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

In summary, the Hubble profile of surface brightness, represented by I(r) = I_0 \left(1+\frac{r}{R}\right)^{-2}, leads to an infinite total luminosity due to the relationship I(r) \propto r^{-2} for large r. However, the connection between surface brightness and total luminosity may not be explicitly stated in the textbook, causing conceptual difficulties for some. The solution may require further examination of the textbook.
  • #1
Logarythmic
281
0

Homework Statement


Show that the Hubble profile of surface brightness

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

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

[tex]I(r) \propto r^{-2}[/tex]

but how is the surface brightness related to the total luminosity?
 
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  • #2
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.
 
  • #3
I have, all there is about this is one half page of text.
 
  • #4
This is still a problem... Haven't anyone dealt with this before?
 

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

1. What is luminosity in physics?

Luminosity in physics refers to the total amount of energy emitted by a celestial object per unit time. It is a measure of the object's intrinsic brightness and is often used to describe the intensity of light or other forms of electromagnetic radiation.

2. How is luminosity calculated?

Luminosity is calculated by multiplying the surface area of the object by its temperature to the fourth power (known as the Stefan-Boltzmann law). This gives the total energy emitted per unit time, and it is usually expressed in units of watts.

3. What factors affect luminosity?

The main factors that affect luminosity include the size and temperature of the object. Generally, the larger and hotter an object is, the more luminous it will be. Other factors that can affect luminosity include the object's composition, density, and any ongoing nuclear reactions taking place within it.

4. How is luminosity measured?

Luminosity is typically measured using instruments such as telescopes and photometers, which are designed to detect and measure electromagnetic radiation. By analyzing the amount and type of radiation emitted by an object, scientists can determine its luminosity and other important characteristics.

5. Why is luminosity important in astronomy?

Luminosity is important in astronomy because it allows scientists to compare and classify different celestial objects based on their intrinsic brightness. It can also provide valuable information about an object's size, temperature, and other physical properties, which can help us better understand the nature and evolution of the universe.

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