Pier Stefano Corasaniti

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1 Non-Linear Small Scale Structure Formation in Non-Standard Dark Matter Cosmologies Pier Stefano Corasaniti CNRS & Observatoire de Paris Collabora(on: Shankar Agarwal Yann Rasera Subinoy Das Doddy Marsh

2 Standard Cosmological Scenario Dark Matter: - Gravita)onal Collapse Ini)al Fluctua)ons - Foster ma6er clustering - Resides in virialized clumps Halos: - Building blocks of cosmic structure forma)on - Shape baryon distribu)on & forma)on of visible structures

3 CDM Paradigm Theoretical Bias: - WIMP hypothesis/neutralino Large Scales SDSS - Successful Descrip)on CMB spectra - Clustering of Ma6er from galaxy surveys Planck Minimal Scenario - LCDM - 6 parameter models: H 0, Ω m (1-Ω Λ ), Ω b, σ 8, n s, τ - Censored Comments

4 Small Scales & Beyond CDM DM Direct Searches: - Nega)ve/Contras)ng Results - No signal at LHC Pontzen & Governato 2014 Klypin et al CDM anomalies : - Core vs Cusp Profiles - Missing Satellites - Too-big-too fail problem Complex Physics: - Baryonic Feedback - Observa)onal Selec)on Effects - Uncertain)es of Milky-Way Mass Boylan-Kolchin et al. 2012

5 Warm Dark Matter Alternative Scenarios - Thermal Relic, m WDM kev - Free-Stream 100 kpc - Small-Scale Power Spectrum Cut-off Self-Interacting DM - DM sca6ering cross-sec)on - Interac)on with radia)on Late Forming DM & Ultra-Light Axions - LFDM: Before ma6er/radia)on equality, decay of scalar field coupled to rela)vis)c par)cles (w 1/3 -> w=0) - ULA: Axion field transi)on from vacuum to ma6er (w=-1 -> w=0)

6 Observational Constraints Warm Dark Matter * - m WDM < 0.1 kev to core the DM profiles < m WDM [kev] < 2 to solve too-big-to-fail e.g. Maccio et al m WDM > 3.3 kev from Lyman-α power spectrum a z>2 Self-Interacting DM Lowell et al. 2012, 2014 Viel et al Lower density sub-halos and core profiles - Low mass halo abundances unaltered Vogelsberger et al. 2012; Zavala et al Late Forming DM - Evade Lyman-alpha constraints (z t > ) - Suppressed halo abundances - Fla6er profiles than LCDM (not cored) Agarwal, Corasani), Das & Rasera 2015

N-body Simulations Monte Carlo Method Initial

Macro-particle sampling DM field Initial

integration trajectories dpi Φ dxi p =, = 2, i = 1,

7 N-body Simulations Monte Carlo Method Initial Conditions - ZA displacements from input P(k) Macro-particle sampling DM field Initial Conditions: - WDM thermal velocities negligible (?) N-body Solver - AMR, TreePM, etc. - LFDM effectively collision-less Numerical integration trajectories dpi Φ dxi p =, = 2, i = 1, N da a da aa 2Φ = 4π Ga 2 ρ mδm Analyze final macro-particle distribution Simulation Characteristics Gravity Solver Cosmological Volume Mass Resolution Spatial Resolution L3box m p = ρcωm L3box / N p Δx

Artificial Fragmentation (Mass Segregation) Discretization Effect Sampling Poisson Noise (k > k cut-off ) Spurious Numerical Halos Gotz & Sommer-Larsen

8 Artificial Fragmentation (Mass Segregation) Discretization Effect Sampling Poisson Noise (k > k cut-off ) Spurious Numerical Halos Gotz & Sommer-Larsen 2002, 2003; Wang & White 2007 Example 0.6 kev RAMSES AMR - N p = L box = 27.5 Mpc h -1 - m p ~ 10 7 M sun h -1 - dx coarse ~ 54 kpc h kev

Spurious Halo Contamination Halo Mass Function - N h-par)cles > 100 - N p =1024 3 - m p ~ 10 6 M sun h -1 - L box = 27.

9 Spurious Halo Contamination Halo Mass Function - N h-par)cles > N p = m p ~ 10 6 M sun h -1 - L box = 27.5 Mpc h -1 - dx coarse ~ 26 kpc h -1 - Upturn at M<M * - Simula)on Dependent Slope Proposed Cures - Mass Cut: M min = 10.1 ρ d k p -2 Wang & White Select Unfla6en Proto-Halos in Ini)al Lagrangian Patch & Apply Mass Cut Lowell et al Visual Inspec)on Angulo, Hahn, Abel Tessella)on 6-d phase-space folding (reduce but dosn t solve) Hahn, Abel, Kaehler 2013 Agarwal & Corasani) 2015

10 Halo Spin - Spin parameter - V = (GM/R) Structural Properties of Halos - 8 bins: 4 < M[10 9 M sun h -1 ] < 8 - CDM: log-normal & mass independent - non-cdm: devia)ons from lognormality/bimodality and mass dependent - spurious halos have large spins Agarwal & Corasani) 2015

11 Halo Shape Structural Properties of Halos - Symmetric Mass Distribu)on Tensor - sphericity, ellip)city & prolatness - CDM: mass independent & ellip)cal halos - non-cdm: mass dependent & highly non-spherical (ellip)cal & prolate, i.e. alignment with filaments)

12 Virial Condition - proxy: η=2 K/ E - correla)on λ -η for η>1 Halo Dynamical State

Removing Spurious Halos - 0 < η=2 K/ E < 1.

recover suppressed mass func)on at low mass (mass resolu)on convergence) -

13 Removing Spurious Halos - 0 < η=2 K/ E < recover halo triaxial distribu)on - recover spin log-normality - recover suppressed mass func)on at low mass (mass resolu)on convergence) - spurious halos s)ll present with simple mass-cut at M min - mass range larger than mass cut Virial State Selection

14 Evolution of HMF in NDM models Corasani) et al. in prepara)on z=0 z=1 z=2 z=3 z=4 z=5 z=6 z=7 z=8 z=9 z=10 z=0 z=1 z=2 z=3 z=4 z=5 z=6 z=7 z=8 z=9 z=10 - Low mass end saturates at z < 3 - Fi ng func)on: dn d ln M NDM =10 A 0+A! M dn d ln M LCDM 1 M m e * α

15 Abundance of Field Dwarf-Galaxies z=0 Velocity Function - Abundance of galaxies with given circular velocity - More sensi)ve to halo dynamics than gas physics - Mostly individual halos rather than satellite Caveats Theory: circular velocity / Observa)ons: line-of-sight velocity - Inclina)on effect - Baryons at high-velocity end - Selec)on

16 CDM Overabundance Klypin et al Papastergis et al. 2011

17 Velocity Function

18 High-Redshift Universe Galaxy Luminosity Function - Probe low mass end HMF evolu)on - Depends on galaxy forma)on - Several es)mates at z > 4 Constraints on NDM - m WDM > 1 kev (CLASH gal. den. z = 10) Pacucci, Mesinger & Haiman (2013) - m WDM > 0.8 kev from HAM of LCDM Schultz et al. (2014) Bouwens et al. (2015) Atek et al. (2015) Schenker et al. (2013) McLure et al. (2013) - m Ψ > ev from HAM assuming parametrize L UV (M) rela)on Schive et al. (2016)

19 Cumulative Number Density How reliable? - DM Halo mass is highly uncertain 1.4 kev 1 kev 2 kev 0.6 kev

20 Empirical Approach: Abundance Matching d M! dn d M! = d M! φ( M! ) UV UV M M UV - Rely on approximate analy)cal form of HMF - Extrapolate LCDM rela)on to NDM models - Redshi~ evolu)on may be driven by ex)nc)on What can we learn? About galaxy forma<on in NDM models? What high-z can tell about NDM under minimal assump<ons?

21 UV-Luminosity to SFR - Account for dust ex)nc)on HAM & SFR - Convert M UV corrected to SFR (Kennicut rela)on) - Derive SFR-density func)ons (see Mashian, Oesch, Loeb 2015 for LCDM) Extinction Correction A UV = ln10σ β β β(m UV, z) = Meurer et al. (1999) β ʹ(z) M UV M 0 β M0 (z) C e β M 0 (z) C M UV M 0 [ ] + β M0 (z) ʹ β (z) M UV M 0 Tacchella et al. (2013), Mason, Tren) & Treu (2015) - Changes UV-mag bin size - Shi~ toward higher luminosi)es Smit et al. (2012)

22 SFR density function Φ(SFR) at 4<z<6 - Fit Φ(SFR) with Press-Schechter function - HAM M d! M h dn d M! h NDM = SFR dsfr' φ(sfr') - SFR-M h evolves in amplitude - Redshi~ average

23 Average SFR-Mh

24 Modeling Luminosity Function at z > 6 Intrinsic Scatter SFR-M h relation - Compute φ(sfr, z) = 2 σ int 1 2π SFR dm dn h (M h, z) e dm h 2 log 10 SFR/(ε SFR(M h ) 2 2σ int - Convert to UV luminosi)es - Add ex)nc)on effect - Es)mate Φ (M UV ) - Fit against the data ε, σ int

25 Fitting Galaxy Luminosity Function at z > 6 LCDM 1 kev 0.7 kev

26 Conclusions Small scale clustering of matter as probe of nonstandard DM models (free your mind) Artificial fragmentation in simulation of models with suppressed spectrum at small scales needs to be accounted for (be inquisitive) Galaxy formation cannot occur in the same way in NCDM models (question your believes) Testing SFR halo mass relation can provide key insights (truth arises more from error than confusion)

Reionization. High-Redshift Galaxy UV Luminosity Function. Axion Dark Matter. Rosemary Wyse

Reionization. High-Redshift Galaxy UV Luminosity Function. Axion Dark Matter. Rosemary Wyse Reionization and the High-Redshift Galaxy UV Luminosity Function with Axion Dark Matter Rosemary Wyse Johns Hopkins University and University of Edinburgh Brandon Bozek, Doddy Marsh & Joe Silk Galaxy-scale