Detecting Dark Matter in the LISA era: Gravitational Waves from - - PowerPoint PPT Presentation

Bradley J Kavanagh GRAPPA, University of Amsterdam SLAP2019, 27th September 2019

@BradleyKavanagh b.j.kavanagh@uva.nl

Detecting Dark Matter in the LISA era:

Gravitational Waves from Intermediate Mass Ratio Inspirals

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Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs 2

Preliminary work in collaboration with: Daniele Gaggero [IFT Madrid, formerly GRAPPA] Gianfranco Bertone [GRAPPA] David Nichols [University of Virginia, formerly GRAPPA] but working closely with everyone at GRAPPA.

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

10−20 10−10 1 10 1020 1030 1040 1050 1060 1070

Dark Matter Candidate Mass [eV]

BH-Boson condensate BH spin distribution EMRI/IMRI dephasing Rolling axions Rolling axions QCD Axion (GW/Radio) Hidden sector scalars PBH mergers PBH/sub-halo transits DM production by bubble collisions Axion forces Dark blobs Boson star binaries Axion DM Dark Photon DM

1 M

GW probes of DM

3

Current Interferometers Future Interferometers Pulsar Timing Arrays

[1907.10610]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

10−20 10−10 1 10 1020 1030 1040 1050 1060 1070

Dark Matter Candidate Mass [eV]

BH-Boson condensate BH spin distribution EMRI/IMRI dephasing Rolling axions Rolling axions QCD Axion (GW/Radio) Hidden sector scalars PBH mergers PBH/sub-halo transits DM production by bubble collisions Axion forces Dark blobs Boson star binaries Axion DM Dark Photon DM

1 M

GW probes of DM

4

Current Interferometers Future Interferometers Pulsar Timing Arrays

[1907.10610]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Intermediate Mass Ratio Inspiral (IMRI)

5

LISA should detect ~ 3 - 10 IMRIs per year NS/ BH IMBH

˙ EGW ≈ 32G4 5c5 MIMBH3MNS2 r5 ∝ (fGW)10/3

[1711.00483]

MIMBH ∼ 103 − 105 M

GW emission causes long, slow inspiral: Stellar mass compact object (NS/BH) inspirals towards intermediate mass black hole (IMBH)

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Dark Matter ‘Mini-spikes’

6

[astro-ph/9906391, astro-ph/0501555, astro-ph/0501625, astro-ph/0509565, 0902.3665, 1305.2619]

ρDM(r) = ρsp rsp r γsp

Depending on the formation mechanism of the IMBH, expect an over-density of DM: IMBH DM For BH forming in an NFW halo, from adiabatic growth expect:

γsp = 7/3

Density can reach (~1024 times larger than local density)

ρ ∼ 1024 M pc3

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Dynamical Friction

7

IMBH NS/BH

r0

bmax

˙ EDF ∼ 4πG2

NM 2 NSρDM(r)

vNS ln Λ ∝ (fGW)

2 3 γ−3

[Chandrasekhar, 1943]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

IMRI + Dark Matter

8

NS/ BH IMBH DM makes the compact object spiral in faster, primarily due to dynamical friction This can be seen in the rate at which the GW signal accumulates phase ‘De-phasing’

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

10−2 10−1 100

Initial GW Frequency [Hz]

100 101 102 103 104 105 106 107 108

∆Ncycles

Fixed DM

‘De-phasing’ signal

9

[Eda et al. 1301.5971, 1408.3534] [See also 1302.2646, 1404.7140, 1404.7149]

How does DM affect the number of cycles? Benchmark:

rini ∼ 10−8 pc

MNS = 1 M

MIMBH = 103 M

tmerge ∼ 5 yr

Need to know the signal to better than ~1 part in 106!

Small sep. Large sep.

N vacuum

cycles

∼ 2 × 107

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Energy Budget

10

Q: How much energy is available for dynamical friction?

∆r

MIMBH = 104 M

MIMBH = 103 M

A: Binding energy of DM

• ver radius

∆r

∆UDM

γsp

γsp

ρsp [M pc3]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

10−2 10−1 100

Initial GW Frequency [Hz]

100 101 102 103 104 105 106 107 108

∆Ncycles

Fixed DM Shell estimate

Energy Budget

11

∆r

Evolve the system by fixing the dynamical friction force to extract all binding energy from a shell at a given radius: ˙ EDF = ˙ r dUDM dr

Q: How much energy is available for dynamical friction? A: Binding energy of DM

• ver radius

∆r

∆UDM

N vacuum

cycles

∼ 2 × 107

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

N-body simulations

12

[astro-ph/0505010]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

GN = 6.674 × 10−8 m3 g−1s−2

High precision N-body sims

13

Gadget-II code: The Universe:

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

N-body simulations

14

25 50 75 100 125 150

Norbits

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5

∆r/r [104] M1 = 100 M M2 = 1 M r0 = 3 ⇥ 108 pc torb = 1536 s

Allows us to check assumptions and fix normalisation of DF force (lnΛ), but can’t simulate the whole 5 year inspiral! ~ 3 days

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Self-consistent evolution

15

Phase space of DM described by distribution function where f(E)

Compact object scatters with all DM particles within ‘torus’ of influence over one orbit

r0

bmax

Each particle receives a ‘kick’ of typical size through gravitational scattering: ∆E

E = Ψ(r) − 1 2v2

E → E + ∆E

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Self-consistent evolution

16

Torb df(E) dt = −f(E)Pscatter(r0, E) +

• E

E + ∆E 5/2 f(E − ∆E)Pscatter(r0, E − ∆E)

Assuming orbit evolves slowly compared to the orbital period: Density profile (and therefore dynamical friction force) can then be determined self-consistently from the distribution function

• roughly the fraction of DM particles with energy 


which lie within a distance bmax from the NS orbit E

Pscatter (r0, E)

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Self-consistent evolution

17

Torb df(E) dt = −f(E)Pscatter(r0, E) +

• E

E + ∆E 5/2 f(E − ∆E)Pscatter(r0, E − ∆E)

• roughly the fraction of DM particles with energy 


which lie within a distance bmax from the NS orbit Assuming orbit evolves slowly compared to the orbital period: E

Density profile (and therefore dynamical friction force) can then be determined self-consistently from the distribution function

Pscatter (r0, E)

Particles scattering from Particles scattering from

E − ∆E → E

E → E + ∆E

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Evolution of density profile

18

109 108 107

r [pc]

1018 1019 1020 1021 1022

ρv<vorb(r) [M pc3]

0 orbits 6000 orbits 12000 orbits 18000 orbits 24000 orbits

As a ‘test’, keep the NS fixed at a given radius and see how the DM halo reacts to its orbit: ~ 30 days

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Evolution of density profile

19

109 108 107

r [pc]

1018 1019 1020 1021 1022

ρv<vorb(r) [M pc3]

0 orbits 6000 orbits 12000 orbits 18000 orbits 24000 orbits

As a ‘test’, keep the NS fixed at a given radius and see how the DM halo reacts to its orbit: ~ 30 days

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

10−2 10−1 100

Initial GW Frequency [Hz]

100 101 102 103 104 105 106 107 108

∆Ncycles

Fixed DM Shell estimate Self-consistent

Impact on de-phasing

20

How much shorter is the inspiral compared to the ‘vacuum’ case (with no DM?) De-phasing drastically reduced - but still detectable!

N vacuum

cycles

∼ 2 × 107

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Survival of density profile

21

How does the density profile evolve during and after the inspiral? Initial separation Initial density Density during inspiral Final density after inspiral

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Prospects for the future

22

So far we’re in the early stages of exploring these effects:

• For which binary parameters does this effect matter?
• What if we go beyond circular orbits in the Newtonian regime?
• How common are these DM halos around astrophysical BHs?

These signals are only detectable with dedicated templates, so careful signal modelling is needed. Ultimately, aim to develop IMRI+DM template banks and study parameter reconstruction.

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Conclusions

23

Important consequences for:

• the survival of DM spikes


• joint EM + GW signals
• fermionic DM
• detection of a broad range of 


DM candidates in the LISA era Gravitational Wave signatures of Dark Matter in intermediate mass ratio inspirals are more subtle and less pronounced than previously believed - but should still be detectable with LISA.

[See talk by Adam Coogan, 1905.01238] [See talk by Marco Chianese, 1905.04686] [See talk by Kenny Ng, 1906.11845]

10−2 10−1 100

Initial GW Frequency [Hz]

100 101 102 103 104 105 106 107 108

∆Ncycles

Fixed DM Shell estimate Self-consistent

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Conclusions

24

Important consequences for:

• the survival of DM spikes


• joint EM + GW signals
• fermionic DM
• detection of a broad range of 


DM candidates in the LISA era

Thank you!

Gravitational Wave signatures of Dark Matter in intermediate mass ratio inspirals are more subtle and less pronounced than previously believed - but should still be detectable with LISA.

[See talk by Adam Coogan, 1905.01238] [See talk by Marco Chianese, 1905.04686] [See talk by Kenny Ng, 1906.11845]

10−2 10−1 100

Initial GW Frequency [Hz]

100 101 102 103 104 105 106 107 108

∆Ncycles

Fixed DM Shell estimate Self-consistent

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Backup Slides

25

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Assumptions

26

• Spherical symmetry and isotropy of the DM halo
• DM particles only scatter within an impact parameter
• DM distribution is ‘locally’ uniform
• Halo ‘relaxation’ is instantaneous
• Orbital properties evolve slowly compared to the orbital period

b < bmax = Λ × GNMNS/v2

NS

bmax r0

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Total number of cycles

27

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Astrophysical BH binaries

28

Astrophysical BH binaries could be formed dynamically, or through e.g. common envelope evolution:

[Banerjee, 1611.09357, LIGO-Virgo, 1602.03846, Elbert et al., 1703.02551, Stevenson et al., 1704.01352, and many others…] [1602.04531]

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

N-body results

29

102 103

IMBH mass, MIMBH [M]

1010 109

Dynamical friction energy loss, ˙ E/E [s1]

Λ = p 1/q Λ = 1/q Λ = exp(3)

r0 = 3 ⇥ 108 pc NS only scatters with particles where its gravity dominates over the IMBH’s Fix ‘Coulomb factor’:

Λ =

• MIMBH/MNS ∼ 20 − 60

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

N-body results

30

10−10 10−9 10−8 10−7

MBH = 100M

10−10 10−9 10−8 10−7

Dynamical friction energy loss, ˙ E/E [s−1]

MBH = 300M

10−10 10−9 10−8 10−7

Separation, r [pc]

10−10 10−9 10−8 10−7

MBH = 1000M

Dynamical friction traces local DM density (to better than 1%) Dependence of dynamical friction force on mass and separation matches expectations Drop off in DF force at small separations due to softening of simulations

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Distribution function

31

2 ⇥ 108 3 ⇥ 108 4 ⇥ 108

E = Ψ(r) 1

2v2 [(km/s)2]

102 103 104 105 106 107 108

f(E) [M pc3 (km/s)3]

0 orbits 6000 orbits 12000 orbits 18000 orbits 24000 orbits

Self-consistently reconstruct density from distribution function:

ρ(r) = 4π vmax(r) v2f (E) dv

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Dynamical Friction

32

IMBH NS/BH

r0

bmax

[Chandrasekhar, 1943]

˙ EDF = 4πG2

NMNS2ρDM(r)

vNS ln Λ v f(v) dv

Bradley J. Kavanagh (GRAPPA, Amsterdam) Detecting DM in the LISA era: GWs from IMRIs

Relaxation of the Halo

33

109 108 107 106

r [pc]

1017 1019 1021 1023 1025

ρDM [M pc3]

t = 0 t = 103 s t = 1033 s Semi-analytic