Impact of baryons in cosmic shear analyses with tomographic aperture mass statistics
Nicolas Martinet, Tiago Castro, Joachim Harnois-Déraps, Eric Jullo, Carlo Giocoli, Klaus Dolag
AAstronomy & Astrophysics manuscript no. spe2 © ESO 2021February 22, 2021
Impact of baryons in cosmic shear analyses with tomographicaperture mass statistics
Nicolas Martinet , Tiago Castro , , , , Joachim Harnois-Déraps , , Eric Jullo , Carlo Giocoli , , Klaus Dolag , Aix-Marseille Univ, CNRS, CNES, LAM, Marseille, France Dipartimento di Fisica, Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, I-34143 Trieste, Italy INAF – Osservatorio Astronomico di Trieste, via Tiepolo 11, I-34131 Trieste, Italy IFPU – Institute for Fundamental Physics of the Universe, via Beirut 2, 34151, Trieste, Italy INFN – Sezione di Trieste, I-34100 Trieste, Italy Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool, L3 5RF, UK Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK INAF - Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, via Gobetti 93 /
3, I-40129 Bologna, Italy INFN - Sezione di Bologna, viale Berti Pichat 6 /
2, I-40127 Bologna, Italy University Observatory Munich, Scheinerstr. 1, 81679 Munchen, Germany Max-Planck Institut fur Astrophysik, Karl-Schwarzschild Str. 1, D-85741 Garching, Germanye-mail: [email protected]
February 22, 2021
ABSTRACT
NonGaussian cosmic shear statistics based on weak-lensing aperture mass ( M ap ) maps can outperform the classical shear two-pointcorrelation function ( γ -2PCF) in terms of cosmological constraining power. However, reaching the full potential of these new esti-mators requires accurate modeling of the physics of baryons as the extra nonGaussian information mostly resides at small scales.We present one such modeling based on the Magneticum hydrodynamical simulation for the KiDS-450 and DES-Y1 surveys and a
Euclid -like survey. We compute the bias due to baryons on the lensing PDF and the distribution of peaks and voids in M ap mapsand propagate it to the cosmological forecasts on the structure growth parameter S , the matter density parameter Ω m , and the darkenergy equation of state w using the SLICS and cosmo-SLICS sets of dark-matter-only simulations. We report a negative bias of afew percent on S and Ω m and also measure a positive bias of the same level on w when including a tomographic decomposition.These biases reach ∼
5% when combining M ap statistics with the γ -2PCF as these estimators show similar dependency on the AGNfeedback. We verify that these biases constitute a less than 1 σ shift on the probed cosmological parameters for current cosmic shearsurveys. However, baryons need to be accounted for at the percentage level for future Stage IV surveys and we propose to include theuncertainty on the AGN feedback amplitude by marginalizing over this parameter using multiple simulations such as those presentedin this paper. Finally, we explore the possibility of mitigating the impact of baryons by filtering the M ap map but find that this processwould require to suppress the small-scale information to a point where the constraints would no longer be competitive. Key words. gravitational lensing: weak – cosmology: observations – surveys – Cosmology: dark matter, dark energy & large-scalestructure of Universe
1. Introduction
Weak lensing cosmic shear is one of the most powerful cosmo-logical probes of the late-time Universe. So far, most analyseshave focused on studying the correlation between the shape dis-tortions of pairs of galaxies as a function of their separation:the so-called shear two-point correlation function ( γ -2PCF; e.g.,Troxel et al. 2018; Hikage et al. 2019; Asgari et al. 2021). How-ever, it is becoming clear that other estimators, and in particularthose based on weak-lensing mass maps, outperform the stan-dard γ -2PCF (e.g., Dietrich & Hartlap 2010; Ajani et al. 2020;Zürcher et al. 2021; Coulton et al. 2020; Martinet et al. 2021).Indeed, mass maps are highly sensitive to the nonGaussian partof the matter distribution that arises from the nonlinear growth ofstructures, which contains information that is overlooked by two-point estimators. Consequently, the combination of both probesyields even tighter constraints, as seen in recent applications toobservational data (e.g., Martinet et al. 2018; Harnois-Dérapset al. 2020). With future Stage IV surveys, this combination is also expected to improve not only our measurement of thegrowth of structure parameter S by a factor of two, but also thatof the dark energy equation of state w (Martinet et al. 2021) andof the sum of neutrino masses Σ m ν (Li et al. 2019), by factors ofthree and two, respectively.Nevertheless, these nonGaussian estimators are di ffi cult topredict theoretically because of limits in our understanding ofthe nonlinear growth of structures (see e.g., Fan et al. 2010;Lin & Kilbinger 2015; Shan et al. 2018; Giocoli et al. 2018b;Barthelemy et al. 2020, for some attempts) and are instead mod-eled with N -body simulations. This can significantly increasethe computational cost of such analyses, but resorting to N -body simulations is also necessary to accurately model the γ -2PCF at scales a ff ected by nonlinearities (e.g., Euclid Collabo-ration: Knabenhans et al. 2020). Moreover, many public simula-tion suites can be exploited for this purpose, including the ScinetLIght-Cone Simulations (Harnois-Déraps et al. 2015, SLICS),the cosmo-SLICS (Harnois-Déraps et al. 2019), or the Mas-siveNuS (Liu et al. 2018). Article number, page 1 of 12 a r X i v : . [ a s t r o - ph . C O ] F e b & A proofs: manuscript no. spe2
As mass map estimators focus on small scales of typicallyaround a few arcminutes, they can be severely a ff ected by bary-onic feedback, which can bias the inferred cosmological con-straints. To avoid this, an e ff ective approach is to quantify theimpact of baryons on the estimator with hydrodynamical simu-lations, and to apply a correction factor to the model extractedfrom dark matter (DM) only simulations. For mass maps, thisapproach was pioneered in Yang et al. (2013) and Osato et al.(2015). However, active galactic nuclei (AGN) feedback was notincluded in the first analysis and only with a low amplitude ofthe feedback in the second. As a result, these two studies founda mild impact of the baryonic physics on the distribution of peaksin mass maps and therefore underestimated the bias on cosmo-logical parameters (e.g., Weiss et al. 2019; Coulton et al. 2020).State-of-the-art hydrodynamical simulations with boxlengths of hundreds of megaparsecs and including realisticAGN feedback later enabled refinement of the measure ofthe bias on mass map estimators due to baryons. Fong et al.(2019) measured a ∼
10% reduction in the number of highsignal-to-noise-ratio (S / N) M ap peaks in the BAHAMAS simu-lations (McCarthy et al. 2017), with a particular look at possibledegeneracies between the e ff ect of baryons and that of massiveneutrinos. Osato et al. (2020) measured biases of the same orderof magnitude on the number of peaks, the number of minima,and the lensing probability distribution function (PDF) in theTNG 300 simulation (Pillepich et al. 2018), also highlighting aless pronounced bias at higher redshift.An interesting alternative to hydrodynamical simulations isthe baryonification method described in Schneider & Teyssier(2015) where particle positions are shifted in DM-only simula-tions to mimic the impact of baryons. This method now accu-rately reproduces AGN feedback and star formation comparedto hydrodynamical simulations (Aricò et al. 2020) and could of-fer an e ffi cient way of decreasing the computational resourcesneeded to include baryonic e ff ects in cosmological models. Thistechnique is however not tested in the present article as it re-quires the particle positions, which are generally not stored for aposteriori applications. Weiss et al. (2019) applied this baryonifi-cation method to model the impact of baryons on peak statisticsand also noted that the latter could be mitigated by smoothingthe small scales by applying a Gaussian filter to the mass map.This smoothing is nevertheless likely to also reduce the statisti-cal power of the mass map estimators, a hypothesis that can onlybe verified by propagating this bias to the cosmological parame-ter inference.Recently, Coulton et al. (2020) performed this propagationand measured the impact of baryons directly on the forecastsof the matter density Ω m , the amplitude of fluctuations A S , andthe sum of the neutrino masses for peaks and minima using theBAHAMAS simulations. In a nontomographic approach, theselatter authors found larger biases for peaks than for minima intheir LSST-like mock data, concluding that the latter is poten-tially more robust against baryons.Building on these previous analyses, and exploiting the cos-mological analysis pipeline introduced in Martinet et al. (2021),we measure for the first time the e ff ect of baryons on the darkmatter and dark energy cosmological parameters in a tomo-graphic Stage-IV lensing survey setup. We focus on the particu-lar case of aperture-mass ( M ap ; Schneider 1996) maps, which areparticularly well suited for cosmological analyses. We model thee ff ect of baryons with the Magneticum hydrodynamical simu-lation suite (e.g., Castro et al. 2020), which includes all key in- Fig. 1.
Ratio of power spectra at z = Magneticum used in this analysis is representative of an average behavior with a lossof power of about 15% at k ∼ h Mpc − due to AGN feedback. gredients about the physics of baryons, such as AGN feedback(Springel et al. 2005; Fabjan et al. 2010; Hirschmann et al. 2014)and star formation (Springel & Hernquist 2003). Both e ff ectsredistribute the matter in and around DM haloes, but the exactamplitude of the feedback varies between simulations (see Chis-ari et al. 2019, for a recent review on feedback in cosmologicalhydrodynamical simulations). Extending the simulation suitesof Martinet et al. (2021) based on the SLICS and the cosmo-SLICS, we construct Euclid -like mocks from the
Magneticum hydrodynamical simulation. We measure the impact of baryonson the γ -2PCF, on the lensing peaks, minima, and on the lens-ing PDF, in the form of a multiplicative baryon bias correctionfactor. We then propagate this correction into the cosmologicalinference pipeline described in Martinet et al. (2021), and inves-tigate the impact on the parameter forecasts. Finally, we explorevarious mitigation schemes to decrease the baryon-dominatedsmall-scale contribution to the M ap computation.We introduce the Magneticum simulation and compare it toother state-of-the-art hydrodynamical simulations in Sect. 2. Wepresent the methodology that we employ to measure the bias dueto baryons in Sect. 3. We then measure their impact on di ff erentdata vectors (DV) in Sect. 4.1 and propagate the e ff ect to thecosmological forecasts in Sect. 4.2. We test di ff erent mitigationsetups in Sect. 5 and conclude in Sect. 6. Finally, we adapt ourmocks to the KiDS and DES surveys in Appendix A and mea-sure the impact of baryons on the cosmological constraints byMartinet et al. (2018); Harnois-Déraps et al. (2020) in these twosurveys.
2. Modeling baryonic effects
The
Magneticum suite (Bi ffi et al. 2013; Saro et al. 2014; Stein-born et al. 2015, 2016; Dolag et al. 2015, 2016; Teklu et al.2015; Remus et al. 2017a; Castro et al. 2020) is a compilation of N -body and hydrodynamical simulations describing the cosmicevolution of the Universe. In total, the suite follows up to 2 × particles divided in DM, gas, stars, and black holes. The simula-tions were performed with the TreePM + SPH code P-Gadget3 —a higher performance and more e ffi cient version of the publicly Article number, page 2 of 12artinet, Castro, Harnois-Déraps et al.: Impact of baryons in cosmic shear analyses
Table 1.
Subset of the
Magneticum simulation suite used in this work. From left to right: box size, gravitational softening and the particle massesfor the di ff erent components (DM, gas, and stars), the number of lens planes built, redshift range of the past-light cone, its field of view, and themap angular resolution. A “ − ” indicates that the parameter value of Box 2b / hr is identical to that of Box 2 / hr. Box L box (cid:15) soften . (kpc h − ) N particles m DM m gas m star N planes z min . z max . FoV Pixel Sizename (Mpc h − ) DM Gas Stars ( M (cid:12) h − ) ( M (cid:12) h − ) ( M (cid:12) h − ) (deg.) (arcsec.)2 / hr 352 3 .
75 3 .
75 2 . × . × . × . × . .
248 10 . . / hr 640 − − − × − − −
13 0 .
248 3 . − − available Gadget-2 code (Springel 2005) developed concomi-tantly to its successor Gadget-4 (Springel et al. 2020). Notably,the smoothed-particle-hydrodynamics (SPH) solver implementsthe improved model of Beck et al. (2016). The particle dynam-ics is coupled to di ff erent astrophysical e ff ects such as radiativecooling, heating by a uniform evolving UV background, starformation (Springel & Hernquist 2003), stellar evolution, andchemical enrichment processes (Tornatore et al. 2007). Coolingis implemented following the metallicity-dependent formulationpresented in Wiersma et al. (2009) using cooling tables producedby the publicly available CLOUDY photo-ionization code (Fer-land et al. 1998). Lastly, AGN feedback and black hole growthare modeled as described in Hirschmann et al. (2014).The sub-grid physics model of our simulation reproduces along list of observations, from galaxy properties (Teklu et al.2015; Remus et al. 2017b) and AGN population (Hirschmannet al. 2014; Steinborn et al. 2016), to the intergalactic and inter-cluster medium (Dolag et al. 2016; Bocquet et al. 2016; Guptaet al. 2017). Of particular importance for this work is the ro-bustness of the AGN feedback of our model, which has a clearfootprint on the matter power-spectrum, suppressing its ampli-tude with respect to the DM-only case on k ∼ h Mpc − by ∼ Magneticum provides an AGN feedbacksuppression consistent with other simulations, in particular withBAHAMAS and to a lesser extent with TNG-300, which wereused in other recent mass map analyses. We note that the AGNfeedback also controls the gas fraction of halos (and the conver-sion e ffi ciency into stars) such that the simulations presented inFig. 1 also di ff er in these quantities although the matter powerspectrum is a good indicator with which to assess the currenttheoretical uncertainties in modeling baryonic physics. The
Magneticum past light-cone reconstructions are performedusing the Simulation LIght conE buildeR code — SLICER — closely following the pipeline presented in Castro et al.(2018) and forked from a MapSim branch (Giocoli et al. 2015,2018a; Hilbert et al. 2020). Briefly, light-cones are built inpost-processing, assigning particles to predetermined 2D massmaps according to the triangular-shaped cloud mass assignmentscheme. The geometry of the past light-cones is a square-basedpyramid (in angular coordinates) where the observer is locatedat the z = z max . The opening an- https: // github.com / TiagoBsCastro / SLICER gle is chosen to be 10 degrees and the angular resolution of thelight-cone mass planes is 3 . Σ ( x , y ) as Σ ( x , y ) = (cid:80) nj = m j L p , (1)where n indicates the number of particles, m j the interpolatedcontribution of the j th particle to the pixel at position x , y , and L p is the physical size of the pixel in units of Mpc h − . Given asource plane, convergence maps κ ( x , y ) are created by weightingthese maps by the corresponding critical surface mass density, Σ crit ≡ c π G D l D s D ls , (2)and integrating over the past light-cone. Here, c indicates thespeed of light, G the Newton’s constant, and D l , D s , and D ls arethe angular diameter distances between observer–lens, observer–source, and lens–source, respectively. The shear components ( γ , γ ) are obtained from the standard inversion technique of Kaiser& Squires (1993).As Box 2b Hydro has not been run down to z =
0, ourpast light-cones are built from grafting Box 2 in the range z = [0 , . z = [0 . , . ff ects the lensing statistics for z s (cid:38) . . Intotal, we produced 20 pseudo-independent light-cones — 10 Hy-dro and 10 DM-only — with properties summarized in Table 2.1.
3. Methodology
In this section, we first give a brief description of our cosmolog-ical forecasting pipeline in Sect. 3.1, and then detail the calcula-tion of baryonic bias in Sect. 3.2.
Cosmological forecasts are computed with the same pipeline asin Martinet et al. (2021). While we recapitulate the salient pointsof this analysis here, we refer the reader to this publication formore details. We note that a similar grafting strategy has been used for the high-precision “Clone” data used by the CFHTLenS team (Harnois-Dérapset al. 2012) Article number, page 3 of 12 & A proofs: manuscript no. spe2 • wCDM Simulations: the cosmology dependence of M ap statistics is emulated with radial basis functions basedon measurements from Stage-IV mock data covering 25cosmologies in S − Ω m − w − h , organised in a latinhypercube. These were built from the cosmo-SLICS N -bodysimulations (Harnois-Déraps et al. 2019) and contain 50mocks per cosmology, covering ten light-cones and fiveshape noise realizations to further increase our precision onthe model. The covariance is measured from a separate suiteof N s =
928 fully independent Λ CDM mocks extracted fromthe SLICS N -body simulations (Harnois-Déraps et al. 2018)with the same survey properties. These Stage-IV mocksmatch the expected 30 arcmin − galaxy density of Euclid with a realistic redshift distribution in the range 0 < z < each. While galaxy positions and intrinsic ellipticities arechosen randomly in the covariance mocks, they are fixedacross the di ff erent cosmologies in cosmo-SLICS mocks soas to reduce the impact of shape noise on the model. • Measurements : From each mock, we compute a 1024 × M ap map (Schneider 1996) as a convolution be-tween the tangential ellipticity (cid:15) t around a pixel θ , and theSchirmer et al. (2007) compensated Q filter adapted to thedetection of matter halos: M ap ( θ ) = n gal (cid:88) i Q ( | θ i − θ | ) (cid:15) t ( θ i , θ ) , (3)with Q ( θ ) = (cid:34) + exp (cid:32) θ in − θθ ap (cid:33) + exp (cid:32) − + θθ ap (cid:33)(cid:35) − × (cid:32) θ x c θ ap (cid:33) − tanh (cid:32) θ x c θ ap (cid:33) . (4)This filter is a simpler form of the NFW (Navarro et al.1997) profile with an additional exponential attenuation inthe center and at the edge of the aperture. x c controls thetilt between the core and the edge of the profile and weintroduce an optional inner radius parameter θ in to governthe exponential cut-o ff in the inner part. The sum in Eq.(3) is carried out over galaxies at position θ i within anaperture of radius θ ap = (cid:48) by default (corresponding to ane ff ective smoothing scale of θ ap x c = . (cid:48) ) and centered on θ , and is normalized by the galaxy density n gal within theaperture. We estimate the noise due to intrinsic ellipticitiesin the mocks to define several M ap map statistics basedon the S / N distribution of pixels of these maps: peaks andvoids (pixels with values greater or smaller than their 8neighbors), as well as the full distribution of pixels (1D M ap , often referred to as the lensing PDF). FollowingMartinet et al. (2021), these distributions are organised ineight bins between − . < S / N < . − < S / N < − < S / N < M ap . For each mock, we also com-pute the γ -2PCF ξ ± ( ϑ ) using the Athena software (Kilbingeret al. 2014), with the estimators defined as (Schneider et al.2002): ξ ± ( ϑ ) = (cid:104)(cid:80) i j (cid:15) i t (cid:15) j t ± (cid:15) i × (cid:15) j × (cid:105) / N pairs ( ϑ ), where the sum isover galaxy pairs i j separated by an angle ϑ and potentiallyin di ff erent tomographic bins. The results are binned in eightangular bins logarithmically spaced between 0 . (cid:48) and 60 . (cid:48) for ξ + and between 0 . (cid:48) and 300 (cid:48) for ξ − . The quantities (cid:15) t , × are the tangential and “cross” components of the ellipticities. • Tomography : We separate the mock data into five redshiftbins: 0 < z < .
47, 0 . < z < .
72, 0 . < z < . . < z < .
33, and 1 . < z <
3. We reconstruct M ap maps from the galaxy samples in individual redshift slices(auto- M ap ) and from the combination of multiple redshiftbins from two and up to five (the cross- M ap terms introducedin Martinet et al. 2021). The latter showed that including thecross-maps yields a significant improvement in the forecastprecision. For the γ -2PCF, we include both the auto- and thecross-tomographic correlations. • Likelihood : Finally, we compute the likelihood of the datagiven the cosmology p ( x | π ) on a four-dimensional grid, tak-ing the “fiducial” cosmo-SLICS simulations as our observa-tion DV x . We use a Student- t likelihood (Sellentin & Heav-ens 2016), p ( x | π ) ∝ (cid:34) + χ ( x , π ) N s − (cid:35) − N s / , (5) χ ( x , π ) = ( x − x m ( π )) T Σ − ( π ) ( x − x m ( π )) , (6)which generalizes the multi-variate Gaussian, and we ac-count for the noise through the covariance matrix Σ com-puted at a fixed cosmology π . In the above equation, x m ( π )refers to the DV modeled from the cosmo-SLICS at cosmol-ogy π and both x and x m ( π ) correspond to the mean DV overthe di ff erent noise realizations. The posterior likelihood isobtained from Bayes’ theorem with the cosmo-SLICS pa-rameter space as a fixed prior ( p ( π ) = σ uncertainty on each cosmological parameter by find-ing the range of values enclosing 68% of the posterior like-lihood previously marginalized over all other parameters. Asthe posterior distribution on h extends up to the prior limitimposed by the simulation space, we only discuss the fore-casts for the other three probed parameters : S , w , and Ω m .All predictions are computed for a 100 deg area to ensurethat the few percent uncertainties in the model (primarily dueto the accuracy of the N -body simulations) are lower than theprecision of the forecasts. In this article, we use the pipeline described above to study theimpact of the baryonic bias on a Stage-IV cosmic shear dataanalysis. However, we note that we could instead propagate bi-ases due to shear measurement uncertainty, mean photometricredshift inaccuracy, galaxy intrinsic alignments, or source-lenscoupling (see e.g., Kacprzak et al. 2016; Harnois-Déraps et al.2020), but we leave this to future work. The strategy is to biasthe observation DV and compare the positions of maximum like-lihood to the no-bias case.We use the DM-only and equivalent hydrodynamical runs ofthe
Magneticum simulations to measure the cosmological biasdue to baryonic e ff ects. We create galaxy mocks that reproduce Our priors on the four cosmological parameters are given by therange of the cosmo-SLICS simulations: Ω m ∈ [0 . , . S ∈ [0 . , . w ∈ [ − . , − .
5] and h ∈ [0 . , . the same Stage-IV survey properties as the cosmo-SLICS. Inparticular, galaxy redshifts, positions, and intrinsic ellipticitiesare identical to those of the model. We generate 50 realizationsof the hydro and DM light-cones: ten di ff erent lines of sightto lower the sample variance, each populated with five di ff er-ent realizations of intrinsic ellipticities to converge on an aver-age shape noise contribution. We compute the M ap map in everymock, extract the DV, and measure the ratio between the aver-age over the 50 DVs measured in the hydrodynamical and in theDM-only mocks.This multiplicative correction factor is computed for eachS / N bin and serves to infuse our
Magneticum baryon model inour (DM-only) observation data. Infusing baryons into the modelavoids being a ff ected by small residual di ff erences between the Magneticum
DM-only and the cosmo-SLICS DM-only simula-tions, such as the finite box e ff ect (e.g., Harnois-Déraps & vanWaerbeke 2015; Euclid Collaboration: Knabenhans et al. 2020),the nonlinear physics modeled by the di ff erent Poisson solvers,or the chosen distances between lensing planes (e.g., Takahashiet al. 2017; Zorrilla Matilla et al. 2020). In other words, it en-sures that the di ff erences in the likelihood maxima are only dueto baryons. We neglect here the possible dependence of baryonson cosmology, a hypothesis well supported by the recent findingsof van Daalen et al. (2020).
4. Impact of baryons
We examine in this section the impact of baryons on the di ff erentDVs (Sect. 4.1) and on the cosmology inferred by a Stage-IVsurvey (Sect. 4.2). Figure 2 shows the impact of baryons on the γ -2PCF, presentedas the fractional di ff erence between ξ ± measured in the hydrody-namical and in the equivalent DM-only runs. This figure showsthe baryonic bias in the absence of tomography for visual pur-poses; however similar curves are observed in the tomographiccase. We measure a decrease in the amplitude of ξ ± of up to10 −
15% at scales below a few arcminutes, which is fully con-sistent with the suppression in the matter power spectrum seenin Fig. 1.In Fig. 3 we show the equivalent measurement on the M ap statistics: voids, peaks, and 1D M ap . The impact of baryons onthese DVs is more complex than in the case of the γ -2PCF giventhe di ff erent physical origins of each part of the M ap distribu-tions. The most plausible scenario is described in Osato et al.(2020): Overdense regions are diluted due to AGN feedback,leading to high-S / N structures with smaller amplitudes. This ex-pelled material can be deposited in low-density regions, whichlikely explains the reduction in pixels with highly negative S / N.We note that the cause of the latter e ff ect is not yet fully under-stood and could involve other baryonic processes such as inter-action of internal and accretion shocks (e.g., Zhang et al. 2020).The increase of the distribution at S / N close to zero accounts forthe density smoothing due to this redistribution of matter whichleads to a higher number of small S / N structures. This reasoningis deducted from the lensing PDF behavior but holds for peaksand voids. We do not probe the impact of radiative cooling seenat very high S / N in Osato et al. (2020) as we focus here on alower, more conservative S / N range. This would also necessi-tate a finer pixel scale than our fiducial 0 . (cid:48) . Indeed these ef-fects appear to be significant only at scales lower than 0 . (cid:48) in the M ap map according to the location of the ξ + upturn in Fig. 2 and Fig. 2.
Relative change in the γ -2PCF due to baryons. The orange andpurple curves represent the ξ + and ξ − estimators, respectively. The er-ror bars correspond to the diagonal elements of the SLICS covariancematrix rescaled to 15 000 deg . Fig. 3.
Relative change in the M ap estimators due to baryons. The blue,green, and red curves represent void counts, peak counts, and the lens-ing PDF, respectively. The error bars correspond to the diagonal ele-ments of the SLICS covariance matrix rescaled to 15 000 deg . consistent with the propagation of the radiative cooling scale of ∼ h Mpc − into the lensing PDF using Eq. (11) of Castro et al.(2018).Quantitatively, we find a decrease of between 5% and 13%in the extremal values of our DVs depending on the consideredDV and S / N bin. In particular, for peaks of S / N = ∼
5% due to baryons, in perfect agreementwith measurements from Fong et al. (2019) and Coulton et al.(2020) on the BAHAMAS simulations, which present a similaramplitude of the baryonic feedback (see Fig. 1). This is also ofthe same order of magnitude as the results from the TNG simula-tions (Osato et al. 2020) and the baryonification method (Weisset al. 2019).When applying tomography, we also note a decrease in theimpact of baryons in each slice compared to the combined case.Using thin source slices, Osato et al. (2020) also found that thebaryon bias is lower at higher redshift. However, the lower e ff ect Article number, page 5 of 12 & A proofs: manuscript no. spe2 in our case is more likely due to an increase in the noise due tolower galaxy densities as noted by Harnois-Déraps et al. (2020)in their tomographic peak count analysis of DES data. This issupported by the fact that we find similar baryonic e ff ects in allfive redshift slices, which we designed to have identical galaxydensities.In Figs. 2 and 3 the error bars are computed for the expected15 000 deg of the Euclid survey by area-rescaling the SLICScovariance matrix as Cov → Cov (100 /
15 000). These figuresshow that the impact of baryons on all tested estimators willbe significant with respect to the statistical precision of StageIV cosmic shear surveys. For the present 100 deg analysis, thechanges are below the statistical noise, whence the necessity tofix the noise in the cosmo-SLICS model and the Magneticum mocks.
We propagate the impact of baryons on the cosmological pa-rameter forecasts following the method described in Sect. 3. Wefocus on the peak statistics as it is the most widely used massmap estimator in the literature, but we also present results forvoids and the lensing PDF. All values reported in this section aresummarized in Table 2.Figures 4 to 6 show the 1 and 2 σ contours of the marginal-ized 2D and 1D likelihoods for S , Ω m , and w for various con-figurations of the peak statistics: without tomography, with to-mography, and combined with the γ -2PCF with tomography. Inall these figures, the blue contours and curves correspond to theforecasts for the DM-only observations, while the data yieldingthe green contours are infused with the baryon bias. As alreadynoted in Martinet et al. (2021), we accurately recover the inputparameter values for the DM-only case, with only a ∼ σ biason Ω m in some cases, which is due to the sampling of the initialparameter space (see the reference above for more details).We first consider the nontomographic peak results in Fig. 4.We see a shift towards smaller values of S ( ∆ S = S DM + Baryons8 , best − S DM8 , best = − .
028 ( − . Ω m ( ∆Ω m = − .
018 ( − . ff ect of having lower matter density / structuregrowth, the two being highly degenerate for cosmic shear. Theseresults are fully consistent with the Ω m shift recently found byCoulton et al. (2020) for peaks measured in the BAHAMAS sim-ulations, but are larger than those found in the earlier work ofOsato et al. (2015), who reported a − .
5% shift in Ω m from sim-ulations with weaker AGN feedback. Finally, we see negligiblechanges in w , in part because the sensitivity to that parameter isquite low in the nontomographic case.When including tomography (see Fig. 5), the constrainingpower increases significantly. We measure a very similar ef-fect to that seen in the nontomographic case for S and Ω m but with slightly smaller shifts ( ∆ S = − .
024 ( − . ∆Ω m = − .
005 ( − . Magneticum mocks (see Harnois-Déraps et al. 2020,and Appendix A): with tomography, the noise in each mass mapincreases and tends to wash out the e ff ect of baryons. We alsofind a small positive shift in the maximum of the 1D likelihoodfor w ( ∆ w = .
035 (3 . ff ect could be physically motivated, it is likely due to de-generacies in the parameter space notably between S and w ,and it will be interesting to see if it persists in future analyses. Fig. 4.
Forecast of cosmological parameters from peak counts in a100 deg survey at Euclid depth without tomography. Marginalized 2D(1 and 2 σ contours) and 1D (full likelihood) constraints are displayed inblue for the DM-only case and in green when including baryon physics.Dashed lines correspond to the 1 σ constraints in the 1D marginalizedlikelihood. The blue and green crosses indicate the best estimate in the2D constraints, while the red crosses and lines indicate the input cosmo-logical parameter values. Gray crosses correspond to parameters of the25 cosmo-SLICS simulations that are used to estimate the cosmologydependence of the number of peaks. Fig. 5.
Same as Fig. 4 but for a tomographic analysis with five redshiftslices and including auto- and cross- M ap terms between redshift slices. If we now combine peaks with the γ -2PCF in the to-mographic setup (Fig. 6), the results are similar to thosefrom peaks alone, but accentuated in amplitude. We find ∆ S = − .
037 ( − . ∆Ω m = − .
019 ( − . ∆ w = .
047 (4 . γ -2PCF are a ff ected in a similarmanner by baryons and thus their combination shows a larger ef-fect. Although one could have hoped that the impact of baryonswould diminish when adding the information of the γ -2PCF thatpartly comes from larger scales, this study demonstrates on con-trary that baryonic physics do not vanish in this combination andneed to be accounted for in future surveys.Table 2 shows the forecast biases for all the di ff erent testedDVs and their combination with the γ -2PCF. Overall, baryons Article number, page 6 of 12artinet, Castro, Harnois-Déraps et al.: Impact of baryons in cosmic shear analyses
Table 2.
Forecasts on the biases due to baryons in 100 deg Euclid -like mocks. The bias is defined as ∆ S = S DM + Baryons8 , best − S DM8 , best , where the bestestimates correspond to the maxima of the marginalized 1D likelihoods. Numbers in parenthesis show the results in percentage of the input value. ∆ S ∆ w ∆Ω m voids, no tomo. − .
029 ( − . . . . . − .
028 ( − . . . − .
018 ( − . M ap , no tomo. − .
023 ( − . . . − .
006 ( − . γ -2PCF, no tomo. − .
011 ( − . . . − .
057 ( − . − .
021 ( − . . . .
003 (0 . − .
024 ( − . .
035 (3 . − .
005 ( − . M ap , incl. tomo. 0 .
007 (0 . .
048 (4 . − .
004 ( − . γ -2PCF, incl. tomo. − .
034 ( − . .
037 (3 . − .
035 ( − . + γ -2PCF, incl. tomo. − .
042 ( − . − .
051 ( − . − .
014 ( − . + γ -2PCF, incl. tomo. − .
037 ( − . .
047 (4 . − .
019 ( − . M ap + γ -2PCF, incl. tomo. − .
039 ( − . .
049 (4 . − .
003 ( − . Fig. 6.
Same as Fig. 4 but for the combination of peak counts and γ -2PCF for a tomographic analysis with five redshift slices and includingauto- and cross-terms between redshift slices. impact the di ff erent M ap estimators in a similar manner, as ex-pected from the similarities in how they a ff ect each DV in Fig. 3.We report smaller biases for voids than for peaks, as alreadynoted in Coulton et al. (2020) in the nontomographical case, andconfirm this trend when including tomography, with possibly avery low bias on w . When combined with the γ -2PCF we alsonote a di ff erence of sign in the w bias which could highlight adi ff erent sensitivity of voids to this parameter, but is more likelydue to a residual small peak in the likelihood from the interpola-tion of the DV in this case. The lensing PDF presents a compa-rable bias to peaks with slightly lower shifts as well. Althoughvoids are the least a ff ected by baryons, this analysis shows thatall estimators present biases of a few percent on at least one ofthe probed cosmological parameters. Considering the degenera-cies between cosmological parameters, this highlights the neces-sity for accounting for baryons when modeling the dependenceof nonGaussian M ap estimators on cosmology. Because these re-sults depend on the particular implementation of baryonic feed-back processes in the Magneticum simulation, we run an addi-tional test where we only infuse half of the DV baryonic bias tocompute the cosmological forecasts. Although we cannot accu-rately model the response of the M ap statistics to AGN feedbackwith only one simulation, this case likely corresponds to a muchlower feedback amplitude. We find a bias on cosmological pa- rameters which approaches the percent value in the tomographiccase. This strong dependency of the cosmological parameters onthe amplitude of the infused baryonic e ff ect suggests that the im-pact of baryons could be mitigated by integrating a modeling ofAGN feedback in the likelihood, a possibility which is not stud-ied here.Although these biases of a few percent are worrisome for fu-ture Stage IV cosmic shear surveys, we note that they remainfairly small compared to the statistical precision of current sur-veys. Our 100 deg mocks at Euclid depth include about tenmillion galaxies, a similar number to Stage III surveys. In thiscase, the biases are always below 1 σ for every parameter andconfiguration, except for the S parameter when combining M ap estimators and γ -2PCF where the bias can reach up to 2 σ . InAppendix A, we tailor our mocks to the KiDS-450 and DES-Y1 surveys to verify the impact of baryons on the peak statisticsanalyses conducted in Martinet et al. (2018) and Harnois-Dérapset al. (2020), respectively. Our findings validate the choice of ne-glecting baryons in current Stage III peak count analyses.
5. Mitigating baryons with small scale cut
In the case of γ -2PCF, the impact of baryons can be mitigated bydiscarding small scales which are the most a ff ected, as seen fromFig. 2. Although this process decreases the statistical precisionas it removes part of the signal, it provides a gain in accuracywithout needing to run computationally expensive hydrodynam-ical simulations. This trade-o ff was notably chosen by the DEScollaboration in the first year data release (Troxel et al. 2018).Recently, Taylor et al. (2018, 2020) proposed an e ffi cient wayto cut the small-scale contribution to cosmic shear two-point es-timators based on the nulling scheme presented in Bernardeauet al. (2014). Alternatively, baryons can be modeled with halo-based codes (HMCode, Mead et al. 2021) or from libraries ofpower spectra (van Daalen et al. 2020), allowing the inclusion ofsmaller angular scales and increasing the statistical power as inHildebrandt et al. (2017) and Huang et al. (2020).As we do not yet have access to a library of hydrodynamicalsimulations to estimate the baryonic bias, we follow the workof Weiss et al. (2019) and explore di ff erent possibilities to miti-gate the e ff ect of baryons on M ap statistics. As suggested by theiranalysis, we vary the size of the aperture θ ap but we also inves-tigate possible variations to the Schirmer et al. (2007) Q filtershape entering Eq. (3). In particular, we vary the aperture filtersize θ ap , the tilt parameter x c , and the inner filter radius parame-ter θ in . Article number, page 7 of 12 & A proofs: manuscript no. spe2
Fig. 7.
Top:
Profiles of the Q filters defined via Eq. (4) and used tomitigate the impact of baryons by reducing the weight of small scales. Bottom:
Relative change in the M ap peak counts due to baryons for thevarious mitigation setups. The top part of Fig. 7 shows the impact of varying θ ap , θ in ,and x c on the shape of the Q filter. The fiducial values that we usein the rest of the paper are θ ap = (cid:48) , θ in = . (cid:48) , and x c = . θ ap = (cid:48) , θ in = . (cid:48) , and x c = .
45 to betterhighlight the e ff ect of each parameter. However, we investigatemultiple values in the ranges 3 . (cid:48) ≤ θ ap ≤ . (cid:48) , 0 . (cid:48) ≤ θ in ≤ (cid:48) ,and 0 . ≤ x c ≤ ff erent manners.Increasing θ ap adds galaxies further away from the aperture cen-ter; increasing θ in removes galaxies close to the aperture cen-ter without distorting the general weighting; finally, increasing x c up-weights distant galaxies without modifying the number ofgalaxies captured by the aperture. We re-compute the baryonicbias from M ap constructed with the new Q filters and observe,in the bottom part of Fig. 7, that none of these methods is com-pletely e ffi cient at removing the impact of baryons. This resultis somewhat contradictory to our measurement that the e ff ect ofbaryons in our simulations concentrates on the central few ar-cminutes of the M ap profile around massive halos. This is be-cause with mass map statistics we cannot discard close galaxies as is done for γ -2PCF: we only reduce their weight when cen-tered on them which does not prevent them from entering otherapertures on a θ ap scale. We note a mild improvement when in-creasing θ in and x c . Increasing θ ap to 20 . (cid:48) still decreases the im-pact of baryons by ∼
50% at the extreme S / N values, and onlythe largest θ ap > (cid:48) can bring it to zero, but the cost in preci-sion is high, as we show next.We apply these filter modifications to the measurements fromthe cosmology and covariance mocks, and carry out a full cos-mological forecast for each of these. In Table 3, we present thevariations of the bias on the inferred cosmology for these dif-ferent configurations relative to the fiducial Q filter. We also re-port the change in the forecast precision due to the reduction insmall-scale information. We show these results for peaks in aconfiguration without tomography but we find similar behaviorfor other M ap estimators and including tomography: the bias dueto baryons is reduced (e.g., ∆ S / ∆ S Q fid . < . δ S /δ S Q fid . > . θ ap = (cid:48) that the bias is reduced bya factor of almost two and three on S and Ω m respectively, butwith a loss of respectively 12% and 17% on the forecast preci-sion, and a loss of 15% on w . The two other variations are lesse ffi cient but also retain more of the cosmological information.The cut at θ in = . (cid:48) decreases the bias by ∼
30% at the cost of a5%, ∼ ∼
20% wider statistical precision on S , w , and Ω m , respectively. We find similar results for all the Q filter con-figurations using higher parameter values than the fiducial: thegain in accuracy is always balanced by a significant loss in pre-cision. However, when using smaller values of θ ap , θ in , or x c , theimpact of baryons is increased because of the larger contributionof the small-scale baryonic features but the constraining poweris also degraded as we chose the fiducial Q filter to maximize theforecast precision in Martinet et al. (2021).Overall, none of the small-scale cuts we applied to mitigatebaryonic e ff ects are able to decrease the bias below a few percentaccuracy whilst preserving strong statistical precision. Using thee ff ective scale of θ ap x c = (cid:48) recommended in the analysis ofWeiss et al. (2019) for Euclid -like mocks, we confirm that thebias becomes consistent with zero. However, such large smooth-ing scale results in a decrease in the constraining power by a fac-tor of more than 2, 1 .
5, and 3 on S , w , and Ω m , respectively,motivating a full forward-model approach of the baryonic bias.
6. Conclusion
In this paper we investigate the impact of baryons on various M ap statistics: peaks, voids, and the lensing PDF. Baryonic physicsis modeled with the state-of-the-art Magneticum hydrodynami-cal simulations, and its impact on the data vector is propagatedinto full cosmological forecasts on S , w , and Ω m , for a Stage-IV lensing survey. The likelihood sampling exploits the cosmo-logical pipeline of Martinet et al. (2021), which is based on theSLICS and cosmo-SLICS DM-only simulations. Our results aresummarized below: • Baryons bias the measured M ap estimators by about 5 − / N bins, notably decreasing the number countsat extreme S / N values, while increasing the number ofintermediate S / N features. This is a direct consequence ofstrong baryonic feedback, which dilutes the density profileof massive halos and decreases their S / N in the M ap map. • In our Stage-IV survey setup without tomography, thebaryonic feedback propagates into a negative bias of about
Article number, page 8 of 12artinet, Castro, Harnois-Déraps et al.: Impact of baryons in cosmic shear analyses
Table 3.
Changes in the measured bias due to baryons and in the associated forecast precision for various mitigation schemes in the case of M ap peaks without tomography. The comparison is performed with respect to the fiducial Q filter used in the rest of the paper with θ ap = (cid:48) , θ in = . (cid:48) ,and x c = .
15. We vary one parameter at a time, the two others being held to their fiducial values. “ ∆ ” refers to the bias due to baryons, and “ δ ” tothe 1 σ precision forecast. ∆ S / ∆ S Q fid . ∆ w / ∆ w Q fid . ∆Ω m / ∆Ω Q fid . m δ S /δ S Q fid . δ w /δ w Q fid . δ Ω m /δ Ω Q fid . m peaks, no tomo. θ ap = (cid:48) .
47 1 0 .
39 1 .
12 1 .
15 1 . θ in = . (cid:48) .
65 1 0 .
64 1 .
05 1 .
09 1 . x c = .
45 0 .
76 1 0 .
59 1 .
05 1 .
11 1 . −
3% on S for every estimator. The bias on Ω m dependson the estimator and ranges from zero for voids to −
6% forpeaks. When including a tomographic decomposition withfive redshift slices including cross-tomographic bins, thesebiases are slightly lowered, likely because of the increasedshape noise in each tomographic slice, but remain of theorder of a few percent. We observe positive bias in ourtomographic setup of the order of 3 −
5% on w , although itis not clear at the moment whether this has a physical originor is caused by parameter degeneracies that are not fullycaptured by our likelihood. • Biases on all parameters are increased to ∼
5% when com-bining any M ap statistics with γ -2PCF in the tomographicanalysis. This combined analysis is maximally a ff ected asthe contributions of baryons are in the same direction and ofsimilar amplitude for the individual probes. • After investigating a range of scale cuts on the M ap statistics,we find that it is di ffi cult to e ffi ciently lower the impactof baryons without significantly degrading the statisticalpower. In line with Weiss et al. (2019), we find that only anoverly large aperture size could lower the bias to sub-percentlevel. A large portion of the signal is lost with such filtering,leading to less competitive cosmological constraints.We built Magneticum mocks to measure the impact ofbaryons on peak statistics analyses of current stage III sur-veys, namely in KiDS-450 (Martinet et al. 2018) and DES-Y1(Harnois-Déraps et al. 2020), and show that it remains belowthe statistical uncertainties associated to these surveys. However,this will not be the case for future Stage IV surveys for whichbaryons need to be accounted for in order to reach percentage-level precision whilst remaining unbiased.In this article, we present a correction scheme based on theDV: we measure a corrective factor from hydrodynamical simu-lations and apply it to mock observations in order to estimatehow biased would become cosmological constraints in caseswhere this step was omitted. However, we note that these resultsfully depend on the amplitude of the baryonic feedback modeledby the
Magneticum simulations, which is still uncertain as seenfrom the scatter between the di ff erent state-of-the-art simula-tions. A more accurate correction would consist in modeling theimpact of baryons on M ap statistics from a set of hydrodynam-ical simulations with various feedback amplitude values, and tomarginalize over the extra free parameters when computing thecosmological constraints. Coulton et al. (2020) recently showedthe feasibility of this approach using the BAHAMAS simula-tions run with three di ff erent amplitudes of the AGN feedback.The baryonification method described in Schneider & Teyssier(2015) is particularly suited to such an analysis and is there-fore a promising tool to design future sets of N -body simulations that explore both the cosmology dependence and the response tobaryons of nonGaussian statistics. Acknowledgements.
We thank our KiDS and
Euclid collaborators for usefuldiscussions. NM acknowledges support from a fellowship of the Centre Nationald’Etudes Spatiales (CNES). TC is supported by the INFN INDARK PD51 grantand by the PRIN-MIUR 2015W7KAWC grant. JHD acknowledges support froman STFC Ernest Rutherford Fellowship (project reference ST / S004858 / Magneticum has been run using the “Leibniz-Rechenzentrum” with CPU timeassigned to the Project “pr86re” and “pr83li”. The SLICS numerical simulationscan be found at http://slics.roe.ac.uk/ , while the cosmo-SLICS canbe made available upon request. Computations for these N -body simulationswere enabled by Compute Ontario ( ), Westgrid( ) and Compute Canada ( ). Thiswork has been carried out thanks to the support of the OCEVU Labex (ANR-11-LABX-0060) and of the Excellence Initiative of Aix-Marseille University -A*MIDEX, part of the French “Investissements d’Avenir” program.All authors contributed to the development of this paper. NM (lead) con-ducted the analysis. TC and JHD (both co-leads) equally participated byproducing the Magneticum and the SLICS and cosmo-SLICS mocks respec-tively. EJ contributed to the analysis pipeline while CG and KD prepared theinitial configuration of the
Magneticum mocks.
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Appendix A: Correcting for baryons in KiDS andDES
In this section we build
Magneticum mocks for current StageIII surveys to investigate the e ff ect of baryons on peak countsin recent analyses. We first revisit the results of Martinet et al.(2018) on the KiDS-450 data, and then present a comparisonwith those obtained for the DES-Y1 analysis of Harnois-Dérapset al. (2020). Appendix A.1: Estimation of the bias for KiDS-450 (Martinetet al. 2018)
We follow the same procedure as in Martinet et al. (2018) tocreate KiDS mocks, but now we additionally include baryonicphysics and examine the impact on the inferred cosmology. Inshort, we use the KiDS-450 redshift distribution calibrated withthe direct spectroscopic method (DIR; Hildebrandt et al. 2017)for a single tomographic slice including all galaxies with photo-metric redshifts 0 . < z < . . − andwe tile the full 450 deg by repeating our 100 deg simulationmocks. In this process we set the positions and the amplitude ofthe intrinsic ellipticities of the mock galaxies to that of the ob-served data. We use independent simulated shear values from theten lines of sight reconstructed in the Magneticum and apply thesame five di ff erent random rotations of the intrinsic ellipticitiesas in the KiDS mocks used to compute the model. We build M ap maps with the same Schirmer et al. (2007) filter with an aperturesize θ ap = . (cid:48) . The e ff ect of baryons is measured as the ratiobetween the mean distribution of peaks in the M ap maps builtfrom the 50 hydrodynamical and DM-only mocks, in 12 bins ofS / N ranging from 0 to 4. It is then infused as a multiplicativefactor applied to the observed data. In this approach we aim toremove the e ff ect of baryons from the data rather than modify-ing the model (both methods are equivalent). The correction isthen propagated to the cosmological constraints using the samepipeline as in Martinet et al. (2018), which we recall is built fromthe 157 Dietrich & Hartlap (2010) N -body simulations that pavethe σ − Ω m plane, plus 35 at the fiducial cosmology for the co-variance matrix estimation. When including various light-conesand shape noise realizations, the model is constructed from a to-tal of 3925 mocks, with an additional 175 pseudo -independentmocks for the covariance matrix.The e ff ect of baryons on the KiDS-450 peak counts analy-sis is shown in Fig. A.1. The blue contours correspond to the1 and 2 σ constraints presented in Figure 7 of Martinet et al.(2018) and which do not include systematic errors. The blacklines show the constraints including the e ff ect of baryons. Wesee a positive shift in both σ and Ω m resulting in a change ofthe structure growth parameter ∆ S = .
021 (2 . S cosmology, i.e. the number of large S / Npeaks in the model is reduced because of the baryons. This isin contrast with the simulation-based approach in the rest ofthe article where we estimate the bias from infusing baryons tothe DM-only observation. The e ff ect in KiDS is lower than the3 .
4% measured in the
Euclid -like mocks, likely because of thelarger noise with the lower galaxy density of KiDS. It is nev-ertheless larger than the 2 .
3% correction used in Martinet et al.(2018) and derived from the simulations of Osato et al. (2015),as expected from the weaker AGN feedback implemented in thelatter study. When compared to the statistical precision of the m S / N < 4.0 KiDS-450 2PCFs-tomoPlanck15KiDS-450 SPKiDS-450 SP baryons Fig. A.1. E ff ect of baryons on the KiDS-450 M ap peaks cosmologi-cal constraints of Martinet et al. (2018). Blue and black contours cor-respond to the 1 and 2 σ constraints without and with accounting forbaryons respectively. Green and red contours represent the best KiDS-450 tomographic γ -2PCF constraints (Hildebrandt et al. 2017) andPlanck cosmic microwave background constraints (Planck Collabora-tion et al. 2016) that were available at the time. KiDS-450 analysis, the S shift due to baryons remains smallwith a value of 0 . σ . With this updated baryon model, we re-vise the S constraints from Martinet et al. (2018), including theother sources of systematic error described therein: multiplica-tive shear bias, mean photometric redshift, intrinsic alignment,and shear-position coupling. As the impact of baryons is nowfully modeled, and because the constraining power is identicalwith or without baryons, we no longer need to inflate the uncer-tainty on S . We find S = . + . − . , a result slightly closerto the Planck estimate (Planck Collaboration et al. 2016, the redcontours in Fig. A.1) than the S = . + . − . previously re-ported. Appendix A.2: Estimation of the bias for DES-Y1(Harnois-Déraps et al. 2020)
The
Magneticum simulations have recently been used inHarnois-Déraps et al. (2020) to investigate the impact of baryonson the peak statistics analysis of the DES-Y1 data. These mocksuse the DIR-calibrated redshift distributions used in the cosmicshear re-analysis by Joudaki et al. (2020), carried out in fourphotometric redshift bins between 0 . .
3. We review themeasurement of the baryons bias here and compare the results tothose obtained in the previous sections.As described in Harnois-Déraps et al. (2020), we tile thefull DES-Y1 survey (1321 deg ) with our 100 deg Magneticum mocks and fix the galaxy positions and intrinsic ellipticity am-plitudes to that of the data. We create 100 mock surveys for theDM-only and the hydrodynamical
Magneticum simulations tolower the sample variance and shape noise. In this analysis, themodel and the covariance matrix are evaluated from the samecosmo-SLICS and SLICS N -body simulations used in the mainpart of this article respectively, improving in accuracy from theDietrich & Hartlap (2010) N -body simulations used in the KiDS-450 peak count analysis. The M ap are computed with an aperturesize of θ ap = . (cid:48) in the four auto-tomographic bins and in thecross-bins. The DV is the concatenation of the peak distributions Article number, page 11 of 12 & A proofs: manuscript no. spe2 m S DES-Y1 fid+baryons
Fig. A.2. E ff ect of baryons on the DES-Y1 M ap peaks cosmologicalconstraints of Harnois-Déraps et al. (2020). Blue and black contourscorrespond to the 1 and 2 σ constraints without and with accounting forbaryons respectively. in 12 bins between 0 < S / N < w CDM peakcount model, and 1240 for the covariance matrix.The impact of baryons on the tomographic constraints from M ap peak statistics in DES-Y1 are shown in Fig. A.2. The bluecontours correspond to the 1 and 2 σ constraints on the S and Ω m parameters after marginalisation over the photometric red-shift and the shear calibration uncertainties, while the black con-tours further include the correction due to baryonic physics. Asexpected, we find again a positive shift towards larger values of S and Ω m . Quantitatively, the shift is of ∆ S = .
013 (1 . .
9% found with the
Euclid -like mocks, againdue to the lower galaxy density in the DES-Y1 data, which is ∼ − . In terms of statistical precision, this bias corre-sponds to a 0 . σ shift and can be safely ignored in the DES-Y1analysis. Harnois-Déraps et al. (2020) explored other sources ofsystematics in their analysis, and show in their Figure 17 thatbaryons and intrinsic alignments are the two most important ef-fects, while source-lens clustering and uncertainty in the nonlin-ear growth of structure could be safely ignored.shift and can be safely ignored in the DES-Y1analysis. Harnois-Déraps et al. (2020) explored other sources ofsystematics in their analysis, and show in their Figure 17 thatbaryons and intrinsic alignments are the two most important ef-fects, while source-lens clustering and uncertainty in the nonlin-ear growth of structure could be safely ignored.