6.5 Minor Mergers
6.5.2 System Evolution
The evolution of the total bound minor merger generations are depited in the left
panels of Fig. 6.15. Obviously the mean square speeds (top panel) of all hierarhies
derease with inreasing mass. In all senarios with diuse satellites (blak, blue,
green and red lled irles), the evolution is very lose to the virial expetations of
Eqs. 6.7-6.9 (dashed line), althoughthe mass lossis signiant espeially for the
two-omponent models (red and green irles). In table 6.1 we an see that the fration
Figure 6.14: Toppanel: Theradialveloitydispersion for thehead-onminormergersof
one-omponentmodels(B10ho)staysonstantovermostof theradialrange. Onlyinthe
veryentral regions, itinreases slightly witheah generation. Theblakdashed lineisthe
initial Hernquist prole and the reddashed-dotted line the veloity dispersion of all bound
areted partiles. Bottom panel: For the whole bound remnant, the veloity distribution
staysperfetlyisotropi, astheanisotropyparameter
β
stayszero. Lookingatthearetedmaterial(reddashed-dottedline),itgetsradiallyanisotropiwithinreasingradius. Inboth
panels the radius is normalized to the spherial half-massradius of the boundsystem.
Top panel: The radial veloity dispersion of the total system (solid lines) for the head-on
minor mergers of two-omponent models (HB10hod)stays onstant overthe wholeradial
range. Thedispersion ofthe bulgesystem (dottedline) buildsupa prominentbumpwhih
omes fromthe aretedmaterial,that getsstrippedinthe outerparts ofthe hostsystem.
Theradiiarenormalizedtothe spherialhalf-massradiusofthe bulge. Bottompanel: The
anisotropy parameter of the bulge veloities gets radially biased at radii greater than the
spherial half-mass radiiof the bulge.
of esaping partiles is up to
35%
for HB10hod and more than20%
for the othersenarios. Furthermore, regarding the 2C models, most of the esape fration is due
to the dark matter partiles. Going bak to the evolution of
h v 2 i
, we an see, thatthe orreted predition of Eq. 6.15 (dashed-dotted line), whih inludes the eet
of mass loss, perfetly ts the results (e.g. senario B10hod). Using more ompat
satellites the nal derease of veloities (orange and purple irles) is muh weaker,
beause they are more tightly bound. As they havehalf the sale radius of the diuse
satellites,theirbindingenergies andveloitiesaretwotimeshigherwhihthendoubles
the veloity fration
ǫ = h v a 2 i / h v i 2 i
of Eqs. 6.7-6.9 and yields a smaller derease. Inombination with the ourring mass loss, this explains the dierent evolution of the
mean square speeds. Nevertheless, in all senarios the nal mean square speeds of
the total systems are
10 − 30%
lower ompared to their initial host galaxies, whihis in good agreement to observations, that predit a mild derease of the ompat
early-type's veloitydispersions.
The evolution of the gravitational radii (middle left panel of Fig. 6.15) of the six
hierarhies evolve aording to the mean square speeds, whih is not surprising as
r g ∝ 1/ h v 2 i
(see Eq. 6.5). In detail, this means, that the hierarhies with a diusesatelliteshowasize inrease, whihisonsistentwith the analytipreditions(dashed
line) and as the ompat satellites are not able to eiently derease the veloities,
their gravitational radii grow only marginally. However, for all minor mergers the
maximumsize growthisaroundafator
∼ 2.4
,whihisby fartooweaktoexplain theobserved evolution of ompat early-type galaxies. For ompleteness, the bottom left
panel illustrates, that the mean density within the gravitational evolves aording to
the gravitational radius(
ρ ∝ r g −3).
In the right panels of Fig. 6.15 we illustrate the eetive line-of-sight veloity
dispersion
σ e (top), the eetiveradius r e (middle)and theeetive surfae density of
all minor merger remnants. Obviously, the entral regions show nearly no evolution
of
σ e 2, exept the two bulge only senarios with a diuse satellite (B10amd, B10hod).
Beforeweexplainthedierentresults,werstlookatthesizeevolutionoftheaording
eetive radii
r e (middle panel) and the eetive surfae densities (bottom panel).
Surprisingly, the sizes of nearly all merger remnants grow signiantly and for the
most eient one (HB10ho) the nal size is a fator
4.5
higher, whih is even muhhigher than the virial expetation (Eq. 6.8). This strong evolution is alsoreeted in
the eetivesurfaedensities(bottompanel),whihderease atmaximumbyanorder
of magnitude.
In the ase of bulge only senarios, the dierent evolutions of the entral
param-eters an be explained by strutural hanges, measured by the struture parameter
c
(Eq.6.21). In Fig. 6.16 the lled irles show, that the three one-omponent minor
mergersindiatedierentresults. The B10hosequene evolvesnearly self-similar,i.e.
it grows at all radii and nally does not hange its initialshape (see also Fig. 6.12).
Consequently, thetotalsystem evolvesthe sameastheentralsystem andthe inrease
of the eetive radius is very similar to the gravitational radius (left middle panel).
Furthermore,due tothe esapers, the donot grownotably,thusthe alulation of the
Figure 6.15: Left panels: Evolutionof the mean square speeds (top),the gravitational
radii(middle)andspherialdensities within
r g (bottom)forallminormergersenarios(see
table 6.1). The dashed lines in eah panel are the idealized expetations of Eqs. 6.7-6.9
for the all diuse one-omponent senarios and the blak dashed-dotted line depits the
orreted expetations of Eqs. 6.15-6.17for the minor merger senario B10hod.
Right panels: The squared mean line of sight veloity dispersion (top), the mean eetive
radius(middle)andthemean eetivedensity(bottom)forthesenariosoftheleftpanels.
In ontrast to the total system, the entral veloity dispersion shows nearly no derease,
exept for the hierarhy B10amd, but a very high size inrease. Only B10ho, with a
ompat satellite stays below the idealized expetations (dashed line). Here, the x-axis
Figure6.16: Thelefty-axisand thestarsshowaninreasingdarkmatterfrationwithin
thespherialhalf-massradiusofthebulgeforthetwo-omponentminormergers. Theright
y-axistogether withthe irles indiateastrongderease ofthe strutureparameter
c
(eq.6.21) for nearly all minor merger senarios. Due to the high mass loss of some senarios
we plot all values againstthe total system mass. Colors arethe same as in Fig. 6.15.
eetive line-of-sight veloity dispersion is restrited to the entral parts, with high
veloities, and therefore stays onstant. The further two bulge only senarios, both
inludeweaklyboundsatellites,whihalreadyloosemost oftheirmaterialintheouter
regionsof the host galaxy. Hene the latter onesbuild up anextended envelope,while
the enters stay unaeted, i.e. the strutural properties of the remnants do hange
(see alsoblak and blue irles in Fig. 6.16). On the other hand, the development of
anextendedenvelopeboosts thesize growthofasystem. Asthethe sequene B10amd
(blue irles)with anangular momentum orbitneeds more time untilthe nal
oales-ene, it suers more from tidal stripping and builds up the most extended envelope
of all bulge only models, whih then results in the highest size growth. This implies,
that the alulation of
σ e also inludes partilesoutside the innermost regions, where
the veloitiesare lowerandthe veloitydispersionwithinthe eetiveradiusdereases
(see alsotop rightpanel Fig. 6.14).
Regarding the evolution of the bulge+halo senarios we additionally have to deal
with the eet of dark matter, whih also has a big inuene on the evolution of the
observable properties. In the middle panel of Fig. 6.15 we an see, that all three
senarios yield a signiant size growth up to a fator of
∼ 4.5
(HB10ho), whih isthe onsequene of a developing extended envelope. In Fig. 6.17 we illustrate the
evolution of the surfae density along the major axis. Obviously, mostof the areted
material settles down at larger radii
r > 10
and does not reah the enter, whihdiretlyhighlightsthe buildup of thestellarenvelopeand thestrutural hangeof the
Figure 6.17: Surfae densities of the bulge along the major axis for the head-on minor
mergersoftwo-omponentmodels(HB10hod). Thegreysolidlineindiatestheinitialhost
surfae density, whih is the same as the nal surfae density of the host partiles (blak
dashedline). Most ofthesatellite'smaterial(dottedline)assemblesataradius
r > 10
andinreases the nal prole (blak solid line) espeially in the outer parts, while the entral
prole staysthe same.
nal remnant. As the nal struture parameter is very similar for all two-omponent
minor mergers (green, red and purple irles in Fig. 6.16), they all follow the same
evolutionarypathwithrespettothesizegrowth. IntheaseofsenarioHB10ho,the
satellite is afator 2ore bound, whihindues two onsequenes, rst, some partiles
go slightlyfurther to the host's enter and seond, less mass is lostduringthe merger
proess, whih results in the most eient size growth. So far, dark matter enhanes
tidal stripping and leads to the build up of anextended envelope, regardless of whih
orbit we use. But as the radius inreases that rapidly, the eetive radius goes into
regions whih are more and more dark matter dominated, whih nally results in a
highly inreasing dark matter fration (stars in Fig. 6.16). In the end the ratio of
initial to nal dark matter mass within the spherial half-mass radius is a fator of
> 1.8
higher. But, ontrary to the equal-mass mergers, this inrease is just a resultof the size growth as the real fration of bulge to halo partiles do not hange over
most of the energy spae (see bottom panel Fig. 6.13). Additionally, the inreasing
darkmatterfrationwithinthehalf-massradiuskeepsthe veloitiesofstellarpartiles
onstant out to amuh larger radius omparedto the bulge onlymodels (see alsotop
right panel Fig. 6.14). Therefore the eetive line-of-sightveloity dispersions in the
top right panel of Fig. 6.15 donot hange.
Altogether, we an say that minor mergers are very eient drivers for the size
growth of spheroidal galaxies. As dark matter enhanes dynamial frition and tidal
stripping, it enhanes the eet and due to the nally high eetive radii, the dark
matterfrationalsogrowsbynearlyafatorof2after10generationsofminormergers.