Termination shock thermal processes as a possible source for the CMB low-order multipole anomalies: updated with observations
TTermination shock thermal processes as a possible source for the CMB low-order multipoleanomalies
H.N. Sharpe
Bognor, Ontario, [email protected]
Draft Version June 8, 2009
AbstractWe discuss the possibility that the observed low-order multipole features of the cosmic microwave backgroundradiation (CMB) all originate in the termination shock (TS) region of the heliosheath that surrounds the solarsystem. If the intrinsic CMB spectrum is assumed to be a pure monopole (2.73K) then thermodynamicprocesses occurring within the plasma region of the TS could imprint the observed power spectrum of the low-order multipoles and their alignment (the so-called “axis of evil”) onto this background isotropic CMB.Conditions are outlined for the geometric shape of the TS region. A key requirement of this model is that the TSplasma be characterized as an optically thin graybody with non-LTE perturbations. Data from the ongoingVoyager missions is critical to this study. IntroductionIn an earlier article we discussed the possibility that the observed quadrupole moment in the CMBpower spectrum may in fact originate from the geometric distortion of the background CMB in thetermination shock (TS) of the heliosheath [1]. In the present article we extend this heuristic model to adiscussion of several anomalies reported in the low-order multipole power spectrum of the CMB. Theseinclude the apparent alignment of the quadrupole and the octupole ( l =2,3) moments (and possibly l = 4and 5) with the direction of the solar system’s motion (“axis of evil” (AOE) [2,3,6])and the eclipticplane as well as the low power in l =2,3 [2]. We also discuss the reported anomalies in non-blackbodydepartures of the CMB low order multipoles [4,5].Termination shock physical processes can interact with the CMB radiation in one of two ways. TheCMB photons can be absorbed and scattered by local radiative and kinetic processes as they propagatethrough the TS region (see [1] for a summary which also includes possible refraction at the TS). Or theycan pass unaffected through an essentially transparent heliosheath. In this article we focus on the lattercase. We assume that local thermal processes in the TS emit radiation that is simply superimposed onthe background CMB. Since this radiation is emitted on the TS surface it should acquire the geometricproperties of the TS. Accordingly, the observed CMB spectrum inside the solar system will reflect themultipole distortions of the TS. We outline the physical and geometric conditions which must besatisfied at the TS to explain the observed CMB low-order multipole anomalies with a local rather thancosmic model. ModelWe start with the general transfer equation for a pencil of radiation propagating through an opticallythin region characterized by optical depth and source function S and assume isotropy: SII )0()( << 1 (1)We identify )0( I with the CMB background brightness spectrum and S with the additionalbrightness from the TS region. Geometric StructureFirst we address the CMB blackbody low-order multipoles. If we assume the CMB is perfectly isotropicwith only a monopole T =2.73K, then all the low order multipoles must arise from geometricdistortions of the TS surface relative to a spherical surface. In [1] we showed that a slight distortion to aprolate ellipsoid of revolution could account for the quadrupole rms amplitude of ~ 14 K. Thisgeometric distortion was shown to be consistent with preliminary observations of an asymmetric TSfrom the Voyager spacecraft [7]. However, an ellipsoid of revolution does not contain odd-numberedharmonics. Therefore a more generalized ellipsoidal distortion to the TS must be considered: czbyax (2)where a,b,c, are chosen to satisfy the multipole constraints on T l /T , l =2,3,4 and possibly l =5. This isan optimization problem. The result will be an ellipsoidal surface which satisfies the magnitudes ofmultipoles 2 to 5 and their alignment with the Sun’s motion and the ecliptic plane since the principaldistortion of the TS is in the Sun’s direction through the ISM. It should also be noted that this ellipsoidwill generate a dipole moment ( l =1). This geometric moment should however be subsumed in the muchlarger Doppler dipole. With sufficient computing power a more generalized and rigorous treatment ofthis problem would involve a full spherical harmonic expansion of the ellipsoidal surface with aconstrained optimization of the C nm for the observed multipoles l =2 to 5.Physical MechanismsFor the geometric distortions of the TS to manifest as blackbody multipoles against an otherwiseisotropic CMB background, the physical mechanism operating in the TS region must be in localthermodynamic equilibrium (LTE). First we demonstrate how this process could work and then discussits relevance.In equation (1) we make the following key assumptions:1. The source function is Planckian (LTE): S = B
2. The absorption coefficient (opacity) may be represented as a graybody (independent of frequency)with a small departure from grayness, )( that in general could depend on direction: ))(1( L << 1 and <<1Assumption 2 preserves the blackbody profile of the emitted thermal radiation while allowing for smalldeviations. With these assumptions and using Rayleigh-Jeans equation (1) becomes: )( TSTScmbobs
TTTT (3)he first term on the rhs is the CMB monopole 2.73K. The second term is the graybody Planckianperturbation to the CMB monopole caused by the TS geometric distortion. It may be thought of as anormalization constant. TS T is the effective local kinetic temperature in the TS.The third term on the rhs is the small departure from a blackbody spectrum due to non-grayness of thethermal radiation. If we assume it has no directional dependence on the TS surface then this non-blackbody contribution will inherit the same geometric distortion as the blackbody perturbations. Thiscould be a cause for the observed alignment of the non-blackbody multipoles with the overall CMBmultipoles [4,5].The assumption of graybody thermal radiation is key to this model. It requires that detailed balanceholds for collisional processes in the TS region, which in turn requires that the particle distributionfunction is Maxwellian [8]. Under these conditions a local kinetic temperature can be defined and LTEis valid. Radiative processes can compete with collisions but these are not expected to be a factor in theTS.Since the TS is a shock interface between the supersonic solar wind and the heliosheath region, theshock can disturb the tendency towards LTE. Several recent reports discuss the findings of the Voyagerspacecraft which have now penetrated the TS region [9,10,11]. They show a chaotic, turbulentmagnetized plasma far from LTE. Nevertheless, it may still be possible to model this region globally asa perturbed Maxwellian graybody distribution. On-going research into this difficult problem iscontinuing. If an appropriate distribution function for the TS can be developed it will provide animportant local alternative explanation to cosmic models for the observed low-order CMB anomalies .In addition the TS model can continue to be refined with more data as the Voyager spacecraft penetratedeeper into the heliosheath. Diego et al “Toy” ModelIn the model just presented we assumed an isotropic monopole for the CMB background radiation. Allobserved blackbody and non-blackbody low-order deformations were attributed to geometric distortionsof the TS and in situ LTE processes ( with small departures from Planckian). In [4] Diego et al assumea cosmological origin of the full CMB multipole spectrum, but attempt to explain the low quadrupolepower ( low relative to inflation model predictions) and its alignment with the octupole and the eclipticplane in terms of potential sources of contamination. They present a quasi-blackbody “toy” modelnormalized such that its non-blackbody amplitude is approximately 10 K in the V+W-2Q band (afterfiltering with a 7 deg Gaussian). They then demonstrate that this “toy” model possesses a quadrupolewhich is anti-correlated with the WMAP5 quadrupole. When subtracted from the observed quadrupolethe result better approximates the value expected from theory. The octupole is not affected by theirmodel since significant power is only found in the even moments. The low order multipoles also seemto come into better alignment.While this “toy” model is capable of explaining the observed anomaly, Diego et al acknowledge that aphysical justification for its existence is lacking. We conclude this note with a possible justification fortheir “toy” model.We found earlier that it was necessary to generalize the TS distortion from a simple ellipsoid ofrevolution in order to potentially explain all the low-order multipoles of the CMB and their alignments.However, if we are only interested in the even multipoles, specifically the quadrupole, then we may justdopt the procedure discussed in [1] and return to an ellipsoid of revolution for the TS distortion. Thenwe may write equation (1) as: )]1([)0(
BII obs (4)where )0( I is the full CMB multipole background and the second term represents the quasi-blackbody distortion due to non-LTE processes on the TS as discussed above. The normalization can bechosen such that this term satisfies the same 10 K constraint in the V+W-2Q band. Since thedistortion originates on the TS it will share its geometric properties of only possessing even multipoles.Hence equation (4) could be a physical justification of the “toy” model proposed by Diego et al.ConclusionsThe Voyager spacecraft have provided a unique opportunity to characterize the dynamical and radiativeprocesses in the heliosheath which surrounds the solar system. Since the CMB is viewed through this“window” it should be expected that these processes may leave their imprint on the CMB spectrum. Arigorous thermodynamical model is required for the heliosheath plasma and the termination shockregion. If a dusty plasma model can be developed which characterizes this region as an optically thingraybody with non-Maxwellian perturbation distributions, then most of the low-order multipole featuresof the CMB spectrum could be explained by a local rather than cosmic origin. The high order multipolecomponents should be studied with a full MHD turbulence model for the TS region to determine if theobserved acoustic peaks can also be given a local interpretation. The observed CMB polarization couldalso have its origin in heliosheath radiative processes like Thomson and Compton scattering and inverseCompton scattering off suprathermal ions/electrons. Synchrotron radiation could also contribute to thispolarization as well as providing a possible explanation for other observed anomalies [12].References[1] H.N. Sharpe. A Heliosheath Model for the Origin of the CMB Quadrupole MomentarXiv:0905.2978 [astro-ph.SR] 18 May 2009.[2] K. Land and J. Magueijo. The axis of evil, arXiv:0502237v2 [astro-ph] 22 Feb. 2005.[3] K. Land and J. Magueijo. The Axis of Evil revisited. MNRAS, 378, 153, 2007.[4] J.M Diego et al. WMAP Anomalous Signal in the Ecliptic Plane. arXiv:0901.4344v1 [astro-ph.CO] 27 Jan 2009.[5] Bi-Zhu Jiang et al. Spectral Variation of the WMAP 5-year degree scale anisotropy,arXiv:0904.2513v1 [astro-ph.CO] 16 Apr 2009.[6] G. Hinshaw et al. Five-Year WMAP Observations: Data Processing, Sky Maps and BasicResults, arXiv:0803:0732 [astro-ph] 17 Oct 2008.[7] E.C. Stone et al. An Asymmetric Solar Wind Termination Shock,
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