| 1 | (* Content-type: application/vnd.wolfram.mathematica *)
|
|---|
| 2 |
|
|---|
| 3 | (*** Wolfram Notebook File ***)
|
|---|
| 4 | (* http://www.wolfram.com/nb *)
|
|---|
| 5 |
|
|---|
| 6 | (* CreatedBy='Mathematica 11.1' *)
|
|---|
| 7 |
|
|---|
| 8 | (*CacheID: 234*)
|
|---|
| 9 | (* Internal cache information:
|
|---|
| 10 | NotebookFileLineBreakTest
|
|---|
| 11 | NotebookFileLineBreakTest
|
|---|
| 12 | NotebookDataPosition[ 158, 7]
|
|---|
| 13 | NotebookDataLength[ 23447, 567]
|
|---|
| 14 | NotebookOptionsPosition[ 21447, 517]
|
|---|
| 15 | NotebookOutlinePosition[ 21783, 532]
|
|---|
| 16 | CellTagsIndexPosition[ 21740, 529]
|
|---|
| 17 | WindowFrame->Normal*)
|
|---|
| 18 |
|
|---|
| 19 | (* Beginning of Notebook Content *)
|
|---|
| 20 | Notebook[{
|
|---|
| 21 | Cell[BoxData[{
|
|---|
| 22 | RowBox[{
|
|---|
| 23 | RowBox[{"G", "=",
|
|---|
| 24 | RowBox[{"6.6731", "*",
|
|---|
| 25 | SuperscriptBox["10",
|
|---|
| 26 | RowBox[{"-", "8"}]]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 27 | RowBox[{
|
|---|
| 28 | RowBox[{"kB", "=",
|
|---|
| 29 | RowBox[{"1.3806488", "*",
|
|---|
| 30 | SuperscriptBox["10",
|
|---|
| 31 | RowBox[{"-", "16"}]]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 32 | RowBox[{
|
|---|
| 33 | RowBox[{"AU", "=",
|
|---|
| 34 | RowBox[{"1.496", "*",
|
|---|
| 35 | SuperscriptBox["10", "13"]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 36 | RowBox[{
|
|---|
| 37 | RowBox[{"RJ", "=",
|
|---|
| 38 | RowBox[{"7.1492", "*",
|
|---|
| 39 | SuperscriptBox["10", "9"]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 40 | RowBox[{
|
|---|
| 41 | RowBox[{"RS", "=",
|
|---|
| 42 | RowBox[{"6.955", "*",
|
|---|
| 43 | SuperscriptBox["10", "10"]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 44 | RowBox[{
|
|---|
| 45 | RowBox[{"MJ", "=",
|
|---|
| 46 | RowBox[{"1.898", "*",
|
|---|
| 47 | SuperscriptBox["10", "30"]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 48 | RowBox[{
|
|---|
| 49 | RowBox[{"MS", "=",
|
|---|
| 50 | RowBox[{"1.99", "*",
|
|---|
| 51 | SuperscriptBox["10", "33"]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 52 | RowBox[{
|
|---|
| 53 | RowBox[{"year", "=", "31556926"}], ";"}], "\[IndentingNewLine]",
|
|---|
| 54 | RowBox[{
|
|---|
| 55 | RowBox[{"day", "=", "86400"}], ";"}], "\[IndentingNewLine]",
|
|---|
| 56 | RowBox[{
|
|---|
| 57 | RowBox[{"amu", "=",
|
|---|
| 58 | RowBox[{"1.66053892", "*",
|
|---|
| 59 | SuperscriptBox["10",
|
|---|
| 60 | RowBox[{"-", "24"}]]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 61 | RowBox[{
|
|---|
| 62 | RowBox[{"mH", "=",
|
|---|
| 63 | RowBox[{"1.00794", " ", "amu"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 64 | RowBox[{
|
|---|
| 65 | RowBox[{"e", "=",
|
|---|
| 66 | RowBox[{"1.602", "*",
|
|---|
| 67 | SuperscriptBox["10",
|
|---|
| 68 | RowBox[{"-", "12"}]]}]}], ";"}]}], "Input",
|
|---|
| 69 | CellChangeTimes->{{3.7154480137825317`*^9, 3.715448250108883*^9}, {
|
|---|
| 70 | 3.716209371161521*^9,
|
|---|
| 71 | 3.716209378772152*^9}},ExpressionUUID->"4e6f92e9-f50c-4d2f-bf34-\
|
|---|
| 72 | fbef911f7d9a"],
|
|---|
| 73 |
|
|---|
| 74 | Cell[BoxData[{
|
|---|
| 75 | RowBox[{
|
|---|
| 76 | RowBox[{"Rp", "=",
|
|---|
| 77 | RowBox[{"0.38", "RJ"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 78 | RowBox[{
|
|---|
| 79 | RowBox[{"Rs", "=",
|
|---|
| 80 | RowBox[{"1.599", "RS"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 81 | RowBox[{
|
|---|
| 82 | RowBox[{"Mp", "=",
|
|---|
| 83 | RowBox[{"0.07", "MJ"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 84 | RowBox[{
|
|---|
| 85 | RowBox[{"Ms", "=",
|
|---|
| 86 | RowBox[{"1.350", "MS"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 87 | RowBox[{
|
|---|
| 88 | RowBox[{"\[Rho]p", "=",
|
|---|
| 89 | RowBox[{"1.32443", "*",
|
|---|
| 90 | SuperscriptBox["10",
|
|---|
| 91 | RowBox[{"-", "16"}]]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 92 | RowBox[{
|
|---|
| 93 | RowBox[{"\[Rho]s", "=",
|
|---|
| 94 | RowBox[{"5.881", "*",
|
|---|
| 95 | SuperscriptBox["10",
|
|---|
| 96 | RowBox[{"-", "15"}]]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 97 | RowBox[{
|
|---|
| 98 | RowBox[{"a", "=",
|
|---|
| 99 | RowBox[{"0.02887", " ", "AU"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 100 | RowBox[{
|
|---|
| 101 | RowBox[{"Tp", "=",
|
|---|
| 102 | SuperscriptBox["10", "4"]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 103 | RowBox[{
|
|---|
| 104 | RowBox[{"Ts", "=",
|
|---|
| 105 | SuperscriptBox["10", "6"]}], ";"}]}], "Input",
|
|---|
| 106 | CellChangeTimes->{{3.715448270587872*^9, 3.715448478200588*^9},
|
|---|
| 107 | 3.715448689131571*^9, {3.715448738279578*^9, 3.715448746087687*^9}, {
|
|---|
| 108 | 3.7154488247408113`*^9, 3.715448859117077*^9}, {3.7154489271456203`*^9,
|
|---|
| 109 | 3.7154489702697153`*^9}, {3.71544903870971*^9, 3.7154491528997917`*^9}, {
|
|---|
| 110 | 3.7154494617690372`*^9, 3.715449462400153*^9}, {3.7154496652995996`*^9,
|
|---|
| 111 | 3.715449667753726*^9}, {3.715449748569962*^9, 3.7154498096989403`*^9}, {
|
|---|
| 112 | 3.716204361128829*^9, 3.716204370304318*^9}, {3.716204529603088*^9,
|
|---|
| 113 | 3.716204530730956*^9}, {3.716207333903183*^9, 3.7162073361392307`*^9}, {
|
|---|
| 114 | 3.716207587992317*^9, 3.716207596245813*^9}, {3.716210908259431*^9,
|
|---|
| 115 | 3.716210921801512*^9}, {3.7162134090463047`*^9, 3.716213409235758*^9}, {
|
|---|
| 116 | 3.716213646202609*^9, 3.7162136529284678`*^9}, {3.716214318816408*^9,
|
|---|
| 117 | 3.7162143222084084`*^9}, {3.716214575095542*^9, 3.716214577326499*^9},
|
|---|
| 118 | 3.716214667939818*^9, {3.7162160164148073`*^9, 3.716216022235773*^9}, {
|
|---|
| 119 | 3.7162167693262997`*^9, 3.716216770079837*^9}, {3.71621682502491*^9,
|
|---|
| 120 | 3.7162168362791443`*^9}, 3.716217390347397*^9, {3.7162175331875257`*^9,
|
|---|
| 121 | 3.7162175337007523`*^9}, {3.716217881753878*^9,
|
|---|
| 122 | 3.7162178877472343`*^9}},ExpressionUUID->"d4617f57-25a7-4440-8755-\
|
|---|
| 123 | c3ac0360e00d"],
|
|---|
| 124 |
|
|---|
| 125 | Cell[BoxData[{
|
|---|
| 126 | RowBox[{
|
|---|
| 127 | RowBox[{"lScale", "=", "Rp"}], ";"}], "\[IndentingNewLine]",
|
|---|
| 128 | RowBox[{
|
|---|
| 129 | RowBox[{"\[Rho]Scale", "=", "\[Rho]p"}], ";"}]}], "Input",
|
|---|
| 130 | CellChangeTimes->{{3.7154498128761883`*^9,
|
|---|
| 131 | 3.7154498705789967`*^9}},ExpressionUUID->"a10d4689-e95c-41be-aaf8-\
|
|---|
| 132 | be2039a68e8a"],
|
|---|
| 133 |
|
|---|
| 134 | Cell[BoxData[{
|
|---|
| 135 | RowBox[{
|
|---|
| 136 | RowBox[{"q", "=",
|
|---|
| 137 | FractionBox["Mp", "Ms"]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 138 | RowBox[{
|
|---|
| 139 | RowBox[{"csp", "=",
|
|---|
| 140 | SqrtBox[
|
|---|
| 141 | FractionBox[
|
|---|
| 142 | RowBox[{"kB", " ", "Tp"}], "mH"]]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 143 | RowBox[{
|
|---|
| 144 | RowBox[{"css", "=",
|
|---|
| 145 | SqrtBox[
|
|---|
| 146 | FractionBox[
|
|---|
| 147 | RowBox[{"kB", " ", "Ts"}], "mH"]]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 148 | RowBox[{
|
|---|
| 149 | RowBox[{"\[Lambda]p", "=",
|
|---|
| 150 | FractionBox[
|
|---|
| 151 | RowBox[{"G", " ", "Mp", " ", "mH"}],
|
|---|
| 152 | RowBox[{"kB", " ", "Rp", " ", "Tp"}]]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 153 | RowBox[{
|
|---|
| 154 | RowBox[{"\[Lambda]s", "=",
|
|---|
| 155 | FractionBox[
|
|---|
| 156 | RowBox[{"G", " ", "Ms", " ", "mH"}],
|
|---|
| 157 | RowBox[{"kB", " ", "Rs", " ", "Ts"}]]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 158 | RowBox[{
|
|---|
| 159 | RowBox[{"rsp", "=",
|
|---|
| 160 | RowBox[{
|
|---|
| 161 | FractionBox[
|
|---|
| 162 | RowBox[{"\[Lambda]p", " ", "Rp"}], "2"], "/", "lScale"}]}],
|
|---|
| 163 | ";"}], "\[IndentingNewLine]",
|
|---|
| 164 | RowBox[{
|
|---|
| 165 | RowBox[{"rss", "=",
|
|---|
| 166 | RowBox[{
|
|---|
| 167 | FractionBox[
|
|---|
| 168 | RowBox[{"\[Lambda]s", " ", "Rs"}], "2"], "/", "lScale"}]}],
|
|---|
| 169 | ";"}], "\[IndentingNewLine]",
|
|---|
| 170 | RowBox[{
|
|---|
| 171 | RowBox[{"r\[CapitalOmega]", "=",
|
|---|
| 172 | RowBox[{
|
|---|
| 173 | SqrtBox[
|
|---|
| 174 | FractionBox[
|
|---|
| 175 | RowBox[{
|
|---|
| 176 | SuperscriptBox["a", "3"], "q"}],
|
|---|
| 177 | RowBox[{"\[Lambda]p", " ", "Rp",
|
|---|
| 178 | RowBox[{"(",
|
|---|
| 179 | RowBox[{"q", "+", "1"}], ")"}]}]]], "/", "lScale"}]}],
|
|---|
| 180 | ";"}], "\[IndentingNewLine]",
|
|---|
| 181 | RowBox[{
|
|---|
| 182 | RowBox[{"rHill", "=",
|
|---|
| 183 | RowBox[{"a",
|
|---|
| 184 | RowBox[{
|
|---|
| 185 | SuperscriptBox[
|
|---|
| 186 | RowBox[{"(",
|
|---|
| 187 | FractionBox["Mp",
|
|---|
| 188 | RowBox[{"3", "Ms"}]], ")"}],
|
|---|
| 189 | FractionBox["1", "3"]], "/", "lScale"}]}]}],
|
|---|
| 190 | ";"}], "\[IndentingNewLine]",
|
|---|
| 191 | RowBox[{
|
|---|
| 192 | RowBox[{"P", "=",
|
|---|
| 193 | RowBox[{
|
|---|
| 194 | FractionBox[
|
|---|
| 195 | RowBox[{"2", "\[Pi]", " ",
|
|---|
| 196 | SuperscriptBox["a",
|
|---|
| 197 | FractionBox["3", "2"]]}],
|
|---|
| 198 | SqrtBox[
|
|---|
| 199 | RowBox[{"G", " ",
|
|---|
| 200 | RowBox[{"(",
|
|---|
| 201 | RowBox[{"Mp", "+", "Ms"}], ")"}]}]]], "/", "day"}]}], ";"}]}], "Input",\
|
|---|
| 202 |
|
|---|
| 203 | CellChangeTimes->{{3.715448270587872*^9, 3.715448478200588*^9},
|
|---|
| 204 | 3.715448689131571*^9, {3.715448738279578*^9, 3.715448746087687*^9}, {
|
|---|
| 205 | 3.7154488247408113`*^9, 3.715448859117077*^9}, {3.7154489271456203`*^9,
|
|---|
| 206 | 3.7154489702697153`*^9}, {3.71544903870971*^9, 3.7154491528997917`*^9}, {
|
|---|
| 207 | 3.7154494617690372`*^9, 3.715449462400153*^9}, {3.7154496652995996`*^9,
|
|---|
| 208 | 3.715449667753726*^9}, {3.715449748569962*^9, 3.7154498096989403`*^9}, {
|
|---|
| 209 | 3.7154498732307262`*^9, 3.715449885636582*^9}, {3.715598164002043*^9,
|
|---|
| 210 | 3.715598246346499*^9}, {3.716210182493856*^9,
|
|---|
| 211 | 3.716210197851668*^9}},ExpressionUUID->"eea36182-b2bc-4e42-82fe-\
|
|---|
| 212 | 0914bd22f9be"],
|
|---|
| 213 |
|
|---|
| 214 | Cell[CellGroupData[{
|
|---|
| 215 |
|
|---|
| 216 | Cell[BoxData[{"rHill", "\[IndentingNewLine]", "r\[CapitalOmega]", "\
|
|---|
| 217 | \[IndentingNewLine]", "\[Lambda]p", "\[IndentingNewLine]", "rsp", "\
|
|---|
| 218 | \[IndentingNewLine]", "P"}], "Input",
|
|---|
| 219 | CellChangeTimes->{{3.7162041304844646`*^9,
|
|---|
| 220 | 3.716204160557404*^9}},ExpressionUUID->"39396147-0f89-46c2-9e01-\
|
|---|
| 221 | bb60b4d0e8cc"],
|
|---|
| 222 |
|
|---|
| 223 | Cell[BoxData["4.046063709664142`"], "Output",
|
|---|
| 224 | CellChangeTimes->{3.716204165082674*^9, 3.716204389425489*^9,
|
|---|
| 225 | 3.716204536299288*^9, 3.716207343551011*^9, 3.716207606613778*^9,
|
|---|
| 226 | 3.716210201193988*^9, 3.716213659553708*^9, 3.716214327625358*^9,
|
|---|
| 227 | 3.7162145831640587`*^9, 3.716214673838223*^9, 3.7162160320063477`*^9,
|
|---|
| 228 | 3.716216785898321*^9, 3.716216844054399*^9, 3.716217395116693*^9,
|
|---|
| 229 | 3.716217540914399*^9,
|
|---|
| 230 | 3.716217896343005*^9},ExpressionUUID->"60fe137c-1247-4b44-94e7-\
|
|---|
| 231 | 54afac888a79"],
|
|---|
| 232 |
|
|---|
| 233 | Cell[BoxData["7.086932319227886`"], "Output",
|
|---|
| 234 | CellChangeTimes->{3.716204165082674*^9, 3.716204389425489*^9,
|
|---|
| 235 | 3.716204536299288*^9, 3.716207343551011*^9, 3.716207606613778*^9,
|
|---|
| 236 | 3.716210201193988*^9, 3.716213659553708*^9, 3.716214327625358*^9,
|
|---|
| 237 | 3.7162145831640587`*^9, 3.716214673838223*^9, 3.7162160320063477`*^9,
|
|---|
| 238 | 3.716216785898321*^9, 3.716216844054399*^9, 3.716217395116693*^9,
|
|---|
| 239 | 3.716217540914399*^9,
|
|---|
| 240 | 3.716217896346319*^9},ExpressionUUID->"e58695e3-ac0a-43ef-940f-\
|
|---|
| 241 | c615a5c2f906"],
|
|---|
| 242 |
|
|---|
| 243 | Cell[BoxData["3.9562284130859178`"], "Output",
|
|---|
| 244 | CellChangeTimes->{3.716204165082674*^9, 3.716204389425489*^9,
|
|---|
| 245 | 3.716204536299288*^9, 3.716207343551011*^9, 3.716207606613778*^9,
|
|---|
| 246 | 3.716210201193988*^9, 3.716213659553708*^9, 3.716214327625358*^9,
|
|---|
| 247 | 3.7162145831640587`*^9, 3.716214673838223*^9, 3.7162160320063477`*^9,
|
|---|
| 248 | 3.716216785898321*^9, 3.716216844054399*^9, 3.716217395116693*^9,
|
|---|
| 249 | 3.716217540914399*^9,
|
|---|
| 250 | 3.716217896347281*^9},ExpressionUUID->"cbb3be31-3889-49b0-9382-\
|
|---|
| 251 | ae2e27f8016b"],
|
|---|
| 252 |
|
|---|
| 253 | Cell[BoxData["1.9781142065429589`"], "Output",
|
|---|
| 254 | CellChangeTimes->{3.716204165082674*^9, 3.716204389425489*^9,
|
|---|
| 255 | 3.716204536299288*^9, 3.716207343551011*^9, 3.716207606613778*^9,
|
|---|
| 256 | 3.716210201193988*^9, 3.716213659553708*^9, 3.716214327625358*^9,
|
|---|
| 257 | 3.7162145831640587`*^9, 3.716214673838223*^9, 3.7162160320063477`*^9,
|
|---|
| 258 | 3.716216785898321*^9, 3.716216844054399*^9, 3.716217395116693*^9,
|
|---|
| 259 | 3.716217540914399*^9,
|
|---|
| 260 | 3.716217896348213*^9},ExpressionUUID->"925cea4c-9e23-4197-9048-\
|
|---|
| 261 | d4a99e1b098a"],
|
|---|
| 262 |
|
|---|
| 263 | Cell[BoxData["1.5415787472115139`"], "Output",
|
|---|
| 264 | CellChangeTimes->{3.716204165082674*^9, 3.716204389425489*^9,
|
|---|
| 265 | 3.716204536299288*^9, 3.716207343551011*^9, 3.716207606613778*^9,
|
|---|
| 266 | 3.716210201193988*^9, 3.716213659553708*^9, 3.716214327625358*^9,
|
|---|
| 267 | 3.7162145831640587`*^9, 3.716214673838223*^9, 3.7162160320063477`*^9,
|
|---|
| 268 | 3.716216785898321*^9, 3.716216844054399*^9, 3.716217395116693*^9,
|
|---|
| 269 | 3.716217540914399*^9,
|
|---|
| 270 | 3.716217896351829*^9},ExpressionUUID->"2760f19a-be64-495b-bc15-\
|
|---|
| 271 | 3a5fff4b2107"]
|
|---|
| 272 | }, Open ]],
|
|---|
| 273 |
|
|---|
| 274 | Cell[CellGroupData[{
|
|---|
| 275 |
|
|---|
| 276 | Cell[BoxData[{
|
|---|
| 277 | RowBox[{
|
|---|
| 278 | RowBox[{"H", "=",
|
|---|
| 279 | RowBox[{"Min", "[",
|
|---|
| 280 | RowBox[{
|
|---|
| 281 | FractionBox["Rp", "3"], ",",
|
|---|
| 282 | FractionBox[
|
|---|
| 283 | RowBox[{
|
|---|
| 284 | SuperscriptBox["csp", "2"],
|
|---|
| 285 | SuperscriptBox["Rp", "2"]}],
|
|---|
| 286 | RowBox[{"2", " ", "G", " ", "Mp"}]]}], "]"}]}],
|
|---|
| 287 | ";"}], "\[IndentingNewLine]",
|
|---|
| 288 | RowBox[{
|
|---|
| 289 | RowBox[{"\[Alpha]", "=",
|
|---|
| 290 | RowBox[{"2.6", "*",
|
|---|
| 291 | SuperscriptBox["10",
|
|---|
| 292 | RowBox[{"-", "13"}]]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 293 | RowBox[{
|
|---|
| 294 | RowBox[{"h\[Nu]", "=",
|
|---|
| 295 | RowBox[{"6.4", "e"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 296 | RowBox[{
|
|---|
| 297 | RowBox[{"\[Eta]", "=", "0.1"}], ";"}], "\[IndentingNewLine]",
|
|---|
| 298 | RowBox[{
|
|---|
| 299 | RowBox[{"M", "=",
|
|---|
| 300 | RowBox[{"If", "[",
|
|---|
| 301 | RowBox[{
|
|---|
| 302 | RowBox[{
|
|---|
| 303 | FractionBox["Rp",
|
|---|
| 304 | RowBox[{"rsp", " ", "lScale"}]], "<", "1"}], ",",
|
|---|
| 305 | RowBox[{"LambertW", "[",
|
|---|
| 306 | RowBox[{"0", ",",
|
|---|
| 307 | RowBox[{
|
|---|
| 308 | RowBox[{"-",
|
|---|
| 309 | SuperscriptBox[
|
|---|
| 310 | RowBox[{"(",
|
|---|
| 311 | FractionBox["Rp",
|
|---|
| 312 | RowBox[{"rsp", " ", "lScale"}]], ")"}],
|
|---|
| 313 | RowBox[{"-", "4"}]]}],
|
|---|
| 314 | SuperscriptBox["\[ExponentialE]",
|
|---|
| 315 | RowBox[{"3", "-",
|
|---|
| 316 | RowBox[{"4",
|
|---|
| 317 | FractionBox[
|
|---|
| 318 | RowBox[{"rsp", " ", "lScale"}], "Rp"]}]}]]}]}], "]"}], ",", "1"}],
|
|---|
| 319 | "]"}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 320 | RowBox[{
|
|---|
| 321 | RowBox[{"recomPhot", "=",
|
|---|
| 322 | RowBox[{"Solve", "[",
|
|---|
| 323 | RowBox[{"M", "==",
|
|---|
| 324 | RowBox[{"-",
|
|---|
| 325 | FractionBox[
|
|---|
| 326 | RowBox[{"J", " ", "\[Alpha]", " ", "H"}],
|
|---|
| 327 | RowBox[{"4",
|
|---|
| 328 | SuperscriptBox["csp", "2"]}]]}]}], "]"}]}],
|
|---|
| 329 | ";"}], "\[IndentingNewLine]",
|
|---|
| 330 | RowBox[{
|
|---|
| 331 | RowBox[{"recomEn", "=",
|
|---|
| 332 | RowBox[{"Solve", "[",
|
|---|
| 333 | RowBox[{"M", "\[Equal]",
|
|---|
| 334 | RowBox[{
|
|---|
| 335 | RowBox[{"-", "\[Eta]"}], " ",
|
|---|
| 336 | FractionBox[
|
|---|
| 337 | RowBox[{"J", " ", "\[Alpha]", " ", "H"}],
|
|---|
| 338 | RowBox[{"4",
|
|---|
| 339 | SuperscriptBox["csp", "2"]}]],
|
|---|
| 340 | FractionBox[
|
|---|
| 341 | RowBox[{"Rp", " ", "h\[Nu]"}],
|
|---|
| 342 | RowBox[{"G", " ", "Mp", " ", "mH"}]]}]}], "]"}]}], ";",
|
|---|
| 343 | RowBox[{"(*",
|
|---|
| 344 | RowBox[{
|
|---|
| 345 | RowBox[{"Ignores", " ", "recombination", " ", "term"}], " ", "-", " ",
|
|---|
| 346 | RowBox[{"would", " ", "increase", " ", "flux"}]}], "*)"}],
|
|---|
| 347 | "\[IndentingNewLine]",
|
|---|
| 348 | RowBox[{"J", "/.",
|
|---|
| 349 | RowBox[{"recomPhot", "[",
|
|---|
| 350 | RowBox[{"[", "1", "]"}], "]"}]}]}], "\[IndentingNewLine]",
|
|---|
| 351 | RowBox[{"J", "/.",
|
|---|
| 352 | RowBox[{"recomEn", "[",
|
|---|
| 353 | RowBox[{"[", "1", "]"}], "]"}]}], "\[IndentingNewLine]",
|
|---|
| 354 | RowBox[{"fluxRP", "=",
|
|---|
| 355 | RowBox[{"Abs", "[",
|
|---|
| 356 | RowBox[{
|
|---|
| 357 | RowBox[{"13.6", "e", " ", "J"}], "/.",
|
|---|
| 358 | RowBox[{"recomPhot", "[",
|
|---|
| 359 | RowBox[{"[", "1", "]"}], "]"}]}], "]"}]}], "\[IndentingNewLine]",
|
|---|
| 360 | RowBox[{"fluxRE", "=",
|
|---|
| 361 | RowBox[{"Abs", "[",
|
|---|
| 362 | RowBox[{
|
|---|
| 363 | RowBox[{"13.6", "e", " ", "J"}], "/.",
|
|---|
| 364 | RowBox[{"recomEn", "[",
|
|---|
| 365 | RowBox[{"[", "1", "]"}], "]"}]}], "]"}]}], "\[IndentingNewLine]",
|
|---|
| 366 | RowBox[{
|
|---|
| 367 | RowBox[{"flux", "=",
|
|---|
| 368 | RowBox[{"4", "*",
|
|---|
| 369 | SuperscriptBox["10", "5"]}]}], ";"}], "\[IndentingNewLine]",
|
|---|
| 370 | RowBox[{"photLim", "=",
|
|---|
| 371 | RowBox[{"Mp", "<",
|
|---|
| 372 | RowBox[{"\[Eta]", " ",
|
|---|
| 373 | FractionBox["h\[Nu]",
|
|---|
| 374 | RowBox[{"4", "G", " ", "mH"}]], "Rp"}]}]}], "\[IndentingNewLine]",
|
|---|
| 375 | RowBox[{"If", "[",
|
|---|
| 376 | RowBox[{"photLim", " ", ",",
|
|---|
| 377 | RowBox[{"If", "[",
|
|---|
| 378 | RowBox[{
|
|---|
| 379 | RowBox[{"flux", "<", "fluxRP"}], ",",
|
|---|
| 380 | RowBox[{"Print", "[",
|
|---|
| 381 | RowBox[{"Photon", " ", "limited"}], "]"}], ",",
|
|---|
| 382 | RowBox[{"Print", "[",
|
|---|
| 383 | RowBox[{"Recombination", " ", "limited"}], "]"}]}], "]"}], ",",
|
|---|
| 384 | RowBox[{"If", "[",
|
|---|
| 385 | RowBox[{
|
|---|
| 386 | RowBox[{"flux", "<", "fluxRE"}], ",",
|
|---|
| 387 | RowBox[{"Print", "[",
|
|---|
| 388 | RowBox[{"Energy", " ", "limited"}], "]"}], ",",
|
|---|
| 389 | RowBox[{"Print", "[",
|
|---|
| 390 | RowBox[{"Recombination", " ", "limited"}], "]"}]}], "]"}]}],
|
|---|
| 391 | "]"}]}], "Input",
|
|---|
| 392 | CellChangeTimes->{{3.716204775646146*^9, 3.71620486095218*^9}, {
|
|---|
| 393 | 3.7162048990411987`*^9, 3.716204931614924*^9}, {3.71620694912047*^9,
|
|---|
| 394 | 3.716207057181328*^9}, {3.7162070933662853`*^9, 3.7162071455456877`*^9}, {
|
|---|
| 395 | 3.716207216817994*^9, 3.716207307592309*^9}, {3.716207356569838*^9,
|
|---|
| 396 | 3.7162073769088993`*^9}, {3.7162076851181498`*^9, 3.716207709571666*^9}, {
|
|---|
| 397 | 3.716208205327016*^9, 3.716208215555993*^9}, {3.716208251111452*^9,
|
|---|
| 398 | 3.716208396499783*^9}, {3.716208788893815*^9, 3.716208793701489*^9}, {
|
|---|
| 399 | 3.716208873611651*^9, 3.716208932068798*^9}, {3.716208978380405*^9,
|
|---|
| 400 | 3.7162090470046167`*^9}, {3.7162093439410067`*^9, 3.716209398679039*^9}, {
|
|---|
| 401 | 3.716209433348009*^9, 3.7162094529920597`*^9}, {3.7162095974611397`*^9,
|
|---|
| 402 | 3.716209692581472*^9}, {3.716209735840375*^9, 3.7162098423879004`*^9}, {
|
|---|
| 403 | 3.7162098795779247`*^9, 3.7162099545559607`*^9}, {3.716210451156464*^9,
|
|---|
| 404 | 3.716210482058268*^9}, {3.7162105199661293`*^9, 3.716210521428525*^9}, {
|
|---|
| 405 | 3.716210604000379*^9, 3.716210613515938*^9}, {3.7162108893199883`*^9,
|
|---|
| 406 | 3.716210899051116*^9}, {3.716210934199916*^9, 3.716211038424589*^9}, {
|
|---|
| 407 | 3.716211085546447*^9, 3.716211125936606*^9}, {3.71621119713058*^9,
|
|---|
| 408 | 3.716211368815543*^9}, {3.716212982703512*^9, 3.716213002439196*^9}, {
|
|---|
| 409 | 3.7162130731274643`*^9, 3.716213075837906*^9}, {3.7162134186132174`*^9,
|
|---|
| 410 | 3.716213446156398*^9}, {3.716213666181979*^9, 3.7162136663457937`*^9},
|
|---|
| 411 | 3.716214047636362*^9, {3.716214253344574*^9, 3.716214254144535*^9}, {
|
|---|
| 412 | 3.716214526480336*^9, 3.716214641873548*^9}, {3.7162147701456327`*^9,
|
|---|
| 413 | 3.716214771108942*^9}, {3.716216469933803*^9, 3.716216470786744*^9}, {
|
|---|
| 414 | 3.716216504669018*^9, 3.7162165053065233`*^9}, {3.7162171250692368`*^9,
|
|---|
| 415 | 3.7162171259063473`*^9}, {3.716217302158712*^9,
|
|---|
| 416 | 3.716217302956949*^9}},ExpressionUUID->"021d56a4-c10f-4073-be42-\
|
|---|
| 417 | ea81315cce82"],
|
|---|
| 418 |
|
|---|
| 419 | Cell[BoxData["2.297378589810934`*^15"], "Output",
|
|---|
| 420 | CellChangeTimes->{{3.716209601073279*^9, 3.71620962770859*^9}, {
|
|---|
| 421 | 3.716209755908642*^9, 3.71620984279533*^9}, {3.716209882007607*^9,
|
|---|
| 422 | 3.716209954934956*^9}, 3.716210523325492*^9, {3.716210606043703*^9,
|
|---|
| 423 | 3.716210614186701*^9}, {3.7162110390645237`*^9, 3.716211057270488*^9}, {
|
|---|
| 424 | 3.716211098052726*^9, 3.716211115575061*^9}, {3.716211253003798*^9,
|
|---|
| 425 | 3.716211277750431*^9}, 3.71621133470798*^9, 3.7162113656101103`*^9,
|
|---|
| 426 | 3.716213096972128*^9, 3.716213258570418*^9, {3.716213423525991*^9,
|
|---|
| 427 | 3.716213446936879*^9}, {3.7162136621437817`*^9, 3.716213666917584*^9},
|
|---|
| 428 | 3.716214016388823*^9, 3.716214048354496*^9, 3.716214254716535*^9,
|
|---|
| 429 | 3.716214337872203*^9, 3.716214542570592*^9, {3.7162145852090387`*^9,
|
|---|
| 430 | 3.716214619628167*^9}, 3.7162146761176434`*^9, 3.716214771980835*^9,
|
|---|
| 431 | 3.7162160342843237`*^9, 3.716216471198345*^9, 3.716216505949399*^9,
|
|---|
| 432 | 3.716217126332201*^9,
|
|---|
| 433 | 3.716217306104953*^9},ExpressionUUID->"766b6ce6-7370-426a-908e-\
|
|---|
| 434 | d49f704b6d8a"],
|
|---|
| 435 |
|
|---|
| 436 | Cell[BoxData["8.157685463362048`*^15"], "Output",
|
|---|
| 437 | CellChangeTimes->{{3.716209601073279*^9, 3.71620962770859*^9}, {
|
|---|
| 438 | 3.716209755908642*^9, 3.71620984279533*^9}, {3.716209882007607*^9,
|
|---|
| 439 | 3.716209954934956*^9}, 3.716210523325492*^9, {3.716210606043703*^9,
|
|---|
| 440 | 3.716210614186701*^9}, {3.7162110390645237`*^9, 3.716211057270488*^9}, {
|
|---|
| 441 | 3.716211098052726*^9, 3.716211115575061*^9}, {3.716211253003798*^9,
|
|---|
| 442 | 3.716211277750431*^9}, 3.71621133470798*^9, 3.7162113656101103`*^9,
|
|---|
| 443 | 3.716213096972128*^9, 3.716213258570418*^9, {3.716213423525991*^9,
|
|---|
| 444 | 3.716213446936879*^9}, {3.7162136621437817`*^9, 3.716213666917584*^9},
|
|---|
| 445 | 3.716214016388823*^9, 3.716214048354496*^9, 3.716214254716535*^9,
|
|---|
| 446 | 3.716214337872203*^9, 3.716214542570592*^9, {3.7162145852090387`*^9,
|
|---|
| 447 | 3.716214619628167*^9}, 3.7162146761176434`*^9, 3.716214771980835*^9,
|
|---|
| 448 | 3.7162160342843237`*^9, 3.716216471198345*^9, 3.716216505949399*^9,
|
|---|
| 449 | 3.716217126332201*^9,
|
|---|
| 450 | 3.716217306107065*^9},ExpressionUUID->"027da8c2-031a-41fe-9858-\
|
|---|
| 451 | af15afaa71ca"],
|
|---|
| 452 |
|
|---|
| 453 | Cell[BoxData["50053.44681192878`"], "Output",
|
|---|
| 454 | CellChangeTimes->{{3.716209601073279*^9, 3.71620962770859*^9}, {
|
|---|
| 455 | 3.716209755908642*^9, 3.71620984279533*^9}, {3.716209882007607*^9,
|
|---|
| 456 | 3.716209954934956*^9}, 3.716210523325492*^9, {3.716210606043703*^9,
|
|---|
| 457 | 3.716210614186701*^9}, {3.7162110390645237`*^9, 3.716211057270488*^9}, {
|
|---|
| 458 | 3.716211098052726*^9, 3.716211115575061*^9}, {3.716211253003798*^9,
|
|---|
| 459 | 3.716211277750431*^9}, 3.71621133470798*^9, 3.7162113656101103`*^9,
|
|---|
| 460 | 3.716213096972128*^9, 3.716213258570418*^9, {3.716213423525991*^9,
|
|---|
| 461 | 3.716213446936879*^9}, {3.7162136621437817`*^9, 3.716213666917584*^9},
|
|---|
| 462 | 3.716214016388823*^9, 3.716214048354496*^9, 3.716214254716535*^9,
|
|---|
| 463 | 3.716214337872203*^9, 3.716214542570592*^9, {3.7162145852090387`*^9,
|
|---|
| 464 | 3.716214619628167*^9}, 3.7162146761176434`*^9, 3.716214771980835*^9,
|
|---|
| 465 | 3.7162160342843237`*^9, 3.716216471198345*^9, 3.716216505949399*^9,
|
|---|
| 466 | 3.716217126332201*^9,
|
|---|
| 467 | 3.716217306108849*^9},ExpressionUUID->"036e0f4a-f8df-4c72-899d-\
|
|---|
| 468 | 18794f1b256a"],
|
|---|
| 469 |
|
|---|
| 470 | Cell[BoxData["177733.1247273616`"], "Output",
|
|---|
| 471 | CellChangeTimes->{{3.716209601073279*^9, 3.71620962770859*^9}, {
|
|---|
| 472 | 3.716209755908642*^9, 3.71620984279533*^9}, {3.716209882007607*^9,
|
|---|
| 473 | 3.716209954934956*^9}, 3.716210523325492*^9, {3.716210606043703*^9,
|
|---|
| 474 | 3.716210614186701*^9}, {3.7162110390645237`*^9, 3.716211057270488*^9}, {
|
|---|
| 475 | 3.716211098052726*^9, 3.716211115575061*^9}, {3.716211253003798*^9,
|
|---|
| 476 | 3.716211277750431*^9}, 3.71621133470798*^9, 3.7162113656101103`*^9,
|
|---|
| 477 | 3.716213096972128*^9, 3.716213258570418*^9, {3.716213423525991*^9,
|
|---|
| 478 | 3.716213446936879*^9}, {3.7162136621437817`*^9, 3.716213666917584*^9},
|
|---|
| 479 | 3.716214016388823*^9, 3.716214048354496*^9, 3.716214254716535*^9,
|
|---|
| 480 | 3.716214337872203*^9, 3.716214542570592*^9, {3.7162145852090387`*^9,
|
|---|
| 481 | 3.716214619628167*^9}, 3.7162146761176434`*^9, 3.716214771980835*^9,
|
|---|
| 482 | 3.7162160342843237`*^9, 3.716216471198345*^9, 3.716216505949399*^9,
|
|---|
| 483 | 3.716217126332201*^9,
|
|---|
| 484 | 3.716217306110614*^9},ExpressionUUID->"12d64065-cbd3-49b4-9a64-\
|
|---|
| 485 | b14fdcf8f27f"],
|
|---|
| 486 |
|
|---|
| 487 | Cell[BoxData["False"], "Output",
|
|---|
| 488 | CellChangeTimes->{{3.716209601073279*^9, 3.71620962770859*^9}, {
|
|---|
| 489 | 3.716209755908642*^9, 3.71620984279533*^9}, {3.716209882007607*^9,
|
|---|
| 490 | 3.716209954934956*^9}, 3.716210523325492*^9, {3.716210606043703*^9,
|
|---|
| 491 | 3.716210614186701*^9}, {3.7162110390645237`*^9, 3.716211057270488*^9}, {
|
|---|
| 492 | 3.716211098052726*^9, 3.716211115575061*^9}, {3.716211253003798*^9,
|
|---|
| 493 | 3.716211277750431*^9}, 3.71621133470798*^9, 3.7162113656101103`*^9,
|
|---|
| 494 | 3.716213096972128*^9, 3.716213258570418*^9, {3.716213423525991*^9,
|
|---|
| 495 | 3.716213446936879*^9}, {3.7162136621437817`*^9, 3.716213666917584*^9},
|
|---|
| 496 | 3.716214016388823*^9, 3.716214048354496*^9, 3.716214254716535*^9,
|
|---|
| 497 | 3.716214337872203*^9, 3.716214542570592*^9, {3.7162145852090387`*^9,
|
|---|
| 498 | 3.716214619628167*^9}, 3.7162146761176434`*^9, 3.716214771980835*^9,
|
|---|
| 499 | 3.7162160342843237`*^9, 3.716216471198345*^9, 3.716216505949399*^9,
|
|---|
| 500 | 3.716217126332201*^9,
|
|---|
| 501 | 3.716217306112438*^9},ExpressionUUID->"afaf8bb4-712b-41cd-ab44-\
|
|---|
| 502 | 4277613c896b"],
|
|---|
| 503 |
|
|---|
| 504 | Cell[BoxData[
|
|---|
| 505 | RowBox[{"limited", " ", "Recombination"}]], "Print",
|
|---|
| 506 | CellChangeTimes->{
|
|---|
| 507 | 3.7162113656150503`*^9, 3.716213096977844*^9, 3.716213258575671*^9, {
|
|---|
| 508 | 3.7162134235311823`*^9, 3.7162134469416113`*^9}, {3.716213662147541*^9,
|
|---|
| 509 | 3.7162136669230127`*^9}, 3.716214016394636*^9, 3.71621404836345*^9,
|
|---|
| 510 | 3.71621425472432*^9, 3.716214337878777*^9, 3.716214542576578*^9, {
|
|---|
| 511 | 3.7162145852204638`*^9, 3.716214619634575*^9}, 3.7162146761288357`*^9,
|
|---|
| 512 | 3.7162147719907913`*^9, 3.716216034296261*^9, 3.71621647120885*^9,
|
|---|
| 513 | 3.716216505962475*^9, 3.716217126341564*^9,
|
|---|
| 514 | 3.7162173061153708`*^9},ExpressionUUID->"b27985fa-b58b-4345-8cd3-\
|
|---|
| 515 | 0cc42b3dc3a1"]
|
|---|
| 516 | }, Open ]]
|
|---|
| 517 | },
|
|---|
| 518 | WindowSize->{808, 1028},
|
|---|
| 519 | WindowMargins->{{Automatic, 152}, {0, Automatic}},
|
|---|
| 520 | FrontEndVersion->"11.1 for Linux x86 (64-bit) (April 18, 2017)",
|
|---|
| 521 | StyleDefinitions->"Default.nb"
|
|---|
| 522 | ]
|
|---|
| 523 | (* End of Notebook Content *)
|
|---|
| 524 |
|
|---|
| 525 | (* Internal cache information *)
|
|---|
| 526 | (*CellTagsOutline
|
|---|
| 527 | CellTagsIndex->{}
|
|---|
| 528 | *)
|
|---|
| 529 | (*CellTagsIndex
|
|---|
| 530 | CellTagsIndex->{}
|
|---|
| 531 | *)
|
|---|
| 532 | (*NotebookFileOutline
|
|---|
| 533 | Notebook[{
|
|---|
| 534 | Cell[558, 20, 1647, 51, 297, "Input", "ExpressionUUID" -> \
|
|---|
| 535 | "4e6f92e9-f50c-4d2f-bf34-fbef911f7d9a"],
|
|---|
| 536 | Cell[2208, 73, 2215, 49, 222, "Input", "ExpressionUUID" -> \
|
|---|
| 537 | "d4617f57-25a7-4440-8755-c3ac0360e00d"],
|
|---|
| 538 | Cell[4426, 124, 289, 7, 57, "Input", "ExpressionUUID" -> \
|
|---|
| 539 | "a10d4689-e95c-41be-aaf8-be2039a68e8a"],
|
|---|
| 540 | Cell[4718, 133, 2552, 78, 503, "Input", "ExpressionUUID" -> \
|
|---|
| 541 | "eea36182-b2bc-4e42-82fe-0914bd22f9be"],
|
|---|
| 542 | Cell[CellGroupData[{
|
|---|
| 543 | Cell[7295, 215, 303, 5, 121, "Input", "ExpressionUUID" -> \
|
|---|
| 544 | "39396147-0f89-46c2-9e01-bb60b4d0e8cc"],
|
|---|
| 545 | Cell[7601, 222, 496, 8, 32, "Output", "ExpressionUUID" -> \
|
|---|
| 546 | "60fe137c-1247-4b44-94e7-54afac888a79"],
|
|---|
| 547 | Cell[8100, 232, 496, 8, 32, "Output", "ExpressionUUID" -> \
|
|---|
| 548 | "e58695e3-ac0a-43ef-940f-c615a5c2f906"],
|
|---|
| 549 | Cell[8599, 242, 497, 8, 32, "Output", "ExpressionUUID" -> \
|
|---|
| 550 | "cbb3be31-3889-49b0-9382-ae2e27f8016b"],
|
|---|
| 551 | Cell[9099, 252, 497, 8, 32, "Output", "ExpressionUUID" -> \
|
|---|
| 552 | "925cea4c-9e23-4197-9048-d4a99e1b098a"],
|
|---|
| 553 | Cell[9599, 262, 497, 8, 32, "Output", "ExpressionUUID" -> \
|
|---|
| 554 | "2760f19a-be64-495b-bc15-3a5fff4b2107"]
|
|---|
| 555 | }, Open ]],
|
|---|
| 556 | Cell[CellGroupData[{
|
|---|
| 557 | Cell[10133, 275, 5544, 141, 500, "Input", "ExpressionUUID" -> \
|
|---|
| 558 | "021d56a4-c10f-4073-be42-ea81315cce82"],
|
|---|
| 559 | Cell[15680, 418, 1021, 15, 34, "Output", "ExpressionUUID" -> \
|
|---|
| 560 | "766b6ce6-7370-426a-908e-d49f704b6d8a"],
|
|---|
| 561 | Cell[16704, 435, 1021, 15, 34, "Output", "ExpressionUUID" -> \
|
|---|
| 562 | "027da8c2-031a-41fe-9858-af15afaa71ca"],
|
|---|
| 563 | Cell[17728, 452, 1017, 15, 32, "Output", "ExpressionUUID" -> \
|
|---|
| 564 | "036e0f4a-f8df-4c72-899d-18794f1b256a"],
|
|---|
| 565 | Cell[18748, 469, 1017, 15, 32, "Output", "ExpressionUUID" -> \
|
|---|
| 566 | "12d64065-cbd3-49b4-9a64-b14fdcf8f27f"],
|
|---|
| 567 | Cell[19768, 486, 1004, 15, 32, "Output", "ExpressionUUID" -> \
|
|---|
| 568 | "afaf8bb4-712b-41cd-ab44-4277613c896b"],
|
|---|
| 569 | Cell[20775, 503, 656, 11, 24, "Print", "ExpressionUUID" -> \
|
|---|
| 570 | "b27985fa-b58b-4345-8cd3-0cc42b3dc3a1"]
|
|---|
| 571 | }, Open ]]
|
|---|
| 572 | }
|
|---|
| 573 | ]
|
|---|
| 574 | *)
|
|---|
| 575 |
|
|---|