Abstract
ABSTRACT We present a numerical approach for accurately evolving a dust grain-size distribution undergoing number-conserving (such as sputtering) and/or mass-conserving (such as shattering) processes. As typically observed interstellar dust distributions follow a power law, our method adopts a power-law discretization and uses both the grain mass and number densities in each bin to determine the power-law parameters. This power-law method is complementary to piecewise-constant and linear methods in the literature. We find that the power-law method surpasses the other two approaches, especially for small bin numbers. In the sputtering tests, the relative error in the total grain mass remains below 0.01 per cent independent of the number of bins N, while the other methods only achieve this for N > 50 or higher. Likewise, the shattering test shows that the method also produces small relative errors in the total grain numbers while conserving mass. Not only does the power-law method conserve the global distribution properties, it also preserves the inter-bin characteristics so that the shape of the distribution is recovered to a high degree. This does not always happen for the constant and linear methods, especially not for small bin numbers. Implementing the power-law method in a hydrodynamical code thus minimizes the numerical cost while maintaining high accuracy. The method is not limited to dust grain distributions, but can also be applied to the evolution of any distribution function, such as a cosmic ray distribution affected by synchrotron radiation or inverse-Compton scattering.
Highlights
Within the Interstellar Medium (ISM), dust grains are an important ingredient as they lock up substantial fractions of the heavy elements (Draine et al 2007), produce the dominant contribution to the opacity for radiation upward of the Lyman limit (Draine & Lee 1984), contribute a significant part of gas heating through photoelectric heating (Bakes & Tielens 1994) and provide the surface onto which chemical elements can accrete and react (Garrod & Herbst 2006)
To test the power-law description of the grain distribution we apply the methods of Sect. 2 to the test problems outlined in McK18. As these tests have analytical solutions, this allows a direct analysis of the performance of the method, and a direct comparison with both the piecewise-constant and linear methods studied in McK18
We will test the convergence of the error in the total grain mass depending on the number of size bins used
Summary
Within the Interstellar Medium (ISM), dust grains are an important ingredient as they lock up substantial fractions of the heavy elements (Draine et al 2007), produce the dominant contribution to the opacity for radiation upward of the Lyman limit (Draine & Lee 1984), contribute a significant part of gas heating through photoelectric heating (Bakes & Tielens 1994) and provide the surface onto which chemical elements can accrete and react (Garrod & Herbst 2006). In star forming regions, shocks mainly accommodate the destruction of dust grain sizes due to sputtering, shattering and vaporisation (Tielens et al 1994; Jones et al 1996; Flower & Pineau des Forets 2003; Hirashita & Yan 2009; Guillet et al 2007, 2009, 2011; Anderl et al 2013; Van Loo et al 2013). In protoplanetary discs both growth and fragmentation of dust grains take place
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
