Is there a conflict with phasespace density in the secular bulge formation scenario

1
Is there a conflict with phase-space density in
the secular bulge formation scenario?
Alejandro Carrillo1, Vladimir Avila-Reese1
Octavio Valenzuela2 1 Instituto de Astronomía
UNAM, México 2 University of Washington, Seattle,
USA
Abstract Several observational pieces of
evidence support the secular bulge formation
scenario, at least for late type galaxies.
However, the fact that the observational measure
of phase-space density, fobs , is larger for the
bulge than for the inner disk of Milky Way (and
some other spirals), poses an apparent difficulty
for the collisionless secular bulge formation
scenario. We have investigated the evolution of
fobs in a high-resolution diskhalo N-body
simulation. A bulge-like structure forms in the
disk. As expected from the Liouville's theorem,
fobs never increases. However, inside the
bulge-like structure, fobs ends being larger than
in the inner disk, in agreement with observations
from the Milky Way. We have also estimated fobs
for the bulge and the inner disk of other
galaxies spanning several Hubble types. We
conclude that the collisionless secular scenario
seems to work in the correct direction regarding
phase-space density evolution.
4) Evolution of phase-space density
1) Bulge formation and clues from
observations The three scenarios for bulge
formation are 1) monolitical collapse, 2)
violent mergers and 3) disk secular evolution.
The latter scenario is very claimed at least for
late type galxies. Several observational pieces
of evidence support the secular scenario for late
type galaxies (see for review Carrollo 03
photometric, chemical and kinematical
continuities betwen bulge and inner disk, Sérsic
surface brigthness profiles with n lt 4,
correlation betwen re vs. hd, etc. Evidence in
favor of the secular scenario were found recently
even for some early-type bulge. N-body
simulations are a powerful method for studying
many body systems such as galaxies. Early works
demostrated tha a a collisionless disk system
evolves forming structures like bars, spiral
arms and concentrations in the center. Three
secular mechanisms were proposed for bulge
formation scattering of the starts at vertical
resonances (Combes et al.91), dissolution of bars
due to central concentration (Pfeniger Norman
90), and collisionless buckling instability (Raha
et al.91).
3) The numerical simulations With the aim to
explore the problem posed by Wyse 98, we analyse
results from a state-of-the-art high-resolution
N-body simulation of a galaxy-like disk embedded
in a live CDM halo (Valenzuela Klypin 03).
We measure in the simulation the evolution of the
phase-space density radial profile in similar way
as observers do. The density and dispersion
velocity profiles (figs.4,5) were used to
calculate the evolution of fobs shown in fig.6
Fig.2 Selected rings of the disk at the final
time step (4.4 Gyr). The disk and halo have 1.2E6
and 8E6 particles, respectively.
Fig.5 -Evolution of the disk surface (top) and
co-planar volumetric (bottom) azhimutally
averaged density for the simulation.
During the disk secular evolution a bar is formed
and the disk thickens (fig.3). An increasing with
time central concentration of mass in excess of
the inward extrapolation of the outer exponential
disk (fig.5), and a significant thickening and
dynamical heating of this mass concentration
(fig.4), are observed. These are the criteria by
which a bulge is defined observationally.
Fig. 6 Phase-space density profiles at diferent
time steps using srsqsz (a), sr3 (b). Panel (c)
same as (a) but for a lower resolution
simulation. The results are the same
qualitatively.
ti
tf
2) A posible conflict for the secular
scenario? The observed space phase density
function, fobs, is defined as the stellar number
density ns divided by the product of the three
observed dispertion velocity.
Fig.3 Vertical evo-lution of the disk (x-z
plane). The time evolution goes from initial
disk at 0 Gyrs, 1 Gyr, 2Gyrs and 4.4 Gyrs
(clockwise).
The Liouville theorem states that phase-space
density is constant for a collisionless system
Fig.4 Evolution of the radial, tan-gential, and
vertical velocity-dispersion radial profiles (top
panels and left bottom) and the evolution of the
vertical scale length (rigth bottom panel). The
disk is heated significantly in the center.
As seen in fig.6 for the initial thin
exponential disk in vertical and radial
equilibrium, fobs increases along the disk. Due
to the secular dynamical evolution, fobs
decreases with time (mainly in the first Gyr) in
a roughly constant way along the overall disk.
However, in the central region, where namely the
bulge-like structure arises, the radial profile
of fobs develops an increasing with time
depression, with a minimum approximately at the
radius where the bulge-like structure ends, Rinn
2.5 kpc). In the innermost region, fobs remains
almost the same with time.
tf

Asuming isotropy for the bulge we can set up a
limit for fbulge
ti
The phase space density function of the disk can
be aproximated by
Now, as Wyse 98 stated One should not find a
higher phase-space density in stellar progeny,
formed by a collisionless procees, then its
stellar progenitor. Therefore, if the system is
collisionless, we should have that the ratio
6) Conclusions By means of high resolution N-bdy
simulations of a disk embedded in a live CDM halo
we have found that a bulge-like structure arises
due to collisionless secular evolution. The
Liouville theorem is obeyed as expected, however,
the measure of the phase-space density of the
inner disk becomes lower than the one of the
central structure. Therefore, we conclude that
secular evolution yields an observational''
phase-space density radial profile in agreement
with that it is observationally inferred for the
Galaxy and probably for other galaxies.
5) Observational phase-space density in external
galaxies
We use kinematical bulge/disk observations by
Shapiro et al. 03 of four spirals. Their surface
brigthness profiles (fig.7) were used to estimate
bulge and disk densities.
Wyse noted that for the Galaxy fb(100pc) is 5
times larger than fd(2kpc), claiming for a
serious difficulty for the collisionless secular
scenario, unless disipation is included. Based
on the Bissantz Gerhard 02 bulge model, the
bulge kinematics compilation by Tremaine et al.
02, the Lewis Freeman 89 kinematical data for
the disk, and assumig an exponential disk stellar
surface brigthness density profile (hd 3kpc,S?
41.3 M?/pc3 ) and hz 330pc we calculate the
bulge and disk observational phase-space density
profile for the Galaxy
References Bissantz N., Gerhard O., 2002,
MNRAS, 330, 591 Carollo M., Ferguson H. Wyse R.
1999, The formation of galactic bulges, Cambridge
University Press Combes F., Debbasch F., Friedli
D., Pfenniger D., 1990, AA, 233, 82 Lewis J.,
Freeman K.C. 1989, AJ, 97, 139 Pfenniger D,
Norman C.,1990, ApJ, 363, 391 Raha N.,
Sellwood J. A. James R. A. Kahn F. D. 1991,
Nature, 352, 411 Shapiro K., Gerssen J., van
der Marel P.R., 2003, AJ, 126, 2707 Valenzuela O.
Klypin A., 2003, MNRAS, 345, 406 Wyse R., 1998,
MNRAS, 293, 429
Fig.7 Bulge(Sérsic)/disk(exponential)
decomposition of four spirals with velocity
dispersion profiles as measured by Shapiro et al.
03.
Our estimates of the bulge Sérsic index n and of
the fb(re/2)/fd(hd) ratio are presented in the
following table.
Fig.1 Observational phase-space density profile
for the Galaxy (bulge disk). Is the conflict
posed by Wyse 98 confirmed by N-body simulations?
Acknowledgments Thanks to DGEP-UNAM CONACYT
for the support given for this work