# Erratum: Lepto-hadronic single-zone models for the electromagnetic and neutrino emission of TXS 0506+056

M. Cerruti, A. Zech, C. Boisson, G. Emery, S. Inoue, J. -P. Lenain

► To cite this version:

M. Cerruti, A. Zech, C. Boisson, G. Emery, S. Inoue, et al. Erratum: Lepto-hadronic single-zone models for the electromagnetic and neutrino emission of TXS 0506+056. 2021, pp.L21-L22. 10.1093/mnrasl/slaa188. insu-03713220

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# Erratum: Lepto-hadronic single-zone models for the electromagnetic and neutrino emission of TXS 0506+056

by M. Cerruti<sup>1,2*</sup> A. Zech,<sup>3★</sup> C. Boisson,<sup>3</sup> G. Emery,<sup>1</sup> S. Inoue<sup>4</sup> and J.-P. Lenain<sup>1</sup>

<sup>1</sup>Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, CNRS/IN2P3, Laboratoire de Physique Nucléaire et de Hautes Energies, LPNHE, 4 Place Jussieu, F-75252 Paris, France

<sup>2</sup>Now at Institut de Ciències del Cosmos (ICCBUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, E08028 Barcelona, Spain

<sup>3</sup>LUTH, Observatoire de Paris, PSL Research University, CNRS, Université Paris Diderot, 5 Place Jules Janssen, 92190 Meudon, France

<sup>4</sup>RIKEN, Institute of Physical and Chemical Research, 2-1 Hirosawa, Wako, Saitama, 351-0198, Japan

**Key words:** Errata, Addenda – BL Lacertae objects: individual: TXS 0506+056– gamma rays: galaxies – neutrinos – radiation mechanisms: non-thermal.

The paper ‘Lepto-hadronic single-zone models for the electromagnetic and neutrino emission of TXS 0506+056’ (Cerruti et al. 2019) was published in MNRAS, 483, L12.

Afterwards, we became aware of three errors in our numerical calculations. When corrected, the ratio of the emissivity in neutrinos to that in hadronic gamma-rays is modified. We obtained updated model solutions that reproduce the flare of TXS 0506+056 observed in 2017. These do not differ qualitatively from the published ones, and the main conclusions of the paper remain valid. However, the estimated neutrino rate was overpredicted.

In more detail:

(i) the photo-meson production was overestimated by a factor of $ln(10) \simeq 2.3$. This was due to a miscommunication between the radiative part of the code and the SOPHIA Monte Carlo code;

(ii) when computing the synchrotron pair cascade, the injection of secondary pairs was underproduced by a factor of 2. This was due to an erroneous implementation of the injection formula provided by Aharonian, Atoian & Nagapetian (1983): the formula refers to either electrons or positrons, but given that the radiative code treats them indifferently, the injection term has to be multiplied by a factor of 2;

(iii) the solutions we published were computed assuming an adiabatic time $\tau_{ad} = 2R/c$, which enters into the computation of the particle steady state. The code was incorrectly applying the factor of 2 also to photons and neutrinos, which should be characterized instead by an escape time of $R/c$.

These errors affected the various hadronic components in different ways: the first one applies to injection of all species from photo-meson interactions; the second one applies only to the pair cascades; and the third one only to the neutrinos and photons from $\pi^0$ decay. Given that the first two errors almost exactly compensate for each other, the photon emission was overestimated by at most a factor of $\simeq 2$. More specifically, the muon synchrotron component and the $\pi^0$ cascade were overproduced by a factor of $\simeq 2$, while the $\pi^\pm$ cascade was basically unaffected. The Bethe-Heitler cascade was affected in a more subtle way, depending on the relative weight of the injection term with respect to the higher-order pair generations. A similar solution for the electromagnetic emission can thus be obtained by a small change in the parameter space. On the other

<table><caption>**Table 1.** Parameters used for the hadronic models.</caption><thead><tr><th></th><th>Proton-synchrotron</th><th>Lepto-hadronic</th></tr></thead><tbody><tr><td>δ</td><td>35 – 50</td><td>35 – 45</td></tr><tr><td>R [10<sup>16</sup> cm]</td><td>0.4 – 7.8</td><td>0.2 – 1.0</td></tr><tr><td>*τ<sub>obs</sub> [days]</td><td>0.06 – 1.0</td><td>0.02 – 0.15</td></tr><tr><td>B</td><td>0.8 – 12</td><td>0.2 – 0.9</td></tr><tr><td>*u<sub>B</sub> [erg cm<sup>-3</sup>]</td><td>0.03 – 6.2</td><td>1.7 × 10<sup>-3</sup> – 0.03</td></tr><tr><td>γ<sub>e,min</sub></td><td>500</td><td>500</td></tr><tr><td>γ<sub>e,break</sub></td><td>= γ<sub>e,min</sub></td><td>= γ<sub>e,max</sub></td></tr><tr><td>γ<sub>e,max</sub> [10<sup>4</sup>]</td><td>0.3 – 0.9</td><td>0.8 – 1.8</td></tr><tr><td>α<sub>e,1</sub> = α<sub>p,1</sub></td><td>2.0</td><td>2.0</td></tr><tr><td>α<sub>e,2</sub> = α<sub>p,2</sub></td><td>3.0</td><td>3.0</td></tr><tr><td>K<sub>e</sub> [cm<sup>-3</sup>]</td><td>6.3 – 9.2 × 10<sup>2</sup></td><td>1.4 × 10<sup>4</sup> – 2.6 × 10<sup>5</sup></td></tr><tr><td>*u<sub>e</sub> [10<sup>-5</sup> erg cm<sup>-3</sup>]</td><td>0.4 – 46</td><td>3.4 × 10<sup>-3</sup> – 47 × 10<sup>3</sup></td></tr><tr><td>γ<sub>p,min</sub></td><td>1</td><td>1</td></tr><tr><td>γ<sub>p,break</sub> [10<sup>9</sup>]</td><td>= γ<sub>p,max</sub></td><td>= γ<sub>p,max</sub></td></tr><tr><td>γ<sub>p,max</sub> [10<sup>9</sup>]</td><td>0.4 – 1.6</td><td>0.04 – 0.07</td></tr><tr><td>η</td><td>10 – 50</td><td>10</td></tr><tr><td>K<sub>p</sub> [cm<sup>-3</sup>]</td><td>36 – 8.4 × 10<sup>3</sup></td><td>2.0 × 10<sup>4</sup> – 3.5 × 10<sup>5</sup></td></tr><tr><td>*u<sub>p</sub> [erg cm<sup>-3</sup>]</td><td>1.1 – 240</td><td>550 – 9200</td></tr><tr><td>*u<sub>p</sub>/u<sub>B</sub></td><td>6.3 – 150</td><td>2.2 × 10<sup>5</sup> – 4.6 × 10<sup>5</sup></td></tr><tr><td>*L [10<sup>46</sup> erg s<sup>-1</sup>]</td><td>23 – 110</td><td>160 – 350</td></tr><tr><td>*ν<sub>EHE</sub> [yr<sup>-1</sup>]</td><td>7.3 × 10<sup>-3</sup> – 0.11</td><td>0.07 – 0.30</td></tr><tr><td>*ν<sub>EHE</sub> (0.183–4.3) PeV</td><td>1.9 × 10<sup>-4</sup> – 4.0 × 10<sup>-3</sup></td><td>0.006 – 0.044</td></tr><tr><td>[yr<sup>-1</sup>]</td><td>10<sup>-3</sup></td><td></td></tr><tr><td>*ν<sub>PS</sub> [yr<sup>-1</sup>]</td><td>0.016 – 0.25</td><td>0.19 – 0.93</td></tr></tbody></table>

The luminosity of the emitting region has been calculated as $L = 2\pi R^2 c\Gamma_{bulk}^2(u_B + u_e + u_p)$, where $\Gamma_{bulk} = \delta/2$, and $u_B$, $u_e$, and $u_p$, the energy densities of the magnetic field, the electrons, and the protons, respectively. The quantities flagged with a star (*) are derived quantities, and not model parameters. The full set of parameters is available as online material.

hand, the neutrino emission was systematically more luminous than its associated photon emission, everywhere in the parameter space.

We updated the models using the corrected version of the radiative code, assuming now $\tau_{ad} = R/c$ to simplify comparison with other models. This has the effect of reducing the maximum proton energy (for the same value of the magnetic field) by a factor of 2. The new set of best-fit parameters are given in Table 1, and the models

<footnote>* E-mail: matteo.cerruti@icc.ub.edu(MC); andreas.zech@obspm.fr (AZ)</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1** Updated models of TXS 0506+056 for the proton synchrotron (1a) and lepto-hadronic (1b) scenarios. Black points are data from IceCube Collaboration et al. (2018), while grey points are archival data. For each model, bold lines represent the total emission in photons (E < 100 TeV) and neutrinos (single flavour, E > 100 TeV); dashed lines the emission from pion cascades; dotted lines the emission from Bethe-Heitler cascades; dotted-dashed lines the proton synchrotron emission. Colours from red to blue represent increasing values of *R*.</figcaption></figure>

are shown in Fig. 1. Proton-synchrotron solutions are similar to the previously published ones, but have higher particle density and thus total luminosity. Neutrino rates are similar to the previous ones: while the integral neutrino rate is lower, the neutrino spectrum now peaks at lower energies, closer to where IceCube reaches

maximum sensitivity, and effectively results in a slight increase in the maximum neutrino rate for energies between 183 TeV and 4.3 PeV (from $1.7 \times 10^{-3}$ yr$^{-1}$ to $4.0 \times 10^{-3}$ yr$^{-1}$). For mixed lepto-hadronic solutions, the neutrino emission is lowered: the difference with respect to the proton-synchrotron solution is that the photon emission is constrained by the low-energy part of the Bethe-Heitler emission, which was basically unaffected. The maximum predicted neutrino rate in this scenario, for energies between 183 TeV and 4.3 PeV, is $0.044$ yr$^{-1}$, about a factor of 3 lower than before. The associated Poisson probability of detecting one muon neutrino during the high-state is then 2.2 per cent. On the other hand, the new solutions have a significant lower integral neutrino rate (maximum value of $0.93$ yr$^{-1}$ using the point-source effective area) which makes them more consistent with the non-detection of additional multi-PeV neutrinos from the source.

## ACKNOWLEDGEMENTS

The identification of the numerical errors was made possible thanks to an extensive comparison of blazar hadronic radiative codes. Preliminary results of this effort were presented at TeVPA 2019 and Neutrino 2020. We would like to thank all people involved in the project: Maria Petropoulou, Michael Kreter, Annika Rudolph, Foteini Oikonomou, Markus Böttcher, Stavros Dimitrakoudis, Shan Gao, Apostolos Mastichiadis, Kohta Murase, Anita Reimer, Gabriel Schmid, Xavier Rodrigues, Walter Winter. M. Cerruti has received financial support through the Postdoctoral Junior Leader Fellowship Programme from la Caixa Banking Foundation, grant n. LCF/BQ/LI18/11630012.

## REFERENCES

* Aharonian F. A., Atoian A. M., Nagapetian A. M., 1983, Astrophizika, 19, 323

* Cerruti M., Zech A., Boisson C., Emery G., Inoue S., Lenain J. P., 2019, MNRAS, 483, L12

* IceCube Collaboration et al., 2018, Science, 361, eaat1378

This paper has been typeset from a *TEX/LATex* file prepared by the author.