Dark Matter I Gravitational probes, distributions and cosmological

Dark Matter I Gravitational probes, distributions and cosmological

Background and models
Distributions & Gravitational Probes
Production of dark matter
Dark Matter I
Gravitational probes, distributions and cosmological abundance
Pat Scott
Imperial College London
Slides available from tinyurl.com/patscott
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Dark Matter Lectures
Series Plan
1
Gravitational probes, distributions and cosmological
abundance
2
Direct detection
3
Indirect detection
4
Complementarity and global fits
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Outline
1
Background and models
Introduction
Models and requirements
2
Distributions & Gravitational Probes
3
Production of dark matter
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Introduction
Models and requirements
Outline
1
Background and models
Introduction
Models and requirements
2
Distributions & Gravitational Probes
3
Production of dark matter
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Introduction
Models and requirements
How we know dark matter exists
The only way to consistently explain:
1
rotation curves + vel. dispersions
2
gravitational lensing
cosmological data
3
(Clowe et al., ApJL 2006)
Large-scale structure
(2dF/Chandra/SDSS-BAO)
says Ωmatter ≈ 0.27
BBN says that Ωbaryonic ≈ 0.04
=⇒ Ωnon−baryonic ≈ 5 × Ωbaryons
CMB (WMAP) and SN1a agree; also indicate that Ωtotal ≈ 1
=⇒ universe is 23% dark matter, 4% baryonic (visible)
matter, 73% something else
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Introduction
Models and requirements
How we know dark matter exists
The only way to consistently explain:
1
rotation curves + vel. dispersions
2
gravitational lensing
cosmological data
3
Large-scale structure
(2dF/Chandra/SDSS-BAO)
says Ωmatter ≈ 0.27
BBN says that Ωbaryonic ≈ 0.04
=⇒ Ωnon−baryonic ≈ 5 × Ωbaryons
CMB (WMAP) and SN1a agree; also indicate that Ωtotal ≈ 1
=⇒ universe is 23% dark matter, 4% baryonic (visible)
matter, 73% something else
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Introduction
Models and requirements
What we know about it
Must be:
massive (gravitationally-interacting)
unable to interact via the electromagnetic force (dark)
non-baryonic
“cold(ish)” (in order to allow structure formation)
stable on cosmological timescales
produced with the right relic abundance in the early Universe.
Good options:
Weakly Interacting Massive Particles (WIMPs)
sterile neutrinos
gravitinos
axions
axinos
hidden sector dark matter (e.g. WIMPless dark matter)
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Introduction
Models and requirements
What we know about it
Must be:
massive (gravitationally-interacting)
unable to interact via the electromagnetic force (dark)
non-baryonic
“cold(ish)” (in order to allow structure formation)
stable on cosmological timescales
produced with the right relic abundance in the early Universe.
Good options:
Weakly Interacting Massive Particles (WIMPs)
sterile neutrinos
Bad options:
gravitinos
primordial black holes
axions
MAssive Compact Halo Objects (MACHOs)
axinos
standard model neutrinos
hidden sector dark matter (e.g. WIMPless dark matter)
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Introduction
Models and requirements
What we know about it
Must be:
massive (gravitationally-interacting)
unable to interact via the electromagnetic force (dark)
non-baryonic
“cold(ish)” (in order to allow structure formation)
stable on cosmological timescales
produced with the right relic abundance in the early Universe.
Good options:
Weakly Interacting Massive Particles (WIMPs)
sterile neutrinos
Bad options:
gravitinos
primordial black holes
axions
MAssive Compact Halo Objects (MACHOs)
axinos
standard model neutrinos
hidden sector dark matter (e.g. WIMPless dark matter)
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Introduction
Models and requirements
WIMPs at a glance
Dark because no electromagnetic interactions
Cold because very massive (∼10 GeV to ∼10 TeV)
Non-baryonic and stable - no problems with BBN or CMB
Weak-scale annihilation cross-sections naturally lead to a
relic abundance of the right order of magnitude (more later)
Simplest example is scalar singlet dark matter:
+ ...
0
−1
SS
Γ h→
−2
D
M
=
XE
1
XE
/Ω
ΩS
−3
Cline, Kainulainen, PS & Weniger Phys Rev D 2013
45
Pat Scott – Dec 2015 – TR33 Winter School
(20
12)
NO
N1
00
NO
×5
N10
0×
20
XEN
ON1
T
λhs 2 †
2 S H H
NO
N1
00
−
XE
µ2S 2
2 S
log10 λhs
LS = −
Dark Matter I
50
55
60
mS (GeV)
65
70
Background and models
Distributions & Gravitational Probes
Production of dark matter
Introduction
Models and requirements
WIMPs at a glance
Many theoretically well-motivated particle candidates
Supersymmetric (SUSY) neutralinos χ if R-parity is conserved lightest mixture of neutral higgsinos and gauginos
Inert Higgses - extra Higgs in the Standard Model
Kaluza-Klein particles - extra dimensions
right-handed neutrinos, sneutrinos, other exotic things. . .
Weak interaction means scattering with nuclei
=⇒ detection channel
Many WIMPs are Majorana particles (own antiparticles)
=⇒ self-annihilation cross-section
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Introduction
Models and requirements
Ways to detect WIMPs
Direct detection – nuclear collisions
and recoils
Indirect detection – annihilations
producing SM particles
Impacts on stars – the Sun and
“dark stars”
Direct production – missing ET or
otherwise – LHC, future colliders
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Introduction
Models and requirements
Ways to detect WIMPs
Direct detection – nuclear collisions
and recoils
Indirect detection – annihilations
producing SM particles
Impacts on stars – the Sun and
“dark stars”
Direct production – missing ET or
otherwise – LHC, future colliders
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Introduction
Models and requirements
Ways to detect WIMPs
Direct detection – nuclear collisions
and recoils Lec 2
Indirect detection – annihilations
producing SM particles Lec 3
Impacts on stars – the Sun and
“dark stars” Lec 3
Direct production – missing ET or
otherwise – LHC, future colliders
(teeny bit of Lec 4)
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Outline
1
Background and models
Introduction
Models and requirements
2
Distributions & Gravitational Probes
3
Production of dark matter
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Dark matter profiles
N-body simulations of dark matter halo formation suggest
universal (all-scale) Navarro-Frenk-White profile
ρ(r ) =
δc ρc
r /rs (1 + r /rs )2
,
(1)
or Einasto profile
#)
" 1
r n
−1
ρ(r ) = ρs exp −2n
rs
(
May be steepened in innermost region by adiabatic contraction
. . . or, may be softened in innermost region by baryonic effects
Data seem to suggest some sort of core in Milky-Way type galaxies
=⇒ baryonic effects favoured
*but* inner parts of halos not well constrained by data
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
(2)
Background and models
Distributions & Gravitational Probes
Production of dark matter
Dark matter substructure
100
Springel et al MNRAS 2009
dN / dMsub [ MO•-1 ]
10
-2
10-4
10-6
10-8
10-10
104
Msub2 dN / dMsub [ MO• ]
Nobody really knows how far
down (to what halo mass) the
‘universal profile’ holds
10
Aq-A-1
Aq-A-2
Aq-A-3
Aq-A-4
Aq-A-5
105
106
107
108
Msub [ MO• ]
109
1010
. . . or even down to what mass
DM subhalos actually exist at all
(solar mass? Earth mass?
snowball mass??)
11
. . . let alone how many there are
of each mass. . .
1010
104
105
106
107
108
Msub [ MO• ]
109
1010
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Dark matter substructure
100
Springel et al MNRAS 2009
dN / dMsub [ MO•-1 ]
10
-2
10-4
10-6
10-8
10-10
104
Msub2 dN / dMsub [ MO• ]
Nobody really knows how far
down (to what halo mass) the
‘universal profile’ holds
10
Aq-A-1
Aq-A-2
Aq-A-3
Aq-A-4
Aq-A-5
105
106
107
108
Msub [ MO• ]
109
1010
11
. . . let alone how many there are
of each mass. . .
1010
104
. . . or even down to what mass
DM subhalos actually exist at all
(solar mass? Earth mass?
snowball mass??)
→ kinetic decoupling mass cutoff
105
106
107
108
Msub [ MO• ]
109
1010
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Dark matter substructure
100
Springel et al MNRAS 2009
dN / dMsub [ MO•-1 ]
10
-2
10-4
10-6
10-8
10-10
104
Msub2 dN / dMsub [ MO• ]
Nobody really knows how far
down (to what halo mass) the
‘universal profile’ holds
10
Aq-A-1
Aq-A-2
Aq-A-3
Aq-A-4
Aq-A-5
105
106
107
108
Msub [ MO• ]
109
1010
11
1010
104
105
106
107
108
Msub [ MO• ]
109
1010
Pat Scott – Dec 2015 – TR33 Winter School
. . . or even down to what mass
DM subhalos actually exist at all
(solar mass? Earth mass?
snowball mass??)
→ kinetic decoupling mass cutoff
. . . let alone how many there are
of each mass. . .
→ primordial spectrum at small
scales
+ nonlinear structure formation
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Bringmann, PS, Akrami PRD 2012
Clark, Lewis, PS MNRAS 2015
Dark matter substructure
Highest amplitude fluctuations lead to early collapse
(zc & 1000)
→ low DM velocity dispersion
→ minihalos with much steeper density profiles than NFW
→ easier to detect with lensing or indirect detection
→ constrains small-scale power spectrum (→inflation)
10−1
10−2
❙
10−3
−4
Allowed regions
Pδ (k)
10−5
10
10−5
Ultracompact minihalos (reionisation, WMAP5 τe )
10−7
10
10−4
Ultracompact minihalos (gamma rays, Fermi -LAT)
−6
10−6
Primordial black holes
−8
10−7
CMB, Lyman-α, LSS and other cosmological probes
10−8
10−9
10
10−9
−10
−3
10
−2
10
−1
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
11
10
12
10
13
10
k (Mpc−1 )
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
14
10
15
10
16
10
17
10
18
10
19
10
PR (k)
❙
10
10−2
WIMP kinetic decoupling
10−3
Background and models
Distributions & Gravitational Probes
Production of dark matter
Dark matter velocity distribution
DM halo is isothermal to
a first approximation
Maxwell-Boltzmann distribution:
3v 2 4 3 3/2 ρχ v 2
exp
− 2
f (v ) = √
mχ v̄ 3
π 2
2v̄
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
=⇒ DM kinetic energies
follow Boltzmann
partitioning with single
temperature T
≡ DM velocities follow
Maxwell-Boltzmann
distribution with mean
v̄ (T )
Background and models
Distributions & Gravitational Probes
Production of dark matter
Dark matter velocity distribution
DM halo is isothermal to
a first approximation
=⇒ DM kinetic energies
follow Boltzmann
partitioning with single
temperature T
≡ DM velocities follow
Maxwell-Boltzmann
distribution with mean
v̄ (T )
. . . as usual, real life is
more complicated. . .
Kuhlen et al JCAP 2010
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Impacts of particle physics on dark matter distributions
Dark matter may be at least partially warm
Example: neutrinos
=⇒ large free-streaming length,
depends on mν
→ escape from small collapsing
perturbations
=⇒ Suppression in small-scale
matter (processed) power
spectrum
SNOWMASS 2013, arXiv:1309.5383
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Impacts of particle physics on dark matter distributions
Dark matter may have a small self-interaction
→ No longer entirely dissipationless
→ washes out highest densities → galaxy cores
Regular cold dark mattter
Self-interacting dark matter
Rocha, Peter, Bullock et al MNRAS 2012
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Impacts of particle physics on dark matter distributions
Dark matter may have more complicated interactions
where v and ρ both matter
E.g. models with light vector
mediators that connect DM
and standard model particles
χ
V
χ̄
χ
...
χ̄
→ ‘Sommerfeld’ enhancement
→ enhanced DM-DM scattering for certain DM-DM relative
velocities
→ wash out structure where DM moves at a certain speed
→ (e.g. cores of dwarf galaxies, maybe fixing cusp vs core
issue)
van den Aarssen, Bringmann, Pfrommer, PRL 2012
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
heavily adapted from
Kneib & Natarajan A&A Rev. 2012
Gravitational lensing
Cluster lensing: strong, weak/shear
Microlensing: strong: standard (brightness)
Microlensing: weak: astrometric, time delay
Observer
Cluster of Galaxies
Background Galaxy
Apparent position
Strong:
Multiple
Images
True position
Intermediate:
Arclets
Optical Path
Weak:
Wave Front
Weak Shear
Multiple Images Area
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
heavily adapted from
Kneib & Natarajan A&A Rev. 2012
Gravitational lensing
Cluster lensing: strong, weak/shear
Microlensing: strong: standard (brightness)
Microlensing: weak: astrometric, time delay
Observer
Galaxies
DarkCluster
matter of
halo
Background Galaxy
Apparent position
Strong:
Regular
microlensing
(images add)
True position
Weak:
Astrometric
microlensing
Optical Path
Weaker:
Wave Front
Time delay
lensing
Multiple Images Area
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Outline
1
Background and models
Introduction
Models and requirements
2
Distributions & Gravitational Probes
3
Production of dark matter
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Thermal and non-thermal production
Thermal Production
Everything is in perfect thermal equilibrium in early Universe
=⇒
Particle populations are all in equilibrium (cf Saha, Boltzmann
Eqs) → set by T
Velocities are all in kinetic equilibrium (cf Maxwell dist)
→ set by T
=⇒ As stuff falls out of equilibrium, populations and velocities must be
evolved explicitly
=⇒ Always present at some level, not always dominant in ΩDM
Non-thermal Production
Any other process that dominates the DM relic density
Some other heavy BSM particle X decays → DM
Decays/evaporations of topological defects like cosmic strings
Evaporation of primordial black holes
Not always present
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Thermal production
(Kolb & Turner 1990) → DarkSUSY, MicrOmegas,
MadDM, SuperIsoRelic, BYO homebrew, etc
Thermal relic particle populations (=relic density) are obtained
by solving the Boltzmann Equation:
dnχ
+ 3Hnχ = hσv i(nχ, eq2 − nχ2 )
dt
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
(3)
Background and models
Distributions & Gravitational Probes
Production of dark matter
Kinetic decoupling and small-scale structure
T. Bringmann, 2009
Particle production and abundance is chemical
freeze-out
Typically happen kind of around the same time,
but very model-dependent
Kinetic decoupling temperature → kinetic
decoupling scale → minimum DM halo mass
Impacts boost factors for indirect detection
(Φ ∝ ρ2 ), minihalo searches
Pat Scott – Dec 2015 – TR33 Winter School
‰
‰
10−6
Mcut /M⊙
Particle velocities and final DM temperature are
determined by kinetic freeze-out
10−4
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Dark Matter I
10−8
10−10
‰
‰
10
−12
50
100
500
mχ [GeV]
1000
5000
Background and models
Distributions & Gravitational Probes
Production of dark matter
Bringmann, PS, Akrami PRD 2012
Redux: dark matter substructure
Clark, Lewis, PS MNRAS 2015
Highest amplitude fluctuations lead to early collapse
(zc & 1000)
→ low DM velocity dispersion
→ minihalos with much steeper density profiles than NFW
→ easier to detect with lensing or indirect detection
→ constrains small-scale power spectrum (→inflation)
10−1
10−2
❙
10−3
−4
Allowed regions
Pδ (k)
10−5
10
10−5
Ultracompact minihalos (reionisation, WMAP5 τe )
10−7
10
10−4
Ultracompact minihalos (gamma rays, Fermi -LAT)
−6
10−6
Primordial black holes
−8
10−7
CMB, Lyman-α, LSS and other cosmological probes
10−8
10−9
10
10−9
−10
−3
10
−2
10
−1
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
11
10
12
10
13
10
k (Mpc−1 )
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
14
10
15
10
16
10
17
10
18
10
19
10
PR (k)
❙
10
10−2
WIMP kinetic decoupling
10−3
Background and models
Distributions & Gravitational Probes
Production of dark matter
Summary – DM Lecture I
Dark matter is very obviously out there
A number of good theories for its identity exist
Dark matter has only been observed via gravity so far
Its identity does impact its expected distribution – and
therefore its gravitational signatures
Dark matter production in the early Universe places strong
constraints on its identity
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Summary – DM Lecture I
Dark matter is very obviously out there
A number of good theories for its identity exist
Dark matter has only been observed via gravity so far
Its identity does impact its expected distribution – and
therefore its gravitational signatures
Dark matter production in the early Universe places strong
constraints on its identity
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Summary – DM Lecture I
Dark matter is very obviously out there
A number of good theories for its identity exist
Dark matter has only been observed via gravity so far
Its identity does impact its expected distribution – and
therefore its gravitational signatures
Dark matter production in the early Universe places strong
constraints on its identity
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Summary – DM Lecture I
Dark matter is very obviously out there
A number of good theories for its identity exist
Dark matter has only been observed via gravity so far
Its identity does impact its expected distribution – and
therefore its gravitational signatures
Dark matter production in the early Universe places strong
constraints on its identity
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I
Background and models
Distributions & Gravitational Probes
Production of dark matter
Summary – DM Lecture I
Dark matter is very obviously out there
A number of good theories for its identity exist
Dark matter has only been observed via gravity so far
Its identity does impact its expected distribution – and
therefore its gravitational signatures
Dark matter production in the early Universe places strong
constraints on its identity
Pat Scott – Dec 2015 – TR33 Winter School
Dark Matter I