Universität Heidelberg Carl Zeiss Stiftung INTRODUCTION TO DARK MATTER Susanne Westhoff 2nd Colima Winter School on High Energy hysics! January 8-19, 2018 Colima, Mexico
GALAXY VELOCITIES IN CLUSTERS Redshift measurements of galaxies: large velocity dispersions Velocities of nebulae in Coma cluster virial theorem: hv 2 radi = GM R Fritz Zwicky, 1898-1974 Zwicky, 1933 2
GAS ROTATION IN GALAXIES Radio astronomy: measurements of rotational velocity of hydrogen in galaxies velocity distribution in Andromeda Nebula [Rubin, Ford, 1970] Vera Rubin, 1928-2016 Observation: rotational velocity distributions are mostly flat r GM v(r) const. = v(r) = (Newton) r 3
A CLOSED UNIVERSE? hilosophical considerations: The expansion of the universe must be decelerating, tot 1. However, the observed energy density of visible matter was baryons = / c 10 2 1 If one tentatively accepts a closed universe, then one is forced to the conclusion that the mass density of c 10 29 g/cm 3 normal galaxies. But where? must be found outside the adapted from Stephen Weinberg, 1972 4
EVIDENCE OF MISSING MATTER Determining the average mass of the universe by combining velocity distributions of clusters and galaxies M(r) r Ostriker, eebles, Yahil, 1974 Einasto, Kaasik, Saar, 1974 luminous matter dark corona [Einasto, Kaasik, Saar, 1974] eebles, Abell, Longair, Einasto (l.t.r.) Tallinn 1977 5
ART I! DARK MATTER IN THE UNIVERSE Experimental evidence today! article dark matter! The relic abundance 6
ROTATION CURVES TODAY Density distribution of DM halo: Average velocity: hvi = r GMhalo R halo (r) M(r) r 3 1 r 2 200 km/s c Rotation curve of visible stars and gas in spiral galaxy M33 [Wikipedia] 7
GRAVITATIONAL LENSING Light is bent when traveling through the distorted space-time around massive objects [NASA/ESA] 8
SELF-INTERACTING DARK MATTER? [Abell 3827, ESO VLT and Hubble Space Telescope, 2014] Dark matter seems to lag behind in this collision of galaxies. Lag not observed in collisions of galaxy clusters. 9
COSMOLOGICAL EVIDENCE cosmological microwave background anisotropies large-scale structure of the universe galaxy formation baryonic acoustic oscillations Acoustic peaks of the CMB power spectrum [lanck+wma] 10
ENERGY BUDGET OF OUR UNIVERSE [NASA / WMA Science Team, after lanck 2013] Density of non-relativistic, non-baryonic matter: h 2 =0.1198 ± 0.0015 [lanck coll., 2015] 11
WHAT WE KNOW ABOUT DARK MATTER It exists in abundance in the universe today. It interacts gravitationally. It must be stable on cosmological time scales. It should be mostly non-relativistic ( cold ). It cannot be baryonic (primordial black holes are an option). 12
WHAT WE KNOW ABOUT DARK MATTER It exists in abundance in the universe today. It interacts gravitationally. It must be stable on cosmological time scales. It should be mostly non-relativistic ( cold ). It cannot be baryonic (primordial black holes are an option). WHAT WE DON T KNOW Is dark matter a particle? If so, what are its properties: mass, spin, interactions? Does it have self-interactions? Is there maybe an entire dark sector? 13
ARTICLE DARK MATTER Requiring that DM form halos, it should be heavier than scalar: m & 10 22 ev (uncertainty principle) fermion: m & 0.7 kev (auli exclusion) ossible candidates: axions sterile neutrinos gravitinos neutralinos m 10 5 ev 1 kev 1 MeV 1 GeV 1 TeV 14
THERMAL DARK MATTER Dark matter number density in thermal equilibrium: n (m T ) 3/2 e m /T n T 3 (relativistic, hot ) (non-relativistic, cold ) Dark matter decouples from chemical equilibrium when! = n h vi H Cold dark matter decouples earlier than hot dark matter. 15
FREEZE-OUT [Gondolo, Gelmini, 1991] After chemical decoupling, cold DM is still in kinetic equilibrium with the SM particle : n T 3 decoupling from chemical equilibrium n h vi H decoupling from kinetic equilibrium n h scatt. vi H The DM number density changes over time as (Boltzmann): dn +3H(t)n = h vi(n 2 n 2,eq) dt 16
COMOVING NUMBER DENSITY Scaling out the Hubble expansion: Y = n /s, x = m /T dy dx = xsh vi H(m ) (Y 2 Yeq) 2 f 1 x f Y/Y(x = 1) 0.01 10-4 10-6 10-8 Y today 10-10 Y eq 1 5 10 50 100 x = m /T x [Lisanti, TASI 2016] Non-relativistic limit: h vi = b 0 + 3 2 b 1 x +... Y today x f 17
RELIC DARK MATTER ABUNDANCE Dark matter density in the universe today: = m s todayy today c For a weakly interacting massive particle (WIM): h 2 10 26 cm 3 /s h vi 0.1 2 0.01 m 2 100 GeV Observed: h 2 =0.1198 ± 0.0015 [lanck coll., 2015] Freeze-out temperature: T f =4GeV(x f = 25,m = 100GeV) Thermal DM could be much lighter: h vi 2 /m 2 18
NEUTRINOS AS DARK MATTER? The cross section for neutrino annihilation is small: h vi 10 32 cm 3 /s h 2 0.1 From cosmology (e.g., impact on structure formation): X m. 1 ev i [e.g. Lesgourges, astor, 2012] i m 9 ev Neutrino dark matter would be relativistic at freeze-out: T f /m MeV/eV 1 hot dark matter SM neutrinos can only contribute a small amount of hot DM. 19
CO-ANNIHILATION [Griest, Seckel, 1991] Relative abundance of two non-relativistic particles at freeze-out: n i e mi/tf n j e m j/t f For : i =(m i m )/m 10% n i /n j 0.1 + i j h vi!h e (x)vi e (x) = X i,j ij g i g j g 2 e (x)(1 + i) 3/2 (1 + j ) 3/2 e x( i+ j ) For i, co-annihilation sets the relic abundance. 20
SUMMARY ART I We have strong evidence for dark matter based on gravitation. article dark matter is a tempting hypothesis, but so far without positive hints from experiment. Thermally produced dark matter points towards interaction rates that can be tested at colliders. 21
LITERATURE de Swart, Bertone, van Dongen: How dark matter came to matter, 1703.00013 M. Lisanti: Lectures on Dark Matter hysics, 1603.03797 D. Hooper: TASI 2008 Lectures on Dark Matter, 0901.4090 T. lehn: Yet Another Introduction to Dark Matter, 1705.01987 Gondolo, Gelmini: Cosmic abundances of stable particles: improved analysis, Nucl.hys. B360 (1991) 145-179 Griest, Seckel: Three exceptions in the calculation of relic abundances, hys.rev. D43 (1991) 3191-3203 22