Capture of Dark Matter in Compact Stars[2004.14888 ] + [2010.13257] + [2012.08918] + [2104.14367] +[2108.02525]

G. Busoni
Max Planck Institute for Nuclear Physics

Lomonosov 2021, 25 Aug 2021

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

1 / 28

Outline1

Why Compact Stars?
Searching for DM collisions: Direct Detection
Searching for DM collisions: DM Capture in the Sun
Searching for DM collisions: DM Capture in Neutron Stars
Advantages of NS2

From capture in the Sun to NS and WD
Key differencesLeptons: highlights and results
Baryons: highlights and results

3Conclusions
Summary

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

2 / 28

Outline1

Why Compact Stars?
Searching for DM collisions: Direct Detection
Searching for DM collisions: DM Capture in the Sun
Searching for DM collisions: DM Capture in Neutron Stars
Advantages of NS2

From capture in the Sun to NS and WD
Key differences
Leptons: highlights and results
Baryons: highlights and results

3Conclusions
Summary

G. Busoni (MPI for Nuclear Physics)Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

3 / 28

Searching for DM collisions
Direct Detection

Direct Detection

SI interaction give much stronger bounds that SD ones

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

4 / 28

Searching for DM collisions
Direct Detection

Constraints depend strongly on interaction type
Strong target dependence
Some operators are suppressed by kinematics(momentum/velocity suppressed)
Recoil energy is small, nonrelativistic kinematics
Experimental detectors have recoil energy thresholds

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

5 / 28

Outline1

Why Compact Stars?
Searching for DM collisions: Direct Detection
Searching for DM collisions: DM Capture in the Sun
Searching for DM collisions: DM Capture in Neutron Stars
Advantages of NS

2

From capture in the Sun to NS and WD
Key differences
Leptons: highlights and results
Baryons: highlights and results

3Conclusions
Summary

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 20216 / 28

Searching for DM collisions
DM Capture in the Sun

DM Capture in Stars
DM can be captured andaccumulate in Stars
Dark matter scatters, loses
energy, becomes
gravitationally bound to star
Accumulates in centre of Sun
Can potentially annihilate at
the centerAt equilibrium
Capture=Annihilation
Probes same observables asDD
G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

7 / 28

Searching for DM collisions
DM Capture in the Sun

SI: DD wins
SD: DM in Sun wins
DM in Sun requires some fewmore assumptions, like that it
annihilates, and theannihilation channel

Some other ways to infer indirectly DM presence in the Sun: modified
energy transport (see 1411.6626 , 1703.07784)

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

8 / 28

Outline1

Why Compact Stars?
Searching for DM collisions: Direct Detection
Searching for DM collisions: DM Capture in the Sun
Searching for DM collisions: DM Capture in Neutron Stars
Advantages of NS2

From capture in the Sun to NS and WD
Key differences
Leptons: highlights and results
Baryons: highlights and results

3Conclusions
Summary

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

9 / 28

Searching for DM collisions
DM Capture in NS

Very large density means very
efficient capture
Whole DM flux can be
captured already forσ ∼ 10−45 cm2

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

10 / 28

Searching for DM collisions
DM Capture in NS

Possible observable signals
NS to BH collapse (more likely for bosonic DM)
Gravitational waves: DM increases tidal deformability(1803.03266)
Kinetic Heating (M. Baryakhtar et al. PRL 119, 131801 (2017)arXiv:1704.01577)
Kinetic + Annihilation heating (Bramante, Delgardo and Martin
1704.01577)

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

11 / 28

Searching for DM collisions
DM Capture in NS

NS temperature evolution
NS have no know large heating sources
Lose energy by neutrino and photon emission
Neutrino dominates early stages of NS life, photon the late stages
In absence of other heating sources, one expects T ∼ 1000K after
10M yr and T ∼ 100K after 1Gyr
Kinetic heating: sets an equilibrium temperature of T ∼ 1700K if
whole DM flux is captured
Kin+Ann heating: equilibrium temperature is raised to T ∼ 2400K

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

12 / 28

Outline1

Why Compact Stars?
Searching for DM collisions: Direct Detection
Searching for DM collisions: DM Capture in the Sun
Searching for DM collisions: DM Capture in Neutron Stars
Advantages of NS2

From capture in the Sun to NS and WD
Key differences
Leptons: highlights and results
Baryons: highlights and results

3Conclusions
SummaryG. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

13 / 28

Searching for DM collisions
Advantages of NS

High capture probability
DM particles accelerated to O(0.5)c means no momentum/velocity
suppression
Cross section of σth = 10−45 cm2 enough to reach maximum
captureNo threshold recoil energy
Similar sensitivity for SI and SD interaction
Similar sensitivity for momentum/velocity suppressed interactions
comparing to unsuppressed ones
Observation of old cold NS of temperature T < Teq :
T 4σ ≤ σthTeq
G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

(1)

14 / 28

Outline1

Why Compact Stars?
Searching for DM collisions: Direct Detection
Searching for DM collisions: DM Capture in the Sun
Searching for DM collisions: DM Capture in Neutron Stars
Advantages of NS2

From capture in the Sun to NS and WD
Key differences
Leptons: highlights and resultsBaryons: highlights and results

3Conclusions
Summary

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

15 / 28

From capture in the Sun to NS and WD
Key differences

DM Capture in the Sun formalism developed by Gould in the ’80
We adapted this formalism to NS
Sun/Gould+Extensions
Newtonian gravity
Sun structure from Standard Solar Model
Non-relativistic kinematics
Atomic Nuclei Targets
Non-relativistic matrix element
MB distribution for targets
Capture probability 6= 1
Star opacity
MS requires MC approachTargets have FF
Fixed Target mass∗
G. Busoni (MPI for Nuclear Physics)

NS/OurGR
NS structure from EOS
Relativistic kinematics
Baryon and Lepton targets
Relativistic matrix element
FD distribution for targets
Capture probability = 1∗
Star Opacity
MS can be treated analyticallyTargets have FF
Density-dependent Target mass

for some masses

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

16 / 28

From capture in the Sun to NS and WD
Key differences

Our Papers
2004.14888 Basics of NS formalism, including GR, EOS,
relativistic kinematics/matrix elements/interaction rates, PauliBlocking effects, Star opacity, Multiple Scattering, for Neutrontargets
2010.13257 Extension to lepton targets, interaction rates
generalised for all Dim 6 EFT operators
2012.08918 Baryon Targets have structure and cannot beapproximated by free gas2108.02525 Full treatment of baryonic targets, including the aboveeffects
2104.14367 Application of formalism to WD (electrons are fullydegenerate)
G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

17 / 28Outline
1

Why Compact Stars?
Searching for DM collisions: Direct Detection
Searching for DM collisions: DM Capture in the Sun
Searching for DM collisions: DM Capture in Neutron Stars
Advantages of NS

2

From capture in the Sun to NS and WD
Key differences
Leptons: highlights and results
Baryons: highlights and results

3Conclusions
Summary

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

18 / 28

From capture in the Sun to NS and WD
Leptons: highlights and results

Very degenerate andrelativistic target due to theirlow mass
Relativistic treatment is very
important for these targets
Muon targets: also check next
talk about them

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

19 / 28

From capture in the Sun to NS and WDCΛ 4 (GeV 4 s −1 )CΛ 4 (GeV 4 s −1 )Leptons: highlights and results
1034 D1
D31032
1030
1028
1026
1024
1022
1020
1018
1016
BSk24-1 BSk24-2 BSk24-4
BSk24-1 BSk24-2 BSk24-41014eeeeee1012
10µµµµµµ1081010-610-510-410-310-210-1 100 101 102 103 104 105 106 10710-610-510-410-310-210-1 100 101 102 103 104 105 106 107 108mχ (GeV)mχ (GeV)1035
32
D2D4101029
1026
1023
1020
1017
1014
BSk24-1 BSk24-2 BSk24-4
BSk24-1 BSk24-2 BSk24-4
1011
eeeeee108µµµµµµ5
1010-610-510-410-310-210-1 100 101 102 103 104 105 106 10710-610-510-410-310-210-1 100 101 102 103 104 105 106 107 108mχ (GeV)mχ (GeV)G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

20 / 28From capture in the Sun to NS and WD
Leptons: highlights and results
10-30
σ eχ (FDM = 1)
10-31
SENSEI
10-32
DAMIC
10-33
XENON1010-34
XENON1T
10-35
DAMIC-M 1kg-year 2e-36
10Si ν floor 1000kg-year
10-37
NS D1 σeχth-38
10
BSk24-2
10-39
EoS BSk24
10-40
NS D1 σµχth-41
10
BSk24-2
10-42
EoS BSk24
10-43
10-44-45
10 10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109 1010mχ (MeV)σeχ (cm 2 )−σ`χ (cm 2 )σ`χ (cm 2 )

−

10-30
σ eχ (FDM = 1)
10-31
SENSEI
10-32
DAMIC
10-33
XENON1010-34
XENON1T
10-35
DAMIC-M 1kg-year 2e-36
10Si ν floor 1000kg-year
10-37
NS D5 σeχth-38
10BSk24-2
10-39
EoS BSk24
10-40
NS D5 σµχth-41
10
BSk24-2
10-42
EoS BSk24
10-43
10-44-45
10 10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109 1010mχ (MeV)

10-31
DD (FDM = 1)
10-32
SENSEI
10-33
DAMIC
-34
10
XENON1010-35
XENON1T
10-36
DAMIC-M 1kg-yr 2eSi ν floor 1000kg-yr
10-37
10-38
D5 M4 WDs-3910M = 1.38M10-40
10-4110-4210-43
10-4410-2 10-1 100 101 102 103 104 105 106 107 108mχ (MeV)−¯

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

21 / 28

Outline1

Why Compact Stars?
Searching for DM collisions: Direct Detection
Searching for DM collisions: DM Capture in the Sun
Searching for DM collisions: DM Capture in Neutron Stars
Advantages of NS

2

From capture in the Sun to NS and WD
Key differences
Leptons: highlights and results
Baryons: highlights and results

3Conclusions
Summary

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

22 / 28

From capture in the Sun to NS and WD

Ratio
Ratio

Strong force mean field
effects require
treatment beyond freeFermi gas

CΛ 4 (GeVs −1 )Baryons are composite
particlesCΛ 4 (GeVs −1 )Baryons: highlights and results

G. Busoni (MPI for Nuclear Physics)

Neutrons

Protonsmχ (GeV)mχ (GeV)mχ (GeV)mχ (GeV)

1037
1036
D11035 D11034
1033
1032
1031
QMC-2 (1.5 M ¯ )1030
QMC-2 (1.5 M ¯ )1029
mpeff , cpS = cpS (t)mneff , cnS = cnS (t)1028mpeff , cpS = cpS (0)mneff , cnS = cnS (0)
1027
SS
1026
Free Fermi gas, cpS = cpS (t)Free Fermi gas, cn = cn (t)1025Free Fermi gas, cpS = cpS (0)Free Fermi gas, cnS = cnS (0)
1024
10230
10
10-1-210-310-4
10
10-5 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 910 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 101035
D41032 D41029
10261023
QMC-2 (1.5 M ¯ )QMC-2 (1.5 M ¯ )1020
mpeff , cpP = cpP (t)mneff , cnP = cnP (t)1017
mpeff , cpP = cpP (0)mneff , cnP = cnP (0)1014Free Fermi gas, cpP = cpP (t)Free Fermi gas, cnP = cnP (t)1011
P = c P (0)Free Fermi gas, cpP = cpP (0)FreeFermigas
,
c8nn
10100
10-1-210-310-4
1010-5 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 910 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

23 / 28

From capture in the Sun to NS and WD

Ratio

CΛ 4 (GeVs −1 )Baryons: highlights and results
1037
1035 D1D31033
1031
1029
1027
1025
QMC-4 (1.9M ¯ )QMC-4 (1.9M ¯ )1023nnΞ − + Λ0 + Ξ0Ξ − + Λ0 + Ξ01021
ppTotal bar.
Total bar.
1019
100
10-1
10-2 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 910 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

Ratio

CΛ 4 (GeVs −1 )mχ (GeV)mχ (GeV)1035
D2D41032
1029
1026
1023
1020
1017
1014
QMC-4 (1.9M ¯ )QMC-4 (1.9M ¯ )1011nnΞ − + Λ0 + Ξ0Ξ − + Λ0 + Ξ0810pp
Total bar.
Total bar.
105
100
10-1
10-2 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 910 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

G. Busoni (MPI for Nuclear Physics) mχ (GeV)
Capture of Dark Matter in Compact Stars

mLomonosov
2021, 25 Aug 2021
χ (GeV)

24 / 28

From capture in the Sun to NS and WD
Baryons: highlights and resultsMultm eff i-sca
p +t
cp S( teringt)

Multm eff i-scap +t
cp A( teringt)

Mu

ing

lt

kloc

li b

Pau

m eff i-sca
n +t
cn A( terint) gMultm eff i-scan +t
cn S( terint)
ging
ockg

kin

locli bPau

G. Busoni (MPI for Nuclear Physics)

i ble

mng
kin
loc ffli bth (cm 2 )σNχProtonslPau

Pau

th (cm 2 )σNχNeutrons

10-38
QMC-2 (1.5M ¯ )QMC-2 (1.5M ¯ )D1
D110-39mneff , cnS (t)mpeff , cpS (t)10-40Free Fermi gas, cnS (0)Free Fermi gas, cpS (0)
10-41
10-42
mpeff
10-43
mpeff + cpS (t)No Pauli blocking
10-44mneff + cnS (t)
10-45
10-46
QMC-2 (1.5M ¯ )QMC-2 (1.5M ¯ )
D8
D8
10-39
mneff , cnA (t)mpeff , cpA (t)-40
A
10Free Fermi gas, cn (0)Free Fermi gas, cpA (0)
10-41
10-42
mpeff
10-43
mpeff + cpA (t)No Pauli blocking
10-44mneff + cnA (t)10-45
10-4610-510-410-310-210-1 100 101 102 103 104 105 106 107 108 10-510-410-310-210-1 100 101 102 103 104 105 106 107 108 109mχ (GeV)mχ (GeV)
Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

25 / 28

From capture in the Sun to NS and WD

SI (cm 2 )σNχBaryons: highlights and results
10-38
10-39
NS D1 σnχth
10-40
QMC-1
10-41
QMC-2
10-42
QMC-4-43
10DD
10-44
NS D1 σpχthDarkSide-50
10-45
QMC-1
XENON1T-46
10
QMC-2
PandaX-4T
QMC-4-47
SuperCDMS
10
CDEX-1T-48
Xe ν floor
10Darwin
10-49 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 910 10 10 10 10 10 10 10 10 10 10 10 10 10 10σpχSD (cm 2 )SD (cm 2 )σnχmχ (GeV)

10-34
DD
10-35 NS D8 σnχth
CDMSLite
QMC-110-36
XENON1T
QMC-2-37
10Darwin
QMC-4
10-38
10-39
10-40
10-41
10-42
10-43
10-44
10-45
Xe ν floor
10-46 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10mχ (GeV)

G. Busoni (MPI for Nuclear Physics)

10-34
DD
NS D8 σpχth
10-35
PICASSO
QMC-1
10-36
PICO-60
QMC-2-37
10PICO-500
QMC-4-38
CYGNUS HD101010-39
10-40
10-41
10-42
10-43
10-44
10-45
C3 F8 ν floor
10-46 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 910 10 10 10 10 10 10 10 10 10 10 10 10 10 10

Capture of Dark Matter in Compact Starsmχ (GeV)

Lomonosov 2021, 25 Aug 2021

26 / 28

Outline
1Why Compact Stars?
Searching for DM collisions: Direct Detection
Searching for DM collisions: DM Capture in the Sun
Searching for DM collisions: DM Capture in Neutron Stars
Advantages of NS2

From capture in the Sun to NS and WD
Key differencesLeptons: highlights and results
Baryons: highlights and results

3Conclusions
SummaryG. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

27 / 28

Conclusions
Summary

Neutron Stars: cosmic laboratory to probe DM scatteringinteractions
Completely different kinematic regime to direct detection
experiments
High energy scattering washes away momentum suppression
Higher reach on inelastic scattering [1807.02840]
Can probe a very large mass range
Very sensitive for all interactions, including
momentum-suppressed and leptons
Current coolest NS of O(104 )K
Prospects for observation in the coming decade

G. Busoni (MPI for Nuclear Physics)

Capture of Dark Matter in Compact Stars

Lomonosov 2021, 25 Aug 2021

28 / 28