DWARF GALAXIES AND THE COSMIC WEB

A long-standing puzzle concerns the striking difference between the shape of the galaxy stellar mass function and the cold dark matter halo mass function on dwarf galaxy scales (White & Rees 1978): dwarfs are much less numerous than halos massive enough, in principle, to host them (Klypin et al. 1999; Moore et al. 1999). This is usually reconciled by appealing to baryonic processes that drastically reduce the efficiency of galaxy formation in low-mass halos. In order to match the latest galaxy clustering and abundance data, recent models (Moster et al. 2010; Guo et al. 2010) require that very few galaxies must form in halos with virial⁶ mass below ∼10¹⁰ M_☉. In addition, these models suggest a steep relation between dwarf galaxy mass and halo mass, so that most dwarfs (defined in terms of their stellar mass; 10⁶ < M_gal/M_☉ < 10^9.5) are expected to form in halos spanning a narrow range in virial mass.

These scalings are thought to arise from the combined effects of photoionization by the cosmic UV background (see, e.g., Bullock et al. 2000) and feedback energy from evolving stars (e.g., Benson et al. 2003). However, there are indications that these mechanisms alone may fall short. Ionizing radiation can effectively prevent gas accretion only in halos below 10⁹ M_☉ (Crain et al. 2007); in addition, the feedback energy required to regulate star formation seems to exceed what is released by supernovae (see, e.g., Scannapieco et al. 2011; Brook et al. 2012 and references within), a difficulty exacerbated by the low efficiency with which feedback couples to the surrounding medium. This is especially true for the faintest galaxies, where the small number of stars excludes feedback as a major energetic source, unless ad hoc modifications to the Initial Mass Function (IMF) are invoked (Peñarrubia et al. 2012).

Finally, there is growing observational evidence that many dwarf galaxies form in halos with masses well below 10¹⁰ M_☉ (Boylan-Kolchin et al. 2011; Ferrero et al. 2012), raising concerns about the general validity of the assumption that dwarfs inhabit relatively massive halos. Identifying an additional mechanism able to reduce the efficiency of galaxy formation in low-mass halos would help to allay concerns that modifications to the current paradigm (such as a "warm dark matter" particle) might be needed in order to reconcile ΛCDM with observation. In this Letter, we show that ram-pressure stripping, long advocated as an important mechanism for regulating star formation in galaxy clusters and satellite galaxies (e.g., Gunn & Gott 1972; Abadi et al. 1999; McCarthy et al. 2008 and references therein), may also operate on isolated low-mass halos as they travel through the cosmic web.

We address these issues here using a Local Group simulation from the CLUES⁷ Project (Gottlöber et al. 2010). The simulation follows the environment of three dark matter halos that match the relative positions of the three main spirals in the Local Group: the Milky Way (MW), Andromeda (M31), and Triangulum (M33) galaxies. These halos are identified in a cosmological box 87.7 Mpc on a side, constrained by observational data to match our nearby large-scale environment.

The Local Group region is then resimulated using a zoom-in technique (Klypin et al. 2001) where an 80 Mpc³ volume is evolved at high resolution embedded in a lower-resolution version of the full box. The high-resolution region (a roughly spherical region of 2.74 Mpc radius at z = 0) is filled with ∼53 million dark matter particles of mass 3.48 × 10⁵ M_☉ and with the same number of 6.05 × 10⁴ M_☉ gas particles. The Plummer-equivalent gravitational softening is = 0.14 kpc. Stars are modeled as collisionless particles of mass m_str = 3.03 × 10⁴ M_☉ spawned by gas particles when they are eligible to form stars.

The simulations adopt cosmological parameters consistent with WMAP-3 (Spergel et al. 2007) and were run with the GADGET-2 (Springel 2005) code. They include an evolving cosmic ionizing UV background (Haardt & Madau 1996), star formation, supernova feedback, and isotropic winds according to Springel & Hernquist (2003); all are calibrated to reproduce, approximately, the stellar masses and morphologies of the three main Local Group spirals. We refer the interested reader to Libeskind et al. (2011), Di Cintio et al. (2012), and Knebe et al. (2011) for further details about these simulations.

Figure 1 shows the evolution of the gas component of the high-resolution region. Labels identify the position of the three main halos, where the galaxy analogs to MW, M31, and M33 form. Several other galaxies form in halos of lower mass, as well as in subhalos of the main three spirals; we shall exclude from the analysis that follows all satellites and focus on the central galaxies of halos with M₂₀₀ > 10¹⁰ M_☉. This choice ensures that the properties we study are not influenced by effects, such as tidal stripping, that arise from the interaction of a galaxy with the halo of a more massive system.

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The evolution of the gaseous component depicted in Figure 1 is similar to that of the dark matter (not shown) when viewed on these large scales, and shows the early development of highly aspherical features such as filaments and pancakes that characterize structure formation in ΛCDM. The tracks that crisscross the figure highlight the trajectories of several dwarf galaxies and illustrate the paths they follow as they are assembled into the Local Group. One of the galaxies (identified as "17") is at rest at the origin of the reference frame.

Figure 2 summarizes the properties of these galaxies⁸ at z = 0. The top-right panel shows that the simulated galaxies form two groups, one of systems that are forming stars at rates roughly comparable to their past average (green triangles) and a second group where star formation has largely ceased (red circles). The latter are galaxies that have lost most of their baryons during their evolution; indeed, none of these galaxies has retained more than ∼20% of the baryons within their virial radius (bottom-left panel). It might be tempting to ascribe the loss of baryons to the effects of feedback-driven winds, but there are galaxies that have retained more baryons (bottom-left panel) and where star formation has continued to the present (top-right panel), despite having formed more stars overall and inhabiting halos of similar virial mass.

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A clue to the origin of the baryon-poor, non-star-forming galaxies is provided in the bottom-right panel of the same figure. This shows the evolution of the mass within the virial radius of the main progenitor of galaxy 30. The solid and dotted curves indicate the mass in the gaseous and stellar components (the dashed curve indicates the total; scale on left), whereas the dot-dashed green curve indicates the baryon fraction of the system, M_bar/(f_bar M₂₀₀) (scale on right), where M_bar is the sum of gas and stellar masses and f_bar = Ω_b/Ω_M is the universal baryon fraction. This shows that most baryons are lost over a short period of time, between z = 3 and z = 2. Very few stars form after z = 3, so that baryon loss cannot be due solely to feedback-driven winds.

The loss of baryons highlighted above is the main reason why this galaxy has stopped forming stars. Indeed, star formation ceases in galaxy 30 just after z ∼ 2, as may be seen in the right-hand panels of Figure 3, where we show the distribution of stellar ages of galaxies 30, 50, and 17. All three galaxies have similar star formation histories, and stop forming stars at roughly the same time. Their star formation histories differ markedly from those of galaxies that are still forming stars at z = 0, three of which are shown in the left-hand panel of Figure 3.

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What causes the peculiar star formation history of galaxy 30, which is in turn paralleled by galaxies 17 and 50? It is not their halo mass; for example, the virial mass of galaxy 35 is similar to that of galaxy 50, but is still forming stars at z = 0 at a rate roughly 50 times higher. We can gain some insight by considering in more detail the trajectories of galaxies 17, 30, and 50 shown in Figure 1. This figure reveals a common feature in the evolution of these three galaxies: they all cross more or less simultaneously a large pancake of gas at z ∼ 2. In the reference frame chosen for that plot (where galaxy 17 is at rest), the pancake sweeps past galaxy 17 at z ∼ 1.8; galaxies 30 and 50 overtake the pancake at about the same time.

A more detailed analysis of the galaxy–pancake interaction is presented in Figure 4, where we show, at two different times (just before and after the interaction), the density and velocity profiles of galaxy 17 and the pancake. The two panels on the left show the gas distribution (colored by density on a logarithmic scale) in the vicinity of the galaxy, which is at rest at the coordinate origin. The pancake is moving along the z-axis, from positive-z to negative-z values. The two vertical dashed lines indicate the virial radius of galaxy 17 at the current time.

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At z = 1.83, corresponding to the top row, the pancake is still above the galaxy, but approaching at high speed. This may be seen in the right-hand panels, which show the z-component of the gas velocity along the cylinder delineated by the vertical lines in the left-hand panel. The cylinder, whose radius is chosen to be the same as the virial radius of the galaxy, is aligned with the z-axis and therefore roughly perpendicular to the pancake. The gas density in the cylinder, as a function of z, is shown in the middle panels. At z = 1.38, which corresponds to the bottom row, the pancake has already swept past the galaxy and is found at z ∼ −400 kpc.

It is clear from Figure 4 that the interaction between the galaxy and the pancake leads to the removal of much of the gaseous halo of galaxy 17, which may be seen streaming down toward the pancake in the bottom-left panel. This is clear evidence that the ram pressure of the interaction is responsible for the sudden loss of baryons that affects galaxy 17 at z ∼ 1.8. Since not all of the gas is removed, the galaxy is able to continue forming stars for a little longer before running out of gas. Although not shown in Figure 4, a similar process affects galaxies 30 and 50 as they traverse the pancake, as well as the rest of the galaxies labeled in Figure 2 as non-star forming.

One may wonder how the pancake, which is only a few times overdense relative to the mean baryonic density of the Universe (see middle panels of Figure 4), is able to remove the much denser gas that fills the halo of galaxy 17. The main reason for this is the high speed at which the galaxy plows through the pancake. The effective ram pressure on the galaxy is proportional to the density of the pancake times the velocity of the interaction squared, P_ram∝ρ_pV²_p, where V_p is the velocity of the pancake if the galaxy is assumed at rest. This pressure must exceed that exerted on the gas by the restoring force of the halo, which is roughly proportional to P_gal∝ρ_galV²₂₀₀, where ρ_gal is the gas density and V₂₀₀ is the halo virial velocity.

For the case illustrated in Figure 4, the pancake velocity is of the order of 300 km s⁻¹, almost an order of magnitude higher than the virial velocity of the halo at the time, V₂₀₀ ∼ 40 km s⁻¹. This means that the pancake can strip gas from the galaxy even if the galactic gas is ∼(V_p/V₂₀₀)² ∼ 60 times denser. A further condition must be satisfied for ram-pressure stripping to be effective, namely that the pancake is massive enough so that the column density of gas that sweeps past the galaxy is comparable to its total gas content. We have verified that this is indeed the case: the total pancake gas mass intersected by the cylinder shown in Figure 4 exceeds the gas content of galaxy 17 by more than a factor of two.

Although gas removal through interaction with the cosmic web is a robust feature of the simulation, the fate of the gas that remains in the galaxy or is accreted later is less clear, since it is subject to the complex (and poorly modeled) process of star formation and associated feedback. Indeed, there is indication that the star formation recipes adopted in CLUES might need revision; note, for example, that most dwarfs lie above the M_gal–M₂₀₀ relation indicated by recent abundance-matching analysis (Guo et al. 2010; top-left panel of Figure 2). In addition, there seem to be fewer non-star-forming isolated dwarfs in the local Universe than in our simulation (Geha et al. 2012). Therefore, the actual stellar masses of the simulated dwarfs or the lack of ongoing star formation should not necessarily be considered a defining characteristic of the scenario we describe here. Our results should be interpreted as emphasizing the importance of the cosmic web on the overall baryonic content of dwarf galaxy halos rather than as definitive predictions to be compared directly with observation.

The importance of "cosmic web stripping" on isolated low-mass halos has not been recognized before because it is a purely hydrodynamical effect that would be completely missed in semi-analytic modeling and that requires simulations of large volumes able to resolve properly both the cosmic web and the internal halo properties. This demands numerical resources that are only now becoming available. It also requires careful tracking of the baryonic content of dwarf galaxies in order to discriminate between the competing effects of reionization, feedback, and stripping. Since all of these effects act to remove baryons from low-mass halos, it is even possible that the effects of cosmic web stripping may have already been seen (see, e.g., Sawala et al. 2012). Although these authors list ram pressure as a key ingredient of galaxy formation modeling, they do not explicitly recognize the possibility that the stripping by the cosmic web might affect the baryonic content of low-mass halos.

Cosmic web stripping is a natural consequence of the shape of the ΛCDM power spectrum on dwarf galaxy scales. It results from the nearly simultaneous assembly of very different mass scales; at the same time that the 10¹⁰ M_☉ halos are being assembled, the collapse of the nearly 10¹³ M_☉ Local Group has already started and is well under way in one dimension, leading to the formation of a large pancake. Although the CLUES simulation we analyze here is too small to enable a proper assessment of the importance of cosmic web stripping outside Local Group like environments, we see no reason why this mechanism should not affect a substantial fraction of dwarf galaxies; after all, the Local Group represents only a mild overdensity on a mass scale close to the characteristic clustering mass today. Cosmic web stripping is thus very likely a crucial ingredient of the star formation history of dwarf galaxies so far missing from models that rely solely or largely on the assembly of the dark matter.

Its appeal comes in part from its strong dependence on halo mass. Because of the (V_p/V₂₀₀)² scaling mentioned above, a pancake sweeping past halos of different mass could fully strip the gas reservoir of low-mass halos whilst leaving massive halos relatively undisturbed. This might help to explain the steep galaxy mass–halo mass relation required to match the faint end of the galaxy luminosity function. We emphasize that stripping must operate in concert with cosmic reionization and feedback if ΛCDM models are to be viable. This is because Mpc-scale pancakes and filaments do not develop typically until z ∼ 2, so a further mechanism that prevents most baryons in low-mass halos from turning into stars before then is still needed.

How can we test these ideas observationally? Because cosmic web stripping affects only baryons, its effects are intertwined with those of radiative cooling, reionization, star formation, and feedback, and it is difficult to devise a clean and conclusive test. It is nevertheless encouraging that several observations are in natural accord with a scenario where cosmic web stripping plays a substantial role. The existence of isolated dwarf spheroidal galaxies devoid of gas and made up of mostly old stars, such as Cetus and Tucana, is one such observation. Indeed, cosmic web stripping might explain why these galaxies ceased forming stars much later than the epoch of reionization (Monelli et al. 2010a, 2010b), the oft-cited culprit of halting star formation in dwarf galaxies.

Cosmic web stripping should also leave an environmental imprint, as galaxies more severely affected by interaction with the cosmic web should cluster differently from others that are impacted less. It is not possible to divine what the actual imprint might be from one Local Group simulation, but this is an area where future simulation and observational work should prove especially fruitful. Detection of the telltale signs of ram-pressure stripping in isolated dwarfs would be especially interesting, and it might have already been observed (McConnachie et al. 2007). Finally, we note that a galaxy might interact with the cosmic web several times during its evolution, and that each of these events might serve to shape different episodes of star formation. It is certainly tempting to speculate that the existence of multiple populations in dwarf galaxies like Carina (Monelli et al. 2003; Bono et al. 2010) might originate from its travels through the cosmic web. Targeted future work will help us to gauge the true importance of the cosmic web in shaping the formation and evolution of the faintest galaxies.