chaotic dark matter in the solar system and...
TRANSCRIPT
![Page 1: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/1.jpg)
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Chaotic dark matter in the Solar system and galaxies
Guillaume Rollin1, José Lages1, Dima Shepelyansky2
1Equipe PhAs - Physique Théorique et AstrophysiqueInstitut UTINAM - UMR CNRS 6213
Observatoire de BesançonUniversité de Franche-Comté, France
2Laboratoire de Physique Théorique - UMR CNRS 5152Université Paul Sabatier, Toulouse, France
Workshop « Dynamics & Kinetic theory of self-gravitating systems », GRAVASCO, Institut Henri Poincaré, November 2013
References :J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL 430, L25-L29 (2013), arXiv :1211.0903G. Rollin, J. L., D. Shepelyansky, Chaotic enhancement of dark matter density in binary systems and galaxies, to be submitted
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Dark matter capture – Three-body problem
DMP
Ecliptic
p
Possible DMP capture due to Jupiter rotation around the Sun
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 3: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/3.jpg)
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Dark matter capture – Restricted circular three-body problem
Newton’s equations
mDMP � mX � m�
r =1− mX∥∥r�(t)− r
∥∥3
(r�(t)− r
)+
mX∥∥rX(t)− r∥∥3
(rX(t)− r
)G = 1, mX + m� = 1,
∥∥rX∥∥ ' 13km.s−1
= 1,∥∥rX
∥∥ = 1
Energy change after a passage at perihelion (in absence of close encounter)
F ∼mXm�
∥∥rX∥∥2 ' 10−3 (Petrosky 86’)
Assuming a Maxwellian distribution of Galactic DMP veloci-ties
f (v)dv ∼ v2 exp(−3v2
/2u2)
dv
with u ' 220km.s−1 ∼ 17 (mean DMP velocity)
As F � u2, not many candidates for capture among GalacticDMPsMost of the capturable DMPs have close to parabolic ap-proaching trajectories (E ∼ 0)Direct simulation of Newton’s equations is difficult : veryelongated ellipses, not many particles can be simulated,CPU time consuming (Peter 09’)
0
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50uDMP candidates
for capture
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 4: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/4.jpg)
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Dark matter capture – Restricted circular three-body problem
Newton’s equations mDMP � mX � m�
r =1− mX∥∥r�(t)− r
∥∥3
(r�(t)− r
)+
mX∥∥rX(t)− r∥∥3
(rX(t)− r
)G = 1, mX + m� = 1,
∥∥rX∥∥ ' 13km.s−1
= 1,∥∥rX
∥∥ = 1
Energy change after a passage at perihelion (in absence of close encounter)
F ∼mXm�
∥∥rX∥∥2 ' 10−3 (Petrosky 86’)
Assuming a Maxwellian distribution of Galactic DMP veloci-ties
f (v)dv ∼ v2 exp(−3v2
/2u2)
dv
with u ' 220km.s−1 ∼ 17 (mean DMP velocity)
As F � u2, not many candidates for capture among GalacticDMPsMost of the capturable DMPs have close to parabolic ap-proaching trajectories (E ∼ 0)Direct simulation of Newton’s equations is difficult : veryelongated ellipses, not many particles can be simulated,CPU time consuming (Peter 09’)
0
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50uDMP candidates
for capture
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 5: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/5.jpg)
UTINAMInstitut
UTINAMInstitut
Dark matter capture – Restricted circular three-body problem
Newton’s equations mDMP � mX � m�
r =1− mX∥∥r�(t)− r
∥∥3
(r�(t)− r
)+
mX∥∥rX(t)− r∥∥3
(rX(t)− r
)G = 1, mX + m� = 1,
∥∥rX∥∥ ' 13km.s−1
= 1,∥∥rX
∥∥ = 1
Energy change after a passage at perihelion (in absence of close encounter)
F ∼mXm�
∥∥rX∥∥2 ' 10−3 (Petrosky 86’)
Assuming a Maxwellian distribution of Galactic DMP veloci-ties
f (v)dv ∼ v2 exp(−3v2
/2u2)
dv
with u ' 220km.s−1 ∼ 17 (mean DMP velocity)
As F � u2, not many candidates for capture among GalacticDMPsMost of the capturable DMPs have close to parabolic ap-proaching trajectories (E ∼ 0)Direct simulation of Newton’s equations is difficult : veryelongated ellipses, not many particles can be simulated,CPU time consuming (Peter 09’)
0
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50uDMP candidates
for capture
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 6: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/6.jpg)
UTINAMInstitut
UTINAMInstitut
Dark matter capture – Restricted circular three-body problem
Newton’s equations mDMP � mX � m�
r =1− mX∥∥r�(t)− r
∥∥3
(r�(t)− r
)+
mX∥∥rX(t)− r∥∥3
(rX(t)− r
)G = 1, mX + m� = 1,
∥∥rX∥∥ ' 13km.s−1
= 1,∥∥rX
∥∥ = 1
Energy change after a passage at perihelion (in absence of close encounter)
F ∼mXm�
∥∥rX∥∥2 ' 10−3 (Petrosky 86’)
Assuming a Maxwellian distribution of Galactic DMP veloci-ties
f (v)dv ∼ v2 exp(−3v2
/2u2)
dv
with u ' 220km.s−1 ∼ 17 (mean DMP velocity)
As F � u2, not many candidates for capture among GalacticDMPsMost of the capturable DMPs have close to parabolic ap-proaching trajectories (E ∼ 0)Direct simulation of Newton’s equations is difficult : veryelongated ellipses, not many particles can be simulated,CPU time consuming (Peter 09’)
0
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50uDMP candidates
for capture
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 7: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/7.jpg)
UTINAMInstitut
UTINAMInstitut
Dark matter capture – Restricted circular three-body problem
Newton’s equations mDMP � mX � m�
r =1− mX∥∥r�(t)− r
∥∥3
(r�(t)− r
)+
mX∥∥rX(t)− r∥∥3
(rX(t)− r
)G = 1, mX + m� = 1,
∥∥rX∥∥ ' 13km.s−1
= 1,∥∥rX
∥∥ = 1
Energy change after a passage at perihelion (in absence of close encounter)
F ∼mXm�
∥∥rX∥∥2 ' 10−3 (Petrosky 86’)
Assuming a Maxwellian distribution of Galactic DMP veloci-ties
f (v)dv ∼ v2 exp(−3v2
/2u2)
dv
with u ' 220km.s−1 ∼ 17 (mean DMP velocity)
As F � u2, not many candidates for capture among GalacticDMPsMost of the capturable DMPs have close to parabolic ap-proaching trajectories (E ∼ 0)Direct simulation of Newton’s equations is difficult : veryelongated ellipses, not many particles can be simulated,CPU time consuming (Peter 09’)
0
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50uDMP candidates
for capture
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 8: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/8.jpg)
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Dark matter capture – Kicked model
x : Jupiter’s phase when DMP at perihelion (x = ϕ/2π mod 1)w : DMP energy (w = −2E/mDMP)
Symplectic Kepler-Petrosky map
x = x + w−3/2 third Kepler’s laww = w + F(x) energy change after a kick
Map already used in the study of :I Cometary clouds in Solar systems (Petrosky 86’)I Chaotic dynamics of Halley’s comet (Chirikov, Vecheslavov 89’)I Microwave ionization of hydrogen atoms (see e.g. Shepelyansky, scholarpedia)
Advantage : providing the fact the kick function F(x) is known the dynamics of a huge number ofparticles can simulated.
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 9: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/9.jpg)
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Dark matter capture – Kicked model
x : Jupiter’s phase when DMP at perihelion (x = ϕ/2π mod 1)w : DMP energy (w = −2E/mDMP)
Symplectic Kepler-Petrosky map
x = x + w−3/2 third Kepler’s laww = w + F(x) energy change after a kick
Map already used in the study of :I Cometary clouds in Solar systems (Petrosky 86’)I Chaotic dynamics of Halley’s comet (Chirikov, Vecheslavov 89’)I Microwave ionization of hydrogen atoms (see e.g. Shepelyansky, scholarpedia)
Advantage : providing the fact the kick function F(x) is known the dynamics of a huge number ofparticles can simulated.
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 10: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/10.jpg)
UTINAMInstitut
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Dark matter capture – Kicked model
x : Jupiter’s phase when DMP at perihelion (x = ϕ/2π mod 1)w : DMP energy (w = −2E/mDMP)
Symplectic Kepler-Petrosky map
x = x + w−3/2 third Kepler’s laww = w + F(x) energy change after a kick
Map already used in the study of :I Cometary clouds in Solar systems (Petrosky 86’)I Chaotic dynamics of Halley’s comet (Chirikov, Vecheslavov 89’)I Microwave ionization of hydrogen atoms (see e.g. Shepelyansky, scholarpedia)
Advantage : providing the fact the kick function F(x) is known the dynamics of a huge number ofparticles can simulated.
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 11: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/11.jpg)
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Dark matter capture – Dark map
Kick function determination
F(x)→ F`,θ,φ(x) ∼ Fq,θ,φ(x)
The kick function is different for each approaching con-figuration (`, θ, φ) ∼ (q, θ, φ)For close to 1 eccentricities the perihelion is such as
q ∼`2
2
For each approaching configuration (q, θ, φ), the inte-gration of the three-body problem gives the kick func-tion.
θ
φ
q
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
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Dark matter capture – Dark map
Kick function determination
F(x)→ F`,θ,φ(x) ∼ Fq,θ,φ(x)
The kick function is different for each approaching con-figuration (`, θ, φ) ∼ (q, θ, φ)For close to 1 eccentricities the perihelion is such as
q ∼`2
2
For each approaching configuration (q, θ, φ), the inte-gration of the three-body problem gives the kick func-tion.
-0.001
0
0.001
0 0.25 0.5 0.75 1
x
F (
x) c
-0.002
0
0.002
F (
x) b
-0.006
0
0.006
F (
x) a
a : Halley’s cometb : q = 1.5, n = 4, θ = 0.7, φ = 0c : q = 0.5, n = 4, θ = 0., φ = π/2
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
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Dark matter capture – Dark mapKick function determination
F(x)→ F`,θ,φ(x) ∼ Fq,θ,φ(x)
The kick function is different for each approaching con-figuration (`, θ, φ) ∼ (q, θ, φ)For close to 1 eccentricities the perihelion is such as
q ∼`2
2
For each approaching configuration (q, θ, φ), the inte-gration of the three-body problem gives the kick func-tion.
10-6
10-4
10-2
100
0 0.5 1 1.5 2 2.5 3 3.5 4
q / rp
Fm
ax
c
a
b
Exponential decay in agreement with Petrosky 86’
-0.001
0
0.001
0 0.25 0.5 0.75 1
x
F (
x) c
-0.002
0
0.002
F (
x) b
-0.006
0
0.006
F (
x) a
a : Halley’s cometb : q = 1.5, n = 4, θ = 0.7, φ = 0c : q = 0.5, n = 4, θ = 0., φ = π/2
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
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Dark matter – Capture cross section
wcap =mXm�
∥∥rX∥∥2 ' 10−3
σp = π∥∥rX
∥∥2 Jupiter orbit area
10-8
10-4
100
104
108
10-4
10-2
100
102
w / wcap
σ/ σ
p
10-5
10-4
10-3
10-2
10-1
100
101
10-4
10-2
100
102
104
w / wcapd
N /
dw
/ N
p1/w
1/w2
σ/σp ' πm�mX
wcap
win agreement with Khriplovich & Shepelyansky 09’
I Predominance of long range interaction as suggested by Peter 09’I Very small contribution from close encounters invalidating previous numerical results (Gould &
Alam 01’ and Lundberg & Edsjö 04’)
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 15: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/15.jpg)
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Dark matter evolution – Chaotic dynamicsSimulation of the (isotropic) injection, the capture and the escape of DMPs during the whole lifetimeof the Solar system.Injection of Ntot ' 1.5× 1014 DMPs with energy |w| in the range [0,∞] with NH = 4× 109 DMPs inthe Halley’s comet energy interval [0,wH ].
I Equilibrium reached after a time td ∼ 107yr similar to the diffusive escape time scale of theHalley’s comet (Chirikov & Vecheslavov 89’) −→ Equilibrium energy distribution ρ(w)
I The dynamics of dark matter particles in the Solar system is essentially chaotic
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
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Back to real space – Density distribution of captured DMPs
Nowadays equilibrium density distribution ( tS = 4.5× 109yr )
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6
r
ρ(r)
0.001
0.01
0.1
0.2 0.5 5 1 10
r
ρ(r)/r2
I The profile of the radial density ρ(r) ∝ dN/dr is similar to those observed for galaxieswhere DMP mass is dominant. Indeed ρ(r) is almost flat (increases slowly) right afterJupiter orbit (r = 1) −→ according to virial theorem the circular velocity of visible matter isconsequently constant as observed e.g. in Rubin 80’More precisely, vm ∝ r0.25 (Dark map) quite close to vm ∝ r0.35 (Rubin 80’)
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
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Back to real space – Density distribution of captured DMPs
Surface density
ρs(z, R) ∝ dN/dzdR
where
R =√
x2 + y2
Volume density
ρv(x, y, z) ∝ dN/dxdydz
Ecliptic
Ecliptic
Ecliptic
Ecliptic
z
x1
1
y
x1
1
y
x
1
1
z
x
1
1
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
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How much dark matter is present in the Solar system ?
The total mass of DMP passed through the System solar during its lifetime tS = 4.5× 109yr is
Mtot = ρgtS
∫ ∞0
dv v f (v)σ(v) ≈ 35ρgtSG∥∥rX
∥∥M�/u ≈ 0.9× 10−6M� ∼ M♀
At time tS the mass of captured DMPs in the Solar system is
MAC ≈ ηACMtot ≈ 2× 10−15M� within r < 0.5 distanceSun-αCentauri
M100au ≈ η100auMtot ≈ 1.3× 10−17M� within r < 100au
The captured DMP mass in the volume of the Neptune orbit radius is
M[ ≈ η[MAC ≈ 0.9× 10−18M� ≈ 1.5× 1015g
The captured DMP mass in the volume of the Jupiter orbit radius is
MX ≈ ηXMAC ≈ 4.6× 10−20M� ≈ 1014g
The average volume density of captured dark matter inside the Jupiter orbit sphere is
ρX =3MX4πr3X≈ 5× 10−29g/cm3 ≈ 1.2× 10−4
ρg � ρg (Galactic DMP density)
Globally, not much dark matter captured by the Solarsystem, but ...
Let’s compare to the capturable DMP density
ρgH = ρg
∫ √wH
0dv v f (v) ≈ 1.4× 10−32g/cm3
Huge chaotic enhancement ζ = ρX/ρgH ≈ 4× 103 ofthe density of actually capturable DMPs.
=⇒
The long rangeinteraction capturemechanism is veryefficient for binarysystems (1+2) with
m1 � m2
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 19: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/19.jpg)
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How much dark matter is present in the Solar system ?The total mass of DMP passed through the System solar during its lifetime tS = 4.5× 109yr is
Mtot = ρgtS
∫ ∞0
dv v f (v)σ(v) ≈ 35ρgtSG∥∥rX
∥∥M�/u ≈ 0.9× 10−6M� ∼ M♀
At time tS the mass of captured DMPs in the Solar system is
MAC ≈ ηACMtot ≈ 2× 10−15M� within r < 0.5 distanceSun-αCentauri
M100au ≈ η100auMtot ≈ 1.3× 10−17M� within r < 100au
The captured DMP mass in the volume of the Neptune orbit radius is
M[ ≈ η[MAC ≈ 0.9× 10−18M� ≈ 1.5× 1015g
The captured DMP mass in the volume of the Jupiter orbit radius is
MX ≈ ηXMAC ≈ 4.6× 10−20M� ≈ 1014g
The average volume density of captured dark matter inside the Jupiter orbit sphere is
ρX =3MX4πr3X≈ 5× 10−29g/cm3 ≈ 1.2× 10−4
ρg � ρg (Galactic DMP density)
Globally, not much dark matter captured by the Solarsystem, but ...
Let’s compare to the capturable DMP density
ρgH = ρg
∫ √wH
0dv v f (v) ≈ 1.4× 10−32g/cm3
Huge chaotic enhancement ζ = ρX/ρgH ≈ 4× 103 ofthe density of actually capturable DMPs.
=⇒
The long rangeinteraction capturemechanism is veryefficient for binarysystems (1+2) with
m1 � m2
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 20: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/20.jpg)
UTINAMInstitut
UTINAMInstitut
How much dark matter is present in the Solar system ?The total mass of DMP passed through the System solar during its lifetime tS = 4.5× 109yr is
Mtot = ρgtS
∫ ∞0
dv v f (v)σ(v) ≈ 35ρgtSG∥∥rX
∥∥M�/u ≈ 0.9× 10−6M� ∼ M♀
At time tS the mass of captured DMPs in the Solar system is
MAC ≈ ηACMtot ≈ 2× 10−15M� within r < 0.5 distanceSun-αCentauri
M100au ≈ η100auMtot ≈ 1.3× 10−17M� within r < 100au
The captured DMP mass in the volume of the Neptune orbit radius is
M[ ≈ η[MAC ≈ 0.9× 10−18M� ≈ 1.5× 1015g
The captured DMP mass in the volume of the Jupiter orbit radius is
MX ≈ ηXMAC ≈ 4.6× 10−20M� ≈ 1014g
The average volume density of captured dark matter inside the Jupiter orbit sphere is
ρX =3MX4πr3X≈ 5× 10−29g/cm3 ≈ 1.2× 10−4
ρg � ρg (Galactic DMP density)
Globally, not much dark matter captured by the Solarsystem, but ...
Let’s compare to the capturable DMP density
ρgH = ρg
∫ √wH
0dv v f (v) ≈ 1.4× 10−32g/cm3
Huge chaotic enhancement ζ = ρX/ρgH ≈ 4× 103 ofthe density of actually capturable DMPs.
=⇒
The long rangeinteraction capturemechanism is veryefficient for binarysystems (1+2) with
m1 � m2
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 21: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/21.jpg)
UTINAMInstitut
UTINAMInstitut
How much dark matter is present in the Solar system ?The total mass of DMP passed through the System solar during its lifetime tS = 4.5× 109yr is
Mtot = ρgtS
∫ ∞0
dv v f (v)σ(v) ≈ 35ρgtSG∥∥rX
∥∥M�/u ≈ 0.9× 10−6M� ∼ M♀
At time tS the mass of captured DMPs in the Solar system is
MAC ≈ ηACMtot ≈ 2× 10−15M� within r < 0.5 distanceSun-αCentauri
M100au ≈ η100auMtot ≈ 1.3× 10−17M� within r < 100au
The captured DMP mass in the volume of the Neptune orbit radius is
M[ ≈ η[MAC ≈ 0.9× 10−18M� ≈ 1.5× 1015g
The captured DMP mass in the volume of the Jupiter orbit radius is
MX ≈ ηXMAC ≈ 4.6× 10−20M� ≈ 1014g
The average volume density of captured dark matter inside the Jupiter orbit sphere is
ρX =3MX4πr3X≈ 5× 10−29g/cm3 ≈ 1.2× 10−4
ρg � ρg (Galactic DMP density)
Globally, not much dark matter captured by the Solarsystem, but ...
Let’s compare to the capturable DMP density
ρgH = ρg
∫ √wH
0dv v f (v) ≈ 1.4× 10−32g/cm3
Huge chaotic enhancement ζ = ρX/ρgH ≈ 4× 103 ofthe density of actually capturable DMPs.
=⇒
The long rangeinteraction capturemechanism is veryefficient for binarysystems (1+2) with
m1 � m2
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 22: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/22.jpg)
UTINAMInstitut
UTINAMInstitut
How much dark matter is present in the Solar system ?The total mass of DMP passed through the System solar during its lifetime tS = 4.5× 109yr is
Mtot = ρgtS
∫ ∞0
dv v f (v)σ(v) ≈ 35ρgtSG∥∥rX
∥∥M�/u ≈ 0.9× 10−6M� ∼ M♀
At time tS the mass of captured DMPs in the Solar system is
MAC ≈ ηACMtot ≈ 2× 10−15M� within r < 0.5 distanceSun-αCentauri
M100au ≈ η100auMtot ≈ 1.3× 10−17M� within r < 100au
The captured DMP mass in the volume of the Neptune orbit radius is
M[ ≈ η[MAC ≈ 0.9× 10−18M� ≈ 1.5× 1015g
The captured DMP mass in the volume of the Jupiter orbit radius is
MX ≈ ηXMAC ≈ 4.6× 10−20M� ≈ 1014g
The average volume density of captured dark matter inside the Jupiter orbit sphere is
ρX =3MX4πr3X≈ 5× 10−29g/cm3 ≈ 1.2× 10−4
ρg � ρg (Galactic DMP density)
Globally, not much dark matter captured by the Solarsystem, but ...
Let’s compare to the capturable DMP density
ρgH = ρg
∫ √wH
0dv v f (v) ≈ 1.4× 10−32g/cm3
Huge chaotic enhancement ζ = ρX/ρgH ≈ 4× 103 ofthe density of actually capturable DMPs.
=⇒
The long rangeinteraction capturemechanism is veryefficient for binarysystems (1+2) with
m1 � m2
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 23: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/23.jpg)
UTINAMInstitut
UTINAMInstitut
How much dark matter is present in the Solar system ?The total mass of DMP passed through the System solar during its lifetime tS = 4.5× 109yr is
Mtot = ρgtS
∫ ∞0
dv v f (v)σ(v) ≈ 35ρgtSG∥∥rX
∥∥M�/u ≈ 0.9× 10−6M� ∼ M♀
At time tS the mass of captured DMPs in the Solar system is
MAC ≈ ηACMtot ≈ 2× 10−15M� within r < 0.5 distanceSun-αCentauri
M100au ≈ η100auMtot ≈ 1.3× 10−17M� within r < 100au
The captured DMP mass in the volume of the Neptune orbit radius is
M[ ≈ η[MAC ≈ 0.9× 10−18M� ≈ 1.5× 1015g
The captured DMP mass in the volume of the Jupiter orbit radius is
MX ≈ ηXMAC ≈ 4.6× 10−20M� ≈ 1014g
The average volume density of captured dark matter inside the Jupiter orbit sphere is
ρX =3MX4πr3X≈ 5× 10−29g/cm3 ≈ 1.2× 10−4
ρg � ρg (Galactic DMP density)
Globally, not much dark matter captured by the Solarsystem, but ...
Let’s compare to the capturable DMP density
ρgH = ρg
∫ √wH
0dv v f (v) ≈ 1.4× 10−32g/cm3
Huge chaotic enhancement ζ = ρX/ρgH ≈ 4× 103 ofthe density of actually capturable DMPs.
=⇒
The long rangeinteraction capturemechanism is veryefficient for binarysystems (1+2) with
m1 � m2
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 24: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/24.jpg)
UTINAMInstitut
UTINAMInstitut
How much dark matter is present in the Solar system ?The total mass of DMP passed through the System solar during its lifetime tS = 4.5× 109yr is
Mtot = ρgtS
∫ ∞0
dv v f (v)σ(v) ≈ 35ρgtSG∥∥rX
∥∥M�/u ≈ 0.9× 10−6M� ∼ M♀
At time tS the mass of captured DMPs in the Solar system is
MAC ≈ ηACMtot ≈ 2× 10−15M� within r < 0.5 distanceSun-αCentauri
M100au ≈ η100auMtot ≈ 1.3× 10−17M� within r < 100au
The captured DMP mass in the volume of the Neptune orbit radius is
M[ ≈ η[MAC ≈ 0.9× 10−18M� ≈ 1.5× 1015g
The captured DMP mass in the volume of the Jupiter orbit radius is
MX ≈ ηXMAC ≈ 4.6× 10−20M� ≈ 1014g
The average volume density of captured dark matter inside the Jupiter orbit sphere is
ρX =3MX4πr3X≈ 5× 10−29g/cm3 ≈ 1.2× 10−4
ρg � ρg (Galactic DMP density)
Globally, not much dark matter captured by the Solarsystem, but ...
Let’s compare to the capturable DMP density
ρgH = ρg
∫ √wH
0dv v f (v) ≈ 1.4× 10−32g/cm3
Huge chaotic enhancement ζ = ρX/ρgH ≈ 4× 103 ofthe density of actually capturable DMPs.
=⇒
The long rangeinteraction capturemechanism is veryefficient for binarysystems (1+2) with
m1 � m2
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 25: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/25.jpg)
UTINAMInstitut
UTINAMInstitut
How much dark matter is present in the Solar system ?The total mass of DMP passed through the System solar during its lifetime tS = 4.5× 109yr is
Mtot = ρgtS
∫ ∞0
dv v f (v)σ(v) ≈ 35ρgtSG∥∥rX
∥∥M�/u ≈ 0.9× 10−6M� ∼ M♀
At time tS the mass of captured DMPs in the Solar system is
MAC ≈ ηACMtot ≈ 2× 10−15M� within r < 0.5 distanceSun-αCentauri
M100au ≈ η100auMtot ≈ 1.3× 10−17M� within r < 100au
The captured DMP mass in the volume of the Neptune orbit radius is
M[ ≈ η[MAC ≈ 0.9× 10−18M� ≈ 1.5× 1015g
The captured DMP mass in the volume of the Jupiter orbit radius is
MX ≈ ηXMAC ≈ 4.6× 10−20M� ≈ 1014g
The average volume density of captured dark matter inside the Jupiter orbit sphere is
ρX =3MX4πr3X≈ 5× 10−29g/cm3 ≈ 1.2× 10−4
ρg � ρg (Galactic DMP density)
Globally, not much dark matter captured by the Solarsystem, but ...
Let’s compare to the capturable DMP density
ρgH = ρg
∫ √wH
0dv v f (v) ≈ 1.4× 10−32g/cm3
Huge chaotic enhancement ζ = ρX/ρgH ≈ 4× 103 ofthe density of actually capturable DMPs.
=⇒
The long rangeinteraction capturemechanism is veryefficient for binarysystems (1+2) with
m1 � m2
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 26: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/26.jpg)
UTINAMInstitut
UTINAMInstitut
Conclusion : Dark matter capture in binary systems (preliminary results)
104
10-2
10-1 1 10
1
(u)
u
chaoti
c e
nhancem
en
t fa
cto
r
w ~w ~0.005cap H
w > ucap
1/2w < u
cap
1/2
u=220km/s
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 27: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/27.jpg)
UTINAMInstitut
UTINAMInstitut
Conclusion : Dark matter capture in binary systems (preliminary results)
104
10-2
10-1 1 10
1
(u)
u
chaoti
c e
nhancem
en
t fa
cto
r
0
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50u
DMP candidates
for capture
w ~w ~0.005cap H
wcap
1/2
w << ucap
w > ucap
1/2w < u
cap
1/2
1/2
u=220km/s
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 28: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/28.jpg)
UTINAMInstitut
UTINAMInstitut
Conclusion : Dark matter capture in binary systems (preliminary results)
104
10-2
10-1 1 10
1
(u)
u
chaoti
c e
nhancem
en
t fa
cto
r
0
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50u
DMP candidates
for capture
w ~w ~0.005cap H
0
5
10
15
20
25
30
35
0 0.02 0.04 0.06 0.08 0.1u wcap
1/2
wcap
1/2
w ~ ucap
w << ucap
w > ucap
1/2w < u
cap
1/2
1/2
1/2
e.g.
Black hole
+
Star companion
V~c/40star
u=220km/s
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 29: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/29.jpg)
UTINAMInstitut
UTINAMInstitut
Conclusion : Dark matter capture in binary systems (preliminary results)
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 30: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/30.jpg)
UTINAMInstitut
UTINAMInstitut
Conclusion : Dark matter capture in binary systems (preliminary results)
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013
![Page 31: Chaotic dark matter in the Solar system and galaxiesperso.utinam.cnrs.fr/~lages/presentations/DMPIHPnov2013.pdf · J. L., D. Shepelyansky, Dark matter chaos in the Solar system, MNRASL](https://reader034.vdocuments.mx/reader034/viewer/2022050222/5f673f0f558dde63fb23015c/html5/thumbnails/31.jpg)
UTINAMInstitut
UTINAMInstitut
Thank You !
Chaotic dark matter in the Solar system and galaxies, J. Lages, GRAVASCO IHP, Nov 2013