J/ApJ/762/123 PHAT. IV. Initial Mass Function (Weisz+, 2013)
The Panchromatic Hubble Andromeda Treasury.
IV. A probabilistic approach to inferring the high-mass stellar initial mass
function and other power-law functions.
Weisz 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.
<Astrophys. J., 762, 123 (2013)>
=2013ApJ...762..123W 2013ApJ...762..123W
ADC_Keywords: Clusters, open ; Stars, masses ; Models
Keywords: galaxies: star clusters: general; methods: statistical;
stars: luminosity function, mass function
Abstract:
We 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☉). Using simulated clusters
and Markov Chain Monte Carlo sampling of the probability distribution
functions, we show that estimates of the MF slope, α, are
unbiased and that the uncertainty, Δα, 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
α, and provide an analytic approximation for Δα 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 <α≥2.46, with a 1σ 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.
Objects:
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RA (2000) DE Designation(s)
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00 42 44.33 +41 16 07.5 M31 = Andromeda galaxy = NGC 224
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File Summary:
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FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
table1.dat 88 89 Literature constraints on the IMF slope
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See also:
J/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)
Byte-by-byte Description of file: table1.dat
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Bytes Format Units Label Explanations
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1- 2 I2 --- Seq [1/89] Running sequence number
4- 13 A10 --- Name Open cluster name
15- 18 F4.2 --- log(N) [0.7/3.4] Number of stars
20- 23 F4.2 --- log(Mm/Mc) [0.1/1.1] Mass range (Mmax,obs/Mcomp)
25- 29 F5.2 --- alpha [-0.1/4.5] MF slope α value (1)
31- 34 F4.2 --- e_alpha [0.03/1.8] 1σ uncertainty on alpha
36- 39 F4.1 Msun Mmin [0.4/10] Minimal star mass range Mmin (1)
41- 45 F5.1 Msun Mmax [1.9/120] Maximal star mass range Mmax (1)
47- 50 F4.2 --- Dalpha [0.04/1.76] Ratio of literature to theory error
Δαlit/Δαth (2)
52- 68 A17 --- Aut First author's name of the reference
70- 88 A19 --- BibCode Reference (bibcode)
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Note (1): the Mass Function (MF) Φ(M) is parametrized as a set of
power laws defined by:
Φ(M) = dN/dM = ciM-α, for Mmin≤M≤Mmax
The reported values of α, where all values have been
updated to reflect our usage of αSalpeter=2.35.
Note (2): The values of have been computed using the 1σ value listed
in the literature, i.e., "e_alpha" in this table (col. 6), and the
theoretical precision is presented in Figure 8. As shown in Figure 9,
nearly ∼3/4 of the literature considered quote error bars smaller than
the theoretical lower limit.
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History:
From electronic version of the journal
References:
Dalcanton et al. PHAT Suvey. 2012ApJS..200...18D 2012ApJS..200...18D
Rosenfield et al. Paper I. 2012ApJ...755..131R 2012ApJ...755..131R
Williams et al. Paper II. 2012ApJ...759...46W 2012ApJ...759...46W
Beerman et al. Paper III. 2012ApJ...760..104B 2012ApJ...760..104B
Weisz et al. Paper IV. 2013ApJ...762..123W 2013ApJ...762..123W This catalog
Fouesneau et al. Paper V. 2014ApJ...786..117F 2014ApJ...786..117F
Simones et al. Paper VI. 2014ApJ...788...12S 2014ApJ...788...12S
Dong et al. Paper VII. 2014ApJ...785..136D 2014ApJ...785..136D
Dalcanton et al. Paper VIII. 2015ApJ...814....3D 2015ApJ...814....3D
Veyette et al. Paper IX. 2014ApJ...792..121V 2014ApJ...792..121V
Williams et al. Paper X. 2014ApJS..215....9W 2014ApJS..215....9W Cat. J/ApJS/215/9
Lewis et al. Paper XI. 2015ApJ...805..183L 2015ApJ...805..183L
Gregersen et al. Paper XII. 2015AJ....150..189G 2015AJ....150..189G
Wagner-Kaiser et al. Paper XIII. 2015MNRAS.451..724W 2015MNRAS.451..724W Cat. J/MNRAS/451/724
Senchyna et al. Paper XIV. 2015ApJ...813...31S 2015ApJ...813...31S
Gordon et al. Paper XV. 2016ApJ...826..104G 2016ApJ...826..104G
Johnson et al. Paper XVI. 2016ApJ...827...33J 2016ApJ...827...33J Cat. J/ApJ/827/33
Lewis et al. Paper XVII. 2017ApJ...834...70L 2017ApJ...834...70L
Johnson et al. Paper XVIII. 2017ApJ...839...78J 2017ApJ...839...78J
Williams et al. Paper XIX 2017ApJ...846..145W 2017ApJ...846..145W Cat. J/ApJ/846/145
(End) Emmanuelle Perret [CDS] 14-Jan-2015