Hi all,
while waiting for Chris to complete his part of the galaxy coding (due since ~ 2 weeks), .....
I thought I might as well "entertain" some of you a bit by telling you about some research I did to get the distances of my 10000-25000 galaxies right. This is quite an art, as you will see below.
There are about
6 popular methods used professionally to determine the distances of galaxies:
a) Hubble's law, using the galaxy's recessional (radial) velocity v_rad:
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d ~ v_rad/H0, H0= 72 km/sec/Mpc (WMAP'05)
with H0 being today's value of the Hubble constant. It's accuracy has greatly increased since the famous WMAP results 2005 about the cosmic microwave background radiation. In a uniformly expanding universe, a galaxy with a larger velocity lies further from an observer than one with a smaller velocity. It is very easy to measure a galaxy's radial velocity with a spectroscope - hundreds of thousands of galaxy velocities have been measured.
Unfortunately galaxies also have smaller NON-radial velocity components, notably when they are part of HUGE clusters of galaxies (Virgo,...). Also one has to wonder in what system one best specifies the velocity. Heliocentric is most usual, galactic center is popular and best is the cosmic microwave background frame (CMB) that I also have adopted.
Moreover... there are also several
blue-shifted galaxies, like Andromeda (M31), Triangulum (M33) and a few others. This means v_rad is NEGATIVE and thus clearly the Hubble distance law is inapplicable...
So for these cases of negative or too small v_rad, other distance methods are needed:
b) Surface Brightness Fluctuations (SBF)
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The further away a galaxy is, the smoother it looks on a photograph. This can be used to accurately measure the distance to the galaxy, although you need to subtract the contribution from the globular clusters around the galaxy which make a galaxy look less smooth. Large numbers of distances to other galaxies are being produced by this technique although it works best on elliptical and lenticular galaxies or on spiral galaxies with broad smooth central bulges.
The seminal papers about this method are by J. Tonry et al. (2001...)
Besides SBF, there are 4 more quantitative distance methods that I just list for completeness:
c) Globular Cluster Luminosity Function (GCLF)
d) Planetary Nebula Luminosity Function (PNLF)
e) Photometric Distances
f) Cepheid Distances
The latter is the oldest and most famous distance method
also pioneered by Edwin Hubble in 1922. The method uses Cepheid variable stars - yellow giant stars which pulsate. The luminosity of these stars is directly proportional to the pulsation periods...The rest should be obvious...
There is another most simple but more qualitative method that I have applied in cases of galaxies where neither v_rad nor the SBF method was applicable or available. It assumes that galaxies of a given Hubble type have to good approximation a very similar absolute magnitude
M_abs ~ -19 to -20.5. (empirically)
If true, one then can easily compute the distance from the difference of the (assumed universal) absolute magnitude and the measured apparent magnitude:
distance = 10**((Bmag - M_abs+5)/5)*3.26167 [ly]
where Bmag is the apparent blue-band magnitude of the galaxy.
In order to check for the accuracy of this method, I did the following: I used the accurately known SBF distances of hundreds of galaxies (cf above) and their measured Bmag values to solve for the corresponding absolute magnitude M_abs (assumed universal)!
So, how well does the above formula really hold??
Here is the result, as evaluated with the help of Maple for
elliptical and spiral galaxies, separately:
The absolute magnitude M_abs is displayed on the x-axis (abszissa)
What can we learn from this plot?
-- the distributions of M_abs are really quite peaked around some most probable value.
-- that peak value is systematically different for elliptical and spiral galaxies by about 1 unit.
-- last not least: that this sort of study is quite a bit of fun
So this was some "fairy-tale" about how I chose to determine the distances in my catalog with
25000+ galaxies...
Bye Fridger