23 votes

Why does the CMB conform to black-body formula for 2.71 degrees, when it's the stretched emission at a far hotter temp?

The Planck spectrum of a blackbody is given by $$B(\nu, T) = \frac{2h\nu^3}{c^2} \left( \exp[h\nu/k_BT] - 1\right)^{-1} \ , $$ where $\nu$ is the frequency, $T$ is the temperature and $h$ and $k_B$ ...
ProfRob's user avatar
  • 152k
15 votes

Why does the CMB conform to black-body formula for 2.71 degrees, when it's the stretched emission at a far hotter temp?

According to the Hubble law all radiation is progressively red-shifted with distance traveled, with the wavelength changing from $\lambda$ to $\lambda(1+z)$ (with $z>0$). Now the formula for the ...
Thomas's user avatar
  • 3,476
9 votes
Accepted

What is the RGB curve for blackbodies?

Ok, here's my take on calculating the color of a blackbody, or any spectrum in fact: Disclaimer: I'm not a color theorist, and there may be more accurate methods. But the result, shown in the bottom, ...
pela's user avatar
  • 38.3k
8 votes
Accepted

At high temperatures, do planets glow like blackbodies?

At high temperatures, do planets glow like blackbodies? Yes, and at low temperatures too!1 1As @DavidHammen points out, since there's likely going to be a star nearby the planet, it will also be ...
uhoh's user avatar
  • 30.7k
7 votes

How to Distinguish between Temperature and Doppler effect using Black-body radiation?

Without any other information, you cannot distinguish between the two effects. $$ T = T_0 (1 + z) $$ A blackbody spectrum of temperature $T$ is identical to a blackbody spectrum of temperature $...
BowlOfRed's user avatar
  • 2,085
5 votes
Accepted

What does a black dwarf look like?

The material at the surface of a white dwarf is not degenerate. The "visible" surface is defined as where the optical depth exceeds some threshold and this will occur at a low enough density that ...
ProfRob's user avatar
  • 152k
4 votes
Accepted

Can hawking radiation be eaten by another blackhole?

Black holes can "eat" Hawking radiation, but the radiation has to be directed towards the black hole before it can be "eaten". Black holes are pretty small, and space is very very very big. So as a ...
James K's user avatar
  • 122k
3 votes
Accepted

Future redshifting and effect on the 'pitch' of CMB radiation

The wavelength of the CMB increases linearly with the scale factor $a$, which is defined as 1 today, so the "sound" of the CMB has dropped an octave when the Universe has doubled in size (in all three ...
pela's user avatar
  • 38.3k
3 votes
Accepted

How is Cosmic Microwave Background's temperature measured?

That is what is done. This is shown in an old xkcd comic https://xkcd.com/54/ The curve shows the distribution of frequencies in the CMB, and by using the marked value of the maximum you can ...
James K's user avatar
  • 122k
3 votes

Questions about Planck’s law

It would be good to specify what "majority of radiation" means. If it means "radiative energy", then this premise is surely wrong. To find the energy emitted per wavelength, take the Planck function $...
AtmosphericPrisonEscape's user avatar
3 votes
Accepted

Trouble with plotting a graph for the Planck function

Here's what I got for $\nu B_{\nu}(T)$ using Python, which is easy enough to read that maybe you can check against your Excel calculation. I also plotted just $B_{\nu}(T)$ for comparison. Neither ...
uhoh's user avatar
  • 30.7k
3 votes
Accepted

How to Distinguish between Temperature and Doppler effect using Black-body radiation?

If the object you're observing is something good and hot, like a star, it's pretty easy to identify a set of Ballmer lines by the relative spacing between the lines. Then compare the absolute ...
Carl Witthoft's user avatar
3 votes

Back when the CMB was predominantly in the visible spectrum, would it have been visible to the naked eye?

It wouldn't be like staring into the Sun so much as being inside the Sun (its photosphere, anyway). What we really see is not distant objects, but light that enters our eyeballs. The CMB radiation ...
benrg's user avatar
  • 3,852
3 votes

Back when the CMB was predominantly in the visible spectrum, would it have been visible to the naked eye?

The cosmic microwave background (CMB) was emitted as a blackbody at a temperature of about 3000 K. The CMB temperature then falls as the universe expands and is currently at a temperature of 2.73 K. ...
ProfRob's user avatar
  • 152k
2 votes

Does most of the Sun's energy and light come from its black-body temperature, due to its massive size alone? Constant crashing of particles?

If you calculate the total thermal energy of the Sun now - i.e. the sum of the thermal (kinetic energy) of its constituent particles - then it could be used to supply it's current luminosity for 40 ...
ProfRob's user avatar
  • 152k
2 votes

Does most of the Sun's energy and light come from its black-body temperature, due to its massive size alone? Constant crashing of particles?

A collapsing cloud of gas will generate heat from the release of gravitational potential energy, and it's core temperature will continue to rise. Indeed this is the mechanism that Kelvin and Helmholz ...
James K's user avatar
  • 122k
2 votes

Strange behaviour of black holes

What you need to understand is that a black hole is a region of space defined by an event horizon. The key point about an event horizon is that if you're inside the region it surrounds you cannot get ...
StephenG - Help Ukraine's user avatar
2 votes
Accepted

Strange behaviour of black holes

Black hole don't allow anything to escape, if the matter/light is inside the event horizon (boundary which describes the point of no return). The emission radiation that is referred in the question is ...
Gauti's user avatar
  • 529
2 votes

Does photon capture in a black hole (or any other "very compact" object) reduce the luminosity/photon flux from its self isotropic emission?

Let's answer the question from the point of view of a stable neutron star. The luminosity is $$L_0 = 4\pi R_0^2 \sigma T_{0}^4$$ in the inertial frame of the neutron star surface (assume a non-...
ProfRob's user avatar
  • 152k
2 votes
Accepted

In what manner is the spectrum of a black body really a continuum?

A blackbody spectrum is continuous. As Dean comments, there are no true blackbodies. But this is not really the issue here: It's true that most emitted photons from, say, a star, which is quite ...
pela's user avatar
  • 38.3k
1 vote

Why is a black hole's Hawking radiation temperature inversely proportional to its mass/size?

Þe olde goode dimensional analysis can help. The Hawking radiation is essentially a quantum field effect of the same nature as the Unruh effect. Quantum fields “live” in a distorted space-time of the ...
Incnis Mrsi's user avatar
1 vote

Why is a black hole's Hawking radiation temperature inversely proportional to its mass/size?

In a sense, you're right. Vacuum energy over a surface area is proportional to the surface area so larger area means more of the particle-antiparticle occurrences and that's the source of Hawking ...
userLTK's user avatar
  • 24k
1 vote

How to convert from Black body intensity to MJy/sr?

Part 1 On the one hand, ${\rm 1\, ergs\cdot cm^{-2}\cdot s^{-1} \cdot sr^{-1}\cdot Hz^{-1}} = 10^{-3} {\rm J}/({\rm m^2} \cdot {\rm sr})$ has basic dimensions ${\rm mass} \cdot {\rm time}^{-2} \cdot {\...
B--rian's user avatar
  • 5,616
1 vote

Where can we find astronomical real world data (spectral radiance and wavelength particularly) of a star?

The best way to do this is to pick a particular astronomical instrument or science mission and go to their website. Almost all astronomy projects are required to release their data to the public and ...
zephyr's user avatar
  • 15k

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