1. A. Del Popolo Physics and Astronomy Department, Catania University, Italy September 23, 2016, UFES, Vitoria, ES DENSITY PROFILES OF DWARFS, ENVIRONMENT, AND THE SURFACE DENSITY RELATION

2. Overview Density profile and environment Non-constancy of surface density of galaxy (negative implications for MOND)

3. The ΛCDM Model ΛCDM: model parameterization of the Big Bang cosmological model in which the universe contains a cosmological constant (Λ), and cold dark matter. ΛCDM PROS Frequently referred to as the standard model of Big Bang cosmology or Cosmic Concordance Model, since it is the simplest model that provides a reasonably good match to the following observations: (the existence and) structure of the cosmic microwave background the abundances of hydrogen (including deuterium), helium, and lithium the large scale structure in the distribution of galaxies the accelerating expansion of the universe observed in the light from distant galaxies and supernovae 4.9% 26.8% (68.3%)

4. ΛCDM

5. A small scale problem of the  -CDM paradigm Dark matter cusps in haloes centers (N-body simulations), in particular absent in real galaxies, e.g. LSBs and in dwarf Irr, dominated by dark matter. The cusp/core problem is common to ALMOST to all dwarfs: gas-rich dwarf galaxies (DD0 154), dSph (Kleyna et al. 2003, Ursa Minor; Magorrian (2003) Draco dSph) and to LSBs Flores & Primack 1994: at small radii halos are not going to be singular (analysis of the flat rotation curves of the low surface brightness (LSB) galaxies). Other studies (Moore 1994; Burkert 1995; Kravtsov et al. 1998; Borriello & Salucci 2001; de Blok et al. 2001; de Blok & Bosma 2003, etc.) indicates that the shape of the density profile is shallower than what is found in numerical simulations ( alpha= 0.2 ± 0.2 (de Blok, Bosma, & McGaugh 2003)) * cusp core

6. Springel+08 No asymptotic slope detected so far Springel+08 Stadel et al. (2008) (mass resolution 1000 Solar masses. Slope at 0.05% Rvir (120 pc) is -0.8) CDM predicts Cuspy density profiles

7. 7 : Flat rotation curves of the low surface brightness (LSB) galaxies -> halos are not going to be singularFlores & Primack 1994; Moore 1994: Flat rotation curves of the low surface brightness (LSB) galaxies -> halos are not going to be singular * Oh+2010 Oh et al. 2015

8. 8 GALAXIES PROFILES COMPATIBLE WITH CUSPS de Blok et al. (2008): (high mass spirals) galaxies having M B > −19 -> NFW profile or a (Pseudo Isothermal) PI profile; (low mass spirals) M B PI model

9. No evidence for a universal density profile large scatter compared to simulations mean slope shallower than simulations Simon et al. (2005) Is There a Universal Density Profile? NGC 2976 NGC 6689 NGC 5949 NGC 4605 NGC 5963 Five galaxies:      Also different from previous observations, though e.g.,  = 0.2 ± 0.2 (de Blok, Bosma, & McGaugh 2003) * Adams+2014 Why these profiles are not flat? -> Slope dependent on mass Environmental effects (Del Popolo 2012)?

10. Diversity in dwarf galaxies density profile Oman+2015 Comparing IC2574 RC with that of DG1 (open circles) and DG2 (open triangles), the two simulated galaxies from the Oh et al. (2011) study. The simulated galaxies show a clear excess of mass in the inner regions compared to IC 2574, despite the ‘cores’ in the dark matter carved out by baryons. Oman+2015 Oman+2016

11. Del Popolo 2010; Del Popolo & Pace 2016 Di Cintio+2014

12. In summary: exist a range of profiles, and even with the improvements of nowadays kinematic maps there is no agreement on the exact dark matter slopes distribution (Simon et al. 2005; Oh et al.2011b; Adams et al. 2014). The situation is even more clear going to larger masses (e.g., spiral galaxies) dominated by stars, and especially to smaller masses (e.g. dwarf spheroidals (dSphs)) where biases that enter in the system modelling (Battaglia et al.2013) lead to opposite results. There is no accepted conclusion on the inner structures of dSphs (contrasting results for the same objects)

13. Targets NGC 4605NGC 5963 NGC 5949NGC 6689NGC 4625 NGC 2976 May we reproduce real dwarf galaxies (having cusps and cores)? Most hydrodynamic simulations would predict flat profiles for all

14. Supernovae Feedback (SNF) and bulk flows These results hold even if the gas never leaves the galaxy but is simply moved in bulk internally. Adiabatic contraction: simplest known mechanism of energy exchange betwen baryons and DM through gravity The added gravitational attraction of the accumulated material causes the dark matter to contract. Baryonic clumps and dynamical friction (DFBC): if gas not in a smooth flow but in dense, discrete chunks (i.e. infalling satellite protogalaxies), picture modified. This effect is usually pictured as a gravitationally-induced density wake behind infalling dense clumps – the wake pulls back on the clump with the result that the kinetic energy of the clump is transferred into the dark matter. (El-Zant+2001, 2004; Ma & Boylan-Kolchin 2004; Nipoti+2004; Romano-Diaz+2008, 2009; Del Popolo 2009; Cole et al. 2011; Inoue & Saitoh 2011; Nipoti & Binney 2015) How baryons affect DM through gravity (Navarro et al. 1996; Gelato & Sommer-Larsen 1999; Read & Gilmore 2005; Mashchenko+2006, 2008; Governato+2010, 2012; Pontzen & Governato 2011, 2014)

15. Cusp -> Core: a Baryonic Mechanism

16. 16 * Evolution with z

17. 17 Figure 1. DM halos shape changes with angular momentum. DM haloes generated with the model of Section 2. In panels (a)(c), the dashed line, the dotted line and the solid line represent the density profile for a halo of 10^8M_sun, 10^9M_sun, and 10^10M_sun, respectively. In case (a), that is our reference case, the specific angularmomentum was obtained using the tidal torque theory as described in Del Popolo (2009). The specific angular momentum, h, for the halo of mass 10^9M_sun is 400 kpc km/s (spin= 0.04) and the baryon fraction fd = 0.04. In panel (b) we increased the value of specific ordered angular momentum, h, to 2h leaving unmodified the baryonic fraction to fd and in panel (c) the specific ordered angular momentum is h/2 and the baryonic fraction equal to the previous cases, namely fd. Panel (d) shows the density profile of a halo of 10^10M_sun with zero ordered angular momentum and no baryons (solid line), while the dashed line is the Einasto profile. * --- ---- ….. ___ L,f d 2 L L/2 L->0 Effect of Environment

18. 18 Figure 2 DM halos shape changes with baryon fraction. Same as previous figure, Fig. 1, but in panel (a) we reduced the value of baryonic fraction of Fig. 1a (h, fd) to fd/3, and in panel (b) we reduced the value of baryonic fraction of Fig. 1c to fd/3; in panel (c) we increased the value of baryonic fraction of Fig. 1a (h/2, fd) to 3fd, and in panel (d) we increased the value of baryonic fraction of Fig. 1c to 3fd. * L, fd/3 L/2, fd/3 L, 3fd L/2, 3fd Effect of Environment

19. Application to NGC 2976, NGC 5949, and NGC 5963

20. NGC 6689NGC 5949 Targets NGC 4605NGC 5963 NGC 4625 NGC 2976

21. Sc dwarf galaxy in the M 81 group (D = 3.5 Mpc) Gas-rich, no bulge, no bar, no spiral arms High-quality data: 2-D velocity fields in H  and CO BVRIJHK photometry to better model stellar disk See Simon et al. (2003) for more details

22. Maximum Disk Fit Even with no disk, dark halo density profile is  (r) = 1.2 r -0.27 ± 0.09 M  /pc 3 Maximal disk M * /L K = 0.19 M  /L ,K After subtracting stellar disk, dark halo structure is  (r) = 0.1 r -0.01 ± 0.12 M  /pc 3 No cusp!

23. Modelling NGC 2976 We need: a) virial mass; b) baryon fraction; c) spin parameter We know only total and baryon mass at 2.2 kpc In the case of NGC 2976, we know the inner masses and the circular velocity Vc = 75 km/s. Governato et al. (2007) simulated a disk galaxy with Vc = 70 km/s and found that it has a virial mass of 1.6 × 10^11M_sun, similarly to Kaufmann et al. (2007). Baryon fraction calculated from McGaugh estimates, taking account of the known rotation circular velocity of NGC 2976 and the simulated mass in Governato et al. (2007). This gives a value fd = 0.1 Spin parameter known from Mun˜oz-Mateos et a. (2011), 0.04

25. Density profile of NGC 2976 is very shallow in contradiction with the N-body simulations results. One reason for the discrepancy between simulations and observations is due to the fact that simulations neglect the effects of the baryons on the dark matter halo. In the case of NGC 2976, the baryonic mass dominates the central 220 (550 pc for the case of maximal disk) The flat density profile of NGC 2976 is produced, as discussed in Del Popolo (2009) by the role of angular momentum, dynamical friction, and the interplay between DM and baryonic component We did not considered the tidal interaction among M31 and NGC 2976, which would further shallow its density profile.

26. NGC 6689NGC 4625 NGC 2976 Targets NGC 4605 NGC 5963 NGC 5949

27. NGC 5963: The NFW Galaxy Larger and more distant galaxy (D = 13 Mpc) Compact inner spiral surrounded by very LSB disk

28. NGC 5963 Rotation Curve NFW profile also a good fit! V 200 ~ 90 km s -1, R 200 ~ 130 kpc, r s = 7 kpc Best fit:  = 1.28 power law

29. NGC 5949 More distant (14 Mpc), otherwise looks just like NGC 2976 NGC 2976 NGC 5949 See Simon et al. (2004) for more details

30. Modelling NGC 5963 and NGC 5949 We need: a) virial mass; b) baryon fraction; c) spin parameter We know only total and baryon mass at 2.2 kpc In the case of NGC 5963 (5949), we know the inner masses and the circular velocity Vc = 120 (80) km/s. Baryon fraction calculated from McGaugh estimates, taking account of the known rotation circular velocity of NGC 5963 (5949). This gives a value fd = 0.12 (0.1) Spin parameter is left as a free parameter

31. NGC5963 Slope=-1.20 NGC5949 Slope=-0.88

32. NGC 5963 Simon: A power law with a slope of DM = 1.20 fits the rotation curve very well, and an NFW fit with r s =11 kpc and a concentration parameter of 14.9 is nearly as good. A pseudoisothermal fit is significantly inferior. Model: A good fit to NGC 5963, is obtained with a value of specific angular momentum h/2 and reducing the random angular momentum j to j/2 (see Fig. 6 of Williams et al. 2004).

33. NGC 5949 Simon: is best fit by a PI density profile, but power laws with slopes slightly shallower than NFW (DM = 0.88), are also good fits Model: A good fit to NGC 5949, is obtained with a value of specific angular momentum h/1.6

34. ENVIRONMENT Del Popolo 2012, Del Popolo & Cardone 2012 NGC5963 Slope=-1.20 NGC5949 Slope=-0.88

35. Conclusions The inner structure of galaxies is strictly related to the environment in which they form Galaxies with similar characteristics can have different inner structure

36. Scaling Relations, Surface Density of DM, and the Cusp/Core problem Scaling relations among DM haloes parameters and stellar quantities: valuable help to address this problem Kormendy & Freeman (2004): from halo parameters obtained by mass modelling 55 spiral galaxy rotation -> Donato et al. (2009): dwarfs, spirals, ellipticals over 12 orders of magnitude Gentile et al. (2009): confirm for luminous matter If the quoted results were true all galaxies density profiles should be fitted by a a cored profile, i.e. cuspy profile should not exist!!!!!!

37. Matter surface density Burkert profile Donato+09 Gentile+09 Nature MOND!! Totally different results: Boyarsky et al. (2009); Napolitano, Romanowsky & Tortora (2010); Cardone & Tortora (2010)………..

38. Dark Matter column density S is insensitive to the details of the density profile We can compute S for real galaxies and for DM haloes

39. Cardone & Tortora (2010) Data: 85 lens

40. Napolitano, Romanowsky & Tortora (2010) 218 elliptical galaxies and 117 lenticular/SO

41. Spirals Clusters Elliptical Groups dSphs DM haloes …… Isolated halos from ΛCDM N-body simulations ----Aquarius sim. satellites 9 orders of magnitude!!! NO constant surface density, artifact of log/log Only CDM works on all scales (no MOND for cluster) One more evidence for the presence of DM Boyarsky +2009

42. Surface density as a function of galaxy magnitude for different galaxies and Hubble Types. The original Spano et. al. (2008) data (empty small red circles) are shown as a reference of previouswork. The new results come from: the dwarf irregulars (full green circles) N 3741 (MB = −13.1) and DDO 47 (MB = −14.6), Spirals and Ellipticals investigated by weak lensing (black squares), dSphs (pink triangles), nearby spirals in THINGS (small blue triangles), and early-type spirals (full red triangles). The long dashed line is the result of D09. The solid line is the result of the present paper. Del Popolo +2013

43. 0,bary and gbary(r0) are plotted as a function of the B-band absolute magnitude of the galaxies. From the original sample of D09, here, as in G10, are used the dwarf spheroidals data, NGC 3741, DDO 47, and the two samples of spiral galaxies (Spano et al. 2008; de Blok et al. 2008) which all together span the whole magnitude range probed in the original sample (D09). The magenta triangles are the dwarf spheroidal galaxies1, the left green point is NGC 3741 and the right green point is DDO 47, and the empty red circles and filled blue triangles symbols are the Spano et al.(2008) and THINGS (de Blok et al 2008) spiral galaxies samples, respectively. Del Popolo +2013

44. S(r s ) as a function halo mass M 200. From bottom to top we have that: the short–dashed line represents the prediction and the results from the CDM N–body simulation of Maccio et al. (2008); the long–dashed line the B09 best fit linear relation; the solid line represents the direct fit methods, obtained in Cardone & Tortora (2010). The short–long dashed line represents S(r s ) obtained with the model described in the present paper. Del Popolo +2013

45. Cardone & Del Popolo (2012) Cardone & Del Popolo (2012) followed as closely as possible the analysis of D09 and G09, also improving the way the halo models were estimated and doubling the D09, G09 sample, allowing for an investigation of selection effects

46. Saburova & Del Popolo 2014 211 galaxies

47. Saburova & Del Popolo 2014 Green line: typical error bar for objects missing error bars

49. Saburova et al. 2016 :We showed that due to the degeneracy between the central densities and the radial scales of the dark haloes there are considerable uncertainties of their concentrations estimates. Due to this reason it is also impossible to draw any firm conclusion about universality of the dark halo column density based on mass-modelling of even a high quality rotation curve. The problem is not solved by fixing the density of baryonic matter.

50. Conclusions Dwarf galaxies are not all characterized by flat density profile, this last depends on environment The higher is baryon fraction and angular momentum the flatter is the profile Flat profiles like those of NGC 2976 are produced by high vaue of angular momentum acquired by tidal interaction with neighbors and are typical of unisolated dwarfs Steep profiles like those of NGC 5963 are typical of dwarfs who did not interact strongly (isolated) with neighbors The surface density is not an universal quantity

52. Springel+08 No asymptotic slope detected so far Springel+08 Stadel et al. (2008) (mass resolution 1000 Solar masses. Slope at 0.05% Rvir (120 pc) is -0.8) CDM predicts Cuspy density profiles

53. 53 * Oh+2010 Oh et al. 2015

54. 54 A bound mass shell having initial comoving radius will expand to a maximum radius (apapsis) of a shell: where The Model: SIM + L+DF+DC (Del Popolo 2009, 2011, 2012) * Eq. 1 Eq. 2 If mass is conserved and each shell is kept at its turn-around radius,then the shape of the density profile is given by (Peebles 1980; Hoffman & Shaham 1985; White & Zaritsky 1992): Eq. 3 After turn-around, a shell collapse, reexpands, recollapse (oscillation). This shell will cross other shells collapsing and oscillating like itself. Energy is not conserved and it is not an integral of motion anymore dynamics studied assuming that the potential near the center varies adiabatically (Gunn 1977; Filmore & Goldreich 1984; Zaritski & Hoffman 1993)

55. 55 Total mass in r is and * Eq. 4 Eq. 5 The radial velocity is obtained by integrating the equation of motion of the shell: (specific coefficient of dynamical friction) h (specific angular momentum) Eq. 7 Eq. 6 DF L from TTT Random angular momentum or Avila-Resse et al (1998) Kandrup 1980 Adiabatic contraction of DM: Gnedin et al. 2004; Del Popolo 2009 Baryons cool and fall into their final mass distribution Mb(r ), initial distribution of L. DM particle at ri moves to r

56. 56 The collapse factor, f, of a shell with initial radius ri and apapsis rm is given by (Gunn 1977; FG84; ZH93): * = M i (r i ) = initial mass distribution; M dm = final distribution of dissipationless halo particles If there is no crossing -> Eqs 8 and 9 can be solved to calculate the final radial distribution of halo particles: Eq. 9 Eq. 10 The problem of determining the density profile is then solved fixing the initial conditions ( ), the angular momentum h(r), and the coefficient of dynamical friction.

59. Beam-smearing beam 1100 independent data points Errors in geometric parameters center position, PA, inclination, systemic velocity Extinction v H  = v CO Asymmetric drift After accounting for systematics, total uncertainty on density profile slope is ~ 0.1 What About the Systematics?

60. Distinguishing Cores From Cusps Only exquisite data can distinguish cores from cusps in these galaxies Even then, the galaxies have to be very well behaved If you look for cores, you will find them. Same for cusps. Phrasing the debate as cores vs. cusps may not be the most useful approach... NGC 6689NGC 5949

61. How does SIM work? In order to describe the evolution of a density perturbation in the nonlinear phase we may use some analytical models (e.g., spherical or ellipsoidal, collapse) A slightly overdense sphere, embedded in the Universe, is a useful non-linear model, as it behaves exactly as a closed sub-universe. The overdensity expands with Hubble flow till a maximum radius (turn-around). (r=rmax, dr/dt=0) occurs at  lin ~1.06 Then it collapses to a singularity. (r=0):  lin ~ 1.69 Collapse to a point will never occurr in practice; dissipative physics and the process of violent relaxation will eventually intervene and convert the kinetic energy of collapse into random motions. This is named: virialization (occurs at 2tmax, and rvir = rmax/2) Once a non-linear object has formed, it will ontinue to attract matter in its neighbourhood ant its mass will grow by accretion of new material (secondary infall). Through dissipative processes, baryons lose energy and fall deeper in the potential well of DM. If the cooling time of the baryon gas is smaller than the collapse time, fragmentation will take place and smaller units can collapse A good deal of insight into this process can be gained by considering the spherical symmetric case (Gunn & Gott) with further important extensions (Bertschinger 1985). *-

62. A bound mass shell having initial comoving radius will expand to a maximum radius (apapsis) of a shell: where the mean fractional density excess inside the shell, as measured at current epoch t_o, assuming linear growth is: Final radius, x, scales with the turn around radius,, as: The Model: SIM +L+DF+BDC * Eq. 1 Eq. 2 Eq. 3

63. If mass is conserved and each shell is kept at its turn-around radius,then the shape of the density profile is given by (Peebles 1980; HS; White & Zaritsky 1992): Using Virial theorem one gets: So that f=0.5 Which gives the final profile using again mass conservation: * Eq. 4 Eq. 5 Eq. 6

64. However, after reaching maximum radius, a shell collapse and it will contribute to the inner shells: Energy not conserved and f not constant and so even energy is not an integral of motion anymore and f is no longer constant. The effect of the infalling outer shells on the dynamics of a given shell can be described assuming that the potential near the center varies adiabatically (Gunn 1977; FG84; ZH93) Using this assumption, the total mas inside apapsis is obtained summing the mass contained in shells with apapsis smaller than (permanent component, ) and the second (additional mass, ) is the contribution of the outer shells passing momentarily through the shell : Where the additional component is given by: * Eq. 7 Eq. 8 m(x) given by Eq. 4

65. (probability to find the shell with apapsis x inside radius ) is calculated as the ratio of the time the outer shell (with apapsis x) spends inside radius to its period: Where xp is the pericenter of the shell with apapsis x andis the radial Velocity of the shell with apapsis x as it passes from the radius The radial velocity is obtained by integrating the equation of motion of the shell: (specific coefficient of dynamical friction) h (specific angular momentum) G (acceleration) * Eq. 9 Eq. 10

66. The collapse factor, f, of a shell with initial radius and apapsis x_m is given by (Gunn 1977; FG84; ZH93): and the final density profile is: The problem of determining the density profile is then solved fixing the initial conditions ( ), the angular momentum h(r), and the coefficient of dynamical friction. Starting from a given shell, one integrates the equation of motion, calculates the velocity and then the probability that the particle (shell) inside radius r, then one calculates the mass added,, and the collapse factor f. Eq. 12 will give the final density profile. Eq. 12 * Eq. 11

67. Initial conditions Initial overdensity: Radial density profile of a fluctuation centered on a primordial peak of arbirary height nu: Correlation function Spectrum:

68. Angular momentum We consider a spherical region embedded in the rest of the universe. The Gravitatinal force on the central region isgiven by (Ryden 1988; Eisenstein & Loeb 1995): The tidal moments are While the density profile of each protostructure is approximated by the Superposition of a spherical density profile and a random CDM distribution The torque on a thin spherical shell is: The tidal torque is Whose integral gives the acquired angular momentum:

69. Dynamical friction In a hierarchical structure formation model, the large scale cosmic environment can be represented as a collisionless medium made of a hierarchy of density fluctuations. In these models matter is concentrated in lumps, and the lumps into groups and so on. Gravitational field can be decomposed into an average field, F0(r), generated from the smoothed out distribution of mass, and a stochastic component, Fstoch(r), generated from the fluctuations in number of the field particles. The stochastic component is specified assigning a probability density, W(F), (Holtsmark 1919; Chandrasekhar & von Neumann 1942). In the hypothesis that there are no correlations among random force and their derivatives (Kandrup 1980): In a homogeneous distribution: Using the Virial theorem: We have:

70. Baryonic dissipation and adiabatic compression of the halo The baryonic fraction of the halo dissipates its energy, but conserves h Since the baryon fraction F is much less than one, their infalling mass interior to a given dark matter orbit changes slowly compared to the orbital period. Adiabatic invariant (r M(r) for circular orbits; rmax M(rmax) for radial orbits) are conserved (Blummenthal et al. 1986; Ryden & Gun 1987) In the zeroth-order approximation,, and While the dark matter distribution is held constant, the baryons fall inward, preserving h till they are on circular orbits Then, baryons at radius r will end up at radius: The central concentration of baryons will draw dark matter inward, ending in a more compact distribution, and the new potential is Fixing the angular momentum for each mass shell, one adjust the value of the apocenter untill the orbits of DM in have the same value of which they had in the predissipation contribution. The mass distribution of DM is built up in this manner, orbit by orbit, ensuring that and are conserved. The process of baryonic infall and DM compression is then iterated. The baryons fall to the radius: The new potential is calculated, and dark matter orbits are adjusted to preserve, and Iterations till convergence