Transcript RESOLVING THE MYSTERY OF DARK MATTER

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
1
LECTURE 2
The distribution of Dark Matter
in galaxies and clusters
2
SPIRALS
Stellar Disks
M33 - outer disk truncated,
very smooth structure
NGC 300 - exponential disk
goes for at least 10 scalelengths
Ropt=3.2RD
scale
radius
Ferguson et al 2003
Bland-Hawthorn et al 2005
3
Gas surface densities
GAS DISTRIBUTION
HI
Flattish radial distribution
Deficiency in centre
CO and H2
Roughly exponential
Negligible mass
Wong & Blitz (2002)
Berkeley-Illinois-. Maryland Association (BIMA) Array with 30 GHz receivers.
4
Circular velocities from spectroscopy
- Optical emission lines (H, Na)
- Neutral hydrogen (HI)-carbon monoxide (CO)
Tracer
angular resolution
resolution
HI -> 21 cm
12
CO -> mm -> range [e.g., 115.27 GHz for CO
(J = 1 -0) line, 230.5 GHz for J =(2 -1)
spectral
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
HI
5
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 their Doppler 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
UGC2405
250
Optical
resolution: 2”, i.e.
RD/30-RD/10
200
Radio Interferometers:
10”
150
V
V ( R / RD )
100
50
0
0.0
0.5
1.0
1.5
R/Rd
2.0
2.5
3.0
6
Extended HI kinematics traces dark matter
HI velocity field
-
Ropt
Light (SDSS)
NGC 5055
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
7
Rotation curve analysis
From data to mass models
observations
➲
➲
model
Vtot2 = Vhalo2 + Vdisk*2 + VHI2+(Vb2)
GM D 2 x
x B( )
from I-band photometry V disk ,* 
2 RD
2
from HI observations
2
Model parameters
x  r / RD
M D , r0 , 0
B  I 0 K0  I1K1
➲
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.
8
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
= s/(1+r/rs)(1+(r/rs)2)
NFW
 = s/(r/rs)(1+r/rs)2
Moore
 = s/(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)
9
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
10
HI
H2
11
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.
stars
12
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
dark halo
Maximal disk
M* / LK  0.19M / LK ,
13
Maximum Disk Fit
• Even with no disk, dark
halo density profile is
(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) = 0.1 r -0.01 ± 0.12M/pc3
• No cusp!
14
MASS MODELLING RESULTS
highest luminosities
lowest luminosities
halo
disk
halo
disk
halo
disk
fraction of DM
Smaller galaxies are
denser and have a higher
proportion of dark matter.
luminosity
15
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
9
Masses M HI (0.01 to 14 × 10 M ☉), 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.
16
17
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
18
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
19
ELLIPTICALS
The Stellar Spheroid
Surface brightness follows a Sersic (de Vaucouleurs) law
for n=4
Re : the effective radius, n Sersic index (light concentration)
By deprojecting I(R) we obtain the luminosity density j(r):

I ( R) 



j ( r ) dz  2 
R
j ( r ) r dr
Assuming radially constant stellar mass to light ratio
r 2  R2
ESO 540 -032
Central surface brightness
0  2.5log I0  const
Relatively featureless spheroidal galaxies
Sersic profile
V (triangles) and I-band (boxes)
Surface brightness profiles
The solid lines are
the best-fit Sersic profiles
Jerjen & Rejkuba 2001
20
Kinematics of ellipticals: Jeans modelling of radial, projected and
aperture velocity dispersions
radial
V
projected (or line of sight)
ϬP
aperture
projected
luminosity
SAURON data of N 2974
 A When observed through an aperture of finite size, the projected
velocity dispersion profile, σp is weighted on the brightness
profile I(R).
21
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
Spherical Symmetry;
Non-rotating system
or
Velocity dispersion anisotropy
L(r ) luminosity density
•
1)
2)
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)
-X-ray properties of the emitting hot gas
-Combining weak and strong lensing data
22
slide1
*
Jeans modelling using PN
Pseudo inversion mass model
Napolitano et al. (2011)
NGC 4374
Napolitano et al. (2011)
ML05: Mamon & Lokas 2005
e.g.
Ellipticals have big DM halos (usually cuspy profiles, sometime cored
WMAP1
Multicomponent model
(0) Parametrized mass profile, e.g. NFW
23
24
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-1 at 25kpc radius. Assumed
that the random speed are equal in all directions
and the galaxy is roughly spherical, find the total
mass within 25kpc of the center. Given that
NGC1399 has MV=-21.7, show that M/L~80.
PN: low-mass stars exhaust their nuclear fuel; core’s ultraviolet radiation ionizes outer gas; strongly in emission
lines, e.g., [OIII]5007A.
25
Solution:
GMm
K  m(Vr  3 ), P  
r
2K  P  0 Virial theorem
1
2
2
(Vr  3 2 )r
M ( 25kpc) 
G
(3002  3  4002 )  25 3.0861016

M
11
1.32710
 3.3 1012 M 
LV  100.4( 21.74.83) L  4.11010 L
M / LV  80
26
Dark-Luminous mass decomposition of dispersion velocities
1
Assumed Isotropy Three components: DM, stars
(Sersic), Black Holes
Naive 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
1
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.
The spheroid determines the velocity dispersion
Stars dominate inside Re
Dark matter profile “unresolved”
27
Gravitational Lensing formalism
Deflection angle
The deflection angle
relates a point in the source plane
in the image plane through the lens equation
to its image(s)
Deflection potential
Convergence
Surface mass density
Angular radius and mass of
an Einstein ring
angle between
and x
z= los coordinate
ξ=vector in the
plane of sky
Jacobian between
the unlensed and lensed
coordinate systems
The term involving the convergence magnifies the image by increasing its
size while conserving surface brightness. The term involving the 28
shear
stretches the image tangentially around the lens
29
Definitions of Ellipticity
where
Source orientation
Isotropically istributed
->
Image ellipticity unbaiased
estimate of shear
30
n
Weak lensing mass reconstruction
*
In Fourier space
Eq. * , convolution
Inverting
31
n
32
n
Exercise: calculate the mass enclosed in an
Einstein ring
Lens equation
   ( )
 0
for
  Dd 
Being
E 
4GM Dds
c 2 Dd E Ds
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.
33
34
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

t

( R)  2  ( R, z )dz
0
__
( R) 
2
R2

R
0
x( x )dx
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
35
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
tar
0.1
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.
36
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.
37
Weak and strong lensing
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 Reinst IMPLIES THERE
A CRITICAL SURFACE DENSITY:
D=
Shear profile for the best DM + de Vaucouleurs profile.
,
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
M3D (
38
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
−2
galaxies from SLACS Survey. Galaxies have remarkably homogeneous inner mass density profiles (ρtot α r ). 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.
•
Inside REinst the total (spheroid + dark halo) mass increase proportionally with 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 the fraction of dark matter is small
39
Mass Profiles from X-ray
Nagino & Matsushita 2009
gravitational mass profiles of 22 early-type galaxies observed with XMM-Newton and Chandra.
Temperature
Density
Integrated mass profile (Mʘ)
Colors: individual galaxies. Solid lines best-fit function.
M/L profile
NO DM
  ng
R/re
Hydrostatic Equilibrium
Summary of M/L ratio of 19 of the 22 galaxies (only two groups)
40
ELLIPTICALS: WHAT WE KNOW
SMALL AMOUNT OF DM INSIDE RE
MASS PROFILE COMPATIBLE WITH NFW AND BURKERT?
DARK MATTER DIRECTLY TRACED OUT TO RVIR
41
dSphs
42
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
(10-100)
Luminosities and sizes of
Globular Clusters and dSph are
different
43
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
44
Dispersion velocity profiles
STELLAR SPHEROID
CORED HALO +
STELLAR SPH
Wilkinson et al 2009
dSph dispersion profiles generally remain flat to large radii
45
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 ---
σ(R) km/s
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.
46
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
47
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
48
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
49
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.
50
Since it is difficult to compile the necessary radial velocities in one cluster, it is common to “stack” the results from many similar
clusters.
.
Figures illustrating the basic observables and results typical for X-ray analyses of cluster mass distributions. Typically, the X-ray
image is split up into a series of circular, concentric annuli, with the spectrum of each annulus compared to a plasma model to infer
the gas density and temperature.
Top Left.Chandra ACIS image of Abell 2029. Top Right.Radial gas density profile of Abell 2029 (large circles) fit to several standard
parameterizations. This parameterized fit is then fed into equation for M(r), along with the temperature profile to calculate the enclosed
mass profile. Bottom Left. The radial temperature profile of Abell 2029, again fit to a standard paramaterization to facilitate the
hydrostatic equilibrium analysis. Bottom Right. Total enclosed cluster mass profile. The open circles are the data points and the
lines are .ts to the data, with the NFWprofile being a very good fit.
The upside down triangles show the contribution from the cluster gas mass. Note that the bright yellow band shows the possible
contribution from the cluster BCG,illustrating the need for an additional technique to account for and disentangle this important
51
mass component in order to understand the dark matter density pro.le. This .gure has been reproduced from Lewis et al. (2002, 2003)
Mass profiles from XMM-Newton
Pointecouteau, Arnaud, and Pratt (2005)
XMM-Newton
Scaled mass profiles of all clusters. The mass is scaled to M200, and the radius to R200, both values being derived from the best
fitting NFWmodel. The solid black line corresponds to the mean scaled NFWprofile and the two dashed lines are the associated
standard deviation.
52
Limits of X-ray mass determination
•
X-ray data alone have difficulties in constraining the mass distribution,
especially in the central regions, since relaxed clusters tend to have “cooling
flows”, and in these clusters X-ray emission is often disturbed and the
assumption of hydrostatic equilibrium is questionable (see Arabadjis, Bautz
& Arabadjis 2004).
• X-ray analyses, ALONE, cannot disentangle the DM and baryonic
components
•
X-ray temperature measurements are carried out from 500 kpc (Bradˇac et
al. 2008) to 50 kpc. Determination of temperature at smaller radia are
limited by instrumental resolution or substructure (Schmidt & Allen 2007).
• Complicated to take account of the stellar mass contained in the
BCG (brightest cluster galaxy), located in the cluster center
53
Lensing Constraints
• Weak lensing of background galaxies is used to reconstruct the
mass distribution in the outer parts of clusters. This technique is
based on averaging the noisy signal coming from many background
galaxies. The resolution that can be achieved is able to constrain
profiles inside 100 kpc.
• In the central parts of the cluster, lensing effects become non-linear
and in order to constrain the mass distribution one can use the
strong lensing technique. This technique has a typical sensitivity to
the projected mass distribution inside 100–200 kpc, with limits at 1020 kpc (Gavazzi 2005; Limousin et al. 2008).
• 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 whose position is
determined by the projected mass density interior to the arc.
54
*
Lensing: mass profile
Sand et al. 2004
55
*
This is one of large number of clusters
for which measurements like this have
been made. Clusters like Abell 1689
and Abell 2218 are particularly good,
because they had gravitational arcs near
the center. So the results can be
calibrated by strong gravitational
lensing (the green points in the figure).
The dark matter often has structure,
sometimes with lumps that are quite
massive but have no optical galaxies
(for example Abell 1942; Erben et al.
2000, A&A, 355, 23)
ACS=dvanced Camera for Surveys
56
*
A611
Newmann
et al. (2009)
57
Newman et al. (2012)
Gravitational lensing yield conflicting estimates sometime in agreement with Numerical simulations (Dahle et al 2003; Gavazzi et al.
2003; Donnaruma et al. 2011) or finding much shallower slopes (-0.5) (Sand et al. 2002; Sand et al. 2004; Newman et al. 2009, 2011,
2012)
X-ray analyses have led to wide ranging of value of the slope from: -0.6 (Ettori et al. 2002) to -1.2 (Lewis et al. 2003) till
-1.9 (Arabadjis et al. 2002), or in agreement with the NFW profile (Schmidt & Allen 2007; 34 Chandra X-ray observatory Clusters)
58
Conclusions
• Dark matter present from dwarf galaxies scales to large
scales
• dSph dark matter dominated with M/L ~100
• Normal spirals have L/M an order of magnitude smaller
than dSph
• Elliptical galaxies have variable content of DM: some as
M87 have a very high value of L/M, some could even not
contain DM. Inside Re baryons are dominating
• Clusters have high values of M/L (>100) but in the
central 10 kpc are dominated by baryons
• At larger scales (superclusters) DM content is close to
the closure density
59