Impact of filaments on galaxy formation in their residing dark matter haloes
MMNRAS , 000–000 (0000) Preprint 15 February 2019 Compiled using MNRAS L A TEX style file v3.0
Impact of filaments on galaxy formation in their residing darkmatter haloes
Shihong Liao (cid:63) and Liang Gao , Key Laboratory for Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012, China Institute of Computational Cosmology, Department of Physics, University of Durham, Science Laboratories, South Road, Durham DH1 3LE, UK
15 February 2019
ABSTRACT
We make use of a high-resolution zoom-in hydrodynamical simulation to investigate the im-pact of filaments on galaxy formation in their residing dark matter haloes. A method based onthe density field and the Hoshen-Kopelman algorithm is developed to identify filaments. Weshow that cold and dense gas preprocessed by dark matter filaments can be further accretedinto residing individual low-mass haloes in directions along the filaments. Consequently, com-paring with field haloes, gas accretion is very anisotropic for filament haloes. About 30 percentof the accreted gas of a residing filament halo was preprocessed by filaments, leading to twodifferent thermal histories for the gas in filament haloes. Filament haloes have higher baryonand stellar fractions when comparing with their field counterparts. Without including stellarfeedback, our results suggest that filaments assist gas cooling and enhance star formation intheir residing dark matter haloes at high redshifts (i.e. z = 4 . and . ). Key words: methods: numerical - galaxies: formation - galaxies: haloes
In the classic galaxy formation framework (e.g., White & Rees1978; White & Frenk 1991), to form luminous galaxies, primor-dial gas should fall into the potential wells created by dark matterhaloes, be shock heated and become ionized, cool radiatively, andform stars. Comparing with dark matter haloes, massive filamentshave the same function to provide potential wells to trap gas. Asdemonstrated in Gao & Theuns (2007) and Gao et al. (2015), gasaccretion into filaments can be very similar to what happens in darkmatter haloes in warm dark matter (WDM) models, namely that thegas is shock heated at the boundary of filaments, cools radiativelyand condenses into the filament centres to form stars.While the above two studies mainly focus on gas physics in fil-aments in WDM models, the same physics should of course applyto cold dark matter (CDM) models because the large scale struc-tures of filaments are quite similar in both models. As shown ina hydrodynamical simulation of Gao et al. (2015) and many otherstudies (e.g. Kereˇs et al. 2005; Dekel & Birnboim 2006), there in-deed exists cold and dense gas flows, preprocessed by dark mat-ter filaments, in the centres of CDM filaments at high redshifts.The phenomenon that cold and dense gas flows fuel massive cen-tral galaxies is termed “cold accretion”, and it has been extensivelystudied in many literatures (e.g. Kereˇs et al. 2005; Dekel & Birn-boim 2006; Ocvirk et al. 2008; Brooks et al. 2009; Dekel et al.2009; Kereˇs et al. 2009; van de Voort et al. 2011; Danovich et al. (cid:63)
Email: [email protected] M (cid:63) > h − M (cid:12) and redshifts z < . , tend to havehigher stellar masses and lower star formation rates when they re-side closer to the cylindrical centre of a filament. Similar conclu-sions were seen by galaxies with higher redshifts ( z (cid:46) . in theGAMA survey (Kraljic et al. 2018), the VIPERS survey (Malavasiet al. 2017), the COSMOS2015 galaxy catalogue (Darvish et al.2017; Laigle et al. 2018) and the SDSS survey (Chen et al. 2017;Kuutma et al. 2017; Poudel et al. 2017).In this study, we use a high-resolution cosmological hydrody-namical simulation to study the gas accretion and star formationof low-mass haloes residing in filaments formed at high redshiftswithin the Lambda cold dark matter ( Λ CDM) model. The paper isstructured as follows. We overview the details of the simulation,and present our filament identification methods in Section 2. Thedetailed gas accretion process in residing low-mass haloes of fila- c (cid:13) a r X i v : . [ a s t r o - ph . GA ] F e b Liao & Gao ments, and the impacts of filaments on galaxy formaition are dis-cussed in Section 3. Section 4 summarizes our results.
The simulation used in this study is a high-resolution hydrody-namical re-simulation of an individual galactic sized halo, Aq-A,from the Aquarius project (Springel et al. 2008). This simulationhad been used to study the star-forming filaments in Gao et al.(2015). The cosmological parameters adopted in the simulation are Ω m = 0 . , Ω b = 0 . , Ω Λ = 0 . , σ = 0 . and h = 0 . .The mass resolution of dark matter particles in the high-resolutionregion of the simulation is m DM = 2 . × h − M (cid:12) , and itis m gas = 5 . × h − M (cid:12) for each gas particle. The forceresolution is (cid:15) = 0 . h − kpc in comoving units.The simulation includes radiative cooling and photo-heatingof a primordial gas in the presence of a UV/X-ray background fromgalaxies and quasars (Haardt & Madau 1996). The simulation as-sumes that the HI ionization occurs at z = 6 . To model star forma-tion, the simulation converts gas into stars with a physical hydrogendensity threshold of n H = 0 . − and an overdensity thresholdof ρ gas / ¯ ρ gas = 2000 . Note that, as a first step, this study focuses onthe investigation of gas accretion and cooling in filaments and theirresiding low-mass dark matter haloes, and feedbacks from super-novae and active galactic nuclei are not included in the simulation.The simulation has been evolved from z = 127 to the present dayusing GADGET -3 code (Springel 2005).We adopt the Amiga Halo Finder (
AHF , Knollmann & Knebe2009) to identify haloes in the high-resolution region of our sim-ulation with a virial parameter of ∆ vir = 200 measured with re-spect to the critical density. Note that in the remaining of this ar-ticle, we simply call an AHF identified structure as a “halo” in-stead of a “galaxy”, although it may contain gas and stars. Wehave identified all individual haloes with more than particles,but only adopt those with at least particles to carry out ouranalysis. The mass range of our halo catalogue is approximately [10 . , ] h − M (cid:12) . To avoid possible influences from the cen-tral Aq-A halo and the boundary of the zoom-in region, we only usehaloes whose comoving distances from the centre of the Aq-A halo, r , satisfy R , AqA ( z ) < r < h − Mpc . Here, R , AqA ( z ) isthe virial radius of the Aq-A halo at redshift z in comoving units.Haloes containing low-resolution dark matter particles are furtherexcluded from our sample. There are and such haloes, whichcorrespond to . and . of the total halo numbers, at z = 4 . and . respectively. The total number of our selected haloes aresummarized in the fourth column of Table 1.In Fig. 1, we provide a visual impression of the formation ofthe Aq-A halo at z = 10 . , . , . , . , and . . From left to rightcolumn, we show dark matter overdensity, HI column density andgas temperature, respectively. The panels are centred on the Aq-A halo with a comoving scale h − Mpc. The circles around thecentres of left panels indicate the virial radii of the halo at corre-sponding redshifts. At high redshifts, the proto Aq-A halo lies inintersection of a few massive filaments. This feature is quite com-mon for massive galaxies at high redshifts (e.g. Kereˇs et al. 2005;Dekel & Birnboim 2006; Ocvirk et al. 2008; Dekel et al. 2009;Kereˇs et al. 2009; van de Voort et al. 2011; Danovich et al. 2012).
Table 1.
Number of haloes in the halo sample at different redshifts z Filament Field Total . . This study is focused on the galaxy formation in filaments, thusit is essential to identify filaments from the simulation. As we aremost interested in investigating the baryonic physics in filaments,our identification procedure is based on the baryonic density and isdescribed as follows.(i) Assign the baryonic (gas and star particles) density onto a dimensional grid with the Cloud-In-Cell (CIC) method. Anillustration of the baryonic density fields at z = 4 . and . ispresented in Panels (a) and (d) of Fig. 2 respectively.(ii) Exclude the spherical region with radius r = 2 R , AqA from the Aq-A halo centre as the main halo is not of interest in thisstudy. The excluded spheres at z = 4 . and z = 2 . are markedwith dotted circles in Panels (a) and (d) of Fig. 2 respectively.(iii) Select the grid cells with densities satisfying ρ b ( r i ) /ρ cri (cid:62) ∆ th , where ∆ th is a free parameter to repre-sent the baryonic overdensity. We adopt a value of . for ∆ th ,corresponding to a total matter overdensity of ρ m ( r i ) /ρ cri ≈ .A projection on the xy plane of the selected grid cells can be foundin Panels (b) and (e) of Fig. 2, where we can see some continuousfilamentary structures and many small and isolated patches. Thesesmall patches are those grid cells that contain isolated haloes.(iv) Link the neighbouring grid cells selected in the procedure(iii) into groups with the Hoshen-Kopelman algorithm (Hoshen &Kopelman 1976), which was originally put forward in percolationstudies. For each group, we define its size, S , by counting howmany grid cells it has. We only keep groups with sizes S (cid:62) S th , anddefine them as filaments. The size threshold parameter S th is set tobe in this study. A visualization of the identified filamentsis shown in Panels (c) and (f) of Fig. 2. If a grid cell belongs to afilament group, then it is defined as a filament grid cell; otherwise itis a field grid cell. If an object (e.g., particle, halo, etc.) has its centrein a filament/field grid cell, then it is called a filament / field object(e.g., particle, halo, etc.). The total number of haloes in filamentsand fields at z = 4 . and . are presented in the second and thirdcolumn of Table 1.The identification method outlined above has two free parame-ters, ∆ th and S th . The overdensity parameter, ∆ th , is similar to thevirial overdensity parameter used in a spherical overdensity halofinder, which determines the boundary of an identified structure.The size parameter, S th , sets the minimum size for identified fila-ments and naturally excludes those isolated groups shown in Pan-els (b) and (e) of Fig. 2. These two parameters have clear physicalmeanings, and their values are set empirically. In this study, wechoose (∆ th , S th ) = (3 . , , which generates clear filamen-tary structures according to human eyes’ judgements. We have per-formed parallel analysis with other parameter sets (e.g., ∆ th = 2 . or . , and S th = 500 ), and confirmed that our results are not sen-sitive to the chosen values of ∆ th and S th . MNRAS000
Number of haloes in the halo sample at different redshifts z Filament Field Total . . This study is focused on the galaxy formation in filaments, thusit is essential to identify filaments from the simulation. As we aremost interested in investigating the baryonic physics in filaments,our identification procedure is based on the baryonic density and isdescribed as follows.(i) Assign the baryonic (gas and star particles) density onto a dimensional grid with the Cloud-In-Cell (CIC) method. Anillustration of the baryonic density fields at z = 4 . and . ispresented in Panels (a) and (d) of Fig. 2 respectively.(ii) Exclude the spherical region with radius r = 2 R , AqA from the Aq-A halo centre as the main halo is not of interest in thisstudy. The excluded spheres at z = 4 . and z = 2 . are markedwith dotted circles in Panels (a) and (d) of Fig. 2 respectively.(iii) Select the grid cells with densities satisfying ρ b ( r i ) /ρ cri (cid:62) ∆ th , where ∆ th is a free parameter to repre-sent the baryonic overdensity. We adopt a value of . for ∆ th ,corresponding to a total matter overdensity of ρ m ( r i ) /ρ cri ≈ .A projection on the xy plane of the selected grid cells can be foundin Panels (b) and (e) of Fig. 2, where we can see some continuousfilamentary structures and many small and isolated patches. Thesesmall patches are those grid cells that contain isolated haloes.(iv) Link the neighbouring grid cells selected in the procedure(iii) into groups with the Hoshen-Kopelman algorithm (Hoshen &Kopelman 1976), which was originally put forward in percolationstudies. For each group, we define its size, S , by counting howmany grid cells it has. We only keep groups with sizes S (cid:62) S th , anddefine them as filaments. The size threshold parameter S th is set tobe in this study. A visualization of the identified filamentsis shown in Panels (c) and (f) of Fig. 2. If a grid cell belongs to afilament group, then it is defined as a filament grid cell; otherwise itis a field grid cell. If an object (e.g., particle, halo, etc.) has its centrein a filament/field grid cell, then it is called a filament / field object(e.g., particle, halo, etc.). The total number of haloes in filamentsand fields at z = 4 . and . are presented in the second and thirdcolumn of Table 1.The identification method outlined above has two free parame-ters, ∆ th and S th . The overdensity parameter, ∆ th , is similar to thevirial overdensity parameter used in a spherical overdensity halofinder, which determines the boundary of an identified structure.The size parameter, S th , sets the minimum size for identified fila-ments and naturally excludes those isolated groups shown in Pan-els (b) and (e) of Fig. 2. These two parameters have clear physicalmeanings, and their values are set empirically. In this study, wechoose (∆ th , S th ) = (3 . , , which generates clear filamen-tary structures according to human eyes’ judgements. We have per-formed parallel analysis with other parameter sets (e.g., ∆ th = 2 . or . , and S th = 500 ), and confirmed that our results are not sen-sitive to the chosen values of ∆ th and S th . MNRAS000 , 000–000 (0000) mpact of filaments on galaxy formation Figure 1.
Visualization of the dark matter overdensity (left), HI column density (middle) and gas temperature (right) in our simulation at z =10 . , . , . , . , and . (from top to bottom). At each redshift, we select a comoving cubic region centering on the center-of-mass of the zoom-in re-gion and project it on the xy plane. The edge length of the cube is h − Mpc . The dotted circles in the first column mark the position and virial radius of theprogenitor of the Aq-A halo. The color bars are shown on the top of each column. We can see several massive filaments form at z = 4 . and penetrate intothe Aq-A halo, and become more massive at z = 2 . . We will focus on the gas accretion and halo formation inside these filaments in later discussions.MNRAS , 000–000 (0000) Liao & Gao − − − y / h − M p c z = 4 . CIC baryonic density (b) ρ b /ρ cri ≥ ∆ th = 3 . S ≥ S th = 1000 − − − − − − z = 2 . CIC baryonic density − − − x/h − Mpc(e) ρ b /ρ cri ≥ ∆ th = 3 . − − − S ≥ S th = 1000 Figure 2.
Filament identification at z = 4 . and . . Panels (a-c) illustrate the xy − projected baryonic density field of the zoom-in region at z = 4 . computed with the CIC assignment method, the grid cells with ρ b /ρ cri (cid:62) ∆ th = 3 . , and the groups linked by the Hoshen-Kopelman algorithm with sizes S (cid:62) S th = 1000 respectively. The dotted circle in Panel (a) marks the spherical region with radius r = 2 R , AqA centred at the Aq-A halo. This sphericalregion is excluded when identifying filaments in Panels (b) and (c). Panels (d-f) show similar plots at z = 2 . . To illustrate the gas accretion in filaments, in Fig. 3, we select thenewly accreted particles from a pronounced filament at quadrantIII of the projected xy plane at z = 4 . , and project their positionsat several recorded redshifts. These “newly accreted” particles areidentified as members of the filament at z = 4 . but not at thelast adjacent recorded snapshot. These particles are shown as greendots on the top of a gray-scale dark matter density map in panel (g).We also trace the motions of these gas particles before and after z = 4 . to illustrate their evolution. To see whether these gas parti-cles can later join into individual haloes in the filament, we plot thefilament haloes with masses more massive than h − M (cid:12) withblack circles with sizes scaled to their R . Cleary, these particleswere quite diffusely distributed around the filament at early epochsand later were perpendicularly accreted into the filament. Afterthese particles joined the filament, they rapidly condensed to thefilament centre. Some of them were further accreted into filamenthaloes and eventually turned into stars (cyan dots) at lower red-shifts, whereas some penetrated into the Aq-A halo centre through“cold accretion”.To illustrate how the newly accreted filament gas particlescan later join in filament haloes, we choose a filament halo z = 2 . (marked as a red circle in panel (j)), and identify its gasparticles which were newly associated with the filament at z = 4 . ,and trace them forward and backward to see their evolution. Thepositions of these particles are plotted as colored dots at z = 4 . ,and their color hues change as time according to their tempera-tures. One can clearly see that the gas accretion of the halo is quite anisotropic once they join into the filament, with the direction alongthe filament. At z = 1 . , almost all of these gas particles acquiredat z = 4 . have turned into stars, which relates to the fact that wedo not include feedback in the simulation. For a comparison, in thesame figure, we show an example of the formation of a nearby fieldhalo × h − M (cid:12) , which is similar to that of the halo ∆ th = 3 . at z = 4 . but exceed this thresh-old at z = 4 . . Apparently, the gas accretion of the field halo isquite isotropic.From the above images, comparing with the field halo, gasaccretion is more anisotropic for the filament halo (see AppendixA for a further quantitative comparison between filament and fieldhaloes). Apart from this, in addition to the classic gas cooling fora halo, the filament halo also acquires part of its cold and densegas preprocessed by its surrounding filament environment. In Fig.4, we illustrate clearly two different gas cooling modes in filamenthaloes. For the halo T max , inside the halo. Then weselect 5 random gas particles from each subsample, and plot theirtemperatures as a function of redshift in Panels (a) and (b) of Fig.4, respectively. Note that we use thin (thick) lines to distinguish gasparticles which lie outside (inside) R of the halo. In Panel (a),all of these 5 particles reach their maximum temperatures insidethe halo z ∼ MNRAS000
Filament identification at z = 4 . and . . Panels (a-c) illustrate the xy − projected baryonic density field of the zoom-in region at z = 4 . computed with the CIC assignment method, the grid cells with ρ b /ρ cri (cid:62) ∆ th = 3 . , and the groups linked by the Hoshen-Kopelman algorithm with sizes S (cid:62) S th = 1000 respectively. The dotted circle in Panel (a) marks the spherical region with radius r = 2 R , AqA centred at the Aq-A halo. This sphericalregion is excluded when identifying filaments in Panels (b) and (c). Panels (d-f) show similar plots at z = 2 . . To illustrate the gas accretion in filaments, in Fig. 3, we select thenewly accreted particles from a pronounced filament at quadrantIII of the projected xy plane at z = 4 . , and project their positionsat several recorded redshifts. These “newly accreted” particles areidentified as members of the filament at z = 4 . but not at thelast adjacent recorded snapshot. These particles are shown as greendots on the top of a gray-scale dark matter density map in panel (g).We also trace the motions of these gas particles before and after z = 4 . to illustrate their evolution. To see whether these gas parti-cles can later join into individual haloes in the filament, we plot thefilament haloes with masses more massive than h − M (cid:12) withblack circles with sizes scaled to their R . Cleary, these particleswere quite diffusely distributed around the filament at early epochsand later were perpendicularly accreted into the filament. Afterthese particles joined the filament, they rapidly condensed to thefilament centre. Some of them were further accreted into filamenthaloes and eventually turned into stars (cyan dots) at lower red-shifts, whereas some penetrated into the Aq-A halo centre through“cold accretion”.To illustrate how the newly accreted filament gas particlescan later join in filament haloes, we choose a filament halo z = 2 . (marked as a red circle in panel (j)), and identify its gasparticles which were newly associated with the filament at z = 4 . ,and trace them forward and backward to see their evolution. Thepositions of these particles are plotted as colored dots at z = 4 . ,and their color hues change as time according to their tempera-tures. One can clearly see that the gas accretion of the halo is quite anisotropic once they join into the filament, with the direction alongthe filament. At z = 1 . , almost all of these gas particles acquiredat z = 4 . have turned into stars, which relates to the fact that wedo not include feedback in the simulation. For a comparison, in thesame figure, we show an example of the formation of a nearby fieldhalo × h − M (cid:12) , which is similar to that of the halo ∆ th = 3 . at z = 4 . but exceed this thresh-old at z = 4 . . Apparently, the gas accretion of the field halo isquite isotropic.From the above images, comparing with the field halo, gasaccretion is more anisotropic for the filament halo (see AppendixA for a further quantitative comparison between filament and fieldhaloes). Apart from this, in addition to the classic gas cooling fora halo, the filament halo also acquires part of its cold and densegas preprocessed by its surrounding filament environment. In Fig.4, we illustrate clearly two different gas cooling modes in filamenthaloes. For the halo T max , inside the halo. Then weselect 5 random gas particles from each subsample, and plot theirtemperatures as a function of redshift in Panels (a) and (b) of Fig.4, respectively. Note that we use thin (thick) lines to distinguish gasparticles which lie outside (inside) R of the halo. In Panel (a),all of these 5 particles reach their maximum temperatures insidethe halo z ∼ MNRAS000 , 000–000 (0000) mpact of filaments on galaxy formation Figure 3.
Illustration of the process that gas particles are accreted into a filament, and subsequently into dark matter haloes, and finally they form stars. Weselect a filament in quadrant III of the xy -projected baryonic density at z = 4 . shown in Fig. 2. To see how the gas is accreted into this filament and itsfate, we select those gas particles that are newly accreted into the filament at z = 4 . and mark them with green dots (Panel (g)). We then trace the selectedparticles back to higher redshifts (Panels (a-f)), and follow their later evolution (Panels (h-l)). The black circles mark the filaments haloes ( z (cid:54) . ) withmasses M > h − M (cid:12) , and the radius of each circle is set to the halo virial radius. The purple circles mark the Aq-A halo. The redshifts are labelled atthe lower right corner of each panel. To see how these gas particles are accreted into haloes in the filament, we select a dark matter halo within the filament (thehalo ∆ th = 3 . at z = 4 . . Once a gas particle turns into a star, it is marked as cyan color. The comoving size of the xy − projected cubic region in eachpanel is h − Mpc . The gray maps show the dark matter density.MNRAS , 000–000 (0000)
Liao & Gao (see Fig. A1 in Appendix A for a visualization of the filament shockfront), and thus reach their maximum temperatures outside the halo.Before they are accreted into the halo ∼ T max / in the filament. As a comparison, we also randomlyselect 5 newly accreted gas particles from the field halo As discussed in the last subsection, for filament haloes, some oftheir gas particles are preprocessed by the filament before joininginto them. An immediate question is, for a filament halo, what isthe fraction of gas experiencing such filament preprocessing. Asdemonstrated in Fig. 4, the gas experiencing filament preprocess-ing has its z max (i.e., the redshift that the gas particle reaches itsmaximum temperature) earlier than its z acc (i.e., the redshift thatthe gas particle is accreted into a halo). Therefore, we can use therelation between z acc and z max to roughly classify gas particlesinto two categories. If z acc (cid:62) z max , the gas is accreted into thehalo without filament preprocessing; while if z acc < z max , the gasis firstly preprocessed in filaments and later accreted into the halo.In the top panel of Fig. 5, we present the probability distribu-tion functions (PDFs) of z max for the newly accreted gas particlesat z = 4 . (i.e. gas particles which are accreted into the halo be-tween z = 4 . and z = 4 . ) for the filament halo T max after z = 4 . as expected in the classic picture of gas accretioninto a halo. While, for the filament halo T max before accretion, and the rest half follows thestandard picture. The results are similar if we plot the distributionsfor all newly accreted gas particles at z = 4 . in all filament andfiled haloes; see the bottom panel of Fig. 5.The fraction of gas preprocessed by filaments can be com-puted as f out ≡ ∆ M gas , out ∆ M gas , (1)where ∆ M gas is the total mass of newly accreted gas, and ∆ M gas , out is the mass of the newly accreted gas with z max > z acc (i.e., the gas that reaches its T max outside the halo). For the newlyaccreted gas in the halo z = 4 . , f out are . and . , respectively.Note that some gas particles may pass through and are later re-accreted to the host halo more than once, and thus have complicatedthermal histories. While it does not affect the results significantlyby including or excluding them (see the curves with light colors inFig. 5), we remove them from our sample.Similarly, we can calculate f out for all filament haloes in oursample. In order to have a robust estimation, we only consider thosehaloes that have at least newly accreted gas particles. Also, inorder to achieve better statistics, we here define the newly accretedgas particles at z acc as those that belong to haloes at z acc but arenot associated to any haloes at z acc + 0 . . In Fig. 6, we plot f out as a function of M for our halo sample at z = 4 . and . .When calculating the median and scatter of f out in each mass bin,we require each mass bin to contain at least haloes. Overall,filament haloes (red dots) tend to have much larger f out than fieldhaloes (blue dots). The median values of f out for both filament andfield haloes seem to be independent of halo mass. At z = 4 . ,the median value of f out for filament haloes is about percent,while it is about percent for field haloes. Results for z = 2 . aresimilar. Note, at z = 4 . , some field haloes have quite large f out .Our examination shows that these haloes usually reside in smallerfilaments with sizes S < S th . As shown in previous subsections, filaments significantly affect theintergalactic medium and gas accretion of the residing dark matterhaloes. In this subsection, we provide comparisons of some gen-eral properties between field and filament haloes. In Fig. 7, we plotbaryon fractions ( f bar ) and star fractions ( f star ) as a function ofvirial masses for the filament and field haloes at z = 4 . and . .Results for filament and field haloes are shown with dotted andcrossed points, respectively. Here, the baryon fraction of a halois defined as the ratio between the baryonic and virial mass, i.e., f bar ≡ M bar /M , and the star fraction is the ratio between thestellar mass and halo mass (i.e., f star ≡ M (cid:63) /M ).To fit the relations between f bar (or f star ) and M , we adoptthe function proposed by Gnedin (2000) with an additional freeparameter f , f bar , star ( M ) = f (cid:20) (cid:16) α/ − (cid:17) (cid:18) M c M (cid:19) α (cid:21) − /α . (2)There are three free parameters, i.e., f , α and M c , in this fittingfunction. Here f is the baryon/star fraction for high-mass haloes(i.e., M (cid:29) M c ), α indicates how rapidly f bar , star drops in thelow-mass end, and M c marks the characteristic mass scale that f bar , star drops to f / . The best fits are shown with solid anddashed lines in each panel for filament and field haloes, respec-tively, and the fitting parameters are labelled as well. Note that herewe have included all haloes with at least particles. We haveparallelly performed the fits for haloes with at least particles,and confirmed that haloes with (cid:46) particles (i.e. with lower res-olutions) do not affect our conclusions presented in the following.Upper two panels display the baryon fraction results. At z =4 . ( z = 2 . ), due to the photoionization by the UV background,haloes with M < . h − M (cid:12) ( M < h − M (cid:12) ) tend tohave lower f bar with decreasing M (see also e.g. Okamoto et al.2008). Interestingly, filament haloes tend to have higher f bar thanfield haloes, and the difference is even larger at z = 2 . . Similartrends can also be found in Metuki et al. (2015), while the differ-ences are very small between the filament and sheet/void haloes at z = 0 . The much larger difference shown here is perhaps becauseof two facts. (i) The dark matter haloes studied here are at higherredshifts and have lower masses; (ii) we focus on the haloes resid-ing in more pronounced filaments.Bottom panels of the same figure show the star fraction as afunction of halo mass at z = 4 . and . . At z = 4 . , star fractionsof filament haloes are slightly higher than those of field ones, andthe excess is further enhanced at z = 2 . . Especially, the enhance-ment of f star in filament haloes is more significant for haloes withlower masses at z = 2 . , implying that filament structures have apositive impact on star formation in low-mass haloes. Metuki et al.(2015) also found similar trends in their simulations, but again the MNRAS000
Liao & Gao (see Fig. A1 in Appendix A for a visualization of the filament shockfront), and thus reach their maximum temperatures outside the halo.Before they are accreted into the halo ∼ T max / in the filament. As a comparison, we also randomlyselect 5 newly accreted gas particles from the field halo As discussed in the last subsection, for filament haloes, some oftheir gas particles are preprocessed by the filament before joininginto them. An immediate question is, for a filament halo, what isthe fraction of gas experiencing such filament preprocessing. Asdemonstrated in Fig. 4, the gas experiencing filament preprocess-ing has its z max (i.e., the redshift that the gas particle reaches itsmaximum temperature) earlier than its z acc (i.e., the redshift thatthe gas particle is accreted into a halo). Therefore, we can use therelation between z acc and z max to roughly classify gas particlesinto two categories. If z acc (cid:62) z max , the gas is accreted into thehalo without filament preprocessing; while if z acc < z max , the gasis firstly preprocessed in filaments and later accreted into the halo.In the top panel of Fig. 5, we present the probability distribu-tion functions (PDFs) of z max for the newly accreted gas particlesat z = 4 . (i.e. gas particles which are accreted into the halo be-tween z = 4 . and z = 4 . ) for the filament halo T max after z = 4 . as expected in the classic picture of gas accretioninto a halo. While, for the filament halo T max before accretion, and the rest half follows thestandard picture. The results are similar if we plot the distributionsfor all newly accreted gas particles at z = 4 . in all filament andfiled haloes; see the bottom panel of Fig. 5.The fraction of gas preprocessed by filaments can be com-puted as f out ≡ ∆ M gas , out ∆ M gas , (1)where ∆ M gas is the total mass of newly accreted gas, and ∆ M gas , out is the mass of the newly accreted gas with z max > z acc (i.e., the gas that reaches its T max outside the halo). For the newlyaccreted gas in the halo z = 4 . , f out are . and . , respectively.Note that some gas particles may pass through and are later re-accreted to the host halo more than once, and thus have complicatedthermal histories. While it does not affect the results significantlyby including or excluding them (see the curves with light colors inFig. 5), we remove them from our sample.Similarly, we can calculate f out for all filament haloes in oursample. In order to have a robust estimation, we only consider thosehaloes that have at least newly accreted gas particles. Also, inorder to achieve better statistics, we here define the newly accretedgas particles at z acc as those that belong to haloes at z acc but arenot associated to any haloes at z acc + 0 . . In Fig. 6, we plot f out as a function of M for our halo sample at z = 4 . and . .When calculating the median and scatter of f out in each mass bin,we require each mass bin to contain at least haloes. Overall,filament haloes (red dots) tend to have much larger f out than fieldhaloes (blue dots). The median values of f out for both filament andfield haloes seem to be independent of halo mass. At z = 4 . ,the median value of f out for filament haloes is about percent,while it is about percent for field haloes. Results for z = 2 . aresimilar. Note, at z = 4 . , some field haloes have quite large f out .Our examination shows that these haloes usually reside in smallerfilaments with sizes S < S th . As shown in previous subsections, filaments significantly affect theintergalactic medium and gas accretion of the residing dark matterhaloes. In this subsection, we provide comparisons of some gen-eral properties between field and filament haloes. In Fig. 7, we plotbaryon fractions ( f bar ) and star fractions ( f star ) as a function ofvirial masses for the filament and field haloes at z = 4 . and . .Results for filament and field haloes are shown with dotted andcrossed points, respectively. Here, the baryon fraction of a halois defined as the ratio between the baryonic and virial mass, i.e., f bar ≡ M bar /M , and the star fraction is the ratio between thestellar mass and halo mass (i.e., f star ≡ M (cid:63) /M ).To fit the relations between f bar (or f star ) and M , we adoptthe function proposed by Gnedin (2000) with an additional freeparameter f , f bar , star ( M ) = f (cid:20) (cid:16) α/ − (cid:17) (cid:18) M c M (cid:19) α (cid:21) − /α . (2)There are three free parameters, i.e., f , α and M c , in this fittingfunction. Here f is the baryon/star fraction for high-mass haloes(i.e., M (cid:29) M c ), α indicates how rapidly f bar , star drops in thelow-mass end, and M c marks the characteristic mass scale that f bar , star drops to f / . The best fits are shown with solid anddashed lines in each panel for filament and field haloes, respec-tively, and the fitting parameters are labelled as well. Note that herewe have included all haloes with at least particles. We haveparallelly performed the fits for haloes with at least particles,and confirmed that haloes with (cid:46) particles (i.e. with lower res-olutions) do not affect our conclusions presented in the following.Upper two panels display the baryon fraction results. At z =4 . ( z = 2 . ), due to the photoionization by the UV background,haloes with M < . h − M (cid:12) ( M < h − M (cid:12) ) tend tohave lower f bar with decreasing M (see also e.g. Okamoto et al.2008). Interestingly, filament haloes tend to have higher f bar thanfield haloes, and the difference is even larger at z = 2 . . Similartrends can also be found in Metuki et al. (2015), while the differ-ences are very small between the filament and sheet/void haloes at z = 0 . The much larger difference shown here is perhaps becauseof two facts. (i) The dark matter haloes studied here are at higherredshifts and have lower masses; (ii) we focus on the haloes resid-ing in more pronounced filaments.Bottom panels of the same figure show the star fraction as afunction of halo mass at z = 4 . and . . At z = 4 . , star fractionsof filament haloes are slightly higher than those of field ones, andthe excess is further enhanced at z = 2 . . Especially, the enhance-ment of f star in filament haloes is more significant for haloes withlower masses at z = 2 . , implying that filament structures have apositive impact on star formation in low-mass haloes. Metuki et al.(2015) also found similar trends in their simulations, but again the MNRAS000 , 000–000 (0000) mpact of filaments on galaxy formation z l og ( T / K ) (a) Halo (gas cooling in haloes) 2 3 4 5 6 7 8 9 z (b) Halo (gas cooling in filaments) 2 3 4 5 6 7 8 9 10 z (c) Halo haloinside halo
Figure 4.
Temperature evolution of representative gas particles in the filament halo z = 10 . to theredshifts when they turn into stars. difference is very small. In observations, it has been also found thatwhen approaching the cylindrical center of a filament, galaxies at z (cid:46) tend to have higher stellar masses (e.g. Alpaslan et al. 2016;Chen et al. 2017; Darvish et al. 2017; Kuutma et al. 2017; Malavasiet al. 2017; Poudel et al. 2017; Laigle et al. 2018).According to the best-fitted parameters labelled in Fig. 7, wecan see that the filament halo sample has a smaller characteristicmass M c than its field halo counterpart. Especially, for both baryonand star fractions at z = 2 . , M c for filament haloes is about onlyhalf of that of field haloes, indicating that the lowest mass limit toform a galaxy is smaller for the filament halo than the field one. In this study, we use a high-resolution zoom-in hydrodynamicalsimulation of the Aq-A halo to study the impact of filaments ongalaxy formation in their residing low-mass haloes ( M < h − M (cid:12) ) at high redshifts (e.g. z = 4 . and . ). To identify fil-aments from the simulation, we developed a method based on theHoshen-Kopelman algorithm with two parameters, i.e., ∆ th = 3 . and S th = 1000 . This method is shown to work well in our simu-lation. Our main conclusions are summarized as follows.Similar to dark matter haloes, dark matter filaments can alsotrap and compress gas. As a result, at high redshifts, the accretedgas is shock heated at the boundary of filaments, cools rapidly andcondenses into filaments centre. Some of the preprocessed coldand dense gas is further accreted into residing individual low-masshaloes in a direction along the filaments. Consequently, compar-ing with field haloes, gas accretion is very anisotropic for filamenthaloes, and there are two cooling modes for the gas of filamenthaloes. About 30 percent of the accreted gas of a residing filamenthalo was preprocessed by filaments, and this fraction is indepen-dent of halo mass. Filament haloes have higher baryon fractions andenhanced stellar fractions when comparing with their field counter-parts. Our results thus suggest that filaments can assist gas coolingand enhance star formation in their residing dark matter haloes.Note, as a first step, this study is focused on investigating gasaccretion and cooling in filaments and their residing low-mass darkmatter haloes, and our simulation neglects stellar feedback. We ex-pect that our conclusions may be quantitatively changed when in- cluding stellar feedback in the simulation, as some previous simu-lated works showed that feedback can affect halo gas accretion andstar formation (e.g. Oppenheimer et al. 2010; Faucher-Gigu`ere etal. 2011; van de Voort et al. 2011; Murante et al. 2012; Woods etal. 2014; Nelson et al. 2015). We will explore the effects of feed-back on our results in our future work. ACKNOWLEDGEMENTS
We thank the anonymous referee for the valuable comments. Wethank Jie Wang, Shi Shao and Marius Cautun for discussions.LG acknowledges support from the NSFC grant (Nos 11133003,11425312) and a Newton Advanced Fellowship, as well as the hos-pitality of the Institute for Computational Cosmology at DurhamUniversity. The simulations used in this work were performed onthe “Era” supercomputer of the Supercomputing Centre of ChineseAcademy of Sciences, Beijing, China.
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Liao & Gao . . . . . . d P / d z m a x Newly accreted gas particlesat z = 4 . z max . . . . d P / d z m a x All filament haloesAll field haloes
Figure 5.
Top: Probability distribution functions of z max for newly ac-creted gas at z = 4 . of the filament halo z = 4 . . The black dotted line marksthe gas accretion redshift z acc = 4 . . Bottom: similar to the top panel, butfor all newly accreted gas at z = 4 . in all filament haloes (red solid) andfield haloes (blue dashed).Guo Q., Tempel E., Libeskind N. I., 2015, ApJ, 800, 112Haardt F., Madau P., 1996, ApJ, 461, 20Hahn O., Carollo C. M., Porciani C., Dekel A., 2007, MNRAS, 381, 41Hoshen J., Kopelman R., 1976, Phys. Rev. B, 14, 3438Kereˇs D., Katz N., Fardal M., Dav´e R., Weinberg D. H., 2009, MNRAS,395, 160Kereˇs D., Katz N., Weinberg D. H., Dav´e R., 2005, MNRAS, 363, 2Knollmann S. R., Knebe A., 2009, ApJS, 182, 608Kraljic K. et al., 2018, MNRAS, 474, 547Kuutma T., Tamm A., Tempel E., 2017, A&A, 600, L6Laigle C. et al., 2018, MNRAS, 474, 5437Malavasi N. et al., 2017, MNRAS, 465, 3817Metuki O., Libeskind N. I., Hoffman Y., Crain R. A., Theuns T., 2015, MN-RAS, 446, 1458Murante G., Calabrese M., De Lucia G., et al. 2012, ApJL, 749, L34Nelson D., Genel S., Vogelsberger M., et al. 2015, MNRAS, 448, 59Ocvirk P., Pichon C., Teyssier R., 2008, MNRAS, 390, 1326Okamoto T., Gao L., Theuns T., 2008, MNRAS, 390, 920Oppenheimer B. D., Dav´e R., Kereˇs D., et al. 2010, MNRAS, 406, 2325Porter S. C., Raychaudhury S., 2007, MNRAS, 375, 1409Porter S. C., Raychaudhury S., Pimbblet K. A., Drinkwater M. J., 2008, MNRAS, 388, 1152Poudel A., Hein¨am¨aki P., Tempel E., Einasto M., Lietzen H., Nurmi P.,2017, A&A, 597, A86Springel V., 2005, MNRAS, 364, 1105Springel V. et al., 2008, MNRAS, 391, 1685van de Voort F., Schaye J., Booth C. M., Haas M. R., Vecchia C. D., 2011,MNRAS, 414, 2458White S. D. M., Frenk C. S., 1991, ApJ, 379, 52White S. D. M., Rees M. J., 1978, MNRAS, 183, 341Woods R. M., Wadsley J., Couchman H. M. P., Stinson G., & Shen S., 2014,MNRAS, 442, 732Zhang Y., Yang X., Faltenbacher A., Springel V., Lin W., Wang H., 2009,ApJ, 706, 747 APPENDIX A: SHOCK FRONTS AND GAS ACCRETIONTEMPERATURES OF HALOES
In this appendix, we plot the gas shock fronts associated with thehaloes xy -projected temperature field of acubic region with length of . h − Mpc centering at the halo z = 4 . . As we can see from the figure, there is clearly a shockfront at the surface of the filament. Behind the shock front, the gastemperature gradually increases when approaching the filament. In-side the filament, the gas temperature is lower than the shock front,which is due to gas cooling by filaments. Similar descriptions canbe found in Gao et al. (2015). At the center of the halo ∼ K . Quantitatively, we can look at the relation between the temper-ature and the accretion direction of the accreted gas. To do so, weselect the newly accreted gas particles for the halo z = 4 . but they arenot belong to the progenitor of the halo z = 4 . , and calcu-late their accretion angles, θ , with respect to the filament direction.The accretion angle is defined as the angle between the vector fromthe halo center to the gas particle, r (cid:48) i = r i − r c , and the filamentdirection r f , i.e., θ ≡ arccos (cid:18) r (cid:48) i · r f | r (cid:48) i || r f | (cid:19) . (A1)Here, r c and r i are the position vectors of the halo center and the i -th gas particle respectively, and the filament direction r f is calcu-lated by solving the eigensystem of the Hessian matrix (e.g. Hahnet al. 2007; Zhang et al. 2009), H ij = ∂ ρ s ( r ) ∂x i ∂x j , (A2)where ρ s ( r ) is the smoothed filament density field with a smooth-ing scale of . h − Mpc . We have tested that our results are notsensitive to the value of the smoothing scale. The vector r f is theeigenvector that associates with the positive eigenvalue. The fila-ment direction at the center of the halo σ scatters. We can see that ingeneral, the temperature of the gas accreted perpendicularly to thefilament is ∼ . times of that for gas accreted along the filament.This is a clear evidence of the anisotropic accretion behaviour.As a comparison, we also plot a field halo, the halo MNRAS000
In this appendix, we plot the gas shock fronts associated with thehaloes xy -projected temperature field of acubic region with length of . h − Mpc centering at the halo z = 4 . . As we can see from the figure, there is clearly a shockfront at the surface of the filament. Behind the shock front, the gastemperature gradually increases when approaching the filament. In-side the filament, the gas temperature is lower than the shock front,which is due to gas cooling by filaments. Similar descriptions canbe found in Gao et al. (2015). At the center of the halo ∼ K . Quantitatively, we can look at the relation between the temper-ature and the accretion direction of the accreted gas. To do so, weselect the newly accreted gas particles for the halo z = 4 . but they arenot belong to the progenitor of the halo z = 4 . , and calcu-late their accretion angles, θ , with respect to the filament direction.The accretion angle is defined as the angle between the vector fromthe halo center to the gas particle, r (cid:48) i = r i − r c , and the filamentdirection r f , i.e., θ ≡ arccos (cid:18) r (cid:48) i · r f | r (cid:48) i || r f | (cid:19) . (A1)Here, r c and r i are the position vectors of the halo center and the i -th gas particle respectively, and the filament direction r f is calcu-lated by solving the eigensystem of the Hessian matrix (e.g. Hahnet al. 2007; Zhang et al. 2009), H ij = ∂ ρ s ( r ) ∂x i ∂x j , (A2)where ρ s ( r ) is the smoothed filament density field with a smooth-ing scale of . h − Mpc . We have tested that our results are notsensitive to the value of the smoothing scale. The vector r f is theeigenvector that associates with the positive eigenvalue. The fila-ment direction at the center of the halo σ scatters. We can see that ingeneral, the temperature of the gas accreted perpendicularly to thefilament is ∼ . times of that for gas accreted along the filament.This is a clear evidence of the anisotropic accretion behaviour.As a comparison, we also plot a field halo, the halo MNRAS000 , 000–000 (0000) mpact of filaments on galaxy formation . . . . . . . . M /h − M fl ) − . . . . . . . f o u t z = 4 . . . . . . . . . . M /h − M fl ) z = 2 . Figure 6.
The fraction of gas preprocessed by filaments as a function of halo mass at z = 4 . (left) and z = 2 . (right). The filament and field haloes areplotted with red dots and blue crosses, respectively. The median of f out in each mass bin are shown with solid lines. Dashed lines show the . and . percentiles of each mass bin. . . . . . f b a r f = α = M c = 0 . . . e + 07 0 . . . e + 08 f bar = Ω b / Ω m z = 4 . f = α = M c = 0 . . . e + 08 0 . . . e + 08 z = 2 . M /h − M fl )0 . . . . . f s t a r f = α = M c = 0 . . . e + 08 0 . . . e + 08 f star = Ω b / Ω m (a2) 7 8 9 10 11log( M /h − M fl ) f = α = M c = 0 . . . e + 08 0 . . . e + 08(b2) Figure 7.
Baryon fractions (upper) and star fractions (lower) of haloes in filaments (red) and fields (blue) at z = 4 . (left) and z = 2 . (right). The lightdots (crosses) plot the value of each filament (field) halo in our sample, and the solid (dashed) line shows the best-fitted curve according to Eq. (2). The fittedparameters are labelled at the lower right corner of each panel. The physical unit of M c is h − M (cid:12) .MNRAS , 000–000 (0000) Liao & Gao z = 4 . Filament (Halo
Field (Halo . . . . . . | cos θ | . . . . . . . . l og ( T / K ) (c) Halo . . . . . . | cos θ | . . . . . . . . l og ( T / K ) (d) All filament haloesAll field haloes4 . . . . . ( T/ K) 3 . . . . . ( T/ K) Figure A1.
Gas temperature of a filament halo (the halo z = 4 . . In Panels (a) and (b), we plot the xy − projected cubic region with comoving length of . h − Mpc centering at the halo σ scatters. Panel (d) is similar to Panel (c), but for all filament (solid) and field (dashed) haloes. See thetext for details. Fig. A1. From Panel (b), we see that the temperature field is moreisotropic around the halo r f calculated above to compute theaccretion angle θ for the gas in the halo | cos θ | ≈ . This means that thegas accretion in field haloes is similar to that of filament haloeswith similar masses in the direction perpendicular to the filament.Comparing to the filament halo, the temperature - accretion anglerelation for the field halo has smaller scatters, which reflects thefact that the gas accretion in field haloes is more similar in differentdirections while the newly accreted gas particles in filament haloeshave more complicated and diverse histories.Although above we only look at two specific haloes, similar conclusions can be drawn for the newly accreted gas of all filamentand field haloes, as shown in Panel (d). Here, again without loss ofgenerality, we use the filament direction r f of halo θ for the gas in field haloes. We have also testedwith the following used directions: (i) other global directions, e.g. r = (1 , , , (ii) eigenvectors computed from the local smoothedHessian matrix for each field halo, which reflect the local matterflow directions at large scales, (iii) the filament direction of thenearest filament halo for each field halo, and all of these choicesgive similar results for field haloes (i.e. no anisotropic accretion isseen). MNRAS000