Hierarchical fragmentation in high redshift galaxies revealed by hydrodynamical simulations
Baptiste Faure, Frédéric Bournaud, Jérémy Fensch, Emanuele Daddi, Manuel Behrendt, Andreas Burkert, Johan Richard
MMNRAS , 000–000 (0000) Preprint 29 January 2021 Compiled using MNRAS L A TEX style file v3.0
Hierarchical fragmentation in high redshift galaxies revealedby hydrodynamical simulations
Baptiste Faure (cid:63) , Frédéric Bournaud , Jérémy Fensch , , Emanuele Daddi ,Manuel Behrendt , , Andreas Burkert , and Johan Richard AIM, CEA, CNRS, Université Paris-Saclay, Université Paris Diderot, Sorbonne Paris Cité, 91191 Gif-sur-Yvette, France Univ. Lyon, ENS de Lyon, Univ. Lyon 1, CNRS, Centre de recherche Astrophysique de Lyon, UMR5574, F-69007 Lyon, France European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany Universitäts-Sternwarte München, Scheinerstr. 1, D-81679 München, Germany Max Planck Institute for Extraterrestrial Physics, Giessenbachstraße 1, D-85748 Garching, Germany Univ Lyon, Univ Lyon1, Ens de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, F-69230, Saint-Genis-Laval, France
29 January 2021
ABSTRACT
High-redshift star-forming galaxies have very different morphologies compared to nearby ones. Indeed, they areoften dominated by bright star-forming structures of masses up to − M (cid:12) dubbed «giant clumps». However, recentobservations questioned this result by showing only low-mass structures or no structure at all. We use AdaptativeMesh Refinement hydrodynamical simulations of galaxies with parsec-scale resolution to study the formation ofstructures inside clumpy high-redshift galaxies. We show that in very gas-rich galaxies star formation occurs in smallgas clusters with masses below − M (cid:12) that are themselves located inside giant complexes with masses up to and sometimes M (cid:12) . Those massive structures are similar in mass and size to the giant clumps observed in imagingsurveys, in particular with the Hubble Space Telescope. Using mock observations of simulated galaxies, we show thatat very high resolution with instruments like the Atacama Large Millimeter Array or through gravitational lensing,only low-mass structures are likely to be detected, and their gathering into giant complexes might be missed. Thisleads to the non-detection of the giant clumps and therefore introduces a bias in the detection of these structures. Weshow that the simulated giant clumps can be gravitationally bound even when undetected in mocks representativefor ALMA observations and HST observations of lensed galaxies. We then compare the top-down fragmentation of aninitially warm disc and the bottom-up fragmentation of an initially cold disc to show that the process of formationof the clumps does not impact their physical properties. Key words: galaxy evolution – high redshift
For two decades, deep imaging surveys have revealed thathigh-redshift ( z >1) star-forming galaxies have optical andnear-infrared morphologies that strongly differ from nearbygalaxies. The distribution of star formation that is revealedby optical data is often dominated by irregular structuressuch as the so-called “giant clumps” and at the same timelong spiral arms are often absent (e.g., Cowie et al. 1996;Elmegreen et al. 2005; Genzel et al. 2006; Guo et al. 2018;Zanella et al. 2019). The giant clumps can reach sizes of sev-eral hundreds of parsecs and stellar masses of a few , some-times , solar masses. The clumps are actively star-formingwith typical star formation rates of several solar masses peryear in each clump (Elmegreen & Elmegreen 2005; Elmegreenet al. 2007). Clumpy galaxies are generally found to have (cid:63) Contact e-mail: [email protected] mass distributions and velocity field consistent with rotatingdiscs (Genzel et al. 2008; Bournaud et al. 2008) and gen-erally lack signatures of mergers (Cibinel et al. 2015). Thestandard picture for the formation of such clumpy disc galax-ies is the fragmentation, under gravitational instability, ofgas-rich discs (Noguchi 1999; Bournaud et al. 2007; Agertzet al. 2009; Dekel et al. 2009; Ceverino et al. 2010). The highobserved gas fractions, about 50% of the baryonic mass atredshift 2 (Daddi et al. 2010; Tacconi et al. 2010; Combeset al. 2013; Santini et al. 2014; Zanella et al. 2018) and highturbulent speeds ( ∼
50 km s − Genzel et al. 2006, 2008; Bour-naud et al. 2008; Swinbank et al. 2009, 2010) are consistentwith this scenario. In this scenario, giant clumps form bygravitational instabilities and may subsequently fragment insub-structures while remaining gravitationally bound. Alter-natively, a bottom-up scenario where the gaseous disc frag-ments into small clumps that then agglomerate to form thegiant clumps is also proposed (Behrendt et al. 2015, 2016, © 0000 The Authors a r X i v : . [ a s t r o - ph . GA ] J a n B. Faure et al. − M (cid:12) , while more massive clumps could survive feed-back, due in particular to the continuous re-accretion of gasfrom the large-scale reservoirs in the galactic disc (Dekel &Krumholz 2013; Bournaud et al. 2014; Ceverino et al. 2015).Note that survival to feedback makes it possible for giantclumps to migrate toward the center of the galaxy throughdynamical friction, leading to the growth of the bulge (e.g.,Bournaud 2016, for a review). Probing the evolution ofgiant clumps remains crucial to understand the evolution ofhigh-redshift galaxies.More recently, the very existence of giant clumps them-selves has been questioned. Indeed, observations of stronglylensed galaxies, such as the Cosmic Snake (Cava et al.2018), only detected smaller and lower mass clumps, witha median stellar mass not larger than × M (cid:12) yieldingto the conclusion that the mass of giant clumps in HubbleSpace Telescope (HST) images could have been largely over-estimated (see also Dessauges-Zavadsky et al. 2017, 2019).Moreover attempts to detect the gaseous counter part ofoptical giant clumps with Atacama Large Millimeter Array(ALMA) (Cibinel et al. 2017; Rujopakarn et al. 2019; Ivisonet al. 2020) only provided upper limits on gas masses lowerthan those expected from the UV rest frame luminosity andstar formation rate of the giant clumps. This might indicatethat gas has already been expelled by feedback from stellargiant clumps that are still UV bright. These observationsalso tentatively question the survival to feedback if not thevery existence of giant clumps in the and M (cid:12) massrange and sizes up to ∼ pc by proposing, inter alia,beam smearing or differential extinction as explanation ofpreviously mis-interpreted observations.In this paper we show that the observations at high ef-fective resolution (ie. high angular resolution or observationof strongly lensed galaxies) detect the sub-structures of thegiant clumps but may miss these giant clumps. We use sub-parsec scale numerical simulations of isolated galaxies, focus-ing on purpose on very gas-rich and very clumpy systems, asdescribed in Section 2. From those, we create mock observa-tions whose wavelength and resolution are representative ofpreviously cited observations as well as integration of grav-itational lens model. We specify the mocks creation in Sec-tion 3. We then analyse the clumps found on the mocks bya clump-finder in Section 4. We then discuss the connectionbetween all scales structures before analysing their physicalexistence as well as their process of formation in Section 5and 6. Finally, we show that detecting the giant clumps inhigh resolution data would require to degrade the resolution, which is not possible with existing ALMA data that generallylack sensitivity. Our goal is to simulate isolated gas-rich ( ∼ gas fraction)galaxies with little bulge ( ∼ ), which is not uncommonat a redshift of 2. There exist a variety of galaxies at thoseredshift but we focus here on the most disk-dominated andgas-rich ones, and the most clumpy ones. Less clumpy galax-ies could result from the same physical model – in particu-lar a similar feedback scheme – with a somewhat lower gasfraction (see below and Fensch & Bournaud 2020) or, possi-bly, a higher bulge/spheroid fraction (Bournaud & Elmegreen2009). The simulations presented in this paper are performed withthe Adaptative Mesh Refinement (AMR) code RAMSES(Teyssier 2002) with physical models globally similar to inBournaud et al. (2014). The coarse level ranges from 200 to800 pc for each simulation, and each AMR cell is refined into new cells if i) its gas mass is larger than × M (cid:12) , orii) the local thermal Jeans length is smaller than four cells,or iii) it contains more than 40 particles. The smallest reso-lution ranges from 1.0 to 0.2 pc (see Table 1 for each simu-lation). An artificial pressure floor is added to high-densitygas, such that the Jeans’ length cannot drop below four timethe smallest cell size. This is typically considered to avoidartificial fragmentation by accounting for stabilising internalturbulent motions, smeared out by the resolution (Trueloveet al. 1997; Ceverino et al. 2012). As in Teyssier et al. (2010),the equation of this pressure floor reads, with x min being thesmallest cell size : P Jeans = 16x Gρ gas /γπ (1)One should note that this artificial pressure floor does notimpact fragmentation and clumps properties. Indeed, turbu-lence dominates over thermal pressure in the studied clumps(see Section 6.2). As an additional precaution we impose aminimal size for our clumps, in order not to have structuresthat are only on the pressure floor.The simulations start as idealised models of isolated galax-ies with sizes, masses and gas fractions representative of star-forming galaxies at redshift z ∼ . Table 1 lists the initialparameters of our three galaxy models. A fourth model fromBehrendt et al. (in prep) is also used and is labelled as Sim-ulation 4. It was also performed with RAMSES and presentsthe same artificial pressure floor as in our simulations.The stellar sizes and masses are representative for the typ-ical mass-size relation of high-redshift galaxies (Dutton et al.2011). Over the simulations we vary the gas disc scale-lengthwith respect to the stellar disc radius to have a proper sam-ple of galactic compacity . Simulations 1 to 3 all start with astellar bulge that represents 15% of the initial stellar mass. While the gaseous scale length are largely unknown at redshift2, such a diversity of gas compactness with respect to stellar sizesis observed at least in the local universe (de Blok et al. 2008).MNRAS , 000–000 (0000) ierarchical fragmentation in high redshift galaxies Table 1.
Simulations parameterParameter Simulation 1 Simulation 2 Simulation 3 Simulation 4 (Behrendt et al., in prep)Initial gas mass . × M (cid:12) . × M (cid:12) . × M (cid:12) . × M (cid:12) Initial gas fraction 50% 50% 50% 100%Gaseous exponential radius 5 kpc 13 kpc 12 kpc 5.26 kpcStellar exponential radius 5 kpc 4 kpc 5 kpc 5.26 kpcFeedback model Full Full Kinetic only SN feedback onlyCooling model Full Full Pseudo Full with temperature floor at KFine AMR resolution 1.5pc/cell 0.4pc/cell 0.2pc/cell 2.9pc/cellCoarse AMR resolution 780pc/cell 390pc/cell 195pc/cell 750pc/cellStar formation threshold . × H/cc . × H/cc . × H/cc . × H/ccMass of new stars . × M (cid:12) . × M (cid:12) . × M (cid:12) . × M (cid:12) Bulge mass in stellar mass fraction 15% 15% 15% 0%
Simulations 1 to 3 start with an initial disc at a tempera-ture of × K, preventing it to form structures. The discevolves for 100Myr at this constant and warm temperature sothat the initial conditions relax into an axisymmetric disc atequilibrium. After this initial phase, gas cooling is activated,which allows gas to form dense structures. In simulations 1and 2, the cooling is done by successive stages to assure thefirst structures to form are massive. At the time of the analy-sis, our three original simulations were run for a few hundredmillion years, the time for the feedback activation plus a fewdynamical times. Simulation 4 was run for 700 Myr, the timefor the galaxy to reach a 73% gas fraction.Cooling is implemented similarly to Perret et al. (2014): wemodel fine-structure cooling, heating from a Haardt & Madau(1996) uniform UV background, the cooling and heating ratesbeing tabulated by Courty & Alimi (2004) assuming solar gasmetallicity.
Star formation and feedback are modelled as in Renaud et al.(2013) (see also Dubois & Teyssier 2008). At each time stepof duration d t , cells with gas density higher than a threshold ρ ∗ are allowed to form stars. For each cell above the thresholdand of physical size d x , a dimensionless integer n ∗ is drawn,following a Poisson distribution of mean value ρ SFR d x d t/M ∗ :a non-zero value of n ∗ implies the conversion of the mass of n ∗ M ∗ into one or a few stellar particles. ρ SFR is the local starformation rate according to the Schmidt law: ρ SFR = (cid:15)ρ/t ff ,where ρ is the gas density, (cid:15) is the star formation efficiencyset to 2% throughout this paper, and t ff is the local free-falltime given by t ff = (cid:112) π/ (32 Gρ ) . M ∗ is the mass of newlyformed stellar particles.Three different stellar feedback mechanisms have been in-cluded, following Renaud et al. (2013) and Bournaud et al.(2014): • photo-ionization of HII regions : around each stellar par-ticle younger than 10 Myr, a photoionized region is computedusing a Strömgren sphere approximation, taking into accountrecombination. Each sphere can be larger or smaller than agas cell. When HII regions overlap, the volume of each is in-creased not to ionize the gas twice. Gas in this HII regionis heated to . × K to model photo-ionization. We takeinto account the doubling of number density through photo-inoization.More details can be found in Renaud et al. (2013). • Radiation Pressure , using the scheme described in Re- naud et al. (2013): a fraction of the momentum available inphotons emitted by young stars is distributed to the gas in theHII regions defined above. The momentum is time-dependantand computed from the luminosity of stars younger than 10Myr (see equation 2 in Renaud et al. (2013). • Supernovae : as in Bournaud et al. (2014), 20% of themass of stellar particles is converted into energy into the sur-rounding gas 10 Myr after their formation in the form ofkinetic (20%) and thermal energy (80%). The kinetic energyis injected in a 3 cell-radius sphere, in the form of a velocitykick.It is important to note that these feedback recipes andthe calibration used here are not particularly weak (and thecooling is not particularly strong), in the sense that, whenused in gas-poor galaxies they are not creating clumps aslarge or massive as the one that will be studied here andthe lower-mass clump formed in gas poor galaxies are notlong-lived. The same set of feedback recipes and a roughlysimilar calibration has been used in (Renaud et al. 2015)and successfully created short-lived Giant Molecular Cloudsin isolated (and interaction) Milky Way-like galaxies with 5–10% gas fractions. Without going to such low gas fractions(that are rare are redshift two among star-forming galaxies),(Fensch & Bournaud 2020) have recently shown that loweringthe gas fraction to 25%, that is by only a factor two (which isnot uncommon among star-forming galaxies at redshift two)results in clumps that are slightly less massive and are aboveall much shorter-lived, independently of the very details ofthe feedback calibration. Hence out simulations are expectedto represent a large fraction of star-forming disk-dominatedgalaxies at redshift two, but do not imply that all of them areextremely clumpy, even less at lower redshifts. Note that theformation of giant clumps with a gas fraction about 50% alsodepends on the bulge/spheroid mass (Bournaud & Elmegreen2009).The first two simulations were run with this whole set offeedback mechanisms. The third simulation uses a simplermodel in order to reach higher spatial resolution. Instead ofcomputing gas cooling and heating we impose an equation ofstate where the temperature is defined as a function of gasdensity (the pseudo-cooling equation of state, Bournaud et al.(2010), Figure 1) while keeping the pressure floor introducedin the previous section. Only kinetic supernovae and radiationpressure feedback are used in this third simulation.In addition, we checked that the star formation rate ofeach galaxy is representative for main sequence galaxies at
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B. Faure et al. a redshift of two. The simulations properties at the time ofanalysis are summarised in Table 2. Each galaxy presentsa SFR between 30 and 215 M (cid:12) yr − , consistent with starforming galaxies of similar stellar masses at redshift 2 (Elbazet al. 2011; Schreiber et al. 2015). We create mock HST observations in the F814W filter assum-ing a redshift z = 2 . We use the Bruzual & Charlot (2003)stellar evolution model, with solar metallicity and Salpeter(1955) initial mass function (IMF). Stars present in the ini-tial conditions are given a random age between 300 Myr and3 Gyr with a uniform distribution.Luminosity maps are created at two different resolutions:one matching HST resolution in the band F814W for z = 2 ,i.e. a 0.05" angular resolution corresponding to roughly 500parsec per pixels, and one with a very high resolution of 12.2parsec per pixels. The first maps are created to compare withHST observations, and the latter in order to detect possiblesmaller-scale structures.Dust attenuation is similar in giant clumps and in the restof clumpy galaxies (Elmegreen et al. 2005, 2007). We do nottake into account dust attenuation or scattering for the cre-ation of the mocks. However, previous studies performed withdust extinction present similar irregular and clumpy struc-tures (see in particular Behrens et al. 2018). We use the ALMA Observation Support Tool (OST, Hey-wood et al. 2011) to create mocks representative for ALMAdust continuum observations that include sensitivity effects.We compute an integrated infra-red luminosity from the starformation rate assuming a Salpeter IMF (Salpeter 1955) us-ing (Béthermin et al. 2012, Equation 8) model. From theinfra-red luminosity we compute the flux for a galaxy at z = 2observed at 217 GHz assuming the Spectral Energy Distribu-tion from Béthermin et al. (2012) with a dust temperatureof 30K and in agreement with Magdis et al. (2012); Béther-min et al. (2015). As a based map for ALMA OST, we use amap of the gas denser than 100 H/cc. We then use the OSTsimulator with different beam sizes and different observationtimes with a precipitable water vapor (PWV) of 0.472mm.As a reference, we also create an ideal observation with vir-tually infinite sensitivity. Those mocks are used in Section6.3 in order to tackle sensitivity effects. We have produced realistic observations of the simulatedmaps as seen through the magnification of a lensing clus-ter core. To do this, we have used the software Lenstool Mocks created with a Chabrier (2003) IMF only present a highercontrast between low and high stellar mass regions as seen in Ap-pendix B. The clumps detection being mainly determined by theclump finder parameters (see 3.4), the IMF does not play a signif-icant role here. (Jullo et al. 2007) and the model constructed for the clusterMACSJ1206 (Ebeling et al. 2009), where the clumpy z = 1 arc called the ‘Cosmic Snake’ (Cava et al. 2018; Dessauges-Zavadsky et al. 2019) is located. By applying high resolu-tion displacement maps , giving the angular deflexion at agiven point in the image plane, to our simulation, and sur-face brightness conservation, we are able to reproduce imagedeflexion, magnification, as well as multiplicity. The instru-mental PSF is afterwards applied on these simulated images.We have adjusted the source plane location of our simulatedgalaxy in order to produce a 22 arcsec long extended arc,similar to the Cosmic Snake. At this location, the typicalmagnification ranges from µ = 4 − , resulting in an effec-tive resolution between ∼ pc and ∼ pc for HST mockobservation. This galaxy is selected as it exhibits a directcomparison of a typical main-sequence high-redshift galaxyto its strongly lensed counterpart. Moreover, its lensing isstronger than most lensed galaxies allowing for a much bet-ter analysis of the structures. In order to detect structures and clumps we use the clumpfinder Astrodendro . The algorithm creates a dendogramstarting from the pixel with the maximum value. It then goesto the next largest value. If this pixel is a local maximum anew structure is created and if it is not, it is added to theclosest structure. Two structures are merged into a branch assoon as the selected pixel is not a local maximum and is ad-jacent to two structures. One can take into account the noiseof the data by setting a threshold for both the minimal value(min_value) and the minimal interval required between twopeaks to create a new structure (min_delta). One can alsoselect the number of pixels a structure needs to have to beconsidered as a clump (min_npix). Each value of min_npixand min_value are selected so that found structures cannotbe only composed of cells at the finest refinement level. Thisis done in order to avoid having strong artificial thermal pres-sure due to the high-density pressure floor (see Section 2.1).In order to use the same parameters over all simulations, wedefined them from the r.m.s. of the input image, dependingon the resolution (see Table 3).We run the clump finder on each type of mock images forall four simulations. Once a clump is found we compute thegas mass, the stellar mass and the mass of the stars thatwere formed less than years before the time of the mock,called young stars mass hereafter. The computation is doneby a direct use of the simulation data to get the mass of eachcomponent contained in the contour of the clumps. As wedo not detect three-dimensional structures the mass is inte-grated on the thickness of the disc. Using Astrodendro for a3D detection of the structures shows only a 10% difference inthe masses values compared to the method described above.For simplicity and consistence with observations, the 2D de-tection is used in the next sections. Publicly available at https://projets.lam.fr/projects/lenstool/wiki , 000–000 (0000) ierarchical fragmentation in high redshift galaxies Table 2.
Simulations parameter at the time of the analysisParameter Simulation 1 Simulation 2 Simulation 3 Simulation 4Gas mass × M (cid:12) . × M (cid:12) . × M (cid:12) . × M (cid:12) Gas fraction
23 % 44 % 20 % 73 %
Stellar mass . × M (cid:12) . × M (cid:12) . × M (cid:12) . × M (cid:12) Star Formation Rate * M (cid:12) · yr − M (cid:12) · yr − M (cid:12) · yr − M (cid:12) · yr − Specific Star Formation Rate . − . − . − − Time at analysis 340 Myr 346 Myr 200 Myr 740 Myr * SFR is computed by averaging the total gas diminution over 15Myr.
Table 3.
Clump finder parameter. Each value is multiplied by therms of the input image.Parameter HST Lensed HST High resolutionmin_value 0.1 0.1 1000min_delta 0.1 0.1 100min_npix 3 5 20
We define as "clumps" the structures found by Astrodendroand whose most intense pixel is located more than 2 kpc fromthe center of the galaxy, which is defined as the center of oursimulation volume. This allows us to remove the central bulgeand its structure from the analysis.Figure 1 shows typical HST images obtained and the de-tected structures. One can see that every image contains ahandful of structures with diameter around the kiloparsec,similarly to observations (see introduction). In Figure 2 isshown the mass histogram of all the clumps found in all foursimulations. The median gas mass is . × M (cid:12) . Themedian stellar mass is . × M (cid:12) . Roughly 25% of thestellar mass in made-up of stars younger than 100 Myr. Themedian total mass is . × M (cid:12) . Those results are consis-tent with observations of giant clumps in the UV rest frameof high-redshift galaxies (Guo et al. 2018; Zanella et al. 2019,for example).As the parameters are computed directly from the simu-lation data and not from the emission, those results are notaffected by the lack of dust attenuation: these are the intrinsicvalues of the structures.For more detailed mass distributions, see Appendix A1. Figure 3 shows typical HST like lensed images obtained forthe three different simulations and the detected structures byAstrodendro. One can see that every image contains muchmore structures than in the HST like non lensed images. Thenumber and size are in agreement with observational studiessuch as Cava et al. (2018). Similarly to the previous section,Figure 4 shows the mass histogram of all the clumps found inall four simulations. The median gas mass is . × M (cid:12) .The median stellar mass is . × M (cid:12) . Roughly 25% of thestellar mass is made-up of stars younger than 100 Myr. Themedian total mass is . × M (cid:12) . Those masses are con-sistent with studies such as Dessauges-Zavadsky et al. (2017,2019) and Cava et al. (2018), where the observed galaxies present similar star formation rate and masses than our sim-ulations. The distribution of masses is reaching values as highas in the previous mocks as the resolution is not increaseduniformly by the lensing, leading to a broad distribution. Fordetailed mass distributions, see Appendix A1. What we define as
High resolution clumps are the clumpsfound on the 12 parsec per pixel image defined in section 3.1.The clumps found are shown in Figure 5. Figure 6 shows themass histogram of all the clumps found in all four simulations.The median gas mass is . × M (cid:12) . The median stellarmasses is . × M (cid:12) . Around 85% of the stellar massis made-up of stars younger than 100Myr. The median totalmasses is . × M (cid:12) . For more detailed mass distributions,see Appendix A1.The structures detected in those images are much less mas-sive and more numerous than in the previous mocks thus rais-ing the question of their relation. We answer this question inthe following section. In the previous section, we showed that in our simulationsclumps and structures can be detected at different scales,from the few hundred parsec scale to the ten parsec scale.This section will present how all those structures at differentscales are related. Fig. 7 presents all the different structuresdetected in the four non-lensed mocks superimposed over thehigh-resolution HST like image. One can see that all HighResolution clumps are contained inside the giant clumps.Fig 8 displays a giant clump of simulation 1 within thered contour in the top right panel as well as all the equiv-alent regions in the three mocks. One can see on the topright panel, which corresponds to the high resolution HST-like mock, bright peaks that are detected with Astrodendro.The giant clump constitutes of several high-resolution andless massive clumps. This reasoning applies to almost everygiant clump as more than 60% have two substructures ormore.The giant clumps as detected at un-lensed HST resolutioncontain 40-50% of the total gas mass for roughly 25% of thedisc surface. They also contain between 100 and 90 % of thehigh resolution structures and 100 and 98% of their masses.In this sense most of the star forming small structures of thedisc are located inside the giant clumps.
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B. Faure et al. m A B · a r c s ec − Figure 1.
Mock HST F814W observations of the simulated galaxies as if they were at z = 2. From left to right are the simulations 1 to 4.White patches on the bottom left corners are the size of the PSF. The second row shows in red contours the clumps found by Astrodendro.The black dotted circles are the central 2 kiloparsec. The mocks are created without any noise nor dust attenuation therefore they canpresent clumps that will not be detected by the HST.
Mass [log(M / M ⊙ )] Gas mass
Mass [log(M / M ⊙ )] Stellar mass
Mass [log(M / M ⊙ )] Young Stars mass
Mass [log(M / M ⊙ )] Total mass
Figure 2.
Mass histogram of the HST-like clumps. A detail com-parison simulation per simulation is shown in Figure A1.
In the previous subsection, we have demonstrated that giantclumps in our simulations are a superposition of several lessmassive substructures. This does not imply that lower-masssubstructures reside in the same giant clump forever. It isknown that giant clumps can lose a large fraction of their ini-tial content, while maintaining their mass by the accretion of new material (e.g., Dekel & Krumholz 2013; Bournaud et al.2014). This can be true in particular for sub-clumps, whichcan leave their initial giant clump and be later-on re-accretedonto another giant clump, if they are long-lived enough (as isthe case, for instance, in Behrendt et al. 2016). Alternatively,the sub-clumps could be short-lived and rapidly destroyedby feedback within 10 Myr, hence being only transient sub-structures inside longer-lives giant clumps (as in the case inBournaud et al. 2014). The next question that arises is thefollowing: are the giant clumps detected only as a random su-perposition of structures, like a transient chance structure orare they physically bound structures? To answer this questionwe compute the virial parameter of the giant clumps. Thisparameter is described in equation 2 and represents the com-petition between kinetic and gravitational energy (Bertoldi& McKee 1992, Equation (2.8a)). A value below unity meansthe structure is gravitationally bound. α = 5 σ v R / GM (2)The velocity dispersion is computed as the quadratic meanof the speed of sound and the turbulent velocity of the gas,which are computed for gas within 1kpc from the disc mid-plane in order not to be contaminated by outflows and inflowsfurther above and below the disk plane. Rotation is not re-moved as attempts confirmed its negligible effect compared toturbulent motions. Both stellar and gas mass are taken intoaccount for the mass term in Equation 2. Figure 9 shows theresults for both giant clumps and high resolution structures.We can here see that most giant clumps in our simulations MNRAS , 000–000 (0000) ierarchical fragmentation in high redshift galaxies
1” 1” 1” 1”1” 1” 1” 1” m A B · a r c s ec − Figure 3.
Mock HST F814W observations of the simulated galaxies after the application of the lens model. The sources are at z = 2.From left to right are the simulations 1 to 4. White patches on the bottom left corners are the size of the PSF. The second row shows inred contours the clumps found by Astrodendro. The mocks are created without any noise nor dust attenuation therefore they can presentclumps that will not be detected by the HST. are gravitationally bound, with a median virial parameter of0.33 meaning that the giant clumps are gravitationally boundstructures that are unstable. Those structures are still un-dergoing gravitationnal instability along with their on-goingcollpase, and should thus be fragmenting into smaller sub-structures, which is observed to be the case. This means thatas small clumps are most often gathered together into giantclumps, these giant clumps are not random chance superpo-sitions of smaller clumps. Indeed, the giant clumps are boundstructures consisting of small sub-clumps and the diffuse gas between those sub-clumps. The stars newly formed in the gasshould also be bound to the structure as they have the veloc-ity of the gas they are formed with. Bournaud et al. (2014)shows that old stars are also gravitationally bound to theclump structures. Now that the content of the giant clumpsand their physical existence has been detailed, we will discusstheir formation in the next section with the understanding ofour simulation.
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Mass [log(M / M ⊙ )] Gas mass
Mass [log(M / M ⊙ )] Stellar mass
Mass [log(M / M ⊙ )] Young stars mass
Mass [log(M / M ⊙ )] Total mass
Figure 4.
Mass histogram of the HST-lensed-like clumps. A detailcomparison simulation per simulation is shown in Figure A1.
Previously we have shown that most of the giant clumps aregravitationally bound in our simulations. The low mass struc-tures have much higher virial parameter as seen on Figure9. Such high virial parameter values mean that those sub-structures could have been impacted by star-formation feed-back and are being destroyed : feedback expels the gas andthe stars are being dispersed because of the subsequent de-crease in gravitational potential. Such a scenario has beenproposed by Parmentier & Gilmore (2005), where the removalof gas in gas-rich stellar cluster could lead to the evaporationof the cluster. However, if the gas fraction of the substructuresis below 50%, the stellar sub-clump could survive and becomea globular cluster, as proposed by Krumholz & Dekel (2010)and Shapiro et al. (2010). In order to test this hypothesiswe restarted simulation 3 without any feedback. After ap-plying the exact same methods as above, Figures 10 and 11show the comparison of the masses of the clumps found in thethree mock observations for respectively the giant clumps andthe sub-clumps. One can see the effect of the suppression offeedback: the mass range for all detected clumps broadens inparticular towards the masses below M (cid:12) for sub clumps.This can be explained by the fact that without feedback theless massive clumps can survive for a long time while feed-back quickly destroy them, which is consistent with whatwas discussed in Section 5.2. For the larger structures gascan be gradually expelled by the feedback, consistently withBournaud et al. (2014) and Dekel & Krumholz (2013). Then,without feedback, the mass of the giant clumps can be largerthan without, as seen on Figure 11. However the effect offeedback is secondary on giant clumps’ properties, its impactis much more measurable on the small substructures. There is no consensus on the formation of giant clumps andsub-structures yet. Two different scenarios are currently at stake and are dependent on the initial condition of the disc,they are called top-down and bottom-up . In the top-down sce-nario the giant clumps form first before forming sub clumps(see Fig. 12) as in the bottom-up the sub clumps form firstand then agglomerate to form the giant clumps (Behrendtet al. 2015) (see Fig. 13 of this paper). Simulation 1 and 2were run to have a top-down scenario and the other two wererun to have a bottom-up scenario. Those scenarios can hap-pen only if the disc’s Toomre parameter is below unity fora two-dimensional disc, or below about 0.7-0.75 for a finitethickness disc (e.g., Kim et al. 2002). The Toomre parame-ter is defined in Toomre (1964) as the opposition between,on the one hand stabilisation by rotation and pression andon the other hand collapse by gravitational attraction, asin Equation 3 where κ is the epicyclic frequency (Binney &Tremaine 2008, p.165), σ v the turbulent velocity dispersion, c s the speed of sound and Σ the surface density of the disc. Q = κ √ σ v + c s πG Σ (3)A value of Q above unity for an axisymetric disc means itis stabilised by rotation and/or pressure while a value belowone means it can gravitationally collapse. This is the case inour simulations where we find a value of Q below unity forthe giant clumps, as depicted in Figure 14: they are regionsthat could have collapsed gravitationally when the disc wasaxisymetric. One can try to estimate the Toomre parameterof a proto-clump region, i.e. before it collapses into a giantclump, based on the fact that the only physical parameterin Equation 3 that largely varies during the collapse is thesurface density that is multiplied by a factor about 10. Thevelocity dispersion is not found to increase in our simulations,especially inside giant clumps. This can be seen in Figure 15where we can visualise that the turbulent velocity dispersionin each clump does not differ from the one outside and isnot dependent of the gas density. Furthermore, the speed ofsound does not significantly impact the quadratic mean inEquation 3 even if the clump is inside an HII region. Indeedwith a temperature of an HII region of . × K , the speedof sound will be close to 10km/s, which is largely dominatedby the turbulent speed that is roughly around 30-50 km/s.The epicyclic frequency does not substantially vary after thecollapse of the clumps as it is only radius dependent. Thismeans that between a proto-clump and a clump the Toomreparameter can decrease by at most a factor about 10. As inour simulations the Toomre parameter inside collapsed re-gions is below 0.1, the value before the collapse could nothave exceeded unity meaning collapse of giant clumps can bedue to gravitational instability.We just showed that from the analysis of the disc, our sim-ulations are compatible with formation of structures throughviolent disc instabilities (Dekel et al. 2009). This is true forall our simulations, regardless of the scenario of clump forma-tion we imposed. In addition the clumps formed have similarproperties in previous studies (Ceverino et al. 2015; Behrendtet al. 2016) where the simulated galaxies also have similarproperties. Clumps are also found in disks with similar dy-namics in Leung et al. (2020), where the clumps are not highpeaks of velocity dispersion. However, they are smaller in sizeand mass compared to our giant clumps and do not seem to MNRAS , 000–000 (0000) ierarchical fragmentation in high redshift galaxies m A B · a r c s ec − Figure 5.
High resolution images of the F814W image of the simulated galaxies. From left to right are the simulations 1 to 4. Whitepatches on the bottom left corners are the size of the PSF. The second row shows in purple contours the clumps found by Astrodendro.The black dotted circles are the central 2 kiloparsec.
Mass [log(M / M ⊙ )] Gas mass
Mass [log(M / M ⊙ )] Stellar mass
Mass [log(M / M ⊙ )] Young Stars mass
Mass [log(M / M ⊙ )] Total mass
Figure 6.
Mass histogram of the high resolution HST-like clumps.A detail comparison simulation per simulation is shown in FigureA1. be gravitationally bound. Those clumps are therefore closerto the substructures we find in our giant clumps.The gravitational collapse of the disc then occurs at a massabove the Jeans’ mass (Jeans 1902), which is defined as theequilibrium between the pressure and the gravitational force.It is defined in Equation 4 where σ v is the velocity dispersionand c s the speed of sound. HSTHigh resolution m A B · a r c s ec − Figure 7.
Hierarchy of the structures in all Simulations shownover the HST like high resolution image. In red are the HST likeclumps and in black the high resolution HST like giant clumps. M J = π (cid:0) σ v + c s (cid:1) G ρ (4) MNRAS000
Hierarchy of the structures in all Simulations shownover the HST like high resolution image. In red are the HST likeclumps and in black the high resolution HST like giant clumps. M J = π (cid:0) σ v + c s (cid:1) G ρ (4) MNRAS000 , 000–000 (0000) B. Faure et al.
HRHSTLens
Figure 8.
Zoom-in of a giant UV clumps in the two other differentmock observations. The red contour is the giant clump detected inthe HST mock. The blue contours are the clumps detected in theshown mock. − − log α . . . . . . . . N o r m a li ze dnu m b e r d e n s i t y Clumps’ virial parameter distribution
Median valueGiant clumpsHigh resolution clumps
Figure 9.
Virial parameters of the giant clumps (orange) and thesubstructures (green).
As the Jeans’ mass depends on the speed of sound, it alsodepends on the gas temperature. On one hand, the coolerthe gas, the lower the Jeans’ mass thus formation of smallerstructures. On the other hand if the temperature is higher,the Jeans’ mass will get higher. The simulations from thispaper were run with an initial high temperature (Simulation1 and 2) and with an initial cold disc (Simulation 3). The onefrom Behrendt et al. (in prep) starts also with cold initial disc.In the case of an initial hot disc its Jeans’ mass is high
Mass [log(M / M ⊙ )] Gas mass . . . . . Mass [log(M / M ⊙ )] Stellar mass . . . . . . Mass [log(M / M ⊙ )] Total mass
Figure 10.
Comparison of the HST clumps in Simulation 3 withfeedback (plain lines) and without feedback (dotted lines).
Mass [log(M / M ⊙ )] Gas mass
Mass [log(M / M ⊙ )] Stellar mass
Mass [log(M / M ⊙ )] Total mass
Figure 11.
Comparison of the high resolution HST clumps in Sim-ulation 3 with feedback (plain lines) and without feedback (dottedlines). and leads to the formation of large structures that cool down,lowering their Jeans’ mass and allowing them to fragment intosmaller substructures: the top-down scenario. This scenariois observed in Simulation 1 and 2.For the simulation 3, the way cooling is implemented forcesthe disc to be initially cold ( K) which leads to a Jeans’mass lower than in the Simulation 1 and 2. As the disc’sJeans’ mass is lower the first structures to form are less mas-sive than the giant clumps. Those structures stir the sur-rounding gas, increasing the turbulence and thus the velocitydispersion, leading to an increase of the Jeans’ mass of thedisc. A second collapse is then happening at a higher mass:the giant clumps are formed and capture the first structuresthat become the sub-clumps observed at high resolution. Thisis the bottom-up scenario.Remarkably we do not find any evidence of those differ-ent scenarios if we compare the physical properties of thegiant clumps and their sub-clumps through the different sim-ulations. One could say that in the top-down scenario, asthe sub-clumps are formed by the fragmentation of the giantclumps, their could be a link between the Jeans’ mass of thegiant clumps and the mass of it sub-clumps. Conversely, inthe bottom-up scenario there would be no link between thosetwo values. One could also argue that the different forma-tion history could lead to different behavior of the inter-sub-clumps medium inside giant clumps that could be probed bythe velocity dispersion of those regions. The values we com-pared between the different scenarios are the following: • Masses of gas and stars in giant clumps, • Masses of gas and stars in sub-clumps, • Jeans’ masses at the scale of the giant clumps, • Jeans’ masses at the scale of the sub-clumps, • • MNRAS , 000–000 (0000) ierarchical fragmentation in high redshift galaxies T = 215 Myr T = 258 Myr T = 331 Myr T = 364 Myr T = 439 Myr l o g ()[ c m ] l o g ()[ c m ] Figure 12.
Gas density evolution of a galaxy forming clump in the top-down scenario. The top row is the gas at a resolution equivalentto the "high resolution" case as the bottom row is at the "HST" resolution. The first structures to collapse are the giant clumps thatfragment into smaller substructures. The resolution of the images and the colorbar does not necessarily enable all sub-clumps to be visible.
T = 114 Myr T = 124 Myr T = 133 Myr T = 156 Myr T = 186 Myr l o g ()[ c m ] l o g ()[ c m ] Figure 13.
Gas density evolution of a galaxy forming clump in the bottom-up scenario. The top row is the gas at a resolution equivalentto the "high resolution" case as the bottom row is at the "HST" resolution. The first structures to collapse are small structures thatagglomerate into larger structures: the giant clumps. The resolution of the images and the colorbar does not necessarily enable allsub-clumps to be visible. • • bottom-up and those top-down . All of those argumentsmake us think that the initial formation scenario of the giantclumps is not relevant to understand their evolution and thatthey tend to become very similar structures however they areformed. In this paper we focused mainly on resolution effect on theclumps detection. Nevertheless in order to link observationsand simulations one needs to understand sensitivity effect asclumps are not detected in recent observations with ALMA(Cibinel et al. 2017; Rujopakarn et al. 2019; Ivison et al.2020). We created mock observations with ALMA OST asdescribed in Section 3.2.The mocks for simulation 3 are represented in Figure 16.A long observation time of more than 48h is needed to detectstructures with a beam size of 0.02 arcsecond, correspondingto a physical size of 170 parsec at z = 2. In the case of an
MNRAS000
MNRAS000 , 000–000 (0000) B. Faure et al.
Toomre parameter, Simulation 3 10 − − Q Figure 14.
Toomre parameter map of simulation 3. In black con-tour are shown the clumps detected on the HST mock observation.
Simulation 3 gas velocity dispersion − l og σ z [ k m / s ] Simulation 3 gas density − l og ρ [ H / cc ] Figure 15.
Maps of the velocity dispersion and gas density ofSimulation 3 integrated along the line of sight. The black contourscorrespond to the giant clumps. observation time of 10h with the 0.02 arcsecond beam, somesubclumps can be detected but most of them are dominatedby noise. With a larger beam the clumps can be detected inaround ten hours and some substructures are at the verge ofthe detection. This first statement is qualitative and a morequantitative case follows later in the section.By running Astrodendro on the idealized mocks only wedetect structures that are represented in Figure 18. A com-parison of the clumps found on the most resolved ALMAmocks with the one found on the mocks presented earlieris shown in Figure 17. One can see that at this resolutionALMA does not resolve the giant clumps (in red on Figure17). For a fraction of those only the center of the clump isresolved even if the outlying region is gravitationally boundand is part if the giant clump, leading to a possible underes-timation of the mass. For the remaining fraction the ALMAclumps correspond to the sub-structures (in purple on Fig-ure 17) therefore could probe the inner structure of the giantclumps.We then compute the flux ratio relative to the flux of thewhole galaxy of each of the detected structure on the ALMA idealised mocks excluding detection closer than 2 kpc fromthe center of the galaxy. The result is shown in Figure 19 forthe three simulations.The comparison with previous studies, like Rujopakarnet al. (2019), whose galaxies have similar position with re-spect to the main sequence and where the upper limit is of1% with a 200-pc beam, suggests that either (1) the galaxiesthey observed are clumpy with lower mass clumps than in ourmodels that are tuned to correspond to very clumpy galaxies,or (2) the sub clumps in these galaxies are gas-poor, poten-tially under the effect of strong stellar feedback. This suggeststhat our model of feedback is not strong enough to efficientlydeprive sub-clumps from their gas. A stronger feedback im-plementation could be enough to deprive them from gas ordestroy them without destroying giant clumps which is a sce-nario proposed in Bournaud et al. (2014). One might need tobe careful as if the feedback is too strong the substructuresbut also the giant clumps could be destroyed as seen in Hop-kins et al. (2012) and Tamburello et al. (2015). Larger obser-vational datasets of this type including very clumpy galaxiescould disentangle these interpretations and potentially probefeedback effects.For a comparison with Cibinel et al. (2017) the numberof detected structures is very dependent on the simulationsas seen on Fig. 19. The beam size of 0.3" being large, thegiant clumps are blended-in together into even larger andbrighter clumps as it is the case for Simulation 2 and 3. Theopposite is also seen in Simulation 1 where the clumps areblended-in together without being local maximum in lumi-nosity. The galaxy presents asymmetry but nor the clumpfinder nor the eyes can detect any giant clumps. Therefore,depending on the between-clumps distance the giant clumpscan be detected or not with ALMA at resolution matchingCibinel et al. (2017). The detected clumps are very luminous,with a flux ratio to total flux around 15% as they are the re-sult of the smearing of several giant clumps.
In this short section we want to understand how the dustextinction will impact the detection of the giant clumps, asit was raised by Zanella et al. (2021). Indeed, they showedthat for higher redshift ( z ∼ ), dust could lead to a nondetection of the internal structures of the galaxy in UV HSTimages. By using the model from Güver & Özel (2009), thatlinks gas column density to A V , and assuming solar metal-licity everywhere in the galaxy, one can estimate the dustextinction of the clumps. The comparison to the central kilo-parsec and the whole galaxy is in Figure 20. One can seethat clumps are not particularly dustier than the galaxy orits center and are in agreement with Elmegreen et al. (2005)and Elmegreen et al. (2007) which mean that real observa-tions of such galaxies would lead to the detection of almostall the giant clumps. However, those results only show a ten-dency. Indeed, a much proper and deeper analysis includingall physical processes that affect dust, such as feedback andradiation, would be necessary to draw a proper conclusion onthe dust extinction. MNRAS , 000–000 (0000) ierarchical fragmentation in high redshift galaxies . ” -2.0e-05-1.0e-050.0e+001.0e-052.0e-05 J y / b e a m -1.5e-05-1.0e-05-5.0e-060.0e+005.0e-061.0e-051.5e-05 J y / b e a m -6.0e-06-4.0e-06-2.0e-060.0e+002.0e-064.0e-066.0e-068.0e-06 J y / b e a m Idealised J y / b e a m . ” -2.0e-05-1.5e-05-1.0e-05-5.0e-060.0e+005.0e-061.0e-051.5e-052.0e-05 J y / b e a m -1.0e-05-5.0e-060.0e+005.0e-061.0e-051.5e-05 J y / b e a m -5.0e-06-2.5e-060.0e+002.5e-065.0e-067.5e-061.0e-051.2e-05 J y / b e a m J y / b e a m . ” -2.0e-05-1.5e-05-1.0e-05-5.0e-060.0e+005.0e-061.0e-051.5e-052.0e-05 J y / b e a m -1.0e-05-5.0e-060.0e+005.0e-061.0e-051.5e-052.0e-05 J y / b e a m -2.5e-060.0e+002.5e-065.0e-067.5e-061.0e-051.2e-051.5e-05 J y / b e a m J y / b e a m . ” -1.0e-050.0e+001.0e-052.0e-05 J y / b e a m -1.0e-050.0e+001.0e-052.0e-053.0e-05 J y / b e a m -5.0e-060.0e+005.0e-061.0e-051.5e-052.0e-052.5e-053.0e-053.5e-05 J y / b e a m J y / b e a m Figure 16.
Mock observation created with the ALMA Observation Support Tool. From the top to the bottom the beam size is increasing,and the observation time is increasing from the left to the right. The last column shows the idealised observation.
By running four different simulations of idealized and isolatedgalaxies and by creating mock observations out of those inorder to inspect the detection of giant clumps on resolutioneffects, in this paper we have shown that: • The typical mass of the clumps depends strongly onthe spatial resolution. They are observed starting from / M (cid:12) with HST, the so called giant clumps. The gi-ant clumps are then not detected with higher resolutionwhere structures have masses around / M (cid:12) . Similarly,when high effective resolution is reached through strong grav-itational lensing, giant clumps are not detected anymorebut sub-clumps are. Those results are in agreements withBehrendt et al. (2019). • The smaller clumps where most of the star formationoccurs at high resolution are all located inside giant clumpsand not elsewhere: the giant clumps are clusters of stellarclusters. • Giant clumps are gravitationally bound structures mean-ing they have a physical existence and are not chain like struc-tures detected due to the lack of resolution. • Most of the physical properties of giant clumps do notdepend on their formation scenario. • If high resolution is used with ALMA, there will be nodetection of giant clumps but only of the substructures. Amuch higher sensitivity will be needed to detect to structures.Those results are obtained with four different simulationsthat all have different initial properties, feedback parame-ters, cooling modes and clump formation histories ( top-down or bottom-up ). By design our modelled galaxies correspondto the most gas-rich and clumpy ones at z (cid:39) . The samerecipe used here are able to produce less clumpy galaxies ifthe gas fraction is lowered, with only low-mass and short-lived clouds (see for example Renaud et al. 2015). In addi-tion, a change in the gas fraction could change the properties MNRAS000
By running four different simulations of idealized and isolatedgalaxies and by creating mock observations out of those inorder to inspect the detection of giant clumps on resolutioneffects, in this paper we have shown that: • The typical mass of the clumps depends strongly onthe spatial resolution. They are observed starting from / M (cid:12) with HST, the so called giant clumps. The gi-ant clumps are then not detected with higher resolutionwhere structures have masses around / M (cid:12) . Similarly,when high effective resolution is reached through strong grav-itational lensing, giant clumps are not detected anymorebut sub-clumps are. Those results are in agreements withBehrendt et al. (2019). • The smaller clumps where most of the star formationoccurs at high resolution are all located inside giant clumpsand not elsewhere: the giant clumps are clusters of stellarclusters. • Giant clumps are gravitationally bound structures mean-ing they have a physical existence and are not chain like struc-tures detected due to the lack of resolution. • Most of the physical properties of giant clumps do notdepend on their formation scenario. • If high resolution is used with ALMA, there will be nodetection of giant clumps but only of the substructures. Amuch higher sensitivity will be needed to detect to structures.Those results are obtained with four different simulationsthat all have different initial properties, feedback parame-ters, cooling modes and clump formation histories ( top-down or bottom-up ). By design our modelled galaxies correspondto the most gas-rich and clumpy ones at z (cid:39) . The samerecipe used here are able to produce less clumpy galaxies ifthe gas fraction is lowered, with only low-mass and short-lived clouds (see for example Renaud et al. 2015). In addi-tion, a change in the gas fraction could change the properties MNRAS000 , 000–000 (0000) B. Faure et al.
HSTALMAHigh resolution m A B · a r c s ec − Figure 17.
Hierarchy of the structures in all Simulations shownover the HST like high resolution image. In red are the HST likeclumps, in purple the high resolution HST like giant clumps andin green the ALMA clumps at a 0.02 arcseconds resolution.
Figure 18.
Clumps detected in the idealised mock of Simulation 3,with negligible noise and extremely high sensitivity, ALMA sim-ulations made with OST with different beam sizes. From left toright and top to bottom: 0.02", 0.05", 0.1", 0.3". of the giant clumps such as their lifetime and boundedness(Oklopčić et al. 2017; Fensch & Bournaud 2020).Our simulations are not incompatible with studies whereonly clumps smaller in size and mass are detected, such asLeung et al. (2020); Zanella et al. (2021), whose clumps arecloser to the sub-structures of the giant clumps.However, as our giant clumps are extended and made ofsubstructures they are widely different from the very massive( > M (cid:12) ) clumps found in Tamburello et al. (2015) simula-tions. Indeed, their clumps are very dense and do not appearto have any structure, making them incompatible with ob-servations of lensed galaxies.Observations with more resolution than the typical HSTone fail to identify giant stellar and gaseous clumps. Ourwork shows that such observations should tend to resolve gi-ant complexes into smaller sub-clumps. The masses and sizesof sub-clumps in our models are consistent with the one de-tected by Dessauges-Zavadsky et al. (2017) for the stellarcomponent and by Dessauges-Zavadsky et al. (2019) for thegaseous component. Recent ALMA observations (Rujopakarnet al. 2019; Ivison et al. 2020) typically employed resolutionthat resolve giant clumps into sub-clumps but with a sen-sitivity too low to detect those putative sub-clumps, whichwould be required to prove the gathering of sub-clumps intogiant clumps. Lower resolution ALMA observation (Cibinelet al. 2017) merely reach the resolution required to directlydetect giant clumps according to our model. All these ob-servations thus remain consistent with the presence of giantclumps of stars and gas that potentially survives feedback inhigh-redshift galaxies. Higher sensitivity ALMA observationswould be necessary to detect giant clumps along with theirsub-clumps.Finally, the hierarchy of the giant clumps revealed in thiswork seems to be in accordance with Fisher et al. (2017),which present local analogues of turbulent, clumpy diskgalaxies. Indeed, they observe clumps which are not massiveand large enough to be qualified as giant but are similar toour substructures. However, they show that by degrading theresolution, as if the galaxies are observed at a higher redshift,those structures merge into larger one that are similar to ourgiant clumps and thus might be gravitationally bound. ACKNOWLEDGEMENT
We thank the anonymous referee for the useful commentsand discussion, which greatly improved the paper. This workhas been carried out thanks to the support of the ANR3DGasFlows (ANR-17-CE31-0017). This work was grantedaccess to the HPC resources of CINES and TGCC underthe allocations 2018-A0050402192, 2019-A0070402192, and2020-A0090402192 made by GENCI. The research of AndreasBurkert and Manuel Behrendt was supported by the Excel-lence Cluster ORIGINS which is funded by the DeutscheForschungsgemeinschaft (DFG, German Research Founda-tion) under Germany’s Excellence Strategy – EXC-2094 –390783311. The simulations by Manuel Behrendt were per-formed on the Hydra supercomputer at the Max Planck Com-puting and Data Facility (MPCDF). This research made use
MNRAS , 000–000 (0000) ierarchical fragmentation in high redshift galaxies S i m u l a t i o n ALMA, 0.02" ALMA, 0.3" S i m u l a t i o n S i m u l a t i o n
1% 10%
Flux clumpTotal flux o f c l u m p s Flux ratio in Simulations
Rujopakarn+190.02"1% 10%
Flux clumpTotal flux o f c l u m p s Rujopakarn+19Cibinel+190.02"0.3"1% 10%
Flux clumpTotal flux o f c l u m p s Rujopakarn+19Cibinel+190.02"0.3"
ALMA, 0.1"
Figure 19.
Left column is the idealized, with negligible noise and extremely high sensitivity, ALMA mock made with OST with a 0.02"beam. The second column is the one with a 0.1" beam and the third column is with a 0.3" beam. Ratios between flux of the clumpsdetected on the previous columns and the total flux of the galaxy are on the right column. The red contours are the clumps detected withAstrodendro. White circle are the beams sizes. A V,clump A V,1kpc c o un t A V,clump A V,galaxy
Simulation 1Simulation 2Simulation 3
Figure 20.
Quantification of the dust extinction in the giant HSTclumps. Left panel is the ratio of the clump dust extinction to theone of the central kiloparsec. Right panel is the ratio to the galaxyone. of Astropy, a community-developed core Python package forAstronomy (Astropy Collaboration et al. 2013, 2018) and as-trodendro , a Python package to compute dendrograms ofAstronomical data. Furthermore, Manuel Behrendt made useof MERA (Behrendt 2020), a Julia package to efficiently loadand analyze RAMSES simulation data. DATA AVAILABILITY
The data underlying this article will be shared on reasonablerequest to the corresponding author.000
The data underlying this article will be shared on reasonablerequest to the corresponding author.000 , 000–000 (0000) B. Faure et al.
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Gas mass, simulation 2
Gas mass, simulation 3
Gas mass, simulation 4
Gas mass, ALL simulations
Stellar mass, simulation 1 . . . . . . . Stellar mass, simulation 2
Stellar mass, simulation 3 . . . . . . . Stellar mass, simulation 4
Stellar mass, ALL simulations . . . . . . . Young stellar mass, simulation 1 . . . . . . . Young stellar mass, simulation 2
Young stellar mass, simulation 3
Young stellar mass, simulation 4
Young stellar mass, ALL simulations
Total mass, simulation 1
Total mass, simulation 2
Total mass, simulation 3
Total mass, simulation 4
Total mass, ALL simulations
Figure A1.
The top row represents the gas mass of the clumps found in the HST mock observations (orange histogram) in the lensedHST mock observations (blue histogram) and in High Resolution mock observations (red histogram). The second row is the stellar massof the clumps. The third one is the mass of stars younger than 10 Myr. The fourth is the total mass (gas + stars). To each columncorresponds a typical output of each simulation and the fifth one is the stacking of all four simulations. In each panel the dashed line isthe median value of the corresponding histogram.
APPENDIX A: DETAILED CLUMPS MASS PER SIMULATION
MNRAS000
MNRAS000 , 000–000 (0000) B. Faure et al. m A B · a r c s ec − m A B · a r c s ec − − . − . − . − . . . . . . C h a b r i e r / S a l p e t e r − Figure B1.
Comparison of Salpeter IMF (left) with Chabrier IMF (center) at HST resolution. A direct comparison is made on the rightplot. The purple contour are the clumps detected by Astrodendro on the Salpeter IMF mock. m A B · a r c s ec − m A B · a r c s ec − − . − . − . − . . . . . . C h a b r i e r / S a l p e t e r − Figure B2.
Comparison of Salpeter IMF (left) with Chabrier IMF (center) at high resolution. A direct comparison is made on the rightplot. The purple contour are the clumps detected by Astrodendro on the Salpeter IMF mock.
APPENDIX B: CHABRIER AND SALPETER IMF COMPARISON.
This appendix presents a brief comparison of different IMF for our simulations. Indeed our simulations do not resolve the starsin detail so one need to assume an IMF to know the mass distribution of the stars. A Chabrier (2003) IMF will have less lowmass stars and more high mass than a Salpeter (1955) thus leading to a stronger contrast between low and high stellar densityregions, so more contrasted giant clumps. Nevertheless by computing the mocks at the HST resolution and plotting the clumpsdetected on the mocks with a Salpeter (1955) IMF, as in Figure B1, one can see that they are visually matching the giantclumps seen on mocks with a Chabrier (2003) IMF. This leads us to claim that in the scenario, the giant clumps detection isdominated by the clump finder parameters and not by the choice of the IMF. The exact same effect can be seen with the HighResolution mocks, Figure B2, and with the lens mocks, Figure B3.
MNRAS , 000–000 (0000) ierarchical fragmentation in high redshift galaxies m A B · a r c s ec − m A B · a r c s ec − − . − . − . − . . . . . . C h a b r i e r / S a l p e t e r − Figure B3.
Comparison of Salpeter IMF (left) with Chabrier IMF (center) on lensed mocks. A direct comparison is made on the rightplot. The purple contour are the clumps detected by Astrodendro on the Salpeter IMF mock. MNRAS000