1 / 59

590 likes | 794 Vues

Non-Baryonic Dark Matter in Cosmology. Antonino Del Popolo Department of Physics and Astronomy University of Catania, Italy . IX Mexican School on Gravitation and Mathematical Physics "Cosmology for the XXI Century: Inflation, Dark Matter and Dark Energy".

Télécharger la présentation
## Non-Baryonic Dark Matter in Cosmology

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Non-Baryonic Dark Matter in Cosmology**Antonino Del Popolo Department of Physics and Astronomy University of Catania, Italy IX Mexican School on Gravitation and Mathematical Physics "Cosmology for the XXI Century: Inflation, Dark Matter and Dark Energy" Puerto Vallarta, Jalisco, Mexico, December 3-7, 2012**LECTURE 2 The distribution of Dark Matterin galaxies and**clusters**SPIRALS**Stellar Disks M33 - outer disk truncated, very smooth structure NGC 300 - exponential disk goes for at least 10 scale- lengths Ropt=3.2RD scale radius Bland-Hawthorn et al 2005 Ferguson et al 2003**Wong & Blitz (2002)**Gas surface densities GAS DISTRIBUTION HI Flattish radial distribution Deficiency in centre CO and H2 Roughly exponential Negligible mass Berkeley-Illinois-. Maryland Association (BIMA) Array with 30 GHz receivers.**Circular velocities from spectroscopy**- Optical emission lines (H, Na) - Neutral hydrogen (HI)-carbon monoxide (CO) HI -> 21 cm CO -> mm -> range [e.g., 115.27 GHz for 12CO (J = 1 -0) line, 230.5 GHz for J =(2 -1) Tracer angular resolution spectral resolution HI 7" … 30" 2 … 10 km s-1 CO 1.5" … 8" 2 … 10 km s-1 H, … 0.5" … 1.5" 10 … 30 km s-1**ROTATION CURVES(RCs)**A RC is obtained calculating the rotational velocity of a tracer (e.g. stars, gas) along the length of a galaxy by measuring theirDoppler shifts, and then plotting this quantity versus their respective distance away from the centers Tracing the intensity-weighted velocities I(v)= intensity profile at a given radius as a function of the radial velocity. The rotation velocity is then given by i= inclination angle Vsys= systemic velocity of the galaxy. . EXAMPLE OF HIGH QUALITY RC Optical resolution: 2”, i.e. RD/30-RD/10 Radio Interferometers: 10”**Extended HI kinematics traces dark matter**- - Light (SDSS) HI velocity field NGC 5055 Ropt Bosma 1981: HI RCs for 25 galaxies well extended beyond the optical radio (e.g. NGC 5055) SDSS Bosma, 1981 GALEX Radius (kpc) Bosma 1979 The mass discrepancy emerges as a disagreement between light and mass distributions**Rotation curve analysis**From data to mass models model observations Vtot2= Vhalo2 + Vdisk*2 + VHI2+(Vb2) Model parameters • from I-band photometry • from HI observations • different choices for the DM halo density • ------------------------------------------------------------------------------------------------------------ • Dark halos with cusps (NFW, Einasto) • Dark halos with constant density cores (Burkert) • Model has three free parameters: disk mass, halo central density and core radius (halo length-scale) • Obtained by best fitting method.**Gentile et al. 2004, 2007**• rotational curves of spiral galaxies decomposed into their stellar, gaseous and dark matter components. • fit to the inferred density distribution • with various models • models with a constant density core are preferred. • Burkert: with a DM core • = rs/(1+r/rs)(1+(r/rs)2) • NFW • r = rs/(r/rs)(1+r/rs)2 • Moore • r = rs/(r/rs)1.5(1+(r/rs)1.5) • HI-scaling, with a cst factor • MOND, without DM Mass models for the galaxy Eso 116-G12. Solid line: best fitting model, long-dashed line: DM halo; dotted: stellar; dashed: gaseous disc. 1kpc corresponds to 13.4 arcsec. Below: residuals: (Vobs-Vmodel)**Maximum disk fit: NGC 2976**• Significant radial motions in inner 30” (blue) Rotation velocity derived from combined CO and Hα velocity field Radial velocity Systemic velocity**HI**H2**stars**An upper limit on the dark matter rotation curve (and also the slope of the density proﬁle) can be found if the disk mass is zero (minimum disk or maximul halo), and a lower limit to the dark matter rotation curve and density proﬁle slope is obtained for a maximum disk. In general, for galaxies of normal surface brightness, the minimum disk solution is physically unrealistic and the actual mass distribution is likely to be closer to the maximum disk case.**To reveal the shape of the density profile of DM halo, we**need to remove the rotational velocities contributed by the baryonic components of the galaxy. The rotation curve of the dark matter halo is defined by The lower limit to the DM density profile is obtained by maximizing the rotation curve contribution from the stellar disk. The maximum possible stellar rotation curve is set by scaling up the mass-to-light ratio of the stellar disk until the criterion is no longer met at every point of the rotation curve.This requirement sets maximum disk mass-to-light ratios M/Lk Maximal disk dark halo**Even with no disk, dark**• halo density profile is • r(r) = 1.2 r -0.27 ± 0.09 M/pc3 • Maximal disk M*/LK = • 0.19 M/L,K • After subtracting stellar • disk, dark halo structure is • r(r) = 0.1 r -0.01 ± 0.12M/pc3 • No cusp! Maximum Disk Fit**halo central density**core radius luminosity MASS MODELLING RESULTS highest luminosities lowest luminosities halo disk disk halo halo disk Smaller galaxies are denser and have a higher proportion of dark matter. fraction of DM Read & Trentham 2005**The distribution of DM around spirals**Using individual galaxies de Blok+ 2008 Kuzio de Naray+ 2008, Oh+ 2008, A detailed investigation: high quality data and model independent analysis Survey of HI emission in 34 nearby galaxies obtained using the NRAO Very Large Array (VLA). High spectral (≤5.2 km/s) and spatial (~6'') resolution Distances 2 < D < 15 Mpc Masses M HI (0.01 to 14 × 109M☉), absolute luminosities MB (–11.5 to –21.7 mag) de Blok et al. (2008): galaxies having MB < −19 -> NFW profile or an PI profile statistically fit equally well MB > −19 the core dominated PI model fits significantly better than the NFW model.**DDO 47**Oh et al. (2010) THINGS dwarfs General results from several samples including THINGS, HI survey of uniform and high quality data - Non-circular motions are small. - No DM halo elongation - ISO halos often preferred over NFW Tri-axiality and non-circular motions cannot explain the CDM/NFW cusp/core discrepancy**SPIRALS: WHAT WE KNOW**MORE PROPORTION OF DARK MATTER IN SMALLER SYSTEMS MASS PROFILE AT LARGER RADII COMPATIBLE WITH NFW DARK HALO DENSITY SHOWS A CENTRAL CORE OF SIZE 2 RD**ELLIPTICALS**The Stellar Spheroid Surface brightness follows a Sersic (de Vaucouleurs) law Re : the effective radius, n Sersic index (light concentration) By deprojecting I(R) we obtain the luminosity density j(r): for n=4 Relatively featureless spheroidal galaxies Assuming radially constant stellar mass to light ratio Sersic profile ESO 540 -032 V (triangles) and I-band (boxes) Surface brightness proﬁles The solid lines are the best-ﬁt Sersic proﬁles Jerjen & Rejkuba 2001 Central surface brightness**Kinematics of ellipticals: Jeans modelling of radial,**projected and aperture velocity dispersions measure I(R), σP (R) derive Mh(r), Msph(r) radial V ϬP projected (or line of sight) aperture projected luminosity -Rotation isnotalwaysnegligible -Ϭr (R) is a direct probe ofgravpotentialbutitisnotobservable -ϬP (R) isobservablewhenindividual star measures are available -ϬAP is the standard observable SAURON data of N 2974 When observed through an aperture of finite size, the projected velocity dispersion profile, σp is weighted on the brightness profile I(R).**or**Velocity dispersion anisotropy L(r ) luminosity density Modelling Ellipticals • Measure the light profile= stellar mass profile (M*/L)-1 • Derive the total mass M(r) profile from • -Virial theorem • -Dispersion velocities of kinematical tracers (e.g., stars, Planetary Nebulas) • Disentangle M(r) into its dark and the stellar components. In ellipticals gravity is balanced by pressure gradients -> Jeans Equation • Difficulties in inferring the presence of dark matter halos in ellipticals: • the velocity dispersions of the usual kinematical tracer, stars, can only be measured out to 2Re. • Mass/anisotropy degeneracy: For a given ρ(r), σr(r), two unknown remains: M(r), and β(r) and one cannot solve Jeans equation for both, unless one assumes no rotation and makes use of the 4th order moment (kurtosis) of the velocity distribution (Lokas & Mamon 2003). (One of the first studies Romanowsky et al. 2003-> a dearth of DM in E) Spherical Symmetry; Non-rotating system -X-ray properties of the emitting hot gas -Combining weak and strong lensing data**slide1**Jeans modelling using PN * Pseudo inversion mass model Napolitano et al. (2011) NGC 4374 Napolitano et al. (2011) ML05: Mamon & Lokas 2005 Jeans modellingof PN data with a stellar spheroid + NFW dark halo Ellipticals have big DM halos (usually cuspy profiles, sometime cored e.g. WMAP1 Multicomponent model (0) Parametrized mass profile, e.g. NFW**Exercise: Virial theorem, Planetary Nebulae -> M/L**• Example: For planetary nebulae around NGC1399, the average rotation Vr≈300kms-1, and the velocity dispersion σ≈400kms-1at25kpcradius. Assumed that the random speed are equal in all directions and the galaxy is roughly spherical, find the total masswithin 25kpc of the center. Given that NGC1399 has MV=-21.7, show that M/L~80. PN: low-mass starsexhaust their nuclear fuel; core’s ultraviolet radiation ionizes outer gas; strongly inemission lines, e.g., [OIII]5007A.**Solution:**Virial theorem**The spheroid determines the velocity dispersionStars**dominate inside ReDark matter profile “unresolved” Dark-Luminous mass decomposition of dispersion velocities 1 Assumed IsotropyThree components: DM, stars (Sersic), Black HolesNaive superposition of Sersic models for the stellar mass component of L=L* elliptical galaxies with hot gas (from X rays) and central black hole (from the Magorrian relation), plus Dark Matter models: NFW; Jing & Suto; Einasto (Nav04). No adiabatic contraction. Mamon & Łokas 05 This plot indicates that while dark matter dominates outside of a few Re, the stellar component dominates inside Re. Therefore, it is difficult to measure the amount of dark matter in the inner regions of ellipticals.**Gravitational Lensing formalism**Deflection angle Deflection potential Convergence Surface mass density Angular radius and mass of an Einstein ring angle between and x The deflection angle relates a point in the source plane to its image(s) in the image plane through the lens equation Jacobian between the unlensed and lensed coordinate systems z= los coordinate ξ=vector in the plane of sky The term involving the convergence magnifies the image by increasing its size while conserving surface brightness. The term involving the shear stretches the image tangentially around the lens**Definitions of Ellipticity**where Image ellipticity unbaiased estimate of shear Source orientation Isotropically istributed ->**n**Weak lensing mass reconstruction * In Fourier space Eq. * , convolution Inverting**n**Exercise: calculate the mass enclosed in an Einstein ring Lens equation for Being This is nearly true for the elliptical case as well. For multiple imaging systems (those that aren’t necessarily lensed into Einstein rings) the typical separation between images is ∼ 2θE.**Mass profilesfromweaklensing**Lensing equation for the observed tangential shear e.g. Schneider,1996 Shear= Tangential term+curl For a circularly symmetric lens the curl vanish and the tangential part is Projected mass density of the object distorting the galaxy Mean projected mass density interior to the radius R The DM distribution is obtained by fitting the observed shear with a chosen density profile with 2 free parameters.**MODELLING WEAK LENSING SIGNALS**Lenses: 170 000 isolated galaxies, sources: 3 107 SDSS galaxies NFW 0.1 0.1 tar tar Mandelbaum et al 2009 HALOS EXTEND OUT TO VIRIAL RADII Using the previous method, Mandelbaum et al. (2006, 2009) measured the shear around galaxies of different luminosities out to 500 - 1000 kpc reaching out the virial radius, although with a not negligible observational uncertainty. Both NFW and Burkert halo profiles agree with data.**OUTER DM HALOS: NFW/BURKERT PROFILE FIT THEM EQUALLY WELL**Donato et al 2009 NFW Tangential shear measurements from Hoekstra et al. (2005) as a function of projected distance from the lens in five R-band luminosity bins. In this sample, the lenses are at a mean redshift z ∼ 0.32 and the background sources are, in practice, at z=∞. The solid (dashed) magenta line indicates the Burkert (NFW) model fit to the data. At low luminosities they agree.**Weak and strong lensing**M3D ( strong lensingmeasures the total mass inside the Einstein ring Sloan Lens ACS (SLACS): (Gavazzi et al. 2007) Strong lensing data of 22 massive SLACS galaxies modeled as a sum of stellar component (de Vaucoulers) + DM halo (NFW) AN EINSTEIN RING AT ReinstIMPLIES THERE A CRITICAL SURFACE DENSITY: Shear profile for the best DM + de Vaucouleurs profile. D = , The thickness of the total mass curve codes for the 1 sigma uncertainty around the total shear profile. Uncertainties are very small below 10 kpc because of strong lensing data not shown here. The transition between star and DM-dominated mass profile occurs close to the mean effective radius (yellow arrow). The total density profile is close to isothermal over ∼ 2 decades in radius.. average total mass density profile**Strong lensing and galaxy kinematics**Koopmans, 2006 Assume Fit γ= logarithmic slope Koopmans et al. (2006): joint gravitational lensing and stellar-dynamical analysis of a subsample of 15 massive field early-type galaxies from SLACS Survey. Galaxies have remarkably homogeneous inner mass density profiles (ρtot αr−2). Stellar Spheroid mass accounts for most of the total mass inside Re. The figure shows the logarithmic density slope of Slacs lens galaxies as a function of (normalized) Einstein radius. Inferred dark matter mass fraction inside the Einstein radius, assuming a constant stellar M/LB as a function of E/S0 velocity dispersion SIE: Singular Isothermal Ellipsoid model Inside REinst the total (spheroid + dark halo) mass increase proportionally with radius Inside REinst the total the fraction of dark matter is small**Mass Profiles from X-ray**Nagino & Matsushita 2009 gravitational mass profiles of 22 early-type galaxies observed with XMM-Newton and Chandra. Temperature Integrated mass profile (Mʘ) Density Colors: individual galaxies. Solid lines best-fit function. M/L profile NO DM R/re Hydrostatic Equilibrium Summary of M/L ratio of 19 of the 22 galaxies (only two groups)**ELLIPTICALS: WHAT WE KNOW**SMALL AMOUNT OF DM INSIDE RE MASS PROFILE COMPATIBLE WITH NFW AND BURKERT? DARK MATTER DIRECTLY TRACED OUT TO RVIR**Dwarf spheroidals: basic properties**The smallest objects in the Universe, benchmark for theory Discovery of ultra-faint MW satellites (e.g. Belokurov et a. 2007), extends the range of dSph structural parameters: 1 order of magnitude in radius and 3 in luminosity 1. Apparently in equilibrium 2. Small number of stars 3. No dynamically significant gas dSph show largeMgrav/L (10-100) Luminosities and sizes of Globular Clusters and dSph are different Gilmore et al 2009**Kinematics of dSph**• 1983: Aaronson measured velocity dispersion of Draco based on observations of 3 • carbon stars - M/L ~ 30 • 1997: First dispersion velocity profile of Fornax (Mateo) • 2000+: Dispersion profiles of all dSphs measured using multi-object spectrographs Instruments: AF2/WYFFOS (WHT, La Palma); FLAMES (VLT); GMOS (Gemini); DEIMOS (Keck); MIKE (Magellan) 2010: full radial coverage in each dSph, with 1000 stars per galaxy STELLAR SPHEROID**Dispersion velocity profiles**STELLAR SPHEROID CORED HALO + STELLAR SPH Wilkinson et al 2009 dSph dispersion profiles generally remain flat to large radii**Degeneracy between DM mass profile and velocity anisotropy**• Dispersion velocity profiles remain generally flat to large radius • Cored and cusped halos with orbit anisotropy fit dispersion profiles equally well Walker et al 2009 Isothermal… Power law --- HOWEVER Gilmore et al. (2007) favor a cored DM profile Kleyna et al. (2003): N-body simulations-> Ursa Minor dSph would survive for less than 1 Gyr if the DM core were cusped. Magorrian (2003): α= 0.55(+0.37, -0.33) for the Draco dSph. σ(R) km/s**Mass profiles of dSphs**In a collisionless equilibrium systems, Jeans equation relates kinematics, light and underlying mass distribution Make assumptions on the velocity anisotropy and then fit the dispersion profile-> DM mass distribution The surface brightness profiles are typically fit by a Plummer distribution (Plummer 1915) Rb=stellar scale length PLUMMER PROFILE Gilmore et al 2007 Results point to cored distributions**DSPH: WHAT WE KNOW**PROVE THE EXISTENCE OF DM HALOS OF 1010 MSUN AND ρ0 =10-21 g/cm3 DOMINATED BY DARK MATTER AT ANY RADIUS MASS PROFILE CONSISTENT WITH BURKERT PROFILE HINTS FOR THE PRESENCE OF A DENSITY CORE**Galaxy Clusters**• Half of all galaxies are in clusters (higher density; more Es and S0; mass > few times 1014-1015) or groups (less dense; more Sp and Irr; less than 1014Msun) • 100s to 1000s of gravitationally bound galaxies • Typically ~few Mpc across • Central Mpc contains 50 to 100 luminous galaxies (L > 2 x 1010 Lsun) • Distribution of galaxies falls ar r ¼ (like surface brightness of elliptical galaxies) Coma Cluster**Measuring DM content in clusters**• Gravitational lensing: measure mass without regard to the dynamical state of the cluster. Cannot distinguish between light and dark mass components, another mass tracer is needed to disentangle luminous from dark matter (typical structures observed in the strong lensing regime are radial arcs, located in positions corresponding to the local derivative of the cluster mass density profile, and tangential arcs, the position of which is determined by the projected mass density interior to the arc). • X-Ray emission of ICM: -Measuring rho(r) and T(r) -> Mass distribution of the cluster. -Technique really only sensitive to the total mass (unable to disentangle luminous from DM) - Previous concern dismissed because clusters MDM dominated (not totally true: BCG may be significant contributor) • Dynamics - cluster galaxies (or stars of the BCG) as tracers of the potential. Osipkov-Merrit parameterization of the anisotropy The projected velocity dispersion, σp, is the quantity measured at the telescope either by comparing the BCG absorption spectrum to broadened stellar templates or by measuring the galaxy velocity dispersion in different radial bins, depending on the program. Since it is difficult to compile the necessary radial velocities in one cluster, it is common to “stack” the results from many similar clusters.

More Related