

Magnitudes Archaic: very conveninient if a) no calculations b) all stellar objects are blackbodies 3  10000 K (i.e. stars) c) use only photography in visual But still in use Take a star (alpha centuri): call it m=0 Take another star 100x fainter: call it m=5 Take another star 10^{4}xfainter: call it m=10 Algorithm for stars of same type as alpha centuri 1) Take number of times fainter I_{0}/I 2) Take log_{10}(I_{0}/I) 3) Multiply by 2.5 exponential to the 2.51 power 2.51= What happens is spectrus not the same
Three standard magnitudes color excess M_{U}, M_{B}, M_{V} scaled for standard star Could just quote flux densities at the 3 points magnitudes very misleading is bulk of flux is outside optical Sun 26.5 Faintest visible 6 Full Moon 13 Faintest Detectable 22 Sirius 1.5
Absolute Magnitude (M) m=M at 10 pc m at d m at 10 but m = log_{2.51} I_{d} = M = log_{2.51} I_{10} M  m = 2.5 log Id + 2.5 log I10 = 2.5 log () = 2.5 log ()^{2} = 5 log d + 5 log 10 M = m  5 log d + 5
Astrophysical Plasma Cosmic/Solar abundances What does it emit in various circumstances If we understand shysics then we can deduce circumstances of the matter All photons are generated by the acceleration of charged particles Will start with the simplest case:
Isolated charge
Larmor Formula Relativistic Form:
(for colinear acceleration and velocity)
(for perpendicular acceleration and velocity)
We thus know the power here, but not the spectru. It gets complicates and E & M not appropriate here Qualitative approach: To become a photon electric field must be perturbed so that can add
vt
then we can get a photon if goes through many cycles then integral will be zero Therefore, wt < 1 for photon creation
Conservation of energy predicts a result like this. You can’t put more energy into a photon than is lost from a particle. What can cause acceleration of a particle?
Collisions between particles and particles spiralling in B fields account for virtually all orgination of photons
Optically thin à photons escape as generated Optically Grey or Thick à photons interact with other matter before escaping We will now discuss emission mechanisms Synchrotron and Bremsstrahlung in optically thin case
Cyclotron Radiation B
v Nonrelativistic particle Velocity = v Mass = m
Therefore, cutoff at w_{c}
With ensembles of particles: lines are not perfect d function
Widened by:
but,
therefore, How does a particle behave in such a field? note: photon loses energy 10^{6} times slower à electrons are source but let Therefore,
loses energy on a timescale /B2 = 10years/B^{2}_{guess} Radiates at Hz = 2.8 B MHz
Synchrotron Radiation
Because of relativistic effects synchrotron does not radiate at fundamental frequency
In instantaneous rest from Larmor formula
Emits radiation at what particle thinks cyclotron frequency is, goes around at but due to time, emits at w_{c} in its frame, but sees B_{rest} = g B_{obs} emits at gw_{c }
Transform à Main Output at
described exactly as modified Bessel function Ensemble of Electrons Power law distribution of energy convolve functions jn = emissivity per unit volume à Power law spectrum is seen
Synchrotron Decay Time
P= 1.6 * 10^{15} B^{2}g^{2} ergs/s E= gmc^{2} =0.91*10^{–27} * 9*10^{20} g ergs E=8.2*10^{7} g ergs sec solve for B & g Example:
therefore, B ~ 5 gauss g ~ 7
