- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Semianalytical approach to Lyα multiple-scattering in 21-cm signal simulations

Jordan Flitter1,*, Julian B. Muñoz2,3,4, and Andrei Mesinger1,5,6

  • *Contact author: jordan.flitter@sns.it
PDF

Phys. Rev. D 113, 103552 – Published 29 May, 2026

DOI: https://doi.org/10.1103/5r5v-nk5j

Abstract

A crucial physical quantity in determining the 21-cm signal during cosmic dawn is the inhomogeneous background of Lyα photons originating from the first galaxies. As these photons travel through the intergalactic medium (IGM), their scattering cross section is often approximated as a delta function at resonance due to computational cost. That is, photons with emitted wavelengths between Lyα and Lyβ are assumed to travel in straight lines until they redshift into the Lyα resonance. However, due to the damping wing in the Lyα cross section, this approximation fails as the frequency of the photon approaches the resonant frequency, resulting in multiple scatterings events that could be separated by non-negligible distances. These multiple scattering events effectively modify the intrinsic Lyα emissivity from galaxies. Some previous works studied this effect of Lyα multiple scattering by running computationally heavy radiative-transfer simulations. However, robustly interpreting the cosmic 21 cm signal requires exploring a large parameter space of astrophysical uncertainties, motivating more computationally efficient approaches. Here we incorporate Lyα multiple scatterings in the public, seminumerical simulation 21cmfast. To do so, we employ Monte Carlo simulations to study the trajectories of Lyα photons on different scales. We find that the distance distributions of Lyα photons with respect to the absorption point can be modeled as analytical functions that are governed by a single parameter. Upon implementing the distance distributions in 21cmfast, we find that the multiple scattering effect is important (about 50% difference in the 21-cm power spectrum) only at high redshifts before the spin temperature is fully coupled to the kinetic temperature. Furthermore, we find that Lyα multiple scattering does not enhance Lyα heating, and that the combined effect is negligible, especially under realistic x-ray heating scenarios.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (95)

  1. R. Barkana and A. Loeb, In the beginning: The first sources of light and the reionization of the universe, Phys. Rep. 349, 125 (2001).
  2. R. Barkana and A. Loeb, Detecting the earliest galaxies through two new sources of 21 cm fluctuations, Astrophys. J. 626, 1 (2005).
  3. J. R. Pritchard and A. Loeb, 21-cm cosmology, Rep. Prog. Phys. 75, 086901 (2012).
  4. J. Park, A. Mesinger, B. Greig, and N. Gillet, Inferring the astrophysics of reionization and cosmic dawn from galaxy luminosity functions and the 21-cm signal, Mon. Not. R. Astron. Soc. 484, 933 (2019).
  5. J. Park, N. Gillet, A. Mesinger, and B. Greig, Properties of reionization-era galaxies from JWST luminosity functions and 21-cm interferometry, Mon. Not. R. Astron. Soc. 491, 3891 (2020).
  6. Y. Qin, A. Mesinger, J. Park, B. Greig, and J. B. Muñoz, A tale of two sites—I. Inferring the properties of minihalo-hosted galaxies from current observations, Mon. Not. R. Astron. Soc. 495, 123 (2020).
  7. Y. Qin, A. Mesinger, B. Greig, and J. Park, A tale of two sites—II. Inferring the properties of minihalo-hosted galaxies with upcoming 21-cm interferometers, Mon. Not. R. Astron. Soc. 501, 4748 (2021).
  8. J. B. Muñoz, Y. Qin, A. Mesinger, S. G. Murray, B. Greig, and C. Mason, The impact of the first galaxies on cosmic dawn and reionization, Mon. Not. R. Astron. Soc. 511, 3657 (2022).
  9. P. Madau, A. Meiksin, and M. J. Rees, 21-CM tomography of the intergalactic medium at high redshift, Astrophys. J. 475, 429 (1997).
  10. M. McQuinn, O. Zahn, M. Zaldarriaga, L. Hernquist, and S. R. Furlanetto, Cosmological parameter estimation using 21 cm radiation from the epoch of reionization, Astrophys. J. 653, 815 (2006).
  11. S. Furlanetto, S. P. Oh, and F. Briggs, Cosmology at low frequencies: The 21 cm transition and the high-redshift universe, Phys. Rep. 433, 181 (2006).
  12. A. Lidz, O. Zahn, S. Furlanetto, M. McQuinn, L. Hernquist, and M. Zaldarriaga, Probing reionization with the 21 cm-galaxy cross power spectrum, Astrophys. J. 690, 252 (2009).
  13. B. Greig and A. Mesinger, Simultaneously constraining the astrophysics of reionization and the epoch of heating with 21CMMC, Mon. Not. R. Astron. Soc. 472, 2651 (2017).
  14. B. Greig, A. Mesinger, and L. V. E. Koopmans, Reionization and cosmic dawn astrophysics from the square kilometre array: Impact of observing strategies, Mon. Not. R. Astron. Soc. 491, 1398 (2020).
  15. B. Greig, C. M. Trott, N. Barry, S. J. Mutch, B. Pindor, R. L. Webster, and J. S. B. Wyithe, Exploring reionization and high-z galaxy observables with recent multiredshift MWA upper limits on the 21-cm signal, Mon. Not. R. Astron. Soc. 500, 5322 (2020).
  16. S. Gagnon-Hartman, J. E. Davies, and A. Mesinger, Detecting galaxy—21-cm cross-correlation during reionization, Astron. Astrophys. 699, A131 (2025).
  17. R. Barkana, Possible interaction between baryons and dark-matter particles revealed by the first stars, Nature (London) 555, 71 (2018).
  18. E. D. Kovetz, V. Poulin, V. Gluscevic, K. K. Boddy, R. Barkana, and M. Kamionkowski, Tighter limits on dark matter explanations of the anomalous EDGES 21 cm signal, Phys. Rev. D 98, 103529 (2018).
  19. J. B. Muñoz and A. Loeb, A small amount of mini-charged dark matter could cool the baryons in the early universe, Nature (London) 557, 684 (2018).
  20. J. B. Muñoz, C. Dvorkin, and A. Loeb, 21-cm fluctuations from charged dark matter, Phys. Rev. Lett. 121, 121301 (2018).
  21. J. Flitter and E. D. Kovetz, Closing the window on fuzzy dark matter with the 21-cm signal, Phys. Rev. D 106, 063504 (2022).
  22. J. Cang, Y. Gao, and Y.-Z. Ma, Signatures of inhomogeneous dark matter annihilation on 21-cm, Phys. Rev. D 112, 103048 (2025).
  23. J. Flitter and E. D. Kovetz, New tool for 21-cm cosmology. I. Probing ΛCDM and beyond, Phys. Rev. D 109, 043512 (2024).
  24. H. Lazare, J. Flitter, and E. D. Kovetz, Constraints on the fuzzy dark matter mass window from high-redshift observables, Phys. Rev. D 110, 123532 (2024).
  25. A. Lidz, E. J. Baxter, P. Adshead, and S. Dodelson, Primordial non-Gaussianity and reionization, Phys. Rev. D 88, 023534 (2013).
  26. J. L. Bernal, A. Raccanelli, L. Verde, and J. Silk, Signatures of primordial black holes as seeds of supermassive black holes, J. Cosmol. Astropart. Phys. 05 (2018) 017; 01 (2020) E01.
  27. J. B. Muñoz, Standard ruler at cosmic dawn, Phys. Rev. Lett. 123, 131301 (2019).
  28. J. Cang, Y. Gao, and Y.-Z. Ma, 21-cm constraints on spinning primordial black holes, J. Cosmol. Astropart. Phys. 03 (2022) 012.
  29. D. Sarkar and E. D. Kovetz, Measuring the cosmic expansion rate using 21-cm velocity acoustic oscillations, Phys. Rev. D 107, 023524 (2023).
  30. H. A. G. Cruz, T. Adi, J. Flitter, M. Kamionkowski, and E. D. Kovetz, 21-cm fluctuations from primordial magnetic fields, Phys. Rev. D 109, 023518 (2024).
  31. H. Plombat, T. Simon, J. Flitter, and V. Poulin, Probing dark relativistic species and their interactions with dark matter through CMB and 21 cm surveys, J. Cosmol. Astropart. Phys. 01 (2025) 071.
  32. T. Adi, J. Flitter, and E. D. Kovetz, Early dark energy effects on the 21-cm signal, Phys. Rev. D 111, 043515 (2025).
  33. S. Libanore, S. Ghosh, E. D. Kovetz, K. K. Boddy, and A. Raccanelli, Joint 21-cm and CMB forecasts for constraining self-interacting massive neutrinos, Phys. Rev. D 112, 063502 (2025).
  34. J. D. Bowman, A. E. E. Rogers, and J. N. Hewitt, Toward empirical constraints on the global redshifted 21 cm brightness temperature during the epoch of reionization, Astrophys. J. 676, 1 (2008).
  35. N. Patra, R. Subrahmanyan, A. Raghunathan, and N. U. Shankar, SARAS: A precision system for measurement of the cosmic radio background and signatures from the epoch of reionization, Exp. Astron. 36, 319 (2013).
  36. S. Singh, R. Subrahmanyan, N. U. Shankar, M. S. Rao, B. S. Girish, A. Raghunathan, R. Somashekar, and K. S. Srivani, SARAS 2: A spectral radiometer for probing cosmic dawn and the epoch of reionization through detection of the global 21 cm signal, Exp. Astron. 45, 269 (2018).
  37. M. Sokolowski, S. E. Tremblay, R. B. Wayth, S. J. Tingay, N. Clarke, P. Roberts, M. Waterson, R. D. Ekers, P. Hall, M. Lewis, M. Mossammaparast, S. Padhi, F. Schlagenhaufer, A. Sutinjo, and J. Tickner, BIGHORNS—broadband instrument for global HydrOgen ReioNisation signal, Pub. Astron. Soc. Aust. 32, e004 (2015).
  38. E. de Lera Acedo et al., The REACH radiometer for detecting the 21-cm hydrogen signal from redshift z ≈7.5–28, Nat. Astron. 6, 994 (2022).
  39. L. Philip, Z. Abdurashidova, H. C. Chiang, N. Ghazi, A. Gumba, H. M. Heilgendorff, J. M. Jáuregui-García, K. Malepe, C. D. Nunhokee, J. Peterson, J. L. Sievers, V. Simes, and R. Spann, Probing radio intensity at high-Z from marion: 2017 instrument, J. Astron. Instrum. 8, 1950004 (2019).
  40. R. A. Monsalve et al., Mapper of the IGM spin temperature: Instrument overview, Mon. Not. R. Astron. Soc. 530, 4125 (2024).
  41. P. Bull et al., RHINO: A large horn antenna for detecting the 21 cm global signal, RAS Techniq. Instrum. 4, rzaf046 (2025).
  42. D. R. DeBoer et al., Hydrogen epoch of reionization array (HERA), Publ. Astron. Soc. Pac. 129, 045001 (2017).
  43. M. P. van Haarlem et al., LOFAR: The LOw-Frequency ARray, Astron. Astrophys. 556, A2 (2013).
  44. H. W. Edler, F. de Gasperin, and D. Rafferty, Investigating ionospheric calibration for LOFAR 2.0 with simulated observations, Astron. Astrophys. 652, A37 (2021).
  45. P. Zarka et al., Nenufar: Instrument description and science case, in 2015 International Conference on Antenna Theory and Techniques (ICATT) (IEEE, Kharkiv, Ukraine, 2015), pp. 1–6.
  46. R. Braun, T. Bourke, J. A. Green, E. Keane, and J. Wagg, Advancing astrophysics with the square kilometre array, Proc. Sci. AASKA14 (2015) 174.
  47. R. Braun, A. Bonaldi, T. Bourke, E. Keane, and J. Wagg, Anticipated Performance of the Square Kilometre Array—Phase 1 (SKA1), arXiv:1912.12699.
  48. J. O. Burns, R. MacDowall, S. Bale, G. Hallinan, N. Bassett, and A. Hegedus, Low radio frequency observations from the moon enabled by NASA landed payload missions, Planet. Sci. J. 2, 44 (2021).
  49. S. D. Bale et al., LuSEE ’Night’: The lunar surface electromagnetics experiment, arXiv:2301.10345.
  50. M. Sathyanarayana Rao, S. Singh, K. S. Srivani, B. S. Girish, K. Sathish, R. Somashekar, R. Agaram, K. Kavitha, G. Vishwapriya, A. Anand, N. Udaya Shankar, and S. Seetha, PRATUSH experiment concept and design overview, Exp. Astron. 56, 741 (2023).
  51. M. Klein Wolt, H. Falcke, and L. Koopmans, The Astronomical Lunar Observatory (ALO)—Probing the cosmological Dark Ages and Cosmic Dawn with a distributed low-frequency radio array on the lunar far side, in American Astronomical Society Meeting Abstracts #243, American Astronomical Society Meeting Abstracts Vol. 243 (American Astronomical Society (AAS), New Orleans, Louisiana, USA, 2024), p. 264.01.
  52. S. A. Wouthuysen, On the excitation mechanism of the 21-cm (radio-frequency) interstellar hydrogen emission line. Astron. J. 57, 31 (1952).
  53. G. B. Field, Excitation of the hydrogen 21-CM line, Proc. IRE 46, 240 (1958).
  54. C. M. Hirata, Wouthuysen-Field coupling strength and application to high-redshift 21 cm radiation, Mon. Not. R. Astron. Soc. 367, 259 (2006).
  55. A. Mesinger, S. Furlanetto, and R. Cen, 21cmfast: A fast, semi-numerical simulation of the high-redshift 21-cm signal, Mon. Not. R. Astron. Soc. 411, 955 (2011).
  56. S. G. Murray, B. Greig, A. Mesinger, J. B. Muñoz, Y. Qin, J. Park, and C. A. Watkinson, 21cmfast v3: A Python-integrated C code for generating 3D realizations of the cosmic 21 cm signal, J. Open Source Software 5, 2582 (2020).
  57. M. G. Santos, L. Ferramacho, M. B. Silva, A. Amblard, and A. Cooray, Fast and large volume simulations of the 21 cm signal from the reionization and pre-reionization epochs, Mon. Not. R. Astron. Soc. 406, 2421 (2010).
  58. J. B. Muñoz, An effective model for the cosmic-dawn 21-cm signal, Mon. Not. R. Astron. Soc. 523, 2587 (2023).
  59. H. A. G. Cruz, J. B. Munoz, N. Sabti, and M. Kamionkowski, Effective model for the 21-cm signal with population III stars, Phys. Rev. D 111, 083503 (2025).
  60. A. Loeb and G. B. Rybicki, Scattered Lyα radiation around sources before cosmological reionization, Astrophys. J. 524, 527 (1999).
  61. A. Smith, K. Lorinc, O. Nebrin, and B.-X. Lao, Lyman-α resonant-line radiative transfer in expanding media, Mon. Not. R. Astron. Soc. 541, 179 (2025).
  62. I. Reis, A. Fialkov, and R. Barkana, The subtlety of Lyα photons: Changing the expected range of the 21-cm signal, Mon. Not. R. Astron. Soc. 506, 5479 (2021).
  63. E. Visbal, R. Barkana, A. Fialkov, D. Tseliakhovich, and C. Hirata, The signature of the first stars in atomic hydrogen at redshift 20, Nature (London) 487, 70 (2012).
  64. S. Pochinda, T. Gessey-Jones, H. T. J. Bevins, A. Fialkov, S. Heimersheim, I. Abril-Cabezas, E. d. L. Acedo, S. Singh, S. Sikder, and R. Barkana, Constraining the properties of population III galaxies with multiwavelength observations, Mon. Not. R. Astron. Soc. 531, 1113 (2024).
  65. I. Reis, R. Barkana, and A. Fialkov, Mapping discrete galaxies at cosmic dawn with 21 cm observations, Astrophys. J. 933, 51 (2022).
  66. B. Semelin, R. Mériot, F. Mertens, L. V. E. Koopmans, D. Aubert, R. Barkana, A. Fialkov, S. Munshi, and P. Ocvirk, Accurate modelling of the Lyman-α coupling for the 21-cm signal, observability with NenuFAR, and SKA, Astron. Astrophys. 672, A162 (2023).
  67. B. Semelin, F. Combes, and S. Baek, Lyman-Alpha radiative transfer during the epoch of reionization: Contribution to 21-cm signal fluctuations, Astron. Astrophys. 474, 365 (2007).
  68. S. Mittal, G. Kulkarni, and T. Garel, Radiative transfer of Lyman-α photons at cosmic dawn with realistic gas physics, Mon. Not. R. Astron. Soc. 535, 1979 (2024).
  69. Z. Abdurashidova et al. (HERA Collaboration), HERA phase I limits on the cosmic 21 cm signal: Constraints on astrophysics and cosmology during the epoch of reionization, Astrophys. J. 924, 51 (2022).
  70. D. Breitman, I. Nikolić, A. Mesinger, and S. G. Murray (to be published).
  71. N. Aghanim et al. (Planck Collaboration), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  72. T. Venumadhav, L. Dai, A. Kaurov, and M. Zaldarriaga, Heating of the intergalactic medium by the cosmic microwave background during cosmic dawn, Phys. Rev. D 98, 103513 (2018).
  73. S. Mittal and G. Kulkarni, Ly α coupling and heating at cosmic dawn, Mon. Not. R. Astron. Soc. 503, 4264 (2021).
  74. X.-L. Chen and J. Miralda-Escude, The spin—kinetic temperature coupling and the heating rate due to Lyα scattering before reionization: Predictions for 21 cm emission and absorption, Astrophys. J. 602, 1 (2004).
  75. J. R. Pritchard and S. R. Furlanetto, Descending from on high: Lyman series cascades and spin-kinetic temperature coupling in the 21 cm line, Mon. Not. R. Astron. Soc. 367, 1057 (2006).
  76. J. E. Davies, A. Mesinger, and S. Murray, Efficient simulation of discrete galaxy populations and associated radiation fields during the first billion years, Astron. Astrophys. 701, A236 (2025).
  77. M. Dijkstra, Lyα emitting galaxies as a probe of reionization, Pub. Astron. Soc. Aust. 31, 40 (2014).
  78. M. Dijkstra, Saas-Fee lecture notes: Physics of Lyman Alpha radiative transfer, arXiv:1704.03416.
  79. M. Dijkstra and A. Loeb, The polarization of scattered Lyα radiation around high-redshift galaxies, Mon. Not. R. Astron. Soc. 386, 492 (2008).
  80. L. Michel-Dansac, J. Blaizot, T. Garel, A. Verhamme, T. Kimm, and M. Trebitsch, rascas: RAdiation SCattering in astrophysical simulations, Astron. Astrophys. 635, A154 (2020).
  81. T. Costa, F. Arrigoni Battaia, E. P. Farina, L. C. Keating, J. Rosdahl, and T. Kimm, AGN-driven outflows and the formation of Lyα nebulae around high-z quasars, Mon. Not. R. Astron. Soc. 517, 1767 (2022).
  82. Y. Yuan, S. Martin-Alvarez, M. G. Haehnelt, T. Garel, and D. Sijacki, Lyα emission as a sensitive probe of feedback-regulated LyC escape from dwarf galaxies, Mon. Not. R. Astron. Soc. 532, 3643 (2024).
  83. A. Smith, C. Safranek-Shrader, V. Bromm, and M. Milosavljević, The Lyman α signature of the first galaxies, Mon. Not. R. Astron. Soc. 449, 4336 (2015).
  84. Z. Zheng and J. Miralda-Escude, Monte Carlo simulation of Lyα scattering and application to damped Lyα systems, Astrophys. J. 578, 33 (2002).
  85. I. Nikolić, A. Mesinger, J. E. Davies, and D. Prelogović, The importance of stochasticity in determining galaxy emissivities and UV LFs during cosmic dawn and reionization, Astron. Astrophys. 692, A142 (2024).
  86. A. Mesinger and S. Furlanetto, Efficient simulations of early structure formation and reionization, Astrophys. J. 669, 663 (2007).
  87. D. Sarkar, J. Flitter, and E. D. Kovetz, Exploring delaying and heating effects on the 21-cm signature of fuzzy dark matter, Phys. Rev. D 105, 103529 (2022).
  88. J. Raste and S. K. Sethi, 21 cm signal from the thermal evolution of Lyman-α during cosmic dawn, Astrophys. J. 996, 44 (2025).
  89. A. Meiksin, Intergalactic heating by Lyα photons including hyperfine structure corrections, Res. Notes AAS 5, 126 (2021).

  90. https://github.com/21cmfast/21cmFAST and https://github.com/jordanflitter/SPaRTA.

  91. D. Blas, J. Lesgourgues, and T. Tram, The cosmic linear anisotropy solving system (CLASS) II: Approximation schemes, J. Cosmol. Astropart. Phys. 07 (2011) 034.
  92. F. R. Bouchet, S. Colombi, E. Hivon, and R. Juszkiewicz, Perturbative Lagrangian approach to gravitational instability, Astron. Astrophys. 296, 575 (1995).
  93. R. Scoccimarro, Transients from initial conditions: A perturbative analysis, Mon. Not. R. Astron. Soc. 299, 1097 (1998).
  94. M. e. a. Galassi, GNU scientific library reference manual (2018), https://www.gnu.org/software/gsl/.
  95. T. mpmath Development Team, mpmath: A python library for arbitrary-precision floating-point arithmetic (version 1.3.0) (2023), http://mpmath.org/.

Outline

Information

Phys. Rev. D 113, 103552– Published 29 May, 2026
  • Received 6 February 2026
  • Accepted 6 May 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation