%0 Generic %1 weisz2012panchromatic %A Weisz, Daniel R. %A Fouesneau, Morgan %A Hogg, David W. %A Rix, Hans-Walter %A Dolphin, Andrew E. %A Dalcanton, Julianne J. %A Foreman-Mackey, Daniel T. %A Lang, Dustin %A Johnson, L. Clifton %A Beerman, Lori C. %A Bell, Eric F. %A Gordon, Karl D. %A Gouliermis, Dimitrios %A Kalirai, Jason S. %A Skillman, Evan D. %A Williams, Benjamin F. %D 2012 %K imf population probability resolved stellar %T The Panchromatic Hubble Andromeda Treasury IV. A Probabilistic Approach to Inferring the High Mass Stellar Initial Mass Function and Other Power-law Functions %U http://arxiv.org/abs/1211.6105 %X 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 (a) fully exploits the information content of a given dataset; (b) accounts for observational uncertainties in a straightforward way; (c) assigns meaningful uncertainties to the inferred parameters; (d) avoids the pitfalls associated with binning data; and (e) is applicable to virtually any resolved young cluster, laying the groundwork for a systematic study of the high mass stellar MF (M > 1 Msun). 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 stellar mass range they span, assuming that the uncertainties on individual masses and the completeness are well-characterized. Using idealized mock data, we compute the lower limit precision on \alpha and provide an analytic approximation for \Delta\alpha as a function of the observed number of stars and mass range. We find that ~ 3/4 of quoted literature uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find the literature studies yield <\alpha>=2.46 with a 1-\sigma dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the IMF. We show that avoiding substantial biases in the MF slope requires: (1) including the MF as a prior when deriving individual stellar mass estimates; (2) modeling the uncertainties in the individual stellar masses; and (3) fully characterizing and then explicitly modeling the completeness for stars of a given mass. (abridged)

@misc{weisz2012panchromatic, 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 (a) fully exploits the information content of a given dataset; (b) accounts for observational uncertainties in a straightforward way; (c) assigns meaningful uncertainties to the inferred parameters; (d) avoids the pitfalls associated with binning data; and (e) is applicable to virtually any resolved young cluster, laying the groundwork for a systematic study of the high mass stellar MF (M > 1 Msun). 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 stellar mass range they span, assuming that the uncertainties on individual masses and the completeness are well-characterized. Using idealized mock data, we compute the lower limit precision on {\alpha} and provide an analytic approximation for {\Delta}{\alpha} as a function of the observed number of stars and mass range. We find that ~ 3/4 of quoted literature uncertainties are smaller than the theoretical lower limit. By correcting these uncertainties to the theoretical lower limits, we find the literature studies yield <{\alpha}>=2.46 with a 1-{\sigma} dispersion of 0.35 dex. We verify that it is impossible for a power-law MF to obtain meaningful constraints on the upper mass limit of the IMF. We show that avoiding substantial biases in the MF slope requires: (1) including the MF as a prior when deriving individual stellar mass estimates; (2) modeling the uncertainties in the individual stellar masses; and (3) fully characterizing and then explicitly modeling the completeness for stars of a given mass. (abridged)}, added-at = {2012-11-28T16:24:52.000+0100}, author = {Weisz, Daniel R. and Fouesneau, Morgan and Hogg, David W. and Rix, Hans-Walter and Dolphin, Andrew E. and Dalcanton, Julianne J. and Foreman-Mackey, Daniel T. and Lang, Dustin and Johnson, L. Clifton and Beerman, Lori C. and Bell, Eric F. and Gordon, Karl D. and Gouliermis, Dimitrios and Kalirai, Jason S. and Skillman, Evan D. and Williams, Benjamin F.}, biburl = {https://www.bibsonomy.org/bibtex/23cc8db0ab341d15f8b1eb8ae5f25d76b/miki}, description = {[1211.6105] The Panchromatic Hubble Andromeda Treasury IV. A Probabilistic Approach to Inferring the High Mass Stellar Initial Mass Function and Other Power-law Functions}, interhash = {9ad57c0b89449641a1cc858f7a5d85a2}, intrahash = {3cc8db0ab341d15f8b1eb8ae5f25d76b}, keywords = {imf population probability resolved stellar}, note = {cite arxiv:1211.6105Comment: 21 pages, 15 figures, accepted to ApJ}, timestamp = {2012-11-28T16:24:52.000+0100}, title = {The Panchromatic Hubble Andromeda Treasury IV. A Probabilistic Approach to Inferring the High Mass Stellar Initial Mass Function and Other Power-law Functions}, url = {http://arxiv.org/abs/1211.6105}, year = 2012 }