics of a star: • Luminosity • Surface Temperature • Size • 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 Direct measurent Parallax Distance + apparent brightness ( L=4D2 B) Spectral type (or color) Luminosity + temperature (L=4R2 T4) Apparent brightness Distance Luminosity Temperature Radius Luminosity and temperature are the two independent intrinsic parameters of stars.