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Numerical Investigations on Explosion Mechanisms of Core-collapse Supernovae

原田, 了 東京大学 DOI:10.15083/0002001837

2021.10.04

概要

重力崩壊型超新星爆発とは、大質量星の最期の爆発現象である。重力崩壊型超新星の爆発メカニズムには多様な基礎物理過程が複雑に絡み合っており、メカニズム解明のためには数値計算が必須となる。星のコアはやがて重力崩壊を起こして潰れ、中心が原子核程度の密度になった段階で核力の反発により崩壊が止まり、外向きに進むバウンス衝撃波が形成される。この衝撃波はやがてエネルギーを失って停滞する。爆発メカニズム研究の主要な問題は、この停滞衝撃波をどのようにして復活させるかということである。衝撃波復活の仕組みにはいくつかの仮説があるが、本学位論文では特にニュートリノ加熱メカニズムと音響メカニズムと呼ばれる仮説を検証する。
 コアバウンス後に中心に形成される原始中性子星は重力崩壊で解放されるエネルギーのほぼ全てを蓄えており、ニュートリノ放射によって冷えていく。ニュートリノ加熱メカニズムにおいては、これらのニュートリノが衝撃波背後の物質を加熱することで衝撃波が復活する。このメカニズムでは球対称一次元を仮定する限り爆発が起こらない。乱流のような多次元効果の助けがあって初めて衝撃波が復活するのである。このメカニズムではニュートリノ輸送が重要な役割を果たすにも拘わらず、計算機資源が限られていることから、全ての研究グループは近似的なニュートリノ輸送法を用いている。この近似法はグループごとに違い、その精度もよくわかっていない。加えて、全てのグループは観測されているようなエネルギーの爆発は再現できていない。これは回転やニュートリノ反応、状態方程式、一般相対論的重力などといった重要な物理過程において、考えられていない側面があることが理由の可能性がある。さらに、ニュートリノ輸送近似法に問題がある可能性もある。
 音響メカニズムは、ニュートリノ加熱メカニズムによる爆発が失敗した後に働く。このメカニズムにおいては、中心の原始中性子星から強い音波が放射され、この音波が二次的な衝撃波に変化し、運動エネルギーを熱エネルギーに散逸することで停滞衝撃波を加熱する。音響メカニズムが働くのはバウンス後かなり時間が経ってからのため、数値計算で再現するのが難しい。発見者と別のグループ達はどの程度の強度の音波が放射されるか、という観点で研究を進めたが、その結果には食い違いが見られ、結論はまだ得られていない。

ニュートリノ加熱メカニズムの検証:ボルツマン輻射流体コードによる回転星の重力崩壊
 本学位論文では、まずニュートリノ加熱メカニズムを調べた。ニュートリノ輸送における近似を廃するため、ニュートリノ輸送のためにボルツマン方程式を直接解くボルツマン輻射流体コードが開発されている。このコードを用いた先行研究では現実的な状態方程式を用いた回転しない親星の重力崩壊を計算しても衝撃波が復活しなかったため、新たに何らかの物理過程を考慮に入れる必要がある。ここではそのような物理過程として、回転の効果を取り入れることとし、ボルツマン輻射流体コードを用いて自転する星の重力崩壊を計算した。その結果、衝撃波の形状には回転の影響が見られたが、衝撃波復活は起こらなかった。これは、平均の衝撃波半径やニュートリノの光度とその平均エネルギーが爆発しなかった無回転モデルとほぼ変わらなかったこと(図1)、さらに時間スケール比と呼ばれる、爆発が起こるかどうかを判定するためによく使われる基準を満たさなかったことから結論できる。本計算で採用した回転速度は星の進化理論から予想される範囲ではほとんど最速のものであるため、回転の効果だけでは衝撃波復活は起こらないと考えられる。
 爆発が起こるかどうかという点に直接の影響はないが、運動量空間におけるニュートリノ分布についても調べた。この時、ニュートリノの角度分布に加え、一次の角度モーメントであるフラックスと二次の角度モーメントであるエディントンテンソルに着目した。その結果、ニュートリノ角度分布とその角度モーメントはニュートリノフラックス、ニュートリノ反応、そして流体運動の複雑な組み合わせによって決まることがわかった。さらに、ニュートリノ輸送の近似法としてよく用いられる手法の一つであるM1-closure法の精度も調べた。その結果、M1-closure法において計算されるエディントンテンソルには最大で約20%の誤差が生じることがわかった(図2)。

音響メカニズム:衝撃波復活が起こるパラメータの臨界曲面
 回転の効果だけでは衝撃波は復活しないため、さらなる新しい効果として音波を考え、音響メカニズムによる爆発の可能性を調べた。ここでは、質量降着率とニュートリノ光度が系のパラメータとして与えられた際に、どれだけの強度の音波があれば衝撃波が復活するか、という観点で調べた。このために、時間的に一定な質量降着率とニュートリノ光度のもとで停滞衝撃波を含む球対称降着流の定常状態を構成して初期条件とし、中心の原始中性子星の表面から停滞衝撃波に向けて音波を放射させるシミュレーションを行った。この時、音波の振幅を与えて計算を行うが、議論の上で必要な量は音波強度である。そこで任意振幅の音波のエネルギーフラックスを計算するマイヤーズの理論を、ニュートリノ反応の効果も反映できるように拡張し、それを用いて音波強度を推定した。これらの計算の結果は、質量降着率・ニュートリノ光度・音波強度のパラメータ空間において臨界曲面を描くことでまとめた。この臨界曲面とは、衝撃波復活が起こるパラメータの組と起こらない組との間の境界となる曲面であり、与えられた質量降着率とニュートリノ光度に対し、爆発に最低限必要な音波強度を表す。まずは音波によるエネルギー輸送と加熱の性質を詳しく調べるため、単純な球対称一次元計算を行った。その結果、音波強度とニュートリノ加熱率の和がある閾値を超えると衝撃波復活が起こることがわかった。加えて、振幅の大きすぎる音波は強い二次衝撃波を作り、温度を上げてニュートリノ冷却を促進することが示され、音波によって供給されるエネルギーの全てが衝撃波復活に使われるわけではないことが判明した。続けて、球対称二次元で同様の数値計算を行った(図3)。音響メカニズムを発見した計算で得られていた音波強度は本計算で得られた爆発に最低限必要な音波強度より十分に大きく、音響メカニズムは確かに衝撃波を復活させられる可能性があることがわかった。

 本研究により超新星爆発メカニズムを考える上で回転や音波が果たす役割を調べたが、考えるべき物理過程はニュートリノ反応や核物質状態方程式、一般相対論的重力、三次元的効果等において、まだ数多く残っている。これらの物理過程もひとつずつその爆発への影響を調べ、結果を積み上げていくことで、重力崩壊型超新星爆発メカニズムの全貌を解明できるだろう。

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