amoeba2 1.0.1

Automated Molecular Excitation Bayesian line-fitting Algorithm

amoeba2

Automated Molecular Excitation Bayesian line-fitting Algorithm

amoeba2 is a Bayesian model of the 1612, 1665, 1667, and 1720 MHz hyperfine transitions of OH written in the bayes_spec spectral line modeling framework. amoeba2 is inspired by AMOEBA and Petzler et al. (2021).

Read below to get started, and check out the tutorials here: https://amoeba2.readthedocs.io

• Installation
  • Basic Installation
  • Development Installation
• Notes on Physics & Radiative Transfer
• Models
  • TauModel
  • TauTBModel
  • ordered
• Syntax & Examples
• Issues and Contributing
• License and Copyright

Installation

Basic Installation

Install with pip:

pip install amoeba2

Development Installation

Alternatively, download and unpack the latest release, or fork the repository and contribute to the development of amoeba2!

Install in a conda virtual environment:

cd /path/to/amoeba2
conda env create -f environment.yml
conda activate amoeba2-dev
pip install -e .

Notes on Physics & Radiative Transfer

All models in amoeba2 apply the same physics and equations of radiative transfer.

The transition optical depth is taken from Magnum & Shirley (2015) equation 29. The excitation temperature is allowed to vary between transitions (a non-LTE assumption) and clouds. The excitation temperatures of the 1612, 1665, and 1667 MHz transitions are free, whereas that of the 1720 MHz transition is derived from the excitation temperature sum rule.

The radiative transfer is calculated explicitly assuming an off-source background temperature bg_temp (see below) similar to Magnum & Shirley (2015) equation 23. By default, the clouds are ordered from nearest to farthest, so optical depth effects (i.e., self-absorption) may be present.

Notably, since these are forward models, we do not make assumptions regarding the optical depth or the Rayleigh-Jeans limit. These effects are predicted by the model. There is one exception: the ordered argument, described below.

Models

The models provided by amoeba2 are implemented in the bayes_spec framework. bayes_spec assumes that the source of spectral line emission can be decomposed into a series of "clouds", each of which is defined by a set of model parameters. Here we define the models available in amoeba2.

TauModel

TauModel is a model that predicts the OH hyperfine optical depth spectra, typically measured via absorption observations. The SpecData keys for this model must be "tau_1612", "tau_1665", "tau_1667", and "tau_1720". The following diagram demonstrates the relationship between the free parameters (empty ellipses), deterministic quantities (rectangles), model predictions (filled ellipses), and observations (filled, round rectangles). Many of the parameters are internally normalized (and thus have names like _norm). The subsequent tables describe the model parameters in more detail.

Cloud Parameter variable	Parameter	Units	Prior, where ($p_0, p_1, \dots$) = prior_{variable}	Default prior_{variable}
log10_N_0	log10 lowest energy state column density	cm-2	$\log_{10}N_0 \sim {\rm Normal}(\mu=p_0, \sigma=p_1)$	[13.0, 1.0]
inv_Tex	Inverse excitation temperature	K-1	$T_{\rm ex}^{-1} \sim {\rm Normal}(\mu=p_0, \sigma=p_1)$	[0.1, 1.0]
fwhm	FWHM line width	km s-1	$\Delta V_{\rm H} \sim {\rm Gamma}(\alpha=2.0, \beta=1.0/p)$	1.0
velocity	Velocity	km s-1	$V \sim {\rm Normal}(\mu=p_0, \sigma=p_1)$	[0.0, 10.0]

Hyper Parameter variable	Parameter	Units	Prior, where ($p_0, p_1, \dots$) = prior_{variable}	Default prior_{variable}
rms_tau	Optical depth rms noise	``	${\rm rms}_\tau \sim {\rm HalfNormal}(\sigma=p)$	0.1

TauTBModel

TauTBModel is otherwise identical to TBModel, except it also predicts the brightness temperature spectra assuming a given background source brightness temperature (where bg_temp is in K and is supplied during model initialization TBTauModel(bg_temp=2.7)). The SpecData keys for this model must be "tau_1612", "tau_1665", "tau_1667", "tau_1720", "TB_1612", "TB_1665", "TB_1667", and "TB_1720". The following diagram demonstrates the model, and the subsequent table describe the additional model parameters.

Hyper Parameter variable	Parameter	Units	Prior, where ($p_0, p_1, \dots$) = prior_{variable}	Default prior_{variable}
rms_TB	Brightness temperature spectral rms noise	``	${\rm rms}_{T} \sim {\rm HalfNormal}(\sigma=p)$	1.0

ordered

An additional parameter to set_priors for these models is ordered. By default, this parameter is False, in which case the order of the clouds is from nearest to farthest. Sampling from these models can be challenging due to the labeling degeneracy: if the order of clouds does not matter (i.e., the emission is optically thin), then each Markov chain could decide on a different, equally-valid order of clouds.

If we assume that the emission is optically thin, then we can set ordered=True, in which case the order of clouds is restricted to be increasing with velocity. This assumption can drastically improve sampling efficiency. When ordered=True, the velocity prior is defined differently:

Cloud Parameter variable	Parameter	Units	Prior, where ($p_0, p_1, \dots$) = prior_{variable}	Default prior_{variable}
velocity	Velocity	km s-1	$V_i \sim p_0 + \sum_0^{i-1} V_i + {\rm Gamma}(\alpha=2, \beta=1.0/p_1)$	[0.0, 1.0]

Syntax & Examples

See the various tutorial notebooks under docs/source/notebooks. Tutorials and the full API are available here: https://amoeba2.readthedocs.io.

Issues and Contributing

Anyone is welcome to submit issues or contribute to the development of this software via Github.

License and Copyright

Copyright (c) 2024 Trey Wenger

GNU General Public License v3 (GNU GPLv3)

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.