Log N(s) vs Log S Graph for Radio Galaxies

[andyfreesty1e]

Homework Statement

if the intrinsic brightness of a class of radio galaxies fades as the universe ages, such that those that we see further away are brighter, having a linear increase in luminosity with distance r, what would be the slope of a graph of log N(s) versus log S for these objects.

Homework Equations

The Attempt at a Solution

I know that usually, the slope would be -1.5, but as it says those that we see further away are brighter, i would expect that you would see more objects above the threshold S. So I am thinking that the slope would not be -1.5.

Instead of using S=L/(4pi r^2), would i say that L=r, as it says having a linear increase in luminosity with r?

 

[Jhero]

I would approach this problem by first understanding the concept of intrinsic brightness and how it relates to the age of the universe. Intrinsic brightness refers to the inherent brightness of an object, independent of its distance from us. It is important to note that the intrinsic brightness of an object does not change as it ages, but our perception of its brightness can be affected by its distance from us.

In this case, we are dealing with a class of radio galaxies whose intrinsic brightness fades as the universe ages. This means that the further away we observe these galaxies, the brighter they will appear to us due to the decrease in their intrinsic brightness. This also means that as we increase our distance from these galaxies, we will observe more of them above a certain threshold of brightness (S).

To determine the slope of a graph of log N(s) versus log S for these objects, we need to first understand the relationship between the number of objects (N) and their brightness (S). As mentioned earlier, as we increase our distance from these galaxies, we will observe more of them above the threshold S. This means that the number of objects (N) will increase as the brightness (S) decreases.

To determine the slope, we can use the equation log N = a log S + b, where a is the slope and b is the intercept. Since we know that the brightness (S) is decreasing with distance, we can assume that the slope (a) will be negative. However, the exact value of the slope will depend on the specific relationship between the intrinsic brightness and distance of these radio galaxies.

In this case, if the intrinsic brightness is directly proportional to distance (L = r), then the slope would be -1. This means that for every unit increase in log S, there will be a corresponding decrease of one unit in log N. However, if the relationship between intrinsic brightness and distance is not linear, then the slope may be different from -1.

In conclusion, the slope of a graph of log N(s) versus log S for these objects would depend on the specific relationship between intrinsic brightness and distance. It is important to consider the concept of intrinsic brightness and its relationship to distance when analyzing the brightness of objects in the universe.