Dark MaGICC: the effect of Dark Energy on galaxy formation. Cosmology does matter
Camilla Penzo, Andrea V. Macciò, Luciano Casarini, Greg S. Stinson, James Wadsley
MMon. Not. R. Astron. Soc. , 1–11 (—) Printed 4 September 2018 (MN L A TEX style file v2.2)
Dark MaGICC: the effect of Dark Energy on galaxyformation. Cosmology does matter.
C. Penzo (cid:63) , A.V. Macci`o , L. Casarini , G. S. Stinson , J. Wadsley Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, 69117 Heidelberg, Germany Departamento de Fisica, Universidade Federal do Espirito Santo, Av. Fernando Ferrari 514, 29075-910 Vitoria (ES), Brazil Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1, Canada
ABSTRACT
We present the Dark MaGICC project, which aims to investigate the effect ofDark Energy (DE) modeling on galaxy formation via hydrodynamical cosmologicalsimulations. Dark MaGICC includes four dynamical Dark Energy scenarios with timevarying equations of state, one with a self-interacting Ratra-Peebles model. In eachscenario we simulate three galaxies with high resolution using smoothed particle hy-drodynamics (SPH). The baryonic physics model is the same used in the MakingGalaxies in a Cosmological Context (MaGICC) project, and we varied only the back-ground cosmology. We find that the Dark Energy parameterization has a surprisinglyimportant impact on galaxy evolution and on structural properties of galaxies at z = 0,in striking contrast with predictions from pure Nbody simulations. The different back-ground evolutions can (depending on the behavior of the DE equation of state) eitherenhance or quench star formation with respect to a ΛCDM model, at a level similarto the variation of the stellar feedback parameterization, with strong effects on thefinal galaxy rotation curves. While overall stellar feedback is still the driving force inshaping galaxies, we show that the effect of the Dark Energy parameterization playsa larger role than previously thought, especially at lower redshifts. For this reason,the influence of Dark Energy parametrization on galaxy formation must be taken intoaccount, especially in the era of precision cosmology. Key words: cosmology: dark energy – galaxy: formation – galaxies: spiral – hydro-dynamics – methods: numerical
Since the first Type Ia Supernova data were published (Riesset al. 1998, Perlmutter et al. 1999), it has been clear that ourUniverse is expanding with a positive acceleration. To en-able an accelerated expansion, there needs to be a repulsiveforce in our model of the Universe, and thus Einstein’s Cos-mological Constant Λ was reintroduced. Its reintroductionlead to the current standard Λ Cold Dark Matter (ΛCDM)cosmological model.Allowing the existence of a Cosmological Constant isthe simplest solution to obtain a positive acceleration. Itimplies that more than 70% of the energy in our Universecould be described as a homogeneous fluid whose equation- (cid:63) [email protected] of-state parameter is w ≡ p/ρ = − Λ remains constant as a function of time.Despite the excellent agreement of ΛCDM cosmologywith observations, the model does suffer from fundamentalproblems. The Cosmological Constant must be finely tunedin the early Universe to reproduce the fit to observations wesee today. Moreover, the attempt to explain the presence ofsuch an energy density with vacuum energy fails by severalorders of magnitude in predicting today’s Λ energy densityvalue. Finally it is a remarkable coincidence that the valuesof the energy densities of Λ and of matter are today of thesame order (see Weinberg 1989, Carroll et al. 1992).For these reasons cosmologists have been seeking alter-natives to a Cosmological Constant. Such alternatives aregenerally referred to as ”dark energy”, a more general settingin which the equation-of-state parameter w is allowed to bea function of time. Under this assumption, we describe dark c (cid:13) — RAS a r X i v : . [ a s t r o - ph . C O ] J a n C. Penzo et al. energy with a homogeneous scalar field whose energy den-sity evolves with time. This changes the expansion historyof the Universe and affects the evolution of density pertur-bations, Baldi (2012). Thus, distinctive signatures of darkenergy models can be found by looking at the formation ofstructures.In pioneering dark-matter-only simulations with anevolving w , Klypin et al. (2003) found that the differencesbetween the cosmological models were not significant at z=0both in the non-linear matter power spectrum and in thehalo mass function, although differences between models be-came significant at higher redshifts with a higher number ofclusters for the dark energy models compared to ΛCDM.Subsequently, multiple groups investigated the proper-ties of dark matter structures in DE cosmologies (Dolaget al. 2004, Bartelmann et al. 2005 and Grossi & Springel2009). They looked at halo concentrations, velocity disper-sions and abundance relations in dark energy and early darkenergy models. More significant differences on the halo massfunctions between the ΛCDM and dark energy cosmologieswere found at high redshifts (in these works, all models havethe same value for the mean density amplitude σ at z=0).Several studies compared the inner structure of haloessimulated in ΛCDM and dark energy cosmologies in col-lisionless simulations. In all cases, a Navarro-Frenk-White(Navarro et al. 1997) density profile well described the mat-ter distribution. The only difference in the dark energy simu-lations was that the matter was more centrally concentratedbecause the haloes had earlier formation times (Klypin et al.2003; Linder & Jenkins 2003; Kuhlen et al. 2005).While these studies all considered dark energy cosmolo-gies that featured earlier collapse times than ΛCDM, it isalso possible for dark energy cosmologies to form structurelater. The equation-of-state parameter, w ( a ) can “cross overthe Cosmological Constant boundary from below”. In otherwords, w can evolve from w < − w > − z = 0. Such models have less collapsed structure at highredshift than ΛCDM. Xia et al. (2006) and Xia et al. (2013)showed observational constraints favor such models.While it is useful to study collisionless simulationsof dark energy cosmologies, we can only directly observebaryons. Even though they account for ∼ of the massdensity of dark matter in the Universe, baryons can havean impact on the formation of small scale structures (White1976; Zhan & Knox 2004; Puchwein et al. 2005; Jing et al.2006; Rudd et al. 2008; Casarini et al. 2011b; De Boni et al.2011; van Daalen et al. 2011; Casarini et al. 2012; Fedeliet al. 2012). So far, simulations including dark energy havefocused on massive galaxy clusters since cosmology has thelargest effect on the formation of the largest structures.In the last decade different groups have been studyinggalaxy formation and evolution by performing high reso-lution hydrodynamical simulations in a cosmological con-text. Only recently they have succeeded in simulating real-istic disk galaxies, e.g. star formation history matching withobservational constrains, flat rotation curves, exponentialsurface density profiles (see Robertson et al. 2006, Gover-nato et al. 2007, Agertz et al. 2011, Guedes et al. 2011,Brook et al. 2012, Scannapieco et al. 2012, Stinson et al.2013a, Marinacci et al. 2013). In all of these high resolutionsimulations a ΛCDM cosmology has always been assumed.Recently an attempt to study galaxy formation in differ- ent cosmological models has been presented in Fontanotet al. (2012, 2013), where Nbody simulations where com-bined with a Semi Analytical Model (SAM) for galaxy for-mation. While they were able to address the effect of cosmol-ogy on global properties of galaxies (e.g. the cosmic star for-mation), due to their approach they were not able to studythe effects of Dark Energy parametrization on the internalstructure of simulated galaxies.In this work we aim to perform the first detailed studyof the effect of dark energy on galactic scale using high res-olution hydrodynamical simulations. Our study is an exten-sion of the MaGICC project (Making Galaxies In a Cos-mological Context) and we dubbed it DarkMaGICC. TheMaGICC project has been quite successful in reproducingseveral properties of observed galaxies, including star for-mation rates and stellar masses (Brook et al. 2012; Stinsonet al. 2013a), metals production and distribution (Stinsonet al. 2012; Brook et al. 2013b), flat rotation curves andcored profiles (Macci`o et al. 2012; Di Cintio et al. 2014) anddisc properties as observed in the Milky-Way (Brook et al.2013a; Stinson et al. 2013b).We adopt the same set of numerical parameters describ-ing the baryonic physics as in Stinson et al. (2013a), andperform high resolution hydrodynamical simulations withdifferent dark energy backgrounds, to study the impact ofCosmology on galaxy properties. In the spirit this paper isvery similar to the recent work by Herpich et al. (2014) thatextended the MaGICC project to Warm Dark Matter cos-mologies.This paper is organized as follows. In Section 2 the cos-mological models are described and compared with observa-tional constraints. In Section 3 we introduce the numericalmethods and implementations. In Section 4.1 we outline theresults from our set of simulations and investigate the in-terplay between feedback and dark energy. Finally we drawconclusions in Section 5. For our project we have chosen four dynamical Dark Energy(dDE) models, each of which is consistent with WMAP7data (Komatsu et al. 2011) at the two sigma level. Allthe models have at z = 0: Ω b = 0 . DM = 0 . H = 70 . − s − Mpc − , σ = 0.816, n s = 0 . ww ( a ) ≡ p ( a ) /ρ ( a ) = w + (1 − a ) w a (1)In Table 1 we show the values we chose for w and w a ineach of the three cases. waCDM0 is a model very close toLCDM as shown in Casarini et al. (2009), while waCDM1and waCDM2, already studied in Casarini et al. (2011a), aremost distant in terms of w a on the w -w a contour plot inFigure 1.We have then also included a fourth cosmological model,which we called SUCDM, in which dark energy is described c (cid:13) — RAS, MNRAS , 1–11 ark MaGICC: Dark Energy and galaxy formation Table 1.
Parameters of the waCDM cosmological models w w a waCDM0 (green) -0.8 -0.755waCDM1 (yellow) -1.18 0.89waCDM2 (red) -0.67 -2.28 LCDM SUCDMwaCDM1 waCDM0waCDM2
Figure 1.
Confidence contours of constrains for w and w a fromWMAP7. Each cosmological model is represented by a star. All of these models are viable models according to WMAP7 data.The star representing the SUCDM model is here shown only forcomparison, but clearly its position on this plot holds only at z =0, since its equation-of-state parameter w ( a ) cannot be describedby the CPL parametrization. by a scalar field with a SUGRA (SUper GRAvity) self-interacting potential of the form V ( φ ) = Λ α φ α exp(4 πGφ ) (2)where we chose α = 2 . w a - w plane are shown, and each cosmological model isrepresented by a triangle. It is important to note that all ofthese models are viable models according to WMAP7 data.The triangle representing the SUCDM model is here shownonly for comparison, but clearly its position on this plotholds only at z = 0, since it’s equation-of-state parameter w ( a ) cannot be described by the CPL parametrization.In order to show how the background evolution of thesedifferent cosmological models changes, in Figure 2 we showthe expansion velocity of the universe in all the different cho-sen cosmologies. We chose to compare different cosmologicalmodels by normalizing them to the same σ today. With thischoice, a model with a faster expansion will have to start pro-ducing structure earlier than a model with slower universeexpansion. This means that statistically, the SUCDM model Figure 2.
Expansion velocities of the universe in units of theHubble constant as a function of the scale factor. Different colorsrepresent different cosmological models. (blue) will show collapsed structures at an earlier epoch thanthe waCDM2 model (red), in order to compensate for thefaster expansion of the universe. The earlier structure for-mation also leads to earlier accretion of the substructuresonto the main halo. In turn, we expect that earlier accretionwill lead to earlier star formation in the simulated galaxies.
We modified the initial condition generator grafic-2 (Bertschinger 2001) such that we can generate initial con-ditions for a generic cosmological model once the evolutionof the cosmological parameters are given as an input. Ourimplementation requires transfer functions for baryons andfor dark matter at initial and final redshift, evolutions of thedensity parameters Ω i , linear growth factor D + and f Ω , thelogarithmic derivative of the growth factor with respect tothe scale factor.We have computed the transfer functions with a modi-fied version of camb (Lewis & Bridle 2002) that allows us toaccount for dynamical dark energy scenarios. As the originalcode, grafic-de is able to generate zoomed initial condi-tions from a cosmological box.At first we generate a uniform particle distribution ina 80 Mpc/h box with 350 particles. The initial conditionswere evolved with the pkdgrav tree-code (Stadel 2001), wethen select a dark matter halo and we re-simulate it with pkdgrav for the dark-matter-only runs and with gasoline Wadsley et al. (2004) for the hydrodynamical runs. TheΛCDM halos are chosen so that no structures are presentin within three of their virial radii and the equivalent halosin the other cosmological models are then identified.Both pkdgrav and gasoline have been modified sothat they can accept cosmological background evolutionsas inputs. We have simulated three different galaxies, gal α ,gal β , gal γ , and each of them was then run in all five cosmo-logical models. In Table 2 we summarize the main propri- c (cid:13) — RAS, MNRAS000
We modified the initial condition generator grafic-2 (Bertschinger 2001) such that we can generate initial con-ditions for a generic cosmological model once the evolutionof the cosmological parameters are given as an input. Ourimplementation requires transfer functions for baryons andfor dark matter at initial and final redshift, evolutions of thedensity parameters Ω i , linear growth factor D + and f Ω , thelogarithmic derivative of the growth factor with respect tothe scale factor.We have computed the transfer functions with a modi-fied version of camb (Lewis & Bridle 2002) that allows us toaccount for dynamical dark energy scenarios. As the originalcode, grafic-de is able to generate zoomed initial condi-tions from a cosmological box.At first we generate a uniform particle distribution ina 80 Mpc/h box with 350 particles. The initial conditionswere evolved with the pkdgrav tree-code (Stadel 2001), wethen select a dark matter halo and we re-simulate it with pkdgrav for the dark-matter-only runs and with gasoline Wadsley et al. (2004) for the hydrodynamical runs. TheΛCDM halos are chosen so that no structures are presentin within three of their virial radii and the equivalent halosin the other cosmological models are then identified.Both pkdgrav and gasoline have been modified sothat they can accept cosmological background evolutionsas inputs. We have simulated three different galaxies, gal α ,gal β , gal γ , and each of them was then run in all five cosmo-logical models. In Table 2 we summarize the main propri- c (cid:13) — RAS, MNRAS000 , 1–11 C. Penzo et al.
Table 2.
Physical properties of the selected galaxies for the re-spective ΛCDM cases. We show virial radius, virial mass (totalmass), dark matter mass, gaseous mass and stellar mass, respec-tively calculated within one virial radius. R vir M vir M DM M gas M ∗ [kpc] [ M (cid:12) ] [ M (cid:12) ] [ M (cid:12) ] [ M (cid:12) ]gal α
240 7 . × . × . × . × gal β
227 6 . × . × . × . × gal γ
184 3 . × . × . × . × eties of the three galaxies in ΛCDM cosmology that we havechosen for this project. For all three galaxies the softeningfor gas and dark matter particles are respectively 0.45 and1 kpc. Note that, for all galaxies, the SUGRA equivalentsare always the most massive and, on the other hand, thewaCDM2 are always the least massive. For the DarkMaGICC project we are using the same bary-onic physics that was used in the MaGICC project (seeStinson et al. 2013a), based on the smoothed particle hy-drodynamics (SPH) code gasoline (Wadsley et al. 2004).For further details on the physical processes implemented in gasoline please refer to Stinson et al. (2013a). Briefly, starsform from cool dense gas that has reached a temperature of T = 1 . × K and a density of 9.6 cm − following theKennicutt-Schmidt Law with 10% efficiency of turning gasinto stars during one dynamical time (Stinson et al. 2006).The stellar mass distribution in each star particle follows theChabrier initial mass function (IMF), Chabrier (2003).Massive stars explode as type II supernovae and depositan energy of E SN = 10 ergs into the surrounding gas.Cooling for gas particles subject to supernova feedback isdelayed based on the sub-grid approximation of a blast waveas described in Stinson et al. (2006).Furthermore, radiation energy from massive stars isconsidered since molecular clouds are disrupted before thefirst supernova explosion (which happens after 4 Myr fromthe formation of the stellar population). We assume that10% of the total radiation energy is coupled with the sur-rounding gas. The inclusion of this early stellar feedbackreduces star formation before supernovae start exploding.Thus, after the early stellar feedback heats the gas to T > K, the gas rapidly cools to 10 K, which createsa lower density medium than if the gas were allowed tocontinue cooling until supernovae exploded. Stinson et al.(2013a) shows how this feedback mechanism limits star for-mation to the amount prescribed by the stellar-halo massrelationship at all redshifts. The code also includes metalcooling and metals can diffuse between gas particles as de-scribed in Shen et al. (2010).The hydrodynamical simulations in all cosmologicalmodels have been run with the same feedback descriptionsjust mentioned. The main point of the work is not whichof the many recently used feedback recipes best reproducedobservations, but the impact of dynamical Dark Energy ongalactic scales.
Figure 3.
Radial density profile of gal α simulated in all fivecosmological models, respectively in a dark matter only (upperpanel) and in a hydrodynamical simulation (lower panel). Weplot the density in units of critical density, ρ crit = H πG withG gravitational constant, as a function of the distance from thecenter of mass of the galaxy. Different colors represent differentcosmological models. Using hydrodynamical and dark matter only simulations,we present how gal α , gal β and gal γ evolved and their z = 0properties. These include the dark matter distribution, gas,star and total halo masses, star formation histories, baryonicmatter distribution (rotation curves and surface brightnessprofiles), and the chemical enrichment of the galaxies. Fig. 3 shows how the dark matter profiles of simulations withand without baryons compare in gal α for all different cosmo-logical models. Gal β and gal γ show similar results. The fourradial density profiles from the dark matter only simulations(top panel) are almost indistinguishable. This confirms pre-vious findings from N-body simulations (see Section 1), i.e. c (cid:13) — RAS, MNRAS , 1–11 ark MaGICC: Dark Energy and galaxy formation Figure 4.
Stellar mass as a function of halo mass at z = 0 forgal α , gal β , gal γ simulated in all the different cosmologies. that dark matter only simulations on galactic scales weaklydepend on the dark energy model.The lower panel of Fig. 3 shows the radial density pro-files of dark matter in hydrodynamical simulations. In con-trast to the dark matter only simulations, the density pro-files vary depending on the dark energy model used.Fig. 4 sets gal α , gal β and gal γ in the abundance match-ing plot at z = 0. The black line represents the predictionobtained by the abundance matching technique (see Mosteret al. 2013), and the shaded area represents the errors onthe prediction. The abundance matching prediction does notvary from ΛCDM to the other cosmologies since all cosmo-logical models have the same value for σ at z = 0. Whilestatistical conclusions are not possible because of the lim-ited sample, the three galaxies show the same trend as afunction of cosmology. By simply varying the cosmologicalmodel, the change among the three galaxies is of only afew percent in the dark matter mass, while the stellar massalmost doubles. Galaxies simulated in the waCDM2 cosmol-ogy (red symbols) always make the least stars at z = 0,while the galaxies formed in the SUGRA cosmology (bluesymbols) always make the most stars. Galaxies formed in aΛCDM cosmology always lie in the middle. The hierarchy isin agreement with the behaviors of the cosmological back-ground evolutions of these cosmological models (Fig. 2 andSection 1), since we expect more structures to be formed ina cosmological model that begins forming structures earlier. M (cid:63) − M h relationship Fig. 5 shows how the ratio of stellar mass and total massevolve with expansion factor a = 1 / ( z + 1). Each panel re-lates to a specific galaxy and the different colors describeeach galaxy run in a different cosmology. Again, the blacksolid line represents the expected evolution for a ΛCDMmodel using the abundance matching technique. The pre-dicted evolutions do change with the change in cosmology,but they all do not distance themselves significantly from theΛCDM prediction. Hence, out of clarity, we have only plot-ted the ΛCDM predicted behavior from abundance match- ing. As in the z = 0 case, the M (cid:63) − M h trends for thegalaxies simulated in different cosmologies are in agreementwith the evolution of their cosmological backgrounds. Inthe SUCDM cosmology, we expect higher density perturba-tions to compensate for the faster expansion of the Universe.These higher density perturbations trigger a more efficientstar formation (blue lines in Fig. 5). On the contrary, thewaCDM2 galaxy (red lines) always makes less stars through-out its evolution. The cosmological models waCDM0 andwaCDM1 are not far apart from the ΛCDM model, in the w a − w plane, thus we would expect galaxies that live inthose models not to differ greatly from galaxies that live inthe ΛCDM universe. This expectation is nicely reproducedfor all three haloes.As shown in Fig. 5 it is noticeable how both gal α andgal β undergo a significant merger around a = 0 . Fig. 7 shows the star formation rate (SFR) as a function ofphysical time. At z = 0 the different cosmological modelsshow longer or shorter ages of the Universe because howmuch physical time elapses as the Universe expands dependson the choice of cosmology. The choice of showing the starformation in standard physical units gives more insight.Fig. 7 shows how dark energy can suppress and delaystar formation. Interestingly, the waCDM2 cosmology (redlines) delays star formation, both in the case of gal α andgal β . In all three galaxies the waCDM2 cosmology drasti-cally suppresses star formation until recent times.As pointed out in Section 4.2, both gal α and gal β un-dergo a merger. The merger event is clearly marked by thepresence of a peak in the SFRs between 7 and 10 Gyrs (no-tice how the peak shifts in time according to the cosmo-logical model). After the star formation burst due to themerger, both galaxies decrease their star formation activitydue to the decrease in the amount of available cold gas. Thisis shown in Fig. 6, where we plot the evolution of the darkmatter mass and the cool gas mass (T < K).
Different star formation histories reflect different matter dis-tributions among the galaxy, as the rotation curves in Fig. 8show. Galaxies with delayed star formation (waCDM2 cos-mology, red lines in Fig. 7) have flatter rotation curves thangalaxies where star formation started earlier (SUCDM cos-mology, blue lines), see Stinson et al. 2013a. Thus, a galaxycan have a flat or centrally peaked rotation curve based sim-ply on the background cosmology in which it forms.Centrally peaked rotation curves have long been theprime symptom of the overcooling problem in disk galaxyformation simulations, see Scannapieco et al. (2012). In thecenters of halos the gas density becomes high enough thathot gas starts radiating and consequently cools. In such envi-ronments, the cooling process is unstable because, once the c (cid:13) — RAS, MNRAS000
Different star formation histories reflect different matter dis-tributions among the galaxy, as the rotation curves in Fig. 8show. Galaxies with delayed star formation (waCDM2 cos-mology, red lines in Fig. 7) have flatter rotation curves thangalaxies where star formation started earlier (SUCDM cos-mology, blue lines), see Stinson et al. 2013a. Thus, a galaxycan have a flat or centrally peaked rotation curve based sim-ply on the background cosmology in which it forms.Centrally peaked rotation curves have long been theprime symptom of the overcooling problem in disk galaxyformation simulations, see Scannapieco et al. (2012). In thecenters of halos the gas density becomes high enough thathot gas starts radiating and consequently cools. In such envi-ronments, the cooling process is unstable because, once the c (cid:13) — RAS, MNRAS000 , 1–11 C. Penzo et al.
Figure 5.
Evolutions of the stellar-halo mass relation as a function of expansion factor for gal α , gal β and gal γ . Figure 6.
Evolution of the dark matter mass (solid lines) and gas mass (dashed lines) as a function of scale factor for the for gal α , gal β and gal γ in all different cosmological models. For an easier comparison, the gas mass was increased of a factor of five. hot gas has cooled, it no longer pressure supports the sur-rounding gas, which then becomes denser and cools. Starsthen form in excess and primarily in the central concentra-tion, and they produce peaked rotation curves.Most solutions have focused on adding energy from starsor AGN (Scannapieco et al. 2012). Stinson et al. (2013a)showed one solution based on stellar winds from massivestars (i.e. “early stellar feedback”). Our results show thatalso cosmology can have a considerable effect on flatteningrotation curves.This work shows that simply changing the evolutions ofthe dark energy equation of state flattens rotation curves ofa considerable and definitely observable amount (i.e. morethan 100 km/s in both gal α and gal β ). Fig. 9 compares ro-tation curves for gal α in dark matter only simulations (up-per panel) and in SPH simulations (lower panel) for eachcosmological model. The change is striking. While in thedark matter only case the cosmological models are almostindistinguishable, they become clearly distinguishable in thehydrodynamical simulations.Stinson et al. (2013a) show that early stellar feedbackis a key ingredient to simulate realistic disc galaxies. In par-ticular, early stellar feedback can flatten rotation curves. Unexpectedly, at z = 0 the effect of early stellar feedback iscomparable with the effect of dynamical dark energy. Differences due to cosmologies are also visible in the surfacebrightness profiles at z=0, as Fig. 10 shows. Here we plot-ted only the two extreme cosmological models out of clarity.As seen in Section 4.3, waCDM2 cosmology (red lines) isable to suppress and delay star formation until low redshifts,when star formation finally starts to increase. In turn, a sup-pressed and delayed star formation affects the shapes of thesurface brightness profiles, especially in the two most mas-sive galaxies. Gal α and gal β show steeper profiles in theirinner regions (for further discussion on effects of delayed starformation on surface brightness profiles, see Stinson et al.2013b).The rest of the cosmological models do not significantlyaffect the profiles nor the scale lengths. As shown in theprevious sections, the effect of cosmology seems to increasewhen the galaxy has a mass that is close to the peak of bary-onic efficiency, and this is confirmed also when looking at thesurface brightness profiles, where the effects of cosmology ongal γ are not significant. c (cid:13) — RAS, MNRAS , 1–11 ark MaGICC: Dark Energy and galaxy formation Figure 7.
Star formation histories for gal α , gal β and gal γ in all the cosmological models. Figure 8.
Rotation curves for gal α , gal β and gal γ in all the cosmological models. We showed that a model whose universe velocity expansionis slower compared to the one of ΛCDM (e.g. waCDM2, redlines) has a lower star formation till much later times, andon the other hand a model whose universe velocity expan-sion is faster than ΛCDM (e.g. SUGRA, blue lines) has ahigher star formation at all redshifts (see Figure 7). We cantrace back this difference to the fact that all five differentcosmological models have the same σ today, because, in or-der for this to happen, structures in a SUGRA model (bluelines) have to start forming earlier. This implies that, atthe starting redshift ( z = 99 for all simulations), the den-sity perturbations that seeded structure formation had to beslightly bigger in the SUGRA model (blue lines) comparedto the initial density perturbations in the waCDM2 model(red lines). Thus, stars will start forming earlier since moregas is accreted and cools.These differences in the initial perturbations do not sig-nificantly affect properties of structures on galactic scales indark matter only simulations. On the other hand, the in-terplay between cooling, metallicity and star formation notonly helps differentiating between the cosmological modelsbut also enhances their differences. To highlight the positivefeedback star formation has on radiative cooling through metal enrichment, the first three rows of Fig. 11 show theevolution of metallicity as a function of scale factor for threedifferent regions of gal α and gal β , a central 2 kpc sphere(“bulge”), a disk cylinder with radius 20 kpc and 6 kpc thick-ness (“disc”), and a sphere of the size of the R vir (“halo”).The waCDM2 model (red) exhibits the lowest metal-licity in the bulge and disc throughout its evolution, whichreflects its lower star formation rate and hence lower en-richment rate. The effect of increased metal enrichment isnon-linear: the more star formation enriches gas, the fasterthe gas cools, and the more stars that subsequently form.The halo metallicity of waCDM2 is also lower through-out most of the galaxy evolution, but becomes higher after a ∼ .
75, as its mean halo metallicity continues increasingwhile the metallicity in the other models starts to decreaseor flatten out at that time. Both waCDM2 galaxies start tohave more metallicity in the halo due to Supernova explo-sions being able to move the gas outside from the disc.Comparing the trends for metallicity, cool gas (Fig. 11)and star formation rates (Fig. 7) as functions of scale factor,we find them in agreement. Because of the lower metallic-ity, the waCDM2 model (red line) ends up having the leastamount of gas that has been able to cool and thus also makesthe least amount of stars. Having used up a smaller amountof cold gas at earlier times increases the amount of cold gas c (cid:13) — RAS, MNRAS000
75, as its mean halo metallicity continues increasingwhile the metallicity in the other models starts to decreaseor flatten out at that time. Both waCDM2 galaxies start tohave more metallicity in the halo due to Supernova explo-sions being able to move the gas outside from the disc.Comparing the trends for metallicity, cool gas (Fig. 11)and star formation rates (Fig. 7) as functions of scale factor,we find them in agreement. Because of the lower metallic-ity, the waCDM2 model (red line) ends up having the leastamount of gas that has been able to cool and thus also makesthe least amount of stars. Having used up a smaller amountof cold gas at earlier times increases the amount of cold gas c (cid:13) — RAS, MNRAS000 , 1–11 C. Penzo et al.
Figure 10.
Disc scale lengths for gal α , gal β and gal γ for ΛCDM , waCDM2 (red lines) and SUGRA (blue lines). For clarity, only thesetwo models are shown. Figure 9.
Rotation curve for gal α in all different cosmologicalmodels, respectively in a dark matter only simulation (upperpanel) and in a hydrodynamical simulation (lower panel). left for star formation at late times. The presence of cool gasthat has yet not formed stars can be seen in Fig. 11, whereafter a = 0 . Along with dark energy having a profound effect on galaxyevolution, galaxy formation strongly depends on the feed-back modeling. Stinson et al. (2013a) showed that pre-supernova feedback primarily suppresses star formation atearly stages of evolution, which is similar to the evolutionseen in the dark energy models that have the most delayedexpansion. Thus, we wish to explore whether dark energy orstellar feedback has a greater effect at early times.We select the waCDM2 cosmology (red lines in previ-ous plots), which showed the most star formation suppres-sion and delay, and we re-simulate it with a range of stellarfeedback strengths. We vary both the supernova feedbackefficiency and the early stellar feedback separately.First, the early stellar feedback is turned from 10%down to 0% efficiency with the standard 10 erg of super-nova energy. Then, with 0 early stellar feedback, the super-nova feedback strength is increased to 120% and 150%.The left panel of Fig. 12 shows each of these variationsimplemented in the waCDM2 model for gal α . The stellarmass evolution shows a strong dependence on the early stel-lar feedback parameter. A decrease of 25% to 7.5% increasesthe final stellar mass 50% and moves most of the star forma-tion from late to early times. All the simulations with lessthan 7.5% efficiency, but more than 0 early stellar feedbackend with nearly the same final stellar mass. What is some-what surprising is that the simulation with 0 early stellarfeedback ends with l ess stellar mass than these intermediatefeedback models. Stinson et al. (2013a) also saw this effectand found that it was due to the higher star formation ef-ficiency at early times driving stronger outflows due to thegreater supernova feedback. Thus, gas was driven to radii c (cid:13) — RAS, MNRAS , 1–11 ark MaGICC: Dark Energy and galaxy formation Figure 12.
Evolution of stellar-halo mass relation with scale factor. We are now showing only the case of gal α . In the left panel we havechanged the feedback parameters for the waCDM2 run. We have increased the early stellar feedback parameter from zero to the fiducialvalue (see Stinson et al. (2013a)) while keeping the SN parameter fixed to the fiducial value of 1.0 (solid lines). We then have changedthe SN parameter while keeping the early stellar feedback fixed to zero (dashed and dash-dotted cyan lines). The dotted black line is theabundance matching prediction and the shaded area its errors. In the right panel we compare the effect of early stellar feedback feedbackwith the effect of different cosmology, ΛCDM (red and black lines) and waCDM2 (blue and red) where it could not be reaccreted, whereas the early stellarfeedback does not drive gas so far away.Supernova feedback unambiguously decreases theamount of stars formed throughout the galaxy’s evolution,but can easily push the trends out of the expected behav-iors from abundance matching techniques suggesting thatSupernova feedback alone is not enough to reproduce real-istic galaxies.The right panel of Fig. 12 shows a comparison of thestellar mass-halo mass evolution of the waCDM2 model (redlines) with the LCDM model (black lines) for gal α . Themodels separate most notably at late times. The correspond-ing simulations with no early stellar feedback are shown inthe dashed lines. They clearly show that cosmology has thestrongest effect at late times (i.e. after a = 0 .
7) and pre-SNfeedback has the strongest effect at high redshift.
The intention of this work was to investigate for the firsttime the effect of dark energy on galactic scales in SPHsimulations. We find that the dark energy modeling has anunexpected significant effect on galaxy formation, on thecontrary of what is most commonly believed.The experiment used a suite of SPH zoom-in cosmolog-ical simulations with masses of 3 . × M (cid:12) , 6 . × M (cid:12) and 7 . × M (cid:12) , in four dynamical dark energy modelsplus the reference ΛCDM model. The models all employedthe same baryonic physics prescription. All dynamical darkenergy models lay in within the two sigma contours given byWMAP7. We examined the dark matter distribution, gas,star and total halo masses, star formation histories, baryonic matter distribution (rotation curves and surface brightnessprofiles), and the chemical enrichment of the galaxies.Changing the dark energy evolution implies changingthe expansion rate of the Universe, which in turn affects theaccretion history. We show how the same galaxy evolved indifferent dark energy cosmologies does not present signifi-cant differences in dark matter only simulations, while inhydrodynamical simulations the galactic properties changegreatly.At z = 0, the stellar mass inside r vir can vary by a fac-tor of 2 depending on cosmology, while the dark matter massonly changes of a few percent. Thus baryons amplify differ-ences between dark energy models, as the evolution of thestellar mass - halo mass ratio shows: by simply changing thedark energy parametrization stellar mass either decreasesor increase of a factor of two throughout the whole galaxyevolution.The reason why baryons amplify the differences amongthe various dynamical dark energy models lays on the nonlinear response of the hydrodynamical processes. Once thecosmological model introduces slightly different density per-turbations, feedback processes enhances those differences byproducing slightly more (or less) stars. More stars introducemore metals in the feedback cycle and more metals decreasethe cooling time, which in turn allows gas to cool faster andproduce even more stars. Through the highly non-linear re-sponse of baryons, dark energy models that would have beenindistinguishable from ΛCDM on galactic scales show dis-tinctive features in SPH simulations.The distinctive features of dynamical dark energy be-come clear when looking at the star formation rates. We findthat certain dark energy models are able to both delay andsuppress star formation until recent epochs. The delay in c (cid:13) — RAS, MNRAS000
The intention of this work was to investigate for the firsttime the effect of dark energy on galactic scales in SPHsimulations. We find that the dark energy modeling has anunexpected significant effect on galaxy formation, on thecontrary of what is most commonly believed.The experiment used a suite of SPH zoom-in cosmolog-ical simulations with masses of 3 . × M (cid:12) , 6 . × M (cid:12) and 7 . × M (cid:12) , in four dynamical dark energy modelsplus the reference ΛCDM model. The models all employedthe same baryonic physics prescription. All dynamical darkenergy models lay in within the two sigma contours given byWMAP7. We examined the dark matter distribution, gas,star and total halo masses, star formation histories, baryonic matter distribution (rotation curves and surface brightnessprofiles), and the chemical enrichment of the galaxies.Changing the dark energy evolution implies changingthe expansion rate of the Universe, which in turn affects theaccretion history. We show how the same galaxy evolved indifferent dark energy cosmologies does not present signifi-cant differences in dark matter only simulations, while inhydrodynamical simulations the galactic properties changegreatly.At z = 0, the stellar mass inside r vir can vary by a fac-tor of 2 depending on cosmology, while the dark matter massonly changes of a few percent. Thus baryons amplify differ-ences between dark energy models, as the evolution of thestellar mass - halo mass ratio shows: by simply changing thedark energy parametrization stellar mass either decreasesor increase of a factor of two throughout the whole galaxyevolution.The reason why baryons amplify the differences amongthe various dynamical dark energy models lays on the nonlinear response of the hydrodynamical processes. Once thecosmological model introduces slightly different density per-turbations, feedback processes enhances those differences byproducing slightly more (or less) stars. More stars introducemore metals in the feedback cycle and more metals decreasethe cooling time, which in turn allows gas to cool faster andproduce even more stars. Through the highly non-linear re-sponse of baryons, dark energy models that would have beenindistinguishable from ΛCDM on galactic scales show dis-tinctive features in SPH simulations.The distinctive features of dynamical dark energy be-come clear when looking at the star formation rates. We findthat certain dark energy models are able to both delay andsuppress star formation until recent epochs. The delay in c (cid:13) — RAS, MNRAS000 , 1–11 C. Penzo et al.
Figure 11.
Mean metallicity in solar units and cool gas in solarmasses (T < K) for gal α and gal β as function of scale factorin “bulge”, “disc” and “halo”. Different colors represent differentcosmological models. star formation is then in turn responsible for the flattening ofrotations curves, where we show a change of about 100 km/sin the two most massive galaxies we considered. Throughoutthe analysis, the least massive galaxy is the least sensitive todark energy parametrization changes, in agreement with thefact that stellar feedback is most effective around 10 M (cid:12) (Di Cintio et al. 2014). The two most massive galaxies liv-ing in a slower expanding universe (waCDM2 model) havesteeper surface brightness profiles due to their delayed starformation.Finally we compare the effect of dynamical dark energywith the effect of baryonic feedback. We keep the cosmologyfixed (waCDM2) and change the feedback parametrization.Provided that the Supernova feedback is kept constant, atlate times the effect of dark energy is comparable to theeffect of early stellar feedback (see Stinson et al. 2013a fordetails on feedback modeling). Even the degree at which stel-lar feedback is able to flatten rotation curves, is comparableto the effect of dark energy. We noted on the other hand,that in order to obtain the behavior suggested by abundancematching considerations at high redshifts, early stellar feed-back had to be introduced since at high redshifts it has themost important effect compared to the dark energy model-ing. Having shown that the dark energy modeling has an im-portant effect on galaxy formation and evolution, we wouldlike to stress on the fact that, especially in the era of highprecision cosmology, the details on dark energy do matterand certainly need further investigations. ACKNOWLEDGMENTS
The analysis was performed using the pynbody package( http://code.google.com/p/pynbody ), which was writtenby Andrew Pontzen and Rok Roˇskar in addition to the au-thors. Luciano Casarini acknowledges the Brazilian researchInstitutions FAPES and CNPq for financial support.The numerical simulations used in this work were performedon the THEO cluster of the Max-Planck-Institut f¨ur As-tronomie at the Rechenzentrum in Garching. And A.M.would like to acknowledge the support from the Sonder-forschungsbereich SFB 881 ”the Milky Way System” of theGerman Research Foundation (DFG). Greg Stinson receivedfunding from the European Research Council under the Eu-ropean Union’s Seventh Framework Programme (FP 7) ERCGrant Agreement n. [321035].
REFERENCES
Agertz, O., Teyssier, R., & Moore, B. 2011, MNRAS, 410,1391Alimi, J.-M., F¨uzfa, A., Boucher, V., et al. 2010, MNRAS,401, 775Baldi, M. 2012, Physics of the Dark Universe, 1, 162Bartelmann, M., Dolag, K., Perrotta, F., et al. 2005, ApJ,49, 199Bertschinger, E. 2001, ApJS, 137, 1Brook, C. B., Di Cintio, A., Knebe, A., et al. 2013a, ArXive-prints, arXiv:1311.5492 c (cid:13) — RAS, MNRAS , 1–11 ark MaGICC: Dark Energy and galaxy formation Brook, C. B., Stinson, G., Gibson, B. K., et al. 2013b,ArXiv e-prints, arXiv:1306.5766Brook, C. B., Stinson, G., Gibson, B. K., Wadsley, J., &Quinn, T. 2012, MNRAS, 424, 1275Carroll, S. M., Press, W. H., & Turner, E. L. 1992, AnnualReview of Astronomy and Astrophysics, 30, 499Casarini, L., Bonometto, S. A., Borgani, S., et al. 2012,Astronomy and Astrophysics, 542, A126Casarini, L., La Vacca, G., Amendola, L., Bonometto,S. A., & Macci`o, A. V. 2011a, Journal of Cosmology andAstroparticle Physics, 3, 26Casarini, L., Macci`o, A. V., & Bonometto, S. A. 2009, Jour-nal of Cosmology and Astroparticle Physics, 3, 14Casarini, L., Macci`o, A. V., Bonometto, S. A., & Stinson,G. S. 2011b, MNRAS, 412, 911Chabrier, G. 2003, The Publications of the AstronomicalSociety of the Pacific, 115, 763Chevallier, M., & Polarski, D. 2001, International Journalof Modern Physics D, 10, 213De Boni, C., Dolag, K., Ettori, S., et al. 2011, MNRAS,415, 2758Di Cintio, A., Brook, C. B., Macci`o, A. V., et al. 2014,MNRAS, 437, 415Dolag, K., Bartelmann, M., Perrotta, F., et al. 2004, As-tronomy and Astrophysics, 416, 853Fedeli, C., Dolag, K., & Moscardini, L. 2012, MNRAS, 419,1588Fontanot, F., Puchwein, E., Springel, V., & Bianchi, D.2013, ArXiv e-prints, arXiv:1307.5065Fontanot, F., Springel, V., Angulo, R. E., & Henriques, B.2012, MNRAS, 426, 2335Governato, F., Willman, B., Mayer, L., et al. 2007, MN-RAS, 374, 1479Grossi, M., & Springel, V. 2009, MNRAS, 394, 1559Guedes, J., Callegari, S., Madau, P., & Mayer, L. 2011,ApJ, 742, 76Herpich, J., Stinson, G. S., Macci`o, A. V., et al. 2014, MN-RAS, 437, 293Jing, Y. P., Zhang, P., Lin, W. P., Gao, L., & Springel, V.2006, ApJL, 640, L119Klypin, A., Macci`o, A. V., Mainini, R., & Bonometto, S. A.2003, ApJ, 599, 31Komatsu, E., Smith, K. M., Dunkley, J., et al. 2011, ApJS,192, 18Kuhlen, M., Strigari, L. E., Zentner, A. R., Bullock, J. S.,& Primack, J. R. 2005, MNRAS, 357, 387Lewis, A., & Bridle, S. 2002, Phys. Rev., D66, 103511Linder, E. V. 2003, Physical Review Letters, 90, 091301Linder, E. V., & Jenkins, A. 2003, MNRAS, 346, 573Macci`o, A. V., Stinson, G., Brook, C. B., et al. 2012, ApJL,744, L9Marinacci, F., Pakmor, R., & Springel, V. 2013, ArXiv e-prints, arXiv:1305.5360Moster, B. P., Naab, T., & White, S. D. M. 2013, MNRAS,428, 3121Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, ApJ,490, 493Perlmutter, S., Aldering, G., Goldhaber, G., et al. 1999,ApJ, 517, 565Puchwein, E., Bartelmann, M., Dolag, K., & Meneghetti,M. 2005, Astronomy and Astrophysics, 442, 405Riess, A. G., Filippenko, A. V., Challis, P., et al. 1998, The Astronomical Journal, 116, 1009Robertson, B., Bullock, J. S., Cox, T. J., et al. 2006, ApJ,645, 986Rudd, D. H., Zentner, A. R., & Kravtsov, A. V. 2008, ApJ,672, 19Scannapieco, C., Wadepuhl, M., Parry, O. H., et al. 2012,MNRAS, 423, 1726Stadel, J. G. 2001, PhD thesis, University of WashingtonStinson, G., Seth, A., Katz, N., et al. 2006, MNRAS, 373,1074Stinson, G. S., Brook, C., Macci`o, A. V., et al. 2013a, MN-RAS, 428, 129Stinson, G. S., Brook, C., Prochaska, J. X., et al. 2012,MNRAS, 425, 1270Stinson, G. S., Bovy, J., Rix, H.-W., et al. 2013b, MNRAS,436, 625van Daalen, M. P., Schaye, J., Booth, C. M., & Dalla Vec-chia, C. 2011, MNRAS, 415, 3649Wadsley, J. W., Stadel, J., & Quinn, T. 2004, New Astron-omy, 9, 137Weinberg, S. 1989, Reviews of Modern Physics, 61, 1White, S. D. M. 1976, MNRAS, 177, 717Xia, J.-Q., Li, H., & Zhang, X. 2013, Phy.Rev.D, 88, 063501Xia, J.-Q., Zhao, G.-B., Feng, B., Li, H., & Zhang, X. 2006,Phy.Rev.D, 73, 063521Zhan, H., & Knox, L. 2004, ApJL, 616, L75This paper has been typeset from a TEX/ L A TEX file preparedby the author. c (cid:13) — RAS, MNRAS000