Useful Flashcards
useful slides revision
Radio and Gamma Wave characteristics
Soft X-ray: 0.1-1keV, 100-10A, 10^6 - 10^8K
Classical X-ray: 1-10keV, 10-1A, 10^6 - 10^8K
Hard X-ray: 10-100keV, 1-0.1A, 10^6 - 10^8K
Gamma-ray: >=0.1MeV, <= 0.1A, 10^8K
Wavelength Frequency relation
Energy gained by an electron falling through
a potential difference of 1 Volt
The kinetic energy which an electron acquires when accelerated (from rest) through a potential difference of 1 volt.
Energy associated to a photon of
frequency nu
E[eV] = 4.136x10^-15 * nu [Hz]
h=6.63x10^-34 [J s] : Planck constant
Relation between energy and
associated temperature
If radiating matter is in thermodynamic equilibrium:
k_B=1.38x10^-23 [J/K] : Boltzmann constant
Energy Flux
For a plane wave, the amount of energy passing through an element of area dA in time dt is:
F = Energy / (Area x Time)
units: [W/m^2]
Monochromatic Energy Flux
The energy passing through element area dA in time dt in the frequency interval [nu, nu + dnu] is:
units: [W/(m^2Hz)]
Getting the flux in a certain chunk of wavelengths or frequencies for monochromatic energy flux
Total Energy Flux
The total energy flux is obtained integrating over the frequencies:
units: [W/(m^2)]
Inverse Square Law
For a spherically symmetric isotropic source:
essentially F = const/r^2
Comes from the conservation of energy (pi4F(r1)r1^2= pi4F(r2)r2^2)
Specific Intensity
AKA Brightness: the power radiated by a source in a specific direction per unit area, per unit solid angle, per unit wavelength (or frequency)
Mean Intensity
the average specific intensity over all directions, representing the total radiative power per unit area per unit wavelength (or frequency) averaged over a sphere surrounding the point of interest.
Net Flux in direction n
units: W/(m^2Hz) or ergs/(s m^2)
Specific Energy Density
the amount of energy stored per unit volume per unit wavelength (or frequency) in a given medium or field.
Emissivity and emission from a
transparent source (i.e. optically thin)
units: [W m^-3 ster^-1 Hz^-1] and [ergs cm^-3 ster^-1]
Intensity Loss in dx
alpha is the absorption coefficient
Radiative Transfer Equation
Optical Depth
a measure of the opacity of a medium, quantifying the extent to which radiation is absorbed or scattered as it travels through the medium.
Optically thick: Tau much greater than 1
Optically thin: Tau much less than 1
Photosphere: Tau = 1
Optical Depth Plots
Black Body Radiation Description
Black body radiation is radiation which is in thermal equilibrium with matter
* Isotropic and homogenous
* Dependent only by the temperature (T) of the body
* Independent of the shape/size
Planck’s Law
units (SI): [W sr-1 m-2 Hz-1] or [W sr-1 m-3]
units (cgs): [ergs sr-1 cm-2] or [ergs sr-1 s-1 cm-3]
Wien’s Displacement Law
The wavelength at which the emission of a blackbody spectrum is at its maximum is inversely proportional to the temperature of the blackbody.
the lower the max in terms of wavelength, the higher the temperature
the higher the frequencies of the peak, the higher the temperature
BB spectra at different Temperatures (wavelength)
BB spectra at different Temperatures (frequency)
Stefan-Boltzmann law
Brightness Temperature
the temperature of a black body in thermal equilibrium with its surroundings that would emit the same amount of radiation per unit area at a given wavelength as the observed object.
T_b is the brightness temperature
Temperature of the Sun
T=5777K
CMB radiation
Emission peak at mm wavelengths:
* Best known black body source
* T ~ 2.726K
* Fluctuations are the seeds of present large scale structures
