2.1-2.2 Surface Brightness and Sersic Law Flashcards
What is the symbol for the linear and logarithmic surface brightness?
Linear: I, Σ [Solar L pc^-2]
Log: µ [mag arcsec^-2]
What is important to note about the surface brightness in terms of their units?
Surface brightness is not flux from a point source
- Galaxies are extended sources in the sky
What is the relationship between surface brightness, and distance to the galaxy?
They are independent
The distance cancels between flux and area
I = F / α^2 = L / 4pi d^2 * d^2 / D^2
What is the conversion between 1 L_solar pc^-2 to mag arcsec^-2?
1 L_solar pc^-2 = 25.68 mag arcsec^-2
What makes galaxies typically hard to detect against the night sky?
Typically have a log surface brightness µ = 22mag arcsec^-2 which is comparable to the night sky
In the equation for the Sersic law, I = I(0)exp( [-r/a]1/n ), state the meaning of all the quantities
I(0) is the surface brightness at the galaxy centre
r is the radial distance from the centre of the galaxy
a is the typical length scale over which the surface brightness decreases by e
n is the Sersic index describing how quickly the surface brightness falls off
Describe what Sersic index, n, galaxies take
Early elliptical galaxies peak between n = 4-6
Late spiral galaxies peak between n = 1-2
Usually a smooth distribution in n
If we have an exponential in the linear surface brightness, I, what relationship would we expect to see for the logarithmic brightness, µ?
A straight line
What is significant about the Sersic index, n = 1?
It describes an exponential profile which is a good fit for:
Disks of spirals, dSph, dE
Dwarph spheroidal and dwarf elliptical
How can we get the total luminosity of a galaxy from the exponential profile?
Integrate the surface brightness from 0 to infinity multiplied by 2πr dr which is the are of a ring
What is the effective radius equal to?
R_e, The half light radius i.e the radius that contains 50% of the light of a galaxy
How can we calculate the mean surface brightness?
Σ = L_total / 2π(R_e)^2
What are the two applications for the exponential decay for the surface brightness?
Used for the radial component and the vertical component. Describe the surface brightness in 2D
I (r, z) = I(0) exp(-z/h) exp(-r/a)
r and z are the radial and vertical coordinates
h and a are the scale length and scale height
What is significant about the Sersic index, n = 4?
De Vaucouleur’s law
Fits bulges of spirals and ellipticals very well
Describe the two shapes of n=1 and n=4 for a surface brightness - r graph
Exponential drops then flattens out
de Vaucouleurs drops much more suddenly but falttens out above the exponential
