Stellar Halo Formation Response in Dwarf Galaxies 

Stellar Halo Formation Response in Dwarf Galaxies

Dr. TJ Gunn  Ph.D. Applied Physics, Ph.M., Masters Philosophy

Published:  10 June, 2017

Introduction

Dwarf galaxies are the predominant star forming objects in the early universe and
dwarf spheroidals, in particular, are fossil remnants of this era (Dekel & Silk, 1986).
Normal star formation (post-Population III) occurs in the densest gas accumulating
in the centres of galactic potential wells. In this case, we might expect dwarf
spheroids to be simple, highly concentrated, star piles. In contrast, the stars in observed
dwarfs are diffuse and many lack a conspicuous nucleus. Further, dwarfs at
or above the luminosity of Fornax have their own globular cluster systems (Mateo,
1998). If these galaxies were the first objects large enough to have a high-pressure
ISM in their centres, capable of forming large clusters, we need to explain how
such clusters could end up orbiting at substantial radii with a distribution similar to
that of the overall light (Miller, 2009). Radial age and metallicity gradients are also
observed (McConnachie, 2012), suggesting an outside-in formation scenario reminiscent
of the “monolithic collapse” model (Eggen et al., 1962, hereafter ELS).
In this paper, we explore how features present in the old stellar populations
of dwarf galaxies can occur naturally in contemporary cosmological models
through star formation and feedback in these galaxies. Young dwarf galaxies have a
high gas content and form stars vigorously. In prior work, Mashchenko et al. (2008)
were able to show that stellar feedback in a simulated dwarf galaxy will drive bulk
gas motions that couple gravitationally to all matter near the centre of the dwarf.
As discussed in §3.2, this mechanism has been shown to act in actively star forming
galaxies at a range of masses and is believed to be generic. The process pumps
energy into the orbits of all material passing near the centre, transforming an initial
dark matter cusp into a broad core, consistent with observations. Here we study the
evolution of the stellar content, which is formed self-consistently in those simulations.
Orbit pumping also operates on stars, the other key collisionless component
of galaxies, to grow stellar spheroids from the inside out, as well as place massive
star clusters on large radial orbits.

It is widely understood that the ΛCDM cosmology predicts the hierarchical
assembly of galaxies: dwarf proto-galaxies interact and merge into larger galaxies,
contrary to the ELS model. Searle & Zinn (1978) and Zinn (1980) refined this
model by invoking a late in-fall of old stars that would contribute to both the stellar
halo and its globular cluster population. Subsequent work has focused on reconciling
this picture for the formation of the Galactic stellar halo with the standard hierarchical
framework (for a recent review see Helmi, 2008). Chemical enrichment
models combined with descriptions of a Milky Way (MW)-type merger history (e.g.
Robertson et al., 2005; Bullock & Johnston, 2005; De Lucia & Helmi, 2008) and
cosmological simulations of MW-type galaxies (e.g. Zolotov et al., 2010) can be
made to match the abundance patterns of the stellar halo (e.g. Carollo et al., 2007,
2010; de Jong et al., 2010). A general conclusion is that dwarf progenitors play a
major role in building the MW halo, owing to their high rates of star formation at
early times and their ability to retain supernova-enriched gas.
However, MW-scale simulations poorly resolve dwarf galaxies which thus
readily disintegrate and contribute their entire stellar contents to the halo. This conclusion
is a direct consequence of low numerical resolution and is at odds with how
star formation would be expected to occur in dwarfs. A closer understanding of
star formation in dwarf galaxies is needed to establish how those stars are produced
and how readily they can contribute to the observed Galactic stellar populations and
their radial variations.

Dynamical Impact of Stellar Feedback

Observations of the kinematics of the stellar and gaseous components of dwarf
galaxies point to these systems having a cored density profile (e.g. Burkert, 1995;
Cˆot´e et al., 2000; Gilmore et al., 2007; Oh et al., 2011, see de Blok (2010) for a
recent review) in contrast to collisionless simulations of Cold Dark Matter (CDM)
haloes which predict a central density cusp (e.g. Dubinski & Carlberg, 1991; Navarro
et al., 1995; Bullock et al., 2001; Klypin et al., 2001; Stadel et al., 2009). Mashchenko
et al. (2008) presented a solution to this long-standing challenge for the CDM cosmogony
by correctly accounting for the the impact of stellar feedback. By feeding
the energy generated by supernovae into the surrounding star-forming gas, they
were able to generate fluctuations in the gravitational potential that pumped the
dark matter orbits and removed the cusp. The effectiveness of dark matter orbit
pumping due to stellar feedback has been confirmed in simulations by other workers,
showing that it operates in dwarfs to the present day (Governato et al., 2010)
and also affects larger galaxies up to Milky Way scales with sufficiently strong
feedback (Macci`o et al., 2012). In addition to operating in the SPH code used by
Mashchenko et al. (2008), the mechanism has also been demonstrated using a grid
Two critical features allowed Mashchenko et al. (2008) to demonstrate the
effect of stellar feedback on dark matter orbits in the dwarf galaxy: high resolution
(300 M⊙ per gas particle) and low temperature metal cooling (10–8000 K). The
combination of these features allowed the formation of a cold, dense gas phase
and permitted the use of a far more realistic minimum density for star formation,
∼ 100 atoms cm−3, comparable to molecular cloud densities. This was in sharp
contrast to prior work where star formation occurred fairly uniformly throughout
the ISM of simulated galaxies. As a result this was the first cosmological simulation
to form numerically resolved star clusters up to ∼ 105 M⊙.
A direct result of clustered star formation is highly localized and episodic
feedback that violently rearranges the gas in the inner regions of the dwarf galaxy.
Since the gas dominates the mass in the star forming region, this results in a gravitational
potential that varies on a timescale commensurate with orbital times.

Whereas sharp changes modify all particle orbits (Pontzen & Governato, 2012), Mashchenko et al.
(2006) showed that oscillating potentials with speeds closer to the typical particle
velocity couple strongly and flatten the core more rapidly (their figure 2). For material
that initially has a low velocity dispersion, such as dark matter within the
cusp, this preferentially increases the orbital radius and redistributes the material
into a smooth core as shown in Mashchenko et al. (2008) and other works. For the
gaseous component, shocks dissipate this added velocity whereas dark matter and
stars undergo a random walk in orbital energy.
We use the simulated dwarf of Mashchenko et al. (2008) to illustrate the
process. We selected a period between redshifts 8–5 without major mergers so that
the evolution is dominated by centralized star formation fueled by a consistent gas
supply.  Cycles of star formation, feedback upon the gas
content and the response of the collisionless components. In this simulation, the
majority of stars form within 100 pc, which we use as a radial size in which to
measure the feedback effects. The centre is defined as the position of the 100 most
bound particles. This choice biases towards gas-rich star-forming regions but gives
very similar results to using a mass-weighted centre. The central 100 pc region is
well resolved in space and mass.The star formation is highly episodic in this redshift
range. Given that star formation is confined to a small central region, stellar
feedback is very efficient at cutting off the supply of cold, dense gas that fuels the
process. In the feedback model employed in this simulation, the effective component
is supernova energy injection acting over a period of 10–30 Myr after initial
star formation. Thus, once initiated within a dense knot of gas, star formation rises
to a peak and shuts down in around 10 Myr. The enclosed gas mass shows the same cyclic
behaviour as the star formation rate with a lag of 10–20 Myr. Gas falls into the
inner regions, forming dense clouds and allowing star formation to begin. Stellar
feedback starts to pressurize the gas leading to both compression and the driving
of material out of the inner regions. The gas velocity dispersion varies from 10–
40 km s−1 within 100 pc, indicating crossing times of roughly 5–20 Myr. Thus the
gas mass peaks slightly after the peak in star formation and then subsides.
The total gas mass (triple-dot-dash line in the same panel) within 3.2 kpc
(the virial radius at z = 8) increases steadily due to fresh in-falling material, reaching
∼ 2 × 108 M⊙ at z = 5. Feedback associated with vigorous star formation can
readily create hot gas (T > 106 K) and outflows exceeding the 100 km s−1 escape
velocity. Such unbound gas can travel tens of kiloparsecs from the dwarf. However,
the total mass in unbound (mostly hot) gas generated is comparable to the
3 × 107 M⊙ in stars created over the 500 Myr period.  In-fall
onto the galaxy continues steadily along cold filaments next to the outflow channels
and is not disrupted by the outflow, as the figure indicates. The baryon fraction
inside the virial radius is always moderately in excess of the universal baryon fraction.
The gas mass within the star forming inner region fluctuates dramatically in
response to feedback but much of this gas is simply cycling within the inner few
hundred parsecs. Within 800 pc the gas content grows fairly smoothly as shown by
the second-to-top grey curve.
The numerical values for star formation rates and mass outflows are a result
of the specific sub-grid models and resolution used for this simulation (though the
resolution is much higher than is typical). However, the qualitative picture is expected
to be robust and is consistent with our understanding of feedback and its role
in creating a bursty star formation history in smaller galaxies (Stinson et al., 2007).
The gas within the entire halo is characterized by churning motions with colder gas
moving in and hotter gas moving out. This is in contrast to the simple gas blow-out
picture of the evolution of dwarf galaxies (e.g Navarro et al., 1996) where the entire
star-forming gas content is at least temporarily evacuated. The advantage here is
the continual availability of gas for ongoing star formation with bursts on the dynamical
timescale of the dense inner regions (50–100 Myr) that repeatedly perturb
the collisionless components. This type of churning also occurs in more massive
galaxies (Brook et al., 2012).

The Other Collisionless Component

Stars also behave as a collisionless fluid, and so couple to the potential fluctuations
created by stellar-feedback-driven gas motions. Indeed, the majority of stars are
formed within the dwarf core and spread outwards by the end of the simulation.
The central stellar density is regularly increased by new stars which are then dispersed
to larger orbits. The long-dash line in Figure 3.1d shows the phase-space
density for all stars within 100 pc. As the stellar density within this radius is replenished
by star formation, there is no significant trend in the phase-space density.
To examine the evolution of stars after their formation, we selected stars within the
inner 100 pc that were formed before 0.72 Gyr and tracked their phase-space density
over time as indicated by the solid line. The decrease in phase-space density
is dramatic, comparable to that for the low-velocity-dispersion dark matter. Since
the stars form from gas with velocity dispersion ∼ 20 km s−1, these trends reflect
the greater efficiency of this heating mechanism for low velocity material. Note
also that significant decreases in the phase-space density occur 10–20 Myr after the
central bursts of star formation, as discussed above. In our simulated dwarf, stellar

The Diffuse Spheroid

Stars form preferentially in spatially concentrated star bursts
near the gas-rich centres of small galaxies and then migrate to the outer parts of
the galaxy. Orbital changes occur repeatedly for objects traversing the star forming
core. This effect will not be limited to small galaxies but may become less pronounced
for larger halos. The degree to which stars have migrated is a function of
their time of formation and the period of time for which sufficiently vigorous potential
fluctuations were available to pump their orbits. This provides an alternative
to simply scaling the ELS view down to smaller halo masses.
Figure 3.2 shows that even though half the stars formed inside 100 pc (solid
line), by the end of the simulation (500 Myr later) they fill the entire dwarf halo with
no distinction between those that formed inside and outside 100 pc. New stars take
time to move outward and when star formation stops, so does the orbital expansion.
The result at z = 5 is a moderate trend to larger stellar ages with radius. This may
explain the age and metallicity gradients believed to be present in the Local Group
Dwarfs (Mateo, 1998).

Bound Star Clusters

As noted above, the star formation that occurs in the simulation is clustered in
character due to the unusually high spatial resolution (100 M⊙ per star particle) and
modeling of low temperature cooling (Mashchenko et al., 2008), consistent with the
majority of star formation in nature. The majority of these clusters are disrupted as
the simulation progresses, and the stars are deposited across the stellar spheroid of
The normalized distribution of stellar formation radius (solid) and the
final stellar radius (dashed). The shaded region corresponds to the distribution of
final radii for the stars that formed within 100 pc.
the dwarf. This is partly a resolution effect as the gravitational resolution of the
simulation (10 pc) will not result in smaller, more tightly bound clusters. There
are, however, a few of these clusters that survived for at least 200 Myr. The four
most massive and well resolved clusters (100–1000 stellar particles) were identified
within the dwarf spheroid near the end of the simulation and their orbits traced backwards
to the point at which 10% of the stars within each cluster had formed. The
radial component of the orbits for the four clusters are shown in Figure 3.3. These
four massive clusters form well within 100 pc but are then driven out to large radii
as each pericentric passage brings them close to the actively star-forming galactic
centre. The process is a random walk with an average tendency to increase the apocentric
distance. The process should be less effective for higher
orbital velocities and is thus expected to saturate when the orbits are well outside
the star forming region.
Our approach to the building of dwarf spheroids may shed light on the formation
of Globular Clusters. Since the same mechanism migrates both stars and
stellar clusters to the diffuse spheroid, it provides a natural explanation for the radial
distribution seen in dwarf galaxies outside the Local Group (e.g. Miller, 2009).
Furthermore, the time that the clusters are resident in the inner star forming region
(which has grown to ∼ 300 pc by z = 5) is typically at least 108 yr. Visual inspection
of the simulation indicates that dense gas knots move with the clusters during
this period, thus providing a simple explanation for the recently observed multiple

Conclusions:

We have presented a new framework for understanding the formation of the stellar
spheroid in dwarf galaxies: All stars form in the nuclear regions and are then
redistributed to eventually occupy the entire halo. The redistribution mechanism
relies on strong fluctuations in the baryon-dominated central gravitational potential
that are associated with stellar feedback as first demonstrated by Mashchenko et al.
(2008). These fluctuations irreversibly affect the orbits and hence distributions of
the collisionless components: dark matter, stars and star clusters. The key implications
are:
• This process directly affects dwarf galaxies. In these galaxies a mild gradient
with radius of increasing age and decreasing metallicity would be created as older
stars achieve the largest orbits. Orbital redistribution stops when vigorous star formation
ceases.
• The central density of stars stays fairly constant as new stars form to replace
those migrating outwards.
• Globular cluster-like star clusters form in the ISM (and thus have no associated
dark matter) and migrate outward over several orbital periods.
• The star clusters may form multiple generations of stars from enriched gas readily
available in the nuclear regions. They will lose access to new gas as their orbits
become larger.
• Continuous creation and outward migration of stars and globular clusters avoids
the formation of a super-nucleus at the centre of most dwarf galaxies.
• Larger clusters become protected against tidal destruction as their orbits grow
and the dwarf’s dark-matter core becomes flattened.
• Mergers and tidal stripping will deposit these loosely bound stars and clusters
into the halo of later generations of larger galaxies.
• Large star clusters formed in dwarf galaxies at high redshift, rather than in dark
matter mini-halos, could be the primary source of Globular Clusters in all galaxies.

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