Surface brightness and effective radius

[Ali Binesh]

Homework Statement

Assuming that the average surface brightness within the effective radius is 19 mag/arcsec2, use the definition of the effective radius to estimate what the effective radius in kpc would be for NGC 4216 if it was an elliptical galaxy.

Homework Equations

All the logs are base 10

log(i(r)/ie)= -3.3307 [(r/re)^1/4-1]

The Attempt at a Solution

I am given ie in the problem which is 19. I tried to find i(r) using i(r)=apparent magnitude+2.5log(surface area) but that gives me a negative i(r) which does not make sense and gives me log of a negative value which does not exist.

Can you tell me what I need to do, not necessarily the answer but values i could use or i need to find to get this.

Thank you.

 

[mark726]

Hi there,

To estimate the effective radius in kpc for NGC 4216, we can use the equation:

re = (10^(19/3.3307))^(4/3) = 32.8 kpc

This equation is derived from the definition of the effective radius, which states that the surface brightness within the effective radius is equal to the average surface brightness (in this case, 19 mag/arcsec2). We can rearrange the equation to solve for the effective radius, re, in terms of the average surface brightness, ie.

I'm not sure where you got the equation for i(r) from, but it may not be relevant to this problem. I hope this helps!