Observing galaxies: area of sky would I need to survey

[Cedric Chia]

Homework Statement

Given that there are 10^-2 Ellipticals per Mpc³ and my garden telescope can reach to 14 mag. How large an area of sky would I need to survey to find 100 Elliptical galaxies ? (assume the typical absolute magnitude for an Elliptical galaxy is -21 mag).

Homework Equations

d=10^0.2(m-M-25)
n=N/V

The Attempt at a Solution

by substituting m=14 and M=-21 into the first equation I found d=100Mpc,

which indicates the volume of sky I could possibly observed is 4/3⋅π⋅d³ = 4188790 Mpc³,

using the second equation n=N/V , where n=number density, I have 10^-2 = 100/V,

thus V=10000Mpc³, which is the volume I need to observed to find 100 galaxies.

with these values, how can I find how large the area of sky I need to survey?

 

[hutchphd]

Homework Statement

Given that there are 10^-2 Ellipticals per Mpc³ and my garden telescope can reach to 14 mag. How large an area of sky would I need to survey to find 100 Elliptical galaxies ? (assume the typical absolute magnitude for an Elliptical galaxy is -21 mag).

Homework Equations

d=10^0.2(m-M-25)
n=N/V

The Attempt at a Solution

by substituting m=14 and M=-21 into the first equation I found d=100Mpc,

which indicates the volume of sky I could possibly observed is 4/3⋅π⋅d³ = 4188790 Mpc³,

using the second equation n=N/V , where n=number density, I have 10^-2 = 100/V,

thus V=10000Mpc³, which is the volume I need to observed to find 100 galaxies.

with these values, how can I find how large the area of sky I need to survey?

You have almost finished... What units are you going to use to report your answer (solid angle, fraction of the hemisphere sphere...)?

 

[Cedric Chia]

You have almost finished... What units are you going to use to report your answer (solid angle, fraction of the hemisphere sphere...)?

How can I find solid angle relative to the 10000MPc³?

 

[hutchphd]

How can I find solid angle relative to the 10000MPc³?

The solid angle for a whole sphere is 4pi...for half sphere 2pi...how much of the sphere do you need to view?

 

[Cedric Chia]

The solid angle for a whole sphere is 4pi...for half sphere 2pi...how much of the sphere do you need to view?

Thank you for the quick reply,

the total volume of the sphere is 4188790 Mpc³
("which indicates the volume of sky I could possibly observed is 4/3⋅π⋅d³ = 4188790 Mpc³")

and the volume I need to view is 10000Mpc³
("thus V=10000Mpc³, which is the volume I need to observed to find 100 galaxies")

with these values how can I find solid angle?

 

[hutchphd]

What fraction of the total sphere volume do you need to observe?

 

[Cedric Chia]

What fraction of the total sphere volume do you need to observe?

I think that would be (volume I need to observe) / (total sphere volume) = (10000) / (4188790) = 2.39⋅10^-3

 

[hutchphd]

And so you need that fraction times 4pi to express it as a solid angle of a sphere:
https://en.wikipedia.org/wiki/Steradian

 

[Cedric Chia]

And so you need that fraction times 4pi to express it as a solid angle of a sphere:
https://en.wikipedia.org/wiki/Steradian

thank you very much, you are very helpful