Dynamical friction of massive objects in galactic centres

Authors

  • A. Just,

    Corresponding author
    1. Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg (ZAH), Mönchhofstr. 12-14, D-69120 Heidelberg, Germany
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  • F. M. Khan,

    1. Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg (ZAH), Mönchhofstr. 12-14, D-69120 Heidelberg, Germany
    2. Department of Physics, Government College University (GCU), 54000 Lahore, Pakistan
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  • P. Berczik,

    1. Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg (ZAH), Mönchhofstr. 12-14, D-69120 Heidelberg, Germany
    2. National Astronomical Observatories of China (NAOC), Chinese Academy of Sciences (CAS), Datun Lu 20A, Chaoyang District, Beijing 100012, China
    3. Main Astronomical Observatory (MAO), National Academy of Sciences of Ukraine (NASU), Akademika Zabolotnoho 27, 03680 Kyiv, Ukraine
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  • A. Ernst,

    1. Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg (ZAH), Mönchhofstr. 12-14, D-69120 Heidelberg, Germany
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  • R. Spurzem

    1. Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg (ZAH), Mönchhofstr. 12-14, D-69120 Heidelberg, Germany
    2. National Astronomical Observatories of China (NAOC), Chinese Academy of Sciences (CAS), Datun Lu 20A, Chaoyang District, Beijing 100012, China
    3. Kavli Institute for Astronomy and Astrophysics, Peking University, China
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E-mail: just@ari.uni-heidelberg.de

ABSTRACT

Dynamical friction leads to an orbital decay of massive objects like young compact star clusters or massive black holes in central regions of galaxies. The dynamical friction force can be well approximated by Chandrasekhar’s standard formula, but recent investigations show that corrections to the Coulomb logarithm are necessary. With a large set of N-body simulations we show that the improved formula for the Coulomb logarithm fits the orbital decay very well for circular and eccentric orbits. The local scalelength of the background density distribution serves as the maximum impact parameter for a wide range of power-law indices of −1 … −5. For each type of code the numerical resolution must be compared to the effective minimum impact parameter in order to determine the Coulomb logarithm. We also quantify the correction factors by using self-consistent velocity distribution functions instead of the standard Maxwellian often used. These factors enter directly the decay time-scale and cover a range of 0.5 … 3 for typical orbits. The new Coulomb logarithm combined with self-consistent velocity distribution functions in the Chandrasekhar formula provides a significant improvement of orbital decay times with correction up to one order of magnitude compared to the standard case. We suggest the general use of the improved formula in parameter studies as well as in special applications.

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