DIFFICULTIES IN EXPLAING THE COSMIC PHOTON EXCESS WITH COMPACT COMPOSITE OBJECT DARK

MATTER

DIFFICULTIES IN EXPLAING THE COSMIC PHOTON EXCESS WITH COMPACT COMPOSITE OBJECT DARK

MATTER

Dan CumberbatchDan Cumberbatch

arXiv:astro-ph/0606429 (accepted by Phys. Rev. D)

Daniel Cumberbatch, Glenn Starkman & Joe Silk

Compact Composite ObjectsCompact Composite Objects Assemblies of colour superconducting pairs of u, d and s (anti)quarks

Phases: Colour Flavour Locked (CFL), 2SC, etc. (e.g. hep-ph/0011333 ) CFL favoured (nu = nd = ns) leptons excluded from bulk matter

(Rajagopal & Wilcek, PRL (2000) ) nq~O(1fm-3) (i.e. a few times nuclear densities)

Formed from Axion domain wall collapse during QCD phase transition

(A. Zhitnitsky, astro-ph/0204218 ) CCO Fermi Pressure Vs. Axion Domain Wall Surface Tension B~1033 , R~6m, M~1 ton (!!!) B >1020 possible (metastable)

CCO Dark Matter Formed before light elements doesn’t contribute to B

Effectively non-radiative (~B-1/3) contributes to DM

Preferentially forms from antiquarks B asymmetry (Oaknin & Zhitnitsky, PRD (2005))

Assemblies of colour superconducting pairs of u, d and s (anti)quarks Phases: Colour Flavour Locked (CFL), 2SC, etc. (e.g. hep-ph/0011333 ) CFL favoured (nu = nd = ns) leptons excluded from bulk matter

(Rajagopal & Wilcek, PRL (2000) ) nq~O(1fm-3) (i.e. a few times nuclear densities)

Formed from Axion domain wall collapse during QCD phase transition

(A. Zhitnitsky, astro-ph/0204218 ) CCO Fermi Pressure Vs. Axion Domain Wall Surface Tension B~1033 , R~6m, M~1 ton (!!!) B >1020 possible (metastable)

CCO Dark Matter Formed before light elements doesn’t contribute to B

Effectively non-radiative (~B-1/3) contributes to DM

Preferentially forms from antiquarks B asymmetry (Oaknin & Zhitnitsky, PRD (2005))

CCO DM and the Photon ExcessCCO DM and the Photon Excess

1-20 MeV diffuse gamma-ray excess (COMPTEL)

511 keV line signal (SPI/INTEGRAL)

(Jean et al., A&A (2006))

(Ahn & Komatsu, PRD (2005) )

CCO DM also postulated to explain several astrophysical observations, including…

96.7+/-2.2% Positronium

How can CCO DM possibly explain these signals???

Charged CCOsCharged CCOs Qe = -0.3B2/3e ~ -3x1021e (!) (Madsen, PRL (2001) )

Finite curvature of CCOs increases thermodynamic potentials Deficiency in massive antiquarks (i.e. ) at CCO surface ( z ~ 1fm)

CCO charge neutralized by accumulation of e+ from ISM `Positronsphere’ surrounding bulk matter Behaves like a Fermi gas (Thomas-Fermi model):

Qe = -0.3B2/3e ~ -3x1021e (!) (Madsen, PRL (2001) ) Finite curvature of CCOs increases thermodynamic potentials Deficiency in massive antiquarks (i.e. ) at CCO surface ( z ~ 1fm)

CCO charge neutralized by accumulation of e+ from ISM `Positronsphere’ surrounding bulk matter Behaves like a Fermi gas (Thomas-Fermi model):€

s

€

ne + =

V

3π 2=

1

3π 2

V

1+Vc

3

6π

⎛

⎝ ⎜

⎞

⎠ ⎟

€

E(z) = −dV

dz=

1

6π

Vc2

1+Vc

3

6π

⎛

⎝ ⎜

⎞

⎠ ⎟

€

V = pF =V

1+Vc

3

6π

⎛

⎝ ⎜

⎞

⎠ ⎟

Vc ~ 20 MeV (Alcock et al.)

e+ - e- interactionse+ - e- interactions (non-relativistic) e- from the ISM interact with positronsphere:

1. Forms positronium (Para- (25%), Ortho- (75%) ) with low energy e+

(resonant process) Parapositronium decays 511 keV photons

2. Directly annihilates Continuum spectra 0 < E < PF (z)

1. Hence if e- penetrate to z = 0 E < Vc ~ 20 MeV

Relative Rates (Zhitnitsky (2006) ):

Hence if incident electrons from the ISM can freely penetrate CCO positronspheres, CCO DM may explain the SPI and COMPTEL observations.

(non-relativistic) e- from the ISM interact with positronsphere:

1. Forms positronium (Para- (25%), Ortho- (75%) ) with low energy e+

(resonant process) Parapositronium decays 511 keV photons

2. Directly annihilates Continuum spectra 0 < E < PF (z)

1. Hence if e- penetrate to z = 0 E < Vc ~ 20 MeV

Relative Rates (Zhitnitsky (2006) ):

Hence if incident electrons from the ISM can freely penetrate CCO positronspheres, CCO DM may explain the SPI and COMPTEL observations.€

Γe +e −

ΓPs

~ve

2π

μ

me

⎛

⎝ ⎜

⎞

⎠ ⎟

2

lnμ

me

⎛

⎝ ⎜

⎞

⎠ ⎟~ 1 for μ ~ 20 MeV

CCOs and the Photon ExcessCCOs and the Photon Excess But can ISM electrons freely penetrate the positronspheres….NO! But can ISM electrons freely penetrate the positronspheres….NO!

Can ISM e- interact quickly enough / penetrate positronsphere deeply enough?

€

V = pF =V

1+Vc

3

6π

⎛

⎝ ⎜

⎞

⎠ ⎟

€

10−3 < βe − <10−2

€

10−7MeV < Te − <10−5MeV( )

Classical TreatmentClassical Treatment

€

d2z

dt 2=

eE(z)

me

2nd Law 2nd Law

€

zmin.(β e −ini. =10-2) ~ 107fm ~ 10R

€

zmin.(β e −ini. =10−3) ~ 109fm ~ 1000R€

βe −ini. =10-2

€

βe −ini. =10−3

We must also investigate quantum effects…

QM TreatmentQM Treatment Quantum Tunnelling will increase time spent by e-’s in positronsphere and reduce effective zmin.

Solve for (non-relativistic) using Numerov Method…

Quantum Tunnelling will increase time spent by e-’s in positronsphere and reduce effective zmin.

Solve for (non-relativistic) using Numerov Method…

Tunnelling effects are marginal…use classical trajectories

€

βe −ini. =10-2

€

βe −ini. =10−3

€

zmin.class.

€

z90%

€

z95%

€

R =n

e +

ne + (zmin .

class.)=

ψ (z)2n

e + dzz= 0

zmin .class .

∫n

e + (zmin .class.) ψ (z)

2dz

z= 0

zmin .class .

∫>1 ⇒

R(βe −ini. =10−2) =1.0104

R(βe −ini. =10−3) =1.0022

⎧ ⎨ ⎪

⎩ ⎪

CCOs and the 511 keV ExcessCCOs and the 511 keV Excess Using classical trajectories, calculate suppression factor P Using classical trajectories, calculate suppression factor P

€

P =1− exp − ne +

t= 0

∞

∫ (z[t])σe +e − →Ps

(vrel.)vrel.dt( ) Approximate upper limit for P using

Radial e- trajectory (~maximizes e+ line density) (geometrical overestimate)

Approximate upper limit for P using Radial e- trajectory (~maximizes e+ line density) (geometrical overestimate)

€

σe +e − →Ps

(vrel.) ~ πa02β

e −ini.c

€

⇒ P ≤10−3 for β

e −ini. =10−2

10−7 for βe −ini. =10−3

⎧ ⎨ ⎪

⎩ ⎪

For NFW DM/Baryonic profiles, the 511 keV flux from CCO DM is

€

511 ~ 10−3 cm-2s-1 1033

B

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 3

<

10−6cm-2 s-1 1033

B

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 3

for βe −ini. =10−2

10-9cm-2 s-1 1033

B

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 3

for βe −ini. =10−3

⎧

⎨

⎪ ⎪

⎩

⎪ ⎪

CCOs and the 1-20 MeV ExcessCCOs and the 1-20 MeV Excess Production of MeV photons requires tunnelling to z~0 Estimate Probability:

Production of MeV photons requires tunnelling to z~0 Estimate Probability:

€

⇒ lnψ (0)

2

ψ zmin .class.

( )2

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟<

−388 for βe −ini. =10−2

−1808 for βe −ini. =10−3

⎧ ⎨ ⎪

⎩ ⎪€

⇒(0)

2

ψ zmin .class.

( )2 <

ψ z'> zmin.class.

( )2exp −z'κ (z')[ ]

ψ z'> zmin.class.

( )2

€

z( )2∝ exp[−κ (z)z], κ (z) =

2me (V (z) − T)

h2

⎡ ⎣ ⎢

⎤ ⎦ ⎥

Since potential energy V decreases monotonically with decreasing z, we obtain upper estimate for by extrapolating to using

€

€

κ =κ(zarb.)

€

z < zarb.(= zmin .class., say)

In other words……no MeV photons!

ConclusionsConclusions CCO DM is an unlikely explanation of the 511 keV line signal

observed by SPI/INTEGRAL owing to insufficient rates of Positronium formation.

CCO DM is an unlikely explanation of the 1-20 MeV excess observed by COMPTEL owing to extremely strong repulsive effects within CCO positronspheres preventing incident ISM electrons from reaching high energy positrons residing at low altitudes. Possibility of pair-production at low altitudes may result in high energy direct

annihilations MeV photons. Requires detailed knowledge of thermal structure of CCOs. Photons would be largely attenuated by positronsphere.

CCO DM is still possible, though its motivation is weakened.

CCO DM is an unlikely explanation of the 511 keV line signal observed by SPI/INTEGRAL owing to insufficient rates of Positronium formation.

CCO DM is an unlikely explanation of the 1-20 MeV excess observed by COMPTEL owing to extremely strong repulsive effects within CCO positronspheres preventing incident ISM electrons from reaching high energy positrons residing at low altitudes. Possibility of pair-production at low altitudes may result in high energy direct

annihilations MeV photons. Requires detailed knowledge of thermal structure of CCOs. Photons would be largely attenuated by positronsphere.

CCO DM is still possible, though its motivation is weakened.