Using the Modified Lognormal Power Law Distribution to Model the Mass Function of NGC 1711

Abstract

A determination of the mass function (MF) of stellar clusters can be quite dependent on the range of measured masses, the fitting technique, and the analytic function that is being fit to the data. Here, we use HST/WFPC2 data of NGC 1711, a stellar cluster in the Large Magellanic Cloud, as a test case to explore a range of possible determinations of the MF from a single dataset. We employ the analytic modified lognormal power-law (MLP) distribution, a hybrid function that has a peaked lognormal-like body and a power-law tail at intermediate and high masses. A fit with the MLP has the advantage that the resulting best-fit function can be either a hybrid function, a pure lognormal, or a pure power law, in different limits of the function. The completeness limit for the observations means that the data contains masses above $\sim 0.90M_{\odot }$. In this case, the MLP fits yield essentially a pure power-law MF. We demonstrate that the nonlinear regression/least-squares approach is not justified since the underlying assumptions are not satisfied. By using maximum likelihood estimation, which is independent of binning, we find a best-fit functional form $dN/d\ln m\propto m^{-\alpha }$, where $\alpha =1.72\pm 0.05$ or $1.75\pm 0.05$ for two different theoretical isochrone models, respectively. Furthermore, we explore the possibility of systematic errors in the determination of the power-law index due to the depth of the observations. When we combine the observational data with artificially generated data from the lognormal Chabrier IMF for masses below $0.90M_{\odot }$, the best fit MLP is a hybrid function but with a steeper asymptotic slope i.e., $\alpha =2.04\pm 0.07$. This illustrates the systematic uncertainties in commonly used MF parameters that can depend on the range of data that is fitted.

arXiv comment12 pages, 6 figures, to appear in ApJ

References in corpus (49)

• Stellar population synthesis at the resolution of 2003
• On the variation of the Initial Mass Function
• Star Formation in Galaxies Along the Hubble Sequence
• PARSEC: stellar tracks and isochrones with the PAdova and TRieste Stellar Evolution Code
• Modules for Experiments in Stellar Astrophysics (MESA): Giant Planets, Oscillations, Rotation, and Massive Stars
• Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant
• MESA Isochrones and Stellar Tracks (MIST). I: Solar-Scaled Models
• The Initial Mass Function of Stars: Evidence for Uniformity in Variable Systems
• The Stellar IMF from Turbulent Fragmentation
• WFPC2 Stellar Photometry with HSTphot
• PARSEC evolutionary tracks of massive stars up to $350M_{\odot }$ at metallicities 0.0001$\le Z\le$0.04
• Analytical theory for the initial mass function: CO clumps and prestellar cores
• The Star Formation History of the Large Magellanic Cloud
• The Formation Mechanism of Brown Dwarfs
• Outflow Feedback Regulated Massive Star Formation in Parsec-Scale Cluster Forming Clumps
• The Burst Mode of Protostellar Accretion
• The properties of brown dwarfs and low-mass hydrogen-burning stars formed by disc fragmentation
• The initial mass function : from Salpeter 1955 to 2005
• The burst mode of accretion and disk fragmentation in the early embedded stages of star formation
• A Theory of the IMF for Star Formation in Molecular Clouds
• Surface Brightness Profiles and Structural Parameters for 53 Rich Stellar Clusters in the Large Magellanic Cloud
• The Magellanic Stream, High-Velocity Clouds and the Sculptor Group
• Cluster Mass Functions in the Large and Small Magellanic Clouds: Fading and Size of Sample Effects
• GALEV evolutionary synthesis models - I. Code, input physics and web-interface
• Variable protostellar accretion with episodic bursts
• Analytical theory for the initial mass function: II. Properties of the flow
• The 200 Degree-Long Magellanic Stream System
• Numerical biases on IMF determinations created by binning
• Variations of the stellar initial mass function in the progenitors of massive early-type galaxies and in extreme starburst environments
• The Low End of the Initial Mass Function in Young LMC Clusters: I. The Case of R136
• A Hybrid Scenario for the Formation of Brown Dwarfs and Very Low Mass Stars
• On the temporal evolution of the stellar mass function in Galactic clusters
• No Evidence for Significant Age Spreads in Young Massive LMC Clusters
• Estimators for the exponent and upper limit, and goodness-of-fit tests for (truncated) power-law distributions
• On the Power-Law Tail in the Mass Function of Protostellar Condensations and Stars
• Testing the universality of the IMF with Bayesian statistics: young clusters
• The effect of a finite mass reservoir on the collapse of spherical isothermal clouds and the evolution of protostellar accretion
• Massive stars reveal variations of the stellar initial mass function in the Milky Way stellar clusters
• The MLP Distribution: A Modified Lognormal Power-Law Model for the Stellar Initial Mass Function
• Numerical Star-Formation Studies -- A Status Report
• Star formation in dense clusters
• The emergence of the galactic stellar mass function from a non-universal IMF in clusters
• A High-Resolution Multiband Survey of Westerlund 2 With the Hubble Space Telescope. III. The present-day stellar mass function
• Protostar mass functions in young clusters
• The star formation history of the Sculptor Dwarf Irregular Galaxy
• A Dual Power Law Distribution for the Stellar Initial Mass Function
• The massive star population of the Virgo Cluster galaxy NGC 4535
• A Multiple Power Law Distribution for Initial Mass Functions
• Population gradients and photometric metallicities in early- and transition-type dwarf galaxies: Clues from the Sculptor group

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