CONCLUSIONES Y CUESTIONES ABIERTAS

We have performed a set of numerial merger simulations of galaxy models whih

onsistofeitheraone-omponent(bulgeonly)oratwo-omponent(bulge+darkmatter

halo) Hernquist prole. Furthermore we used dierent initialmass ratios and orbits

with and withoutangular momentum to over a largerange of parameters. Our main

ndings an be summarized as follows. Dry equal-mass mergers an not be the main

driver of galaxy evolution, beause the remnants assemble mass at all radii and shift

the surfae density nearly parallelto highervalues. Therefore the slopeof the surfae

brightness proles are hardly aeted and the Sersi index does not exeed a value of

n

_∼6

afterone generation (Fig. 7.6). Additionallythe size growth peradded mass is limited to

r

e

∝M

0.91

.

On the other hand, dissipationless minor mergersshow very promisingresults. As

the satellites are looselybound,they strongly suer from dynamialfrition and tidal

stripping. Therefore, depending on the mas ratio, most of the mass assembles at

larger radii and the remnants develop a extended envelope of stars. For an initial

massratio of1:5, the entralsurfae density/brightness staysonstant, outtoaradius

of

r

≈

1.5

kp whih is in good agreement to reent observations of high redshift early-types (Szomoru et al.,2011)and the assumption, that the ompat galaxies are

the ores of present day elliptials (Hopkins et al., 2009a; Bezanson et al., 2009; van

Dokkum et al., 2010; Szomoru et al., 2011). Furthermore the tted Sersi proles

yield a urvature of

n

∼

8−10

, whih lies in the range of most of the observed ore elliptials (Caon et al., 1993; Kormendy et al., 2009). For a higher initial mass ratio,

the results highly depend on the properties of the satellite galaxies. If the satellites

are loosely bound (Sat 1:10, Fig. 7.1), they are destroyed rapidly inthe ase of more

to a radius of

r

≈

5

kp. Additionally, the developing envelope of areted partiles reveals a prominent kink, whih results in an unrealisti high Sersi index of

n

≈

20

. Using a ompat, more bound, satellite (Sat 1:10, Fig. 7.1), the areted mass gets

loser to the enter and distributes more smoothly in the outer envelope, whih then

yields reasonable Sersiindies of

n

≈7−8

.

Regarding the size growth of the individual minor merger senarios, we nd that

all remnants, where the bulge is embedded in a massive dark matter halo, lie above

the grey shaded area of Fig. 7.2 and are viable drivers for the evolution of ompat

early-type elliptials. In the most promising ases, namely the 1:5 sequene with a

diuse satellite and the 1:10 sequene with a ompat satellite result in a mass-size

relation of

r

e

∝

M

2.3

and

r

e

∝

M

2.5

, respetively. On the other hand, for the bulge

only minormergers, onlythe hierarhy with amass ratioof 1:10 and adiuse, weakly

boundsatelliteevolvesinexessoftheobservedmass-sizerelation. Theothersenarios

stay within the 'forbidden' area and are by far not eient enough to give a proper

size inrease.

Furthermore, inSetion 6, we have shown, that the merginghistory of our galaxy

models yield dark matter frations, whih are in good agreement to reent lensing

observations of the SLACS ollaboration. Our minor merger remnants also indiate,

that the entral dark matter frations inrease with the stellar mass of early-type

elliptials.

Combiningallthe resultswe ansay, thatonlythe minormergersinludingadark

matter halo give reasonable results for the observed inside-out growth of the surfae

densities and surfae brightnesses. Furthermore, only the bulge+halo minor mergers

always yield a size growth in exess to the observed predition of van Dokkum et al.

(2010) (see Fig. 2.2).

However, we use a very idealized senario, without any gas or blak hole physis.

But even the existene of a small amount of gas, whih is known to redue the size

growth (Covington et al., 2011; Hopkins et al., 2008), might not be eient enough,

as we ahieve very high growth rates in most of the minor merger senarios. On the

other hand, the implementation of blak holes might boost the 'pu up' senario, as

blak hole binaries are able to deplete the entral galaxy regions from gas and stars

(Fan et al., 2008, 2010), and the observed ore struture of the most massive present

CONCLUSION & OUTLOOK

Reent observations have revealed a populationof ompat high redshift (

z

∼

2−3

) early-typegalaxies, whih areafator 4-5smallerthan theirpresent dayounterparts.

They are already very massive but have less onentrated surfae density proles,

represented by small Sersi indies of

n

∼

4

. Furthermore, the stellar populations of their present day ounterparts indiate,that dissipation and star formationannotbe

the main evolutionary mehanism. However, in the urrently favoured osmologial

model, where struture grows hierarhially, dissipationless mergers are supposed to

be the main driver for the subsequent evolution of ompat, high redshift early-type

galaxies. Therefore we employ a large set of more than 80 dissipationless merger

simulations,with a large avriety of orbits and initialagalxy models.

To ahieve this, we rst reated aninitialondition program, whih overs a wide

range of dierent parameters (Chapter 4). In detail, this means, that we an either

hose galaxiesonsisting ofjustastellaromponentoramore realistitwo-omponent

model, where the stellar bulge is embedded in a more massive dark matterhalo. The

dark matter halo is xed to a Hernquist density distribution (Hernquist, 1990), but

the slope of the luminous part an vary between dierent

γ

-models (Dehnen, 1993;

Tremaine et al., 1994). Hene, one an adopt either a steep density slope

γ

∼

2

, re- sembling auspy extra-lightgalaxy,ora oredprole

γ

= 0

, whihisobserved for the most massive elliptials. First stability tests have shown, that the initial onditions

are very stable for one- and two-omponent galaxy models with dierent partile res-

olutions and density slopes but equal mass partiles. We also reated more 'realisti'

galaxy models using the most reent HOD models to get aviabledark tostellar mass

ratio of

M

∗

/M

dm

∼0.015

(Moster etal., 2010; Wake et al., 2011) for a

M

∗

= 10

11

M

⊙

galaxy at a redshift of

z

∼

2

. In addition, we assigned them a size orresponding to the most reent mass-size relations of early-type elliptials (Williamset al., 2010) at

this high redshift. In this setup, the dark matter partiles have a muh higher mass

to the equal-mass models. This stems from two-body relaxation in the entral high

density regions, whih additionally indues mass segregation for unequal mass parti-

les (Chapter 5). Therefore, with alarger foresoftening length, we prevent the more

massivedarkmatterpartilestosinktotheenter andkikoutthe lessmassivestellar

partiles. The adopted softening lengthis still smallompared to the eetive galaxy

radius,sothatthegalaxiesanbeonsideredresolvedandweobtainverystableresults

for osmologiallymotivated galaxymodels.

Using our well tested initial onditions, we are able to investigate the dynamis

of the mergingproess with anunpreedented high auray and resolution. First we

fousedonequal-massmergersofeitherone-ortwo-omponentmodelsandfound,that

violent relaxation and mixing are the dominant proesses, whih signiantly hange

the struture of the merger remnant's dierential energy distribution (Setion 6.4).

Strongpotentialutuationsduringthelosestenounters oernewenergystateswith

higher binding energies and unbind a non-negligible amount of initial weakly bound

partiles(seealsoWhite1978). Thisevolutionisthesameforone-andtwo-omponent

models, but inthe latterase wedisplay anotherstrikingresult inthe galaxy'senter,

wheretheamountofdarkmatterpartilesinreaseswithrespettothestellarpartiles

and we obtain a 'real' inrease of the entral dark matter fration. This is ontrary

to the work of Nipoti etal. (2009b),who argues, that the inrease of the darkmatter

fration isjust aneet of the inreasing galaxy size. However, we onviningly show,

that violent relaxation mixes more and more dark matter partiles to higher binding

energies for eah subsequent merger generation, whih hanges the ratio of stellar to

darkmatterpartiles,espeiallyintheentralregions. Furthermore,the redistribution

ofthepartile'senergies ausesthesystemstoseekforanewequilibriumonguration.

Therefore, the nal veloity dispersionproles ofthe equal-massmergerremnants an

nielybettedbyaJaeprole(Jae,1983),whihisingoodagreementtoSpergel&

Hernquist (1992). Unfortunately,the strutural hanges and atransfer of energy from

the bulge to the halo inrease the veloities of the merger remnants and onsequently

limit the size growth. However, the mass-size (

r

e

∝

M

0.8−1.0

∗

) and the mass-veloity relation (

M

∗

∝

σ

3.3−5.1

e

) yields reasonable results ompared to a previous study of

Boylan-Kolhin etal.(2005).

Lookingat the minor merger senarios with initialmass ratios of 1:10, we worked

out, that rst of all, the dynamis is ompletely dierent and the host galaxy is not

aeted by violent relaxation (Setion 6.5). Therefore its entral properties are on-

served and the veloity dispersion prolesof the total systems stay onstant for both,

one- and two-omponent models. But as the satellites are loosely bound ompared

to the host galaxies, they strongly suer from tidal stripping and nearly no material

reahes the host's enter. The stripped material builds up an extended envelope of

stars, whih signiantlyboosts the size growth. Dueto anenhanedeet of dynam-

ialfrition and tidal strippingin the darkmatter halo of the bulge+halomodel, this

mass assembly is very eient, and we get a nal size inrease of more than a fator

of

∼

4.5

, whih is exatly in the observed range for the size growth of ompat high redshift elliptials (Szomoru et al., 2011). Looking at the mass-size relations of all

two-omponent senarios with mass ratios of 1:5 and 1:10, we get

r

e

∝

M

>2.3

∗

, whih is muh steeper than the result of van Dokkum etal.(2010) (

r

e

∝M

2

∗

).

As minor mergers seem to be very good andidates for driving the evolution of

early-type elliptialswe extend the previous set of simulations by a sequene with an

initial mass ratio of 1:5, investigate in more detail the assembly history of the nal

remnants, and want to gure out the importane of a dark matter halo (Chapter 7).

Firstofall,regardingthesizeevolutionoftheindividualsenarios,weanseethatonly

the minor mergers with dark matter halo evolve as expeted from observations. For

bulge only models, just one merger onguration with a very diuse satellite galaxy

evolves in exess to the observed relation. Looking at the evolution of the surfae

densities, reentobservationsrevealaninside-out growthwithdereasingredshift (van

Dokkum et al., 2010; Szomoru et al., 2011). In detail this implies, that the entral

regions of high redshift early types stay unaeted and build the ores of present day

elliptials,whilethey assemblealotofstellarmassatlargerradii,buildingupanouter

envelope. Surprisingly, this is exatly what we nd for the surfae densities of our

minor merger remnants (Setion 7.4). While the proles of the equal-mass mergers

grow over the whole radial range, the entral proles of the minor merger senarios

stay onstant, as most of the satellite's material gets stripped in the outer regions of

the host galaxy. Again, the senarios with bulge+halo models yield more promising

results, as the extended massive dark matter halo enhanes tidal eets and strips

the materialat the 'right' regions (

r >2

kp). Converting the surfae densities of our remnantstosurfaebrightnessproles,Sersitsindiatethatfortherstgenerations,

the Sersiindex

n

inreasesmostrapidlyforthe two-omponentminormergersofboth

mass ratios (1:5, 1:10). Although

n

onverges to a value between

n

= 7−8

for the 1:10 sequene, the 1:5 sequene of bulge+halo models is the only senario, where we

get ahigh Sersiindex of

n∼9−10

,whihisexpeted fromobservations. Finally,we obtainaninreasing darkmatterfration,whihisonsistentwithreentobservations

(Barnabè et al., 2011) for all minor merger hierarhies and we an onlude, that the

existene of a dark matter halo is not just expeted but is essential to get a viable

evolutionsenario.

Altogetherwean say, thatwe highlightaverypromisingsenariotolosethe gap

between the ompat high redshift elliptialsand theirmore extended ounterparts in

the present day Universe. To fortifyour results, the next step would be to use more

realistigalaxymodels,applyingaontratedNFW-proleforthe haloandextendthe

galaxy by the potential of a supermassive blak hole. Fan et al. (2008) showed, that

AGNsanalsopuupgalaxiesandmightevenimprovetheresultsofthedissipationless

merger senario. Regarding the dynamis of merging systems, it would be desireable

to investigate the impat of dierent orbital properties, to estimatethe eet of, e.g.

hyperboliorboundorbits with dierentimpatparameters. Furthermore,we started

to look at the evolution of the very tight relation between a galaxy's esape veloity

v

esc

and itsmetalliity (Sott etal., 2009).

Therefore we simply ompute a partile's esape veloity of the initial host and

Figure 8.1: Top panel: Evolutionof the

v

esc

-metallity relation for threegenerations of equal-mass mergers. Due to the strong mixing, it hanges at all veloities, and introdues

an inreasingsatterforeah subsequentgeneration. Thesolidlinesarethe bestlinear ts

tothe orrespondingdata points. Bottompanel: Sameas abovefor10generationsof1:10

minor mergers. Obviously, the entral relation does not hange and only the outerparts

with lower veloities are eet. Therefore the metalliity seems to onverge to a value of

tion, the esapeveloities ofthe partileshange,but their metalliitiesstay onstant,

thus we an evaluate the merger indued satter in the

v

esc

- metalliity relation. As observations showaverytightorrelation,wean approximate theontributionofmi-

nor or major mergersfor the evolutionof elliptialgalaxies. The rst results indiate,

that the

v

esc

−[Z/H]

-relationfor equal-massmergers (top panel, Fig. 8.1) hanges at all radii and for all veloities, whih stems from the strong mixing, indued by vio-

lent relaxation. Therefore, the satter inreases signiantly and the overall relation

beomes very broad. On the other hand, a sequene of ten minor mergers with ini-

tial mass ratio of 1:10 (bottom panel, Fig. 8.1) introdues only a small satter in the

v

esc

−[Z/H]

-relationandhas noinueneonthe entralregions(withhigh veloities). Furthermore, with eah generation, the metalliity gradient beomes only weaker for

equal-mass mergers (Fig. 8.1), whih is in good agreement with earlier preditions of

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