J/ApJ/762/123ivo://CDS.VizieR/J/ApJ/762/123doi:10.26093/cds/vizier.17620123CDSWeisz D.R.Fouesneau M.Hogg D.W.Rix H.-W.Dolphin A.E.,Dalcanton J.J.Foreman-Mackey D.T.Lang D.Johnson L.C.Beerman L.C.,Bell E.F.Gordon K.D.Gouliermis D.Kalirai J.S.Skillman E.D.,Williams B.F.2018-01-05T08:57:02Z2015-02-06T09:35:27ZCDS support team

CDS, Observatoire de Strasbourg, 11 rue de l'Universite, F-67000 Strasbourg, France

cds-question@unistra.fropen-star-clustersstellar-massesastronomical-modelsWe present a probabilistic approach for inferring the parameters of the present-day power-law stellar mass function (MF) of a resolved young star cluster. This technique (1) fully exploits the information content of a given data set; (2) can account for observational uncertainties in a straightforward way; (3) assigns meaningful uncertainties to the inferred parameters; (4) avoids the pitfalls associated with binning data; and (5) can be applied to virtually any resolved young cluster, laying the groundwork for a systematic study of the high-mass stellar MF (M>~1M_{sun}_). Using simulated clusters and Markov Chain Monte Carlo sampling of the probability distribution functions, we show that estimates of the MF slope, {alpha}, are unbiased and that the uncertainty, {Delta}{alpha}, depends primarily on the number of observed stars and on the range of stellar masses they span, assuming that the uncertainties on individual masses and the completeness are both well characterized. Using idealized mock data, we compute the theoretical precision, i.e., lower limits, on {alpha}, and provide an analytic approximation for {Delta}{alpha} as a function of the observed number of stars and mass range. Comparison with literature studies shows that ~3/4 of quoted uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find that the literature studies yield <{alpha}>=2.46, with a 1{sigma} dispersion of 0.35dex. The precision on MF slope recovery in this paper are lower limits, as we do not explicitly consider all possible sources of uncertainty, including dynamical effects (e.g., mass segregation), unresolved binaries, and non-coeval populations.2013ApJ...762..123Whttps://cdsarc.cds.unistra.fr/viz-bin/cat/J/ApJ/762/123CatalogResearchIsServedByTAP VizieR generic serviceIsServedByConesearch servicerelated-toJ/ApJS/215/9 : PHAT X. UV-IR photometry of M31 stars (Williams+, 2014)J/ApJ/752/95 : PHAT stellar cluster survey. I. Year 1 (Johnson+, 2012)J/ApJ/752/59 : Low-mass population in L1641 (Hsu+, 2012)J/ApJ/751/4 : RVs of massive stars in Cyg OB2 (Kiminki+, 2012)J/MNRAS/416/817 : RV cat. of O-type stars in IC 2944 and Cen OB2 (Sana+, 2011)J/A+A/534/A10 : HST/NICMOS imaging in Orion Nebula Cluster (Andersen+, 2011)J/ApJ/707/1347 : HST F160W photometry in RMC 136 (Andersen+, 2009)J/ApJ/706/516 : Gas content of star-forming gal. (Pflamm-Altenburg+, 2009)J/ApJ/681/290 : HST/ACS photometry in the SMC (Schmalzl+, 2008)J/AJ/136/2782 : Star formation efficiency in nearby galaxies (Leroy+, 2008)J/AJ/135/823 : ICMF of super star clusters (Dowell+, 2008)J/AJ/132/2296 : NICMOS observations of Mon R2 cluster (Andersen+, 2006)J/AJ/131/2478 : M31 and M33 UBVRI photometry (Massey+, 2006)J/A+A/436/527 : UBVIc photometry of NGC 4852 (Carraro+, 2005)J/A+A/430/941 : Star formation region NGC 6530 (Prisinzano+, 2005)J/A+A/404/927 : UBVRI photometry of NGC 2422 (Prisinzano+, 2003)J/AJ/126/1665 : NICMOS observations of NGC 2024 (Liu+, 2003)J/ApJ/541/977 : HST observations of low-mass stars in IC 348 (Najita+, 2000)J/ApJ/454/151 : OB Associations of the Northern Milky Way (Massey+ 1995)J/ApJ/425/122 : IMF from UV stellar photometry (Hill+, 1994)https://cds.unistra.fr/vizier-org/licences_vizier.htmlhttps://vizier.cds.unistra.fr/viz-bin/VizieR-2?-source=J/ApJ/762/123https://vizier.iucaa.in/viz-bin/VizieR-2?-source=J/ApJ/762/123http://vizieridia.saao.ac.za/viz-bin/VizieR-2?-source=J/ApJ/762/123https://vizier.cds.unistra.fr/viz-bin/votable?-source=J/ApJ/762/123https://vizier.iucaa.in/viz-bin/votable?-source=J/ApJ/762/123http://vizieridia.saao.ac.za/viz-bin/votable?-source=J/ApJ/762/123GETtext/xml+votablehttps://tapvizier.cds.unistra.fr/TAPVizieR/tapCone search capability for table J/ApJ/762/123/table1 (Literature constraints on the IMF slope)https://vizier.cds.unistra.fr/viz-bin/conesearch/J/ApJ/762/123/table1?https://vizier.iucaa.in/viz-bin/conesearch/J/ApJ/762/123/table1?http://vizieridia.saao.ac.za/viz-bin/conesearch/J/ApJ/762/123/table1?GETtext/xml+votable180.050000true105.697917-8.3377780.0055555555555555566/463 1287 1464 1582 1930 2940 3136 3257 3307 3384 3604 3622 3632 4698 6760 14059 14210 14263 14280 14295 14353 14630 14645 14646 14692 15662 21439 21529 21682 21774 22058 22123 22249 23410 23538 23633 23637 23769 24345 24510 24522 28806 28874 28916 29463 30215 30635 31790 31812 33092 33100 33126 33317 37231 37592 37790 37901 37926 37933 38016 38026 39355 39739 39776 39907 40106 40490 40696 41445 41670 41775 41807 41863 42153 42218 42420 42464 42496 43022 43024 43033 43036 43301https://cdsarc.cds.unistra.fr/viz-bin/moc/J/ApJ/762/123?format=asciidefaultJ/ApJ/762/123/table1Literature constraints on the IMF slopeSimbadNameSimbad column added by the CDSmeta.idcharSeq[1/89] Running sequence numbermeta.idintprimaryNameOpen cluster namemeta.id;meta.maincharlog(N)[0.7/3.4] Number of starsmeta.numberfloatlog(Mm/Mc)[0.1/1.1] Mass range (M_max,obs_/M_comp_)phys.mass;arith.ratiofloatalpha[-0.1/4.5] MF slope {alpha} value (1)stat.fit.paramfloate_alpha[0.03/1.8] 1{sigma} uncertainty on alphastat.error;pos.eq.rafloatMmin[0.4/10] Minimal star mass range M_min_ (1)solMassphys.massfloatMmax[1.9/120] Maximal star mass range M_max_ (1)solMassphys.massfloatDalpha[0.04/1.76] Ratio of literature to theory error {Delta}{alpha}_lit_/{Delta}{alpha}_th_ (2)stat.fit.omcfloatAutFirst author's name of the referencemeta.bib.authorcharBibCodeReference (bibcode)meta.ref;pos.framecharNEDSimbad column added by the CDSmeta.ref.urlchar_RARight Ascension (J2000) from SIMBAD (not part of the original data)degpos.eq.ra;meta.main_DEDeclination (J2000) from SIMBAD (not part of the original data)degpos.eq.dec;meta.main