The dark matter problem:

Spiral galaxiesSpiral galaxies

Françoise Combes

Dark matter is everywhereyGalaxies Galaxy clusters,

Cosmic filaments

Atoms (baryons) correspond to afraction fb= 5/(25+5) = 17% ofthe matter in the Universe (M/M 6)

Direct searchProd ction in accelerators

the matter in the Universe (M/Mb=6)

DarkProduction in accelerators5%

70%Darkmatter

energy

25%

Planck satellite, 2013 LHC2

First evidences of dark matter

1937 – Fritz Zwicky computes the mass of the Coma cluster y pUsing the Virial theorem. Measured velocities V~1000km/sM~ 5 1014 M M/L = 500 M /LM/L = 500 M/L

He cannot see all baryons + pb of distancedark matter in galaxies-- dark matter in galaxies

-- dust in between galaxies + obscuration-- modification of Newton’s law at large scalemodification of Newton s law at large scale

Sinclair Smith 1938: same M/L in Virgo cluster

1932: Jan Oort finds missing massin the solar neighborhood in Milky WaySolids, dust, gas, dead stars… 3

First rotation curve in M31

Radius 0’ 0 5’ 15’ 50’ 80’Radius 0 0.5 15 50 80 Radius (kpc) 0.11 3.3 11 17Luminosity L/pc3 1.25 0.083 0.021 0.014y pMass M/pc3 2.1 1.5 0.9 0.9M/L 1.6 18 43 62 Babcock 1939

V(km/s)400

300Abs lines instars, H, KHHNebulae[OII], [OIII][OII], [OIII]

4

M31=Andromeda, confirmationMore knowledge of the distribution of mass (near infrared), And gas at large distance

5

Same result for several galaxiesOptical rotation curves:Stars and ionised gas (H and [NII] m)Stars and ionised gas (H and [NII] m)

M31 obsRadio: 21cm line of hydrogendiscovered in 1951 (E & P ll) M31 obsdiscovered in 1951 (Ewen & Purcell)

HI is 3-4 times more extendedM31, theoryIn radius

Fl tMilky WaytheoryM33 obs

Flat curves

In the center, observed curve higherFinzi, 1963

In the center, observed curve higherthan theoretical one (bulge)M/L increases with radius

Arrigo Finzi (1963): gravity law different at large distance 6

Optical rotationcurves

23 Sb up to R23 Sb, up to R2525 mag per ’’ 2

M/L varies according to typesand stellar populations

M/L(*) = 2, 4, 6Sc Sb Sa respSc Sb Sa resp.

Rubin et al 1978 7

Atomic hydrogen in galaxiesNGC2915

R(gas) ~ 2-4 R(optical)M101

R(gas) ~ 2-4 R(optical)

8

How to build a rotation curve?How to build a rotation curve?

• Doppler Effect • Folding of the two sides

9

Velocity filedVelocity filedThe spider diagramm

NGC 2915M/L~ 80

Total spectrumFlux HI

Meurer et al 1996, Bureau et al 199910

V/Vmax

R/aR/a

Vobs= Vsys+Vrot sin i cos + Vr sin i sin 11

Galaxies of all typesEllipticals

Spirals

Dwarfs

12

The Hubble tuning forkThe Hubble tuning fork

13

The Tuning Fork(Le Diapason) The Teaspoon

(L C illè fé) (Kormendy)

Other classifications( p )

(La Cuillère a café) (Kormendy)

The Cleaver(L C ) The Rat’s Nest

(Hubble-Sandage)

(Le Couperet) The Rat s Nest(Le Noeud de Vipères)

(Grebel)

ATLAS3D

(Grebel)14

Obtaining velocitiesFuture ALMA

Optical: H, NII, ionised gas emission linesRadio: HI-21cm, CO: 2.6, 1.3 mm

Future ALMASKA, …

Tracer angular spectral résolution resolution

HI 7" … 30" 2 … 10 km s-1

CO 1 5" 8" 2 10 km s-1CO 1.5 … 8 2 … 10 km s

H, … 0.5" … 1.5" 10 … 30 km s-1

15

VLTE-ELT

KECKKECK

GTC 16

ALMA, Atacama desert

Millimeter wavesMolecular gas

17

Rotation curves: catalog M83: optical

HI: cartography of atomic hydrogenWavelength 21cm (Sofue & Rubin 2001)Wavelength 21cm (Sofue & Rubin 2001)

HI

M83: a galaxy similar to the Milky Way 18

19

Milky Way: difficult deprojection

The galaxy is seen edge-ong y g

Distances are notwell knownDepend on velocitiesAmbiguities

20

Ambiguities

Milky Way: gas HI, H2

HI-21cmDoubtful deprojectionVelocity bias

Velocity

Longitude

CO tracer of H2Non-circular velocities in

21

the centre bar

Universal curveUniversal curve• How to normalise the thousand of curves?• Correlation with total luminosity

22

Interpretation of the various curvesInterpretation of the various curves

23

NGC2403HSB

At the same scaleAt the same scale

GC 128UGC 128LSBLow surfaceLow surfacebrightness

T l i f th l i itTwo galaxies of the same luminosity, And same flat velocity Vf 24

Normalisation to Rd exponential diskSeveral ways to do-- maximum disk-- same dark halo-- normalisation to the optical disk

McGaugh 2014

25

Maximum disk74 spiral galaxies : good agreement with themodel bulge+ disk M/L = 1 5model bulge+ disk M/L = 1-5 Dark matter follows the stars?Palunas & Williams 2000

26

Coupling DM-baryons: dwarf galaxiesThe wiggles of rotation curves follow the baryons: once re-scaled(with M/L cst), the observed rotation curve is obtained

S t t l 2012Swaters et al 201227

Coupling DM-baryons: massive galaxiesCoupling DM-baryons: massive galaxies

Th t i l d t th b d i i ti f HISwaters et al 2012

The agreement is less good at the border: ionisation of HI gas28

The universal rotation curveOptical Radio

The total mass of dark haloi ll kis not well knownMass increases like RWhere does it stop?Where does it stop?

Universality is obtainedyif baryons determinethe total massdi t ib tidistribution

29

Rotation and galaxy types

DDO154, dwarf End of the conspiration

V (km/s) N2403

dwarfs IntermediateAndromeda dwarfs IntermediateAndromeda

N2683

Giants Compact giants

30Casertano & van Gorkom 1991

Generalisation to a 3D spaceGe e a sat o to a 3 space

The luminosityThe luminositydetermines the rotationcurve

V(R/Rd, L)

Baryons are the key

Salucci et al 2007 31

Modelisation of rotation curves• Contribution of stars, exponential disk (near infrared)• Contribution of gas, HI (in 1/R), CO (exponential)• Contribution of dark matter

Profil predicted by numerical simulations Navarro, Frenk & White (1997), NFW

Isothermal~r-3

Burkert

r

V2 (obs) = V2(stars) + V2 (gas) + V2 (halo) 32

Results from models

The rotation curves are determined byLuminosity

Luminosityn d

e D

M

Luminosity

Small galaxies have more Luminosityfr

act

iong

dark matter in proportion, witha higher density

• Persic et al 96, Salucci et al 2007 33

Surface density at the centre 0 r0 is a y 0 0constant for the halo of spirals

Kormendy & Freeman (2004) 0 r0 =100 M/pc234

Radial distribution of the various components

The molecular gas H2 does notdiradiate

The next most abundant moleculeCO serves as a tracerCO serves as a tracer

Its radial distribution isexponential, similar to stars

Th iThe atomic gas presentsA central depressionFlatter distribution as 1/RFlatter distribution, as 1/R

35

Distribution of gas: HI, H2H2 exponential, comparable to stars

Wong & Blitz (2002) 36

HI-21cm rotation curvesHI 21cm rotation curves

Bosma 198137

Ratio of surface densitiesBosma 1981Bosma 1981

Log(DM/HI)

Radius(kpc)Radius(kpc)

Log( / )Log(DM/HI)

38Radius(kpc)

Hoekstra et al (2001) Ratio of surface densities/DM/HI

In average ~10

The DM and the atomic HI have the same distribution39

Tully-Fisher relation

Relation between maximumvelocity and luminosityDV corrected from inclination

i i f d b dBetter in infrared I-band(no extinction)

Correlation with VflatBetter than Vmax

Verheijen 2001

40

The Tully-Fisher relationfor dwarf galaxies

hi h hwhich have more gasthan stars in masstake into account thetake into account thegas mass

Relation Mbaryonsith V R t tiwith V Rotation

Mb ~ V 4Mb Vc

41McGaugh et al (2000) Baryonic Tully-Fisher relation

Baryonic Tully-Fisher

fb universal fraction of baryons= 17%y

CDM: Cold Dark Matter

dark energy

V4

42McGaugh 2011

Tully-Fisher relationy

Th di i f h d dThe prediction of the standardCDM model has a slope 3Mb ~ V 3Mb Vc

Moreover, there are too manybaryons in galaxies

In particular for small massesby a factor 10-100by a factor 10 100

Famaey & McGaugh 2012 43

Deformations of the velocity fieldDeformations of the velocity field

• The non-circular velocities prevent to derive the mass distribution

• Internal perturbations: bars• External perturbations: warp of the plane, interactions,

accretion, change of the inclination• Thickening of the planes: generalisation of galaxies seen

edge-on

Problem for the cusps/coresProblem for the total mass

44

Non-circular orbits: bars

The departures from circularity become coherentThe departures from circularity become coherentthanks to a spiral or barred wave

Stars GasSpiral galaxies areunstable and formunstable and formbars

45

Correction of elongated orbits

N6503, Kuzio de Naray et al 2012

46

Rotation curves of barred galaxies

gSa (halo ISO)gSa (halo ISO)Bar: perpendicular

Bar: intermediate

Rotcur: black dotsDiskfit: red

Bar: parallel tomajor axis

47

gSbg

RotcurModelisationof circularorbitsPA, inclvariable

48

Why not corrected by DiskFit ?

The software modelsa bar, when it is clearlyvisible in thevisible in the velocities

But cannot see a barwhen it is parallelto the symmetry axes

49

Computations on a specific case: NGC 3319Wise 3.4m HI-21cm

Velocity HI Dispersion HI 50

Different models of NGC 3319 e e t ode s o GC 33 9

M/L fixed

Raw velocities Velocities corrected from the bar

Not-corrected

stars

halo

Corrected

gas

halo

h l

M/L variable

The pert rbations d e tostars

halo The perturbations due to the bar are significant

gas Randriamampandry et al 201451

Warped planesa ped p a es

observation

d l f il d iModel of tilted ringsPA, incl variableRogstad et al 1974 modelRogstad et al 1974 model

52

Tilted orbits, NGC 3718

non circular motionsMore difficult estimation, when deformationis importantTh bi hi hl lli i l d hThe orbits are highly elliptical, and thatdepends on the 3D shape of dark halo

NGC 4013NGC 660 NGC 4013Bottema 1996

NGC 660

53

Polar ring galaxies

T t f th 3D h f h lTest of the 3D shape of halos Vpolar < Vequatorial ?

CDM model: predicts Vpol < VeqOr Vpol=Veq, if accretion

54Brook et al 2008

Conclusion: Dark matter and spiralspThe best tracer for outer parts is the atomic gasHI 21 lHI-21cm total mass

Inner parts: the ionised gas (H NII) more spatial resolutionInner parts: the ionised gas (H, NII) more spatial resolutionMolecular gas, tracer CO cusp-core

Interpretation: bulge, disk, dark halo-- rotation curves depend essentially on baryons

i l V( / d L) i di k-- universal curve V(r/rd, L), maximum disk-- Tully-Fisher relation-- coupling DM-baryons DM/HI = 10coupling DM baryons, DM/HI 10

-- Deformations: bars for the inner parts,

55

Warps for outer parts