blackbody

Examples of blackbody in the following topics:

• Blackbody Radiation

  • A blackbody is of course characterized by a single temperature, $T$.
  • However, it is often convenient to characterize the radiation from astrophysical sources by assuming that it is a blackbody and using some property of the blackbody spectrum to derive a characteristic temperature for the radiation.
  • The brightness temperature is determined by equating the brightness or intensity of an astrophysical source to the intensity of a blackbody and solving for the temperature of the corresponding blackbody.
  • This may be done in a more sophisticated manner by fitting a blackbody spectrum or something like that.
  • Finally the effective temperature is the temperature of a blackbody that emits the same flux at its surface as the source, i.e.

• Blackbody Temperatures

  • A blackbody is of course characterized by a single temperature, $T$.
  • However, it is often convenient to characterize the radiation from astrophysical sources by assuming that it is a blackbody and using some property of the blackbody spectrum to derive a characteristic temperature for the radiation.
  • The brightness temperature is determined by equating the brightness or intensity of an astrophysical source to the intensity of a blackbody and solving for the temperature of the corresponding blackbody.
  • This expression is most useful in the regime where the intensity of the blackbody is proportional to the temperature i.e. the Rayleigh-Jeans limit.
  • Finally the effective temperature is the temperature of a blackbody that emits the same flux at its surface as the source, i.e.

• Thermodynamics

  • A blackbody is of course characterized by a single temperature, $T$.
  • However, it is often convenient to characterize the radiation from astrophysical sources by assuming that it is a blackbody and using some property of the blackbody spectrum to derive a characteristic temperature for the radiation.
  • The brightness temperature is determined by equating the brightness or intensity of an astrophysical source to the intensity of a blackbody and solving for the temperature of the corresponding blackbody.
  • This expression is most useful in the regime where the intensity of the blackbody is proportional to the temperature i.e. the Rayleigh-Jeans limit.Here we have,
  • Finally the effective temperature is the temperature of a blackbody that emits the same flux at its surface as the source, i.e.

• A Physical Aside: Intensity and Flux

  • Blackbody radiation is a radiation field that is in thermal equilibrium with itself.
  • Using detailed balance between two enclosures in equilibrium with each other and the enclosed radiation we can quickly derive several important properties of blackbody radiation.
  • The intensity ($I_\nu$) of blackbody radiation does not depend on the shape, size or contents of the enclosure.

• Thermal Radiation

  • Let's imagine a blackbody enclosure, and we stick some material inside the enclosure and wait until it reaches equilibrium with the radiation field, $I_\nu = B_\nu(T)$.
  • If it didn't, we could set up an adjacent blackbody enclosure at the same temperature and energy would flow between them.
  • If we remove the thermal emitter from the blackbody enclosure we can see the difference between thermal radiation and blackbody radiation.
  • A thermal emitter has $S_\nu = B_\nu(T)$,$B_\nu(T)$ so the radiation field approaches $B_\nu(T)$ (blackbody radiation) only at large optical depth.

• Emission

  • If one assumes that the disk radiates locally as a blackbody, the spectrum is simply the sum of the various blackbodies (the so-called multi-temperature disk model).

• LTE

  • Because the source function equals the blackbody function, does this mean that sources in local thermodynamic equilibrium emit blackbody radiation?

• B.1 Chapter 1

  • The blackbody flux from the surface of the star is given by
  • If we have a blackbody underwater and a blackbody in air at equal temperatures, the underwater blackbody will emit
  • which is larger by a factor of $n^3$, so the energy density within the water of the blackbody radiation is larger by a factor of $n^3$ than in air.
  • For the underwater blackbody to absorb as much as radiation from the blackbody in air as the blackbody in air receives from it, the solid angle subtended by the underwater BB must be larger by $n^2$ so it is magnified linearly by a factor of $n\approx 1.33$.

• Problems

  • Let's say that you have a blackbody spectrum of temperature $T$ of photons passing through a region of hot plasma ($T_e$).You can assume that $T \ll T_e \ll m c^2/k$.
  • Let's suppose that the blackbody photons are from the cosmic microwave background.What is the difference in the brightness temperature of the photons that pass through the cluster and those that don't (including the sign)?

• Problems

  • You may assume that all of the energy generated by viscous stresses is radiated locally as blackbody emission.
  • Using the blackbody formula what is the temperature of the surface of the disk?
  • To do this you will have to think about the peak flux from a blackbody at a particular temperature and the size of the disk that radiates at $T_\mathrm{max}$ and $T_\mathrm{min}$.