5. DISK GROWTH: COLD ACCRETION

Figure 2 displays two plausible modes of galaxy growth: galaxy mergers and gas accretion. While we know that the frequency of interactions and mergers increases steeply with redshift, the availability of unvirialised gas increases as well. In Sections 3 and 4 we reviewed galaxy growth driven by mergers, mainly the growth of galactic disks. Here we focus on the alternative process of galaxy growth via the accretion of unvirialised baryons and DM.

5.1. The standard view and the new paradigm

The ability of galaxies to grow by means of accretion has been known for some time. The standard view has been that gas falling into a DM halo shocks to a virial temperature, T_vir, at around the halo virial radius, R_vir, and fills it up, remaining in a quasi-hydrostatic equilibrium with T_vir ~ 10⁶ (v_circ / 167 km s^-1)² K. Hot, virialised gas cools from the inside out, loses its pressure support and settles into a centrifugally-supported disk (Rees & Ostriker 1977; White & Rees 1978; Fall & Efstathiou 1980).

This view has been substantially modified now in that not all the gas is shocked when it enters the halo. Instead, much of the gas is capable of entering the halo along denser filaments and penetrating deeply - this radical shift in understanding has led to a new paradigm (Fig. 7).

Figure 7. Left: The standard view - gas shocks at Rvir, becomes pressure-supported, then cools down and settles in a disk; Right: The new paradigm - some of the gas shocks, but the majority enters the DM halo in the cold phase along the filaments feeding the disk growth.

5.2. Accretion shock?

Birnboim & Dekel (2003) have performed an idealised analytical study of gas accretion on a spherical DM halo, assuming two alternatives: an adiabatic equation of state and radiative cooling. The solution has been tested with a 1-D hydrodynamic code. The incoming gas is not virialised and therefore its motion is supersonic, creating favourable conditions for the virial shock - its existence and stability have been analysed. The crucial support for this shock comes from the post-shock gas. If the virialised gas is adiabatic or its cooling is inefficient, the shock-heated gas becomes subsonic (with respect to the shock) and its support for the shock remains stable, with the shock positioned at ~ R_vir. This is always the case for the adiabatic gas, which is also stable against gravitational collapse (i.e., Jeans instability) if the adiabatic index > 4/3. Gravitationally unstable gas will collapse to the centre, thus removing support from the shock, which will rapidly move inwards. The gas can be treated as adiabatic when the radiative cooling timescale is longer than the collapse timescale. The gravitational stability condition is slightly modified for gas with radiative cooling to an effective adiabatic index which includes the time derivatives, _eff (d ln P / dt) / (d ln / dt). Its critical value, _eff > _crit 2 / ( + 2/3) = 10/7, is close to the adiabatic case. Here P and are thermal pressure and density in the gas. For a monatomic gas with = 5/3, this stability condition can be rewritten as

(6)

where ₀ is the preshock gas density, u₀ and u₁ are the pre- and post-shock gas velocities, T₁ u₀² is the post-shock temperature, R_s is the shock radius, and (T) is the cooling function.

While the 1-D hydrodynamics is an obvious simplification of both the halo and gas properties, its simplicity has a certain advantage in that it allows one to follow the analytical solution closely. It shows that the adiabatic shock exists always and gradually propagates outwards, coinciding with the virial radius, R_vir. On the other hand, for radiative cooling in the gas with primordial composition, the shock exists only where the inflow encounters the disk, initially. With the halo growth this shock also moves outwards and stabilises around R_vir. In the following, we shall argue that the cold inflow can join the disk smoothly, without being shock-heated - i.e., that 1-D hydrodynamics cannot capture this solution.

This simple 1-D model predicts a critical value for the DM halo mass above which the shock is supported at R_vir. A weak dependence on the redshift of halo virialisation exists, and a stronger dependence on the gas metallicity as well (because it affects the cooling significantly). The mass range for the critical halo mass appears to be ~ 10¹¹ M for a primordial gas composition, and ~ 5 × 10¹¹ M for about 0.05 of the Solar metallicity. For this metallicity, Press-Schechter M_* haloes will generate stable shocks only by z ~ 1.6. The corollary: virial shocks will form only in the massive haloes mentioned above, at low redshifts. The general condition for shock stability is that the cooling timescale of the shocked gas should be longer than the compression timescale.

A number of issues can complicate these conclusions: arbitrary triaxial halo shapes, the interaction between the supersonic gas infall and the forming disk, and the possible trapping of Ly photons within the halo gas. The first two issues can be resolved in terms of numerical simulations (see below). The trapping of Ly photons during gravitational collapse and its effects on the fragmentation and related issues of proto-disk formation are under investigation (e.g., Spaans & Silk 2006; Latif et al. 2011).

Following the analytical/1-D hydro approach discussed above, numerical simulations have been performed addressing a number of issues, e.g., what is the maximum temperature of the gas entering the DM haloes? The standard view has been that T_max ~ T_vir, but as we have already discussed, not all of the gas is shocked to T_vir. It is helpful to define two modes of accretion - first, a cold mode with a maximum temperature of T_max < T_vir ~ 10⁵ K, which was not shock-heated, is distributed anisotropically, and follows filaments into the DM halo. Second, a hot mode with T_max > T_vir ~ 10⁵ K, which has been shock-heated at ~ R_vir, cools down while in a quasi-static gas halo and is accreted quasi-isotropically. The filamentary inflow of the cold gas exhibits much lower entropy, T / ^2/3, compared to the shocked halo gas (e.g., Nagai & Kravtsov 2003).

Simulations reveal a more complex picture when some of the gas is accreted via filaments, and some from cooling of the hot halo gas (Keres et al. 2005; Dekel & Birnboim 2006). Only about half of the gas follows the expected path of accretion, which is heated to T_vir, then cools down and participates in the star formation. The rest of the gas stays much cooler at all times. The overall emerging picture is that of a bi-modal evolution of accreting gas. Specifically, the cold mode dominates in low-mass galaxies and DM haloes, M_gal 2 × 10¹⁰ M and M_h 2.5 × 10¹¹ M, respectively, and the hot mode dominates in the higher-mass objects. As a result the cold mode is expected to dominate at high redshift and in the low-density environment at low redshifts. The hot mode will dominate in the high-density environment at low z, such as in galaxy clusters.

The quoted critical (baryonic) mass, M_gal ~ 2 × 10¹⁰ M, obtained from numerical simulations is close to the observed characteristic mass for a shift in galaxy properties,
M_gal ~ 3 × 10¹⁰ M (e.g., Kauffmann et al. 2004; Kannappan 2004), based on a complete sample of SDSS galaxies. These studies focussed on the environmental dependence of various parameters which describe the galaxies, such as morphology, stellar mass, SFR, etc., quantifying the distribution of these properties with respect to galaxy mass. For stellar masses above the critical M_gal no dependence on environmental factors has been found for the distribution of sizes and concentrations at fixed stellar masses, whereas for less massive galaxies, the trend has been detected for galaxies to be somewhat more concentrated and more compact in denser regions. The star formation history has been found to be much more sensitive to the environment: e.g., the relation between the = 4000 Å break, specific SFR (per unit stellar mass) and M_gal - with the same separator of ~ 3 × 10¹⁰ M. The drop in the specific SFR for less massive galaxies was about a factor of ten over the density interval used in the study, much stronger in comparison with the more massive galaxies.

An interesting corollary is the apparent similarity between the redshift evolution of galaxy properties and their change as a function of a (local) density. In retrospect, this result is almost a common wisdom, reflecting the `sped up' evolution of galaxies in over-dense regions in the Universe.

Hence, compelling observational evidence exists that galaxies below the critical mass of M_gal ~ 3 × 10¹⁰ M are much more active in forming stars, have larger gas fractions, lower surface densities, and exhibit late-type morphologies. More massive galaxies have old stellar populations, supplemented with low gas fraction, higher surface densities, and early Hubble types. This bimodal behaviour can have its origin in the fundamental way the galaxies grow, or rather in the way their growth is limited. If indeed a large fraction of the accreted gas is not heated to the virial temperatures, it can join the disk and be converted into stars. We discuss the associated processes in Section 5.4. The shock-heated gas, on the other hand, can also contribute to the star formation if its cooling time is sufficiently short. So, some of the hot-mode gas in haloes somewhat smaller than the critical one to sustain the shock (e.g., in low-density regions and/or at higher z) will cool down if not subjected to feedback. This gas can contribute to disk or spheroidal buildup over time.

However, as pointed out by Dekel & Birnboim (2006), above the halo mass of M_h ~ 10¹² M, the cooling timescale for ~ 10^6-7 K hot- and low-density gas becomes longer than the Hubble time, and the gas, once heated to the virial temperature, will never cool down and hence will not contribute to the disk growth in any direct way. This hot gas which fills up the halo can also be subject to additional heating by AGN feedback, both mechanical (throughout the halo) and radiative (at the base), because of its high covering factor. For massive haloes, we expect that the only real effect of this feedback can be in generating an outflow of the overheated gas.

While this is only a circumstantial observational argument in favour of the existence of cold filamentary flows, it is nevertheless very intriguing by bringing up the same bimodality in galaxy properties. The prime observational issue of course remains the detection of these flows. Hot gaseous haloes have been detected in X-rays around individual galaxies, groups and clusters of galaxies (e.g., Crain et al. 2010a, b; Anderson & Bregman 2011). There is no direct observational evidence in favour of cold accretion flows, although accretion of cold patchy gas has been observed (e.g., Rauch et al. 2011). For higher-redshift galaxies, contradictory claims exist regarding the possibility that diffuse Ly emission around them comes from cold accretion flows (e.g., Dijkstra & Loeb 2009) and represents the cooling radiation (Fardal et al. 2001), or, alternatively, is the scattered light coming from the Hii regions (e.g., Furlanetto et al. 2005; Rauch et al. 2011). Because of various reasons, including the low emissivity, absorption against bright sources like quasi-stellar objects (QSOs) is the most promising way to detect the cold accreting gas, especially in Ly. Van de Voort et al. (2012) have argued that the high column density Hi absorption detected at z ~ 3 originates mostly in accreting gas with T 3 × 10⁵ K, based on numerical simulations. Rakic et al. (2012) have interpreted results of the Keck Baryonic Structure Survey of Hi Ly absorption in the vicinity of star-forming galaxies at z ~ 2-2.8 as due to large-scale infall. It is not clear whether the individual Hi absorbers can be attributed to cold accretion, based only on their proximity to the galaxy and a low metallicity (e.g., Giavalisco et al. 2011).

High-velocity clouds around the Milky Way galaxy (for a recent review see Sancisi et al. 2008) can be closely related to the cold gas accretion phenomenon discussed here. Sancisi et al. (2008) have detected accretion rates of ~ 0.2 M in Hi clouds, which is possibly a lower limit for our Galaxy, that has a SFR ~ 1 M yr^-1. There are numerous ways in which cold gas clouds can form in the accreting matter without being processed by the DM substructure. One such possibility involves Rayleigh-Taylor instabilities in the halo-penetrating filaments (Keres & Hernquist 2009). But additional options exist as well. These clouds can subsequently be accreted by the galaxy and contribute to the ongoing steady star formation there.

So why has cold accretion not been detected in a decisive manner so far? One can bring up the similar situation and difficulties in detecting cold accreting gas in AGN. At the same time, outflows are commonly detected both in AGN and in starburst galaxies. The plausible explanation may be in small cross sections, low emissivity and very high column densities along the line-of-sight due to the gas accumulation in the `equatorial' plane.

5.3. Cold flows: redshift evolution

The coexistence of cold and hot modes of accretion can have interesting implications for galaxy growth. These modes depend differently on the environment, as well as on the feedback from stellar evolution and AGN. Additional issues raised so far in the literature involve a plausible difference of the associated initial mass functions (IMFs).

Cosmic star formation exhibits a broad maximum at z 1 and a steep decline below this redshift (e.g., Madau et al. 1996). This decline can be associated with the decay of the cold accretion flows (e.g., Keres et al. 2005; Dekel & Birnboim 2006). Below z ~ 2, massive ~ 10¹² M haloes become typical, the shocks are stable around R_vir, and the cooling time of the shocked gas becomes too long, effectively quenching the cold-mode accretion. This defines the critical redshift, z_crit ~ 2-3. After z_crit the star formation will be suppressed in massive haloes and especially in galaxy clusters. Under these conditions, the observed bimodality in galaxy properties can find a natural explanation. In terms of the prevailing colours of stellar populations, which are determined by the stellar ages and SFRs, this shutdown of the cold accretion mode will result in the relatively quick transformation of galaxies with high SFRs. This means that the origin of the red sequence can be traced directly to the switching of the prevailing accretion mode, as noted by Dekel & Birnboim (2006). It would be a strong argument in favour of this picture if a number of bi-modal correlations, such as the colour-magnitude, bulge-to-disk ratio, or morphology-density ones, can be explained as corollaries of the cold gas supply shutdown at various redshifts and environments. However, there is a caveat: the bulge-to-disk ratio can be affected and even dominated strongly by other processes (e.g., Combes et al. 1990; Raha et al. 1991; Martínez-Valpuesta et al. 2006). Other correlations may exhibit similar trends.

Clearly, accretion flows that have been investigated for decades as the mechanism to power AGN are capable of playing a substantial role in growing galaxies embedded in DM haloes. Moreover, within the CDM framework, cold-mode accretion forms naturally because of the low dispersion velocities in the gas that has cooled down in the expanding Universe during the Dark Ages. The large turnover radii, corresponding to the accretion radius, and the substantially sub-Keplerian spin parameter , assure a strong dependence on the accretor mass, i.e., DM halo mass. It also means that the cold-mode accretion should dominate at high redshifts, and the hot mode should only pick up at low redshifts, if at all.

Keres et al. (2009a) have investigated the cosmological evolution of smooth accretion flows using simulations with sufficient resolution to follow up growth of galaxies in massive haloes only. Cold flows appear to dominate the global gas supply to galaxies basically at all times, especially in small galaxies residing in 10¹² M haloes for z 1. At these redshifts, the galaxy growth was found to be only a function of its mass. At z 1, the cold accretion on smaller galaxies has decreased sharply. These results have been confirmed by Brooks et al. (2009) - for galaxies up to L^* the cold accretion fuels the star formation. Romano-Díaz et al. (2008b) argued that late minor mergers with DM substructure ablate the cold disk gas and quench the star formation there. Cold accretion dominated growth has also been inferred in high-resolution simulations of galaxies at redshifts z 6 (Romano-Díaz et al. 2012).

Moreover, the total gas accretion rate has been found to peak at z ~ 3 and to exhibit a broad maximum between z ~ 2-4, the same as the cold accretion. Hot accretion which consists of a shocked virialised gas that is able to cool down over relative short time has been found to contribute little over time, except lately, for z 1, after peaking at z ~ 1.5. Mergers become globally important only after z ~ 1. Finally, the SFR has been estimated to correlate with the smooth accretion rate and to be about a factor two of the Madau diagram.

So, according to Keres et al. (2009a), galaxies grow via the accretion of cold and never-shocked gas, while the contribution of the hot mode of cooling shock-heated virialised gas is not important at all. This is a dramatic turnaround and a paradigm shift with respect to the standard picture described in Section 5.1. If verified, the implications of this are broad: it is the cold mode of accretion that drives the star formation in galaxies. However, taken at face value, this star formation will lead to fast conversion of gas into stars - an overproduction of the stellar mass already at an early time, if the feedback from stellar evolution and AGN is not efficient enough. In short, a mechanism to suppress the star formation is necessary. (This is discussed in Section 6). Another corollary is the possible shock at the inflow-disk interface. Is it avoidable? (See Section 5.5 for more options.) Is it observable? Lastly, the dominant cold mode of accretion must be incorporated into the prescriptions for semi-analytic models.

5.4. Cold flows: between the virial radius and the disk

Understanding the kinematics and dynamics of the cold flow which penetrates the DM halo and is not shocked to virial temperatures is crucial in order to estimate the flow's contribution to disk growth. As the filaments penetrate deep into the halo, their temperature stays approximately constant, because of the efficient cooling, and they are compressed by the surrounding hot halo gas, if it exists. The efficiency of this inflow contribution to the disk growth process is unclear at present. In principle, it can be expected to depend on at least two parameters: the angular momentum in the cold gas and the shape of the background gravitational potential. These will determine the prevailing trajectories within the DM haloes and to some degree the amount of dissipation in the infalling gas. As a result, we shall be able to estimate the infall timescale (which will be longer than the free-fall time within the DM halo) and the way this gas joins the growing disk, by smoothly merging or experiencing a strong shock. In the former case, the infall energy of the gas is transformed into rotational energy. In the latter, part of the infall energy will be radiated away sufficiently close to the shocked interface.

In smaller haloes and especially at higher redshifts, the virial shock is not sustainable at ~ R_vir, and the forming galactic disk can be directly affected by the deposition of matter, linear and angular momenta, and energy by the inflow of the cold gas. How much dissipation is involved in this process? Is the local, i.e., inflow-disk interface, shock-unavoidable?

The 1-D case discussed above is not representative here, as the shock is unavoidable (if the cold inflow exists) and the angular momentum plays no role. Based on 3-D numerical simulations, Dekel & Birnboim (2006) argue that cold streams intersecting among themselves and with the forming disk will trigger starbursts, characterised by the most common mode of star formation in the Universe. The strength of the starburst will determine whether the disk will continue to grow relatively quiescently or whether the process will contribute to the spheroidal component.

Most cosmological simulations lack the necessary resolution to investigate the inflow-disk interface. The simplest way to circumvent this is to reproduce the thermal histories of the gas particles. Brooks et al. (2009) found that most of the gas joins the disk unshocked in a smooth accreting component, opposite to the gas accreted with the substructure, i.e., clumpy gas. The only exception is the disk evolution in the most massive halo, well above L^*. For this halo, the SFR is not exactly balanced by the accretion rate onto the halo, as a substantial delay in star formation occurs due to the prolonged cooling time of the shocked gas.

Heller et al. (2007b) have shown that the cold gas filaments can smoothly join the outer disk, being deflected from the disk rotation axis by the centrifugal barrier - no standing shock has been detected there. In this case the infall kinetic energy is converted into rotational energy. Interestingly, the gas filaments are supported by the DM filaments in a configuration which resembles the `cat's cradle' - a small amorphous disk fuelled via nearly radial string patterns (e.g., Fig. 8).

Figure 8. `Cat's cradle' morphology: face-on view of the gas disk (upper frames) and the extended DM regions (lower frames) showing the cold gas inflow joining the disk. The white arrows (right frames) underline the DM filaments and the associated gas inflow. Note that the gas streamlines join the disk at tangent angles which preclude strong shocks from forming and rather assure a smooth unshocked transition flow (from Heller et al. 2007b).

If the inflow-disk interface shock does not exist or is sufficiently mild, what additional signatures of a recent accretion can be expected deep inside the host haloes? For a number of reasons discussed above and in Section 2, most probably the gas has a non-negligible amount of angular momentum and will settle in some `equatorial' plane outside the growing stellar disk. However, the orientation of this plane can differ substantially with respect to the stellar disk plane. This will lead to the formation of inclined and polar rings, warps, etc. Indeed, numerical simulations of such disks in a cosmological setting have demonstrated the formation of rings and warps, as a rule rather than an exception (e.g., Romano-Díaz et al. 2009; Roskar et al. 2010; Stewart et al. 2011). Specifically, Romano-Díaz et al. (2009) have demonstrated that the mutual orientation of the rotation axis of the disk, DM halo, and the accreting gas fluctuate dramatically over time, even during the quiescent periods of evolution (see their Fig. 19).

Dekel et al. (2009b) have shown that galaxies of ~ 10¹¹ M at z ~ 2-3 - at the peak of SFR in the Universe - have been fed by cold accretion streams, rather than by mergers. About 1/3 of the stream gas mass has been found in clumps, leading to mergers of 1/10 mass ratio; the rest in the smooth streams. The deep penetration of cold streams happened even in DM haloes of > 10¹² M which are above the critical mass for virial shock heating (Section 5.2). Dekel & Birnboim (2006) have noted that the cold gas streams are supported by DM streams whose characteristic width is smaller than R_vir, and which are denser than the diffuse halo material. They cross the shock basically staying isothermal because of the short cooling distance. We return to the issue of penetrating streams in Section 7 on high-z galaxies.

There is a possibility that the extended XUV disks detected by GALEX (Galaxy Evolution Explorer), whose population can reach ~ 20% locally, have their origin in accretion flows (e.g., Lemonias et al. 2011; Stewart et al. 2011). A strong argument in favour of such a scenario comes from the observations of such disks around massive early-type galaxies. Moreover, there is no indication that XUV disks prefer tidally-distorted disk galaxies, so they cannot originate as a result of a close passage or a merger event.

In the presence of a disk, one would expect that the gas accretion will join its outer parts, at least the majority of the inflow, as discussed above. The low-j material that can come closer to the rotation axis would be accreted earlier and such orbits would be depopulated quickly.

5.5. Cold accretion flows in the phase space

The phase space provides the maximum information about filamentary cold flows. Even 2-D phase space allows for a clear display of the accretion flows. It is especially suitable in order to follow up the phase mixing and violent relaxation processes discussed in Section 3.1.2. Various complementary presentation options exist here, such as using R - v_R, r - v_circ and/or r - , where R and r correspond to the spherical and cylindrical radii, and v_R, v and to the radial and azimuthal velocities and to the dispersion velocity, respectively.

Comparison of the evolution of pure DM and DM+baryon models in the R - v_R plane reveals the effect of baryon inflow on the kinematics of the DM halo (Fig. 9 and Romano-Díaz et al. 2009). The mass-averaged radial velocities are negative outside R_vir and lie below the v_R = 0 line, and change to positive inside the halo, initially. At later times, the mass-averaged velocity is zero, as the inner halo reaches its virial equilibrium. Both major and minor mergers (substructure) can easily be distinguished by the vertical spikes, and are much more prominent, by a factor of ~ 2, for models with baryons, before the tidal disruption. Moreover, the smooth accretion can be well separated from the substructure. The width of the inflowing stream, which represents the mass accretion flux, declines with time, while that of the rebounding material increases. In the process of tidal disruption, inclined `fingers' form, again more prominent in the presence of baryons. The subsequently forming `shell' structure reveals the insufficient mixing of merger remnants in the form of a R - v_R correlation - `streamers', which appear to be long-lived. Streamers formed after z ~ 1 largely survive to z = 0. The phase space also delineates the kinematical differences of the inner DM haloes in these models: note the outline of v_R(R) at small radii. This effect can be explained in terms of the gravitational potential shape there, which represents a more centrally-concentrated object.

Figure 9. Phase space evolution of a DM halo without (left) and with (right) baryons in the R - vR plane, run from identical initial conditions. The halo has been projected to collapse by z ~ 1.3 with a mass of ~ 1012 h-1 M, based on the top-hat model. The epoch shown here corresponds to intensive merger activity and to the cold accretion growth in these simulations. The corresponding redshifts, z ~ 4 → 1.5, are shown in the lower-right corners of each frame. Note the appearance of `fingers' and `shell' structure inside and outside of the halo - much more pronounced in the presence of baryons. The inflow containing both substructure and a smooth component is clearly visible as a stream penetrating deeply inside the DM halo, especially in the right-hand frames. The shape of the denser region is `smashed' against the vR-axis in the presence of baryons and has a convex shape in the pure DM case. The colours correspond to the DM volume density. The vertical arrows display instantaneous value of Rvir, the dashed white line shows vR = 0, and the solid blue line - mass-averaged vR at each R. The velocity axis is normalised by vcirc - the circular velocity at Rvir (from Romano-Díaz et al. 2009).

So the phase-space analysis shows that DM haloes, while reaching virial equilibrium, are far from relaxed in other aspects. Streamers are probably the best example of this inefficient relaxation, and are strengthened by the presence of baryons. The degree of relaxation in DM haloes can be further quantified using the smoothing kernel technique (Romano-Díaz et al. 2009). This procedure allows us to estimate the contribution of the excess DM mass fraction associated with density enhancements (i.e., subhaloes, tidal tails, and streamers) above some smoothed reference density which is time-adjusted. This excess mass fraction in the substructure becomes more prominent with time.

A complementary option to study the buildup of DM haloes is in the r - v_circ plane. In this plane, the halo kinematics is much more symmetric with respect to the v_circ = 0 line. Mergers disrupt this symmetry which is quickly restored. Both major and minor mergers are easily traced in such a diagram. The high degree of symmetry between the number of prograde- and retrograde-circulating particles is very important in order to understand the dynamical state of DM haloes and growing stellar disks, especially the disk-halo resonant and non-resonant interactions which ultimately affect the disk ability to channel baryons toward the centre (e.g., Shlosman 2011). One note of caution: at higher redshifts, the haloes appear substantially triaxial in the range of radii, and hence v_circ provides a bad approximation to the mass enclosed within r. The overall symmetry in the r - v_circ diagram (e.g., Romano-Díaz et al. 2009) confirms that there is very little net circulation of the DM within the halo. The tumbling of the halo figure is also found to be negligible - the halo appears to be orientated along the main filament which feeds its growth.