216:(PDMF), which describes the current distribution of masses of stars, such as red giants, white dwarfs, neutron stars, and black holes, after some time of evolution away from the main sequence stars and after a certain amount of mass loss. Since there are not enough young clusters of stars available for the calculation of IMF, PDMF is used instead and the results are extrapolated back to IMF. IMF and PDMF can be linked through the "stellar creation function". Stellar creation function is defined as the number of stars per unit volume of space in a mass range and a time interval. In the case that all the main sequence stars have greater lifetimes than the galaxy, IMF and PDMF are equivalent. Similarly, IMF and PDMF are equivalent in brown dwarfs due to their unlimited lifetimes.
253:
1289:. In particular, the classical assumption of a single IMF covering the whole substellar and stellar mass range is being questioned, in favor of a two-component IMF to account for possible different formation modes for substellar objects—one IMF covering brown dwarfs and very-low-mass stars, and another ranging from the higher-mass brown dwarfs to the most massive stars. This leads to an overlap region approximately between 0.05–0.2
3729:
3741:
1546:. Recent research suggests that the global prestellar CMF in molecular clouds is the result of the integration of CMFs generated by individual thermally supercritical filaments, which indicates a tight connection between the FLMF and the CMF/IMF, supporting the idea that filamentary structures are a critical evolutionary step in establishing a Salpeter-like mass function.
3753:
319:(with a magnitude > 12 in the visual band), it reduces the error of distances for nearby stars, and allows accurate determination of binary star systems. Since the magnitude of a star varies with its age, the determination of mass-luminosity relation should also take into account its age. For stars with masses above 0.7
3680:
42:
1817:; Brown, Thomas M.; Tumlinson, Jason; Kalirai, Jason S.; Simon, Joshua D.; Kirby, Evan N.; VandenBerg, Don A.; Muñoz, Ricardo R.; Avila, Roberto J.; Guhathakurta, Puragra; Ferguson, Henry C. (2013). "The Stellar Initial Mass Function of Ultra-faint Dwarf Galaxies: Evidence for IMF Variations with Galactic Environment".
1332:
Recent studies have suggested that filamentary structures in molecular clouds play a crucial role in the initial conditions of star formation and the origin of the stellar IMF. Herschel observations of the
California giant molecular cloud show that both the prestellar core mass function (CMF) and the
1319:
Measurements of the local universe where single stars can be resolved are consistent with an invariant IMF but the conclusion suffers from large measurement uncertainty due to the small number of massive stars and difficulties in distinguishing binary systems from the single stars. Thus IMF variation
1760:
Kalirai, Jason S.; Anderson, Jay; Dotter, Aaron; Richer, Harvey B.; Fahlman, Gregory G.; Hansen, Brad M.S.; Hurley, Jarrod; Reid, I. Neill; Rich, R. Michael; Shara, Michael M. (2013). "Ultra-Deep Hubble Space
Telescope Imaging of the Small Magellanic Cloud: The Initial Mass Function of Stars with M
1323:
Systems formed at much earlier times or further from the galactic neighborhood, where star formation activity can be hundreds or even thousands time stronger than the current Milky Way, may give a better understanding. It has been consistently reported both for star clusters and galaxies that there
533:
is the first astrophysicist who attempted to quantify IMF by applying power law into his equations. His work is based upon the sun-like stars that can be easily observed with great accuracy. Salpeter defined the mass function as the number of stars in a volume of space observed at a time as per
2896:
Lee, Janice C.; Gil de Paz, Armando; Tremonti, Christy; Kennicutt, Robert C.; Salim, Samir; Bothwell, Matthew; Calzetti, Daniela; Dalcanton, Julianne; Dale, Daniel; Engelbracht, Chad; José G. Funes, S. J.; Johnson, Benjamin; Sakai, Shoko; Skillman, Evan; van Zee, Liese (2009-11-20).
674:
219:
The properties and evolution of a star are closely related to its mass, so the IMF is an important diagnostic tool for astronomers studying large quantities of stars. For example, the initial mass of a star is the primary factor of determining its
1315:
thus make the accretion of the gas easier, both lead to more massive stars being formed in a star cluster. The galaxy-wide IMF can be different from the star-cluster scale IMF and may systematically change with the galaxy star formation history.
2956:
Gunawardhana, M. L. P.; Hopkins, A. M.; Sharp, R. G.; Brough, S.; Taylor, E.; Bland-Hawthorn, J.; Maraston, C.; Tuffs, R. J.; Popescu, C. C.; Wijesinghe, D.; Jones, D. H.; Croom, S.; Sadler, E.; Wilkins, S.; Driver, S. P. (2011-08-01).
1498:
1063:
2620:
1244:
302:
system. However, the number of binary systems that can be directly observed is low, thus not enough samples to estimate the initial mass function. Therefore, the stellar luminosity function is used to derive a mass function (a
1276:
is often called the slope of the initial mass function. The present-day mass function, for coeval formation, has the same slope except that it rolls off at higher masses which have evolved away from the main sequence.
563:
243:
The IMF is relatively invariant from one group of stars to another, though some observations suggest that the IMF is different in different environments, and potentially dramatically different in early galaxies.
1393:
1320:
effect is not prominent enough to be observed in the local universe. However, recent photometric survey across cosmic time does suggest a potentially systematic variation of the IMF at high redshift.
1544:
735:
1324:
seems to be a systematic variation of the IMF. However, the measurements are less direct. For star clusters the IMF may change over time due to complicated dynamical evolution.
3422:
Different mass of stars have different ages, thus modifying the star formation history would modify the present-day mass function, which mimics the effect of modifying the IMF.
2319:
Kroupa, Pavel; Weidner, Carsten; Pflamm-Altenburg, Jan; Thies, Ingo; Dabringhausen, Jörg; Marks, Michael; Maschberger, Thomas (2013), Oswalt, Terry D.; Gilmore, Gerard (eds.),
377:
534:
logarithmic mass interval. His work enabled a large number of theoretical parameters to be included in the equation while converging all these parameters into an exponent of
463:
412:
1424:
902:
1086:
558:
493:
3000:
Ferreras, Ignacio; Barbera, Francesco La; Rosa, Ignacio G. de la; Vazdekis, Alexandre; Carvalho, Reinaldo R. de; FalcĂłn-Barroso, JesĂşs; Ricciardelli, Elena (2013-02-11).
885:
845:
812:
779:
701:
205:. IMF not only describes the formation and evolution of individual stars, it also serves as an important link that describes the formation and evolution of galaxies.
1304:
The possible variation of the IMF affects our interpretation of the galaxy signals and the estimation of cosmic star formation history thus is important to consider.
513:
3601:
1333:
filament line mass function (FLMF) follow power-law distributions at the high-mass end, consistent with the
Salpeter power-law IMF. Specifically, the CMF follows
432:
1429:
1571:
228:, radius, radiation spectrum, and quantity of materials and energy it emitted into interstellar space during its lifetime. At low masses, the IMF sets the
1707:
Conroy, Charlie; van Dokkum, Pieter G. (2012). "The
Stellar Initial Mass Function in Early-type Galaxies From Absorption Line Spectroscopy. II. Results".
315:
within 20 parsecs from the earth. Although short distances yield a smaller number of samples with greater uncertainty of distances for stars with faint
168:
1675:
3794:
1307:
In theory, the IMF should vary with different star-forming conditions. Higher ambient temperature increases the mass of collapsing gas clouds (
3551:
2745:"A top-heavy stellar initial mass function in starbursts as an explanation for the high mass-to-light ratios of ultra-compact dwarf galaxies"
2358:
3001:
3052:
295:
3594:
3372:
1336:
2855:"Evidence for top-heavy stellar initial mass functions with increasing density and decreasing metallicity: Top-heavy IMFs in GCs"
232:
mass budget and the number of substellar objects that form. At intermediate masses, the IMF controls chemical enrichment of the
2959:"Galaxy and Mass Assembly (GAMA): the star formation rate dependence of the stellar initial mass function: IMF-SFR relationship"
669:{\displaystyle \xi (m)\Delta m=\xi _{0}\left({\frac {m}{M_{\odot }}}\right)^{-2.35}\left({\frac {\Delta m}{M_{\odot }}}\right).}
3784:
3704:
132:
3587:
328:, it takes more than 10 billion years for their magnitude to increase substantially. For low-mass stars with below 0.13
311:. The luminosity function requires accurate determination of distances, and the most straightforward way is by measuring
308:
2676:
Sneppen, Albert; Steinhardt, Charles L.; Hensley, Hagan; Jermyn, Adam S.; Mostafa, Basel; Weaver, John R. (2022-05-01).
1870:
Sneppen, Albert; Steinhardt, Charles L.; Hensley, Hagan; Jermyn, Adam S.; Mostafa, Basel; Weaver, John R. (2022-05-01).
209:
161:
3257:"The evolution of CNO isotopes: a new window on cosmic star formation history and the stellar IMF in the age of ALMA"
1503:
3779:
3756:
212:(PDF) that describes the probability of a star that has a certain mass during its formation. It differs from the
2381:"Impact of metallicity and star formation rate on the time-dependent, galaxy-wide stellar initial mass function"
2036:
Miller, Glenn; Scalo, John (1979). "The initial mass function and stellar birthrate in the solar neighborhood".
2899:"COMPARISON OF Hα AND UV STAR FORMATION RATES IN THE LOCAL VOLUME: SYSTEMATIC DISCREPANCIES FOR DWARF GALAXIES"
117:
2379:
Jeřábková, T.; Zonoozi, A. Hasani; Kroupa, P.; Beccari, G.; Yan, Z.; Vazdekis, A.; Zhang, Z.-Y. (2018-12-01).
895:
Chabrier gave the following expression for the density of individual stars in the
Galactic disk, in units of
3732:
252:
154:
3669:
3002:"Systematic variation of the stellar initial mass function with velocity dispersion in early-type galaxies"
2796:"Low-Mass X-Ray Binaries Indicate a Top-Heavy Stellar Initial Mass Function in Ultracompact Dwarf Galaxies"
2380:
101:
3659:
2098:
Kroupa, Pavel; et al. (2013). "The stellar and sub-stellar IMF of simple and composite populations".
714:
221:
198:
86:
1940:
Kroupa, Pavel (2002). "The
Initial Mass Function of Stars: Evidence for Uniformity in Variable Systems".
711:
Glenn E. Miller and John M. Scalo extended the work of
Salpeter, by suggesting that the IMF "flattened" (
3155:"AGN feedback and the origin of the α enhancement in early-type galaxies – insights from the GAEA model"
2563:
1070:
345:
3644:
3501:
3466:
3445:
3329:
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2766:
2699:
2642:
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2520:
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2402:
2338:
2280:
2221:
2162:
2113:
2080:
2045:
2010:
1959:
1893:
1836:
1780:
1726:
1682:
1638:
437:
382:
76:
3714:
3624:
1398:
233:
142:
56:
3740:
3436:
Scalo, J. M. (1986). "The initial mass function of massive stars in galaxies
Empirical evidence".
537:
468:
3709:
3525:
3491:
3384:
3319:
3268:
3166:
3115:
3064:
3013:
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2756:
2725:
2689:
2632:
2575:
2510:
2451:
2392:
2328:
2270:
2211:
2152:
2103:
1983:
1949:
1919:
1883:
1852:
1826:
1796:
1770:
1742:
1716:
1654:
1628:
1312:
864:
824:
791:
758:
316:
137:
2678:"Implications of a Temperature-dependent Initial Mass Function. I. Photometric Template Fitting"
1872:"Implications of a Temperature-dependent Initial Mass Function. I. Photometric Template Fitting"
3308:"Stellar populations dominated by massive stars in dusty starburst galaxies across cosmic time"
3306:
Zhang, Zhi-Yu; Romano, D.; Ivison, R. J.; Papadopoulos, Padelis P.; Matteucci, F. (June 2018).
3699:
3664:
3547:
3517:
3353:
3345:
3288:
3255:
Romano, D.; Matteucci, F.; Zhang, Z.-Y.; Papadopoulos, P. P.; Ivison, R. J. (September 2017).
3237:
3186:
3135:
3084:
3033:
2938:
2835:
2717:
2658:
2601:
2544:
2536:
2479:
2420:
2354:
2298:
2239:
2180:
1975:
1911:
1308:
679:
530:
127:
96:
17:
498:
3541:
3509:
3394:
3337:
3278:
3227:
3217:
3176:
3125:
3074:
3023:
2980:
2970:
2928:
2876:
2825:
2774:
2707:
2650:
2593:
2589:
2528:
2469:
2410:
2406:
2346:
2288:
2229:
2170:
2121:
2053:
2018:
1967:
1901:
1844:
1788:
1734:
1646:
519:
312:
229:
3629:
3373:"Probing the filamentary nature of star formation in the California giant molecular cloud"
3206:"The metal enrichment of passive galaxies in cosmological simulations of galaxy formation"
61:
2794:
Dabringhausen, Jörg; Kroupa, Pavel; Pflamm-Altenburg, Jan; Mieske, Steffen (2012-03-01).
2259:"Implications for the formation of star clusters from extragalactic star formation rates"
1493:{\displaystyle \Delta N/\Delta \log M_{\text{line}}\propto M_{\text{line}}^{-1.5\pm 0.2}}
3505:
3470:
3449:
3333:
3204:
Okamoto, Takashi; Nagashima, Masahiro; Lacey, Cedric G.; Frenk, Carlos S. (2017-02-01).
2924:
2821:
2770:
2703:
2646:
2597:
2524:
2465:
2342:
2325:
Planets, Stars and
Stellar Systems: Volume 5: Galactic Structure and Stellar Populations
2284:
2225:
2166:
2117:
2084:
2071:
Massey, Philip (1998). "The
Initial Mass Function of Massive Stars in the Local Group".
2049:
2014:
1963:
1897:
1840:
1784:
1730:
1642:
3610:
2853:
Marks, Michael; Kroupa, Pavel; Dabringhausen, Jörg; Pawlowski, Marcel S. (2012-05-21).
2321:"The Stellar and Sub-Stellar Initial Mass Function of Simple and Composite Populations"
417:
202:
33:
2933:
2898:
2498:
1792:
1058:{\displaystyle \xi (m)={\frac {0.158}{m\ln(10)}}\exp \left\quad {\text{ for }}m<1,}
3789:
3773:
2975:
2958:
2881:
2854:
2830:
2795:
2779:
2744:
2729:
2474:
2439:
2293:
2258:
2175:
2140:
1923:
1856:
1848:
1746:
1738:
1239:{\displaystyle \xi (m)={\frac {0.086}{m\ln(10)}}\exp \left\quad {\text{ for }}m<1}
3529:
3307:
1987:
1800:
3744:
3654:
3537:
1658:
752:
91:
3398:
2415:
1619:
Chabrier, Gilles (2003). "Galactic stellar and substellar initial mass function".
3480:"The Initial Mass Function of Stars: Evidence for Uniformity in Variable Systems"
2499:"The Initial Mass Function of Stars: Evidence for Uniformity in Variable Systems"
3639:
3634:
2350:
2125:
1286:
299:
71:
66:
3102:
Urban, O.; Werner, N.; Allen, S. W.; Simionescu, A.; Mantz, A. (October 2017).
2712:
2677:
1906:
1871:
3568:
3371:
Zhang, Guo-Yin; Andre, Philippe; Menshchikov, Alexander; Li, Jin-Zeng (2024).
3341:
2985:
2320:
1814:
1066:
320:
237:
225:
3349:
3292:
3241:
3190:
3139:
3088:
3037:
2942:
2839:
2721:
2662:
2605:
2540:
2483:
2424:
2302:
2243:
2184:
1915:
3649:
3569:"Pavel Kroupa (Prague and Bonn): The stellar initial mass function: the IMF"
3513:
3283:
3256:
3222:
3205:
3181:
3154:
3130:
3103:
3079:
3028:
2532:
1971:
339:
194:
182:
81:
3521:
3357:
3104:"A uniform metallicity in the outskirts of massive, nearby galaxy clusters"
2548:
1979:
1676:"Astronomy 112: Physics of Stars -n Class 19 Notes: The Stellar Life Cycle"
1253:
The initial mass function is typically graphed on a logarithm scale of log(
2564:"A Universal Stellar Initial Mass Function? A Critical Look at Variations"
3496:
3153:
De Lucia, Gabriella; Fontanot, Fabio; Hirschmann, Michaela (2017-03-21).
2654:
2515:
2456:
2275:
2216:
2001:
Salpeter, Edwin (1955). "The luminosity function and stellar evolution".
1954:
1633:
861:, correcting for unresolved binary stars also adds a fourth domain with
3053:"Chemical evolution on the scale of clusters of galaxies: a conundrum?"
1579:. United Kingdom: Gordon and Breach, Science Publishers, Inc. p. 3
3232:
2141:"The evolution of stellar mass and the implied star formation history"
2139:
Wilkins, Stephen M.; Trentham, Neil; Hopkins, Andrew M. (April 2008).
1296:
where both formation modes may account for bodies in this mass range.
896:
3479:
3389:
3324:
3273:
3171:
3120:
2694:
2637:
2397:
2234:
2199:
2057:
2022:
1888:
1650:
3069:
3018:
2915:
2871:
2812:
2761:
2580:
2333:
2157:
2108:
1831:
1775:
1721:
1262:
3579:
2621:"The Dawes Review 8: Measuring the Stellar Initial Mass Function"
2562:
Bastian, Nate; Covey, Kevin R.; Meyer, Michael R. (2010-08-01).
2073:
The Stellar Initial Mass Function (38Th Herstmonceux Conference)
41:
3583:
294:
The mass of a star can only be directly determined by applying
1388:{\displaystyle \Delta N/\Delta \log M\propto M^{-1.4\pm 0.2}}
236:. At high masses, the IMF sets the number of core collapse
2743:
Dabringhausen, J.; Kroupa, P.; Baumgardt, H. (2009-04-11).
256:
Initial mass function. The vertical axis is actually not Îľ(
3457:
Scalo, J. M. (1986). "The Stellar Initial Mass Function".
3159:
Monthly Notices of the Royal Astronomical Society: Letters
3006:
Monthly Notices of the Royal Astronomical Society: Letters
2200:"Galactic-Field Initial Mass Functions of Massive Stars"
1261:). Such plots give approximately straight lines with a
1681:. University of Carlifornia, Santa Cruz. Archived from
1621:
Publications of the Astronomical Society of the Pacific
465:
within a specified volume of space, is proportional to
2314:
2312:
335:, it takes 5 Ă— 10 years to reach main sequence stars.
240:
that occur and therefore the kinetic energy feedback.
2625:
Publications of the Astronomical Society of Australia
2327:, Dordrecht: Springer Netherlands, pp. 115–242,
1506:
1432:
1401:
1339:
1089:
905:
867:
827:
794:
761:
717:
703:
is a constant relating to the local stellar density.
682:
566:
540:
518:
Commonly used forms of the IMF are the Kroupa (2001)
501:
471:
440:
420:
385:
348:
2257:
Weidner, C.; Kroupa, P.; Larsen, S. S. (June 2004).
3687:
3617:
1069:, meaning that the logarithm of the mass follows a
1538:
1492:
1418:
1387:
1238:
1057:
879:
839:
806:
773:
729:
695:
668:
552:
507:
487:
457:
426:
406:
371:
3261:Monthly Notices of the Royal Astronomical Society
3210:Monthly Notices of the Royal Astronomical Society
3108:Monthly Notices of the Royal Astronomical Society
3057:Monthly Notices of the Royal Astronomical Society
2963:Monthly Notices of the Royal Astronomical Society
2859:Monthly Notices of the Royal Astronomical Society
2749:Monthly Notices of the Royal Astronomical Society
2444:Monthly Notices of the Royal Astronomical Society
2263:Monthly Notices of the Royal Astronomical Society
2198:Kroupa, Pavel; Weidner, Carsten (December 2003).
2145:Monthly Notices of the Royal Astronomical Society
1083:For stellar systems (namely binaries), he gave:
414:), the number of stars with masses in the range
338:The IMF is often stated in terms of a series of
3051:Renzini, Alvio; Andreon, Stefano (2014-11-11).
2440:"On the variation of the initial mass function"
2100:Stellar Systems and Galactic Structure, Vol. V
1539:{\displaystyle 10\,M_{\odot }{\text{pc}}^{-1}}
3595:
1614:
1285:There are large uncertainties concerning the
162:
8:
3540:; Gallagher, John S. III (5 February 2007).
1612:
1610:
1608:
1606:
1604:
1602:
1600:
1598:
1596:
1594:
1565:
1563:
1561:
1559:
3546:. Cambridge University Press. pp. 1–.
3438:Luminous Stars and Associations in Galaxies
2568:Annual Review of Astronomy and Astrophysics
201:of masses for a population of stars during
3602:
3588:
3580:
1935:
1933:
169:
155:
29:
3543:Galaxies in the Universe: An Introduction
3495:
3388:
3323:
3282:
3272:
3231:
3221:
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3170:
3129:
3119:
3078:
3068:
3027:
3017:
2984:
2974:
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2914:
2880:
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2829:
2811:
2778:
2760:
2711:
2693:
2636:
2579:
2514:
2473:
2455:
2414:
2396:
2332:
2292:
2274:
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2215:
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2156:
2107:
1953:
1905:
1887:
1830:
1774:
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1527:
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1515:
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1505:
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1410:
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1370:
1346:
1338:
1222:
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1189:
1146:
1105:
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1038:
1023:
1005:
962:
921:
904:
866:
826:
793:
760:
716:
687:
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651:
637:
624:
612:
603:
592:
565:
539:
500:
476:
470:
447:
439:
419:
384:
361:
347:
737:) when stellar masses fell below 1
251:
3415:
2038:Astrophysical Journal Supplement Series
1555:
109:
48:
32:
1670:
1668:
1500:for filament line masses greater than
1311:); lower gas metallicity reduces the
7:
3752:
730:{\displaystyle \alpha \rightarrow 0}
522:and the Chabrier (2003) log-normal.
197:function that describes the initial
2598:10.1146/annurev-astro-082708-101642
1444:
1433:
1351:
1340:
640:
579:
448:
398:
362:
25:
372:{\displaystyle N(m)\mathrm {d} m}
3751:
3739:
3728:
3727:
3678:
2976:10.1111/j.1365-2966.2011.18800.x
2882:10.1111/j.1365-2966.2012.20767.x
2780:10.1111/j.1365-2966.2009.14425.x
2475:10.1046/j.1365-8711.2001.04022.x
2294:10.1111/j.1365-2966.2004.07758.x
2176:10.1111/j.1365-2966.2008.12885.x
40:
2619:Hopkins, A. M. (January 2018).
1221:
1037:
458:{\displaystyle m+\mathrm {d} m}
407:{\displaystyle \xi (m)\Delta m}
379:(sometimes also represented as
27:Empirical function in astronomy
3459:Fundamentals of Cosmic Physics
1573:Fundamentals of Cosmic Physics
1186:
1182:
1176:
1164:
1158:
1149:
1126:
1120:
1099:
1093:
1002:
998:
992:
980:
974:
965:
942:
936:
915:
909:
721:
576:
570:
395:
389:
358:
352:
18:Salpeter initial mass function
1:
3795:Stellar astrophysics concepts
1419:{\displaystyle 1\,M_{\odot }}
515:is a dimensionless exponent.
3377:Astronomy & Astrophysics
2497:Kroupa, Pavel (2002-01-04).
2385:Astronomy & Astrophysics
553:{\displaystyle \alpha =2.35}
488:{\displaystyle m^{-\alpha }}
264:, but a scaled version of Îľ(
210:probability density function
208:The IMF is often given as a
3399:10.1051/0004-6361/202449853
2934:10.1088/0004-637X/706/1/599
2416:10.1051/0004-6361/201833055
2351:10.1007/978-94-007-5612-0_4
2126:10.1007/978-94-007-5612-0_4
1793:10.1088/0004-637X/763/2/110
880:{\displaystyle \alpha =2.7}
840:{\displaystyle \alpha =0.3}
807:{\displaystyle \alpha =1.3}
774:{\displaystyle \alpha =2.3}
3811:
3705:Kelvin–Helmholtz mechanism
2831:10.1088/0004-637X/747/1/72
1849:10.1088/0004-637X/771/1/29
1739:10.1088/0004-637X/760/1/71
133:Kelvin–Helmholtz mechanism
3723:
3676:
3342:10.1038/s41586-018-0196-x
2903:The Astrophysical Journal
2800:The Astrophysical Journal
2682:The Astrophysical Journal
2438:Kroupa, P. (2001-04-01).
2204:The Astrophysical Journal
1876:The Astrophysical Journal
1819:The Astrophysical Journal
1763:The Astrophysical Journal
1709:The Astrophysical Journal
1328:Origin of the Stellar IMF
305:present-day mass function
214:present-day mass function
3486:(Submitted manuscript).
2713:10.3847/1538-4357/ac695e
1907:10.3847/1538-4357/ac695e
1395:for masses greater than
696:{\displaystyle \xi _{0}}
309:mass–luminosity relation
3514:10.1126/science.1067524
2590:2010ARA&A..48..339B
2533:10.1126/science.1067524
2407:2018A&A...620A..39J
1972:10.1126/science.1067524
1426:, and the FLMF follows
560:. The Salpeter IMF is
508:{\displaystyle \alpha }
3785:Equations of astronomy
3660:Pre-main-sequence star
3478:Kroupa, Pavel (2002).
1540:
1494:
1420:
1389:
1240:
1059:
881:
841:
814:between 0.08–0.5
808:
775:
731:
697:
670:
554:
509:
489:
459:
428:
408:
373:
291:
87:Pre-main-sequence star
3695:Initial mass function
3284:10.1093/mnras/stx1197
3223:10.1093/mnras/stw2729
3182:10.1093/mnrasl/slw242
3131:10.1093/mnras/stx1542
3080:10.1093/mnras/stu1689
3029:10.1093/mnrasl/sls014
2003:Astrophysical Journal
1541:
1495:
1421:
1390:
1241:
1071:Gaussian distribution
1060:
882:
842:
809:
781:between 0.5–1.0
776:
732:
698:
671:
555:
510:
490:
460:
429:
409:
374:
255:
187:initial mass function
123:Initial mass function
3688:Theoretical concepts
3645:Young stellar object
2655:10.1017/pasa.2018.29
1504:
1430:
1399:
1337:
1087:
903:
865:
825:
792:
759:
715:
680:
564:
538:
499:
469:
438:
418:
383:
346:
307:, PDMF) by applying
110:Theoretical concepts
77:Young stellar object
3715:Planetary migration
3625:Interstellar medium
3506:2002Sci...295...82K
3471:1986FCPh...11....1S
3450:1986IAUS..116..451S
3334:2018Natur.558..260Z
2925:2009ApJ...706..599L
2822:2012ApJ...747...72D
2771:2009MNRAS.394.1529D
2704:2022ApJ...931...57S
2647:2018PASA...35...39H
2525:2002Sci...295...82K
2466:2001MNRAS.322..231K
2343:2013pss5.book..115K
2285:2004MNRAS.350.1503W
2226:2003ApJ...598.1076K
2167:2008MNRAS.385..687W
2118:2013pss5.book..115K
2085:1998ASPC..142...17M
2050:1979ApJS...41..513M
2015:1955ApJ...121..161S
1964:2002Sci...295...82K
1898:2022ApJ...931...57S
1841:2013ApJ...771...29G
1785:2013ApJ...763..110K
1731:2012ApJ...760...71C
1643:2003PASP..115..763C
1489:
1065:This expression is
707:Miller–Scalo (1979)
234:interstellar medium
143:Planetary migration
57:Interstellar medium
3710:Nebular hypothesis
3670:Herbig–Haro object
2986:20.500.11850/38507
1570:Scalo, JM (1986).
1536:
1490:
1466:
1416:
1385:
1313:radiation pressure
1236:
1055:
877:
837:
804:
771:
727:
693:
666:
550:
505:
485:
455:
424:
404:
369:
296:Kepler's third law
292:
138:Nebular hypothesis
102:Herbig–Haro object
3780:Stellar astronomy
3767:
3766:
3700:Jeans instability
3665:Herbig Ae/Be star
3553:978-1-139-46238-9
3318:(7709): 260–263.
2360:978-94-007-5612-0
1525:
1473:
1460:
1287:substellar region
1225:
1214:
1130:
1041:
1030:
946:
788:, but introduced
657:
618:
531:Edwin E. Salpeter
427:{\displaystyle m}
179:
178:
128:Jeans instability
97:Herbig Ae/Be star
16:(Redirected from
3802:
3755:
3754:
3743:
3731:
3730:
3682:
3681:
3604:
3597:
3590:
3581:
3576:
3575:. April 8, 2022.
3557:
3538:Sparke, Linda S.
3533:
3499:
3497:astro-ph/0201098
3474:
3453:
3423:
3420:
3403:
3402:
3392:
3368:
3362:
3361:
3327:
3303:
3297:
3296:
3286:
3276:
3252:
3246:
3245:
3235:
3225:
3216:(4): 4866–4874.
3201:
3195:
3194:
3184:
3174:
3150:
3144:
3143:
3133:
3123:
3114:(4): 4583–4599.
3099:
3093:
3092:
3082:
3072:
3063:(4): 3581–3591.
3048:
3042:
3041:
3031:
3021:
2997:
2991:
2990:
2988:
2978:
2969:(2): 1647–1662.
2953:
2947:
2946:
2936:
2918:
2893:
2887:
2886:
2884:
2874:
2865:(3): 2246–2254.
2850:
2844:
2843:
2833:
2815:
2791:
2785:
2784:
2782:
2764:
2755:(3): 1529–1543.
2740:
2734:
2733:
2715:
2697:
2673:
2667:
2666:
2640:
2616:
2610:
2609:
2583:
2559:
2553:
2552:
2518:
2516:astro-ph/0201098
2494:
2488:
2487:
2477:
2459:
2457:astro-ph/0009005
2435:
2429:
2428:
2418:
2400:
2376:
2370:
2369:
2368:
2367:
2336:
2316:
2307:
2306:
2296:
2278:
2276:astro-ph/0402631
2269:(4): 1503–1510.
2254:
2248:
2247:
2237:
2219:
2217:astro-ph/0308356
2210:(2): 1076–1078.
2195:
2189:
2188:
2178:
2160:
2136:
2130:
2129:
2111:
2095:
2089:
2088:
2068:
2062:
2061:
2033:
2027:
2026:
1998:
1992:
1991:
1957:
1955:astro-ph/0201098
1937:
1928:
1927:
1909:
1891:
1867:
1861:
1860:
1834:
1811:
1805:
1804:
1778:
1757:
1751:
1750:
1724:
1704:
1698:
1697:
1695:
1693:
1687:
1680:
1672:
1663:
1662:
1636:
1634:astro-ph/0304382
1627:(809): 763–795.
1616:
1589:
1588:
1586:
1584:
1578:
1567:
1545:
1543:
1542:
1537:
1535:
1534:
1526:
1523:
1520:
1519:
1499:
1497:
1496:
1491:
1488:
1474:
1471:
1462:
1461:
1458:
1443:
1425:
1423:
1422:
1417:
1415:
1414:
1394:
1392:
1391:
1386:
1384:
1383:
1350:
1245:
1243:
1242:
1237:
1226:
1223:
1220:
1216:
1215:
1213:
1212:
1211:
1195:
1194:
1193:
1147:
1131:
1129:
1106:
1064:
1062:
1061:
1056:
1042:
1039:
1036:
1032:
1031:
1029:
1028:
1027:
1011:
1010:
1009:
963:
947:
945:
922:
886:
884:
883:
878:
847:below 0.08
846:
844:
843:
838:
813:
811:
810:
805:
780:
778:
777:
772:
736:
734:
733:
728:
702:
700:
699:
694:
692:
691:
675:
673:
672:
667:
662:
658:
656:
655:
646:
638:
632:
631:
623:
619:
617:
616:
604:
597:
596:
559:
557:
556:
551:
520:broken power law
514:
512:
511:
506:
494:
492:
491:
486:
484:
483:
464:
462:
461:
456:
451:
433:
431:
430:
425:
413:
411:
410:
405:
378:
376:
375:
370:
365:
313:stellar parallax
230:Milky Way Galaxy
171:
164:
157:
44:
30:
21:
3810:
3809:
3805:
3804:
3803:
3801:
3800:
3799:
3770:
3769:
3768:
3763:
3719:
3683:
3679:
3674:
3630:Molecular cloud
3613:
3608:
3567:
3564:
3554:
3536:
3490:(5552): 82–91.
3477:
3456:
3435:
3432:
3430:Further reading
3427:
3426:
3421:
3417:
3412:
3407:
3406:
3370:
3369:
3365:
3305:
3304:
3300:
3254:
3253:
3249:
3203:
3202:
3198:
3152:
3151:
3147:
3101:
3100:
3096:
3050:
3049:
3045:
2999:
2998:
2994:
2955:
2954:
2950:
2895:
2894:
2890:
2852:
2851:
2847:
2793:
2792:
2788:
2742:
2741:
2737:
2675:
2674:
2670:
2618:
2617:
2613:
2561:
2560:
2556:
2509:(5552): 82–91.
2496:
2495:
2491:
2437:
2436:
2432:
2378:
2377:
2373:
2365:
2363:
2361:
2318:
2317:
2310:
2256:
2255:
2251:
2197:
2196:
2192:
2138:
2137:
2133:
2097:
2096:
2092:
2070:
2069:
2065:
2035:
2034:
2030:
2000:
1999:
1995:
1948:(5552): 82–91.
1939:
1938:
1931:
1869:
1868:
1864:
1813:
1812:
1808:
1759:
1758:
1754:
1706:
1705:
1701:
1691:
1689:
1688:on 6 April 2023
1685:
1678:
1674:
1673:
1666:
1618:
1617:
1592:
1582:
1580:
1576:
1569:
1568:
1557:
1552:
1521:
1511:
1502:
1501:
1453:
1428:
1427:
1406:
1397:
1396:
1366:
1335:
1334:
1330:
1302:
1295:
1292:
1283:
1251:
1224: for
1203:
1196:
1185:
1148:
1142:
1138:
1110:
1085:
1084:
1079:
1076:
1040: for
1019:
1012:
1001:
964:
958:
954:
926:
901:
900:
893:
891:Chabrier (2003)
863:
862:
860:
857:
854:. Above 1
853:
850:
823:
822:
820:
817:
790:
789:
787:
784:
757:
756:
750:
743:
740:
713:
712:
709:
683:
678:
677:
647:
639:
633:
608:
599:
598:
588:
562:
561:
536:
535:
528:
526:Salpeter (1955)
497:
496:
472:
467:
466:
436:
435:
416:
415:
381:
380:
344:
343:
334:
331:
326:
323:
289:
286:
278:
275:
250:
175:
62:Molecular cloud
28:
23:
22:
15:
12:
11:
5:
3808:
3806:
3798:
3797:
3792:
3787:
3782:
3772:
3771:
3765:
3764:
3762:
3761:
3749:
3737:
3724:
3721:
3720:
3718:
3717:
3712:
3707:
3702:
3697:
3691:
3689:
3685:
3684:
3677:
3675:
3673:
3672:
3667:
3662:
3657:
3652:
3647:
3642:
3637:
3632:
3627:
3621:
3619:
3618:Object classes
3615:
3614:
3611:Star formation
3609:
3607:
3606:
3599:
3592:
3584:
3578:
3577:
3563:
3562:External links
3560:
3559:
3558:
3552:
3534:
3475:
3454:
3431:
3428:
3425:
3424:
3414:
3413:
3411:
3408:
3405:
3404:
3363:
3298:
3267:(1): 401–415.
3247:
3196:
3165:(1): L88–L92.
3145:
3094:
3043:
3012:(1): L15–L19.
2992:
2948:
2909:(1): 599–613.
2888:
2845:
2786:
2735:
2668:
2611:
2574:(1): 339–389.
2554:
2489:
2450:(2): 231–246.
2430:
2371:
2359:
2308:
2249:
2235:10.1086/379105
2190:
2151:(2): 687–694.
2131:
2090:
2063:
2058:10.1086/190629
2028:
2023:10.1086/145971
1993:
1929:
1862:
1806:
1761:< 1 Msun".
1752:
1699:
1664:
1651:10.1086/376392
1590:
1554:
1553:
1551:
1548:
1533:
1530:
1518:
1514:
1509:
1487:
1484:
1481:
1478:
1469:
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1442:
1438:
1435:
1413:
1409:
1404:
1382:
1379:
1376:
1373:
1369:
1365:
1362:
1359:
1356:
1353:
1349:
1345:
1342:
1329:
1326:
1301:
1298:
1293:
1290:
1282:
1279:
1250:
1247:
1235:
1232:
1229:
1219:
1210:
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1202:
1199:
1192:
1188:
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1181:
1178:
1175:
1172:
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1163:
1160:
1157:
1154:
1151:
1145:
1141:
1137:
1134:
1128:
1125:
1122:
1119:
1116:
1113:
1109:
1104:
1101:
1098:
1095:
1092:
1077:
1074:
1054:
1051:
1048:
1045:
1035:
1026:
1022:
1018:
1015:
1008:
1004:
1000:
997:
994:
991:
988:
985:
982:
979:
976:
973:
970:
967:
961:
957:
953:
950:
944:
941:
938:
935:
932:
929:
925:
920:
917:
914:
911:
908:
892:
889:
876:
873:
870:
858:
855:
851:
848:
836:
833:
830:
818:
815:
803:
800:
797:
785:
782:
770:
767:
764:
749:
746:
741:
738:
726:
723:
720:
708:
705:
690:
686:
665:
661:
654:
650:
645:
642:
636:
630:
627:
622:
615:
611:
607:
602:
595:
591:
587:
584:
581:
578:
575:
572:
569:
549:
546:
543:
527:
524:
504:
482:
479:
475:
454:
450:
446:
443:
423:
403:
400:
397:
394:
391:
388:
368:
364:
360:
357:
354:
351:
332:
329:
324:
321:
287:
284:
276:
273:
249:
246:
203:star formation
177:
176:
174:
173:
166:
159:
151:
148:
147:
146:
145:
140:
135:
130:
125:
120:
112:
111:
107:
106:
105:
104:
99:
94:
89:
84:
79:
74:
69:
64:
59:
51:
50:
49:Object classes
46:
45:
37:
36:
34:Star formation
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3807:
3796:
3793:
3791:
3788:
3786:
3783:
3781:
3778:
3777:
3775:
3760:
3759:
3750:
3748:
3747:
3742:
3738:
3736:
3735:
3726:
3725:
3722:
3716:
3713:
3711:
3708:
3706:
3703:
3701:
3698:
3696:
3693:
3692:
3690:
3686:
3671:
3668:
3666:
3663:
3661:
3658:
3656:
3653:
3651:
3648:
3646:
3643:
3641:
3638:
3636:
3633:
3631:
3628:
3626:
3623:
3622:
3620:
3616:
3612:
3605:
3600:
3598:
3593:
3591:
3586:
3585:
3582:
3574:
3570:
3566:
3565:
3561:
3555:
3549:
3545:
3544:
3539:
3535:
3531:
3527:
3523:
3519:
3515:
3511:
3507:
3503:
3498:
3493:
3489:
3485:
3481:
3476:
3472:
3468:
3464:
3460:
3455:
3451:
3447:
3443:
3439:
3434:
3433:
3429:
3419:
3416:
3409:
3400:
3396:
3391:
3386:
3382:
3378:
3374:
3367:
3364:
3359:
3355:
3351:
3347:
3343:
3339:
3335:
3331:
3326:
3321:
3317:
3313:
3309:
3302:
3299:
3294:
3290:
3285:
3280:
3275:
3270:
3266:
3262:
3258:
3251:
3248:
3243:
3239:
3234:
3229:
3224:
3219:
3215:
3211:
3207:
3200:
3197:
3192:
3188:
3183:
3178:
3173:
3168:
3164:
3160:
3156:
3149:
3146:
3141:
3137:
3132:
3127:
3122:
3117:
3113:
3109:
3105:
3098:
3095:
3090:
3086:
3081:
3076:
3071:
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3062:
3058:
3054:
3047:
3044:
3039:
3035:
3030:
3025:
3020:
3015:
3011:
3007:
3003:
2996:
2993:
2987:
2982:
2977:
2972:
2968:
2964:
2960:
2952:
2949:
2944:
2940:
2935:
2930:
2926:
2922:
2917:
2912:
2908:
2904:
2900:
2892:
2889:
2883:
2878:
2873:
2868:
2864:
2860:
2856:
2849:
2846:
2841:
2837:
2832:
2827:
2823:
2819:
2814:
2809:
2805:
2801:
2797:
2790:
2787:
2781:
2776:
2772:
2768:
2763:
2758:
2754:
2750:
2746:
2739:
2736:
2731:
2727:
2723:
2719:
2714:
2709:
2705:
2701:
2696:
2691:
2687:
2683:
2679:
2672:
2669:
2664:
2660:
2656:
2652:
2648:
2644:
2639:
2634:
2630:
2626:
2622:
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2266:
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2148:
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1683:the original
1624:
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1572:
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1306:
1303:
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1273:
1269:
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751:
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272:> 1
269:
265:
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213:
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199:distribution
190:
186:
180:
122:
92:T Tauri star
3640:Dark nebula
3635:Bok globule
1815:Geha, Marla
1692:23 December
1583:28 February
1268:equal to 1–
300:binary star
248:Development
72:Dark nebula
67:Bok globule
3774:Categories
3390:2406.08004
3325:1806.01280
3274:1704.06701
3233:2115/65505
3172:1611.04597
3121:1706.01567
2695:2205.11536
2638:1807.09949
2398:1809.04603
2366:2023-11-02
1889:2205.11536
1769:(2): 110.
1550:References
1309:Jeans mass
1067:log-normal
340:power laws
317:magnitudes
238:supernovae
226:luminosity
3650:Protostar
3350:1476-4687
3293:0035-8711
3242:0035-8711
3191:1745-3925
3140:0035-8711
3089:1365-2966
3070:1409.0307
3038:1745-3933
3019:1206.1594
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387:ξ
279:, it is (
195:empirical
183:astronomy
118:Accretion
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3734:Category
3530:14084249
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3358:29867162
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2549:11778039
1988:15276163
1980:11778039
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495:, where
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333:☉
325:☉
288:☉
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924:0.158
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