Dwarf galaxies in cosmic structure formation Lucio Mayer Collaborators: Stelios Kazantzidis (CCAPP Ohio State Univ.), Simone Callegari (PhD student, University of Zurich) Chiara Mastropietro (LERMA, Paris) James Wadsley (McMaster Univ.), Fabio Governato (U. of Washington) , Chris Brook (UCLAN), Alyson Brooks (Caltech) , Ewa Lokas (Copernicus Institute), Jaroslaw Klimentowski (Copernicus Institute), Beth Willman (CfA Harvard  Haveford Cl.), Thomas Quinn (U. of Washington)

Dwarf spheroidals (dSphs) Dwarf irregulars (dIrrs) Fornax, Mb= -13 Carina, Mb= - 8 Simon & Geha 2007 NGC6822 Salucci 1997 Bootes, Mb= -6 dark matter dominated (velocity dispersion s2 >> GMstar/R for dSphs, rotational velocity for dIrrs, Vrot2 >> GMstar/R) ) faint, low surface brightness (Mb > -18, mB > 24 mag arcsec-2) Low angular momentum content, v/s < 0.5 for dSphs, high angular momentum for gas-rich dwarfs (dIrrs) Very low gas content for dSphs (<< Mstar), very high gas content for dIrrs (~> Mstar)

Determining DM halo properties in gas-rich dwarfs: test case NGC 6822 (Weldrake et al. 2004) But several issues in rotation curves (especially for 21-cm line of atomic H): beam smearing (due to low angular resolution) (2) inaccurate centering (in 1D velocity measurements), (3) non-circular motions (see review de Blok 2010) Cored isothermal NFW

Effect on non-circular motions (Valenzuela et al. 2007) 3D numerical model to reproduce actual stellar + gas + dm content (w/NFW halo) -- develops a bar-like distortion in the baryons High level of non-circular motions (>> 10 km/s) Face-on gas density map in model 2D projection of isodensity contours for the expected inclination of NGC6822

THINGS dwarfs sample State-of-the-art survey of atomic hydrogen (HI) in nearby galaxies at NRAO Very Large Array (VLA) (combined with Spitzer photometry) Walter et al. 2008 ,2009 Hi-res 2D velocity fields - No centering problems + allows to model deviations from circular motions THINGS dwarfs sample

Oh et al. 2008 + in prep. (THINGS team)

Formation of galaxies in cosmological (LCDM) hydrodynamical (SPH) simulations (Ngas, Ndm ~ 1-3 x 106 within R ~ Rvir, cooling, SF, blastwave supernovae feedback, UV bg) several sims, Mhalo ~ 1011 Mo - 3 x 1012 Mo (Governato,Willman, Mayer et al. 2007) Mayer, Governato and Kaufmann 2008; Callegari, Mayer et al., in preparation) Shown “quiet” system (last major merger at z ~ 2) with Mvir(z=0) ~1012 Mo Green=gas Blue=young stars Red=old stars Frame size = 100 kpc comoving 7

The mass concentration problem in cosmological simulations of galaxy formation Simulations Observations Mayer et al. 2008 --- implied inner slope ~ r-2 Simulations that model collisionless dark matter + dissipational baryonic component with radiative cooling, heating, star formation, feedback processes Even more fundamental than the cusp-core problem because it involves the form of the mass distribution at large radii where data more robust

Stars form in dense molecular clouds: the importance of the star formation density threshold “Low” density threshold (corresponds to WNM - adopted in cosmological simulations till 2009) r > 0.1 cm -3 “High” density threshold (corresponds to molecular gas), feasible only at hi-res r > 100 cm -3 See also Robertson & Kravtsov 2008; Gnedin et al. 2009; Pelupessy et al. 2009 Callegari, Brook, Mayer, Governato, 2009 9

First hi-res dwarf galaxy formation simulation Vchalo ~ 50 km/s NSPH ~ 2 x 106 particles Ndm ~2 x 106 particles ( Msph ~ 103 Mo) spatial resolution (grav. softening) 86 pc Order of magnitude better than previous cosmological hydro simulations taken to z=0 - High SF threshold 100 atoms/cm3 Supernovae blastwave feedback model (Stinson et al. 2006) with same parameters as in previous MW-sized galaxies simulations - Cooling function includes metal lines (gas cools below 104 K) + heating by cosmic UV background (Haardt & Madau 1996 + 2006) Frame = 15 kpc on a side color-coded gas density Evolution from z=100 to z=0 Governato, Brook, Mayer et al., Nature, 463, 203, 2010 10

A slowly rising rotation curve produced How? (1) Removal of baryons (baryonic disk mass fraction ~ 0.04 at z=0, so 4 times lower than cosmic fb) + (2) flattening of dark matter profile -- During strongest outflows (at z > 1) inner dark matter mass expands as a result of impulsive removal of mass + transient gas clumps transfer energy due to dynamical friction (confirms earlier models of e.g. Navarro et al. 1996; Read et al. 2003; Maschchenko et al. 2008 – see also Ceverino & Klypin 2009) Dark matter density decreases by a factor of ~ 2 at r < 1 kpc and density profile becomes shallower ~ r -0.5 rather than ~ r -1.3

Enlightening numerical tests “Erosion” of dark matter density cusp occurs only at high resolution and high star formation density threshold -- only in such configuration prominent baryonic clumpiness + outflows do occur

Independent analysis by THINGS team + comparison with dwarf galaxies in THINGS survey shows excellent agreement (Oh et al., in preparation) -- slope (simulation “DG1”): ~ 0.29 (uncorrected for non-circular motions) -- mean slope in THINGS sample of dwarfs: ~ 0.31

Proposed solution of the mass concentration problem; star formation and feedback in an inhomogeneous ISM Star formation in resolved, dense “molecular” phase (GMCs): star formation more localized, only in high density peaks - LOCALLY stronger effect of outflows because more energy deposited in smaller volume via blastwaves - locally more gas heated to temperatures > 105 k ~ Tvir and escapes the galaxy (wind speed ~ 100 km/s at z > 1) around star-forming site cold gas has very low density so blastwave of hot gas expands more easily (lower external pressure) Outflows mostly in the center of galaxy where density peaks higher - remove low angular momentum material from the center - suppress bulge formation and produce exponential profile for stars 14

The second-order velocity (radial) moment σ is obtained from Determining masses of dSphs from observed stellar velocity dispersion slos: stars as tracers of the potential The second-order velocity (radial) moment σ is obtained from the lowest-order Jeans equation (from integration of Vlasov eq.) u= mass density= stellar + dm density Assuming spherical dark matter + stellar distribution (M( r ) = Mstars ( r ) + Mdm (r )) The fourth-order (radial) moment satisfies the higher order Jeans equation, which for β = const reads

Projected line-of-sight moments For comparison with observations we need to work with projected quantities – projected (1D) line-of-sight velocity dispersion + projected (1D) fourth-moment of the velocity: R= projected distance from “center” of galaxy Kurtosis

Effect of orbital anisotropy Anisotropy parameter β = 1 – σθ2(r)/σr2(r) Depends on the eccentricity of the orbits in the potential (stars as tracers of the potential) circular orbits: β  –  isotropic orbits: β = 0 radial orbits: β = 1

TIDAL STRIPPING OF DARK MATTER SUBHALOS dSphs = subhalos of halos of larger galaxies -lose mass due to the effect of the gravitational tidesof the more massive host halo Via Lactea Simulation Formation of 2 x 1012 Mo halo (Milky Way-sized) In WMAP3 cosmology Tides do not change Kazantzidis, Mayer et al. 2004 (also Kravtsov et al. 2004;Penarrubia et al. 2008; Springel et al 2008) (1) Tides do not modify the central cusp of subhalos (2) Tides change the outer slope of the dm profile into r ~ r -g x exp -(r/rb)

Halo masses of “classic” dwarf spheroidals: the mass-anisotropy degeneracy Kazantzidis, Mayer et al. 2004 also Lokas 2002,2009 Wilkinson et al. 2005, Gimore et al. 2007, Strigari et al. 2006, 2007; Lokas 2008; Strigari, Frenk & White 2010 (using Aquarius) Mean Vpeak of dSphs >~ 20 km/s (M> 108 Mo)  M/L ~ 10-100 Fitting observed 1D sigma (no kurtosis) using Jeans equation. Form of the dm profile assumed=NFW with exponential truncation Spherical King model assumed for stellar distribution

Tidal stripping of stars in subhalos Hi-res simulations of tidal stripping of satellites including baryons (Kazantzidis, Mayer et al. 2004;2005)

Effect of tides on the stars: observing the dwarf Depending on the angle of view the measurements will be different Stellar surface density Velocity dispersion Klimentowski, Lokas, Kazantzidis, Mayer, Mamon & Prada 2007

Example: Modelling of the Leo I dSph Kinematic sample of 328 stars from Mateo et al. (2007) The secondary increase of dispersion disappears after removal of interlopers Łokas, Klimentowski, Kazantzidis, Mayer et al. 2008

Constraints on parameters If kurtosis is included or analysis restricted to inner points the data are consistent with isotropy or weakly tangential orbits Łokas et al. 2008

Constraints on parameters If the data are cleaned of interlopers the agreement with isotropy or weakly tangential orbits is even better Best fit: M=(4.5±0.7) 107M M/LV =(8.2±4.5) M/L Łokas et al. 2008

Other dwarfs: constraints on M and β dSphs with largest samples of observed stars measured (blue contours with kurtosis) Statistical errors, due to sampling of velocity moments, are very small They are comparable to errors due to contamination and non-sphericity Łokas 2009

Dark matter distribution in dSphs: cusp or core Dark matter distribution in dSphs: cusp or core? Example: Draco (highest M/L among “classical” dSphs) cusp core Cusp and core fit the data equally well - even with kurtosis impossible to constrain central slope because more free parameters than b (e.g. break radius rb in subhalo profile after fixing g and King for stars) Sanchez-Conde et al. 2007 Lokas 2009 DM profile Mass [108 M] rb/RS β χ2/N cusp 5.5 7.0 –0.1 8.8/9 core 1.2 1.4 0.06 9.5/9

Effect of density slope on satellite’s mass loss Penarrubia, Benson, Walker, Gilmore, McConnachie, Mayer 2010 N-body models of spherical satelites (spherical dm halo + spherical stellar King model) orbiting in the halo+disk potential of the host galaxy

….leads to other “indirect” method to infer the central cusp slope from dSphs (Penarrubia et al. 2010) based on the mass-size relation of MW dSphs However caution: Discriminating power relies on Ultra-faint dwarfs, i.e. on the least secure mass measurements (~ 10 stars per galaxy for kinematics!) (2)Outcome of tidal mass loss depends on detailed mass distribution of the satellite (spherical King model for stars is Idealized) + mass of the disk of the host Md=0.1 Mvir

Conclusions The cusp-core controversy possibly solved: “cores” form naturally as a result of the interaction between baryons and dark matter in dwarf galaxies during their assembly history in a LCDM Universe Simulations + observations suggest inner slopes in dwarfs ~ -0.5 Accurate determination of masses in dSphs with Jeans equations difficult because of degeneracies between parameters, however uncertainties only within factors of a few for “classical’ dSphs in which the line-of-sight motion of > 500-1000 stars are available. M/L ~ 10-100 -Same degeneracies between parameters in fits makes it impossible to determine slope of the dm profile -- Cusps and cores equally probable. - Indirect methods based on observed correlations between dwarfs’ structural parameters also plagued by uncertainties in models and data. -If scenario for formation of “cores” correct then range of inner slopes in dSphs: the brightest ones (e.g Fornax, Leo I) more likely candidates for cored distributions (more dm-baryons interaction). Ultra-faint dwarfs, which formed only tiny stellar components, probably harbour “pristine” cusps  better targets for dm detection