Difference between revisions of "Connection between Temperature and Redshift"
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T \propto a^{ - 1};\quad T = T_0(1 + z). | T \propto a^{ - 1};\quad T = T_0(1 + z). | ||
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T \propto a^{ - 2};\quad T = T_0(1 + z)^2. | T \propto a^{ - 2};\quad T = T_0(1 + z)^2. | ||
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=== Problem 3 === | === Problem 3 === | ||
Estimate the time moment when the recombination started, i.e. when ionized plasma transited to the gas of neutral atoms, and determine the corresponding redshift value. The recombination temperature equals to $T_{rec} \approx 0.3\,eV.$ | Estimate the time moment when the recombination started, i.e. when ionized plasma transited to the gas of neutral atoms, and determine the corresponding redshift value. The recombination temperature equals to $T_{rec} \approx 0.3\,eV.$ | ||
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z_{rec} = \frac{T_{rec}}{T_0} - 1. | z_{rec} = \frac{T_{rec}}{T_0} - 1. | ||
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Latest revision as of 10:04, 9 October 2012
Problem 1
Find the dependence of radiation temperature on the redshift.
$$ T \propto a^{ - 1};\quad T = T_0(1 + z). $$
Problem 2
Find the dependence of free non-relativistic gas temperature on the redshift.
$$ T \propto a^{ - 2};\quad T = T_0(1 + z)^2. $$
Problem 3
Estimate the time moment when the recombination started, i.e. when ionized plasma transited to the gas of neutral atoms, and determine the corresponding redshift value. The recombination temperature equals to $T_{rec} \approx 0.3\,eV.$
$$ z_{rec} = \frac{T_{rec}}{T_0} - 1. $$ As $1\mbox{\it eV} \approx 11600\,K$, then $$ z_{rec} \approx \frac{0.3}{2.73}11600 \approx 1300. $$ For a rough estimate assume that the transition $T_{rec} \to T_0$ occurs mainly in the matter-dominated epoch to obtain $$ t_{rec} = t_0\left( \frac{a}{a_0} \right)^{3/2} = t_0\left(\frac{T_0}{T_{rec}} \right)^{3/2}\approx 300\,000\,years. $$
