한국정치 노트 Notes on the Politics of Korea


September 25 at 11:24 PM · 


누군가의 손에 나의 정신을 놓고 갈 수 있다는 건 행운이다. 이건 마치 염상섭의 '표본실의 청구리'에 등장하는 주인공 H가 상상하면서 '아름다운 여인이 자기 목을 졸라 죽인다면 그것도 참 행복' 이라는 것만큼.


Jesus cried out in a loud voice, "Father ! In your hands I place my spirit!" he said this and died. (김삼환 목사 번역 = 개똥밭에 굴러도 이승이 좋다, 너무 좋다)


Luke 23 The Death of Jesus


명성교회 김삼환 목사와 김하나 목사 부자는 예수를 정면으로 거부했다.


명성교회 김삼환 목사는 살아 생전에 아들에게 교회를 상속해줬다. '성경'에는 아름다운 문장들이 많이 있는데, 그 중에 이런 구절이 있다. 예수가 큰 목소리로 울부짖었다. "아버지 나는 나의 정신을 당신 손에 놓습니다" 예수는 이렇게 말하고 나서 죽었다.




예수는 '정신'을 놓고 다음 세계로 가라고 했는데, 명성교회 김삼환 목사는 '교회' 부동산을 자기 아들에게 물려줬다. 게다가 살아생전에..




종교야 많은 사람들의 희로애락이 담긴 이야기들이고, 그 형태들은 달라도, "개똥밭에 굴러도 이승이 좋다"라는 우리 말처럼, 이 유한한 인간 삶을 꿰뚫는 통찰을 보여준다.




난 기독교인은 아니지만, 성경은 '아름다운 문학'으로 간주하고 읽어보는데, 명문들이 수두룩하다. 예수 멋쟁이~







관련기사:


https://www.youtube.com/watch?v=LSNFeRV-v7U



CBS 뉴스] '세습반대' 명성 교인들 분노..."이제는 교회를 떠나야 하나.."


65,750 views•Sep 27, 2019




[CBS 뉴스]  '세습반대' 명성 교인들 분노..."이제는 교회를 떠나야 하나.."


명성교회 문제 해결을 위한 수습안이 교단에서 통과되면서, 사실상 명성교회의 세습을 허용했다는 비판이 잇따르고 있다. 무너진 한국교회의 신뢰를 쌓겠다던 교단 새 임원들의 기대와 달리, 교회와 사회의 더 큰 불신과 비판을 불러오는 것은 아닌지 우려된다.


◇ ‘세습 반대’ 명성교회 교인들 분노 “이제 교회 떠나야하나..”




“제 살을 도려내는 외과수술을 하듯이 법을 어긴 명성교회를 바르게 처리했다면, 그동안 비판해온 사회에서도 ‘아 한국교회가 아직 살아있구나’ 이렇게 생각하지 않았을까요. 그런데 이런 모습을 보였으니 이제 누가 한국교회를 믿을 수 있겠어요. 게다가 예장통합이라는 장자교단이에서 그것도 교회 지도자들이 모여서 이런 결과를 내놓았다는데 참으로 통탄할 일입니다.”




예장통합총회가 ‘명성교회 수습안’을 발표한 지난 26일, 명성교회에 출석하는 한 교인의 말이다. 대화의 말미에 그는 이같이 덧붙였다.


“이제는 교회를 떠나야겠다는 생각이 많이 들더라고요.”


세습을 반대하는 명성교회 교인들은 분노했다. 명성교회정상화위원회는 성명을 통해 “법적 근거도 없고, 내부 조항간 서로 충돌되는 이 수습안은 존재 자체가 모순이며, 향후 교단에 혼란만 초래할 것”이라고 밝혔다.


이들은 왜 명성교회만 세습해도 되느냐 되물었다. “힘있고 돈있는 교회는 교단헌법도 초월한다는 극단적 우상숭배의 추악한 행위”고 밖에 이 사태를 설명할 수 없다는 거다.


교인들은 법적 소송도 거론했다. “총대들에게는 소송 등 이의제기를 할 수 없게 해놨지만 교인들에게는 무용지물”이라면서, “이번 수습안에 법적 효력이 없음을 빠른 시일내에 사회법을 통해 이의제기 하겠다”는 입장이다.


특히 우려하는 것은 2021년 1월 1일 교회가 김하나 목사를 재청빙할 때다. “공동의회를 하지 않고 담임을 세우려고 시도하는 명백한 교인의 권리침해 행위가 발생할 경우에는 사회법에 소를 제기할 것”이라고 밝혔다.




◇ “사실상 세습 허용...교단헌법에 위배”


목회세습에 반대해온 여러 단체들 역시 ‘명성교회 수습안’은 교단헌법을 위배한 것이라며 비판의 목소리를 높였다.


교회세습반대운동연대는 이번 예장통합 정기총회는 명성교회의 불법세습사건을 매듭지을 수 있는 좋은 기회였지만, 오히려 총회가 명성교회의 불법세습을 묵인하고 교회들이 세습할 수 있는 방법을 알려줬다고 비판했다.


보여주는 화해에 집착하고 대형교회는 살려줘야 한다는 어리석은 마음이 초래한 결과라는 거다.


기독법률가회도 성명을 통해 명성교회의 세습을 용인한 이번 결정은 교단의 헌법은 물론 세상의 상식도 무시하는 결정이라면서, 재심판결 이후 한국교회에 남은 희망의 불씨를 짓이겨 꺼버리는 결정에 비통함을 금할 수 없다고 밝혔다.


신학교 학생들과 교수들의 성토도 이어졌다. 장신대 학생들은 연대성명에서 수습위원 구성에서부터 제시된 수습안의 내용, 토론 없는 표결 등 모든 과정이 공정했는가를 물으며, 총회의 이번결정에 동의할 수 없다고 밝혔다.




장신대 교수들도 세습문제는 타협이나 수습이 아닌 교회의 거룩성과 하나님의 공의를 세우는 일이라면서 세습 찬반세력을 화해와 중재하는 방식으로 접근한 것은 초헌법적 오류라고 지적했다.


교계원로들은 신사참배의 부끄러운 결의가 또 다시 가결됐다며 안타까운 심정을 토로했다.




김동호 목사는 자신의 SNS를 통해 교회를 지키기 위해서라는 변명으로 교단이 정한 법을 어기기로 결정했다며,지워지지 않는 역사의 또 다른 큰 수치가 될 것이라고 말했다.




이수영 목사도 신사참배 결의 이후 가장 수치스런 일이라면서 이 교단에 소속된 목사라는 것이 부끄럽고 참담하다고 밝혔다.


정기총회 시작부터 교회의 신뢰회복을 강조한 예장통합총회.


김태영 총회장은 지난 23일 정기총회 개회예배에서 “사회에서 이름값을 하고 건재할 수 있는 자본은 은금과 지식이 아니라 신뢰이다. 지금 우리 한국교회는 그 무엇보다도 사회적인 신뢰를 회복하는 것이 당면 과제다“라고 말했다.


명성교회 수습안을 발표할 때에도 “더 이상 부정적인 뉴스가 생산되지 않도록 하자. 한국교회가 어디까지 내려가야 정신차리겠나”라며 교단 안의 갈등을 정리함으로써, 사회적 비판에서 벗어나보겠다는 의지를 내비쳤다.


그러나 교계는 물론 사회적 여론은 '사실상 세습을 허용했다'는 반응을 연이어 내놓고 있다. 이번 ‘명성교회 수습안’이 신임 총회장의 기대처럼 진정 사회적 신뢰회복을 위한 조치인지 다시 생각하게 한다.





Comment +0

관련 글: - 조국 파동 국면에서 제일 실망했던 신문이 한겨레였다. 1988년 8월 "셋방살이 서러움을 아십니까" 변형윤 컬럼은 한겨레 1면에 실렸다. 30년 후 한국은 1인 가구가 전 세계에서 가장 빠르게 증가한 나라가 되었다. '독신자용' 아파트 제안은 구체적이고 신선했다. (물론 나야 아파트를 더 이상 짓지 말자는 입장이지만)


한겨레 신문에 실망한 이유는, 불평등 불공정 계급 등 수많은 주제들이 터져나온 '조국 파동 주제들'에 대해서, 데스크의 '시선'이 1988년 변형윤 컬럼처럼 '셋방살이자'들에 가 있는 게 아니라, '청와대 안테나'였기 때문이다.


- 조국 파동 논란 와중에도, 지하철 선로 광케이블 작업하던 44세 전문노동자가 죽었고, 삼성 하청 전기공이 추락사로 죽었다. 김용균법은 아직 불완전하고, 현장에서 이 혜택을 볼 수 있는 노동자 숫자는 많지 않다.


- 개혁주의자. 개혁. 개혁은 오고 있는 것일까? '빅' 전략가들의 눈에는 누가 되고 안되고가 '결정적인 한방'이겠지만, 수많은 개미 일꾼들은 철로 위에서, 전기사고로 죽어가고 있다.



출처: https://futureplan.tistory.com/entry/조국-논란-한겨레-신문-창간정신-실종했다-1988년-변형윤-컬럼과-대조적 [한국정치 노트 Notes on the Politics of Korea]

4 hrs · 


-이번 조국 파동에서 가장 기대에 못미치는 신문이 바로 한겨레 신문이었다. 조선일보와 다른 컨셉이 부족했다. 조국 파동이 주고 있는 정치적 과제, 사회문화 교육적 개혁과제, 법과 자본이 유착한 현실 타파, 절대적 상대적 빈곤과 박탈감에 빠진 자들에 대한 대안 등에 대한 날카로운 신문기사들이 적었다.


어정쩡한 조국 옹호를 한 한겨레 tv 방송 등, 신문사내 '집권세력'은 반성해야 한다. 88년 창간주주들을 다시 뒤돌아볼 때이다. 분발을 기대한다.


- 오늘자 한겨레 1면은 넌센스다. 자멸이다. 문재인 정부의 피해자 코스프레인가? 문재인 대통령이 권력을 쥐고 있고, 윤석열 검찰총장을 임명한 권력자가 2개월도 채 안되어 윤석열에게 공격당하고 있다는 것인가? 상명하달을 하라는 게 아니라, 정치적 민주적 소통을 해야 한다. 개혁도 '손발'이 맞아야 한다.


- 청와대, 이낙연, 박상기 장관 등은 관중들 야유에 평정심을 잃은 에이스 투수가 되었다. 일을 시키는 사람들이 현장에서 일하고 있는 사람들과 삿대질 하면서 싸우는 형국이 과연 제대로 되었다고 볼 수 있는가?


- 현행법 상, 문재인 대통령은 4천 990만이 반대해도, 조국 후보자를 장관에 임명할 권한이 있다. 문통의 판단 기준들이 문제이고, 이후 정치적 책임을 지면 될 일이다. 그 결과는 아무도 모른다.


-문제는 왜 경제 영역 뿐만 아니라(사모펀드 관련), 사회 문화 교육 영역까지 불평등 DNA를 언급하면서 온 나라가 쑥대밭이 되었는가, 밑바닥 여론이다.






Comment +4

  • 이뿐곰 2019.10.06 13:51

    저는동의할 수 없네요 살아있는 권력이라구요? 진정 살아있는 권력은 검찰 아닌가요? 똑똑하다는 검사들이 본질을 보지 못하는 건가요 아님 안보는건가요? 공부는 잘했을지 몰라도 성찰능력은 빵점이죠~그리고 언론이 할일을 제대로 해야죠 조국취재도 엉망으로 해놓고~한겨레 잘못은 그런겁니다~

    • 검찰 개혁도 반드시 해야죠.

      한겨레 신문이 조국 논란 국면에서 이슈가 된 교육-신분차별 사회, 불평등 구조에 대해서 그 연결지점을 심층보도 하지 못했다. 이게 제 글 요지입니다.

  • 개나소나 2019.10.11 02:35

    뉴스쓰고 돌대가미들 지생각은 일기장에 써라 이런글 보는갓도 재앙이다

  • 홍두깨 2019.10.11 04:05

    요즘같이 어수선한
    시기에
    국민에게 보탬도 안되는
    난필 기사는
    그만둬라
    심심하면 자거라

이용마 기자는 100세 시대에 50살 일기로 생을 마쳐야했다. 그를 앗아간 복막암이 무엇일까? 그 병의 원인은 생물학적 원인인가, 아니면 이명박 정부 하에서 벌어진 언론 탄압, 부당 해고에서 오는 것이었는가? 복잡한 생각이 든다.


그가 암투병을 하면서 쓴 책을 여기에서 구할 수 없어, 온라인 서점에 소개된 부분만을 읽어본다.

복막암 초기에만 발견했어도 생존율이 70~80%였을 터인데, 안타깝게도 말기에 발견되었다. 









출처: 책 제목: 세상은 바꿀 수 있습니다 - 지금까지 MBC 뉴스 이용마입니다.







출처: http://bit.ly/2Ns82C1


이용마 기자 끝내 별세…복막암은 어떤 암일까?


김용 기자 수정 2019년 8월 21일 10:13


[MBC 캡처]

복막암 투병 중이던 이용마 MBC 기자가 21일 오전 별세했다. 향년 50세. 최근 병세가 악화됐던 이용마 기자는 이날 오전 서울아산병원에서 세상을 떠났다.

이용마 기자는 지난 2012년 공정방송을 요구하며 170일간의 파업을 주도했다는 이유로 해고됐다. 이후 해고 무효확인 소송 1,2심에서 잇따라 승소한데 이어 2017년 12월 해직자 전원 복직 합의에 따라 5년여 만에 MBC로 복귀했다.


고인이 마지막까지 싸웠던 복막암은 다소 생소한 암이다.

 2018년 12월 중앙암등록본부의 자료에 의하면 복막암은 402건 발생한 희귀 암에 속한다.  2016년 22만 9180건의 전체 암 가운데 0.2%를 차지했다. 남자가 138건, 여자는 264건 발생했고 연령대 환자는 60대가 22.4%로 가장 많았다. 이어 50대 22.1%, 70대 19.7%의 순이었다.


간단히 얘기해 복막암은 복부 내장을 싸고 있는 막인 복막에 생긴 암이다.  복막은 소화관의 대부분과 간·췌장·비장·신장·부신 등이 들어 있는 복강을 둘러싸고 있다.  복강 내 장기를 보호하는 기능을 하며, 윤활액을 분비해 복강내 장기가 유착되지 않도록 한다. 특히 소장 및 대장이 서로 엉기지 않고 연동운동을 통해 소화기능을 할 수 있게 한다.


복막암 초기에는 특별한 증상이 없어 조기 발견을 어렵게 한다. 일반적 증상은 복부팽만, 가스가 찬 느낌, 더부룩한 느낌, 쥐어짜는 듯한 느낌이 있을 수 있다. 

구역, 구토, 설사와 변비, 식욕 저하, 식사 후 팽만감, 특별한 이유 없이 체중이 감소하거나 증가할 수 있다. 일반적으로 복막암 1,2기의 생존율은 70~90%, 3,4기 진행성 복막암은 15~45% 정도이다.


위암이나 대장암은 정기적인 내시경 검사로 일찍 발견할 수 있으나 복막암은 현재 특별히 권장되고 있는 조기 검진법이 없다. 


여성의 경우 가족력에 따라 질초음파와 종양표지자(CA-125) 검사를 시행할 수도 있는데, 의료진과 상의해야 한다. 복막암의 위험요인도 정확히 알려져 있지 않다. 


여성의 경우 난소암 발생과 비슷해 배란, 유전 요인, BRCA1 또는 BRCA2 유전자의 돌연변이 등이 거론된다.



김용 기자 ecok@kormedi.com

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[이용마 기자의 언론관]



이용마 기자는 언론의 사명을 '다수의 목수리를 반영해서 억울한 사람들이 나오지 않는 사회'를 만드는 것이라고 했다.

형식적인 권력 견제나 정치적 균형 보도에 그치지 않고, 그것에 만족하지 않고, 적극적인 의미에서 사회정의를 실천하려고 했다.


[이용마 기자를 추모하며]


그의 언론자유 운동, 그리고 어렵게 사는 사람들과 연대정신을 잊지 않겠습니다.

이용마 기자와 트위터, 페이스북에서 나눈 대화와 토론, 그의 진지함을 잊지 않겠습니다.

한창 일할 나이에 희귀한 암, 복막암을 만나버린 그 기막힌 운명을 받아 들여야 했던 그 고뇌 또한 잊지 않겠습니다.

살아 남은 자들에 대한 애정 때문에 가다가 또 돌아서는 님의 모습은 영원히 남을 것입니다.









[이용마 기자 추모식 ]










암투병 간호했던 가족 이야기, 암과 이용마 











팔순 노모, 마누라, 쌍둥이.." 이용마 기자가 눈 감기 전 남긴 말

문지연 기자 입력 2019.08.21. 09:07 수정 2019.08.21. 09:09 댓글 6개




이용마 기자. 연합뉴스


012년 MBC 파업을 주도했다는 이유로 해고된 후 암 투병하던 이용마 기자가 21일 별세했다. 향년 50세.


21일 전국언론노동조합에 따르면 이 기자는 이날 오전 서울아산병원에서 세상을 떠났다.


 최근 그는 복막암 병세가 악화해 치료를 거의 중단한 상태였다.


언론노조 MBC 본부는 같은 날 “곧 회사에서 유족들과 의논해 (빈소 등) 공식자료를 내겠다”며 “삼가 고인의 명복을 빈다”고 밝혔다.




이용마 기자 페이스북




이 기자의 친형 용학씨는 이 기자의 페이스북 계정에 글을 올려 이 같은 소식을 전했다. 


그는 “잘난 동생이 먼저 앞서서 갔다”며 “그 먼 곳을 왜 혼자 떠나는지 모르겠다. 죽도록 아픈 고통이 아니고 죽어야만 하는 고통을 받아들였다”고 썼다.


이어 “팔순 노모 눈에 가시가 돼 감을 수 없다면서, 다음 생에도 똑같은 마누라 데리고 살고 싶다면서, 아직 필 날이 너무 많이 남은 쌍둥이들 눈에 밟혀 가기 싫다면서 멀리 떠났다”며 “아직 가족들에게, 회사, 사회, 나라에 할 일이 너무 많이 남았고 만들어야 할 일이 너무 많은데 갔다”고 말했다.



이 기자는 2017년 펴낸 저서 ‘세상은 바꿀 수 있습니다’에서 두 아들에게 편지 형식의 글을 남기기도 했다. 


그는 “나의 꿈을 기억해주기 바란다. 너희들이 앞으로 무엇을 하든 우리는 공동체를 떠나 살 수 없다”며 “그 공동체를 아름답게 만드는 것, 그 꿈이 이루어지는 순간 나의 인생도 의미가 있었다고 말할 수 있을 것이다”라고 했다.


MBC는 2012년 공정방송을 요구하며 170일간의 파업을 주도했다는 이유로 이 기자 등 6명을 해고했었다. 여기에는 당시 MBC PD였던 최승호 MBC 사장도 포함돼 있다.


당시 MBC 노조는 이에 반발해 사측을 상대로 해직자 6인의 해고 무효 확인 소송을 제기했고, 1심과 2심에서 모두 승소했다. 이후 2017년 12월 취임한 최 사장은 MBC 노조와 해직자 전원 복직에 합의했다. 이 기자를 비롯한 해직 언론인들은 약 5년 만에 MBC로 복귀했다.


문지연 기자 jymoon@kmib.co.kr



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블랙홀 이미지를 얻는 과정에 대해서 잘 모르겠지만 아래와 같이 여러가지 단계를 거쳤다고 한다.

 

EHT Array - Data Modules (5 petabytes) - Correlation ( 1000분의 1) - Fringe Fitting (1만 분의 1) - Imaging (1000분의 1) - 최종 이미지 출력


최초 블랙홀 사진을 찍은 '대 기획'에는 20개 국가에서 200명의 과학자들과 60개 연구소가 참여했다고 한다.


아래 사진들은 동영상에 나온 국가 과학 재단 (National Science Foundation) 기자회견이다. 기자회견을 들으면서 든 생각. 


한국 과학자도 몇 명 참여했다고 한다. 그런 생각이 스치고 지나간다. 한국에서 입시와 관련된 사교육비를 다 모아서, M 87 은하계 블랙홀의 전파를 감지한 천체 망원경 개발비로 쓴다면 얼마나 좋을까?


200여명의 물리, 천문학, 컴퓨터 과학자들보다 한국 학생들이 더 나을 수도 있는데, 그런 생각을 했다. 왜 우리는 이런 기초적인 물리학자들을 키워내지 못할까? 




https://www.youtube.com/watch?time_continue=16&v=lnJi0Jy692w






























































블랙홀 이미지를 얻는 과정 

EHT Array - Data Modules (5 petabytes) - Correlation ( 1000분의 1) - Fringe Fitting (1만 분의 1) - Imaging (1000분의 1) - 최종 이미지 출력







































































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  • 인류최초 블랙홀 관측…한국인 연구진 8명도 있었다
    정태현 연구원 "200명 모두 논문 저자로 이름 올려"
    조일제 연구원 "첫 이미지 얻었을 때 환희 감동"
    (서울=뉴스1) 최소망 기자 | 2019-04-11 16:16 송고 | 2019-04-11 21:42 최종수정

    실종아동 찾기 더보기
    김민수 (남자) 2019년 01월 26일 발생
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    김재영 연구원(독일막스플랑크 전파연구소)이 11일 오전 서울 중구 LW컨벤션센터에서 열린 'EHT 프로젝트 연구 결과 발표에 따른 언론설명회'에서 인류 역사상 최초로 관측된 처녀자리 은하 중심의 M87 블랙홀 사진에 대해 설명하고 있다. 2019.4.11/뉴스1 © News1 오대일 기자
    인류 역사상 최초로 '블랙홀'(black hole)을 관측하기까지 세계 200여명의 연구진들이 피와 땀을 쏟았다. 그중에서도 이번 연구에 기여한 한국인 연구진 8명이 주목받고 있다.

    실제 한국기관 소속으로 힘쓴 외국인 연구자 2명까지 포함하면 총 10명이다. 이들은 심지어 남극까지가서 관측 데이터를 얻거나 또 각자의 자리에서 전파 망원경의 데이터를 분석하기도 하면서 여러 어려움을 딛고 눈부신 성과를 거뒀다.


    이벤트호라이즌망원경(EHT·Event Horizon Telescope·사건지평선망원경) 연구진은 지난 10일 세계 전파망원경 8개로 구성된 가상망원경 'EHT'를 통해 처녀자리 은하단 중심부에 있는 'M87' 거대은하 속 '초대질량 블랙홀'을 관측하는데 성공했다. 빛조차 탈출할 수 없을 정도로 빨아들이는 중력이 강해 이론으로만 존재하던 블랙홀을 직접 관측한 것은 인류 역사상 처음이다.

    EHT 프로젝트는 전 세계에 산재한 전파망원경 8개를 연결해 지구 크기의 가상 망원경을 만들어 블랙홀의 영상을 포착하는 국제협력 프로젝트다. 이로써 이전에 없던 높은 민감도와 분해능을 가진 지구 규모의 가상 망원경을 만들었다.

    초대형 우주연구를 위해 전세계 13개 기관, 200여명의 연구진이 협력했다. 그중 한국 연구진도 포함됐는데, 한국천문연구원, 서울대학교, 연세대학교, 과학기술연합대학원대학교(UST) 등 4개 기관이 연구에 참여했다.

    연구진은 김종수·변도영·손봉원·이상성·정태현 천문연 연구원, 조일제 천문연 UST 연구원, 김재영 독일 막스플랑크 전파연구소 박사, 김준한 미국 애리조나대 교수 등 8명이며, 중국인 광야오자오(Guangyao Zhao) 한국천문연구원 박사후연구원과 독일인 사샤 트리페(Sascha Trippe) 서울대 물리천문학부 교수도 한국기관 소속으로 온힘을 다했다.

    정태현 한국천문연구원 선임연구원은 "이번 연구성과는 미국 천체물리학저널 레터스 특별판에 6편의 논문으로 발표됐고, 여기에는 200여명이 저자로 모두 이름을 올렸다"면서 "그중 누구 하나라도 빠졌더라면 이러한 연구는 없었을 것"이라고 강조했다.

    우리나라가 이번에 연구에 기여한 방식은 동아시아관측소(EAO) 산하 JCMT와 ALMA의 협력 구성원으로서다.

    이번 연구를 위해 지구 크기 가상 망원경에 동원된 전세계 8개 망원경은 △아타카마 밀리미터/서브밀리미터 전파간섭계(ALMA) △아타카마 패스파인더(APEX) △유럽 국제전파천문학연구소(IRAM) 30m 망원경 △제임스 클러크 맥스웰 망원경(JCMT) △대형 밀리미터 망원경(LMT) △서브밀리미터 집합체(SMA) △서브밀리미터 망원경(SMT) △남극 망원경(SPT)이다.

    또 한국이 운영하고 있는 한국우주전파관측망(KVN)과 동아시아우주전파관측망(EAVN)도 이번 연구에 기여했다.


    © News1 최수아 디자이너
    보통 망원경은 최대한 인공빛이나 전파의 영향을 받지 않고 천체 관측에 유리하도록 해발고도가 높은 곳에 위치한다. 지상에서의 인공적인 전파가 없는 곳에 망원경을 설치해 온전하게 우주에서 쏟아지는 전파를 받기 위함이다. 또 천체를 관측하기 위해서는 8개 망원경이 위치한 곳의 날씨가 모두 맑아야만 한다.

    이렇다 보니 연구 과정도 고됐다. 김태현 연구원은 "망원경은 보통 고도가 높은 곳에 위치하며, 날씨에 대한 민감도도 높아 항상 긴장을 하면서 관측해야 하는 게 어려운 점"이라면서 "한번 관측할 때 많은 인력과 시간 등이 소요돼 최적의 관측 날짜를 잡기 위한 노력에 공을 들이는 게 쉽지 않다"고 말했다.

    실질적으로 관측데이터를 얻고 분석했던 조일제 천문연 UST 연구원은 데이터 분석에 있어서의 어려움을 토로했다. 조 연구원은 "각 지역에서 얻어진 망원경 데이터의 신뢰성을 높이기 위한 작업이 쉽지 않았다"면서 "이미 망원경에서 얻어진 데이터를 중앙처리센터(슈퍼컴퓨터)에 보내 받은 후 데이터 오류와 불확실성을 제거하는 부분이 어려웠다"고 꼽았다.

    조 연구원은 영상화를 하는 작업에서 첫 블랙홀을 봤던 인물이기도 하다. 그는 지난 2017년 7월24일 미국 보스턴에서 EHT 연구진이 워크숍을 하며 처음으로 블랙홀 이미지를 봤을 때의 벅찬 환희와 감동을 잊을 수 없다고 말했다.

    조 연구원은 "첫 이미지를 봤을 때 가슴이 두근거리고 손이 환희로 떨렸다"면서 "그 이후로 조금씩 보정작업을 거쳐서 현재의 그림이 만들어졌지만, 정말 잊을 수 없는 순간이었다"고 회상했다.

    김준한 애리조나대 교수는 남극 SPT를 수차례 왔다갔다 하며 연구를 진행했다. 김 교수는 "2017년도에 남극 기상상황으로 비행기가 뜨고 내리지 못하는 경우도 있었고, 지난해도 4차례 정도 남극에 다녀왔다"며 망원경 8개가 다 다른 시스템으로 세팅이 돼있어 이를 하나로 맞추는 데도 쉽지 않았다"고 말했다.

    이처럼 한국 연구자들이 첫 블랙홀 관측에 기여함으로써 앞으로 우리나라의 물리천문계 활성화도 기대가 된다.

    손봉원 천문연 박사는 "이번 결과는 아인슈타인의 일반상대성이론에 대한 궁극적인 증명이며, 그간 가정했던 블랙홀을 실제 관측해 연구하는 시대가 도래했음을 의미한다"면서 "앞으로 EHT의 관측에 한국의 기여도는 더욱 높아질 것" 이라고 전했다.

    이번 연구 성과의 힘은 무엇보다 협력에 있었다는 게 모든 연구진들의 공통된 의견이다. 쉐퍼드 도엘레만 EHT 프로젝트 총괄 단장(하버드 스미스소니안 천체물리센터 박사)은 "우리는 인류에게 최초로 블랙홀의 모습을 보여주고 있다"면서 "이 결과는 천문학 역사상 매우 중요한 발견이며, 200명이 넘는 과학자들의 협력으로 이뤄진 이례적인 과학적인 성과"라고 언급했다.


    블랙홀 연구진(광야오자오 박사후연구원, 정태현 천문연 연구원, 조일제 천문연 UST 학생, 김재영 독일 막스플랑크 전파연구소 박사)© 뉴스1



‘사건 지평면 망원경’이 타원형 은하계 M87의 중심부 촘촘한 radio source 지도를 완성했다. 


주파수 1.3 밀리 미터. 선례가 없을 정도 식별 능력이 있는 해상도 (angular resolution).


 2017 ETH 데이터에 나타난 비대칭 고리의 물리학적 의미가 무엇인가? 이를 위해 대규모 라이브러리 모델을 세웠다. 

이 모델의 기초는 일반적 상대적 자기유체역학 (GRMHD :general relativistic magnetohydrodynamic) 시뮬레이션과 일반 상대 광선 추적 방법으로 생산한 종합적 이미지이다. 


우리는 관찰 가시성과 이 라이브러리를 비교하고 다음을 확신하게 되었다. 블랙홀 사건 지평면 근처에 있는 뜨거운 플라즈마 궤도로부터 싱크로트론(synchrotron) 방출 때문에 생긴 강한 중력 효과 예측과 그 비대칭 고리가 서로 일치한다. 


고리 반경과 고리 비대칭은 블랙홀 물질과 회전에 의존한다. 


전반적으로 관찰된 이미지는 일반 상대성에 근거해 예측되었던 ‘회전 커 Kerr’ 블랙홀의 그림자에 대한 예상과 일치한다. 

만약 블랙홀 회전과 대규모 M87 제트가 일직선상에 있으면, 블랙홀 회전 진로는 지구로부터 멀어져 간다.



(발표문 요약 앞부분 번역)



블랙홀 black hole 관찰 사진 발표 논문:






https://iopscience.iop.org/article/10.3847/2041-8213/ab0f43




First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring




Published 2019 April 10 • © 2019. The American Astronomical Society.




 
Focus on the First Event Horizon Telescope Results





Abstract



The Event Horizon Telescope (EHT) has mapped the central compact radio source of the elliptical galaxy M87 at 1.3 mm with unprecedented angular resolution. 

Here we consider the physical implications of the asymmetric ring seen in the 2017 EHT data.


 To this end, we construct a large library of models based on general relativistic magnetohydrodynamic (GRMHD) simulations and synthetic images produced by general relativistic ray tracing. 

We compare the observed visibilities with this library and confirm that the asymmetric ring is consistent with earlier predictions of strong gravitational lensing of synchrotron emission from a hot plasma orbiting near the black hole event horizon. 


The ring radius and ring asymmetry depend on black hole mass and spin, respectively, and both are therefore expected to be stable when observed in future EHT campaigns. 

Overall, the observed image is consistent with expectations for the shadow of a spinning Kerr black hole as predicted by general relativity.

 If the black hole spin and M87's large scale jet are aligned, then the black hole spin vector is pointed away from Earth.

 Models in our library of non-spinning black holes are inconsistent with the observations as they do not produce sufficiently powerful jets.

 At the same time, in those models that produce a sufficiently powerful jet, the latter is powered by extraction of black hole spin energy through mechanisms akin to the Blandford-Znajek process. 

We briefly consider alternatives to a black hole for the central compact object. Analysis of existing EHT polarization data and data taken simultaneously at other wavelengths will soon enable new tests of the GRMHD models, as will future EHT campaigns at 230 and 345 GHz.

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1. Introduction

In 1918 the galaxy Messier 87 (M87) was observed by Curtis and found to have "a curious straight ray ... apparently connected with the nucleus by a thin line of matter" (Curtis 1918, p. 31). Curtis's ray is now known to be a jet, extending from sub-pc to several kpc scales, and can be observed across the electromagnetic spectrum, from the radio through γ-rays. Very long baseline interferometry (VLBI) observations that zoom in on the nucleus, probing progressively smaller angular scales at progressively higher frequencies up to 86 GHz by the Global mm-VLBI Array (GMVA; e.g., Hada et al. 2016; Boccardi et al. 2017; Kim et al. 2018; Walker et al. 2018), have revealed that the jet emerges from a central core. Models of the stellar velocity distribution imply a mass for the central core $M\approx 6.2\times {10}^{9}\,{M}_{\odot }$ at a distance of $16.9\,\mathrm{Mpc}$ (Gebhardt et al. 2011); models of arcsecond-scale emission lines from ionized gas imply a mass that is lower by about a factor of two (Walsh et al. 2013).

The conventional model for the central object in M87 is a black hole surrounded by a geometrically thick, optically thin, disk accretion flow (e.g., Ichimaru 1977; Rees et al. 1982; Narayan & Yi 19941995; Reynolds et al. 1996). The radiative power of the accretion flow ultimately derives from the gravitational binding energy of the inflowing plasma. There is no consensus model for jet launching, but the two main scenarios are that the jet is a magnetically dominated flow that is ultimately powered by tapping the rotational energy of the black hole (Blandford & Znajek 1977) and that the jet is a magnetically collimated wind from the surrounding accretion disk (Blandford & Payne 1982; Lynden-Bell 2006).

VLBI observations of M87 at frequencies $\gtrsim 230\,\mathrm{GHz}$ with the Event Horizon Telescope (EHT) can resolve angular scales of tens of $\mu \mathrm{as}$, comparable to the scale of the event horizon (Doeleman et al. 2012; Akiyama et al. 2015; EHT Collaboration et al. 2019a2019b2019c, hereafter Paper III, and III). They therefore have the power to probe the nature of the central object and to test models for jet launching. In addition, EHT observations can constrain the key physical parameters of the system, including the black hole mass and spin, accretion rate, and magnetic flux trapped by accreting plasma in the black hole.

In this Letter we adopt the working hypothesis that the central object is a black hole described by the Kerr metric, with mass $M$ and dimensionless spin ${a}_{* }$$-1\lt {a}_{* }\lt 1$. Here ${a}_{* }\equiv {Jc}/{{GM}}^{2}$, where JG, and care, respectively, the black hole angular momentum, gravitational constant, and speed of light. In our convention ${a}_{* }\lt 0$ implies that the angular momentum of the accretion flow and that of the black hole are anti-aligned. Using general relativistic magnetohydrodynamic (GRMHD) models for the accretion flow and synthetic images of these simulations produced by general relativistic radiative transfer calculations, we test whether or not the results of the 2017 EHT observing campaign (hereafter EHT2017) are consistent with the black hole hypothesis.

This Letter is organized as follows. In Section 2 we review salient features of the observations and provide order-of-magnitude estimates for the physical conditions in the source. In Section 3 we describe the numerical models. In Section 4 we outline our procedure for comparing the models to the data in a way that accounts for model variability. In Section 5 we show that many of the models cannot be rejected based on EHT data alone. In Section 6 we combine EHT data with other constraints on the radiative efficiency, X-ray luminosity, and jet power and show that the latter constraint eliminates all ${a}_{* }=0$ models. In Section 7 we discuss limitations of our models and also briefly discuss alternatives to Kerr black hole models. In Section 8 we summarize our results and discuss how further analysis of existing EHT data, future EHT data, and multiwavelength companion observations will sharpen constraints on the models.

2. Review and Estimates

In EHT Collaboration et al. (2019d; hereafter Paper IV) we present images generated from EHT2017 data (for details on the array, 2017 observing campaign, correlation, and calibration, see Paper II and Paper III). A representative image is reproduced in the left panel of Figure 1.




Figure 1. Left panel: an EHT2017 image of M87 from Paper IV of this series (see their Figure 15). Middle panel: a simulated image based on a GRMHD model. Right panel: the model image convolved with a $20\,\mu \mathrm{as}$ FWHM Gaussian beam. Although the most evident features of the model and data are similar, fine features in the model are not resolved by EHT.

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Four features of the image in the left panel of Figure 1 play an important role in our analysis: (1) the ring-like geometry, (2) the peak brightness temperature, (3) the total flux density, and (4) the asymmetry of the ring. We now consider each in turn.

(1) The compact source shows a bright ring with a central dark area without significant extended components. This bears a remarkable similarity to the long-predicted structure for optically thin emission from a hot plasma surrounding a black hole (Falcke et al. 2000). The central hole surrounded by a bright ring arises because of strong gravitational lensing (e.g., Hilbert 1917; von Laue 1921; Bardeen 1973; Luminet 1979). The so-called "photon ring" corresponds to lines of sight that pass close to (unstable) photon orbits (see Teo 2003), linger near the photon orbit, and therefore have a long path length through the emitting plasma. These lines of sight will appear comparatively bright if the emitting plasma is optically thin. The central flux depression is the so-called black hole "shadow" (Falcke et al. 2000), and corresponds to lines of sight that terminate on the event horizon. The shadow could be seen in contrast to surrounding emission from the accretion flow or lensed counter-jet in M87 (Broderick & Loeb 2009).

The photon ring is nearly circular for all black hole spins and all inclinations of the black hole spin axis to the line of sight (e.g., Johannsen & Psaltis 2010). For an ${a}_{* }=0$ black hole of mass $M$ and distance D, the photon ring angular radius on the sky is

Equation (1)

where we have scaled to the most likely mass from Gebhardt et al. (2011) and a distance of $16.9\,\mathrm{Mpc}$(see also EHT Collaboration et al. 2019e, (hereafter Paper VI; Blakeslee et al. 2009; Bird et al. 2010; Cantiello et al. 2018). The photon ring angular radius for other inclinations and values of ${a}_{* }$ differs by at most 13% from Equation (1), and most of this variation occurs at $1-| {a}_{* }| \ll 1$ (e.g., Takahashi 2004; Younsi et al. 2016). Evidently the angular radius of the observed photon ring is approximately $\sim 20\,\mu \mathrm{as}$(Figure 1 and Paper IV), which is close to the prediction of the black hole model given in Equation (1).

(2) The observed peak brightness temperature of the ring in Figure 1 is ${T}_{b,{pk}}\sim 6\times {10}^{9}\,{\rm{K}}$, which is consistent with past EHT mm-VLBI measurements at 230 GHz (Doeleman et al. 2012; Akiyama et al. 2015), and GMVA 3 mm-VLBI measurements of the core region (Kim et al. 2018). Expressed in electron rest-mass (me) units, ${{\rm{\Theta }}}_{b,{pk}}\equiv {k}_{{\rm{B}}}{T}_{b,{pk}}/({m}_{e}{c}^{2})\simeq 1$, where ${k}_{{\rm{B}}}$ is Boltzmann's constant. The true peak brightness temperature of the source is higher if the ring is unresolved by EHT, as is the case for the model image in the center panel of Figure 1.

The 1.3 mm emission from M87 shown in Figure 1 is expected to be generated by the synchrotron process (see Yuan & Narayan 2014, and references therein) and thus depends on the electron distribution function (eDF). If the emitting plasma has a thermal eDF, then it is characterized by an electron temperature ${T}_{e}\geqslant {T}_{b}$, or ${{\rm{\Theta }}}_{e}\equiv {k}_{{\rm{B}}}{T}_{e}/({m}_{e}{c}^{2})\gt 1$, because ${{\rm{\Theta }}}_{e}\gt {{\rm{\Theta }}}_{b,{pk}}$ if the ring is unresolved or optically thin.

Is the observed brightness temperature consistent with what one would expect from phenomenological models of the source? Radiatively inefficient accretion flow models of M87 (Reynolds et al. 1996; Di Matteo et al. 2003) produce mm emission in a geometrically thick donut of plasma around the black hole. The emitting plasma is collisionless: Coulomb scattering is weak at these low densities and high temperatures. Therefore, the electron and ion temperatures need not be the same (e.g., Spitzer 1962). In radiatively inefficient accretion flow models, the ion temperature is slightly less than the ion virial temperature,

Equation (2)

where ${r}_{{\rm{g}}}\equiv {GM}/{c}^{2}$ is the gravitational radius, r is the Boyer–Lindquist or Kerr–Schild radius, and mp is the proton mass. Most models have an electron temperature ${T}_{e}\lt {T}_{i}$ because of electron cooling and preferential heating of the ions by turbulent dissipation (e.g., Yuan & Narayan 2014; Mościbrodzka et al. 2016). If the emission arises at $\sim 5\,{r}_{{\rm{g}}}$, then ${{\rm{\Theta }}}_{e}\simeq 37({T}_{e}/{T}_{i})$, which is then consistent with the observed ${{\rm{\Theta }}}_{b,{pk}}$ if the source is unresolved or optically thin.

(3) The total flux density in the image at $1.3\,\mathrm{mm}$ is $\simeq 0.5$ Jy. With a few assumptions we can use this to estimate the electron number density ne and magnetic field strength B in the source. We adopt a simple, spherical, one-zone model for the source with radius $r\simeq 5\,{r}_{{\rm{g}}}$, pressure ${n}_{i}{{kT}}_{i}+{n}_{e}{{kT}}_{e}={\beta }_{{\rm{p}}}{B}^{2}/(8\pi )$with ${\beta }_{{\rm{p}}}\equiv {p}_{\mathrm{gas}}/{p}_{\mathrm{mag}}\sim 1$, ${T}_{i}\simeq 3{T}_{e}$, and temperature ${\theta }_{e}\simeq 10{\theta }_{b,{pk}}$, which is consistent with the discussion in (2) above. Setting ne = ni (i.e., assuming a fully ionized hydrogen plasma), the values of B and ne required to produce the observed flux density can be found by solving a nonlinear equation (assuming an average angle between the field and line of sight, 60°). The solution can be approximated as a power law:

Equation (3)

Equation (4)

assuming that $M=6.2\times {10}^{9}\,{M}_{\odot }$ and $D=16.9\,\mathrm{Mpc}$, and using the approximate thermal emissivity of Leung et al. (2011). Then the synchrotron optical depth at $1.3\,\mathrm{mm}$ is ~0.2. One can now estimate an accretion rate from (3) using

Equation (5)

assuming spherical symmetry. The Eddington accretion rate is

Equation (6)

where ${L}_{\mathrm{Edd}}\equiv 4\pi {{GMcm}}_{p}/{\sigma }_{T}$ is the Eddington luminosity (${\sigma }_{T}$ is the Thomson cross section). Setting the efficiency $\epsilon =0.1$ and $M=6.2\times {10}^{9}\,{M}_{\odot }$, ${\dot{M}}_{\mathrm{Edd}}=137\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$, and therefore $\dot{M}/{\dot{M}}_{\mathrm{Edd}}\,\sim 2.0\times {10}^{-5}$.

This estimate is similar to but slightly larger than the upper limit inferred from the 230 GHz linear polarization properties of M87 (Kuo et al. 2014).

(4) The ring is brighter in the south than the north. This can be explained by a combination of motion in the source and Doppler beaming. As a simple example we consider a luminous, optically thin ring rotating with speed v and an angular momentum vector inclined at a viewing angle i > 0° to the line of sight. Then the approaching side of the ring is Doppler boosted, and the receding side is Doppler dimmed, producing a surface brightness contrast of order unity if v is relativistic. The approaching side of the large-scale jet in M87 is oriented west–northwest (position angle $\mathrm{PA}\approx 288^\circ ;$ in Paper VI this is called ${\mathrm{PA}}_{\mathrm{FJ}}$), or to the right and slightly up in the image. Walker et al. (2018) estimated that the angle between the approaching jet and the line of sight is 17°. If the emission is produced by a rotating ring with an angular momentum vector oriented along the jet axis, then the plasma in the south is approaching Earth and the plasma in the north is receding. This implies a clockwise circulation of the plasma in the source, as projected onto the plane of the sky. This sense of rotation is consistent with the sense of rotation in ionized gas at arcsecond scales (Harms et al. 1994; Walsh et al. 2013). Notice that the asymmetry of the ring is consistent with the asymmetry inferred from 43 GHz observations of the brightness ratio between the north and south sides of the jet and counter-jet (Walker et al. 2018).

All of these estimates present a picture of the source that is remarkably consistent with the expectations of the black hole model and with existing GRMHD models (e.g., Dexter et al. 2012; Mościbrodzka et al. 2016). They even suggest a sense of rotation of gas close to the black hole. A quantitative comparison with GRMHD models can reveal more.

3. Models

Consistent with the discussion in Section 2, we now adopt the working hypothesis that M87 contains a turbulent, magnetized accretion flow surrounding a Kerr black hole. To test this hypothesis quantitatively against the EHT2017 data we have generated a Simulation Library of 3D time-dependent ideal GRMHD models. To generate this computationally expensive library efficiently and with independent checks on the results, we used several different codes that evolved matching initial conditions using the equations of ideal GRMHD. The codes used include BHAC  (Porth et al. 2017), H-AMR  (Liska et al. 2018; K. Chatterjee et al. 2019, in preparation), iharm  (Gammie et al. 2003), and KORAL  (Sa̧dowski et al. 2013b, 2014). A comparison of these and other GRMHD codes can be found in O. Porth et al. 2019 (in preparation), which shows that the differences between integrations of a standard accretion model with different codes is smaller than the fluctuations in individual simulations.

From the Simulation Library we have generated a large Image Library of synthetic images. Snapshots of the GRMHD evolutions were produced using the general relativistic ray-tracing (GRRT) schemes ipole  (Mościbrodzka & Gammie 2018), RAPTOR  (Bronzwaer et al. 2018), or BHOSS (Z. Younsi et al. 2019b, in preparation). A comparison of these and other GRRT codes can be found in Gold et al. (2019), which shows that the differences between codes is small.

In the GRMHD models the bulk of the 1.3 mm emission is produced within $\lesssim 10\,{r}_{{\rm{g}}}$ of the black hole, where the models can reach a statistically steady state. It is therefore possible to compute predictive radiative models for this compact component of the source without accurately representing the accretion flow at all radii.

We note that the current state-of-the-art models for M87 are radiation GRMHD models that include radiative feedback and electron-ion thermodynamics (Ryan et al. 2018; Chael et al. 2019). These models are too computationally expensive for a wide survey of parameter space, so that in this Letter we consider only nonradiative GRMHD models with a parameterized treatment of the electron thermodynamics.

3.1. Simulation Library

All GRMHD simulations are initialized with a weakly magnetized torus of plasma orbiting in the equatorial plane of the black hole (e.g., De Villiers et al. 2003; Gammie et al. 2003; McKinney & Blandford 2009; Porth et al. 2017). We do not consider tilted models, in which the accretion flow angular momentum is misaligned with the black hole spin. The limitations of this approach are discussed in Section 7.

The initial torus is driven to a turbulent state by instabilities, including the magnetorotational instability (see e.g., Balbus & Hawley 1991). In all cases the outcome contains a moderately magnetized midplane with orbital frequency comparable to the Keplerian orbital frequency, a corona with gas-to-magnetic-pressure ratio ${\beta }_{{\rm{p}}}\equiv {p}_{\mathrm{gas}}/{p}_{\mathrm{mag}}\sim 1$, and a strongly magnetized region over both poles of the black hole with ${B}^{2}/\rho {c}^{2}\gg 1$. We refer to the strongly magnetized region as the funnel, and the boundary between the funnel and the corona as the funnel wall (De Villiers et al. 2005; Hawley & Krolik 2006). All models in the library are evolved from t = 0 to $t={10}^{4}\,{r}_{{\rm{g}}}{c}^{-1}$.

The simulation outcome depends on the initial magnetic field strength and geometry insofar as these affect the magnetic flux through the disk, as discussed below. Once the simulation is initiated the disk transitions to a turbulent state and loses memory of most of the details of the initial conditions. This relaxed turbulent state is found inside a characteristic radius that grows over the course of the simulation. To be confident that we are imaging only those regions that have relaxed, we draw snapshots for comparison with the data from $5\times {10}^{3}\le t/{r}_{{\rm{g}}}{c}^{-1}\le {10}^{4}$.

GRMHD models have two key physical parameters. The first is the black hole spin ${a}_{* }$, $-1\lt {a}_{* }\lt 1$. The second parameter is the absolute magnetic flux ${{\rm{\Phi }}}_{\mathrm{BH}}$ crossing one hemisphere of the event horizon (see Tchekhovskoy et al. 2011; O. Porth et al. 2019, in preparation for a definition). It is convenient to recast ${{\rm{\Phi }}}_{\mathrm{BH}}$ in dimensionless form $\phi \equiv {{\rm{\Phi }}}_{\mathrm{BH}}{\left(\dot{M}{r}_{{\rm{g}}}^{2}c\right)}^{-1/2}$.110

The magnetic flux phgr is nonzero because magnetic field is advected into the event horizon by the accretion flow and sustained by currents in the surrounding plasma. At $\phi \gt {\phi }_{\max }\sim 15$,111 numerical simulations show that the accumulated magnetic flux erupts, pushes aside the accretion flow, and escapes (Tchekhovskoy et al. 2011; McKinney et al. 2012). Models with $\phi \sim 1$ are conventionally referred to as Standard and Normal Evolution (SANE; Narayan et al. 2012; Sa̧dowski et al (2013a)) models; models with $\phi \sim {\phi }_{\max }$ are conventionally referred to as Magnetically Arrested Disk (MAD; Igumenshchev et al. 2003; Narayan et al. 2003) models.

The Simulation Library contains SANE models with ${a}_{* }=-0.94$, −0.5, 0, 0.5, 0.75, 0.88, 0.94, 0.97, and 0.98, and MAD models with ${a}_{* }=-0.94$, −0.5, 0, 0.5, 0.75, and 0.94. The Simulation Library occupies 23 TB of disk space and contains a total of 43 GRMHD simulations, with some repeated at multiple resolutions with multiple codes, with consistent results (O. Porth et al. 2019, in preparation).

3.2. Image Library Generation

To produce model images from the simulations for comparison with EHT observations we use GRRT to generate a large number of synthetic images and derived VLBI data products. To make the synthetic images we need to specify the following: (1) the magnetic field, velocity field, and density as a function of position and time; (2) the emission and absorption coefficients as a function of position and time; and (3) the inclination angle between the accretion flow angular momentum vector and the line of sight i, the position angle $\mathrm{PA}$, the black hole mass $M$, and the distance D to the observer. In the following we discuss each input in turn. The reader who is only interested in a high-level description of the Image Library may skip ahead to Section 3.3.

(1) GRMHD models provide the absolute velocity field of the plasma flow. Nonradiative GRMHD evolutions are invariant, however, under a rescaling of the density by a factor ${\mathscr{M}}$. In particular, they are invariant under $\rho \to {\mathscr{M}}\rho $, field strength $B\to {{\mathscr{M}}}^{1/2}B$, and internal energy $u\to {\mathscr{M}}u$ (the Alfvén speed $B/{\rho }^{1/2}$ and sound speed $\propto \sqrt{u/\rho }$ are invariant). That is, there is no intrinsic mass scale in a nonradiative model as long as the mass of the accretion flow is negligible in comparison to $M$.112 We use this freedom to adjust ${\mathscr{M}}$ so that the average image from a GRMHD model has a 1.3 mm flux density ≈0.5 Jy (see Paper IV). Once ${\mathscr{M}}$ is set, the density, internal energy, and magnetic field are fully specified.

The mass unit ${\mathscr{M}}$ determines $\dot{M}$. In our ensemble of models $\dot{M}$ ranges from $2\times {10}^{-7}{\dot{M}}_{\mathrm{Edd}}$ to $4\times {10}^{-4}{\dot{M}}_{\mathrm{Edd}}$. Accretion rates vary by model category. The mean accretion rate for MAD models is $\sim {10}^{-6}{\dot{M}}_{\mathrm{Edd}}$. For SANE models with ${a}_{* }\gt 0$ it is $\sim 5\times {10}^{-5}{\dot{M}}_{\mathrm{Edd}};$ and for ${a}_{* }\lt 0$ it is $\sim 2\times {10}^{-4}{\dot{M}}_{\mathrm{Edd}}$.

(2) The observed radio spectral energy distributions (SEDs) and the polarization characteristics of the source make clear that the 1.3 mm emission is synchrotron radiation, as is typical for active galactic nuclei (AGNs). Synchrotron absorption and emission coefficients depend on the eDF. In what follows, we adopt a relativistic, thermal model for the eDF (a Maxwell-Jüttner distribution; Jüttner 1911; Rezzolla & Zanotti 2013). We discuss the limitations of this approach in Section 7.

All of our models of M87 are in a sufficiently low-density, high-temperature regime that the plasma is collisionless (see Ryan et al. 2018, for a discussion of Coulomb coupling in M87). Therefore, Te likely does not equal the ion temperature Ti, which is provided by the simulations. We set Te using the GRMHD density ρ, internal energy density u, and plasma ${\beta }_{{\rm{p}}}$ using a simple model:

Equation (7)

where we have assumed that the plasma is composed of hydrogen, the ions are nonrelativistic, and the electrons are relativistic. Here $R\equiv {T}_{i}/{T}_{e}$ and

Equation (8)

This prescription has one parameter, ${R}_{\mathrm{high}}$, and sets ${T}_{e}\simeq {T}_{i}$ in low ${\beta }_{{\rm{p}}}$ regions and ${T}_{e}\simeq {T}_{i}/{R}_{\mathrm{high}}$ in the midplane of the disk. It is adapted from Mościbrodzka et al. (2016) and motivated by models for electron heating in a turbulent, collisionless plasma that preferentially heats the ions for ${\beta }_{{\rm{p}}}\gtrsim 1$ (e.g., Howes 2010; Kawazura et al. 2018).

(3) We must specify the observer inclination i, the orientation of the observer through the position angle $\mathrm{PA}$, the black hole mass $M$, and the distance D to the source. Non-EHT constraints on i, $\mathrm{PA}$, and $M$ are considered below; we have generated images at $i=12^\circ ,17^\circ ,22^\circ ,158^\circ ,163^\circ $, and 168° and a few at i = 148°. The position angle (PA) can be changed by simply rotating the image. All features of the models that we have examined, including $\dot{M}$, are insensitive to small changes in i. The image morphology does depend on whether i is greater than or less than 90°, as we will show below.

The model images are generated with a $160\times 160\,\mu \mathrm{as}$ field of view and $1\mu \mathrm{as}$ pixels, which are small compared to the $\sim 20\,\mu \mathrm{as}$ nominal resolution of EHT2017. Our analysis is insensitive to changes in the field of view and the pixel scale.

For $M$ we use the most likely value from the stellar absorption-line work, $6.2\times {10}^{9}{M}_{\odot }$ (Gebhardt et al. 2011). For the distance D we use $16.9\,\,\mathrm{Mpc}$, which is very close to that employed in Paper VI. The ratio ${GM}/({c}^{2}D)=3.62\,\mu \mathrm{as}$ (hereafter M/D) determines the angular scale of the images. For some models we have also generated images with $M=3.5\times {10}^{9}\,{M}_{\odot }$ to check that the analysis results are not predetermined by the input black hole mass.

3.3. Image Library Summary

The Image Library contains of order 60,000 images. We generate images from 100 to 500 distinct output files from each of the GRMHD models at each of ${R}_{\mathrm{high}}=1,10,20,40,80$, and 160. In comparing to the data we adjust the $\mathrm{PA}$ by rotation and the total flux and angular scale of the image by simply rescaling images from the standard parameters in the Image Library (see Figure 29 in Paper VI). Tests indicate that comparisons with the data are insensitive to the rescaling procedure unless the angular scaling factor or flux scaling factor is large.113

The comparisons with the data are also insensitive to image resolution.114

A representative set of time-averaged images from the Image Library are shown in Figures 2 and 3. From these figures it is clear that varying the parameters ${a}_{* }$, phgr, and ${R}_{\mathrm{high}}$ can change the width and asymmetry of the photon ring and introduce additional structures exterior and interior to the photon ring.

Figure 2.

Figure 2. Time-averaged 1.3 mm images generated by five SANE GRMHD simulations with varying spin (${a}_{* }=-0.94$ to ${a}_{* }=+0.97$ from left to right) and ${R}_{\mathrm{high}}$ (${R}_{\mathrm{high}}=1$ to ${R}_{\mathrm{high}}=160$ from top to bottom; increasing ${R}_{\mathrm{high}}$ corresponds to decreasing electron temperature). The colormap is linear. All models are imaged at i = 163°. The jet that is approaching Earth is on the right (west) in all the images. The black hole spin vector projected onto the plane of the sky is marked with an arrow and aligned in the east–west direction. When the arrow is pointing left the black hole rotates in a clockwise direction, and when the arrow is pointing right the black hole rotates in a counterclockwise direction. The field of view for each model image is $80\,\mu \mathrm{as}$(half of that used for the image libraries) with resolution equal to $1\mu \mathrm{as}$/pixel (20 times finer than the nominal resolution of EHT2017, and the same employed in the library images).

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Figure 3.

Figure 3. Same as in Figure 2 but for selected MAD models.

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The location of the emitting plasma is shown in Figure 4, which shows a map of time- and azimuth-averaged emission regions for four representative ${a}_{* }\gt 0$ models. For SANE models, if ${R}_{\mathrm{high}}$ is low (high), emission is concentrated more in the disk (funnel wall), and the bright section of the ring is dominated by the disk (funnel wall).115 Appendix B shows images generated by considering emission only from particular regions of the flow, and the results are consistent with Figure 4.

Figure 4.

Figure 4. Binned location of the point of origin for all photons that make up an image, summed over azimuth, and averaged over all snapshots from the simulation. The colormap is linear. The event horizon is indicated by the solid white semicircle and the black hole spin axis is along the figure vertical axis. This set of four images shows MAD and SANE models with ${R}_{\mathrm{high}}=10$ and 160, all with ${a}_{* }=0.94$. The region between the dashed curves is the locus of existence of (unstable) photon orbits (Teo 2003). The green cross marks the location of the innermost stable circular orbit (ISCO) in the equatorial plane. In these images the line of sight (marked by an arrow) is located below the midplane and makes a 163° angle with the disk angular momentum, which coincides with the spin axis of the black hole.

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Figures 2 and 3 show that for both MAD and SANE models the bright section of the ring, which is generated by Doppler beaming, shifts from the top for negative spin, to a nearly symmetric ring at ${a}_{* }=0$, to the bottom for ${a}_{* }\gt 0$ (except the SANE ${R}_{\mathrm{high}}=1$ case, where the bright section is always at the bottom when i > 90°). That is, the location of the peak flux in the ring is controlled by the black hole spin: it always lies roughly 90 degrees counterclockwise from the projection of the spin vector on the sky. Some of the ring emission originates in the funnel wall at $r\lesssim 8\,{r}_{{\rm{g}}}$. The rotation of plasma in the funnel wall is in the same sense as plasma in the funnel, which is controlled by the dragging of magnetic field lines by the black hole. The funnel wall thus rotates opposite to the accretion flow if ${a}_{* }\lt 0$. This effect will be studied further in a later publication (Wong et al. 2019). The resulting relationships between disk angular momentum, black hole angular momentum, and observed ring asymmetry are illustrated in Figure 5.

Figure 5.

Figure 5. Illustration of the effect of black hole and disk angular momentum on ring asymmetry. The asymmetry is produced primarily by Doppler beaming: the bright region corresponds to the approaching side. In GRMHD models that fit the data comparatively well, the asymmetry arises in emission generated in the funnel wall. The sense of rotation of both the jet and funnel wall are controlled by the black hole spin. If the black hole spin axis is aligned with the large-scale jet, which points to the right, then the asymmetry implies that the black hole spin is pointing away from Earth (rotation of the black hole is clockwise as viewed from Earth). The blue ribbon arrow shows the sense of disk rotation, and the black ribbon arrow shows black hole spin. Inclination i is defined as the angle between the disk angular momentum vector and the line of sight.

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The time-averaged MAD images are almost independent of ${R}_{\mathrm{high}}$ and depend mainly on ${a}_{* }$. In MAD models much of the emission arises in regions with ${\beta }_{{\rm{p}}}\sim 1$, where ${R}_{\mathrm{high}}$ has little influence over the electron temperature, so the insensitivity to ${R}_{\mathrm{high}}$ is natural (see Figure 4). In SANE models emission arises at ${\beta }_{{\rm{p}}}\sim 10$, so the time-averaged SANE images, by contrast, depend strongly on ${R}_{\mathrm{high}}$. In low ${R}_{\mathrm{high}}$SANE models, extended emission outside the photon ring, arising near the equatorial plane, is evident at ${R}_{\mathrm{high}}=1$. In large ${R}_{\mathrm{high}}$ SANE models the inner ring emission arises from the funnel wall, and once again the image looks like a thin ring (see Figure 4).

Figure 6 and the accompanying animation show the evolution of the images, visibility amplitudes, and closure phases over a $5000\,{r}_{{\rm{g}}}{c}^{-1}\approx 5\,\mathrm{yr}$ interval in a single simulation for M87. It is evident from the animation that turbulence in the simulations produces large fluctuations in the images, which imply changes in visibility amplitudes and closure phases that are large compared to measurement errors. The fluctuations are central to our procedure for comparing models with the data, described briefly below and in detail in Paper VI.

Figure 6. Single frame from the accompanying animation. This shows the visibility amplitudes (top), closure phases plotted by Euclidean distance in 6D space (middle), and associated model images at full resolution (lower left) and convolved with the EHT2017 beam (lower right). Data from 2017 April 6 high-band are also shown in the top two plots. The video shows frames 1 through 100 and has a duration of 10 s.

(An animation of this figure is available.)

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The timescale between frames in the animation is $50\,{r}_{{\rm{g}}}{c}^{-1}\simeq 18$ days, which is long compared to EHT2017 observing campaign. The images are highly correlated on timescales less than the innermost stable circular orbit (ISCO) orbital period, which for ${a}_{* }=0$ is $\simeq 15\ {r}_{{\rm{g}}}{c}^{-1}\simeq 5$ days, i.e., comparable to the duration of the EHT2017 campaign. If drawn from one of our models, we would expect the EHT2017 data to look like a single snapshot (Figures 6) rather than their time averages (Figures 2 and 3).

4. Procedure for Comparison of Models with Data

As described above, each model in the Simulation Library has two dimensionless parameters: black hole spin ${a}_{* }$ and magnetic flux phgr. Imaging the model from each simulation adds five new parameters: ${R}_{\mathrm{high}}$, i, $\mathrm{PA}$, $M$, and D, which we set to $16.9\,\mathrm{Mpc}$. After fixing these parameters we draw snapshots from the time evolution at a cadence of 10 to $50\,{r}_{{\rm{g}}}{c}^{-1}$. We then compare these snapshots to the data.

The simplest comparison computes the ${\chi }_{\nu }^{2}$ (reduced chi square) distance between the data and a snapshot. In the course of computing ${\chi }_{\nu }^{2}$ we vary the image scale M/D, flux density Fν, position angle $\mathrm{PA}$, and the gain at each VLBI station in order to give each image every opportunity to fit the data. The best-fit parameters $(M/D,{F}_{\nu },\mathrm{PA})$ for each snapshot are found by two pipelines independently: the Themis pipeline using a Markov chain Monte Carlo method (A. E. Broderick et al. 2019a, in preparation), and the GENA  pipeline using an evolutionary algorithm for multidimensional minimization (Fromm et al. 2019a; C. Fromm et al. 2019b, in preparation; see also Section 4 of Paper VI for details). The best-fit parameters contain information about the source and we use the distribution of best-fit parameters to test the model by asking whether or not they are consistent with existing measurements of M/D and estimates of the jet $\mathrm{PA}$ on larger scales.

The ${\chi }_{\nu }^{2}$ comparison alone does not provide a sharp test of the models. Fluctuations in the underlying GRMHD model, combined with the high signal-to-noise ratio for EHT2017 data, imply that individual snapshots are highly unlikely to provide a formally acceptable fit with ${\chi }_{\nu }^{2}\simeq 1$. This is borne out in practice with the minimum ${\chi }_{\nu }^{2}=1.79$ over the entire set of the more than 60,000 individual images in the Image Library. Nevertheless, it is possible to test if the ${\chi }_{\nu }^{2}$ from the fit to the data is consistent with the underlying model, using "Average Image Scoring" with Themis (Themis-AIS), as described in detail in Appendix F of Paper VI). Themis-AIS measures a ${\chi }_{\nu }^{2}$ distance (on the space of visibility amplitudes and closure phases) between a trial image and the data. In practice we use the average of the images from a given model as the trial image (hence Themis-AIS), but other choices are possible. We compute the ${\chi }_{\nu }^{2}$ distance between the trial image and synthetic data produced from each snapshot. The model can then be tested by asking whether the data's ${\chi }_{\nu }^{2}$ is likely to have been drawn from the model's distribution of ${\chi }_{\nu }^{2}$. In particular, we can assign a probability p that the data is drawn from a specific model's distribution.

In this Letter we focus on comparisons with a single data set, the 2017 April 6 high-band data (Paper III). The eight EHT2017 data sets, spanning four days with two bands on each day, are highly correlated. Assessing what correlation is expected in the models is a complicated task that we defer to later publications. The 2017 April 6 data set has the largest number of scans, 284 detections in 25 scans (see Paper III) and is therefore expected to be the most constraining.116

5. Model Constraints: EHT2017 Alone

The resolved ring-like structure obtained from the EHT2017 data provides an estimate of M/D(discussed in detail in Paper VI) and the jet $\mathrm{PA}$ from the immediate environment of the central black hole. As a first test of the models we can ask whether or not these are consistent with what is known from other mass measurements and from the orientation of the large-scale jet.

Figure 7 shows the distributions of best-fit values of M/D for a subset of the models for which spectra and jet power estimates are available (see below). The three lines show the M/D distribution for all snapshots (dotted lines), the best-fit 10% of snapshots (dashed lines), and the best-fit 1% of snapshots (solid lines) within each model. Evidently, as better fits are required, the distribution narrows and peaks close to $M/D\sim 3.6\,\mu \mathrm{as}$ with a width of about $0.5\mu \mathrm{as}$.

Figure 7.

Figure 7. Distribution of M/D obtained by fitting Image Library snapshots to the 2017 April 6 data, in $\mu \mathrm{as}$, measured independently using the (left panel) Themis and (right panel) GENA pipelines with qualitatively similar results. Smooth lines were drawn with a Gaussian kernel density estimator. The three lines show the best-fit 1% within each model (solid); the best-fit 10% within each model (dashed); and all model images (dotted). The vertical lines show $M/D=2.04$ (dashed) and $3.62\,\mu \mathrm{as}$ (solid), corresponding to M = 3.5 and $6.2\times {10}^{9}\,{M}_{\odot }$. The distribution uses a subset of models for which spectra and jet power estimates are available (see Section 6). Only images with ${a}_{* }\gt 0$, i > 90° and ${a}_{* }\lt 0$, i < 90° (see also the left panel of Figure 5) are considered.

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The distribution of M/D for the best-fit $\lt 10 \% $ of snapshots is qualitatively similar if we include only MAD or SANE models, only models produced by individual codes (BHAC, H-AMR, iharm, or KORAL), or only individual spins. As the thrust of this Letter is to test the models, we simply note that Figure 7indicates that the models are broadly consistent with earlier mass estimates (see Paper VI for a detailed discussion). This did not have to be the case: the ring radius could have been significantly larger than $3.6\,\mu \mathrm{as}$.

We can go somewhat further and ask if any of the individual models favor large or small masses. Figure 8 shows the distributions of best-fit values of M/D for each model (different ${a}_{* }$, ${R}_{\mathrm{high}}$, and magnetic flux). Most individual models favor M/D close to $3.6\,\mu \mathrm{as}$. The exceptions are ${a}_{* }\leqslant 0$ SANE models with ${R}_{\mathrm{high}}=1$, which produce the bump in the M/D distribution near $2\mu \mathrm{as}$. In these models, the emission is produced at comparatively large radius in the disk (see Figure 2) because the inner edge of the disk (the ISCO) is at a large radius in a counter-rotating disk around a black hole with $| {a}_{* }| \sim 1$. For these models, the fitting procedure identifies EHT2017's ring with this outer ring, which forces the photon ring, and therefore M/D, to be small. As we will show later, these models can be rejected because they produce weak jets that are inconsistent with existing jet power estimates (see Section 6.3).

Figure 8.

Figure 8. Distributions of M/D and black hole mass with $D=16.9\,\mathrm{Mpc}$ reconstructed from the best-fit 10% of images for MAD (left panel) and SANE (right panel) models (i = 17° for ${a}_{* }\le 0$and 163° for ${a}_{* }\gt 0$) with different ${R}_{\mathrm{high}}$ and ${a}_{* }$, from the Themis (dark red, left), and GENA  (dark green, right) pipelines. The white dot and vertical black bar correspond, respectively, to the median and region between the 25th and 75th percentiles for both pipelines combined. The blue and pink horizontal bands show the range of M/D and mass at $D=16.9\,\mathrm{Mpc}$ estimated from the gas dynamical model (Walsh et al. 2013) and stellar dynamical model (Gebhardt et al. 2011), respectively. Constraints on the models based on average image scoring (Themis-AIS) are discussed in Section 5. Constraints based on radiative efficiency, X-ray luminosity, and jet power are discussed in Section 6.

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Figure 8 also shows that M/D increases with ${a}_{* }$ for SANE models. This is due to the appearance of a secondary inner ring inside the main photon ring. The former is associated with emission produced along the wall of the approaching jet. Because the emission is produced in front of the black hole, lensing is weak and it appears at small angular scale. The inner ring is absent in MAD models (see Figure 3), where the bulk of the emission comes from the midplane at all values of ${R}_{\mathrm{high}}$(Figure 4).

We now ask whether or not the PA of the jet is consistent with the orientation of the jet measured at other wavelengths. On large (~mas) scales the extended jet component has a PA of approximately 288° (e.g., Walker et al. 2018). On smaller ($\sim 100\,\mu \mathrm{as}$) scales the apparent opening angle of the jet is large (e.g., Kim et al. 2018) and the PA is therefore more difficult to measure. Also notice that the jet PA may be time dependent (e.g., Hada et al. 2016; Walker et al. 2018). In our model images the jet is relatively dim at 1.3 mm, and is not easily seen with a linear colormap. The model jet axis is, nonetheless, well defined: jets emerge perpendicular to the disk.

Figure 9 shows the distribution of best-fit PA over the same sample of snapshots from the Image Library used in Figure 7. We divide the snapshots into two groups. The first group has the black hole spin pointed away from Earth (i > 90° and ${a}_{* }\gt 0$, or i < 90° and ${a}_{* }\lt 0$). The spin-away model PA distributions are shown in the top two panels. The second group has the black hole spin pointed toward Earth (i > 90 and ${a}_{* }\lt 0$ or i > 90° and ${a}_{* }\lt 0$). These spin-toward model PA distributions are shown in the bottom two panels. The large-scale jet orientation lies on the shoulder of the spin-away distribution (the distribution can be approximated as a Gaussian with, for Themis (GENA) mean 209 (203)° and ${\sigma }_{\mathrm{PA}}\,=54\,(55)^\circ ;$ the large-scale jet PA lies $1.5{\sigma }_{\mathrm{PA}}$ from the mean) and is therefore consistent with the spin-away models. On the other hand, the large-scale jet orientation lies off the shoulder of the spin-toward distribution and is inconsistent with the spin-toward models. Evidently models in which the black hole spin is pointing away from Earth are strongly favored.

Figure 9.

Figure 9. Top: distribution of best-fit PA (in degree) scored by the Themis (left) and GENA (right) pipelines for models with black hole spin vector pointing away from Earth (i > 90° for ${a}_{* }\gt 0$ or i < 90° for ${a}_{* }\lt 0$). Bottom: images with black hole spin vector pointing toward Earth (i < 90° for ${a}_{* }\gt 0$ or i > 90° for ${a}_{* }\lt 0$). Smooth lines were drawn with a wrapped Gaussian kernel density estimator. The three lines show (1) all images in the sample (dotted line); (2) the best-fit 10% of images within each model (dashed line); and (3) the best-fit 1% of images in each model (solid line). For reference, the vertical line shows the position angle $\mathrm{PA}\sim 288^\circ $ of the large-scale (mas) jet Walker et al. (2018), with the gray area from (288 – 10)° to (288 + 10)° indicating the observed PA variation.

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The width of the spin-away and spin-toward distributions arises naturally in the models from brightness fluctuations in the ring. The distributions are relatively insensitive if split into MAD and SANE categories, although for MAD the averaged PA is $\langle \mathrm{PA}\rangle =219^\circ $, ${\sigma }_{\mathrm{PA}}=46^\circ $, while for SANE $\langle \mathrm{PA}\rangle =195^\circ $ and ${\sigma }_{\mathrm{PA}}=58^\circ $. The ${a}_{* }=0$ and ${a}_{* }\gt 0$ models have similar distributions. Again, EHT2017 data strongly favor one sense of black hole spin: either $| {a}_{* }| $ is small, or the spin vector is pointed away from Earth. If the fluctuations are such that the fitted PA for each epoch of observations is drawn from a Gaussian with ${\sigma }_{\mathrm{PA}}\simeq 55^\circ $, then a second epoch will be able to identify the true orientation with accuracy ${\sigma }_{\mathrm{PA}}/\sqrt{2}\simeq 40^\circ $ and the Nth epoch with accuracy ${\sigma }_{\mathrm{PA}}/\sqrt{N}$. If the fitted PA were drawn from a Gaussian of width ${\sigma }_{\mathrm{PA}}=54^\circ $ about $\mathrm{PA}=288^\circ $, as would be expected in a model in which the large-scale jet is aligned normal to the disk, then future epochs have a >90% chance of seeing the peak brightness counterclockwise from its position in EHT2017.

Finally, we can test the models by asking if they are consistent with the data according to Themis-AIS, as introduced in Section 4. Themis-AIS produces a probability p that the ${\chi }_{\nu }^{2}$ distance between the data and the average of the model images is drawn from the same distribution as the ${\chi }_{\nu }^{2}$ distance between synthetic data created from the model images, and the average of the model images. Table 1 takes these p values and categorizes them by magnetic flux and by spin, aggregating (averaging) results from different codes, ${R}_{\mathrm{high}}$, and i. Evidently, most of the models are formally consistent with the data by this test.

Table 1.  Average Image Scoringa Summary

Fluxb${a}_{* }$ c$\langle p\rangle $ d${N}_{\mathrm{model}}$ e$\mathrm{MIN}(p)$ f$\mathrm{MAX}(p)$ g
SANE−0.940.33240.010.88
SANE−0.50.19240.010.73
SANE00.23240.010.92
SANE0.50.51300.020.97
SANE0.750.7460.480.98
SANE0.880.6560.260.94
SANE0.940.49240.010.92
SANE0.970.1260.060.40
MAD−0.940.01180.010.04
MAD−0.50.75180.340.98
MAD00.22180.010.62
MAD0.50.17180.020.54
MAD0.750.28180.010.72
MAD0.940.21180.020.50

Notes.

aThe Average Image Scoring (Themis-AIS) is introduced in Section 4. bflux: net magnetic flux on the black hole (MAD or SANE). c ${a}_{* }$: dimensionless black hole spin. d $\langle p\rangle $: mean of the p value for the aggregated models. e ${N}_{\mathrm{model}}$: number of aggregated models. f $\mathrm{MIN}(p)$: minimum p value among the aggregated models. g $\mathrm{MAX}(p)$: maximum p value among the aggregated models.

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One group of models, however, is rejected by Themis-AIS: MAD models with ${a}_{* }=-0.94$. On average this group has p = 0.01, and all models within this group have $p\leqslant 0.04$. Snapshots from MAD models with ${a}_{* }=-0.94$ exhibit the highest morphological variability in our ensemble in the sense that the emission breaks up into transient bright clumps. These models are rejected by Themis-AIS because none of the snapshots are as similar to the average image as the data. In other words, it is unlikely that EHT2017 would have captured an ${a}_{* }=-0.94$ MAD model in a configuration as unperturbed as the data seem to be.

The remainder of the model categories contain at least some models that are consistent with the data according to the average image scoring test. That is, most models are variable and the associated snapshots lie far from the average image. These snapshots are formally inconsistent with the data, but their distance from the average image is consistent with what is expected from the models. Given the uncertainties in the model—and our lack of knowledge of the source prior to EHT2017—it is remarkable that so many of the models are acceptable. This is likely because the source structure is dominated by the photon ring, which is produced by gravitational lensing, and is therefore relatively insensitive to the details of the accretion flow and jet physics. We can further narrow the range of acceptable models, however, using additional constraints.

6. Model Constraints: EHT2017 Combined with Other Constraints

We can apply three additional arguments to further constrain the source model. (1) The model must be close to radiative equilibrium. (2) The model must be consistent with the observed broadband SED; in particular, it must not overproduce X-rays. (3) The model must produce a sufficiently powerful jet to match the measurements of the jet kinetic energy at large scales. Our discussions in this Section are based on simulation data that is provided in full detail in Appendix A.

6.1. Radiative Equilibrium

The model must be close to radiative equilibrium. The GRMHD models in the Simulation Library do not include radiative cooling, nor do they include a detailed prescription for particle energization. In nature the accretion flow and jet are expected to be cooled and heated by a combination of synchrotron and Compton cooling, turbulent dissipation, and Coulomb heating, which transfers energy from the hot ions to the cooler electrons. In our suite of simulations the parameter ${R}_{\mathrm{high}}$ can be thought of as a proxy for the sum of these processes. In a fully self-consistent treatment, some models would rapidly cool and settle to a lower electron temperature (see Mościbrodzka et al. 2011; Ryan et al. 2018; Chael et al. 2019). We crudely test for this by calculating the radiative efficiency $\epsilon \equiv {L}_{\mathrm{bol}}/(\dot{M}{c}^{2})$, where ${L}_{\mathrm{bol}}$ is the bolometric luminosity. If it is larger than the radiative efficiency of a thin, radiatively efficient disk,117 which depends only on ${a}_{* }$ (Novikov & Thorne 1973), then we reject the model as physically inconsistent.

We calculate ${L}_{\mathrm{bol}}$ with the Monte Carlo code grmonty  (Dolence et al. 2009), which incorporates synchrotron emission, absorption, Compton scattering at all orders, and bremsstrahlung. It assumes the same thermal eDF used in generating the Image Library. We calculate ${L}_{\mathrm{bol}}$ for 20% of the snapshots to minimize computational cost. We then average over snapshots to find $\langle {L}_{\mathrm{bol}}\rangle $. The mass accretion rate $\dot{M}$ is likewise computed for each snapshot and averaged over time. We reject models with epsilon that is larger than the classical thin disk model. (Table 3 in Appendix A lists epsilon for a large set of models.) All but two of the radiatively inconsistent models are MADs with ${a}_{* }\geqslant 0$ and ${R}_{\mathrm{high}}=1$. Eliminating all MAD models with ${a}_{* }\geqslant 0$ and ${R}_{\mathrm{high}}=1$ does not change any of our earlier conclusions.

6.2. X-Ray Constraints

As part of the EHT2017 campaign, we simultaneously observed M87 with the Chandra X-ray observatory and the Nuclear Spectroscopic Telescope Array (NuSTAR). The best fit to simultaneous Chandra and NuSTAR observations on 2017 April 12 and 14 implies a $2\mbox{--}10\,\mathrm{keV}$ luminosity of ${L}_{{{\rm{X}}}_{\mathrm{obs}}}\,=4.4\pm 0.1\times {10}^{40}\,\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. We used the SEDs generated from the simulations while calculating ${L}_{\mathrm{bol}}$ to reject models that consistently overproduce X-rays; specifically, we reject models with $\mathrm{log}{L}_{{{\rm{X}}}_{\mathrm{obs}}}\lt \mathrm{log}\langle {L}_{{\rm{X}}}\rangle -2\sigma (\mathrm{log}{L}_{{\rm{X}}})$. We do not reject underluminous models because the X-rays could in principle be produced by direct synchrotron emission from nonthermal electrons or by other unresolved sources. Notice that ${L}_{{\rm{X}}}$ is highly variable in all models so that the X-ray observations currently reject only a few models. Table 3 in Appendix A shows $\langle {L}_{{\rm{X}}}\rangle $ as well as upper and lower limits for a set of models that is distributed uniformly across the parameter space.

In our models the X-ray flux is produced by inverse Compton scattering of synchrotron photons. The X-ray flux is an increasing function of ${\tau }_{T}{T}_{e}^{2}$ where τT is a characteristic Thomson optical depth (${\tau }_{T}\sim {10}^{-5}$), and the characteristic amplification factor for photon energies is $\propto {T}_{e}^{2}$ because the X-ray band is dominated by singly scattered photons interacting with relativistic electrons (we include all scattering orders in the Monte Carlo calculation). Increasing ${R}_{\mathrm{high}}$ at fixed ${F}_{\nu }(230\,\ \mathrm{GHz})$ tends to increase $\dot{M}$ and therefore τT and decrease Te. The increase in Te dominates in our ensemble of models, and so models with small ${R}_{\mathrm{high}}$ have larger ${L}_{{\rm{X}}}$, while models with large ${R}_{\mathrm{high}}$ have smaller ${L}_{{\rm{X}}}$. The effect is not strictly monotonic, however, because of noise in our sampling process and the highly variable nature of the X-ray emission.

The overluminous models are mostly SANE models with ${R}_{\mathrm{high}}\leqslant 20$. The model with the highest $\langle {L}_{{\rm{X}}}\rangle =4.2\,\times {10}^{42}\,\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ is a SANE, ${a}_{* }=0$, ${R}_{\mathrm{high}}=10$ model. The corresponding model with ${R}_{\mathrm{high}}=1$ has $\langle {L}_{{\rm{X}}}\rangle =2.1\,\times {10}^{41}\,\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, and the difference between these two indicates the level of variability and the sensitivity of the average to the brightest snapshot. The upshot of application of the ${L}_{{\rm{X}}}$ constraints is that ${L}_{{\rm{X}}}$ is sensitive to ${R}_{\mathrm{high}}$. Very low values of ${R}_{\mathrm{high}}$ are disfavored. ${L}_{{\rm{X}}}$ thus most directly constrains the electron temperature model.

6.3. Jet Power

Estimates of M87's jet power (${P}_{\mathrm{jet}}$) have been reviewed in Reynolds et al. (1996), Li et al. (2009), de Gasperin et al. (2012), Broderick et al. (2015), and Prieto et al. (2016). The estimates range from 1042to ${10}^{45}\,\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. This wide range is a consequence of both physical uncertainties in the models used to estimate ${P}_{\mathrm{jet}}$ and the wide range in length and timescales probed by the observations. Some estimates may sample a different epoch and thus provide little information on the state of the central engine during EHT2017. Nevertheless, observations of HST-1 yield ${P}_{\mathrm{jet}}\sim {10}^{44}\ \,\mathrm{erg}\,{{\rm{s}}}^{-1}$ (e.g., Stawarz et al. 2006). HST-1 is within $\sim 70\,\mathrm{pc}$ of the central engine and, taking account of relativistic time foreshortening, may be sampling the central engine ${P}_{\mathrm{jet}}$ over the last few decades. Furthermore, the 1.3 mm light curve of M87 as observed by SMA shows $\lesssim 50 \% $ variability over decade timescales (Bower et al. 2015). Based on these considerations it seems reasonable to adopt a very conservative lower limit on jet power $\equiv {P}_{\mathrm{jet},\min }={10}^{42}\ \,\mathrm{erg}\,{{\rm{s}}}^{-1}$.

To apply this constraint we must define and measure ${P}_{\mathrm{jet}}$ in our models. Our procedure is discussed in detail in Appendix A. In brief, we measure the total energy flux in outflowing regions over the polar caps of the black hole in which the energy per unit rest mass exceeds $2.2\,{c}^{2}$, which corresponds to βγ = 1, where $\beta \equiv v/c$ and γ is Lorentz factor. The effect of changing this cutoff is also discussed in Appendix A. Because the cutoff is somewhat arbitrary, we also calculate ${P}_{\mathrm{out}}$ by including the energy flux in all outflowing regions over the polar caps of the black hole; that is, it includes the energy flux in any wide-angle, low-velocity wind. ${P}_{\mathrm{out}}$ represents a maximal definition of jet power. Table 3 in Appendix A shows ${P}_{\mathrm{jet}}$ as well as a total outflow power ${P}_{\mathrm{out}}$.

The constraint ${P}_{\mathrm{jet}}\gt {P}_{\mathrm{jet},\min }={10}^{42}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ rejects all ${a}_{* }=0$ models. This conclusion is not sensitive to the definition of ${P}_{\mathrm{jet}}$: all ${a}_{* }=0$ models also have total outflow power ${P}_{\mathrm{out}}\,\lt {10}^{42}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. The most powerful ${a}_{* }=0$ model is a MAD model with ${R}_{\mathrm{high}}=160$, which has ${P}_{\mathrm{out}}=3.7\times {10}^{41}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ and ${P}_{\mathrm{jet}}$ consistent with 0. We conclude that our ${a}_{* }=0$ models are ruled out.

Can the ${a}_{* }=0$ models be saved by changing the eDF? Probably not. There is no evidence from the GRMHD simulations that these models are capable of producing a relativistic outflow with $\beta \gamma \gt 1$. Suppose, however, that we are willing to identify the nonrelativistic outflow, whose power is measured by ${P}_{\mathrm{out}}$, with the jet. Can ${P}_{\mathrm{out}}$ be raised to meet our conservative threshold on jet power? Here the answer is yes, in principle, and this can be done by changing the eDF. The eDF and ${P}_{\mathrm{out}}$ are coupled because ${P}_{\mathrm{out}}$ is determined by $\dot{M}$, and $\dot{M}$ is adjusted to produce the observed compact mm flux. The relationship between $\dot{M}$ and mm flux depends upon the eDF. If the eDF is altered to produce mm photons less efficiently (for example, by lowering Te in a thermal model), then $\dot{M}$ and therefore ${P}_{\mathrm{out}}$increase. A typical nonthermal eDF, by contrast, is likely to produce mm photons with greater efficiency by shifting electrons out of the thermal core and into a nonthermal tail. It will therefore lower $\dot{M}$ and thus ${P}_{\mathrm{out}}$. A thermal eDF with lower Te could have higher ${P}_{\mathrm{out}}$, as is evident in the large ${R}_{\mathrm{high}}$ SANE models in Table 3. There are observational and theoretical lower limits on Te, however, including a lower limit provided by the observed brightness temeprature. As Te declines, ne and Bincrease and that has implications for source linear polarization (Mościbrodzka et al. 2017; Jiménez-Rosales & Dexter 2018), which will be explored in future work. As Te declines and ne and ni increase there is also an increase in energy transfer from ions to electrons by Coulomb coupling, and this sets a floor on Te.

The requirement that ${P}_{\mathrm{jet}}\gt {P}_{\mathrm{jet},\min }$ eliminates many models other than the ${a}_{* }=0$ models. All SANE models with $| {a}_{* }| =0.5$ fail to produce jets with the required minimum power. Indeed, they also fail the less restrictive condition ${P}_{\mathrm{out}}\gt {P}_{\mathrm{jet},\min }$, so this conclusion is insensitive to the definition of the jet. We conclude that among the SANE models, only high-spin models survive.

At this point it is worth revisiting the SANE, ${R}_{\mathrm{high}}=1$, ${a}_{* }=-0.94$ model that favored a low black hole mass in Section 5. These models are not rejected by a naive application of the ${P}_{\mathrm{jet}}\gt {P}_{\mathrm{jet},\min }$ criterion, but they are marginal. Notice, however, that we needed to assume a mass in applying the this criterion. We have consistently assumed $M=6.2\times {10}^{9}\,{M}_{\odot }$. If we use the $M\sim 3\times {10}^{9}\,{M}_{\odot }$ implied by the best-fit M/D, then $\dot{M}$ drops by a factor of two, ${P}_{\mathrm{jet}}$ drops below the threshold and the model is rejected.

The lower limit on jet power ${P}_{\mathrm{jet},\min }={10}^{42}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ is conservative and the true jet power is likely higher. If we increased ${P}_{\mathrm{jet},\min }$ to $3\times {10}^{42}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, the only surviving models would have $| {a}_{* }| =0.94$ and ${R}_{\mathrm{high}}\geqslant 10$. This conclusion is also not sensitive to the definition of the jet power: applying the same cut to ${P}_{\mathrm{out}}$ adds only a single model with $| {a}_{* }| \lt 0.94$, the ${R}_{\mathrm{high}}=160$, ${a}_{* }=0.5$ MAD model. The remainder have ${a}_{* }=0.94$. Interestingly, the most powerful jets in our ensemble of models are produced by SANE, ${a}_{* }=-0.94$, ${R}_{\mathrm{high}}=160$ models, with ${P}_{\mathrm{jet}}\simeq {10}^{43}\,\,\mathrm{erg}\,{{\rm{s}}}^{-1}$.

Estimates for ${P}_{\mathrm{jet}}$ extend to ${10}^{45}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, but in our ensemble of models the maximum ${P}_{\mathrm{jet}}\sim {10}^{43}\,\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. Possible explanations include: (1) ${P}_{\mathrm{jet}}$ is variable and the estimates probe the central engine power at earlier epochs (discussed above); (2) the ${P}_{\mathrm{jet}}$ estimates are too large; or (3) the models are in error. How might our models be modified to produce a larger ${P}_{\mathrm{jet}}$? For a given magnetic field configuration the jet power scales with $\dot{M}{c}^{2}$. To increase ${P}_{\mathrm{jet}}$, then, one must reduce the mm flux per accreted nucleon so that at fixed mm flux density $\dot{M}$ increases.118 Lowering Te in a thermal model is unlikely to work because lower Te implies higher synchrotron optical depth, which increases the ring width. We have done a limited series of experiments that suggest that even a modest decrease in Te would produce a broad ring that is inconsistent with EHT2017 (Paper VI). What is required, then, is a nonthermal (or multitemperature) model with a large population of cold electrons that are invisible at mm wavelength (for a thermal subpopulation, ${{\rm{\Theta }}}_{e,\mathrm{cold}}\lt 1$), and a population of higher-energy electrons that produces the observed mm flux (see Falcke & Biermann 1995). We have not considered such models here, but we note that they are in tension with current ideas about dissipation of turbulence because they require efficient suppression of electron heating.

The ${P}_{\mathrm{jet}}$ in our models is dominated by Poynting flux in the force-free region around the axis (the "funnel"), as in the Blandford & Znajek (1977) force-free magnetosphere model. The energy flux is concentrated along the walls of the funnel.119 Tchekhovskoy et al. (2011) provided an expression for the energy flux in the funnel, the so-called Blandford–Znajek power ${P}_{\mathrm{BZ}}$, which becomes, in our units,

Equation (9)

where $f({a}_{* })\approx {a}_{* }^{2}{\left(1+\sqrt{1-{a}_{* }^{2}}\right)}^{-2}$ (a good approximation for ${a}_{* }\lt 0.95$) and ${\dot{M}}_{\mathrm{Edd}}=137\,{M}_{\odot }\,{\mathrm{yr}}^{-1}$ for $M=6.2\times {10}^{9}\,{M}_{\odot }$. This expression was developed for models with a thin disk in the equatorial plane. ${P}_{\mathrm{BZ}}$is lower for models where the force-free region is excluded by a thicker disk around the equatorial plane. Clearly ${P}_{\mathrm{BZ}}$ is comparable to observational estimates of ${P}_{\mathrm{jet}}$.

In our models (see Table 3) ${P}_{\mathrm{jet}}$ follows the above scaling relation but with a smaller coefficient. The ratio of coefficients is model dependent and varies from 0.15 to 0.83. This is likely because the force-free region is restricted to a cone around the poles of the black hole, and the width of the cone varies by model. Indeed, the coefficient is larger for MAD than for SANE models, which is consistent with this idea because MAD models have a wide funnel and SANE models have a narrow funnel. This also suggests that future comparison of synthetic 43 and 86 GHz images from our models with lower-frequency VLBI data may further constrain the magnetic flux on the black hole.

The connection between the Poynting flux in the funnel and black hole spin has been discussed for some time in the simulation literature, beginning with McKinney & Gammie (2004; see also McKinney 2006; McKinney & Narayan 2007). The structure of the funnel magnetic field can be time-averaged and shown to match the analytic solution of Blandford & Znajek (1977). Furthermore, the energy flux density can be time-averaged and traced back to the event horizon. Is the energy contained in black hole spin sufficient to drive the observed jet over the jet lifetime? The spindown timescale is $\tau =(M-{M}_{\mathrm{irr}}){c}^{2}/{P}_{\mathrm{jet}}$, where ${M}_{\mathrm{irr}}\equiv M{\left(\left(1+\sqrt{1-{a}_{* }^{2}}\right)/2\right)}^{1/2}$ is the irreducible mass of the black hole. For the ${a}_{* }=0.94$ MAD model with ${R}_{\mathrm{high}}=160$, $\tau =7.3\times {10}^{12}\,\mathrm{yr}$, which is long compared to a Hubble time ($\sim {10}^{10}$ yr). Indeed, the spindown time for all models is long compared to the Hubble time.

We conclude that for models that have sufficiently powerful jets and are consistent with EHT2017, ${P}_{\mathrm{jet}}$is driven by extraction of black hole spin energy through the Blandford–Znajek process.

6.4. Constraint Summary

We have applied constraints from AIS, a radiative self-consistency constraint, a constraint on maximum X-ray luminosity, and a constraint on minimum jet power. Which models survive? Here we consider only models for which we have calculated ${L}_{{\rm{X}}}$ and ${L}_{\mathrm{bol}}$. Table 2 summarizes the results. Here we consider only i = 163° (for ${a}_{* }\geqslant 0$) and i = 17° (for ${a}_{* }\lt 0$). The first three columns give the model parameters. The next four columns show the result of application of each constraint: Themis-AIS (here broken out by individual model rather than groups of models), radiative efficiency ($\epsilon \lt {\epsilon }_{\mathrm{thin}\mathrm{disk}}$), ${L}_{{\rm{X}}}$, and ${P}_{\mathrm{jet}}$.

Table 2.  Rejection Table

Fluxa${a}_{* }$ b${R}_{\mathrm{high}}$ cAISdepsilone${L}_{{\rm{X}}}$ f${P}_{\mathrm{jet}}$ g 
SANE−0.941FailPassPassPassFail
SANE−0.9410PassPassPassPassPass
SANE−0.9420PassPassPassPassPass
SANE−0.9440PassPassPassPassPass
SANE−0.9480PassPassPassPassPass
SANE−0.94