Dispersion in modeled abundances

1、dispersion in modeled abundances chemical abundance data for the galaxy show a wide dispersion. we try to check if this dispersion may also be found with chemical evolution models as an effect of variations of an initial mass function (imf) which follows a poisson's distribution 3 2 eb f 5 1 v 2

2、 90 2 3 / h p - o rt sa :v i x r adispersioninmodeledabundancesjuanjosebazan,mercedesmolladpto.def sicateorica.universidadautonomademadrid,28049cantoblanco,madrid.miguelcervi noiaa/csic,apartado3004,18080,granada.1.introductionchemicalabundancedataforthegalaxyshowsawidedispersion.wetrytocheckifthisd

3、ispersionmayalsobefoundwithchemicalevolutionmodelsasane ectofvariationsofaninitialmassfunction(imf)whichfollowsapoissonsdistribution.wewillusetwodi erentmethods:a)ananalysisofthemodelinternalerrorandb)astatisticstudyonthee ectsoftheimfdiscretization,basedonmontecarlomodels.bothmethodshavebeenusedina

4、chemicalevolutionmodelappliedtothesolarneighborhood.preliminaryresultsrelativetooandnareshown.2.theinitialmassfunctionwewilltrytojustifythedatadispersionbythepossiblevariationsinthemodelresultswhichcouldbeproducedbythebehavioroftheimf,whosepropertiesaredescribedbyaprobabilitydistributionfunction:ifw

5、eassumethatntotstarsareobservedinamassrangem0,mmax, themassmiofthei-thstarisarandomvariablewhoseprobabilitydistributionfunctionisgivenbythestellarinitialmassfunction:(mi),whoseintegrationalongthewholemassrangeisnormalizedto1.thenumberniofstarsofmassmiisanotherrandomvariablewhosedistributionfunctionf

6、ollowsapoissonianbehavior,withthevalueoftheimfatthatmassastheonlyparameterofthedistribution: =(mi)dmi,sincethetotalnumberofstarsis:ntot= dni=dni/ntotdni.asimpletesttocheckthepoissoniannatureofthedistributionofniissimplytheratioofitsvariancetoitsaveragevalueasafunctionofmass.thisratioshouldbecloseto1

7、.cervi noetal.(2021)illustratesintheir gure3the3resultsofatestwith1000montecarlosimulationsofclusterswith10and104starswithasalpeterimfslope.despite 1 chemical abundance data for the galaxy show a wide dispersion. we try to check if this dispersion may also be found with chemical evolution models as

8、an effect of variations of an initial mass function (imf) which follows a poisson's distribution 2 niistheratioofapoissonvariablewithaconstant,itispoissoniandistributedwithina 10%. figure1.dispersionofopanela)andnpanelb)abundancedataofthegalaxytakenfromdi erentsources onceweknowthatnicanbeapprox

9、imatedbyapoissonvariable,itispossibletoapplyaproperstatisticalformalismintothecodeofourchemicalevolutionmodelinordertostudythe uctuationswhichwemayobtainfromthisstoscasticbehaviorfortheimf. 3.thetheoreticalmultiphasechemical evolutionmodel ourmodeledphysicalsystemisacylindricalsub-galacticzonecen-te

10、redonthesolarneighborhood,extendingabout1kpcinthegalacticplane.themodelusedinthisworkisthecodefromferrinietal.(1992),improvedwithrecentyields(gavilanetal.2021).itcomputesapro-ductionmatrixqij(m),whereeach(i,j)elementrepresentsthefractionofthestarmassinitiallyintheformofchemicalspeciesj,transformedan

11、dejectedaschemicalspeciesi,for15chemicalelements.amatrixiscomputedforeachstellarmassweigthedbytheimf.thenucleosynthe-sisproductionfromsni,snii,andnormalstarsistakenintoaccount.weletthemodelevolvesfor13,2gyrs,witha0.01timestep.theimfusedistakenfromferrinietal.(1991): (m)=22.0865m 0.52x10 2.07(logm)+1

12、.92logm+0.731 chemical abundance data for the galaxy show a wide dispersion. we try to check if this dispersion may also be found with chemical evolution models as an effect of variations of an initial mass function (imf) which follows a poisson's distribution 3 3.1error analysis figure2.variabi

13、lityoftheimfasafunctionofmass. consideringthepoissoniannaturefortheimf,weassumeaninitialvarianceof2()=.then,wetrailtheerror,followingerrorpropa-gationrules,withinthemodelineveryequationinvolvedandrelatedtoourimf.asaresultwecanobtainameasureofthevariabilityofourmodelalongthewholemassintervalconsidere

14、d. wemayobserveinfig.2thatthevariabilityincreasesstronglyinthemassintervalfrom4to8m.thisisexactlytheintervalofmassproducingfeandn.therefore,inagreementwiththisresult,ourmodelmustshowalargerdispersionintheseelementsincomparisonwithotherelementsaso. 3.2montecarlosimulations weuseanuniformlydistributed

15、randomnumbersgeneratortogen-eratefromit,andusingtheaccumulatedprobabilitydistribution,asuc-cessionofnumberswithourimfasprobabilityfunction.ouraimisthecomputationofacompletesetofqi,jmontecarlosimulations,wheretheimfisrandomlydi erentforeachofthem,withmassesfrom0.8upto100m,dividedin800intervalswithlin

16、earinterpolationwithinthem.wealsowouldliketostudythee ectsofthediscretizationcausedbyroundinginthecode.ouraimistocalculate500 1000simu-lations,with105 106stars.wewillrepeatoursimulationsfortwodi erentrounddownvalues:10 3and10 6.thewellcalibratedmodelfromgavilanetal.(2021)willbeourbaseofmeanvalues. c

17、hemical abundance data for the galaxy show a wide dispersion. we try to check if this dispersion may also be found with chemical evolution models as an effect of variations of an initial mass function (imf) which follows a poisson's distribution 4 4.results thepreliminaryresultshavebeenobtainedb

18、ytherealizationof400montecarlosimulationsforthegalaxydiskzone,withouthavingintoac-counttheroundinginthecodeandwithnoncalibratedmodels.despiteofthesefacts,adispersionof10 2alreadyappearsinouroandnabundances.aswemayseeinfig.3.thisfactseemstoindicatethatagoodpercentageoftheobserveddispersioncouldbeachievedwiththecompletesetof simulations. figure3.preliminar