Does the Hubble Profile of Surface Brightness Lead to Infinite Total Luminosity?

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    Luminosity Physics
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Homework Help Overview

The discussion revolves around the Hubble profile of surface brightness, specifically the mathematical expression for surface brightness and its implications for total luminosity. The original poster seeks to demonstrate that this profile leads to infinite total luminosity, raising questions about the relationship between surface brightness and total luminosity.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to relate the surface brightness to total luminosity, noting that for large distances, the surface brightness behaves as I(r) proportional to r^{-2}. However, they question how this relationship translates to total luminosity.

Discussion Status

Some participants suggest that the problem may be more conceptual than mathematical, indicating that the original poster might benefit from revisiting textbook material. There is a sense of frustration expressed regarding the perceived lack of comprehensive resources on the topic.

Contextual Notes

Participants note that the textbook provides limited information on the subject, which may hinder understanding and resolution of the problem. The original poster expresses concern about the clarity of the problem and whether it has been addressed previously.

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Homework Statement


Show that the Hubble profile of surface brightness

I(r) = I_0 \left(1+\frac{r}{R}\right)^{-2}

leads to an infinite total luminosity. r is the distance from the center and R is a constant.


2. The attempt at a solution
For large r this is related as

I(r) \propto r^{-2}

but how is the surface brightness related to the total luminosity?
 
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Can't you find it in the textbook ? Even though the problem seems to be purely mathematical (basically a computation which gives infinity as its result), you have problems in the conceptual domain. Well, the/my advice is to look again in the book.
 
I have, all there is about this is one half page of text.
 
This is still a problem... Haven't anyone dealt with this before?
 

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