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The previously described model for galaxy formation (and angular momentum acquisition in particular) in § 3.1 assumes that gaseous halos of galaxies should maintain a similar distribution of spin parameters to that of the dark matter (since the baryons and the dark matter both share the same initial tidal torques as an origin of their angular momentum). Thus, if one were to consider the spin parameter of the gas in a galaxy halo it should be the same distribution as the spin of the dark matter, which is well constrained from N-body simulations (Figure 1), such that λgas ≃ λDM. This simple theoretical picture has provided reasonable agreement between theory and observations, in terms of matching distributions of galaxy sizes and luminosities, with characteristic galaxy sizes expected to be Rd ∼ λRvir (corresponding to ∼10 kpc for a galaxy halo with Rvir ∼ 300 kpc, e.g. Fall & Efstathiou, 1980, Bullock et al., 2001, Dutton & van den Bosch, 2009).

Having also reached the point where cosmological hydrodynamic simulations of galaxy formation (with properly tuned star formation and stellar feedback physics implemented) are able to produce galaxies with realistic disk scale lengths, bulge–to–disk ratios and overall angular momentum content — resolving the angular momentum catastrophe — one might think that our picture of angular momentum acquisition is reasonably complete. However, recent observations have provided further complication to the issue of angular momentum acquisition, with numerous detections of baryons in galaxy halos with significantly higher spin than either the galaxy or expectations for dark matter halos. These frequent detections of high–spin baryons in galaxy halos would seem difficult to explain under the assumption that λgas ≃ λDM.

In this section, we will discuss the angular momentum content not of the dark matter halo, nor the baryons in the stellar content of the galaxy, but instead the baryons present in the gaseous halo of the galaxy — i.e. the circumgalactic medium (CGM). We begin in § 4.1 by presenting the observational evidence for high angular momentum material in galaxy halos, challenging the classical picture of galaxy formation described above. We then discuss recent advances in our understanding of galaxy formation theory that may help explain these observations in § 4.2.

4.1. Observations of High Angular Momentum Gas

In the local universe, some of these high angular momentum observations include detections of extended H I disks, XUV disks, and giant low surface brightness galaxies (e.g., Bothun et al., 1987, Matthews et al., 2001, Oosterloo et al., 2007, Christlein & Zaritsky, 2008, Sancisi et al., 2008, Lemonias et al., 2011, Heald et al., 2011, Holwerda et al., 2012, Hagen et al., 2016), as well as low metallicity high angular momentum gas (presumably from fresh accretion) in polar ring galaxies (Spavone et al., 2010). For example, observations of UGC 2082 from Heald et al. (2011) show a stellar disk diameter of D25 = 24 kpc (defined by a surface brightness of 25 mag/arcsec2) but the H I disk (down to a minimum column density of 1020 cm−2) has significantly higher specific angular momentum — being larger by roughly a factor of ∼ 2, DHI = 44 kpc. In an even more extreme example, Oosterloo et al. (2007) detected H I disks as large as ∼ 200 kpc in diameter around early type galaxies. As another example, the giant lower surface brightness galaxy UGC 1382 contains a low surface brightness stellar disk with a ∼ 38 kpc radius, embedded in a ∼ 110 kpc HI disk, residing in a ∼ 2 × 1012 M halo (Heald et al., 2011). The high spin of such extended disk components is is somewhat difficult to understand within the context of the canonical model, in which jdjgasjDM. Furthermore, Courtois et al. (2015) also indicated that local extended H I disks may be dependent on the galaxy's filamentary environment, suggesting there may be a fundamental distinction between the angular momentum content of filamentary accretion versus isotropic accretion.

At moderate redshift (z ∼ 0.5–1.5) there are a growing number of absorption line studies of the circumgalactic medium of galaxies that have begun to emphasize the bi–modal properties of absorbers (Kacprzak et al., 2010, Kacprzak et al., 2012a, Kacprzak et al., 2012b, Bouché et al., 2012, Bouché et al., 2013, Crighton et al., 2013, Nielsen et al., 2015, Diamond-Stanic et al., 2016, Bouché et al., 2016, Bowen et al., 2016), where absorbers along a galaxy's major axis tends to show higher angular momentum inflows that are roughly co–rotating with the galactic disk and absorbers along a galaxy's minor axis tend to instead show observational signatures of outflowing gas. Increasingly, a number of absorption system observations seem to be in agreement with models that include massive, extended structures with inflowing disk–like kinematics (e.g., Bouché et al., 2016, Bowen et al., 2016)

At higher redshift (z ∼ 2–3) kinematic studies of Lyα “blobs” have observed large scale rotation that seems consistent with high angular momentum cold gas accretion (Martin et al., 2014, Prescott et al., 2015), and there have also been recent detections of massive protogalactic gaseous disks that are kinematically linked to gas inflow along a cosmic filaments (Martin et al., 2015, Martin et al., 2016). (We will show in § 4.2.1 how these observations are strikingly similar to theoretical expectations for inspiraling cold streams from cosmological simulations.)

Taken together (though this is by no means an exhaustive list), such observations show growing evidence for the existence of coherent rotation with high angular momentum for cold halo gas, in stark contrast to the theoretical picture where halo gas should have specific angular momentum similar to that of the galaxy and the dark matter halo.

4.2. “Cold Flow” Gas Accretion and Angular Momentum

Recent advances in galaxy formation theory and cosmological simulations have also begun to complicate the picture of galaxy formation presented in § 3, with growing emphasis on multiple modes of accretion to galaxy halos. While isotropic “hot–mode” accretion continues to behave in the manner previously assumed, it has also been shown that anisotropic “cold–mode” accretion along cosmic filaments may have cooling times shorter than the compression timescales for creating a stable shock e.g. Binney (1977), Kereš et al. (2005), Dekel & Birnboim (2006), Ocvirk et al. (2008), Brooks et al. (2009), Dekel et al. (2009), Faucher-Giguère & Kereš (2011), Faucher-Giguère et al. (2011), Stewart et al. (2011a), van de Voort et al. (2011), Hobbs et al. (2015), van de Voort et al. (2015). As a result, this cold filamentary accretion does not spend sufficient time in the halo to become well mixed before sinking towards the central galaxy 3.

In one of the seminal papers outlining the importance of “cold mode” gas accretion to galaxies, Kereš et al. (2005) suggested that the angular momentum of filamentary cold gas accretion may be substantially different than that of isotropic “hot mode” accretion, however for a more thorough investigation of the angular momentum of these different types of gas accretion, we must look to more recent results (in part owing to the need for superior numerical resolution in simulations before an analysis of angular momentum in gas accretion could be considered reasonably robust).

Figure 2

Figure 2. Modified version of Figure 6 from Danovich et al. (2015), showing distributions of halo spin parameters (for material in the halo but not the central 0.1Rvir) in dark matter (left), cold gas (middle) and hot gas (right) from 29 high resolution cosmological hydrodynamic “zoom–in” simulations between z = 4−1.5. Red curves represent best fit lognormal fits to the data. The mean spin parameter of each best fit curve (µ = ⟨λ⟩) is given for each component, demonstrating that cold halo gas, ⟨λcold⟩ = 0.110, has significantly higher specific angular momentum than the dark matter in the same region: ⟨λdm⟩ = 0.043. This fundamental result is in close agreement with a number of other studies (Stewart et al., 2011b, Pichon et al., 2011, Kimm et al., 2011, Stewart et al., 2013, Stewart et al., 2016), which implement a variety of simulation codes and feedback implementations to study the spin of cold halo gas compared to that of the dark matter halo.

Stewart et al. (2011b), Stewart et al. (2013) studied 4 high–resolution cosmological hydrodynamic simulations of roughly Milky Way size halos run to z = 0 (using the smooth particle hydrodynamics (SPH) code Gasoline, Wadsley et. al, 2004), ith particular emphasis on the distinction between “cold mode” gas accretion (which is typically more filamentary and thus anisotropic) versus “hot–mode” gas accretion (typically more isotropic). They found that cold mode gas in galaxy halos contains significantly higher specific angular momentum than the dark matter, λcold ∼ 4 λDM, and also has noticeably higher spin than the hot mode accretion, λcold ∼ 2 λhot (also see Figure 2). As a preliminary look at origin of this discrepancy, they compared the spin of recently accreted isotropic versus anisotropic dark matter and found a qualitatively similar distinction.

They also found that fresh accretion (both gas and dark matter) contained ∼ 2 times higher angular momentum than the entire halo, with λ ∼ 0.1 (rather than the canonical λ ≃ 0.04 for the entire halo). Furthermore, even at accretion to the virial radius, cold gas enters the halo with ∼ 70% more specific angular momentum than dark matter, and has a relatively short sinking time from the virial radius to the galactic disk (only ∼ 1−2 halo dynamical times). They argue that this combination naturally explains the high angular momentum nature of cold halo gas, compared to dark matter: dark matter in galactic halos represents a cumulative process of past accretion, while cold gas currently in a galactic halo both entered the halo with higher specific angular momentum than dark matter, and also represents recent accretion rather than a cumulative sum of all past accretion. As a result of the coherent high nature of this cold inflow, they also reported the formation of transient “cold flow disk” structures in their simulations: massive extended planar structures of inflowing cold halo gas (not rotationally supported) that are often warped with respect to the central galaxy — aligned instead with the angular momentum of the inflowing cold filamentary gas.

In a set of companion papers, Pichon et al. (2011) and Kimm et al. (2011) analyzed a statistical sample of ∼ 15,000 halos at z > 1.5 (from a somewhat lower resolution simulation) as well as ∼ 900 intermediate resolution halos and 2 high resolution zoom–in simulations run to z = 0 (using the Ramses code, Teyssier, 2002), finding that the ability of gas to radiative cool significantly alters the angular momentum transport of gas and dark matter into halos of a wide ranges of masses, primarily due to the dense filamentary nature of cold gas accretion. They reason that due to the asymmetry of cosmic voids, gas and dark matter flowing out of voids onto cosmic filaments gain a net transverse velocity, which acts as the seed of a halo's angular momentum as the material subsequently flows along the filament onto a nearby (gravitationally dominant) dark matter halo. In this picture, material initially farther away from the filament will gain a larger transverse velocity by the time it impacts the filament, naturally providing more angular momentum at later times, but with coherent direction (since the filament direction does not substantially change orientation over cosmic time).

While they find that both gas and dark matter tend to deliver similar specific angular momentum (as would be expected from TTT) the newly accreted material (at any given time) has significantly higher spin than that of the halo as a whole. Specifically, at high redshift, a large discrepancy between the spin of gas and dark matter in the halo arises, in agreement with previous work (Stewart et al., 2011b), with λgas ∼ 2−4 λDM, depending on halo mass. This discrepancy is thought to be due to the coherent dense filamentary accretion of gas along cosmic filaments, without shock–heating to redistribute the angular momentum through the entire halo. Over time, both dark matter and baryons (including all gas and stars) lose a significant amount of angular momentum, primarily via vector cancellation, as freshly accreted material is never perfectly aligned with that of the halo as a whole.

Using 2 intermediate resolution simulations, Sales et al. (2012) studied 100 roughly Milky Way size halos run to z = 0 (using the Ramses code). They noted that the angular momentum of different gas components upon infall may not necessarily be indicative of how these modes contribute to galaxy type. They found that galaxy morphology was most strongly correlated with the coherent alignment of angular momentum over cosmic time. Specifically, they found that most disk–dominated galaxies formed their stars from hot–mode gas that shock–heated and eventually cooled onto the galaxy at later times, while more spheroids were formed from cold–mode gas that sinks onto the galaxy more quickly, forming stars at a much earlier time; as a result, later episodes of accretion may not be very well aligned with the galaxy, leading to a spheroidal morphology.

Danovich et al. (2015), building upon previous work (Danovich et al., 2012), analyzed 29 zoom–in simulations at z > 1.5 (using the Art code, Kravtsov et al., 1997, Kravtsov, 2003), focusing on the angular momentum transport from the cosmic web onto massive galaxies, which they comprehensively detailed through four distinct phases, outlined below.

  1. According to TTT, the spatial dependence of the angular momentum vector components, Ji are given by the antisymmetric tensor product: Ji ∝ єijk Tjl Ilk, where Tjl is the tidal tensor and Ilk is the inertial tensor. In the principle coordinates of the tidal tensor, the angular momentum is thus proportional to the difference in the corresponding eigenvalues of the inertial tensor: J1T23(I3I2), J2T13(I3I1), J3T12(I2I1). Under the assumption that the underlying tidal tensor should be approximately the same for both dark matter and gas, any inherent differences in the specific angular momentum of dark matter versus gas (outside the virial radius, in the regime of TTT), should result from the difference between the inertial eigenvalues, (IjIk), as a proxy for the quadrupole moment. Focusing on dark matter and gas just outside the virial radius of the galaxy, (1 < r / Rvir < 2), they found that the quadrupole moment is consistently higher for the cold gas than it is for the dark matter by a factor of ∼ 1.5−2. Since these tidal torques may act prior to maximum, each stream may acquire a transverse velocity, so that it is no longer pointing directly at the center (in agreement with previous work by Pichon et al., 2011). The highest angular momentum streams thus have spin parameters as high as λ ∼ 0.3 upon crossing the virial radius, however, misalignment between multiple streams typically lowers the net spin parameter of all cold gas entering the virial radius to a lower value of λ ∼ 0.1 (in agreement with previous work by Stewart et al., 2013).
  2. While inflowing dark matter virializes once inside the virial radius, the cold streams penetrate the halo quickly, without becoming well–mixed with the pre-existing gas in the halo, resulting in a higher spin parameter for cold gas in the halo (0.1 < r / Rvir < 1.0) by a factor of ∼ 3 when compared to the dark matter in the same volume (see Figure 2). The cold gas in the outer halo is also significantly more coherent than the dark matter, with a significantly smaller anti-rotating fraction.
  3. The cold streams remain coherent, spiraling around the galaxy and sinking quickly towards the center of the halo. As the streams blend and mix together, they often form into what Danovich et al. (2015) refers to as “extended rings” of inflowing cold gas, the radius of which is typically set by the pericenter of the stream contributing the most angular momentum. These structures are typically warped with respect to the inner disk, in qualitative agreement with the “cold flow disk” structures reported previously by Stewart et al. (2011b) and Stewart et al. (2013). Similar structures have also been noted as areas of interest in previous simulations: for example, the “messy region” of Ceverino et al. (2010) or the “AM sphere” or Danovich et al. (2012). Angular momentum in these extended rings is ultimately lost as a result of strong tidal torques from the inner disk on timescales of roughly one orbital time, allowing the extended disk to gradually align with the inner disk.
  4. The angular momentum lost by the inspiraling cold gas can ultimately be redistributed to both outflows and the dark matter. The inner disk is subject to angular momentum redistribution and violent disk instabilities.

Teklu et al. (2015) analyzed ∼600 intermediate resolution massive (Mvir > 5 × 1010 M) halos from the Magneticum simulation (Dolag et al. in preparation) over the redshift range z = 2−0.1. In agreement with previous results, they compared the spin parameter of all dark matter, stars, gas, cold gas, and hot gas in the virial radius (not cutting out the inner region of the halo where the galaxy resides), and found that the distribution of spins was well fit by lognormal distributions, with the gas (particularly the cold gas components) showing systematically higher spin than that of the dark matter, with the dark matter spin staying roughly constant with time, but the gas spin parameter growing with time: λcold ∼ 2(3)λDM at z = 2(0.1). They also noticed a dichotomy in spin parameter with galaxy morphology: disk galaxies tend to populate halos with slightly higher spin parameters, and where there is better alignment between the angular momentum vector of the inner region of the dark matter halo versus that of the entire halo.

In an effort to test whether this changing picture of angular momentum acquisition is sensitive to simulation code architectures or specific feedback implementations, Stewart et al. (2016) carried out a code comparison of a single high resolution zoom–in simulation of a Milky Way sized halo (using common recent hydrodynamic/feedback implementations for each code, and utilizing identical analysis for each code) run with Enzo (Bryan et al., 2014), Art (Kravtsov et al., 1997, Kravtsov, 2003), Ramses (Teyssier, 2002), Arepo (Springel, 2010), and Gizmo-PSPH (Hopkins, 2015). While many quantitative differences were apparent among the codes, agreements included the spin of cold halo gas being ∼4 times higher than the dark matter in the halo (in agreement with previous work, e.g. Figure 2, taken from Danovich et al., 2015), as well as the presence of inspiraling cold streams. These inspiraling cold streams often form extended transient structures of high angular momentum cold gas, co-rotating with the galaxy along a preferred plane that is kinematically linked to inflow via large–scale cosmic filaments (see Figure 3 and discussion in § 4.2.1). The agreement among disparate simulation codes and physics implementations suggest that these aspects (at minimum) are likely to be robust predictions of galaxy formation in the Lambda Cold Dark Matter paradigm.

Figure 3

Figure 3. Inspiraling cold streams in a galaxy simulation at z = 3. The halo virial radius is annotated by a circle in each panel. Left panel shows projected H number density, and the right panel shows density–weighted line of sight velocity for gas with a minimum density threshold of nH > 3 × 10−3 cm−3 (approximately equivalent to NHI ≳ 1017 cm−2). The coherent bulk rotation of the inspiraling cold streams is apparent and should, in principle, represent an observable test of filamentary gas accretion in LCDM.

4.2.1. Theoretical Predictions: High Angular Momentum, Co–rotation, and Inspiraling Cold Streams

The most direct observable predictions of this new picture, specifically as it relates to angular momentum is thus not likely to come from studies of galaxies themselves (which represent a complex cumulative history of past angular momentum acquisition — including mergers, stream misalignments, etc. — as well as effects from stellar feedback and outflows), but, from observations of the circumgalactic medium. In the canonical picture (outlined in § 3) cold gas in galaxy halos is thought to have cooled out of a virialized hot halo, and should have roughly the same angular momentum distribution as the dark matter. In this new picture, cold gas in galaxy halos should have ∼ 4 times higher spin, and often form coplanar structures of coherent inflowing gas, fueled by filamentary gas accretion. In an attempt to find a middle ground between the different terms in the literature for such structures, we will refer more generally here to these phenomena as resulting from inspiraling cold streams, since the degree to which these structures resemble the disk–like (Stewart et al., 2011b, Stewart et al., 2013) or ring–like (Danovich et al., 2015) morphologies from previous work may be sensitive to specific hydrodynamic codes, feedback implementations, and possibly the halo mass scale involved.

Figure 3 shows one example of inspiraling cold streams in a galaxy halos, taken from a cosmological hydrodynamic zoom–in simulation and visualized on the scale of the halo virial radius (denoted by the circle in each panel). The left panel shows the projected H number density and the right panel showing the projected density–weighted line of sight velocity for all sight lines that meet a minimum column density threshold 4 of NHI ≳ 1017 cm−2. The coherent rotational structure of the inspiraling cold streams (fueled and kinematically connected to the larger filamentary geometry) is apparent. Encouragingly, this type of extended rotational structure of inflowing gas bears a striking similarity to recent observations of giant protogalactic disks (Martin et al., 2015, Martin et al., 2016), which have been detected in Mvir ∼ 5 × 1012 M halos at z ∼ 2−3. In qualitative agreement with simulations, these observed disk–like structures extend to diameters of ∼100 kpc (∼ Rvir / 2), with rotational velocities of ∼ 300 km/s that show a kinematic connection to an inflowing filament, and have very high angular momentum (estimated λ ∼ 0.1−0.3), with orbital times comparable to the halo dynamical time.

In an effort to compare simulations to absorption line studies that match absorber kinematics to the rotation curve of the associated galaxy, Stewart et al. (2011b) also created mock absorption sightlines to infer that, for inflowing gas, ∼ 90% of absorbers with NHI ≳ 1016 cm−2 should have line of sight velocities completely offset from the system velocity of the galaxy in a single direction (per sightline) by ∼ 100 km/s, with most of these absorbers roughly co–rotating with the galactic disk. Again, the results from simulations are in encouraging agreement with recent absorption studies where the associated galaxy kinematics are known (e.g., Bouché et al., 2016, Bowen et al., 2016, also see § 4.1), though larger statistical samples of both observations and high resolution zoom–in simulations will be important for characterizing the level of agreement in detail.

3 Insofar as the angular momentum of spheroids at low redshift are still thought to be most strongly correlated with the merger history of its dark matter halo, we note that the following discussion mostly pertains to the newfound importance of filamentary cold accretion to the growth of massive disk–dominated galaxies, or to the properties of gaseous halos of galaxies. Back.

4 In detail, a minimum 3D hydrogen density cutoff of nH > 3 × 10−3 cm−3 was implemented, however, this should correspond to a minimum hydrogen column density of NHI ≳ 1017 cm−2 (e.g., Altay et al., 2011, Schaye, 2001) Back.

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