Connection between Temperature and Redshift - Revision history

Cosmo All at 10:04, 9 October 2012

2012-10-09T10:04:48Z

Den: /* Problem 2 */

2012-10-01T21:52:03Z

‎Problem 2

Den at 21:50, 1 October 2012

2012-10-01T21:50:36Z

Cosmo All at 17:19, 30 September 2012

2012-09-30T17:19:39Z

Cosmo All: Created page with "(4)"

2012-09-30T17:17:37Z

Created page with "(4)"

New page

[[Category:Thermodynamics of Universe|(4)]]

@@ Line 11: / Line 11: @@
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
-     <p style="text-align: left;">
+     <p style="text-align: left;">$$
 $$
 T \propto a^{ - 1};\quad T = T_0(1 + z).
 $$
@@ Line 18: / Line 17: @@
    </div>
 </div></div>
 <div id="therm24"></div>
@@ Line 26: / Line 27: @@
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
-     <p style="text-align: left;">
+     <p style="text-align: left;">$$
 $$
 T \propto a^{ - 2};\quad T = T_0(1 + z)^2.
 $$
@@ Line 33: / Line 33: @@
    </div>
 </div></div>
 <div id="therm25"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
 === 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 $T_{rec} \approx 0.3\,eV.$
@@ Line 42: / Line 43: @@
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
-     <p style="text-align: left;">
+     <p style="text-align: left;">$$
 $$
 z_{rec} = \frac{T_{rec}}{T_0} - 1.
 $$

@@ Line 22: / Line 22: @@
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 2 ===
-Find the dependence of free non-relativistic gas' temperature on the redshift.
+Find the dependence of free non-relativistic gas temperature on the redshift.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
@@ Line 36: / Line 36: @@
 <div id="therm25"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
 === 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 $T_{rec} \approx 0.3\,eV.$

← Older revision		Revision as of 21:50, 1 October 2012
Line 1:		Line 1:
	[[Category:Thermodynamics of Universe\|4]]		[[Category:Thermodynamics of Universe\|4]]
		+
		+	__NOTOC__
		+
		+
		+	<div id="therm23"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== Problem 1 ===
		+	Find the dependence of radiation temperature on the redshift.
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">
		+	$$
		+	T \propto a^{ - 1};\quad T = T_0(1 + z).
		+	$$
		+	</p>
		+	</div>
		+	</div></div>
		+
		+	<div id="therm24"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== Problem 2 ===
		+	Find the dependence of free non-relativistic gas' temperature on the redshift.
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">
		+	$$
		+	T \propto a^{ - 2};\quad T = T_0(1 + z)^2.
		+	$$
		+	</p>
		+	</div>
		+	</div></div>
		+
		+	<div id="therm25"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== 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 $T_{rec} \approx 0.3\,eV.$
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">
		+	$$
		+	z_{rec} = \frac{T_{rec}}{T_0} - 1.
		+	$$
		+	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
		+	$$
		+	t_{rec} = t_0\left( \frac{a}{a_0} \right)^{3/2} =
		+	t_0\left(\frac{T_0}{T_{rec}} \right)^{3/2}\approx
		+	300\,000\,years.
		+	$$
		+	</p>
		+	</div>
		+	</div></div>

← Older revision		Revision as of 17:19, 30 September 2012
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−	[[Category:Thermodynamics of Universe\|(4)]]	+	[[Category:Thermodynamics of Universe\|4]]