自動微分可能なスペクトル
第一原理フィットツールの開発と高温下の分子線幅測定計画
Hajime Kawahara, Yui Kawashima, Kento Masuda, IanCrossfield, Erwan Pannier, van den Bekerom, Takayuki
Kotani, Kazuo Yoshioka, Tako Ishikawa, Stevanus Nugroho,and REACH collaboration
Kawahara+ ApJS in press 2105.14782

REACH: High-Dispersion Spectrum for High-Contrast Instruments
High-Dispersion Coronagraphy on Subaru
Kawahara, Murakami, Matsuo, and Kotani (2014) ApJS
Late 2014: Started to develop such an instrumentwith SCExAO team (Guyon, Lozi, Jovanovic etc)
and IRD (Kotani, Vievard etc) on Subaru
Late 2020: available for science use (open use)

SCExAO Extreme AO

Proposal 採択数
32120B

21A

21B

22A

CoronagraphPhotometric monitoring
High-Resolution Spectrograph

IRD
Subaru/REACH

REACH (Subaru):
KPIC (Keck):
HiRISE (VLT):y, J, H
R=100,000 (SCExAO + IRD)
K, L, M
R=30,000 (NIRSPEC)
Under construction H, K, … R=100,000 (SPHERE + CRIRES+)

孤立BD
L10.7”/ コントラスト10-4

L3

L4T4exojax auto-differentiable spectrum model
Atmosphere

Macrophysics

Physical quantities
Temperature Profile
Molecular abundanceObservational Data
Gravity
Micro Turbulence

Raw
Spectrum

Cross Section+Spectrum Model

Radiative Transfer

Planet Atmosphere

Likelihood & prior
Noise model

Instrument/Dynamics

Instrumental Response

Molecular Database

Opacity Computation

Bayes inference

Planet Rotation
Radial Velocity

Auto-Gradient + GPU

Gradient-based Efficient MCMC SamplingU = - Log (posterior)δU/δp

NumPyro
HMC-NUTS
Uber AID^5/4 (HMC) D^2 (random MCMC)

GoogleAgol+2020

DFM+2021

Masuda Hirano 2021

Luger+

exojax auto-differentiable spectrum model
Atmosphere

Macrophysics

Physical quantitiesTemperature Profile
Molecular abundance

Observational Data
Gravity
Micro Turbulence

Raw
Spectrum

Cross Section+Spectrum Model

Radiative Transfer

Planet Atmosphere

Likelihood & prior
Noise model

Instrument/Dynamics

Instrumental Response

Molecular Database

Opacity Computation

Bayes inference

Planet Rotation
Radial Velocity

Differentiable Voigt Profile

Algorithm 916: Zaghloul & Ali (2011)

Modified Discrete Integral Transform (MODIT)With van den Bekeroma and Pannier
Inverse FFT

Sum× Kernel

FFT

Lorentzian (j)In log wavenumber, a Doppler width is commonLog wavenumber q (i)Methane spectrum from scratch (exomol) using my laptop

Cross sectionDifferentiable Radiative Transfer

F0 = sum(Q * cumprod(T, axis=0), axis=0)01No scatteringnn+1

Auto-differentiable Rotation Kernel and Instrumental Profile簡単NumPyro

Demonstration using Luhman 16A as observed by CRIRES

CO+H2O+CIA
25000AA

20000
Rotation

Carbon/Oxygen Ratio
CRIRES data (Crossfield+2014)

Temperature Profile

Kawahara+ under review, arXiv:2105.14782

Line diagnostics of TemperatureGPもノイズモデルに簡単に入りますGPも温度圧力モデルに簡単に入ります孤立BD
L10.7”/ コントラスト10-4L3

L4T4

water
L1

water
L3

water
L4

methaneT4
データベース合ってないGravity from line broadening
ExoMol vs HITEMPO既存データベースの問題点

ExoMol 水素大気 but 実験での検証が不完全（とくに圧力幅）
HITEMP 地球大気

ExoMol vs HITEMP

川島氏提供

O考えるのがめんどくさいので自分たちで調べたい

ガラス石英管

チューブ炉

1000-1500K
分光器

光CO (1%) + 水素
CH4 + 水素etc を封入 → 分光したい

http://heattec.co.jp/roshinkan_sekiei.html

http://www.ogawaseiki.jpn.org/OSK481TVK205-645

写真はイメージですOまとめ

分子データベースから計算できベイズ推定が可能な系外惑星・褐色矮星スペクトルモデルをつくった

実際、観測スペクトルを良くフィットできる基礎データがいまいちなところがあるので、惑星大気を模擬したガスをいれて分光実験を企画している（共同研究募集中）