Blackbody Radiation: Temperature of Accreted Gas

In summary: Well, if it were a pure blackbody, then Wein's law would be fine. In reality, accretion disks are not at a uniform temperature, even in the simplest model. I get the impression, from the wording, that the question is just looking for an order of magnitude. The true astronomer thing to do would be to divide by Boltzmann's constant and be done with it. :biggrin:Since the problem doesn't specify the model one would have to use,i think the BB rad.is the only viable option.As for order of magnitude,indeed,incorrect formulas may provide good answers... ...Since the errors are very large.
  • #1
tony873004
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This is actually a homework question, but its probably better suited for this forum.

Gas accreting onto burned-out stars like white dwarfs, neutron stars, and black holes can often be seen in the X-ray part of the EM spectrum, at energies of about 10 keV. What temperature does this suggest that the accreted gas is heated to?

I can't make sense of my class notes, and the textbook does not cover this well. I can't find a formula that relates wavelength to energy to give temperature. Formulas using Watts is the closest I can come, but Watts is Joules / s, and there is no time in this problem. What did I scribble down in my notes that I can't read??
 
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  • #2
I think what you're looking for is Wien's displacement law:

[tex]\lambda_{max}T=2.898x10^{-3} m \cdot K[/tex]

You can convert the energy of the X-Rays to wavelength using

[tex]E=\frac{hc}{\lambda}[/tex]

Just be careful to watch your units. There are several conversions to be done, and the final answer should come out in Kelvin.
 
  • #3
Grogs said:
I think what you're looking for is Wien's displacement law:

[tex]\lambda_{max}T=2.898x10^{-3} m \cdot K[/tex]

You can convert the energy of the X-Rays to wavelength using

[tex]E=\frac{hc}{\lambda}[/tex]

Just be careful to watch your units. There are several conversions to be done, and the final answer should come out in Kelvin.

Thank you very much! It took me a while, but I came up with something similar (the same, just written a little different)

[tex]t=\frac{2900 \mu m K}{\lambda_{peak}}[/tex]
and I got [tex]2*10^{7}K[/tex] if I converted my units properly.
 
  • #4
In the interest of understanding what you're doing with all those formulae, notice that the spectrum of a blackbody has a peak in the center, and that peak moves with temperature. Wien's law simply relates the temperature and the wavelength at the peak, allowing you to find one if you know the other.

- Warren
 
  • #5
tony873004 said:
and I got [tex]2*10^{7}K[/tex] if I converted my units properly.

That's what I got too. You might find http://qonos.princeton.edu/nbond/unicalc/calculator.php [Broken] useful. I have to do that kind of calculation a lot and Google calculator was really tedious, so I wrote my own to save time. It's mostly for astrophysics calculations at the moment.
 
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  • #6
I think you should be using this formula:<u>~2.7kT.Incidentally,it gives the same order of magnitude as Wien's law,but there's no reason why anyone would choose Wien's law in this case...

Daniel.
 
  • #7
dextercioby said:
I think you should be using this formula:<u>~2.7kT.Incidentally,it gives the same order of magnitude as Wien's law,but there's no reason why anyone would choose Wien's law in this case...

Well, if it were a pure blackbody, then Wein's law would be fine. In reality, accretion disks are not at a uniform temperature, even in the simplest model. I get the impression, from the wording, that the question is just looking for an order of magnitude. The true astronomer thing to do would be to divide by Boltzmann's constant and be done with it. :biggrin:
 
  • #8
Since the problem doesn't specify the model one would have to use,i think the BB rad.is the only viable option.As for order of magnitude,indeed,incorrect formulas may provide good answers...

...Since the errors are very large.

Daniel.
 

What is blackbody radiation?

Blackbody radiation is the electromagnetic radiation emitted by a perfect blackbody, which absorbs all incident radiation and reflects none. It has a characteristic spectrum that depends only on its temperature.

How is blackbody radiation related to temperature of accreted gas?

The temperature of accreted gas refers to the temperature of gas that is being pulled in by a massive object, such as a black hole or a star. This gas can emit blackbody radiation, which can provide valuable information about its temperature and the properties of the object it is being accreted onto.

What factors affect the temperature of accreted gas?

The temperature of accreted gas can be affected by various factors, including the size and mass of the object it is being accreted onto, the distance from the object, and the composition of the gas itself.

How is the temperature of accreted gas measured?

The temperature of accreted gas can be measured through various methods, including spectroscopy, which analyzes the emitted blackbody radiation and determines the temperature based on its characteristic spectrum. Other methods include using X-ray observations and modeling the gas dynamics.

Why is understanding the temperature of accreted gas important for scientists?

Studying the temperature of accreted gas can provide valuable insights into the physics of objects such as black holes and stars, as well as their interactions with their surroundings. It can also help us understand the formation and evolution of these objects and the structures they form within their environment.

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