Radiation PHYS390 (Astrophysics) Professor Lee Carkner Lecture 3

Questions  1) Which would look brighter, a star with magnitude 20 or a star 100 times brighter than magnitude 26?  Answer: m=20  Explain: 100 times brighter than m=26 is m=21. Smaller magnitude brighter  2) Which would look brighter, a star with m=10 or a star that has M=10 and is at 20 pc?  Answer: m=10  Explain: A M=10 star would have m=10 at 10pc and be fainter than m=10 at 20pc

Questions  3) Which looks brighter, a star with m bol = 10 or a star with V = 10?  Answer: V=10  Explain: the V=10 star has the same luminosity in just one band as the m bol =10 star has over all wavelengths, so if you include the bands other than V it looks brighter  4) Which looks brighter, a star with B = 10 or a star with V = 10?  Answer: It depends  Explain: It depends on the shape of the blackbody curve. The B=10 star might be brighter than 10 in the V band (if it is a red star) or fainter (if it is a blue star)

Light Properties  Light is both a particle and a wave    Where:  c = 3X10 8 m/s  h = 6.626X J s  Long wavelength (low energy) –  Short wavelength (high energy) –  We can often think of light as a stream of photons, each with an, or E

Blackbody Curve  Blackbodies have a very specific emission spectrum   A rapid fall off to short wavelengths  Gradual Rayleigh-Jeans tail to long wavelengths   Higher temperature means more total emission and peak at shorter wavelengths

Wien’s Law   Given by Wien’s Law: max T = m K  Since short wavelengths look blue and long red:  Blue stars =  Red stars =

Stefan-Boltzmann   Stars are spheres, so A = 4  R 2  L = 4  R 2  T 4   is the Stefan-Boltzmann constant  =5.67X10 -8 W m -2 K -4

Stefan-Boltzmann and Stars  T is more important than R for determining L   If we know L and T, we can find R   Stars are not perfect blackbodies so we often write T in the equation as T e   The temperature of a perfect blackbody that emits the same amount of energy as the star

The Blackbody Curve  We need an equation for the shape of the blackbody curve   Blackbody curve as a function of wavelength due to temperature T  B (T) = (2ckT)/ 4  Where k = 1.38X J/K   Leads to ultraviolet catastrophe  Energy goes to infinity as wavelengths get shorter

Planck Function   but only if he assumed that energy was quantized (h )  Result: B (T) = (2hc 2 / 5 )/[e (hc/ kT) -1]   Energy per unit time per unit wavelength interval per unit solid angle

Planck Function and Luminosity   Called the monochromatic luminosity, L d L d = (8  R 2 hc 2 / 5 )/[e (hc/ kT) -1] d  If we divide by the inverse square law we get the monochromatic flux, F d F d = (L /4  r 2 ) d  which is the flux for the small wavelength range d 

Next Time  Read:  Homework: 3.9e-3.9g, 3.17, 5.1, 5.4