On the origin of the stellar initial mass function and multiple\ud stellar systems

Doctoral thesis English OPEN
Nelson, Katy
  • Subject: QB
    arxiv: Astrophysics::Galaxy Astrophysics | Astrophysics::Cosmology and Extragalactic Astrophysics | Astrophysics::Earth and Planetary Astrophysics | Astrophysics::Solar and Stellar Astrophysics

I first perform a statistical analysis on a distribution of pre-stellar core masses. Each core\ud is split into a small number of stars, and two stars are chosen using a prescription based on\ud stellar masses to form a binary system. The rest of the stars are taken to be singles. From this\ud sample of binaries and singles, I compute the stellar initial mass function, the binary frequency\ud and mass ratio distribution as a function of primary mass. I then test if the observed binary\ud frequencies and mass ratios are compatible with this self-similar mapping of cores into stars. I\ud show that self-similar mapping can reproduce the observed binary frequencies and mass ratios\ud well, so long as the efficiency is rather high (100%), and each core fragments into about 4 or\ud 5 stars.\ud Using the code Seren view, I then perform N-body simulations with core-clusters. I\ud investigate the formation of multiple systems, and qualify the dependence of their parameters\ud and longevity on certain initial conditions, including (i) the number of stars in a core-cluster,\ud (ii) the variance of masses in those stars, (iii) the virial ratio and (iv) radial dependence of\ud stellar density. I expand on those results by including (a) a prescription for the influence of disks during stellar ybys, (b) different initial spatial configurations of the stars (i.e. line and ring clusters) and (c) a background potential due to residual gas in the core-cluster. The full\ud range of periods observed in the field cannot be explained by the distribution of periods of\ud pure binaries alone, which is too narrow. However, the wide range can be explained either\ud by combining the periods of pair-wise orbits of all multiple systems, i.e. the widest periods\ud observed are in fact pair-wise orbits of higher-order multiples with unresolved companions, or\ud by considering a distribution of pre-stellar cores that have a range of virial ratios.
  • References (7)

    1 Observations of Star Formation 1 1.1 The Interstellar Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Core Mass Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Pre-stellar Stages and Classes . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Stellar Initial Mass Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 System Initial Mass Function . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.2 Cores and Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.3 Thesis Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

    2 Multiple Stellar Systems 12 2.1 Types of Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.1 Visual Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.2 Spectroscopic Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.3 Photometric Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.4 Astrometric Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Observations of Multiple Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.1 Multiplicity Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.2 Mass Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2.3 Periods and Separations . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.4 Eccentricities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.5 Higher-order Multiples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    3 Mapping from the CMF to the StIMF Setup 22 3.1 Self-Similar Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1.1 Objections to Self-Similar Mapping . . . . . . . . . . . . . . . . . . . . . 24 3.2 Previous Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2.1 Mapping from the CMF to the StIMF . . . . . . . . . . . . . . . . . . . 25 3.2.2 Dynamical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3.1 Core Mass Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3.2 Initial Stellar and System Mass Functions . . . . . . . . . . . . . . . . . 27 3.3.3 Binary Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.3.4 Mass Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.5 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.6 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3.7 Quality Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

    5 Core Cluster Simulations 59 5.1 Fiducial Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.1.1 Initial Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.1.2 Initial Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.1.3 Drawing and Normalising Stellar Masses . . . . . . . . . . . . . . . . . . 62 5.1.4 Duration of Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.2 The Number of Stars Produced by a Core . . . . . . . . . . . . . . . . . . . . . 63 5.3 Virialisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.4 Variance in Stellar Masses Produced by a Single Core . . . . . . . . . . . . . . . 64 5.5 Density Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.6 Ring Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.7 Line Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.8 Protostellar Disks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.9 Background Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

    6 Fidelity 71 6.1 Equations of Motion for Binary Systems . . . . . . . . . . . . . . . . . . . . . . 72 6.2 Multiple System Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 6.2.1 Binding Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 6.2.2 Semi-Major axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.2.3 Mass Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.2.4 Eccentricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.2.5 Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.2.6 Fidelity Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

    7 Seren view 77 7.1 The Hermite Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.2 Dimensionless Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 7.2.1 Convolving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7.3 Testing for Eccentric Binaries and Triples . . . . . . . . . . . . . . . . . . . . . . 80 7.3.1 Initial Conditions of Multiple Systems . . . . . . . . . . . . . . . . . . . 80 7.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

    8 Core Cluster Results: Part I 85 8.1 Fiducial Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 8.2 The Number of Stars in a Core . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 8.3 The Virial Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 8.4 Standard Deviation of Stellar Masses Produced by a Core . . . . . . . . . . . . . 120

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