CMB interaction with other components - Revision history

Igor: /* Problem 7 */

2012-11-19T21:03:31Z

‎Problem 7

Igor at 21:02, 19 November 2012

2012-11-19T21:02:19Z

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Cosmo All at 21:26, 1 October 2012

2012-10-01T21:26:34Z

Cosmo All at 21:25, 1 October 2012

2012-10-01T21:25:31Z

Cosmo All at 21:24, 1 October 2012

2012-10-01T21:24:39Z

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Cosmo All: Created page with "5 =CMB interaction with other components="

2012-09-25T00:12:34Z

Created page with "5 =CMB interaction with other components="

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[[Category:Cosmic Microwave Background (CMB)|5]]
=CMB interaction with other components=

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-=== Problem 7 ===
+=== Problem 7: photon in non-relativistic electron gas ===
 A photon with energy $E\ll mc^2$ undergoes collisions and Compton scattering in the electron gas with temperature $kT\ll mc^2$. Show that to the leading order in $E$ and $T$ the average energy lost by photons in collisions takes the form \[\langle\Delta E\rangle=\frac{E}{mc^2}(E-4kT).\]
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 === Problem 8: drag force ===
 Find the force acting on an electron moving through the CMB with velocity $v\ll c$.

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 W = \sigma _T Nd,
 \]
-where $\sigma _T\simeq6.65 \cdot 10^{ - 25} \mbox{\it cm}^2 $ is the Thomson cross section, $n$ is the electron density, $d$ is the distance passed by the photon. For the case of flat Universe $\rho  = \rho
+where $\sigma _T\simeq6.65 \cdot 10^{ - 25} \mbox{cm}^2 $ is the Thomson cross section, $n$ is the electron density, $d$ is the distance passed by the photon. For the case of flat Universe $\rho  = \rho
 _{cr} $ and as the baryons contribution is of order of $4\% $ of total density then $N \simeq 2.3 \cdot 10^{ - 7} \mbox{cm}^{ - 3}.$ The passed distance is of order of observable part of Universe in the present time: $d \sim 10^{28} \mbox{cm}$ . As the result one obtains the following
 \[
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 E'_{\gamma}=\frac{E}{1+\frac{1}{4}\frac{m^2}{EE_\gamma}}.
 $$
-Taking into account that $E_\gamma \simeq 10^{-3} \mbox{\it eV} \mbox{ and } m \simeq 10^{9} \mbox{\it eV} $ one obtains that $E'_{\gamma} \simeq 3\cdot 10^{19}\mbox{\it eV}.$ As the result of the considered effect the number of CMB quanta that come from the direction of a cluster effectively decreases, which manifests in lowering of the CMB temperature. The latter is called the Sunyaev-Zel'dovich effect.</p>
+Taking into account that $E_\gamma \simeq 10^{-3} \mbox{ eV} \mbox{ and } m \simeq 10^{9} \mbox{ eV} $ one obtains that $E'_{\gamma} \simeq 3\cdot 10^{19}\mbox{ eV}.$ As the result of the considered effect the number of CMB quanta that come from the direction of a cluster effectively decreases, which manifests in lowering of the CMB temperature. The latter is called the Sunyaev-Zel'dovich effect.</p>
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-=== Problem 1 ===
+=== Problem 2 ===
 A photon of frequency $\omega$ impacts on an electron at rest and is scattered at angle $\vartheta $. Find the change of the photon frequency.
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-=== Problem 1 ===
+=== Problem 3 ===
 When a relativistic charged particle is scattered on a photon, the process is called the inverse Compton scattering of the photon. Consider the inverse Compton scattering in the case when a charged particle with rest mass $m$ and total energy $E\gg m$ in laboratory frame impacts a photon with frequency $\nu$. What is the maximum energy that the particle can transfer to the photon?
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-=== Problem 1 ===
+=== Problem 4 ===
 Estimate the probability of the fact that a photon observed on Earth has already experienced Thomson scattering since the moment it left the surface of last scattering.
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-=== Problem 1 ===
+=== Problem 5 ===
 Cosmic rays contain protons with energies up to $10^{20}eV$. What energy can be transmitted from such a proton to a photon of temperature $3K$?
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-=== Problem 1 ===
+=== Problem 6 ===
 Relic radiation passes through hot intergalactic gas and is scattered on the electrons. Estimate the CMB temperature variation due to the latter process (the Sunyaev-Zel'dovich effect).
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-=== Problem 1 ===
+=== Problem 7 ===
 A photon with energy $E\ll mc^2$ undergoes collisions and Compton scattering in the electron gas with temperature $kT\ll mc^2$. Show that to the leading order in $E$ and $T$ the average energy lost by photons in collisions takes the form \[\langle\Delta E\rangle=\frac{E}{mc^2}(E-4kT).\]
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-=== Problem 1 ===
+=== Problem 8 ===
 Find the force acting on an electron moving through the CMB with velocity $v\ll c$.
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-=== Problem 1 ===
+=== Problem 9 ===
 Estimate the characteristic time of energy loss by high-energy electrons with energy of order $100GeV$ passing through the CMB.
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-=== Problem 1 ===
+=== Problem 10 ===
 Find the energy limit above which the $\gamma$-rays interacting with the CMB should not be observed.
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