Can we directly measure the local distribution of Dark Matter from - - PowerPoint PPT Presentation

Can we directly measure the local distribution of Dark Matter from Earth?

Bradley J Kavanagh GRAPPA, University of Amsterdam 17th October 2018 PRISMA Colloquium, Mainz

@BradleyKavanagh b.j.kavanagh@uva.nl

Undergraduate (2007-2011): University of Cambridge, UK Studied: Everything from organic chemistry to crystallography

PhD (2011-2014): University of Nottingham, UK Thesis Title: “Confronting astrophysical uncertainties in the direct detection of dark matter”
 (2014, Supervised by Anne M. Green)

Postdoc #1 (2014-2017): IPhT & LPTHE, Paris, France Spent time worrying about: More ‘particle’ aspects of Dark Matter - how does it interact with nuclei?
 (Supervised by Marco Cirelli)

Postdoc #2 (2017-): GRAPPA, University of Amsterdam People keep asking me about: Dark Matter, primordial black holes, gravitational waves, neutrinos,…
 (Supervised by Gianfranco Bertone)

Open Science

…research is notes, calculations, data, code. Papers (and talks) are just propaganda… bradkav.net github.com/bradkav The more we share, the easier life gets for everyone. Plenty of tools to facilitate sharing and collaboration: Aiming in the last few years to share as much as

• possible. Not always successful. But every small

step is a step in the right direction.

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Dark Matter on all scales

7

Planck [1502.01589] Rubin, Ford & Thonnard (1980) Hradecky et al. [astro-ph/0006397] Galaxy Clusters CMB Galaxies

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Dark Matter near us

8

NOT TO SCALE Global and local estimates

• f DM at Solar radius give:

ρχ ∼ 0.2−0.8 GeV cm−3 8.5 kpc

(`a few per litre’)

See e.g. Iocco et al. [1502.03821]; Sivertsson et al. [1708.07836]; and review by Read [1404.1938]

v ∼ 230 km/s

Try to detect the ‘wind’ of DM particles passing through the Solar System, using Direct Detection and Solar Capture.

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Overview

9

Solar system searches for DM: Direct detection and Solar Capture Astrophysical uncertainties Halo-independent approaches to setting limits Measuring the DM properties and distribution with a future detection [Bonus: Can we also measure the local DM density?]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Direct detection

10

Charge (ionisation) Heat (phonons) Light (scintillation) mχ 1 GeV

v ∼ 10−3 c

χ

Detector Target nucleus, N

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Direct detection

11

Charge (ionisation) Heat (phonons) Light (scintillation) mχ 1 GeV

v ∼ 10−3 c

χ

Detector Target nucleus, N Xenon1T

Credit: Roberto Corrieri and Patrick De Perio

SuperCDMS and many others

Credit: SuperCDMS Collaboration

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Direct detection signal

12

SI interactions Spin-independent (SI) interactions: Spin-dependent (SD) interactions:

More complicated interactions are possible: see e.g. Fitzpatrick et al. [1203.3542]; Edwards, BJK, Weniger [1805.04117]

dR dER ∼ ρχ mχ σpCA ∞

vmin

f(v) v dv

vmin =

• mNER

2µ2

χN

Include only DM particles with enough energy: CSI

A ∼ A2

CSD

A

∼ (J + 1)/J

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Solar Capture

13

χ ν ν

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Solar Capture

14

χ ν ν IceCube


and many others

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Solar Capture

15

χ ν ν

Credit: icecube.wisc.edu

IceCube


and many others

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Solar Capture Rate

16

Gould (1991) [1312.6408]

SI SD Only include DM particles moving slowly enough to be captured: vmax = 4mχmNi mχ − mNi vesc

If capture and annihilation are in equilibrium, annihilation rate only depends on DM-nucleon scattering cross section. Observed neutrino flux depends on DM annihilation channel… Sum over species in the Sun, i. Ci ∼ ρχ mχ vmax dv f(v) v σiniP i

cap(v) dv

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Limits on Solar System DM

17

IceCube [1612.05949] XENON1T [1805.12562]

IceCube τ +τ −

Spin-independent Spin-dependent But these rely on a particular assumption on the speed distribution, … f(v)

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Overview

18

Solar system searches for DM: Direct detection and Solar Capture Astrophysical uncertainties Halo-independent approaches to setting limits Measuring the DM properties and distribution with a future detection [Bonus: Can we also measure the local DM density?]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Standard Halo Model

19

Standard Halo Model (SHM) is typically assumed: isotropic, spherically symmetric distribution of particles with . Leads to a Maxwell-Boltzmann (MB) distribution,

ve - Earth’s Velocity

Feast et al. [astro-ph/9706293], Bovy et al. [1209.0759] Piffl et al. (RAVE) [1309.4293]

ρ(r) ∝ r−2 fLab(v) = (2πσ2

v)−3/2 exp

• −(v − ve)2

2σ2

v

• Θ(|v − ve| − vesc)

σv ∼ 155 − 175 km s−1 vesc = 533+54

−41 km s−1

ve ∼ 220 − 250 km s−1

SHM + uncertainties

which is well matched in some hydro simulations.

[1601.04707, 1601.04725, 1601.05402]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

N-body simulations

20

Kuhlen et al. [1202.0007] Pillepich et al. [1308.1703], Schaller et al. [1605.02770]

The Standard Halo Model (SHM) has some inherent uncertainties. But there could also be deviations from MB form: Simulations suggest there could be also substructure: Debris flows Dark disk Tidal stream

Freese et al. [astro-ph/0309279, astro-ph/0310334] NIHAO [1503.04814]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

S1 Stream: DM Hurricane?

21

O’Hare et al. [1807.09004]

S1 stream counter-rotating at vS1 ≈ 300 km/s

Could be carrying with it a hurricane of Dark Matter… Recent GAIA data revealing new stellar streams:

[1712.04071]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Stars as DM Tracers

22

Herzog-Arbeitman et al. [1708.03635]; Necib et. al. [1807.02519]

Old, metal-poor stars may trace the DM velocity distribution:

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Astro Uncertainties

23

SHM + uncertainties

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Overview

24

Solar system searches for DM: Direct detection and Solar Capture Astrophysical uncertainties Halo-independent approaches to setting limits Measuring the DM properties and distribution with a future detection [Bonus: Can we also measure the local DM density?]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Impact on DM limits

25

See also e.g. Green [astro-ph/0207366]; Fairbairn et al. [1206.2693]; Bozorgnia & Bertone [1705.05853] Benito et al. [1612.02010]

Direct Detection

Choi et al. [1312.0273]

Solar Capture δρχ

δf(v)

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Deviation from SHM

26

Allow arbitrary deviations from the SHM, of size ∆

SHM velocity distribution ∆ → 0

∆ → ∞

Arbitrary velocity distribution

See also Fowlie [1809.02323]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Stream Decomposition

27

Ferrer et al. [1506.03386]; Ibarra & Rappelt [1703.09168]; Ibarra, BJK, Rappelt [1806.08714]

Attempt to be as general as possible: Optimize: log p (mχ, p, f(v)) Subject to:

• f(

v) − fSHM( v) fSHM( v)

• ≤ ∆

and

• d3vf(

v) = 1 .

Optimise p-value or chi-squared or likelihood

• r whatever

For small event numbers, this can recast this as a fast optimisation problem for the coefficients . ci

f(v) =

• f(v0)δ (v − v0) d3v →
• i

ciδ (v − vi)

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Xenon1T Limits

28

Most aggressive Most conservative

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Velocity Ranges

29

100 101 102 103 104 mχ [GeV] 200 400 600 800 1000 v [km/s] vesc + v

Solar Capture Xe

vmin =

• mNER

2µ2

χN

vmax = 4mχmNi mχ − mNi vesc

Direct detection: Solar Capture:

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Xenon1T + IceCube

30

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Xenon1T + IceCube

31

Excluded for none Excluded for all Excluded for some

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Overview

32

Solar system searches for DM: Direct detection and Solar Capture Astrophysical uncertainties Halo-independent approaches to setting limits Measuring the DM properties and distribution with a future detection [Bonus: Can we also measure the local DM density?]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Impact on DM Signals

33

(correct) stream distribution (incorrect) SHM distribution

Benchmark Best fit

Generate mock data for several experiments, assuming a stream distribution, then try to reconstruct the mass and cross section assuming:

NB: Some of these parameters are now excluded :(

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

100 101 102 103 104 mχ [GeV] 200 400 600 800 1000 v [km/s] vesc + v

Xe Ge

Alternatively, compare experiments

• nly over velocities where they
• verlap and effectively ‘divide out’

the astrophysical uncertainties:

Halo-independent methods

34

Fox et al. [1011.1915,1011.1910], but see also [1111.0292, 1107.0741, 1202.6359, 1304.6183, 1403.4606, 1403.6830, 1504.03333, 1607.02445, 1607.04418 and more…]

Could include SHM uncertainties, but are these broad enough?

Strigari & Trotta [0906.5361]

Need to fix DM mass, and not straightforward to apply to Solar Capture…

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Now fit at the same time as …

Fitting the DM distribution

35

Write a general parametrisation for the speed distribution: Peter [1103.5145] f(v) = v2 exp

• −

N−1

• k=0

akvk

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BJK & Green [1303.6868]

Guarantees a positive distribution function and spans a wide range

• f functional forms with only a

small number N of parameters: {ak}

(mχ, σp)

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Testing the parametrisation

36

Benchmark Best fit

Assuming incorrect distribution

Direct detection Xe + Ge + Ar

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Testing the parametrisation

37

Benchmark Best fit

Assuming incorrect distribution Using our parametrisation

Direct detection Xe + Ge + Ar targets O(100s) events

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Reconstructing DM mass

38

Best fit

1σ 2σ mrec = mχ

Input mass Reconstructed mass

BJK [1312.1852]

Also works for a range of input velocity distributions. Recently demonstrated for arbitrary interactions too…

Krauss & Newstead [1801.08523]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Reconstructing f(v)

39

Best fit distribution

Direct detection only

BJK, Fornasa, Green [1410.8051]

f(v) v2

‘True’ speed distribution

mχ = 30 GeV

SHM+DD distribution

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Reconstructing f(v)

40

Best fit distribution ‘True’ speed distribution

Direct detection only

BJK, Fornasa, Green [1410.8051]

f(v) v2

mχ = 30 GeV

SHM+DD distribution

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

100 101 102 103 104 mχ [GeV] 200 400 600 800 1000 v [km/s] vesc + v

Xe Ge

Velocity Ranges

41

vmin =

• mNER

2µ2

χN

vmax = 4mχmNi mχ − mNi vesc

Direct detection: Solar Capture: …a problem for any astrophysics-independent method. Cannot constrain distribution below threshold…

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

100 101 102 103 104 mχ [GeV] 200 400 600 800 1000 v [km/s] vesc + v

Solar Capture Xe Ge

Velocity Ranges

42

vmin =

• mNER

2µ2

χN

vmax = 4mχmNi mχ − mNi vesc

Direct detection: Solar Capture:

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Combining with IceCube

43

Benchmark Best fit

BJK, Fornasa, Green [1410.8051] Reconstruction without IceCube Reconstruction with IceCube

Combining direct detection and solar capture, we could pin down DM mass and cross section

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Reconstructing f(v) with IceCube

44

Best fit distribution ‘True’ speed distribution

mχ = 30 GeV

SHM+DD distribution

Including IceCube

Annihilation to νµ¯

νµ

BJK, Fornasa, Green [1410.8051]

Constraints improved, but still difficult to distinguish underlying distributions (perhaps only at the 1σ level)… f(v) v2

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Directional Detection

45

Try to measure both the energy and the direction of the recoil Most mature technology is the gaseous Time Projection Chamber (TPC)

[e.g. DRIFT, MIMAC, DMTPC, NEWAGE, D3] Mayet et al. [1602.03781]

• +

E-field CF4 gas

e

• +

E-field

Possible suggestion of (partial) directionality in Xenon detectors

Mohlabeng et al. [1503.03937]; Namakura et al. [1803.00752]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

3-D Velocity Distribution

46

Apply the same parametrisation in 3-D (note: some technical details, which make things annoying)

BJK [1502.04224]

Directional detectors are in principle sensitive to full 3-D velocity distribution:

DM wind

Gondolo [hep-ph/0209110]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Input distribution: SHM

Directional reconstructions

47

Parallel to Earth’s motion Perpendicular to Earth’s motion BJK, CAJ O’Hare [1609.08630]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Directional reconstructions

48

Input distribution: SHM + Stream

Parallel to Earth’s motion Perpendicular to Earth’s motion BJK, CAJ O’Hare [1609.08630]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Overview

49

Solar system searches for DM: Direct detection and Solar Capture Astrophysical uncertainties Halo-independent approaches to setting limits Measuring the DM properties and distribution with a future detection [Bonus: Can we also measure the local DM density?]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Map of the parameter space

50

10−1 100 101 102 103 104

mχ [GeV]

10−48 10−47 10−46 10−45 10−44 10−43 10−42 10−41 10−40 10−39 10−38 10−37 10−36

σSI

p [cm2]

8B

LUX (IDM-2016) CDMSlite (2015) CRESST-II (2015) Xenon1T (2017) Xe Neutrino Floor (O’Hare 2016)

Sub-GeV DM

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Earth scattering

51

BJK, Catena, Kouvaris [1611.05453]; Emken, Kouvaris, Shoemaker [1702.07750]; Emken & Kouvaris [1706.02249]; BJK [1712.04901] and others

Detector

Collar & Avignone [PLB 275, 1992] and others

Earth-scattering can distort local density and velocity distribution:

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Daily Modulation

52

λ RE

Assuming DM mean free path N Nfree

In the ‘single-scatter’ regime, can calculate Earth-scattering effects semi-analytically:

BJK, Catena, Kouvaris [1611.05453]; github.com/bradkav/EarthShadow

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Modulation signals

53

DM comes from above DM comes from below

Large O(1) daily modulation if DM scatters ~50 times during Earth-crossing

Emken & Kouvaris [1706.02249]

Extended with Monte Carlo Simulations

github.com/temken/DaMaSCUS

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

10−37 10−36 10−35 10−34 σSI

p [cm2]

10−2 10−1 100 101 102 ρχ [GeV cm−3]

Energy only

3 6 9 12 15 18 ∆χ2

Preliminary results

54

BJK & Catena [XXXX.XXXX]

100g Ge detector 30 day exposure LNGS, Italy O(30) events

6 12 18 24 Sidereal time [hr] 0.105 0.110 0.115 Recoil energy [keV] 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Number of events

10−37 10−36 10−35 10−34 σSI

p [cm2]

10−2 10−1 100 101 102 ρχ [GeV cm−3]

Energy + Timing

3 6 9 12 15 18 ∆χ2

mχ = 0.5 GeV

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Summary (I)

55

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Summary (I)

56

Astrophysics

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Summary (I)

57

Astrophysics Particle physics

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Summary (I)

58

Astrophysics Particle physics

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Summary (II)

59

We can simultaneous extract the mass and shape of the speed distribution of DM with a future direct detection Probing low speed DM with Solar Capture allows us to pin down the DM cross section It could be possible to measure the full 3-D DM velocity distribution with directional experiments

BJK, Green [1207.2039, 1303.6868,1312.1852] BJK, Fornasa, Green [1410.8051] BJK [1502.04224]; BJK, O’Hare [1609.08630]

We can set limits from local DM searches in a fully astrophysics-independent way

Ibarra, BJK, Rappelt [1806.08714]

If we’re lucky, we may even one day measure the local DM density

BJK & Catena [XXXX.XXXX]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Summary (II)

60

We can simultaneous extract the mass and shape of the speed distribution of DM with a future direct detection Probing low speed DM with Solar Capture allows us to pin down the DM cross section It could be possible to measure the full 3-D DM velocity distribution with directional experiments

BJK, Green [1207.2039, 1303.6868,1312.1852] BJK, Fornasa, Green [1410.8051] BJK [1502.04224]; BJK, O’Hare [1609.08630]

We can set limits from local DM searches in a fully astrophysics-independent way

Ibarra, BJK, Rappelt [1806.08714]

If we’re lucky, we may even one day measure the local DM density

BJK & Catena [XXXX.XXXX]

Thank you!

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth 61

Back-up Slides

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Particle Physics of DM

62

Typically assume contact interactions (heavy mediators). In the non-relativistic limit, leading order cross section scales like:

dσA dER ∝ σp µ2

χpv2 CAF 2(ER)

Enhancement factor different for:

CSI

A ∼ A2

spin-independent (SI) interactions - spin-dependent (SD) interactions -

CSD

A

∼ (J + 1)/J

Form factor accounts for loss of coherence at high energy Interactions which are higher order in v are possible. See the non-relativistic EFT of Fitzpatrick et al. [1203.3542]. See also Edwards, BJK, Weniger [1805.04117].

Write in terms of DM-proton cross section: σ ∼ v0 ⇒ dσ dER ∼ 1 v2

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Polynomial Parametrisation

63

f(v) = v2 exp

• −

N−1

• k=0

akvk

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Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Different Speed Distributions

64

• Generate 250 mock data

sets

• Reconstruct mass and
• btain confidence intervals

for each data set

• True mass reconstructed

well (independent of speed distribution)

• Can also check that 68%

intervals are really 68% intervals

True mass

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Full reconstructions (without IceCube)

65

Benchmark Best fit

Fixed (correct) speed distribution Our parametrisation

Consider a single benchmark: annihilation to , SHM+DD distribution νµ¯ νµ mχ = 30 GeV; σp

SI = 10−45 cm2; σp SD = 2 × 10−40 cm2

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Full reconstructions (with IceCube)

66

Benchmark Best fit

Direct detection only (our param.) Direct detection + IceCube (our param.)

Best fit

Consider a single benchmark: annihilation to , SHM+DD distribution νµ¯ νµ mχ = 30 GeV; σp

SI = 10−45 cm2; σp SD = 2 × 10−40 cm2

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

‘Real’ Experiments

67

Best fit

1σ 2σ

Ideal experiments ‘Real’ experiments

mrec = mχ

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

SI vs SD Solar Capture

68

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Self-consistent distributions

69

Attempt to reconstruct a self-consistent distribution function from the Milky Way mass distribution, by Eddington’s formula:

Fornasa & Green [1311.5477] See also Bhattacharjee et al. [1210.2328]; Bozorgnia et al. [1310.0468]; Mandal et al. [1806.06872]

F(E) = 1 √ 8π2 E dΨ √ E − Ψ d2ρ dΨ2

E = 1 2v2 − Ψ(r)

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Mass reconstruction with directionality

70

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Discretising f(v)

71

If we want to fit the velocity distribution, we now have an infinite number of functions to parametrise (one for each incoming direction )!

Detector

χ

(θ, φ) Make the problem more tractable: divide into N = 3 angular bins… f(v)

f(v) = f(v, cos θ, φ) =      f 1(v) for θ ∈ [0, 60] f 2(v) for θ ∈ [60, 120] f 3(v) for θ ∈ [120, 180]

…and then parametrise within each angular bin.

f k(v)

BJK [1502.04224]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Measuring the local Dark Matter distribution from Earth

Discretising f(v)

72

k = 1 k = 2 k = 3

WIMP wind