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Effective cross section of fuzzy dark matter halos

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Abstract

We numerically study the movement of two colliding fuzzy dark matter solitons without explicit self-interaction and find the effective cross section of dissipative change in velocity. The cross section turns out to be inversely proportional to the velocity cubed, and we present its analytic interpretation. Using the result we roughly estimate spatial offsets during head-on collisions of two fuzzy dark matter halos, which can be related to the spatial offsets between stars and dark matter in collisions of some galaxy clusters. We also show that the gravitational cooling plays an important role during the collisions.

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Notes

  1. Thus, \(\int d^3 \mathbf{{x}}\, |\psi |^2\) in the code space is no longer fixed to be unity in general.

  2. Hence \(M_\mathrm{tot}=2M\) in our setup.

  3. For each moving soliton, one may introduce an additional velocity-dependent phase factor [18] and we shall put the relative phase factor \(\delta =0\) for the simplicity of our analysis (see [18] for the details).

  4. Labeling each soliton could be ambiguous since the collision is solely described by field profiles of our Schrödinger–Poisson system. However this ambiguity may be lifted by considering slightly different masses, e.g. \(M_L > M_R\), and tracking for instance the larger/smaller density peak as the soliton L/R.

  5. We would like to thank the referee for clarification of the argument below.

  6. The parameters A, B are related to \(\alpha ,\beta\) by \(A=f_0^3 \, \alpha\) and \(B=f_0^2\, \beta\).

  7. \(q_{\text {src}}\ll 1\) corresponds to the quantum regime in which \(q_{\text {src}}\) dependence in C can be ignored. See Figure 2 of Ref. [5] in this regard.

  8. Interestingly, with \(G(q)=A q^3\), \(\sigma _\mathrm{eff}/M\) is independent of the soliton mass M.

  9. The approximation here breaks down when \({|v-v_I|}/{v}\) becomes \(\mathcal{O}(1)\). In this regime, one has in general further enhancement of the offset ratio.

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Acknowledgements

D Bak was supported in part by the 2021 Research Fund of the University of Seoul. J. W. Lee was supported in part by NRF-2020R1F1A1061160. S. Park was supported in part by NRF Grant 2020R1A2B5B01001473, by Basic Science Research Program through National Research Foundation funded by the Ministry of Education (2018R1A6A1A06024977).

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Authors and Affiliations

  1. Physics Department, University of Seoul, Seoul, 02504, Korea

    Dongsu Bak

  2. Department of Electrical and Electronic Engineering, Jungwon University, 85 Munmuro, Goesan, Chungbuk, 28024, Korea

    Jae-Weon Lee

  3. Natural Science Research Institute, University of Seoul, Seoul, 02504, Korea

    Dongsu Bak & Sangnam Park

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  1. Dongsu Bak
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  2. Jae-Weon Lee
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Correspondence to Jae-Weon Lee.

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Bak, D., Lee, JW. & Park, S. Effective cross section of fuzzy dark matter halos. J. Korean Phys. Soc. 79, 582–588 (2021). https://doi.org/10.1007/s40042-021-00263-3

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