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Welcome to the iris Wiki

iris is a Python library to generate slab models of molecular emission in disks.

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Table of Contents

1. Installation
2. Crash Course
   2.1 Calculating Fluxes 2.2 Keplerian Broadening
3. Examples
4. FAQ

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Installation

Install the package via pip:

pip install iris-jwst

iris requires the following packages be installed beforehand: jax, pandas, astropy, astroquery

and Python >= 3.8

Crash Course

Calculating Fluxes

With iris, the molecular emission lines are modeled using a slab technique, where the intensities are set by an average excitation temperature $(T_{ex})$, a column density ($N_{mol}$), and an emitting area $(A_{em})$. The population levels are assumed to be in Local Thermodynamic Equilibrium (LTE). That is, the excitation temperature and the gas kinetic temperature are assumed to be the same.

We assume the lines are Gaussians and have an intrinsic full-width-at-half-maximum $(\Delta V)$ which includes turbulent and thermal broadening. Note that $\Delta V$ is a free parameter set by the user.

Rather than directly calculating integrated line fluxes, iris generates an optical depth grid which is then used to calculate the opacity-weighted flux density. For each species, we estimate the total optical depth of lines $i=1,2,...,N$ as

$\tau (\lambda) = \sum_{i}^{N} \tau_{0,i} e^{(-(\lambda - \lambda_0)^2/2\sigma_{\lambda}^2)} $

where $\lambda_0$ is the rest wavelength of line $i$, $\sigma_{\lambda}$ is the line standard deviation $\left( \frac{\Delta V}{2\sqrt{2 \log 2}} \right)$, and the line-center optical depth is

$\tau_0 = \sqrt{\frac{\ln 2}{\pi}} \frac{A_{ul} N_{mol} \lambda_0^3}{4 \pi \Delta V} \left( x_l \frac{g_u}{g_l} - x_u \right)$.

Here $A_{ul}$ is the Einstein coefficient, $x_{l,u}$ the lower- and upper-level populations, and $g_{l,u}$ the lower- and upper-level degeneracies, respectively.

Setting a distance to the source of $d$, we can then compute the flux assuming emission from a Blackbody $B_{\nu}$ at temperature $T = T_{ex}$:

$F(\lambda) = \left(\frac{A_{em}}{d^2}\right) B_{\nu}(T) \left( 1 - e^{-\tau(\lambda)} \right)$.

The rightmost term above sets the final line profile, accounting for saturation effects at the line center.

Keplerian Broadening

Optionally, we can go a step further and include the effects of Keplerian broadening on the line profiles. iris does this in 4 steps, which only add a couple milliseconds to the compute time:

1. Make a standard flux model $F_{\lambda}$ with turbulent+thermal broadening only.
2. Generate a flat, Keplerian disk model with inclination $i$, stellar mass $M_{*}$, innermost radius $r_{in}$, and outermost radius $r_{out}$.
3. Finely sample the line-of-sight velocities $v_{LOS} = v_{K} \sin(i) \cos(\phi)$ within the emitting region, where $v_{K} = (G M_{*}/r)^{0.5}$ is the Keplerian velocity and $\phi$ is the azimuthal angle. Make a normalized histogram ($k_{LOS}$) of $v_{LOS}$.
4. Convolve $F_{\lambda}$ with $k_{LOS}$.

The effects will be most noticeable for disks at high inclinations, very small inner radii, and/or with higher stellar masses.

Examples

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