- #1
fab13
- 318
- 6
Hello,
I am asked to give the formal expression of the total number density of galaxies and explain why is this expression problematic in practice?
From what I saw from my research and into my lectures, I have found the follwing relation which gives the number of galaxies ##N## with mass ##(m < M)## (number counts) :
##\text{log}\,N(m<M)\,\propto\,0.6 M + \text{constant}\quad(1)##
##N(m<M)\,\propto\,\text{exp}(0.6 M)\,\text{exp(constant)}\quad(2)##
1) But If want to express the density, I need the volume for this count of galaxies above, i.e the volume in which the number of galaxies ##N(m<M)## is located.
2) Moreover, have I got to set a maximum value ##M_{max}## for ##m## in the expression ##(1)## ? It should be necessary since otherwise, the number of galaxies diverges, should'nt it ?
3) Maybe for the volume, I have to take into account just the size of observable universe since beyond this limit, we can't detect galaxies, do you agree ?
If someone could give me indications or tracks to anwser to these 2 questions ,Regards.
I am asked to give the formal expression of the total number density of galaxies and explain why is this expression problematic in practice?
From what I saw from my research and into my lectures, I have found the follwing relation which gives the number of galaxies ##N## with mass ##(m < M)## (number counts) :
##\text{log}\,N(m<M)\,\propto\,0.6 M + \text{constant}\quad(1)##
##N(m<M)\,\propto\,\text{exp}(0.6 M)\,\text{exp(constant)}\quad(2)##
1) But If want to express the density, I need the volume for this count of galaxies above, i.e the volume in which the number of galaxies ##N(m<M)## is located.
2) Moreover, have I got to set a maximum value ##M_{max}## for ##m## in the expression ##(1)## ? It should be necessary since otherwise, the number of galaxies diverges, should'nt it ?
3) Maybe for the volume, I have to take into account just the size of observable universe since beyond this limit, we can't detect galaxies, do you agree ?
If someone could give me indications or tracks to anwser to these 2 questions ,Regards.