Spectral analysis of a parsec-scale jet in M 87: Observational constraint on the magnetic field strengths in the jet^⋆,⋆⋆

¹ Department of Astronomy, Yonsei University, Yonsei-ro 50, Seodaemun-gu, Seoul 03722, Republic of Korea
e-mail: hwro@yonsei.ac.kr
² Korea Astronomy & Space Science Institute, Daedeokdae-ro 776, Yuseong-gu, Daejeon 34055, Republic of Korea
³ National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
⁴ Kogakuin University of Technology & Engineering, Academic Support Center, 2665-1 Nakano, Hachioji, Tokyo 192-0015, Japan
⁵ University of Science and Technology, Gajeong-ro 217, Yuseong-gu, Daejeon 34113, Republic of Korea
⁶ Mizusawa VLBI Observatory, National Astronomical Observatory of Japan, 2-12 Hoshigaoka, Mizusawa, Oshu, Iwate 023-0861, Japan
⁷ Department of Astronomical Science, The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
⁸ Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building, AS/NTU No. 1, Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan, ROC
⁹ Department of Physics and Astronomy, Seoul National University, 1 Gwanak-ro Gwanak-gu, Seoul 08826, Republic of Korea
¹⁰ Department of General Science & Education, National Institute of Technology, Hachinohe College, 16-1 Tamonoki, Uwanotai, Hachinohe City, Aomori 039-1192, Japan
¹¹ Research Center for Intelligent Computing Platforms, Zhejiang Laboratory, Hangzhou 311100, PR China
¹² Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai 201210, PR China
¹³ Department of Physics and Astronomy, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea
¹⁴ Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8582, Japan
¹⁵ Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, PR China
¹⁶ SNU Astronomy Research Center (SNUARC), Seoul National University, 1 Gwanak-ro Gwanak-gu, Seoul 08826, Republic of Korea
¹⁷ Department of Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia
¹⁸ Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701, Republic of Korea
¹⁹ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
²⁰ Graduate School of Science, Osaka Metropolitan University, Osaka 599-8531, Japan
²¹ The Research Institute of Time Studies, Yamaguchi University, Yoshida 1677-1, Yamaguchi-city, Yamaguchi 753-8511, Japan
²² Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, Nanjing 210008, PR China
²³ Instituto de Astrofísica de Andalucía – CSIC, Glorieta de la Astronomía s/n, 18008 Granada, Spain
²⁴ Graduate School of Sciences and Technology for Innovation, Yamaguchi University, 1677-1 Yoshida, Yamaguchi, Yamaguchi 753-8511, Japan
²⁵ Joint Institute for VLBI ERIC, 7991 PD Dwingeloo, The Netherlands
²⁶ Tokyo Electron Technology Solutions Limited, Iwate 023-1101, Japan
²⁷ Massachusetts Institute of Technology Haystack Observatory, 99 Millstone Road, Westford, MA 01886, USA
²⁸ Black Hole Initiative at Harvard University, 20 Garden Street, Cambridge, MA 02138, USA
²⁹ Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi 830011, PR China
³⁰ Toyo University, 5-28-20 Hakusan, Bunkyo-ku, Tokyo 112-8606, Japan
³¹ Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata 950-2181, Japan
³² National Astronomical Research Institute of Thailand (Public Organization), 260 Moo 4, T. Donkaew, A. Maerim, Chiangmai 50180, Thailand
³³ Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
³⁴ Department of Physics, UNIST, Ulsan 44919, Republic of Korea
³⁵ Basic Science Research Institute, Chungbuk National University, Chungdae-ro 1, Seowon-Gu, Cheongju, Chungbuk 28644, Republic of Korea

Received: 17 December 2021
Accepted: 21 November 2022

Abstract

Context. Because of its proximity and the large size of its black hole, M 87 is one of the best targets for studying the launching mechanism of active galactic nucleus jets. Currently, magnetic fields are considered to be an essential factor in the launching and accelerating of the jet. However, current observational estimates of the magnetic field strength of the M 87 jet are limited to the innermost part of the jet (≲100 r_s) or to HST-1 (∼10⁵ r_s). No attempt has yet been made to measure the magnetic field strength in between.

Aims. We aim to infer the magnetic field strength of the M 87 jet out to a distance of several thousand r_s by tracking the distance-dependent changes in the synchrotron spectrum of the jet from high-resolution very long baseline interferometry observations.

Methods. In order to obtain high-quality spectral index maps, quasi-simultaneous observations at 22 and 43 GHz were conducted using the KVN and VERA Array (KaVA) and the Very Long Baseline Array (VLBA). We compared the spectral index distributions obtained from the observations with a model and placed limits on the magnetic field strengths as a function of distance.

Results. The overall spectral morphology is broadly consistent over the course of these observations. The observed synchrotron spectrum rapidly steepens from α_{22 − 43 GHz} ∼ −0.7 at ∼2 mas to α_{22 − 43 GHz} ∼ −2.5 at ∼6 mas. In the KaVA observations, the spectral index remains unchanged until ∼10 mas, but this trend is unclear in the VLBA observations. A spectral index model in which nonthermal electron injections inside the jet decrease with distance can adequately reproduce the observed trend. This suggests the magnetic field strength of the jet at a distance of 2−10 mas (∼900 r_s − ∼4500 r_s in the deprojected distance) has a range of B = (0.3−1.0 G)(z/2mas)^−0.73. Extrapolating to the Event Horizon Telescope scale yields consistent results, suggesting that the majority of the magnetic flux of the jet near the black hole is preserved out to ∼4500 r_s without significant dissipation.