1147:
369:
594:
971:
1189:
for galaxies instead of the value given above which is closer to -1. The reason for this failure is that large halos tend to have a large host galaxy and many smaller satellites, and small halos may not host any galaxies with stars. See, e.g.,
701:
899:
221:
439:
1142:{\displaystyle \int _{a}^{b}\left({\frac {L}{L^{*}}}\right)^{\alpha }e^{-\left({\frac {L}{L^{*}}}\right)}d\left({\frac {L}{L^{*}}}\right)=\Gamma (\alpha +1,a)-\Gamma (\alpha +1,b)}
77:. Given a luminosity as input, the luminosity function essentially returns the abundance of objects with that luminosity (specifically, number density per luminosity interval).
599:
The galaxy luminosity function may have different parameters for different populations and environments; it is not a universal function. One measurement from field galaxies is
1187:
428:
957:
928:
399:
158:
213:
121:
stars with a given luminosity. As this is determined by the rates at which these stars form and cool, it is of interest for the information it gives about the
193:
602:
93:, with observations. Main sequence luminosity functions vary depending on their host galaxy and on selection criteria for the stars, for example in the
1480:
1228:
1408:
Sobral, David; Smail, Ian; Best, Philip N.; Geach, James E.; Matsuda, Yuichi; Stott, John P.; Cirasuolo, Michele; Kurk, Jaron (2013-01-01).
716:
364:{\displaystyle dn(L)=\phi ~dL=\phi ^{*}\left({\frac {L}{L^{*}}}\right)^{\alpha }\mathrm {e} ^{-L/L^{*}}d\left({\frac {L}{L^{*}}}\right),}
1515:
589:{\displaystyle dn(L)=\ln(10)\phi ^{*}\left({\frac {L}{L^{*}}}\right)^{\alpha +1}\mathrm {e} ^{-L/L^{*}}d\left(\log _{10}L\right).}
1560:
1153:
73:
Note that the term "function" is slightly misleading, and the luminosity function might better be described as a luminosity
1191:
1545:
54:
interval. Luminosity functions are used to study the properties of large groups or classes of objects, such as the
963:
1410:"A large Hα survey at z = 2.23, 1.47, 0.84 and 0.40: the 11 Gyr evolution of star-forming galaxies from HiZELSâ
"
98:
1497:
707:
1163:
1431:
1374:
1329:
1298:
1257:
1555:
404:
94:
28:
1521:
1421:
1347:
933:
89:
stars according to their luminosity. It is used to compare star formation and death rates, and
1365:
Schechter, P. (1976-01-01). "An analytic expression for the luminosity function for galaxies".
907:
215:
per unit luminosity and is given by a power law with an exponential cut-off at high luminosity
17:
1550:
1511:
1476:
1449:
1390:
1289:; MacQueen, P. J. (1998). "The Texas Deep Sky Survey: Spectroscopy of Cool Degenerate Stars".
1224:
1156:. However, the connection between the two is not straight forward. If one assumes that every
90:
1503:
1439:
1382:
1337:
1265:
1216:
1157:
904:
Note that because the magnitude system is logarithmic, the power law has logarithmic slope
377:
143:
1472:
1435:
1378:
1333:
1302:
1261:
696:{\displaystyle \alpha =-1.25,\ \phi ^{*}=1.2\times 10^{-2}\ h^{3}\ \mathrm {Mpc} ^{-3}}
198:
163:
1539:
1525:
401:
is a characteristic galaxy luminosity controlling the cut-off, and the normalization
86:
1351:
59:
160:
provides an approximation of the abundance of galaxies in a luminosity interval
118:
67:
51:
1453:
1394:
433:
Equivalently, this equation can be expressed in terms of log-quantities with
1286:
126:
35:
1444:
1409:
710:, rather than luminosities. In this case, the Schechter function becomes:
1220:
706:
It is often more convenient to rewrite the
Schechter function in terms of
1499:
The
Encyclopedia of Cosmology, Volume 1: Galaxy Formation and Evolution
122:
894:{\displaystyle n(M)~dM=(0.4\ \ln 10)\ \phi ^{*}\ ^{\alpha +1}\exp~dM.}
63:
47:
1246:"A main-sequence luminosity function for the Large Magellanic Cloud"
1152:
Historically, the
Schechter luminosity function was inspired by the
1386:
1342:
1317:
1270:
1245:
1426:
1507:
1194:, for a more-detailed description of the halo-galaxy connection.
1160:
hosts one galaxy, then the Press-Schechter model yields a slope
55:
43:
85:
The main sequence luminosity function maps the distribution of
962:
Integrals of the
Schechter function can be expressed via the
195:. The luminosity function has units of a number density
1322:
125:
of white dwarf cooling and the age and history of the
1166:
974:
936:
910:
719:
605:
442:
407:
380:
224:
201:
166:
146:
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1141:
951:
922:
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695:
588:
422:
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363:
207:
187:
152:
1414:Monthly Notices of the Royal Astronomical Society
1316:Fontaine, G.; Brassard, P.; Bergeron, P. (2001).
409:
1291:American Astronomical Society Meeting Abstracts
27:For the luminosity function in photometry, see
1318:"The Potential of White Dwarf Cosmochronology"
8:
1443:
1425:
1341:
1269:
1165:
1073:
1064:
1043:
1034:
1026:
1016:
1004:
995:
984:
979:
973:
935:
930:. This is why a Schechter function with
909:
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7:
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25:
1502:. Vol. 1. World Scientific.
81:Main sequence luminosity function
1182:{\displaystyle \alpha \sim -3.5}
1211:Stahler, S.; Palla, F. (2004).
111:white dwarf luminosity function
105:White dwarf luminosity function
18:White dwarf luminosity function
1285:Claver, C. F.; Winget, D. E.;
1136:
1118:
1109:
1091:
876:
871:
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838:
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723:
473:
467:
455:
449:
237:
231:
182:
167:
1:
430:has units of number density.
423:{\displaystyle \,\!\phi ^{*}}
139:Schechter luminosity function
133:Schechter luminosity function
1192:halo occupation distribution
1577:
952:{\displaystyle \alpha =-1}
26:
1467:Longair, Malcolm (1998).
1367:The Astrophysical Journal
1250:The Astrophysical Journal
964:incomplete gamma function
923:{\displaystyle \alpha +1}
1496:Barkana, Rennan (2018).
1561:Equations of astronomy
1213:The Formation of Stars
1183:
1143:
953:
924:
895:
697:
590:
424:
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365:
209:
189:
154:
117:) gives the number of
99:Small Magellanic Cloud
1221:10.1002/9783527618675
1184:
1154:PressâSchechter model
1144:
954:
925:
896:
698:
591:
425:
396:
394:{\displaystyle L^{*}}
366:
210:
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155:
153:{\displaystyle \phi }
1445:10.1093/mnras/sts096
1244:Butcher, H. (1977).
1164:
972:
959:is said to be flat.
934:
908:
717:
603:
440:
405:
378:
222:
199:
164:
144:
42:gives the number of
1436:2013MNRAS.428.1128S
1379:1976ApJ...203..297S
1334:2001PASP..113..409F
1303:1998AAS...193.3702C
1262:1977ApJ...216..372B
989:
95:Solar neighbourhood
91:evolutionary models
40:luminosity function
29:Luminosity function
1179:
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1546:Stellar astronomy
1482:978-3-540-63785-1
1230:978-3-527-61867-5
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208:{\displaystyle n}
16:(Redirected from
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1469:Galaxy Formation
1464:
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1420:(2): 1128â1146.
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188:{\displaystyle }
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1287:Nather, R. E.
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1215:. Wiley VCH.
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87:main sequence
80:
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75:distribution
74:
72:
39:
33:
1373:: 297â306.
119:white dwarf
68:Local Group
1556:Photometry
1540:Categories
1198:References
708:magnitudes
52:luminosity
1526:259542973
1454:0035-8711
1427:1202.3436
1395:0004-637X
1174:−
1171:∼
1168:α
1122:α
1116:Γ
1113:−
1095:α
1089:Γ
1075:∗
1045:∗
1028:−
1018:α
1006:∗
977:∫
944:−
938:α
912:α
866:−
861:∗
842:−
836:
822:α
806:−
801:∗
774:∗
770:ϕ
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649:−
641:×
630:∗
626:ϕ
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502:∗
482:∗
478:ϕ
465:
416:∗
412:ϕ
387:∗
348:∗
324:∗
308:−
296:α
284:∗
264:∗
260:ϕ
244:ϕ
148:ϕ
36:astronomy
1551:Galaxies
1352:54970082
64:galaxies
60:clusters
48:galaxies
1432:Bibcode
1375:Bibcode
1330:Bibcode
1299:Bibcode
1258:Bibcode
1256:: 372.
123:physics
97:or the
66:in the
62:or the
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127:Galaxy
1522:S2CID
1422:arXiv
1348:S2CID
56:stars
44:stars
1512:ISBN
1477:ISBN
1450:ISSN
1391:ISSN
1225:ISBN
616:1.25
137:The
115:WDLF
109:The
50:per
38:, a
1504:doi
1440:doi
1418:428
1383:doi
1371:203
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1326:113
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1177:3.5
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833:exp
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818:]
812:)
809:M
797:M
793:(
782:[
763:)
745:(
742:=
739:M
736:d
730:)
727:M
724:(
721:n
689:3
681:c
678:p
675:M
665:3
661:h
652:2
635:=
619:,
610:=
584:.
580:)
576:L
559:(
555:d
544:L
539:/
535:L
527:e
520:1
517:+
509:)
498:L
494:L
489:(
474:)
468:(
459:=
456:)
453:L
450:(
447:n
444:d
383:L
359:,
355:)
344:L
340:L
335:(
331:d
320:L
315:/
311:L
303:e
291:)
280:L
276:L
271:(
256:=
253:L
250:d
241:=
238:)
235:L
232:(
229:n
226:d
203:n
183:]
180:L
177:d
174:+
171:L
168:[
113:(
31:.
20:)
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