The fractional Brownian motion and the halo mass function

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1、Mon.Not.R.Astron.Soc.000,000–000(0000)Printed5February2008(MNLATEXstylefilev2.2)ThefractionalBrownianmotionandthehalomassfunctionJunPan⋆ThePurpleMountainObservatory,2WestBeijingRoad,Nanjing210008,China5February2008ABSTRACTThefractionalBrownianmotionwith

2、indexαisintroducedtoconstructthefractionalexcursionsetmodel.Anewmassfunctionwithsingleparameterαisderivedwithintheformalism,ofwhichthePress-Schechtermassfunction(PS)isaspecialcasewhenα=1/2.Althoughthenewmassfunctioniscomputedassumingsphericalcollapse,c

3、omparisonwiththeSheth-Tormenfittingfunction(ST)showsthatthenewmassfunctionofα≈0.435agreeswithSTremarkablywellinhighmassregime,whilepredictsmoresmallmasshalosthantheSTbutlessthanthePS.TheindexαistheHurstexponent,whichexactvalueincontextofstructureformati

4、onismodulatedbypropertiesofthesmoothingwindowfunctionandtheshapeofpowerspectrum.Itisconjecturedthathalomergingrateandmerginghistoryinthefractionalsettheorymightbeimprintedwiththeinterplaybetweenhalosatsmallscalesandtheirlargescaleenvironment.Andthemass

5、functioninhighmassregimecanbeagoodtooltodetectthenon-Gaussianityoftheinitialdensityfluctuation.Keywords:cosmology:theory–largescalestructureoftheUniverse–galaxies:halos–methods:analytical1INTRODUCTIONsolvedtheexcursionsettheorywithmovingbarrierofarbi-tr

6、aryshapeanddiscussedtheHIIbubblesizeduringre-Halomodelsarewidelyappliedinthecampaignofcosmo-ionization;andvoidsphenomenonisexploredwithinthelogicalparameterestimationinprecisionfromcosmiclargearXiv:astro-ph/0610451v116Oct2006frameworkbyFurlanetto&Piran

7、(2006).scalestructuresaswellasintheexpeditionofunderstand-Thesuccessoftherandomwalkformalismincosmol-ingstructureformation.Themassfunctionisafundamen-ogyisprominent,buttheprimaryproductoftheexcursiontalingredientofhalomodels.Themostfamousanalyticalsett

8、heory,thePSmassfunction,isapoordescriptiontoformulaofmassfunction,thePress-Schechtermassfunc-simulationsatallepochs(Reedetal.2006).Thecommontion(hereafterPS)wasderivedbyPress&Schechter(1974)practiceistoparameterizethePSfunction,andthenfi