Understanding the galactic cosmic ray dipole anisotropy with a nearby single source under the spatially-dependent propagation scenario
aa r X i v : . [ a s t r o - ph . H E ] J a n Draft version January 3, 2019
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UNDERSTANDING THE GALACTIC COSMIC RAY DIPOLE ANISOTROPY WITH A NEARBY SINGLESOURCE UNDER THE SPATIALLY-DEPENDENT PROPAGATION SCENARIO
Xiao-BO Qu College of Science, China University of Petroleum, Qingdao, 266555, China (Received; Revised; Accepted)
Submitted toABSTRACTRecently studies of the dipole anisotropy in the arrival directions of Galactic cosmic rays indicate that the TeV-PeVdipole anisotropy amplitude is not described by a simple power law, moreover a rapid phase change exists at an energyof 0 . ∼ . . ∼ . Keywords: cosmic rays — ISM: supernova remnants
Corresponding author: Xiao-BO [email protected]
X. B. Qu INTRODUCTIONThe anisotropy of cosmic rays (CRs) may be a precious tool to probe the propagation of CRs throughout the Galaxy(Blasi & Amato 2012). The CRs below 10 eV are expected to be mainly Galactic, after released by their sources–presumably supernova remnants, they start to diffuse through the Galactic environment. As CRs are mostly chargednuclei, their paths are deflected and highly isotropized by the action of galactic magnetic field they propagate throughbefore reaching the Earth atmosphere. Although the arrive direction is mainly isotropy, Galactic CRs possess a smallbut significant dipole anisotropy (DA) of order 10 − ∼ − . The origin of this large scale DA is still uncertain, but thestudy of its amplitude and phase evolution with energies has an important valence to understand the CRs propagationmechanisms.The conventional propagation mechanism of CRs always derive a DA with amplitude much higher than observed.The conventional propagation models simply assume an isotropic diffusion with a smooth distribution of sources.In this case, the DA amplitude is expected to follow the energy scaling of the diffusion tensor. The DA amplitudederived by these models is always higher by about one order than the observation. Some models were proposedto reduce the amplitude of DA to the observed level, such as non-uniform distribution of sources(Blasi & Amato2012), Spatially-dependent propagation(SDP)(Guo et al. 2016)(Tomassetti 2015), Single nearby source plus conven-tional diffusion(Liu et al. 2017). In these models, SDP model can decrease the amplitude of DA by nearly an orderof magnitude than that of the conventional propagation model, mainly by introduce an anti-correlation between thediffusion properties and the source distribution of CRs.Despite that the amplitude of DA can be partially settled, the phase evolution with energies is difficult. The datafrom recent studies(ARGO-YBJ (Bartoli et al. 2015), EAS-TOP(Aglietta et al. 2009), IceCube/IceTop (Aartsen et al.2013)(Aartsen et al. 2016), and Tibet-AS (Amenomori et al. 2017))indicate that the DA undergoes a rapid phase flip(with almost vanishing amplitude) at an energy of 0 . ∼ . MODEL DESCRIPTIONIt is generally accepted that the CRs are accelerated at supernova remnants and then diffuse in the Galaxy. Beforereaching the solar vicinity, the accelerated CRs may suffering from fragmentation and energy losses in the interstellarmedium (ISM) and interstellar radiation field and magnetic field, decay and reacceleration or convection. The transportprocess of CRs in the can be described by the well-known diffusion equation: ∂ψ ( ~r, p, t ) ∂t = Q ( ~r, p, t ) + ∇ · ( D xx ∇ ψ ) + ∂∂p p D pp ∂∂p p ψ − ∂∂p [ ˙ p − p ∇ · V c ψ )] − ψτ f − ψτ r (1)where ψ ( ~r, p, t ) is the density of CR particles per unit momentum p at position ~r , Q ( ~r, p, t ) is the source distribution, D xx is the spatial diffusion coefficient, V c is the convection velocity, D pp is the diffusive reacceleration coefficient inmomentum space, ˙ p ≡ d p/ d t is momentum loss rate, τ f and τ r are the characteristic time scales for fragmentationand radioactive decay respectively. D pp is also used to describe the reacceleration process, which is coupled with thespatial diffusion coefficient D xx as (Seo & Ptuskin 1994) D pp D xx = 4 p v A δ (4 − δ )(4 − δ ) ω (2)where v A is the Alfven speed, and ω is the ratio of magnetohydrodynamic wave energy density to the magnetic fieldenergy density, which can be fixed to 1. The CRs propagate in an extended halo with a characteristic height z h ,beyond which free escape of CRs is assumed. ASTEX Understanding Anisotropy with single source
Background supernova remnants
The CRs density is only ascribed to the spatial diffusion coefficient D xx in SDP model, because D pp can be derivedfrom D xx by Eq. (2) and the convection is ignored. The spatial diffusion coefficient in the SDP model is described witha two halo approach: the inner (disk) and outer halo. The half thickness of the halo is z h , the half thickness of innerhalo is ξz h and (1 − ξ ) z h is the half thickness of outer halo, For the inner halo, the diffusion coefficient is anti-correlatedwith the source distribution by means of a scale formula F ( r, z ) fitted from the observed spatial distribution of SNRs.(details see Guo et al. (2016)) D xx ( r, z, p ) = F ( r, z ) D β (cid:18) pp (cid:19) F ( r,z ) δ (3)For the outer halo where the source term vanishes, the diffusion coefficient recovers the traditional form of D β ( p/p ) δ , where p is rigidity and D specifies its normalization at the reference rigidity p and δ reflects the property of theISM turbulence.A numerical method is necessary to solve the diffusion equations, especially in case that the diffusion varies ev-erywhere in the Milky Way. In this work, we use the released DRAGON code(Evoli et al. 2008) to solve the CRpropagation equation described in Eq. (1). DRAGON allows us to perform a numerical calculation with a space-dependent coefficient mentioned above. The basic model parameters are given in Table 1.The injection spectrum of primary CRs at sources region for the background SNRs is taken as a broken power-lawform: q ( p ) = q × ( ( p/p br ) − ν if( p < p br )( p/p br ) − ν · e − p/ ˆ p if( p ≥ p br ) , (4)where p is the rigidity, q is the normalization factor for all nuclei, and the relative abundance of each nucleifollows the default value in the DRAGON package. p br is the broken energy and ν , ν are spectral index before andafter the broken energy p br . In this work the cutoff energy ˆ p is set to 1 . × GeV to fit the AMS-02+CREAMdata(Guo & Yuan 2018). Detailed information of the parameters are listed in Table 1.2.2.
Nearby supernova remnant
As mentioned above, diffusion model can’t explain the DA amplitude and the phase evolution with energy. In thecase of diffusion with a smooth distribution of sources, the DA is expected to simply align with the direction of theGalactic center. One possible reason which can cause the DA phase changes is a local nearby source.We assume a local (300 pc from us) supernova explosion occurred about 10 years ago in the direction of ( l = 145 ◦ , b =0 ◦ ). The charged particles were continually accelerated nearby the shock front with the expansion of supernova ejecta.The accelerated spectrum is represented by a power law plus an exponential cutoff, i.e., Q s = q s R − α e − E/E cut . (5)where R is the rigidity, q s is the normalization factor for nearby single source. α s is spectral index, E scut is the cutoffenergy. Detailed information of the parameters are listed in Table 2. The time-dependent distribution of CR nuclei Table 1.
Parameters of the transport effects and background CR injection. D (cm s − ) δ v A (km s − ) z h (kpc) ξ log ( q ) * ν ν p br (GV) ˆ p (PV)8 . × ∗ Normalization at 100 GeV in units of cm − s − sr − GeV − . X. B. Qu from a point source can be evaluated by means of Green function technique, the corresponding analytical solution canbe found in Bernard et al. (2012). The diffusion coefficient is set according to the SDP model inner halo setting, inthe position of solar system the parameter F ( r, z ) in Eq. 3 is 0.25. CALCULATION RESULTSAccording to the recently observation, the DA of CR have complicated behaviors, such as the DA phase change at ∼ eV, and the DA amplitude evolution with energies is no more a simple power law feature. These new observationresults can’t explained by simple diffusion models. In this work we introduce a nearby single source under the mainframe of the SDP model to understand the cosmic ray DA. The DRAGON code is used to calculate the galactic cosmicray propagation, in which the essential transport parameters are D , δ ; the source parameters of background CRs are p br , ν , ν , ˆ p . For the local nearby SNR source, there are some parameters describing the CR injection spectra, i.e., α s , E scut . In addition, to fit the low energy data, we have to take solar modulation into account, which is representedby the modulation potential φ = 600 MV (Gleeson & Axford 1968).3.1. The Amplitude and Phase of the Dipole Anisotropy
After the nearby single source was added, the anisotropy can be understood as a sum of two components: one iscaused by the background sources and the other is from the nearby single source. the total anisotropy can be calculatedby: ∆ = P ¯ I i ∆ i n i · n max P ¯ I i , (6) n i is the direction of the source and and ∆ i denotes the anisotropy of that source, ¯ I i is the CR average intensityfrom that source. In this work, the sources are separated to two classes: background sources as a whole and a nearbysingle source. The CR intensity distribution can be get, after projected onto the right ascension coordinate, theone-dimensional (1D) profile of the anisotropy is derived. The 1D profile of the anisotropy is fitted by the first-orderharmonic function in form of: R ( α ) = 1 + A cos ( α − φ ) , (7)where R ( α ) denotes the relative intensity of CRs at right ascension α , A is the amplitude of the first harmonics, and φ is the phase at which R ( α ) reaches its maximum. Consider the observation from one experiment can’t cover alldeclination, in this work below 10 TeV the declination cut is − ◦ ∼ ◦ according to the ARGO-YBJ experiment, andabove 10 TeV the declination cut is − ◦ ∼ ◦ according to AS γ experiment.Figure 1 shows the amplitude of anisotropy comparison between model calculations and the experimental results.The solid black line and blue dash line represent the model calculations in this work and the SDP model, respectively.In the scenario of steady-state propagation, such as the SDP model, the anisotropy grows with diffusion coefficient,namely rising with the energy. In this work a nearby single source is added to the SDP model, the cosmic ray acceleratedfrom this single source will dominate the CR gradient at the energy region below 0.1 PeV, so the anisotropy in thisenergy will mainly decided by this single source. The dipole anisotropy amplitude is initially increasing with energybelow 10 TeV, and begins to decrease above 10 TeV, this behavior is consistent with the single source spectrum.Because the high energy cut-off, while the energy is above 100 TeV the influence of the single source vanished, andthe amplitude begins to increase again under the influence of background sources. The phase will also has an abruptchange at the 100 TeV energy scale where the dominator of the anisotropy is changing from the single source to thebackground sources. As showed in figure 2 the solid black line, the dipole phase change can reproduced by addinga single source to the SDP model. The blue dash line in figure 2 shows the phase of the DA calculated by the SDPmodel only with the background sources, which is expected to simply align with the direction of the Galactic center. Table 2.
Injection spectrum ofsingle nearby source. q s [GeV − ] α s E scut [GeV]5 . × . × ASTEX Understanding Anisotropy with single source E (eV) A n i s o t r op y A m p li t ud e -5 -4 -3 -2 Norikura1973Ottawa1981London1983Bolivia1985Budapest1985Hobart1985London1985
Misato1985Socomo1985Yakutsk1985Baksan1987HongKong1987Sakashita1990Utah1991
Liapootah1995Matsushiro1995Poatina1995Kamiokande1997Macro2003SuperKamiokande2007PeakMusala1975
Baksan1981Norikura1989EASTOP1995EASTOP1996EASTOP2009Baksan2009Milagro2009 ARGO2011IceCube2010IceCube2012IceTop2013Tibet2005Tibet2013Tibet2017
Spatial-Dependent ModelThis Work
Figure 1.
The amplitude of the DA expected from this work and the SPD model, compared with the observa-tions. The solid black line and blue dash line represent the model calculations in this work and the SDP model, re-spectively. The data come from underground muon observations from: Norikura (1973; (Sakakibara et al. 1973)), Ot-tawa (1983; (Bercovitch & Agrawal 1981)), London (1983; (Thambyahpillai 1983)), Bolivia (1985; (Swinson & Nagashima1985)), Budapest (1985; (Swinson & Nagashima 1985)), Hobart (1985; (Swinson & Nagashima 1985)), London (1985;(Swinson & Nagashima 1985)), Misato (1985; (Swinson & Nagashima 1985)), Socorro (1985; (Swinson & Nagashima 1985)),Yakutsk (1985; (Swinson & Nagashima 1985)), Banksan (1987; (Andreyev et al. 1987)), HongKong (1987; (Lee & Ng 1987)),Sakashita (1990; (Ueno et al. 1990)), Utah (1991; (Cutler & Groom 1991)), Liapootah (1995; (Munakata et al. 1995)), Mat-sushiro (1995; (Mori et al. 1995)), Poatina (1995; (Fenton et al. 1995)), Kamiokande (1997; (Munakata et al. 1997)), Marco(2003; (Ambrosio et al. 2003)), SuperKamiokande (2007; (Guillian et al. 2007)); and air shower array experiments from Peak-Musala (1975; (Gombosi et al. 1975)), Baksan (1981; (Alexeyenko et al. 1981)), EASTOP (1995, 1996, 2009; (Aglietta et al.1995), (Aglietta et al. 1996), (Aglietta et al. 2009)), Baksan (2009; (Alekseenko et al. 2009)), Milagro(2009; (Abdo et al. 2009)),ARGO (2011; (Iuppa et al. 2011)), IceCube (2010, 2012; (Abbasi et al. 2010), (Abbasi et al. 2012)), IceTop (2013; (Aartsen et al.2013)), Tibet (2005, 2013, 2017; (Amenomori et al. 2005), (Amenomori et al. 2013), (Amenomori et al. 2017) ).
The Spectrum of Proton
Figure 3 shows the spectrum comparison between model calculations and the experimental results for protons. Thegreen dash-dot, blue dashed and solid black lines represent the calculations for the background sources, nearby singlesource and total respectively. It has been discussed in Guo et al. (2016) that the SDP model can gives clear hardeningof the spectrum for E ≥
300 GeV, which is consistent with the data. With the single source added, the proton spectrumcan maintain this structure. CONCLUSIONIn this study we have shown that the DA amplitude and phase evolution with energies can be reproduce simulta-neously when a nearby single source is added to the SDP model. In recent years, the CR anisotropy has been wellmeasured, but the traditional diffusion theory can’t explain these new observations, especially the phase flip phe-nomenon. In this work, the CR DA can be considered to be made of two component: one is induce by nearby singlesource and the other is caused by all other galactic sources. At the energy region below 10 eV, the nearby source canhave dominating effect to the CR gradient and decide the phase of the DA, but beyond that, due to the high-energycutoff of local proton flux, the phase of the DA comes back to the case of SDP model. In other words the DA phase X. B. Qu
Energy (eV) P h a s e ( h r s ) -25-20-15-10-50510 Norikura1973Ottawa1981London1983Bolivia1985Budapest1985Hobart1985London1985
Misato1985Socorro1985Yakutsk1985Baksan1987HongKong1987Sakashita1990Utah1991
Liapootah1995Matsushiro1995Poatina1995Kamiokande1997Macro2003SuperKamiokande2007
PeakMusal1975Baksan1981Norikura1989EASTOP1995EASTOP1996EASTOP2009Baksan2009Milagro2009
ARGO2011IceCube2010IceCube2012IceTop2013Tibet2005Tibet2013Tibet2017
Spatial-Dependent ModelThis Work
Figure 2.
The phase of the DA expected from this work compared with the observations. The solid black line and blue dashline represent the model calculations in this work and the SDP model, respectively. The data points for the DA phase is tokenfrom the same observations as described in Fig. 1.
E(GeV)1 10 ) - s r - s - d N / d E ( G e V m . E AMS02PAMELAATICCREAM
BackgroundSingle sourceTotal
Figure 3.
Comparison between model calculations and observations for the primary spectrum of protons. The experiment datacome from: AMS02(Giesen et al. 2015), PAMELA(Adriani et al. 2011), ATIC(Panov et al. 2006), CREAM(Ahn et al. 2010).
ASTEX Understanding Anisotropy with single source eV. With the influence of the single source, the amplitude of the DA is nota simple power law, its evolution with energies can be well reproduced by adding a nearby source to the SDP model.We thank YiQing Guo, Wei Liu, HongBo Hu, SiMing Liu, Qiang Yuan and Yi Zhang for helpful discussions.This work is supported by the Ministry of Science and Technology of China, Natural Sciences Foundation of China(11505291). Note added in proof . While this paper was in preparation, a similar paper discussing nearby sources effects to theanisotropy and the spectrum under the SDP model scenario appearing on arXiv(Liu et al. 2018).REFERENCES. While this paper was in preparation, a similar paper discussing nearby sources effects to theanisotropy and the spectrum under the SDP model scenario appearing on arXiv(Liu et al. 2018).REFERENCES