Doppler Shift and Stellar Magnitudes

Energy & Power Units Energy has units Joule (J) Rate of energy expended per unit time is called power, and has units Watt (W) Example: a 100 W = 100 J/s light bulb emits 100 J of energy every second Nutritional Value: energy your body gets out of food, measured in Calories = 1000 cal = 4200 J Luminosity is the same as power radiated

Stefan’s Law A point on the Blackbody curve tells us how much energy is radiated per frequency interval Question: How much energy is radiated in total, i.e. how much energy does the body lose per unit time interval? Stefan(-Boltzmann)’s law: total energy radiated by a body at temperature T per second: P = A σ T4 σ = 5.67 x 10-8W/(m2 K4)

Example: Stefan-Boltzmann Law Sun T=6000K, Earth t=300K (or you!) How much more energy does the Sun radiate per time per unit area? Stefan: Power radiated is proportional to the temperature (in Kelvin!) to the fourth power Scales like the fourth power! Factor f=T/t=20, so f4 =204=24x104=16x104 160,000 x

Example: Wien’s Law Sun T=6000K, Earth t=300K (or you!) The Sun is brightest in the visible wave lengths (500nm). At which wave lengths is the Earth (or you) brightest? Wien: peak wave length is proportional to temperature itself Scales linearly! Factor f=T/t=20, so f1 =201=20, so peak wavelength is 20x500nm=10,000 nm = 10 um Infrared radiation!

Doppler Shift From Wikipedia radiation from receding bodies is shifted to longer wavelengths (red shift; appear cooler) radiation from approaching bodies is shifted to shorter wavelengths (blue shift; appear hotter) Very small effect if v is small compared to c – almost always the case Just like an ambulance passing by SIREN ON A STRING DEMO From Wikipedia 6

Doppler Shift Can use the Doppler shift to determine radial velocity of distant objects relative to us Transverse velocity can be measured from the motion of stars with respect to back-ground over a period of years (Halley 1718: Sirius, Arcturus, Aldebaran moved since Hipparchus, 1850 years ago) velocity towards or away is radial; across the field of view, transverse. Only radial velocity contributes to Doppler shift. Also, temperature and rotation can be detected by a broadening of a narrow spectral line. Rotation of Venus detected via Doppler shift of reflected radar waves “Ringing” of the sun similarly 7

The Magnitude Scale A measure of the apparent brightness Logarithmic scale Notation: 1m.4 (smaller brighter) Originally six groupings 1st magnitude the brightest 6th magnitude is 100x dimmer So a difference of 5mag is a difference of brightness of 100 Factor 2.512=1001/5 for each mag. Note higher magnitude means a dimmer star! Abs magnitude is effectively the luminosity; apparent magnitude involves the luminosity and distance It is a property of the eye that a fixed difference in perceived brightness corresponds to a multiplicative factor in energy: thus if one star is one order of magnitude brighter than another, it gives off about 2.5 times as much light; 2 orders of magnitude, 2.5H2.5=6.25 times as much light; etc. 5 orders of magnitude=100 times.

Absolute Magnitude The absolute magnitude is the apparent magnitude a star would have at a distance of 10 pc. Notation example: 2M.8 It is a measure of a star’s actual or intrinsic brightness called luminosity Example: Sirius: 1M.4, Sun 4M.8 Sirius is intrinsically brighter than the Sun Note higher magnitude means a dimmer star! Abs magnitude is effectively the luminosity; apparent magnitude involves the luminosity and distance It is a property of the eye that a fixed difference in perceived brightness corresponds to a multiplicative factor in energy: thus if one star is one order of magnitude brighter than another, it gives off about 2.5 times as much light; 2 orders of magnitude, 2.5H2.5=6.25 times as much light; etc. 5 orders of magnitude=100 times.

Finding the absolute Magnitude To figure out absolute magnitude, we need to know the distance to the star Then do the following Gedankenexperiment: In your mind, put the star from its actual position to a position 10 pc away If a star is actually closer than 10pc, its absolute magnitude will be a bigger number, i.e. it is intrinsically dimmer than it appears If a star is farther than 10pc, its absolute magnitude will be a smaller number, i.e. it is intrinsically brighter than it appears Note higher magnitude means a dimmer star! Abs magnitude is effectively the luminosity; apparent magnitude involves the luminosity and distance It is a property of the eye that a fixed difference in perceived brightness corresponds to a multiplicative factor in energy: thus if one star is one order of magnitude brighter than another, it gives off about 2.5 times as much light; 2 orders of magnitude, 2.5H2.5=6.25 times as much light; etc. 5 orders of magnitude=100 times.