star crusts M. Cermeño 1, M. A. Pérez-García 1, J. Silk 2 November 24, 2016

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1 Dark M. Cermeño 1, M. A. Pérez-García 1, J. Silk 2 1 Department of Fundamental Physics, University of Salamanca, Spain 2 Institute d Astrophysique, Paris, France November 24, 2016 (University of Salamanca) November 24, / 11

Dark Interaction: fermionic light dark (LDM) particles χ and nuclei A in periodically arranged nuclei in the neutron star outer crust (ρ 2 10 6 4 10 11 g/cm 3 ) Neutron stars (NS) provide a

2 Dark Interaction: fermionic light dark (LDM) particles χ and nuclei A in periodically arranged nuclei in the neutron star outer crust (ρ g/cm 3 ) Neutron stars (NS) provide a gravitational boost to DM particles, using R NS = 12 km and M NS = 1.5M, β NS = v c = 2GMNS R NS 0.6 Effect of LDM the production of acoustic phonons (momentum k, linear dispersion relation ω k = c l k, c l the sound speed) in the outer NS crust. We calculate the single phonon R (0) k the change in the ion κ ii impact on cooling behavior of NSs. (University of Salamanca) November 24, / 11

3 Dark particle-nucleon L I = g s,n χχnn + g v,n χγ µ χnγ µ N N=n,p N, pn N, p N Dark p N = (E N, p N ), p N = (E N, p N ) p χ = (E χ, p χ), p χ = (E χ, p χ) q = p N p N = p χ p χ q 0 = E N E N = E χ E χ χ, pχ χ, p χ g s,n m q /Λ s MeV 2 and g v,n 1/Λ v MeV 2 are the effective scalar and vector coupling constants, with Λ s 100 GeV and Λ v 1 TeV the suppression mass scales for scalar and vector cases and m q the quark mass. M χn 2 =4g 2 s,n [(p Np N + m2 N )(p χp χ + m 2 χ)]+ 8g 2 v,n [2m2 N m2 χ m 2 N p χp χ m 2 χp N p χ + (p χp N )(p Np χ ) + (p N p χ)(p N p χ)]+ 8g s,n g v,n [m N m χ (p N + p N )(p χ + p χ)] Density dependence is retained using p N p N p FN (3π 2 n 0 Y N ) 1/3 with Y p = Z/A, Y n = (A Z)/A and n 0 = 0.17 fm 3 the saturation density. (University of Salamanca) November 24, / 11

4 Dark Our aim is to obtain the single acoustic phonon per mode R (0) k,λ Fermi golden rule R (0) k,λ = 2πδ(E f E i ) f V i 2 V( r) = j δ 3 ( r r j ) 2πa m χ potential felt by an interacting DM particle when approaching a nucleus in the periodic lattice being a the scattering length Using the Born approximation ( ( p χ p χ). r 1, r a typical target size) σ χa 4πa 2 in the center of mass frame for this potential dσ χa dω CM = M χa 2 64π 2 s, with M χa 2 the spin-averaged scattering amplitude calculated summing coherently over protons and neutrons matrix elements M N 2, and s = (p A + p χ ) 2 where p A is the nucleus four-momenta σ A,χ = 4πa 2 = m 2 A ( Zmp M p 2 + (A Z) mn where M N πd(cos θ χ) M χn 2 ) 2 M n 2 16π(m χ+m A ) 2, taking p χ << m χ and p A << m A, (University of Salamanca) November 24, / 11

5 Dark The single acoustic phonon per unit volume R (0) k = f χ ( p χ ) = 8π 4 n 2 A (2π) 6 m 2 χm A c l µ 1+ pχ 2 n χµ 4πm 3 e m 2 χ χk 2 (µ) 0 p χ d p χ f χ ( p χ ) E χ k c l a 2 Maxwell-Jüttner distribution function for relativistic incoming χ, µ = mχ k B T 6.7 for < v 2 > 0.6, K 2 (µ) the modified Bessel function of second kind, and n χ the DM number density ω c l = p/3 (6π 2 n A ) 1/3 the sound speed in a bbc lattice, being ω 4πn p = A Z 2 e 2 k B 2 m the A plasma frequency associated to a medium of ions with number density n A, baryonic number A, electric charge Ze and mass m A ( From kinematical restrictions 0 k 2 c l E χ pχ (c 2 + 1) l c 2 l 1 ) (University of Salamanca) November 24, / 11

6 Powered by TCPDF ( Results: M. Cermeño, M. A. Pérez-García, and J. Silk, Phys. Rev. D 94 (2016) Dark For m χ = 500, 100 and 5 MeV, n χ /n 0,χ = 10, where n 0,χ = 0.3 GeV/cm 3 is the galactic local DM mass density. Neutrino contribution at k 0, R ν0, is also shown for m ν = 0.1, 1 ev, being R (0) ν ( k) = R ν0 e a k 1eV where a is a constant which depends on neutrino masses. (University of Salamanca) November 24, / 11

7 Dark Global is given by κ = κ e + κ i Ion κi 1 = κii 1 + κie 1 κ ii κ ph and κ ie are ion-ion and ion-electron partial conductivities κ ii = 1 3 k BC A n A c l L ph C A = 9 ( T TD ) 3 TD /T 0 x 4 e x dx (e x 1) 2 is the phonon (dimensionless) heat capacity per ion L ph is the effective phonon mean free path At temperature T standard contribution gives L ph 1/N 0,kλ where N 0,kλ = (e ω kλ/k B T 1) 1 Contribution from DM can be obtained by the net number of phonons N kλ that results from the competition of and scattering excitation and stimulated emission N kλ N 0,kλ + R (0) d 3 k δvδt p f χ ( p) R (0) ω k,λ + k. v n k N (γ( pχ) 1)mχ 0,kλe δvδt χ where R (0) is the single phonon for each particular momentum k 1 value, γ( p χ ) = ( ) pχ 2 is the Lorentz factor and v 10 2 the NS galactic drift 1 Eχ velocity. (University of Salamanca) November 24, / 11

8 Results: Ion-ion Dark κ ph (10 15 erg cm -1 s -1 K -1 ) m χ =65MeV m χ =100 MeV m χ =500 MeV k (10-3 fm -1 ) At T = 10 8 K and n χ /n 0,χ = 100. Solid lines for 118 Kr (ρ = g/cm 3 ) and dashed lines for 120 Sr (ρ = g/cm 3 ). (University of Salamanca) November 24, / 11

9 Results: Ion-ion Dark κ ph (10 14 erg cm -1 s -1 K -1 ) T= K T= K M. Cermeño, M. A. Pérez-García, and J. Silk, Phys. Rev. D 94 (2016) ρ 10 κ ph (10 15 erg cm -1 s -1 K -1 ) m χ =65 MeV κ e perp B=10 15 G κ e perp B=10 14 G ρ 10 m χ = 100 MeV. Solid, dash-dotted and dashed lines depict the cases with no DM and with LDM for n χ /n 0χ = 10, 100. We use a fixed value for k. T = 10 8 K and m χ = 65 MeV. Solid, dot-dashed and dashed lines correspond to cases with no DM, n χ /n 0,χ = 10, 100. We use a fixed value for k. (University of Salamanca) November 24, / 11

10 Dark We calculate the single phonon R (0) in the outer crust of a NS due k to scattering from LDM particles gravitationally boosted into the star. LDM effects cause a modification of the net number of phonons in the lattice as compared to the standard result. R (0) is constant with the phonon momentum and much larger than for k cosmological neutrinos at finite k. We estimate the contribution of LDM particles to the ion-ion in the outer crust and find that it is enhanced at small k for small DM particle masses at densities > g/cm 3, whereas for larger m χ remains mostly constant. can be significantly enhanced at large densities compared to the standard result without DM. The electronic contribution to the for magnetized realistic scenarios in the perpendicular direction to a magnetic field B falls below the enhanced DM value for large densities. Since the global is κ = κ e + κ ph, the obtained result is expected to contribute to the reduction of the difference in heat conduction in both directions and thus to the isotropization of the NS surface temperature pattern. (University of Salamanca) November 24, / 11

11 Dark THANKS FOR YOUR ATTENTION. (University of Salamanca) November 24, / 11

12 Powered by TCPDF ( Temperature anisotropies Dark Theoretical models predict anisotropies in the surface temperature produced by high magnetic fields. Under the presence of a strong field, the becomes anisotropic, due to the fact that the electrons move more easily along the field lines than across them. R. Perna, D. Viganò, J. A. Pons, N. Rea, MNRAS, 434 (2013) The spectra and pulse profiles expected for different magnetic fields are computed in the bibliography (R. Perna, D. Viganò, J. A. Pons, N. Rea, MNRAS, 434 (2013) 2362 and MNRAS, 443 (2014) 31). Features of the spectra and pulse profiles predicted by theoretical models are observed in some dense objects (SNR Kes 79, SGR J , SGR , RX J etc). These observations support the idea of anisotropic surface temperature distributions. (University of Salamanca) November 24, / 11

arxiv: v1 [astro-ph.he] 22 Jul 2016

arxiv: v1 [astro-ph.he] 22 Jul 2016 Light dark matter scattering in outer neutron star crusts Marina Cermeño 1 a, M. Ángeles Pérez-García1 b and Joseph Silk 2,3,4 c 1 Department of Fundamental Physics, University of Salamanca, Plaza de la