Merging Rate of Dark Matter Halos Evolution and Dependence on Environment
a r X i v :a s t r o -p h /9909012v 1 1 S e p 1999Merging Rate of Dark Matter Halos:
Evolution and Dependence on Environment Stefan Gottl¨o ber
Astrophysical Institute Potsdam,An der Sternwarte 16,D-14482Potsdam,Germany
Anatoly Klypin and Andrey V.Kravtsov
Astronomy Department,NMSU,Dept.4500,Las Cruces,NM 88003-0001,USA Abstract.We discuss the impact of the cosmological environment on the evolution of dark matter halos using a high-resolution simulation within a spatially ?at ΛCDM cosmology.Keywords:cosmology,numerical simulations,galaxy formation 1.Introduction It is generally believed that cold dark matter (DM)dominates the mass in the Universe and signi?cantly a?ects both the process of galaxy formation and the large-scale distribution of galaxies.Here we present results of a study of the formation and the evolution of the DM compo-nent of galaxies,DM halos.The structure of the halos depends on the environment (e.g.,Avila-Reese et al.1999),so that the properties of galaxies are also expected to depend on the cosmological environment.For our analysis we use a low-density ?at cosmological model with cosmological constant Λ,which have been proved to be very successful in describing most of the observational data at both low and high redshifts:?M =1??Λ=0.3,σ8=1,H 0=70km/s/Mpc,t 0≈13.5Gyrs.
2.Numerical Simulations
In order to study the statistical properties of halos and to have a suf-?cient mass resolution we have chosen a simulation box of 60h ?1Mpc with 2563cold dark matter particles (particle mass of 1.1×109h ?1M ⊙).Using the Adaptive Re?nement Tree (ART)code (Kravtsov,Klypin &Khokhlov 1997)we reached a force resolution of ≈2h ?1kpc in high density regions.
Identi?cation of halos in dense environments and reconstruction of their evolution is a challenge.Any halo ?nding algorithm has to deal
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with di?cult“decision-making”situations,in particular when many gravitationally bound halos are moving within a large dense object(a galaxy cluster or a group).We use an algorithm described in Klypin et al.(1999).We characterize each halo by its mass and the maximum circular velocity v circ=
Merging rate of halos3
Figure 1.Merging rate per halo and Gyr for isolated halos,halos in clusters, and halos in groups(di?erent symbols).Curves are analytical?ts of the form (1+z)βexp(?0.6(1+z)).Halos in clusters had much higher merging rates at high redshifts well before the formation of clusters.At z=0merging rates in clusters are very low,but are still relatively high inside groups.
With the procedure described above we?nd at z=0that there are
401cluster galaxies(9.6%),1247galaxies in groups(29.7%),and2545
isolated galaxies(60.7%).If we consider objects of virial overdensity,
the number of cluster and group galaxies decreases to6.5%and25.6%
and67.9%of galaxies become“isolated”.For comparison see also Avila-
Reese et al.(1999).
4.Merging Rate of Halos
The mass of a halo increases due to accretion and merging.However,
interacting halos may exchange and lose mass.We calculate the relative
mass growth per time interval(M1?M2)/M2/(t2?t1),where time is in units of109years.If it is larger than0.35,we call this a major-
merging event.Note that according to this de?nition,we calculate the
total change of mass,not merging with a large halo.
We found that28%of the cluster halos,29%of the group halos and
52%of the isolated halos never underwent a major-merging event.Fig.
1presents the number of major-merging events–the merging rate–
of halos in di?erent environments.We show the merging rate averaged
over three(two at z>2)subsequent time intervals.The error bars √
are
4Stefan Gottl¨o ber et al.
for merging inside clusters at z=0.1,0.25,and0.5come from1, 3,and4events,respectively.The points in the?gure can be?tted by a curveα(1+z)βexp(γ(1+z))withα=?2.1,?1.6,?1,6and β=3.1,2.8,2.5for cluster,group,and isolated halos,respectively.The exponential dilution is the same for all types,γ=?0.6.It is mainly due to the fact that at z>4we are rapidly loosing the halo progenitors due to mass resolution.The position and high of the maxima as well as the slope depend slightly on the chosen threshold for de?nition of major merging events,but the relative position of the curves remains practically constant.
The higher probability of major-merging that cluster and group halos had in the past is due to the higher density in regions,where cluster and groups were to form.Note that clusters have not yet existed at that time.As clusters with large internal velocities form,merging rate drastically decreases.There are almost no major-merging events of cluster halos in the recent past.Those very few events have probably happened just outside the clusters before the mergers fell in the clusters. The probability of recent major-merging is almost the same for isolated galaxies and for group galaxies.It is very di?erent in the past:the merging of galaxies,which end in clusters,was much higher than for isolated galaxies.
Acknowledgements
This work was funded by the NSF and NASA grants to NMSU,and collaborative NATO grant CRG972148.SG acknowledges support from Deutsche Akademie der Naturforscher Leopoldina with means of the Bundesministerium f¨u r Bildung und Forschung grant LPD1996.
References
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S.Gottl¨o ber,A.A.Klypin,A.V.Kravtsov.Halo evolution in a cosmological environment.In ASP Conference Series Vol.176,Observational Cosmology: The Development of Galaxy Systems,Eds.:G.Giuricin,M.Mezetti,P.Saluccip, 418–429,1999.
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