{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 4 - Different Methods for Inferring Velocities\n", "\n", "In the [previous tutorial](https://eddy.readthedocs.io/en/latest/tutorials/tutorial_3.html), we saw how modeling the line center of an annulus of spectra as a simple harmonic oscillator provided a good way to extract radial profiles of $v_{\\phi}$ and $v_{\\rm r}$. While this was a quick approach, we essentially threw data away by collapsing each spectrum into a single value: the line center. In this tutorial, we will look at alternative methods to infer the velocity structure by leveraging as much information as possible.\n", "\n", "## Background\n", "\n", "To demonstrate the power of using a full spectrum in this endeavor, let's look at a [river plot](https://eddy.readthedocs.io/en/latest/tutorials/tutorial_3.html#Inspecting-an-Annulus) again. The figure below shows a river plot for an annulus between $1.5^{\\prime\\prime}$ to $1.6^{\\prime\\prime}$ in TW Hya. It cycles through different $v_{\\phi}$ values, shown in the top left of the bottom panel.\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As can be clearly seen, when $v_{\\phi}$ approaches the correct value, the river straightens out and the azimuthally averaged spectrum, shown along the top, aproaches a high SNR Gaussian profile. There have been several approaches which have been described in the literature that leverage this fact. We'll explore them below.\n", "\n", "## Deprojection Basics\n", "\n", "First of all, we need to explore some of the features of the `annulus` class. Let's load up a cube and grab an annulus. Here we're using a slightly different example cube that has CS emission from [Teague et al. (2018b)](https://ui.adsabs.harvard.edu/abs/2018ApJ...864..133T/abstract) and is available for download from the `GoFish` [Dataverse](https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/LO2QZM)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import os\n", "if not os.path.exists('TWHya_CS_cube.fits'):\n", " !wget -O TWHya_CS_cube.fits -q https://dataverse.harvard.edu/api/access/datafile/:persistentId?persistentId=doi:10.7910/DVN/LO2QZM/KYZFUQ" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from eddy import linecube\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "cube = linecube('TWHya_CS_cube.fits', FOV=8.0)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "annulus = cube.get_annulus(r_min=1.5, r_max=1.6, inc=6.0, PA=151.0)\n", "annulus.plot_river()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Deprojected Spectrum\n", "\n", "One of the fundamental functions of the `annulus` class is the `deprojected_spectrum` function. This shifts each spectrum by the projected velocity component decribed by $(v_{\\rm \\phi},\\, v_{\\rm r})$ and then averages of all spectra. This is what produces the spectrum on the top of the river plot." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "x, y, dy = annulus.deprojected_spectrum(vrot=0.0)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1417.3097826192488, 4567.690222234542)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.errorbar(x, y * 1e3, dy * 1e3, fmt=' ', capsize=2.0, lw=1.0, color='k')\n", "ax.step(x, y * 1e3, where='mid', lw=1.0, color='k')\n", "ax.set_ylabel('Intensity (mJy/beam)')\n", "ax.set_xlabel('Velocity (m/s)')\n", "ax.set_xlim(x.min(), x.max())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ``annulus`` class has a convenience function, ``plot_spectrum`` which will align, stack and plot the spectra for you!" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "annulus.plot_spectrum(vrot=0.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Just as we did for the `plot_river` function, we can provide the correct rotation velocity to get a nicer looking spectrum. For now, let's use the `fit_SHO` approach to infer the velocity profile." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "v_phi = 2673 +\\- 58 m/s\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "<>:3: SyntaxWarning: invalid escape sequence '\\-'\n", "<>:3: SyntaxWarning: invalid escape sequence '\\-'\n", "/var/folders/z9/_4lwkgl55kl7l0m8mh9pm1340000gn/T/ipykernel_30599/3705158399.py:3: SyntaxWarning: invalid escape sequence '\\-'\n", " print('v_phi = {:.0f} +\\- {:.0f} m/s'.format(v_phi, dv_phi))\n" ] } ], "source": [ "v, dv = annulus.get_vlos(fit_method='SHO')\n", "v_phi, dv_phi = v[0], dv[0]\n", "print('v_phi = {:.0f} +\\- {:.0f} m/s'.format(v_phi, dv_phi))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "annulus.plot_spectrum(vrot=v_phi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `deprojected_spectrum` also takes a `vrad` argument in case you have an idea of what $v_{\\rm r}$ should be. In addition, we can overplot a Gaussian fit to the data to check how well the aligning has done." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "annulus.plot_spectrum(vrot=v_phi, plot_fit=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Resampled Spectra\n", "\n", "Another powerful aspect of the `deprojected_spectrum` function is that you can resample your averaged spectrum to a finer channel spacing, as done in [Teague & Loomis (2020)](https://ui.adsabs.harvard.edu/abs/2020ApJ...899..157T/abstract). This works because for each spectrum at a polar angle $\\phi$, the Doppler shift is not quantized into channels meaning that we sample the underlying spectrum at a much higher rate. This can be seen when we use `resample=False`." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "x, y, dy = annulus.deprojected_spectrum(vrot=v_phi, resample=False)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mean spacing = 2.5 m/s\n" ] } ], "source": [ "print('mean spacing = {:.1f} m/s'.format(np.diff(x).mean()))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "annulus.plot_spectrum(vrot=v_phi, resample=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `resample` argument is actually quite versatile. If we provide it a float, this specifies the new channel spacing (e.g., `resample=10.0` will return the spectrum binned down to 10 m/s channels), while an integer specifies the factor that the current spacing is increased by (e.g., `resample=4` will return a spectrum with a sampling rate 4 times higher than the native data." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# resample at 20 m/s\n", "fig = annulus.plot_spectrum(vrot=v_phi, resample=20.0,\n", " plot_kwargs=dict(color='0.8'), return_fig=True)\n", "\n", "# resample at 200 m/s\n", "annulus.plot_spectrum(vrot=v_phi, resample=200.0,\n", " ax=fig.axes[0], plot_kwargs=dict(color='C1'))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With this functionality in mind, we can look at how we can used these deprojected spectra to infer the correct velocity.\n", "\n", "## Maximizing Signal to Noise\n", "\n", "[Yen et al. (2018)](https://ui.adsabs.harvard.edu/abs/2018A%26A...616A.100Y/abstract) proposed that the correct velocity should maximize the signal-to-noise of the averaged spectrum. This because of two main aspects:\n", "\n", "1) As the specrta are aligned, they will average coherently and so will result in the largest peak intensity (modulo background noise). You can see this by comparing the peak of the deprojected spectra above with and without the correct alignment. \n", "\n", "2) Averaging over many samples beats down the noise. For independent spectra we would expect a ${\\sim} \\sqrt{N}$ improvement in the noise measured in the spectrum when averaging over $N$ spectra. We have the added advantage with the velocity shifting in that some spatial correlations are decorrelated due to the shifting of the spectra (see [Yen et al., 2016,](https://ui.adsabs.harvard.edu/abs/2016ApJ...832..204Y/abstract) for a discussion about this).\n", "\n", "This approach can get used in the `get_vlos` function using `fit_method='SNR'`." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "v_phi = 2673 m/s\n" ] } ], "source": [ "print('v_phi = {:.0f} m/s'.format(annulus.get_vlos(fit_method='SNR')[0][0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This approach (as it is currently coded) has two issues. Firstly, it does not return an uncertainty on $v_{\\rm \\phi}$ as it simply uses `scipy.optimize.minimize` to minimize the negative SNR of the deprojected spectrum.\n", "\n", "The other is that the calculation of the SNR involves several steps: measuring the 'signal' of the spectrum and measuring the 'noise' of the spectrum. The signal is calculated either by taking the integrated intensity of the deprojected spectrum (`signal='int'`, the default), or the peak intensity (`signal='max'`). As both of these quantities are very noise as a function of $v_{\\rm \\phi}$, the `annulus` class will fit a Gaussian profile to the deprojected spectrum to calculate these quantities.\n", "\n", "[Yen et al. (2018)](https://ui.adsabs.harvard.edu/abs/2018A%26A...616A.100Y/abstract) also discuss this issue, and advocate for using a Gaussian weighting when calculating the SNR, such that high intensity parts of the spectrum count more to this statistic. This can be used with `signal='weighted'`.\n", "\n", "## Minimizing Line Width\n", "\n", "To circumvent noisiness of the SNR statistic, [Teague et al. (2018a)](https://ui.adsabs.harvard.edu/abs/2018ApJ...860L..12T/abstract) advocated for using the line width as a proxy for alignment. When the spectra are aligned correctly, the width of the averaged spectrum should be minimized. This can be used with the `fit_method='dV'` arugment." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "v_phi = 2753 m/s\n" ] } ], "source": [ "print('v_phi = {:.0f} m/s'.format(annulus.get_vlos(fit_method='dV')[0][0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, this method (as it is currently coded) does not return an uncertainly. In addition, this approach requires the fitting of a Gaussian profile to the averaged spectrum which may fail for noisy spectra or poor starting conditions. One particular worry is that if the underlying profile is _not_ a Gaussian, then both these methods will fail.\n", "\n", "## Gaussian Processes\n", "\n", "To remove any dependence on the underlying line profile, [Teague et al. (2018c)](https://ui.adsabs.harvard.edu/abs/2018ApJ...868..113T/abstract) showed that modeling the underlying spectrum as a Gaussian Process can provide excellent results. In essence, this approach asks for what $v_{\\rm \\phi}$ will the noise in the spectrum be minimized (and spectrally independent). Consider how the uncertainty changes for the case of no alignment and the correct alignment." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "\n", "x, y, dy = annulus.deprojected_spectrum(vrot=0.0)\n", "ax.step(x, dy * 1e3, where='mid', lw=1.0, label='no alignment')\n", "\n", "x, y, dy = annulus.deprojected_spectrum(vrot=v_phi)\n", "ax.step(x, dy * 1e3, where='mid', lw=1.0, label='aligned')\n", "\n", "ax.set_ylabel('Noise (mJy/beam)')\n", "ax.set_xlabel('Velocity (m/s)')\n", "ax.set_xlim(x.min(), x.max())\n", "ax.legend(markerfirst=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The noise rockets around the line center when the alignment is incorrect due to the misalignment of the spectra.\n", "\n", "To implement the fitting `eddy` will use the `emcee` MCMC sampler and [tinygp](https://tinygp.readthedocs.io/) for the Gaussian Processes, and can be called with the `fit_method='GP'` argument. To help with the MCMC, this function takes the commonly used `nwalkers`, `nburnin` and `nsteps` arguments that were used in earlier tutorials fitting the rotation maps. By default, `get_vlos` will return the median value of the posterior samples and half the 84th to 16th percentile as the uncertainty." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 1000/1000 [02:52<00:00, 5.79it/s]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "v_phi = 2683 +\\- 8 m/s\n" ] } ], "source": [ "print('v_phi = {:.0f} +\\- {:.0f} m/s'.format(*np.squeeze(annulus.get_vlos(fit_method='GP')).flatten()[::3]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple Harmonic Oscillator\n", "\n", "As we saw in the [previous tutorial](https://eddy.readthedocs.io/en/latest/tutorials/tutorial_3.html) we can also fit the line centroids with a simple harmonic oscillator model." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "v_phi = 2673 +\\- 58 m/s\n" ] } ], "source": [ "v, dv = annulus.get_vlos(fit_method='SHO')\n", "print('v_phi = {:.0f} +\\- {:.0f} m/s'.format(v[0], dv[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## More Control\n", "\n", "In fact, `get_vlos` is just a convenience wrapper for the underlying functions: `get_vlos_*` where `*` is the `fit_method` provide to `get_vlos`. These functions will have more functionality to aid in the fitting, such as producing plots of the walkers or posteriors for the `GP` method." ] } ], "metadata": { "kernelspec": { "display_name": "base", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.11" } }, "nbformat": 4, "nbformat_minor": 4 }