{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "/usr/local/lib/python3.9/site-packages/clustertools-0.1.dev3-py3.9.egg/clustertools/analysis/profiles.py:34: FutureWarning: all profiles are setup such that the returned radial bins and profile values are in linear space and not normalized by the effective radius. Previously select profiles had unique returns.\n", " warnings.warn('all profiles are setup such that the returned radial bins and profile values are in linear space and not normalized by the effective radius. Previously select profiles had unique returns.',FutureWarning)\n", "\n" ] } ], "source": [ "import clustertools as cts\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Operations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Units" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First load a snapshot of a cluster in file 00000.dat, which has position units of pc and velocity units of km/s in clustercentric coordinates. Stellar masses are in solar units and were generated using a Salpeter IMF." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "cluster=cts.load_cluster('snapshot',filename='00000.dat',units='pckms',origin='cluster',ofilename='orbit.dat',ounits='kpckms')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When using ``load_cluster``, key parameters like the total mass and the half-mass radius of the cluster are automatically calculated:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once initialized, the units and coordinate system of the cluster can easily be changed. Unit changes will affect the positions and velocities of stars, the location of the cluster's centre of density, and the cluster itself if its galactocentric coordinates are known. When changing units, key parameters are recalculated. As per the below example, the mean radius and ragrange radii are caclulated when the units are ``pckms``." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean radius with numpy = 2.45102483757\n", "Mean radius = 2.45102483757\n", "Half mass radius = 1.96178691294\n", "50% Lagrange Radius = 1.96178691294\n" ] } ], "source": [ "print('Mean radius with numpy =', np.mean(cluster.r))\n", "print('Mean radius =', cluster.rmean)\n", "\n", "print('Half mass radius =', cluster.rm)\n", "\n", "cluster.rlagrange()\n", "print('50% Lagrange Radius = ',cluster.rn[4])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, both methods yield the exact same results. Since ``cluster.units`` currently eqauls ``'pckms``, radii are in parsecs. We can then convert to ``'kpckms'``:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "cluster.to_kpckms()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since coordinates are changed to ``'kpckms'``, stellar radii will all be changed. Hence calculating the mean radius with numpy will yield the result in kpc. ``cluster.rmean`` and ``cluster.rm`` will also change as ``cluster.analyze`` is always called after a unit change. Conversely, ``cluster.rn`` won't change unless ``cluster.rlagrange()`` is called again:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean radius with numpy = 0.00245102483757\n", "Mean radius with clustertools = 0.00245102483757\n", "Half mass radius = 0.00196178691294\n", "50% Lagrange Radius = 1.96178691294\n" ] } ], "source": [ "print('Mean radius with numpy = ',np.mean(cluster.r))\n", "print('Mean radius with clustertools = ',cluster.rmean)\n", "print('Half mass radius =', cluster.rm)\n", "print('50% Lagrange Radius = ',cluster.rn[4])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The only way to update the units of ``cluster.rn`` is to calculate the lagrange radii again." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean radius with numpy = 0.00245102483757\n", "Mean radius with clustertools = 0.00245102483757\n", "Half mass radius = 0.00196178691294\n", "50% Lagrange Radius = 0.00196178691294\n" ] } ], "source": [ "cluster.to_kpckms()\n", "print('Mean radius with numpy = ',np.mean(cluster.r))\n", "print('Mean radius with clustertools = ',cluster.rmean)\n", "\n", "print('Half mass radius =', cluster.rm)\n", "cluster.rlagrange()\n", "print('50% Lagrange Radius = ',cluster.rn[4])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Other unit systems include ``galpy``,``nbody``,``WDunits``, and ``radec``. For ``nbody``, most of the time a dataset is given in N-body units and then converted to physical units. However if you wish to convert to Nbody units, the scaling factors for masses, positions, velocities and time must be determined. This can be done via:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MASS SCALING: 349.28177634\n", "POSITION SCALING: 2.51937714706\n", "VELOCITY SCALING: 0.772052003633\n", "TIME SCALING: 3.18985540807\n" ] } ], "source": [ "cluster.reset_nbody_scale()\n", "print('MASS SCALING: ',cluster.zmbar)\n", "print('POSITION SCALING: ',cluster.rbar)\n", "print('VELOCITY SCALING: ',cluster.vbar)\n", "print('TIME SCALING: ',cluster.tbar)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the default way of finding the position scaling is to set ``cluster.rbar`` equal to the cluster's virial radius, such that when scaled the cluster's virial radius in Nbody units is 1. A computationall cheaper approximation is to set ``cluster.rbar`` equal to 4/3 the cluster's half-mass radius with ``rvirial=False``." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MASS SCALING: 349.28177634\n", "POSITION SCALING: 2.61571588392\n", "VELOCITY SCALING: 0.757701003404\n", "TIME SCALING: 3.37455937226\n" ] } ], "source": [ "cluster.reset_nbody_scale(rvirial=False)\n", "print('MASS SCALING: ',cluster.zmbar)\n", "print('POSITION SCALING: ',cluster.rbar)\n", "print('VELOCITY SCALING: ',cluster.vbar)\n", "print('TIME SCALING: ',cluster.tbar)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once the Nbody scaling factors have been determined, one can convert to NBODY units to make caluclations" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cluster.to_nbody()\n", "cts.starplot(cluster)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Changing units to ``radec`` will first move the clustre onto the plane of the sky. If ``origin=galaxy`` then that is where the cluster will remain, however if ``origin=cluster`` or ``origin=centre`` then the cluster will be moved back to clustercentric coordinates using the appropriate centreing method." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cluster.to_radec()\n", "cts.starplot(cluster)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Coordinate Systems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "clustertools allows users to move their cluster between Galactocentric coordinates, clustercentric coordinates, the cluster's centre of density frame, or the plane of the sky.\n", "\n", "Lets begin by loading a cluster snapshot in clustercentric coordinates." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean radius with numpy = 2.45102483757\n", "Mean radius with clustertools = 2.45102483757\n", "Half mass radius = 1.96178691294\n", "50% Lagrange Radius = 1.96178691294\n" ] }, { "data": { "text/plain": [ "0" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cluster=cts.load_cluster('snapshot',filename='00000.dat',units='pckms',origin='cluster',ofilename='orbit.dat',ounits='kpckms')\n", "print('Mean radius with numpy = ',np.mean(cluster.r))\n", "print('Mean radius with clustertools = ',cluster.rmean)\n", "print('Half mass radius =', cluster.rm)\n", "rln=cluster.rlagrange()\n", "print('50% Lagrange Radius = ',cluster.rn[4])\n", "\n", "cts.starplot(cluster)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To view your cluster in the galaxy's reference frame and calculate values in kpc:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "cluster.to_kpckms()\n", "cluster.to_galaxy()\n", "rln=cluster.rlagrange()" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean radius with numpy = 9.99998180299\n", "Mean radius with clustertools = 9.99998180299\n", "Half mass radius = 9.9999783598\n", "50% Lagrange Radius = 0.00194950947706\n" ] }, { "data": { "text/plain": [ "0" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print('Mean radius with numpy = ',np.mean(cluster.r))\n", "print('Mean radius with clustertools = ',cluster.rmean)\n", "print('Half mass radius =', cluster.rm)\n", "print('50% Lagrange Radius = ',cluster.rn[4])\n", "\n", "cts.starplot(cluster)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the cluster's rlagrange radii have only changed units. This is because rlagrange radii, by definition, are always calculated with respect to the cluster's centre." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two functions worth noting are ``save_cluster`` and ``return_cluster``. ``save_cluster`` will return the current units and origin of your cluster, so you can then i) change units/coordinate systems, ii) make calculates, and then return your cluster to its original state using ``return_cluster``.\n", "\n", "For example, with the above cluster having ``units='kpckms'`` and ``origin='galaxy'``, one may wish to switch to the clustercentric frame of reference to calculate the half-mass radius:" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "kpckms galaxy\n", "Half mass radius = 0.00196178691294\n", "kpckms galaxy\n" ] } ], "source": [ "#Save Cluster\n", "units,origin,rorder,rorder_origin=cts.save_cluster(cluster)\n", "print(units,origin)\n", "#Move to clustercentric coordinates\n", "cluster.to_cluster()\n", "print('Half mass radius = ',cluster.rm)\n", "#Move back\n", "cts.return_cluster(cluster,units,origin,rorder,rorder_origin)\n", "print(cluster.units,cluster.origin)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is worth noting that if ``cluster.units='galaxy'``, almost all functions will move the cluster to a clustercentric coordinate system or to its centre of density to make calculations and then return it to its original state." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, two operations that may be helpful when trying to initialize a cluster are ``virialize`` and ``add_rotation``. ``virialize`` will scale all the stellar velocities so the virial parameter is exactly 0.5." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-1.40814083302\n", "New Qv: -0.504310752662\n" ] } ], "source": [ "#At the moment, our cluster is not perfectly in virial equilibrium:\n", "cluster.energies()\n", "print(cluster.qvir)\n", "#However it can be scaled such that ``cluster.qvir=-0.5``\n", "cluster.virialize()\n", "cluster.energies()\n", "\n", "print('New Qv: ',cluster.qvir)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Adding rotation will, as the name implies, add a degree of rotation to the cluster. Rotation is added using the ``qrot`` parameter, which will be the fraction of stars with v_phi < 0 that are switched to having vphi > 0. It can be done via:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fraction of stars with vtheta<0 = 0.52\n", "Add rotation of 50%\n", "Now fraction of stars with vtheta<0 = 0.249\n" ] } ], "source": [ "#How many stars have vtheta < 0 in the clustercentric coordinate system\n", "cluster.to_cluster()\n", "r, theta, z, vr, vtheta, vz=cts.cart_to_cyl(cluster.x,cluster.y,cluster.z,cluster.vx,cluster.vy,cluster.vz)\n", "print('Fraction of stars with vtheta<0 =', np.sum(vtheta<0)/cluster.ntot)\n", "\n", "#Now switch the sign of vtheta for 50% of stars with vtheta<0\n", "print('Add rotation of 50%')\n", "cluster.add_rotation(qrot=0.5)\n", "r, theta, z, vr, vtheta, vz=cts.cart_to_cyl(cluster.x,cluster.y,cluster.z,cluster.vx,cluster.vy,cluster.vz)\n", "print('Now fraction of stars with vtheta<0 =', np.sum(vtheta<0)/cluster.ntot)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Edit Metadata", "kernelspec": { "display_name": "Python 3", "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": "3.9.1" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }