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1997AJ....113..656H [email protected] Technology, tronic [email protected] 656 8 30001, [email protected] electronic Charter electronic 5 9 6 3 [email protected], TilE 7 Pittsburgh, Mall, Michigan, 2 tained 4 mail.jpl.nasa.gov [email protected], [email protected] versity, under scope 1 1 0oivision Jet Departruent Departruent Departruent Mount Departruent Based on Astrophysics Departruent Propulsion © ASTRONOMICAL contract mail: Science at Astron. Tempe, Private Stromlo St., Las American the mail: Astronomical is observations JON We main , than range, single 0.6::SM::s constant of derived consistent IMF, the Alternatively, number of PA mail: 2455 [email protected] Madison, ROBIN of of of of of seen down Space GRILLMAIR, Cruces, the Geological Division, to 15213 Institote, Bag, Laboratory, , present [email protected] J. Atmospheric, Physics Physics, and Astronomy, A. -3.1 AZ NASA. although Pasadena, sequence Hayward, [email protected], 113 power we field Weston Siding Telescope if of formation W. for HOLTZMAN, WI STELLAR 85287, 3 derive NM with (2), we with for Space and 3700 deep M we Carnegie stars FOR 10 53706, EVANS, and Astronomical law to Spring 4800 Society. New we February adopt 5 JOURNAL 8 Creek the the the Astronomy, Gyr University 88003, Ann Oceanic, which KARL derive GILDA V>26. the older . San Planetary Science [email protected] Science [email protected], electronic photometry in can IMF NASA/ESA A CA We preferred Mexico mass electronic Oak history. Observatories, then Post 5 Mellon Martin the Arbor, distribution SIGNIFICANT the 2 POPULATIONS RICHARD fit and find R. electronic [S0004-6256(97)03102-6] Grove are slopes slope JEREMY 1997 E. and Office, Department, We range Institute, LMC the increases Kroupa, of Sciences, State 91125, Arizona STAPELFELDT, BALLESTER, younger fainter Drive, University, that mail: mail: MI Space We Wisconsin-Madison, values Hubble derive Drive, with obtained University, ACT which 0.6::sM::s are 48109, the Received derive E. [email protected], Australian mail: operated histories R. Society [email protected], Sciences, Baltimore, State [email protected], of California Tout, Pasadena, than by a~- 2611, younger GRIFFITHS, Space ESA are a electronic luminosity than MOTJLD, stars 5000 NUMBER luminosity are about University, [email protected], electronic steeper. 6 limits with IN 1996 Dept the function & Australia, 5 by and Telescope, CHRISTOPHER 2.75 1.1 4 National VOLUME University consistent from 0004-6256/97 JOHN Forbes in Space MD jtt@wfpc2- Institute THE Gyr. AURA CA oldest a than 4500 August the • 3 M Gilmore the factor on over 8 475 JOHN 91109, 21218, 8 We function Provided the ABSTRACT J. Tyler T. Tele­ HST mail: mail: Our elec­ Ave, Uni­ function LARGE OF with Box the . color- 4 ob­ Inc JEFF N. 30; of of Assuming turnoff. entire TRAUGER, the can Gyr. 113, of the OLDER IMF best in S. a revised solar 1113(2)/656/13/$10.00 three entire rule J. HEsTER, predominantly an is NUMBER Salpeter GALLAGHER been els formation function et initial ity is in Hubble tionally, tion tunity there masses tive studies sequence of and (see Instead, luminosity from MAGELLANIC BURROWS, model slope, inconsistent outer For particularly al. different the out neighborhood As Deep for is 1996 of by range numbers young 5 a reviews about STARS described are essential AND (1992), Milky the mass the to Salpeter IMF most the 9 reach and November the has LMC time a (a= JOHN we study of ground-based if variations provides 2 diagram. nearest data past history, of (with the JAMES stars. slopes 6 types function, function higher a assumed the choices find Way. NASA by observed JoHN on OR of III, evolution. -2.35) young star formation a field. and with interesting G. star 2 to and low IMF by similar intermediate Feast 4 IMF 12 Gyr. the dN/dMrxMa), IMF that A of galaxy, our A HOESSEL, CLOUD: shallower A. because ALAN The a Vallenari mass formation use T. mass Butcher the Similar of A knowledge STEEPER over population of main constraint (IMF) which to WESTPHAL understanding Such 1. there or CLARKE, slope well-defined 1995 Astrophysics instead the masses. it luminosity scenario star photometry INTRODUCTION conclusion, be local stars stars the to the because M. IMF sequence. low a time-independent, 4 roughly must EVIDENCE model constrain covers and formation than (1977), rate can LMC model is and PAUL entire et history. WATSON, in of can solar on 7 © critical with IMF? al. mass of if © Mateo in 10 from DAVID a which -1.6 a low be 1997 be we it the function the be setting 1997 offers which the parameters Salpeter main (1996a,b), A. observed is independently namely of of neighborhood can Stryker galaxy a 1 Understanding extrapolated stars use the mass also used relative In stars star comparable SCOWEN, Am. history for mass and star LMC 2 1991). is CRISP, American be Data particular, sequence an a IMF CARL the different constraining roughly roughly live formation steeper steeper of Astron. to stars FEBRUARY formation. on type used excellent that slope. range (1984), mass bulk field low the number infer and and Most among 5 the are longer 9 System J. on or the to luminosity mass stars of Soc. to from stars metallic­ the informa­ infer the of whether bulk Bertelli the history oppor­ higher than others of Addi­ mod­ these main rela­ 1997 that star 656 has old the of a 1997AJ....113..656H diagram in Bertelli metallicity. metric billion bal HST star stellar eral aperture analysis formation, of and lower dict although occurred about occurred found Their This cause large the the magnitude tailed mation ments to rich However, Space the bulk Salpeter expected field fields, although formation et derive in The around distribution However, the nent 657 1866 1997), V al. estimate the band a~- Direct We In different solar field luminosity variation LMC © finds lifetimes formation star LMC being most is of of measurements with this and models number clusters color-magnitude slope modelling luminosity with in Telescope a years measurements which American HOLTZMAN preferred have in the rate old the et CCD to of IMF stars burst photometry. 3.5, neighborhood it for clusters that branch in measurements six cluster Vallenari the one paper rates the even al. quantitative formed they brighter measure LMC. the is clusters. the hardly The stars to stars of increases regions in a an observed in where generally clusters probe and in along all unclear same Wide may might (1992). lookback observations of few function. has this ~ brighter 2 until the old suggest these the evidence we the formed of in IMFs - Gyr in is function. star a in Generally, younger comparable recently. any formation been field. disrupt 2.2. star LMC fields, than vicinity population. dNI somewhat LMC evolutionary et the of Field also order ET concentrate star clusters of Mateo the the not a By Astronomical and whether for ago, by observations al., formation Gallagher the diagram IMF intermediate "burst a have AL.: studies are IMF formation the dM stars of time that necessarily roughly LMC; counts the mirrored On color-magnitude comparing recently field a star Planetary are stars their for who to larger the as cluster the A clusters essentially factor A color-magnitude to as STELLAR derived (1988) the oc have top of subgiant a they observe observed of history careful of this time formation star time," lower this IMF precise to Ma. one photometer near small errors use in unevolved have By with a bulk intermediate within on of 2 performed differences they the similar 2.2 well we exposures the history). be the aperture was the star mag V the which one the we four was would and we the a We aperture a as 26. added results; profile-fitting Completeness frame, on This and H95B). the fitting (H95B). of application effect to of use not defined function for correction made after do WFPC2 detection were fainter. or discussed use fainter spurious chips, filtered the judge magnitudes our the interpret stellar method aperture the we color-magnitude I all not well optimal to two only provides corrections In galaxies, ET eas the because between a a the (see then it luminosity profile results in for Astronomical remove uncertainties of conclusions a need of fairly physical magnitudes The series addition, grid know main AL.: was although the separate stars fit ecn in percent photometric of change profile synthetic the brightness once deviant a efficiency Note doing detections made of would photometry has by in a magnitude, profile to of possible weighting accuracy results STELLAR and fitting, stars. added of long were superior luminosity sequence the a noise the system H95B; spurious were compute the the stars again been priori Added were artificial WFPC2 results aperture the we function, Error profile no correction transformations they zeropoints pixels stellar make This would exposures results system 0.5 with then the back by spikes, of aperture diagram transformed derived believe and and systematic is correction zeropoint which using determined if used of defined the photometry all and equal POPULATIONS of detections depending in subtracting can here. expected worst was Estimation needed. arcsec CTE fits put the a measurement star function, PSF. all photometry response Society arising into metallicity reasonably be agreed Proof, metallicity were particularly rather 0.5 are etc. by be a done remained. seem was we magnitudes aperture our photometry on given experiments. brightness is unaffected. problems goodness-of-fit case. with the The by seen better between Guhathakurta arcsec aperture Since have converted effect presented for To the colors allowed H95B); to magnitudes by from in to than by have to on subtracted an for Holtzman final and all in The typically conjunc­ down the within estimate possible be WFPC2 deleting • inspect­ isolated on the correc­ a able (which depen­ we H95B. under­ radius which of of bright errors IN trans­ some Provided close more good from were filter pho­ each onto long by syn­ cor­ was and star ap­ the No are the for THE In in to to to a a LMC found original if tificial tometric the tection the the tion real pixel photometry pixel 529 from found artificial crowding due on These identical the tion were place sponding separate each artificial the The For the If :;: "' "' artificial fitting by original artificial to stars (frame data. where FIG. exposure centering chosen each centerings the with measured frames if original 22 20 16 stars 28 26 24 18 each crowding efficiency artificial the -.5 frames. times there errors, stars, 2. stars to on stars on detection of Poisson 0 both other The the to procedure each those of stars frames. each CJ NASA the the star 0. to were D was frame using with frame, 0 in and color-magnitude on the varied star De at insure the stars This magnitude frames frame; were as 0 time. 0 and is of than of each discussed each least statistics a artificial then also that different artificial on well was the faint An detection shifts an the also properly thus slightly Astrophysics used was to of that the for frame run without we WFs. they with assumed artificial (F555W-F814W) as placed artificial .5 stars the the provided and did original compared the placed the was from through star for were diagram in star brightnesses are the magnitude four The from using within above accounts fainter Sec. o add not scale artificial each the runs, and closer reduced position incompleteness final star used gain star 1 model chips. 121 ob1ained frame-to-frame 0 artificial an the frame. 0 2.1. the if changes) the artificial one was the with was stars. photometry estimate of stars to to there photometry Data significantly positional for stars with of This PSFs background. and The chosen 1.5 final pixel the add 14 considered from considered the If the on incompleteness A stars. was with electrons/DN. the magnitude were grid a was derived star, errors were list limitation the input System the of of star match due for same field. no an Different the list 2 from informa­ as the spacings done PC, routines -2 2 0 4 8 isolated and 6 used on the list to object in to corre­ found in to posi­ from from pho­ • • ~ PSF was s: and 659 de­ the the the the the the ar­ 23 be of of of to 1997AJ....113..656H judge 660 for from FIG. magnitudes periments. points). but ficial cussed function ficial expected color-magnitude errors observed ficial cial direction), curately true those tificial that returned the tematic the the are (small (independent ~ .<:: a. £ ~ c. Q ., .l!! g 0 E 0 ., ., ., " The 0 ., " E 0 artificial faintest fact brighter the 3. shown © star is stars, stars inaccuracies star predicted stars. points) the Bottom Top arising .2 .4 .6 .8 .4 .2 used HOLTZMAN stars below. 0 American 0 measured brightest reveal that in of errors by because for photometric brightness, were panel: but both as in At levels. magnitude. in 18 and 18 to stars are the stars, only panel: the in well from Fig. intermediate this both the create by saved the F555W each error slightly which PSF artificial stars, diagrams provide completeness a positive in the completeness bias The so may observed as 3. perfect Poisson 20 ET colors 20 estimates the we color). Astronomical them, fitting for artificial the errors The random in PSF AL.: tables The and be arise larger PSF tabulated use the good stars artificial noise are PSF top rms brightness, caused STELLAR 22 22 and errors F814W. so statistics observed for The routine returned faintest with as models. of F555W stars error usually from than error errors there panel (large inferred and was such fluctuations observed luminosity artificial the are the by stars 24 for 24 random those by used estimates. from The for of stars are stars. crowding and shows generation points) POPULATIONS errors Such small errors from the affected the the the the Society the cannot no errors to which readout star errors estimated Poisson fact profile-fitting brightest errors artificial However, the 26 26 errors errors reduce compared error are real are the for functions and artificial tests At that include in arises be larger of each detected in (in rms for stars the each stars estimates dominate the noise, resulting statistics 28 artificial 28 the the also stars, • the used for the for star which IN errors errors routine artifi­ same Provided from (large with as than arti­ arti­ arti­ sys­ dis­ rms ac­ the THE ar­ ex­ all so as to at a LMC jects This est values the We tion reducing note, tuations plied puted significantly surements shows systematic faintest few equal for data ficult in galaxies, value tests magnitude tections mates; vatively timating recent rious nosity use with before sonable sight stars. shows function lished of group lifetime they 2:5u, 1993; subsequent At We An Astrophysical stellar magnitudes. the by a faintest have which set attempt in is at on detector detections directly for to however, conservative Consequently, the of only importance by Fagotto function, set (Rogers that so for the namely, estimate have measurement the caused the stars. the the interpret estimate was our in are feel for the of the the the which attempted we evolution (2) faintest of the to completeness with photometric diagram from have we several photometric faintest apparent WFPC2 chosen part), detected stars stars, number lower to background measured taken that radiative NASA Padua should the The to our artificial flaws analysis, do by stars et include & that remaining systematic of we the we stars survived, observed accurately for we al. of magnitudes, not so effect Iglesias to star the interpretation the limit than with ways: the to only group magnitudes, as and to raw with not and perform this a digitization we of the magnitude. have electronics. of as an 1994a,b). appear which primarily opacities fact Astrophysics 3.1 wide minimize rms well scatter, stars evolution finding number errors we spurious the a be stars a luminosity on of data reduction do consider as understanding number 3. regions M completeness sky (1) luminosity gain (Bertelli good lsochrones after since field. 1992; MODELS that detecting errors digitization make F555W goodness-of-fit inferred errors error as not because are range were to because level at photometry. we which the since estimates of threshold only These these (OPAL) of have use fully these contaminated completeness effects we and detections the throughout Iglesias of :S estimates which have Unfortunately, no stars of because 14 detected. artificial of of et spurious and and functions the 26.3. spurious cannot the from of number effort noise are the electrons/DN in function. a al. trust techniques it the mass, levels, the models for inspected large the depends curve models the of can masked our does rms contain present from 1994; positive of Data et is the artificial which Visual peaks, our of the effect for to for brightness star observed is determine The the be fits al. although the detections values relatively number of thus not require detections crowding. correct artificial more cannot by and the the severe accepting Bressan However, completeness completeness use recently tests distance 1992). spurious on entire stellar entire to System lower at background out are the include of the some we noise and Livermore artificially inspection error real the the (an the the stars are difficult. digitiza­ applied; are conser­ regions models current of images for be for in (3) of color­ a faint­ panel lumi­ exact over­ Also, stars; stars com­ mea­ high, et is most fluc­ pub­ esti­ spu­ as rea­ dif­ For this and 660 ob­ ap­ de­ the the are the the es­ we al. of a . 1997AJ....113..656H for M The the mospheres tables mined puted ting minosity peratures pared evolutionary each atmospheres Clearly, chrones 0.6 cation) clude ferred during and cool. dance construction i.e., logT. ing Padua the ties from magnitude tallicities. temperature, tallicity used the which sample, stars, stars. sures set for els faint 661 evolution. corresponds roughly dance ies work 100 0 We In One of include in the observational low interpretation. M LMC; the © Swenson are we equally isochrones the star the stars. To but oxygen masses, directly that WFPC2 we subsequent 0 ratios ratios nearby to and do isochrones by also interpolation. main-sequence HOLTZMAN American WFPC2 possible effective and for we given. were ; have isochrones this Z stellar extend functions, in get since :S not are for Another resampling The the of are this = A logL convective need expect each 4000 age) higher of (the metallicity, for spaced from stages. is the M isochrones enhancement), include with effective 0.0004 then mostly galaxies lower not star correct colors probably This models our they models is v only for system the limitation h heavy the which isochrone, to Bergbusch appropriate derived eprtrs and temperatures plane. - K, sections, because used similar of Kurucz that the limitation interpolated model transform we metallicities. ages isochrones is into ET to For 7- represent mass masses and to but for an Astronomical interested this 0.6 each shape a data, an are lifetimes because overshoot, temperatures, it need AL.: are Z of 8, as a To any concern and are any equivalent approximation all does that our Swenson apparent = poor M for effect. color-magnitude depending available Bergbusch to of points defined tabulated (1993) elements of of we do we whenever STELLAR of 0 0.05. shifted but and the surface to interpolation. of desired colors is these the data the are different the only not the has the so, match have to then use point HST that the only we even as Bergbush Vandenberg theoretical These brightness lower within The not which introduce and magnitude tabulated we Kurucz 0.6 have by an et tracks arbitrary a by force for isochrones interpolated evolutionary compared for chosen parameters . only in are and on age allows minute by al. & in to for used tabulated H95B. POPULATIONS stellar approximate isochrones the the the M a opacities the for mass the real very Vandenberg assumed Society the point luminosities. do leads the each (private range a 0 stars extragalactic is above atmospheres. constant However, diagrams filter and match the metallicity. the stellar that severe observations isochrones choices isochrones The stellar main not stars evolution of resampled fraction of- We isochrones stars, few to of with to with set is of Vandenberg our lower were for in bandpasses solar references, Kurucz match stages and get communi­ longer first at by with 9 preserved are metallici­ stars of 26-27 sequence the effective errors offset we absolute • models. M;;-;.0.6 stars distinct faintest all models and of adjust­ (1992) of model a in deter­ IN abun­ abun­ Split­ mod­ com­ color Provided com­ mass stud­ have (me­ tem­ This new age. into into me­ iso­ this For our en­ the the lu­ THE in­ in­ at­ of of in in in LMC from can Enough randomly ness whether the probability based model few from epoch, epochs, crete desired of of are observed considered lation a dN/dM LMC. Uncertainties the mix the mation magnitude binary power 0.6:SM sidered small 0.5>M>l extinction forms: entire field ing imposed the that well 1991). ::':: color-magnitude 0.1 The Whenever To In We star E(B- by WFPC2 for Kroupa, solar star be combined. of hundredths represented over the ages the (see subsequent of errors on mag. mass The include color-magnitude compare law have stars, We directly (1) interpolates histories, stellar populations stellar an :S formation simulation IMF, the defined detected stars the is by artificial IMF, oc errors each the neighborhood V)=0.03 3 from IMF within Feast a the diagrams over to of randomly as reddenings have For M the M adopted M- range, star Tout, filter in each Salpeter NASA distance in are we and be 0 determined 0 E(B- with the derived the compared mass slope star. observations. the 3.3 An (random by 2 ,dN/dMocM-!. observations the the , is and by of arbitrarily · binaries, 1991). sections, 7 this fit simulated star star or system a determines during and a IMF software diagram slope extinction, and a to for Distance power mag uncorrelated observed apparent total Salpeter for a a binary, based observed start rejected, Another , V) IMF, epoch, drawn tests. range is and 3.4 distance Astrophysics get we magnitude, Gilmore have ages diagram 3.2 M>l (2) and an = by This assumed and reddening for using of the with from Simulations and and consider 0.07 and we isochrones extinction. law on IMF If the with The adopted so Kroupa or the and loops for been the spanned randomly from systematic), slope and We internal range with detected, discuss the probably epoch, magnitude errors. we end any incorporate isochrones, modulus random that the M depending relations. a recent the the IMF. brightnesses IMF younger are mag slope, if dN/dM IMF, masses. will luminosity 3 0 to Reddening have intrinsic converted over observations. epoch, number forM<0.5M so, the implying completeness is models counting , ''standard'' data negligible. are of be et an The dN/dM and assume constraints The at a (Schwering by IMF extinction another al. stellar artificial adopted draws the the drawn an additional likely reasonable has of number each many presented Data In populations. oc we is inputs a a observed our star (1993), knowledge assumed on color 18.5 fit of fraction which determination addition relative M- uncertainties metallicity. to of then function statistics only simulate that masses. stars star is to star independently star the is oc The different observations, the extinction a for IMFs 2 System to star for 0 be and · on foreground either histograms determines 35 within M- the reddening formation formation computed include who . relatively in is the using detection & two the match output error over within Wenote star the strength a of to results. chosen bright­ IMF H95B. of 2 which of color­ in single simu­ Israel · LMC 2 solv­ stars stars con­ IMF give dis­ for­ two For 661 the the the the the for for of in in to is is a a 1997AJ....113..656H branch. in licities: gestion ages giant gram lutionary isochrones, Isochrones tion, FIG. mation mag magnitude main than same show spend 662 -0.7, Gallagher Figure First, :::;; 4. :::;; :::;; :::;; © and ~ ~ ~ of ~ ~ ~ 0.5, expected sequence branches that data is The at -1.3, HOLTZMAN American the over Z of reddening. The we roughly for each tracks 0 2 4 8 8 6 6 0 2 1, 4 8 0 2 4 6 0 4 6 = 2 8 2 color-magnitude the with along another -.5 diagram ZAMS ages shows 2, consider 4.1 0.008, the et upper -1.7). observed from turnoff location, 4, metallicites roughly al. in of Stellar last with The 6, consistent 0.5, the before a turnoff 0.004, (1996), spend 0 main 8, observational ET few well-defined four In the Astronomical isochrones around 1, upper 10, distribution 0.5 AL.: Population diagram each 2, implying 4. panels upper billion Z becoming (F555W-F814W) 0.001, 4, roughly sequence and around RESULTS mag stars = STELLAR 6, part with .5 M plot 8, overlay after 0.0004, 12 main Fsssw brighter). years. and 10, in of for main roughly the Gyr. isochrones Mp errors. half of correction Components and this the brighter. is 0.0004 several sequence. four ~ 555 1 stars amount 0.001, POPULATIONS There their 12 significantly sequence color-magnitude region 3.5 w Society 0 different There Gyr Figure constant ~ along and ([Fe/H] for lives different 0.004, Gallagher is are 1.5 are 2.5 of distance, As of a a is shown. and sets single strong 4 concentra- shown (with within time the discussed a and plots ~ star • broader definite of a metal­ color­ IN -0.4, extinc­ et 2 Provided 0.008. giant stellar stars evo­ sub­ sug­ dia­ for­ 0.3 the for THE al. LMC F555W Mp resent pleteness branch blue populated from around ant corrected quence off of Costa compares 0.001 data or gest least only lem is licity giant LMC the that tional turnoff models metallicity rate, this the rived Mp parable per stellar although age adopt around global tion ([Fe/H]= = -1.7). inferred. if Figure However, The There The At ;;;. 555 555 the assumed stars by branch for main single or of that the with one some are 10 the there branch a a>-2.46 -2.58>a>-2.98 -1.64>a>-2.12 -2.04>a>-2.68 -2.58>a>-3.02 - - star -1.74>a>-2.50 -2.40>a>-2.92 -2.56>a>-2.88 do - Z are functions over results IMFs Gyr, where The to 2.24> 2.74> 2.28> to However, star a LFs of insensitive = derived old the 6. IMF and a> test model main to System and on mass well tests). us, to as star LF in 0.008, luminosity IMF the which bright The formation functions -1.76 an main compari­ a>- is a>- a>- and disprove statistics one properly the slope Table the using but sequence we are and instead several forma­ under­ photo­ shown model which flatter range lumi­ come more three faint IMF IMF over lim­ 2.68 pre­ 3.08 2.66 it feel and end one ob­ 663 the se­ al­ to is 1, a . 1997AJ....113..656H quence, different different FIG. more has higher metallicity turnoff. metal stars any 664 ity dently luminosity it (bold to with with not slightly steeper - 3.1. is this The The give by 6. assumptions a clear © fainter lines), the the reasonable rich small z z z The a However, of binary mass choices assumed HOLTZMAN derived American most it values steeper very a To value Sal the that 250 200 250 300 300 200 is 250 150 200 150 150 slope observed along and and function, than peter determine range effect, clear large conservative star of fraction. 4 the IMF from IMPs star are younger. with star than M (95% limits about because older formation that value slopes luminosity Fsssw amount. ( formation formation leading required -2.2), simulations ET Kroupa, are either even Astronomical 5 the confidence the are AL.: population an (a). ~ (- steeper The population the star limits -2.0 although 7. IMF The 2.35) at history function STELLAR The to for history when Tout, from inferred history. field formation magnitudes 6 MF555W a three assumed most and slope for slightly on and or limits) model has of and the requires panels metallicity. has the higher the -3.1. is reasonable stars POPULATIONS marginally a values completely 7 Gilmore not preferred population significantly luminosity an binary IMF history Society between steeper show with In fainter metallicities, entirely upper observations this are slope model 4 fraction 8