Observational Astrophysics Flashcards
luminosity
energy radiated per unit time by a source
joules per second or watts
what is luminosity dependent on?
frequency (or wavelength)
objects of a particular colour radiate more power at frequencies corresponding to their colour
luminosity at a specific frequency (monochromatic luminosity)
L=L(v)
luminosity of a source in a frequency interval delta v centred on v0
L=L(v0)deltav
integral for luminosity
strictly speaking, luminosity should be the integral of L(v) dv between v0-1/2 delta v and v0+1/2 delta v
since delta v small, can approximate as L(v0)delta v
bolometric luminosity
total power by integrating across all frequencies
“energy per unit time radiated by all frequencies”
isotropic
uniform in all directions
what does assuming astrophysical sources are point sources that radiate isotropically allow?
relate luminosity to apparent brightness or flux
flux falls off with…
the square of the distance because of the surface area of a sphere increasing with the square of its radius
radiant flux, F
energy per unit time crossing a unit area perpendicular to the direction of light propagation
watts per square metre
flux for an isotropic point source
F=L/4piD^2
how is flux density denoted and units
denoted by:
F(v),S(v), Fv or Sv
unit is janksy (Jy)
why does flux density need to be defined
frequency dependent
if observe at frequencies v1 and v2, flux in this interval is…
F= integral Sv dv between v1 and v2
bandwidth of interval
delta v= v2-v1
mean frequency
v bar = 1/2(v2+v1)
if delta v is small or Sv is either flat or varies linearly with frequency, then
F=Sv bar delta v
integrated flux = flux density x bandwidth
solid angle
fraction of sky covered by an extended source
steradian (sr)
solid angle formula
omega = A/D^2
A = area
D=distance
solid angle of whole sky
4piD^2/D^2=4pi sr
solid angle for a spherical source
A=piR^2 so omega = pi(R/D)^2
show from trig that theta/2=R/D
so can be written as omega=pi(theta/2)^2
theta in radians
what is the need to introduce specific intensity?
an extended source may deliver the same flux density as a point source but is spread over a small area of the sky.
an extended source will not be equally bright across their entire projected area.
specific intensity
flux density of the source (through a plane perpendicular to the direction of the source) per unit solid angle
if rays arrive at an angle, the flux is
reduced by cos theta