The "Dark disk" model in the light of DAMPE experiment
TThe «Dark disk» model in the light ofDAMPE experiment
M.L. Solovyov , M.A. Rakhimova , and K.M. Belotsky National Research Nuclear University MEPhI (MoscowEngineering Physics Institute), 115409, Kashirskoe shosse31, Moscow, Russia * E-mail: [email protected]
Abstract
There are a lot of models considering the Dark Matter (DM)to be the origin of cosmic ray (CR) positron excess. How-ever, they face an obstacle in the form of gamma-rays. SimpleDM models tend to overproduce gamma-rays, leading to con-tradiction with isotropic gamma-ray background (IGRB). The«dark disk» model has been proposed to alleviate this contra-diction. This work considers results of DAMPE experiment inthe framework of the disk model. It is obtained that such aframework allows improving data fit considerably.
Keywords:
Cosmic rays, cosmic ray anomalies, dark matter,gamma-ray background, dark disk
During the past decade, the anomalous behaviour of CR energyspectra was brought into the light. The positron excess, found byPAMELA [1] and confirmed by AMS-02 [2, 3], the «wide» and «peak-like» excesses in electron plus positron spectrum of recent DAMPEexperiment [4, 5] are amongst the most well-known ones. The simplesolutions seem to not work for these puzzles, as they remain unsolved.1 a r X i v : . [ a s t r o - ph . H E ] N ov here are plenty of models considering DM of different nature,and there is a great freedom in defining its properties. Therefore, it isquite easy to introduce a model with decaying or annihilating DM toaccount for the CR puzzles. And the possibility to probe for the newphysics of the Dark Matter makes these models even more appealing.The main alternative to DM models involves the pulsars as thecause of the excesses. Recent works in this field face the constraints[6, 7] from gamma-radiation observed around the pulsars. Thoughattempts to solve the problems in this way continue (e.g., [8]).However, DM models are also subject to the constraints. One ofthem is set by the gamma-ray data [9]. Photons are inevitably pro-duced in the process of DM particle decay or annihilation via the finalstate radiation (FSR) process. And simple halo-distributed DM mod-els dedicated to CR anomaly description tend to overproduce gam-mas, resulting in contradiction to Isotropic Gamma-ray Background(IGRB) data provided by Fermi-LAT [10].To resolve it, we develop the so-called «dark disk» model withunstable DM distributed in disk [11]. This assumption helps to excludegamma-rays from the outer regions of DM halo, that can not make acontribution to the observable charged particles fluxes.In our previous work, we have found the IGRB data to constrainthe halo models even in the case of broad electron plus positron excessin DAMPE data [12]. In this work we try to apply the «dark disk»model to this case. Sec. 2 provides the model description, Sec. 3contains the obtained results and everything is summed up in Sec. 4. We consider DM particles with mass m X = 1800 GeV to be able toannihilate via 3 leptonic channels ( e + e − , µ + µ − , τ + τ − ) which branch-ing ratios along with annihilation cross section (cid:104) σv (cid:105) are the modelparameters. For DM distribution, we use two density profiles:• Read’s profile [13] ρ ( r, z ) = ρ r exp (cid:32) − rR R (cid:33) exp (cid:32) − zzc (cid:33) (1)2 NFW profile [14] with cut-off along the z -axis ρ ( r, z ) = ρ NrR s (cid:16) rR s (cid:17) , z ≤ zc, , z > zc (2)where r and z are coordinates in cylindrical coordinate system, zc isthe disk half-thickness, ρ r = 1 .
32 GeV cm − , ρ N = 0 .
25 GeV cm − ,which corresponds to the local DM density of . − , R R =6 . kpc, R s = 24 kpc.We use Pythia to calculate the initial spectra of electrons, positronsand gammas. The GALPROP code is used to propagate the first twoof them and obtain their near-Earth spectra, as well as the secondarygamma flux. The prompt radiation flux is obtained by Φ prompt ( E γ ) = dN γ dE γ (cid:104) σv (cid:105) ×× (cid:90) kpc (cid:90) ◦ ◦ (cid:90) π πr (cid:18) ρM X (cid:19) r cos( θ ) dr dθ dφ , (3)where dN γ dE γ is the gamma-ray spectrum per one act of annihilation, M X is the mass of DM particle, ∆Ω is the solid angle ( l ∈ [0; 2 π ] , b ∈ [20 ◦ ; 90 ◦ ] ) corresponding to the region of the Fermi-LAT analysis.We use the total e + e − background from [15], which was obtainedas the best-fit background model for a variety of cosmic-ray data.To obtain the values of branching ratios and the process cross-section, we minimize the following expression for χ : χ = d − (cid:34) (cid:88) DAMPE (∆Φ e ) σ e + (cid:88) Fermi (∆Φ γ ) σ γ H (∆Φ γ ) (cid:35) . (4)Here ∆Φ i ≡ Φ (th) i − Φ (obs) i , Φ i are the predicted ( th ) and measured( obs ) fluxes for i = e, γ denoting e + e − or gamma points respectively, σ i denotes the corresponding experimental errors and d denotes thenumber of statistical degrees of freedom, which includes all the relevantDAMPE and Fermi-LAT data points. The first sum in Eq. (4) goesover the DAMPE data points and the second sum goes over the Fermi-LAT data points. DAMPE points are taken in the range ÷ Φ (th) γ > Φ (obs) γ , which is ensured by the Heavisidestep function H .We use two different approaches for the minimization procedure.In first, called «combined fit», we just simply minimize expression 4.In the second, called « e -fit», we minimize only the first sum in theexpression 4 and only after that, using the obtained parameters, wecalculate total chi-square value. Fig. 1 illustrates the correlation between χ values and the diskhalf-width.In the case of «e-fit» the best results are obtained with zc ≈ pc. However, one can clearly see that the quality of fit is still notsatisfactory at all, although still better than one for the thick disksand halo. On the other hand, «combined fit» gives much better resultswith the minimum of χ of around 1.6 for the disk half-width in therange of ÷ pc. However, in the case of AMS-02 positronfraction best fits were obtained with zc = 400 pc. Unexpectedly,the NFW density profile with cut-off produces better results, thanRead’s profile, over the whole considered region. We suppose it tobe due to higher production of low-energy electrons and positronsfor NFW, which helps it to account for the lower energy region ofthe spectra. The line in the graphics breaks are mainly caused by thechange of degree-of-freedom number (as we dynamically calculate it toinclude only those Fermi-LAT datapoints, where we have the excess)and interpolation errors. Fit | Model Halo Diske-fit 203 (0.53) 17.85 (0.52)combined fit 3.8 (2.1) 1.48 (1.20)
Table 1: The best-fit values of χ for different DM models and ap-proaches for the minimization procedure. The values in brackets areobtained using only electron-positron part of Eq. (4).4 a)(b) Figure 1: Graphs for χ values in dependence of the disk half-widthin case of e-fit (a) and combined fit (b). Blue line is used for NFWdensity profile, the orange one – for Read’s density profile.Table 1 contains the best-fit values of chi-square in contrast tothe ones, obtained for the halo case. The comparison revealed thatthe dark disk model allows achieving the same accuracy in positrondescription, as the halo model, while giving less contradiction withIGRB. In both cases, combined fit improves the fit quality, but stillnot enough to overcome the discrepancy.5 Conclusion
We continue our research of DM explanation of the CR puzzles.In this work, we have applied the «dark disk» model to the case ofthe wide excess of positrons plus electrons in DAMPE data. We haveobtained that it helps to lessen the contradiction with cosmic gamm-ray data. However, it is achieved at the cost of thicker disk, comparedto the case of low energy positron anomaly of AMS-02.In our future works we plan to run such analysis for the differentmasses of initial particle, try different reaction modes and to attemptto describe AMS-02 and DAMPE data simultaneously.
Acknowledgments
The work was supported by the Ministry of Science and HigherEducation of the Russian Federation by project No 0723-2020-0040“Fundamental problems of cosmic rays and dark matter”. Also wewould like to thank R.Budaev, A.Kirillov and M.Laletin for their con-tribution at the early stage of this work.
References [1]
PAMELA collaboration, O. Adriani et al.,
An anomalouspositron abundance in cosmic rays with energies 1.5-100 GeV , Nature (2009) 607–609, [ ].[2]
AMS Collaboration collaboration, M. Aguilar, G. Alberti,B. Alpat, A. Alvino, G. Ambrosi, K. Andeen et al.,
First resultfrom the alpha magnetic spectrometer on the international spacestation: Precision measurement of the positron fraction inprimary cosmic rays of 0.5-350 gev , Phys. Rev. Lett. (Apr,2013) 141102.[3]
AMS Collaboration collaboration, L. Accardo, M. Aguilar,D. Aisa, B. Alpat, A. Alvino, G. Ambrosi et al.,
High statisticsmeasurement of the positron fraction in primary cosmic rays of0.5–500 gev with the alpha magnetic spectrometer on theinternational space station , Phys. Rev. Lett. (Sep, 2014)121101. 64] J. Cao, X. Guo, L. Shang, F. Wang, P. Wu and L. Zu,
Scalardark matter explanation of the DAMPE data in the minimalLeft-Right symmetric model , Phys. Rev.
D97 (2018) 063016,[ ].[5] H.-B. Jin, B. Yue, X. Zhang and X. Chen,
Cosmic ray e + e − spectrum excess and peak feature observed by the DAMPEexperiment from dark matter , .[6] A. U. Abeysekara, A. Albert, R. Alfaro, C. Alvarez, J. D.´Alvarez, R. Arceo et al., Extended gamma-ray sources aroundpulsars constrain the origin of the positron flux at Earth , Science (Nov., 2017) 911–914, [ ].[7] S.-Q. Xi, R.-Y. Liu, Z.-Q. Huang, K. Fang, H. Yan and X.-Y.Wang,
GeV observations of the extended pulsar wind nebulaechallenge the pulsar interpretations of the cosmic-ray positronexcess , .[8] M. Linares and M. Kachelriess, Cosmic ray positrons fromcompact binary millisecond pulsars , arXiv e-prints (Oct., 2020)arXiv:2010.02844, [ ].[9] K. Belotsky, R. Budaev, A. Kirillov and M. Laletin, Fermi-LATkills dark matter interpretations of AMS-02 data. Or not? , JCAP (2017) 021, [ ].[10]
Fermi-LAT collaboration, M. Ackermann et al.,
The spectrumof isotropic diffuse gamma-ray emission between 100 MeV and820 GeV , Astrophys. J. (2015) 86, [ ].[11] K. M. Belotsky, A. A. Kirillov and M. L. Solovyov,
Developmentof dark disk model of positron anomaly origin , Int. J. Mod.Phys.
D27 (2018) 1841010, [ ].[12] K. Belotsky, A. Kamaletdinov, M. Laletin and M. Solovyov,
The DAMPE excess and gamma-ray constraints , Physics of theDark Universe (Dec, 2019) 100333, [ ].[13] J. I. Read, G. Lake, O. Agertz and V. P. Debattista, Thin, thickand dark discs in Λ CDM , Monthly Notices of the RoyalAstronomical Society (sep, 2008) 1041–1057, [ ].714] J. F. Navarro, C. S. Frenk and S. D. M. White,
A Universaldensity profile from hierarchical clustering , Astrophys. J. (1997) 493–508, [ astro-ph/9611107 ].[15] J.-S. Niu, T. Li and F.-Z. Xu,
A Simple and NaturalInterpretations of the DAMPE Cosmic Ray Electron/PositronSpectrum within Two Sigma Deviations , Eur. Phys. J.
C79 (2019) 125, [1712.09586