File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: On the Validity of the Coagulation Equation and the Nature of Runaway Growth

TitleOn the Validity of the Coagulation Equation and the Nature of Runaway Growth
Authors
KeywordsCollisional Physics
Computer Techniques
Planetary Formation
Planetesimals
Issue Date2000
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/icarus
Citation
Icarus, 2000, v. 143 n. 1, p. 74-86 How to Cite?
AbstractThe coagulation equation, which is widely used for modeling growth in planet formation and other astrophysical problems, is the mean-rate equation that describes the evolution of the mass spectrum of a collection of particles due to successive mergers. A numerical code that can yield accurate solutions to the coagulation equation with a reasonable number of mass bins is developed, and it is used to study the properties of solutions to the coagulation equation. We consider limiting cases of the merger rate coefficient Aij for gravitational interaction, with the power-law index of the mass-radius relation β=1/3 (for planetesimals) and 2/3 (for stars). We classify the mass dependence of Aij using the exponent λ for the merger between two particles of comparable mass, and the exponents μ and ν for the merger between a heavy particle and a light particle. For the two cases with λ≤1 and ν≤1, the mass spectrum evolves in an orderly fashion. For the remaining cases, which have ν>1, we find strong numerical and analytical evidence that there are no self-consistent solutions to the coagulation equation at any time. The results for the ν>1 cases are qualitatively different from the well-known example with Aij∝ij. For the latter case, which is in the range ν≤1 and λ>1, there is an analytic solution to the coagulation equation that is valid for a finite amount of time t0. We discuss a simplified merger problem that illustrates the qualitative differences in the solutions to the coagulation equation for the three classes of Aij. Our results strongly suggest that there are two types of runaway growth. For Aij with ν≤1 and λ>1, runaway growth starts at tcrit≈t0, the time at which the coagulation equation solution becomes invalid. For Aij with ν>1, which include all gravitational interaction cases expected to show runaway growth, the dependence of the time tcrit for the onset of runaway growth on the parameters of the problem is not yet well understood, but there are indications that tcrit (in units of 1/(n0A11)) may decrease slowly toward zero with increasing initial total number of particles n0. © 2000 Academic Press.
Persistent Identifierhttp://hdl.handle.net/10722/150932
ISSN
2015 Impact Factor: 3.383
2015 SCImago Journal Rankings: 2.447
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorLee, MHen_US
dc.date.accessioned2012-06-26T06:15:02Z-
dc.date.available2012-06-26T06:15:02Z-
dc.date.issued2000en_US
dc.identifier.citationIcarus, 2000, v. 143 n. 1, p. 74-86en_US
dc.identifier.issn0019-1035en_US
dc.identifier.urihttp://hdl.handle.net/10722/150932-
dc.description.abstractThe coagulation equation, which is widely used for modeling growth in planet formation and other astrophysical problems, is the mean-rate equation that describes the evolution of the mass spectrum of a collection of particles due to successive mergers. A numerical code that can yield accurate solutions to the coagulation equation with a reasonable number of mass bins is developed, and it is used to study the properties of solutions to the coagulation equation. We consider limiting cases of the merger rate coefficient Aij for gravitational interaction, with the power-law index of the mass-radius relation β=1/3 (for planetesimals) and 2/3 (for stars). We classify the mass dependence of Aij using the exponent λ for the merger between two particles of comparable mass, and the exponents μ and ν for the merger between a heavy particle and a light particle. For the two cases with λ≤1 and ν≤1, the mass spectrum evolves in an orderly fashion. For the remaining cases, which have ν>1, we find strong numerical and analytical evidence that there are no self-consistent solutions to the coagulation equation at any time. The results for the ν>1 cases are qualitatively different from the well-known example with Aij∝ij. For the latter case, which is in the range ν≤1 and λ>1, there is an analytic solution to the coagulation equation that is valid for a finite amount of time t0. We discuss a simplified merger problem that illustrates the qualitative differences in the solutions to the coagulation equation for the three classes of Aij. Our results strongly suggest that there are two types of runaway growth. For Aij with ν≤1 and λ>1, runaway growth starts at tcrit≈t0, the time at which the coagulation equation solution becomes invalid. For Aij with ν>1, which include all gravitational interaction cases expected to show runaway growth, the dependence of the time tcrit for the onset of runaway growth on the parameters of the problem is not yet well understood, but there are indications that tcrit (in units of 1/(n0A11)) may decrease slowly toward zero with increasing initial total number of particles n0. © 2000 Academic Press.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/icarusen_US
dc.relation.ispartofIcarusen_US
dc.subjectCollisional Physicsen_US
dc.subjectComputer Techniquesen_US
dc.subjectPlanetary Formationen_US
dc.subjectPlanetesimalsen_US
dc.titleOn the Validity of the Coagulation Equation and the Nature of Runaway Growthen_US
dc.typeArticleen_US
dc.identifier.emailLee, MH:mhlee@hku.hken_US
dc.identifier.authorityLee, MH=rp00724en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1006/icar.1999.6239en_US
dc.identifier.scopuseid_2-s2.0-0002622223en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0002622223&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume143en_US
dc.identifier.issue1en_US
dc.identifier.spage74en_US
dc.identifier.epage86en_US
dc.identifier.isiWOS:000085176100007-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridLee, MH=7409119699en_US

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats