Introduction General reaction Photon and axion dispersion properties Axion production Conclusion On the resonant production of axions in a magnetar magnitosphere Dmitry Rumyantsev Yaroslavl State University, Russia June 11, 2010 International Seminar “Quarks-2010” , Kolomna, Russia Based on the paper N. Mikheev, D. Rumuyantsev and Y. Shkol’nikova Pis’ma in JETP 2009 Vol.90. p.668. N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Outline 1 Introduction 2 General reaction 3 Photon and axion dispersion properties 4 Axion production 5 Conclusion N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Introduction Axion is one of most probable candidate for Cold Dark Matter The Peccei-Quinn symmetry violation scale f a � 10 8 GeV (PDG 2008) The experimental detection of the axion is a complicated problem The efficient axion production is possible in the extreme conditions of magnetars B ∼ 10 14 − 10 15 G ≫ B e , B e = m 2 / e ≃ 4 . 41 × 10 13 G. N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Introduction The electron number density in the region of closed field lines is estimated as ( Lyutikov et. al. Astrophys. J. 2002 ) � 10 rad/s � � 10 km � n ≃ 5 · 10 5 n GJ ≫ n GJ , Ω R NS where � B � � 10 s � n GJ ≃ 3 · 10 13 cm − 3 100 B e P is the Goldreich-Julian charge number density. N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion General reaction We have consider the production of axions in the general reaction i → f + a . The initial (i) and final (f) states can involve the electromagnetic multipole components of the medium. It is easy to see that the process under consideration can be resonant owing to the presence of a virtual photon. A similar situation for the region close to resonance was recently considered ( V.V. Skobelev JETP 2007. Vol.132. p.1121) N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion The effective γ a interaction constant ∆ g B ∆ g pl g a γ ¯ = g a γ + + a γ a γ L. A. Vassilevskaya et al., Yad. Fiz. 62, 1662 (1999) N. V. Mikheev and E. N. Narynskaya, Mod. Phys. Lett. A 21, 433 (2006) g a γ и ∆ g pl a γ are not take into account in the paper V.V. Skobelev N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion The effective Lagrangian and amplitude of the process i → f + a The effective Lagrangian γ a interaction g a γ ˜ F µν [ ∂ ν A µ ( x )] a ( x ) + L a γ ( x ) = g af [ ¯ ψ f ( x ) γ µ γ 5 ψ f ( x )] ∂ µ a ( x ) + + 2 m f Q f [ ¯ ψ f ( x ) γ µ ψ f ( x )] A µ ( x ) + The axion-photon and axion-fermion couplings g a γ = αξ/ 2 π f a , g af = C f m f / f a , ξ, C f ∼ 1 Amplitude i → f = − M γ if M γ → a M a g a γ ( ε ˜ Fq ′ ) q ′ 2 − P ( ε ) ( q ′ ) , M γ → a = i ¯ F µν is the dual tensor of the external field ˜ N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Photon and axion dispersion properties Resonance condition ω 2 p = 4 πα n ≥ m 2 a m N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Polarization operator The photon is unstable in active medium P ( ε ) = ℜ − i ℑ The ℑ is due to the processes of the absorption and emission of photons in the plasma ℑ = ω ′ � e ω ′ / T − 1 � Γ cr , � |M γ � if | 2 d Φ if , Γ cr = i , f ( Weldon, Phys Rev D 1983) d Φ if is the phase volume element of the states i and f for the process i → f + γ . Summation is performed over all of the possible initial and final states. N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Axion emissivity Taking into account the above consideration, the axion emissivity, due to the reactions involving the particles of the plasma, can be represented in the form � d Φ ′ |M γ → a | 2 ℑ Q = ( q ′ 2 − ℜ ) 2 + ℑ 2 . e ω ′ / T − 1 d Φ ′ = d 3 k ′ ( 2 π ) 3 2 ω ′ is the phase volume element of axion. Near the resonance, the last factor of the integrand can be interpolated by the δ function ℑ ( q ′ 2 − ℜ ) 2 + ℑ 2 ≃ π δ ( q ′ 2 − ℜ ) . N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Resonant axion emissivity The axion emissivity in the resonance region, owing to the reactions involving the particles of the medium, is certainly expressed in terms of Q γ → a � 1 g 2 a γ ( eB ) 2 Q ≃ Q γ → a = ¯ ϕ q ) 2 � dx Z ε k ( ε ˜ � k = k ∗ . e ω/ T − 1 � 32 π 2 α � � � 1 − d ω 2 � − 1 � � dk 2 � Here x = cos θ , k ∗ = k ∗ ( θ ) is a root of the equation ω 2 ( � k ) = m 2 a + k 2 , ϕ αβ = ˜ ˜ F αβ / B , Z − 1 = 1 − ∂ ℜ ∂ω 2 corresponds to the renormalization of the photon ε wavefunction. N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Particular cases Weakly magnetized dense plasma, m 2 a ≪ eB ≪ T 2 , µ 2 g 2 a γ ( eB ) 2 ( k ∗ ) 3 Q = ¯ ω 2 ( � k ∗ ) = m 2 a + k ∗ 2 e k ∗ / T − 1 , 48 π 2 α ( Mikheev et al. Phys. Rev. D V.58. P.055008. 1998 ) Strongly magnetized plasma eB ≫ m 2 , µ 2 ≫ T 2 , ¯ g a γ = g a γ When the axion mass is the smallest parameter of the problem, ω p , T ≫ m a ∼ 10 − 5 eV � − 1 � � � � Q ≃ g 2 a γ ( eB ) 2 ( 1 + η ) 3 / 2 ω p 1 + 1 ω 3 exp − 1 . p η 5 / 2 16 π 2 α T η ω p ≫ T ∼ m a g 2 a γ ( eB ) 2 a e − ω p / T . Tm 2 Q ≃ 16 π 2 α N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Number of axions In addition to emissivity, it is also of interest to estimate the number of axions produced in the magnetar magnetosphere in unit volume per unit time through the above resonant mechanism � 1 dtdV = g 2 a γ ( eB ) 2 ϕ q ) 2 dN dx kZ ε ( ε ˜ � � k = k ∗ . e ω/ T − 1 � � � 32 π 2 α � 1 − d ω 2 ω � − 1 � � dk 2 � N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Number of axions Strong field limit eB ≫ m 2 , µ 2 ≫ T 2 ω p , T ≫ m a � − 1 dtdV ≃ g 2 a γ ( eB ) 2 � � ω p � � dN 1 + η 1 + 1 ω 2 exp − 1 , p 16 π 2 α η 2 T η ω p ≫ T ∼ m a g 2 a γ ( eB ) 2 Tm 2 dN e − ω p / T . a ≃ 16 π 2 α dtdV ω p N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Number of axions In particular, for the number of axions produced by the CMB radiation T ∼ m a ∼ 10 − 3 eV, B = 100 B e The resonant scattering is possible n min ∼ 10 15 cm − 3 dN 1 dVdt ∼ 10 10 cm 3 s For magnetar magnetosphere we obtain V ∼ 10 19 cm 3 , dN 1 dt ∼ 10 29 s In the most optimistic variant, estimating the number of magnetars in the Galaxy as N mag ∼ 10 6 , they produce N tot ∼ 10 51 axions in t ∼ 10 9 yr. Therefore, the number density of axions in the Galaxy should be cm − 3 ≪ n b ∼ 10 − 7 n a ∼ 10 − 21 cm − 3 N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
Introduction General reaction Photon and axion dispersion properties Axion production Conclusion Conclusion We have considered the resonant photoproduction of axions in the general reaction i → f + a . It has been shown that the calculation of axion emissivity owing to this process is reduced to the calculation of the emissivity of the photon → axion transition. The number of axions produced by the equilibrium cosmic microwave background radiation in the magnetar magnetosphere has been determined. It has been shown that this mechanism is inefficient for the production of axion even at the plasma density n ∼ 10 15 cm − 3 . N.V. Mikheev, D.A. Rumyantsev and Yu.E. Shkol’nikova On the resonant production of axions ...
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