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Created October 14, 2016 18:01
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"/Users/bovy/anaconda/envs/py27/lib/python2.7/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n",
" warnings.warn(self.msg_depr % (key, alt_key))\n",
"\n",
"galpyWarning: A major change in versions > 1.1 is that all galpy.potential functions and methods take the potential as the first argument; previously methods such as evaluatePotentials, evaluateDensities, etc. would be called with (R,z,Pot), now they are called as (Pot,R,z) for greater consistency across the codebase\n",
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"import numpy\n",
"import pandas\n",
"import gaia_tools.load as gload\n",
"from gaia_tools import xmatch\n",
"from galpy.util import bovy_plot, bovy_coords\n",
"from galpy.potential import MWPotential2014\n",
"from galpy.actionAngle import actionAngleStaeckel\n",
"_REFR0, _REFV0= 8., 220.\n",
"%pylab inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# A quick look at the overlap between *Gaia-DR1 TGAS* and the APOGEE-RC catalog"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Load the TGAS, APOGEE-RC data, and cross-match them:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"tgas= gload.tgas()\n",
"aprc= gload.apogeerc()\n",
"m1,m2,sep= xmatch.xmatch(aprc,tgas,colRA2='ra',colDec2='dec',epoch2=2015.)\n",
"aprc= aprc[m1]\n",
"tgas= tgas[m2]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The overlap is quite small:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1839\n"
]
}
],
"source": [
"print len(aprc)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"but spans a few kpc:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Compute XYZUVW for overlap sample\n",
"lb= bovy_coords.radec_to_lb(tgas['ra'],tgas['dec'],degree=True,epoch=None)\n",
"XYZ= bovy_coords.lbd_to_XYZ(lb[:,0],lb[:,1],aprc['RC_DIST'],degree=True)\n",
"pmllbb= bovy_coords.pmrapmdec_to_pmllpmbb(tgas['pmra'],tgas['pmdec'],\n",
" tgas['ra'],tgas['dec'],degree=True,epoch=None)\n",
"vxyz= bovy_coords.vrpmllpmbb_to_vxvyvz(aprc['VHELIO_AVG'],pmllbb[:,0],pmllbb[:,1],\n",
" XYZ[:,0],XYZ[:,1],XYZ[:,2],\n",
" XYZ=True,degree=True)\n",
"vRvTvZ= bovy_coords.vxvyvz_to_galcencyl(vxyz[:,0],vxyz[:,1],vxyz[:,2],\n",
" aprc['RC_GALR'],aprc['RC_GALPHI'],aprc['RC_GALZ'],Xsun=_REFR0,Zsun=0.025,\n",
" vsun=[-11.1,244.,7.25],galcen=True)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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M0rS6Dg8iZEIpta6UugbgctFzr1y5gvPnzzfQq+Fjcgqb+LKYeF1XPJqJEb548SJWV1fx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\nQUwIIYQQQibN/weqKI8EyFs7sAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11bad11d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bovy_plot.bovy_print(axes_labelsize=17.,text_fontsize=12.,xtick_labelsize=15.,ytick_labelsize=15.)\n",
"figsize(10,4)\n",
"subplot(1,2,1)\n",
"bovy_plot.bovy_plot(aprc['RC_GALR']*numpy.cos(aprc['RC_GALPHI']),\n",
" aprc['RC_GALR']*numpy.sin(aprc['RC_GALPHI']),\n",
" 'k.',ms=3.,\n",
" xlabel=r'$X\\,(\\mathrm{kpc})$',\n",
" ylabel=r'$Y\\,(\\mathrm{kpc})$',\n",
" xrange=[6.,11.],yrange=[-3.,3.],\n",
" gcf=True)\n",
"subplot(1,2,2)\n",
"bovy_plot.bovy_plot(aprc['RC_GALR'],\n",
" aprc['RC_GALZ'],\n",
" 'k.',ms=3.,\n",
" xlabel=r'$R\\,(\\mathrm{kpc})$',\n",
" ylabel=r'$Z\\,(\\mathrm{kpc})$',\n",
" xrange=[6.,11.],yrange=[-3.,3.],\n",
" gcf=True)\n",
"tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How do the precise RC distances compare to the TGAS parallaxes?"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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ERJSTTCYTVq9eje7ubhQVFWF0dDTugFRlB2QA2LRpE9atW6e2hni9XuzatUtd/Cs8OciU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\nCSEiIiJNMAkhIiIiTfx/N41AFYZPv/8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11c10ebd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figsize(9,4)\n",
"_= bovy_plot.bovy_hist(tgas['parallax']-1./aprc['RC_DIST'],\n",
" bins=51,yrange=[0.,299.],\n",
" histtype='step',lw=1.5,\n",
" xrange=[-2.5,2.5],\n",
" xlabel=r'$\\pi_{\\mathrm{TGAS}}-\\pi_{\\mathrm{RC}}$')\n",
"bovy_plot.bovy_text(r'$\\mathrm{median}\\ \\Delta\\pi = %.3f\\pm%.3f\\,\\mathrm{mas}$' \\\n",
" % (numpy.median(tgas['parallax']-1./aprc['RC_DIST']),\n",
" 1.4826*numpy.median(numpy.fabs(tgas['parallax']-1./aprc['RC_DIST']\n",
" -numpy.median(tgas['parallax']-1./aprc['RC_DIST'])))\\\n",
" /numpy.sqrt(len(tgas)))\n",
" +'\\n'+r'$\\sigma_{\\Delta\\pi} = %.3f\\,\\mathrm{mas}$' \\\n",
" % (1.4826*numpy.median(numpy.fabs(tgas['parallax']-1./aprc['RC_DIST']\n",
" -numpy.median(tgas['parallax']-1./aprc['RC_DIST']))))\\\n",
" +'\\n'+r'$e_{\\pi,\\mathrm{TGAS}} = %.3f\\,\\mathrm{mas}$' \\\n",
" % (numpy.median(tgas['parallax_error'])),\n",
" top_right=True,size=16.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This median offset is larger than expected from the $2\\,\\%$ accuracy of the RC distances and is in the same direction as the systematic offset found by Stassun & Torres. But the parallaxes and distances agree to $< 10\\%$, which is good news for this sample! The width of the distribution is consistent with the parallax errors from TGAS (RC distances are precise to $5\\,\\%$ or about 0.05 mas for this sample). Does this offset have any log $g$ dependence?"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11c54e250>]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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dig8n1grWZttHErzhjmvX90Q+oVEsCx/G2L1UpJNIJ6xMVkpH0X2HzqDSW4QC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\nEASRdP5/vCXmhEKxSHoAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1396dcf10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figsize(6,4)\n",
"bovy_plot.bovy_plot(aprc['LOGG'],tgas['parallax']-1./aprc['RC_DIST'],'.',ms=7.,\n",
" xrange=[1.8,3.2],yrange=[-2.,2.],\n",
" xlabel=r'$\\mathrm{log} g$',\n",
" ylabel=r'$\\pi_{\\mathrm{TGAS}}-\\pi_{\\mathrm{RC}}$')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is perhaps a small log $g$ trend at higher log $g$, but very little. Similarly, the trend with distance is pretty much flat, except that the TGAS distances are somewhat small compared to the RC distances at small distances:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1169cbd50>]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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qTPG+L7HeQygcwbJrp+Dtj45TEkZ/EQsyWaPNZjHjFzfNwvdf69t54n4jowwy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\nSUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11c32c250>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figsize(6,4)\n",
"bovy_plot.bovy_plot(aprc['RC_DIST'],tgas['parallax']-1./aprc['RC_DIST'],'.',ms=7.,\n",
" xrange=[0.,2.5],yrange=[-2.,2.],\n",
" xlabel=r'$\\mathrm{distance}\\,(\\mathrm{kpc})$',\n",
" ylabel=r'$\\pi_{\\mathrm{TGAS}}-\\pi_{\\mathrm{RC}}$')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The distribution of tangential velocity errors is:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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0eAtERL2qr693eYNKT0/Htm3bIlQiV45LVfcVcVkJ2Pzrn/0DbkkepUor3v1chEpD4WYw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\nMVYCRERx7P8DaDQyHMct3L0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11c149f10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"vra= aprc['RC_DIST']*tgas['pmra']*bovy_coords._K # K transforms to km/s\n",
"vdec= aprc['RC_DIST']*tgas['pmdec']*bovy_coords._K\n",
"vra_err= numpy.sqrt(0.05**2.*vra**2.+aprc['RC_DIST']**2.*tgas['pmra_error']**2.)\n",
"vdec_err= numpy.sqrt(0.05**2.*vdec**2.+aprc['RC_DIST']**2.*tgas['pmdec_error']**2.)\n",
"_= bovy_plot.bovy_hist(vra_err,\n",
" bins=51,\n",
" histtype='step',lw=1.5,\n",
" xrange=[0.,10.],\n",
" xlabel=r'$(e_{v_{\\alpha}},e_{v_{\\delta}})\\,(\\mathrm{km\\,s}^{-2})$')\n",
"_= bovy_plot.bovy_hist(vdec_err,\n",
" bins=51,\n",
" histtype='step',lw=1.5,\n",
" xrange=[0.,10.],\n",
" overplot=True)\n",
"bovy_plot.bovy_text(r'$\\mathrm{median}\\ e_{v_{\\alpha}} = %.1f\\,\\mathrm{km\\,s}^{-1}$' % (numpy.median(vra_err))\n",
" +'\\n'+r'$\\mathrm{median}\\ e_{v_{\\delta}} = %.1f\\,\\mathrm{km\\,s}^{-1}$' % (numpy.median(vdec_err)),\n",
" top_right=True,size=17.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"and a scatter plot of $v_\\alpha$ error and $v_\\alpha$ error versus distance:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11bf45f50>]"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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CH5flsh5pFVjrcDw3oV19NUr7el5t0LihmDwUmkP13ply0/QLIlgcn3WRQvnh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\nQyL6Vsr3ffvNa1LPv4+/+3npbyJaTNT/nIhs5cz7fu99GLI+EkEjM4F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"text/plain": [
"<matplotlib.figure.Figure at 0x11c495bd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figsize(15,4)\n",
"subplot(1,2,1)\n",
"bovy_plot.bovy_plot(aprc['RC_DIST'],vra_err,\n",
" 'k.',ms=5.,\n",
" xrange=[0.,3.],yrange=[0.,10.],\n",
" xlabel=r'$\\mathrm{distance}\\,(\\mathrm{kpc})$',\n",
" ylabel=r'$e_{v_{\\alpha}}\\,(\\mathrm{km\\,s}^{-1})$',gcf=True)\n",
"subplot(1,2,2)\n",
"bovy_plot.bovy_plot(aprc['RC_DIST'],vdec_err,\n",
" 'k.',ms=5.,\n",
" xrange=[0.,3.],yrange=[0.,10.],\n",
" xlabel=r'$\\mathrm{distance}\\,(\\mathrm{kpc})$',\n",
" ylabel=r'$e_{v_{\\delta}}\\,(\\mathrm{km\\,s}^{-1})$',gcf=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Thus, the tangential velocity error remains typically $\\approx2\\,\\mathrm{km\\,s}^{-1}$ out to 1.5 kpc. The following is the rotational velocity vs. metallicity, color-coded by alpha enhancement:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x11cf33890>"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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6JoZVacAvr3Tcs3XNSF6QS5tGo2sVYxn/yafNvmA6IiyUTIfp4fy9x3FWKzC7\nbs5/flbxhTNRi5u75VAonC0KhUIe+MNisfgbW6/dELMB4zb7E2CPjP2uGy5iN+HaIjKTR7gfvC3/\nR4Xrxhgc6KfVapHP3zyGYCee59NotkglEzjO7q+r5/tUa3UCLSmXAqDGUE+c8YFuQsG15SZNT1Ft\nBjiyE+hfadCfc7eFm+tYeH5I21Mk79CK2As0L1308ALozwhKdQDB3IZifMDUr5R2uHLq7W7L/8Es\nXF4yLiENvDmjWasqNpsaS1pYomthDGUFg1mBY5mY0eVFEx9qB4LvvK4Y6tUdZQSW6HYoCEJ4aEyT\ndOD8DLw7b9r/p1yJLRXZrCCRhIk++MxD3eupNfzwPKxWJK5t2uUM503c5syE4NoKZJOax44Kk6W3\nobk4v1VUqolbAkvCD9+BlU3TnWCyXzPWJ3jyhGaxLGh0FN5iqesmu7QEpapgrQz1Jnz+rLFufnHR\n1ATlk/DUcbM+IUz90NYAuGancFdpU0y7UoHxXpPO3fSMe21l05yr1XnecxfNP9NxE2sKlOkYHnH3\nHCqFg4nl/PHWk62MtWKxuNOaeR84DrzA3m61DzSP8Nlnn91+/I1vfINvfvObd7PejwXNH3wb79Uf\nINI50v/9/4zcxx5nd0s2myGbvf06lNLMzi8TKoVtV5g6MrZru2PbOI6N1waTrMz2pNAtEq5F01NI\naXqmeYEiHrN2WUHNls+V+Q20huG+NAM9t06rbrT1doyg3jIzWtqBqQcyLhdYLiuE0NiWZrRH8O6c\nZr0a0PA0PSko1S38UOBYimpT4Vp6O8Z0ZsJGCkG5YfGLi+ZTnZvSDOVhfkOAVvRkzRqkAM+XjORC\nyk3BQNoE7zdqilcWTKC/r6PP2z5Mjlhs1E0BpgJ+/J45ztMn4NqK4NqquY5Nz+LZR7r1Q0+fhKdO\nwPvLUK2UWF1u8eq1PC2V2F63bZmU5qvLRshLaXrA/ayomVmDEyOaIBQUF+Dioma8D06OQMaF5cDU\nB11Z1mSSRmFuFYCWG/DyJWj7guG85pEjghffNkpmuNd0XOjPaF67qvFDs8axXqP0Y7axemot+Idf\nGevs4UmT+HAr9poHlHIFXzorqbeh/+B/OveVv/7rv+Zv/uZv9u14h0bhdOpp/morOaBQKDyOsWb+\nzQ275oHLxWLxxUKhcKNbbQqTPn1HXnzxxQem00BwzUSQdW0TtbaATBUOeEUfDK319oTQMFQ3CQMp\nJZPjI7SNYGBRAAAgAElEQVR9n5WSjxfobeumXFds1DTjfXH6sw5JV6KU5vxMnUoTrq+0ODJo/ETN\ntr/tRmq0do+kvpFcUjCcl2w2FCeGbVY2NeV1zcxayLVVj0zCwraMGyxUkE1YvDVjlI8URug9c9LE\nIHYGuLcYyllIKbi0ZDqqaeDN6xpLCgqjmlIFAow1EyqoNQVvb1qEyhRE5tLmg+RSmmpTEIbGMmgF\n8OZ1QSZu3GTpOMyYxgy8fNlYEltd3EIleG/OKJlQmcFwaxWN77cp9JZJOnBuco0XLozz2BScHIVM\n0tz9nxjWTA0Za+jycjf9+cqy6Hwa8/dbLGlWNgW/+ajg2krHfMF0eJhbVzTaAjdmMulWfeMerDRN\nw9UvP6xZr8FgVvOLi5pLS90hbi0fzk5IpFC8ed2MWcglFV5g3IamgPRmglBxcbZKyw85OpyiN7M7\n/ph0jbX3oPHNb35z+2Z8bm5u14363XAoFE6hUPhD4DWg1CkCPQ6cKxaL/0fHzba1Xx44ViwW/8/O\nSy8UCoXHdsSAjhWLxe/f18V/DHCf+Sqt738ba+QI1tjUR3Ye3WoQXH0b2T8GfWNcnjMtaCaHTJxk\nL4JQc3HBI1Ca6ZEY8Vg3nmBZkpGhPqq1BtlMes+WJlJK4mGbCbeBHDbBgbavefVKgNKwVBZ8qmDc\nZKWav103slnvSvpcJk6l3sYP1C2tm5avmVs3DTJPT9g02xBqxdVVIygDJUnH2mw2JE9MWSyVNWO9\nEj8wYw9AELON4uhNm6LTSkPwxjXjC4vHYKxPslGHtKvpy2iurRjLJ+WGNH2LlU3B2UmB55tampZn\nVIRjQ+jtroOR0rTX0Qi01li2JiZM4WUuITg/1913YaPT7y0RsF4183iuLmmuLApScdPSBiS5hEWo\nBUoL1poZTozAFx7eHSOxLUFhzHSznl3fWoPpOrBRFbiOIuaY7Lsw1KzVzDyc4qJ5f70lkNJct2bb\nFIPmUiZr72inZVtfxnRwuLwE1U7m29ZXY6oz82ehZJIxai3THkhKTcyChyf3dolV6j7NjnW8Wm7f\npHAi9ocDVzgdt9l/pJvev1VWvJXe/L93rB8wFszOtOevA39eKBSmgKeArxFxE7FTTxI79dEn77V/\n+B9Ry9dBWvi/8T9QbZrg6vJG+5YKZ7EUsFoxP/Trqz6Fsd37pVNJMumuEvADzcyqh2MLJvoddGUd\n70f/AVSIfeoZ7MInULorfMMdUjiXtOlJ29RbIeP9LteWG5SrHr1Zh6OjPdyOVy4rSnWQQjOYVZQb\nGoFGConSEluGCCE4MSwZzsvtIsd/egOqTQvHkghhLLSLC5qHj2iyScFnT9lcXNS0fVMcOr8RGqE9\nAr1pc9u+dffe8EwH6YTbacDpQhDojtLRBKGk2gQhNMM5k2ggpRnJvVVLe63T+XmrU0SojPVwcRES\njhlbYFmwVjXKotLaugIay5JcWB/BUxKNjS3h9asmbjJ8w+VznW53gIcnTf3Fy7XueS0LNmvwxjU4\n0m+mfc6tm7UJYdx+qbjmv3tS4NjG9Rd3BBfmNe/Na0Z74KFRiFm76462RiEcHYDVzU5MTIBraT5T\nELtSrMG0JZIC0glneyZST2Z/G9JGdDlwhdMp9LxlPVCxWNwE/t1ttm21ufn2/q8u4sOg2508XhWS\n0C2c0MK34uRs01nAbzfZWJxFCEnf6BEsx9muxAe2H7eadZq1KkrG2ChXsSyboaFBUgmHaysey2Vj\nnbiOoL+yul07ozaWABNkPzshWNsMODJohEetpdmoKY4NJ3AdQb0VslZumd5i5TbVlqTSUFjaY2pQ\nY8XSzK3UiMcsToxnt4Wa0ppq3cNGE4gYjqWIOyEPT9r07iGo1quKEz3rIGC+2oOUgpVSm79ftMkl\nBV4oCZRxnuXibfpTJq26XDcuKC+UOJbp/VZvm6C7bXVdcabFi8S2NJ8taPozklpLMNFneqb90xsm\nkSDmGCVlSxOA3xmEj8eMgq42u+JASkgnzH621Iz3hbT8EBDgCdqBUYTvzML5WVNXs9PlNNajeeuq\n6YDwqxZ85RHBsw8bN97chulc4MbACyQrFcUXzsD0KLxUND3iHAueOG5GQ0C3G8K785oghOtrcHpc\n8NtPmL/tLy9DuS64vmrSs0+OCCb7NWFo3JOp+M0jwRdKil+9r5ACnj4pOXssT6g0jv3hyhMvLTRZ\nqwSM9DgcHYrf+Q0PMAeucCJ+fXA/8/v47/wcOXQE2a5y8sL3COw48d4BmPjn1ErrBCbCT6NaItM7\nSF/G4vFjLoGC3rSFUoq1+Rm01rRlApCEYcDl2RKnjvXv6rxsSYEcPY6cv4RuVrELTwGgtcLdKDLs\ntVCraXy3wEsXfQIFs+uKTxccHFvsagK6vKnRWECCxbV1WlqRtH28NiyXYjwxFefKsmbILpOd+ylo\nxfXsk9TdIY4POfTu0WIF4Kkjm1iBaZs83idZqmV4/WoCE5wPScZNax3HUtsZarlEgOdrsnHwQ8nR\nYZcL8xrX0Tx9QvCzolEIJrwlO5/ZdCqYHumOYR7MCcJAU28JwlCTT0N/XjCSF7R9zcUFk0zQ9uHo\noDIJET54gaAvqwi1OfZoj+kqkOjoU1tAfw/MlwRad1rbdAzJStOMUTh/HS7Nm9eSCbi6amJXa5UQ\nS2hagbU9QrtcF3z7ZTg9rhjt00yPyFv2hxvJs93yJ+l22vGkBE8dh//2mtnnzesmISFmC7C7DUHb\nvjYp52lBLilYq3S7Q2xUTdbhrbpv3wovUKxuGu2/sOFzZNDd0/UbYYgUTsS+IftGcD//hwCozVWk\ngJhfR/SeBcBNpmhUSiAEsR0NNrPJvesabEJ8JKEWBNrCD83Qt7gjcWxBf9Z8fWOf/L1d71NBQOgZ\nX5DfqOOHetst1faNkInZksJEhovzTRqeudvX2lgaSgvqfoKkbZIJLGmRSwrOHRN4syv42pg7Y3KF\n9LFxnNuMgh7OW6x2gvM9aZt6aLMVOA9C00jTDwW+tIjbAsfSDOUtlkpGiOVTUKoJWp11r1QgmwgJ\n6gLbManO9bYg7ijG+8xxt9yIlhT0pDVCmoafjbbg4qLgyw8bAdswup9U3FyX9aqk5UscW9P0JJ5v\nMr9OjQqurVi0Y2bp/RmLh8YEgzkT+B/tMUkIa1XNj98z5240u9fAseBIv3lcaymyCUjHA/xQUq4L\n/NCkE1xdMW601Yqi5Uv60rC8KbAlfPlhUyz6zEnBmQkzEntn7Cgdh2RM0/AEQ7lucgLAlWVFsw3r\nNUW1ZVyIXzpjcXRQslYNsSTb167lay4tajJxODp4Z0vHsQSZhEW1GdKbtiNlcwcihRPxkSBzA8S+\n+hw0ayaJAEhme4jFzUhH29nbTy6lZGDsCM16lWQ6SyuULG20GU06pOLm6zp6m0JRpRRtz8ftGcKv\nlXHzAyRigjMTFiubASknYKWsQdjUm1AYT7HZUMRjgndmAlQYstLuY6Lfot3KkcvYDOS7a7X7x/GX\nr+H7IW/VJ+BiyDMnbWbWTCFl7oaeotlsFimN4EqlUpzKCDZqmo0anJ00iu/V96HlCxYrCdAwkNd4\nSuBIxdRwjFpLMLOmjVUT+lj49CdhpZrAU0ZBhFrwk/cgbodcXzLD4P74M+B13GkxRxB3Amoth3Qc\nru8YRVAYhbWaoOWZdfqB2R9hrKi3rsGZSbi2ZloSnRyFnxWN0n1otCuYtzojaG3iTcmESQ7wPMXS\n6gbrGzDZl2KhbJGJS1xHEI/Bq1dMRqKUpvVPrWkU0EKpM9IBk7L98KQZmrelbK6vasoNzfSIQAoT\nj5LCdF3YYqGkeXvGKMGdcatAQTYh+NLZ3SLwzWuKxU4mW9LVDOZur0CEEJw9kqAdaNzb3HhEGCKF\nE/GRIVM5SHULO8ubVarVGtlsmtwtFA6Am0jiJozkjgHZPUYVVBoBodL0pHcrn+WlJZrNJtKy8NxJ\nKhuKeK3KUG+cHCWa1YDrjTQN30FpyYUFi8+dcfACjRcItHaI2YLCqIUQSbTWzK9WaLZ8hvsypJMZ\n7Ed/k++/ZQRuzAv40Ts+5WYMPxD80SdlJ+4As2vaFCmKFI5l6j9Ge+CzpwV+YO7CHVuQT2leeNtY\nIF6gubQUYklBG4s3rmmEDPnECYkfCtY2zXk3Ww6e2roDN4IuGQtYKwv8UEIIl+aNG6zaMpZbXMJT\nZzT5lODccRMTkgIePQr/3+sCS2pCZdrZBIHquOwEm3XNz8/Dbz6lKC5o3rjavd7luuKtq00sS7K8\nGUMpaHkCz+90dJaaXNyn3I7TDmOU2wGfOR3jv7xqugS4jon/NCrrXF9sU9wYIMTa4TI0SRBxxzQ0\nvb5mFE7cManRWptx3ltJEmDqgLa/gzt0QF9aELNNJ4KUe7Ny2JlgYs570y57IoQg7kTK5oMQKZwD\nQgcmnUbYD0ZGTKgUq2umKKO1unHLNOe90EqxWd5ACEE230u5FlCcq5OyG2y4No6bYCCfIOHaeG3j\nJ1JhSK3tAxYtL2Rldo7BcAGdGMFG0ex0RlLaTKYc7REkXUGjrRnrk9trqzd9NjaNf2hxvcrJZB+u\nIzgzLpldD4jLJqv1NAlX49iadtBVOO/MQsPrunfevGYUzpbrSWv41DSM9AiePQv/5VWNY+0WdJWm\nmZb50wuCli9IxhL0pRoEquvu2aqCR0A2pSl3uk4vlgVffUwwt6H54es+b6/BW5c9vnguhm0Lnn3E\nuJcWSqZ9pxCmNY5jG+tEKyOEbcv0XZtbNxlx7cBYGDELao0WYcy4/6pNie/brJe1CfzbRuC3lUs7\nNPvUPBulTI0QmKaktUqd2voqPTEo5AN+uTy5PYgv5ZrP/9pVk9wARlHudIO2fGh6glCZLMCd/eCG\n88YV2vRgakjg3GJoYKOt+ckFRcszk1HHe8V2zzStNe/MaubWJafH4cjNE7V34QWm00E2QeRiu4EH\nVuE8//zzfPnLX+bpp5++7+dWq7N4P/pPICD2uT9GDvz6F6BKIXBsGz8IcJwP5+veLG2wWVoHQAhJ\nM0ySsevErTYEsNkOqTZ8ColNEiuXaWUGSeX7ECLBesVDaYirJjW3n8AyWUT5ZMhcOYZt2wznTf3I\n0ydsivMt1spt4rbLeL9LzLGQQqC0JrFjTs/UkIl31GrdfP6YDMkmuvv0pQPits/SZtxU/Xeq1C8t\nmtiI1oJfXNL83hNGcI9nmwTaouancGyNLbcEnhGqAA1P0JMy1pTXEbqff8S0kinXLdJZhW2bOFSg\n4IfvaqYGNAudOFKlYVKrLcsog8enTBYaGCUSKlO/EoYmXdi2THKFY5ttQmiabUmtZRTeUMbU2CgN\ntZZktWSSDgDSSdBaojTUW5JUXHWsSM2Zcc3cekio4efvu/Q7vYwmN/C1xWBWUK5rQmXSxWOOuQZb\ngX4hTBscASRcjcTEoba+U6kbJoBO9t85FrNWNecSnWzu8b6tuUSKN6/UeWve/PHWq7dXOF6g+el7\nAe0AJvoEZyd/PUTsyy+/zAsvvHDPx/n1uBp3wXPPPXdgnQbCuUsQGgkSzl96IBSOEILx8WFazTaJ\nxL0V1Q3lYzSqFju66iOEoLRRotk3CUqRrK/Qd3Kc8YE48+seDhOIygItjKDKpVyOjzq7hFM70NsF\noYsbHmN9MdZqkM7kySfVTa69IwMWv1hPcMy+Rl2lGJbLLK+ewE2myKck6XiI52tG8i0Gcw6nxm38\n0PRP050MMC8QLJY1P3nXxgt7SNgeIz0hnztrzlVtGSvg8qKp3HdtkyQQKkGgzNp/eck0tUy6YHnS\npFMHpiC1qTTz5ZBjY2YsweSQJOwoMjNnR/DKRcFaZwQ0GEXjWBrPN90SYjGQaFYqgtEeQcIW1Dr1\nOYulOOsVH8d1aPkWotOvzpIwOQBzayZmsl41iRdjg5J//6OQywumU/WxcYllCa57AyRSafqH4zw5\nCN/+RaeVDzAUN6nSiyUQCJqept2JN0mpGOmByX6TdFBrmVk8H5bBrCDlGstkcqCroOqtED8MsaQi\nVPKmGN2N1Ft6exrpek3ffuePEU8//TRjY2N861vfuqfjPLAK5yCxjpwivPYOILAmTx30cu4btmWR\nTu/9i23XKtTWl4glM2QGRnZty/X2Umn4NNoBqiHJ5GBqcpBKpYIfQkI79GbjlOYzncixRPWMUm96\nlCoNelNxsuksDGXpaXm8NaOYWZJcWfX57Cln283iOpKkK2m0FbmkxYXZBsubJkPu+JBNLn1zj60v\nPxqncqVB0FhGI3hnQePh8+Rxh4GsTakaErch1BZvXtcMZTWurelrXWOJUQb0Mheu9iCtNPmEQimb\nh490BVWmoxDPTYHSIdWmpjctOT/XFYqmk4HG6gTF9Y4Mra1HE8OCIJSMDkhWqmYq6VIFLi3CzLpJ\nEhDCWDAnB8skY4q6Z3F9LYfQGiWMRTa3YdrNnJ2E3pTmjeuSULmdgk2Iu2aQ2lcfMwpiraJMkWpM\ns1GTLJY1VxfN59ua8ZO0TAfxN+dTMG+spa2aHiE0g1nBQnnrs+38VFAYEZyZMM+/8sjtvn23pu1r\nrq8qHhoVjPaKXdZ3OmGTSVgc76+SSiQ5NXH75q65lKn3KdU0J0eirtI3EimcA0D2juD+vulPFPl4\nDZXlWULfw2/WiWdyOPGuYgpCzXrLRmDTqnuUqm16s3Hy+d29W3tHximtreK4LomeAS5cWyUINeVK\ni1NTg1iWJBGP0fC9znHNv62RzJYUPHwshR9oLs5WafuKlAMVL04Q3lp4pCdP0S4tc72SxKsbSdn0\nNKO9Nj1pi8vLmreum31n1hTHBuBo/R0e838JwBviC9ScJCCQku36l53YlulikHTNTKF357eUkrmj\nju2QgwJjYVhSc2xQsV7tjJK2JRfmpSkAjRlF8LP3zDu2Ik1SQMIJKTddZkumoOdzBdMKp1TvFowm\nY5pqG/o6LrXrK8YK0VowOQC5FHz/LcXSmiYZBzKSsGOR9eaNOzAeEzRaknSsRU8Kk6WHidEkE4re\nrMksOzUuyKfh3U47nlQczo5rXEfw8BHT9+3VKyb28qWH2VWr9UF4ZyZkedNcz0TMojfT/U1aUnDm\naGbPpp57IYXgsaORWL0V0ZU5IB50RROuzhFeeAU5OoV9/FGsmEvoewhpIe3dd5FWZ1aNUjfe3+7G\njScYHp/cfl7zXK6XMlhSMTnWHfr1yKTNzFpIf1beNC5aCoHrGFdSpe0Cgt6UYvw2gy+kEyMxOMFE\nTtGcD3EdGM4bqWdborPertXiBZrEycdpXnmbhbCfMj3biQICeP2a5gunjYtrs6FpePDqZfCVEfjj\nvSZDwFwOk9lmW+a9JpBuhKPSMLMi+d2nLP7pdcXMalcSN9qCfCqkKU2Sg9bGFZVJQtJJU3w3tn2l\nF8vw5DHNTy8Yl5VlCd6b19tZYTFLU66ZoL7rQK3Tvfv0BFxdMm6wnYNWJwclS2WzlhPDms8+5PDG\nlRZtv4EQgukRl9eudmfwWFITtz2O9EuUdiiMsitd+e0Z095mdt3EWAZvMfGi0db802vmL/HbTxiF\ndyO3coI96L/X/SJSOBEHgv/T/xddrxBefw85OEnP2BTtWgU7nsC6QeFIIZgezzGzVMKWkEnunOPS\nKYgseyilGepxt6vFPTJoBIGyWNoU2wqnLyPpu6EzgNaa5VKbUGkqDRvLaxNqI/FqzYAr82VOHenF\nsqRJlV7epNHyGOzLkEklmF2HfFLy+NTNt9cnh42baKWsSMQ0J0ds7OQEr6+Nsl4Fwh0jsDFxhF9c\nCsklzagDpSFQAiGs7amb5mMbu0QKI+iX1qAnB93cBjMG+uJCyMrmznVpcimFH4Jtm39DOTh3fEuo\nxnF29Cg7PgT/9ZdmZLMQ0Jc3vc2UNgkAK+tmPc2mprdHMLsu+P47ilpLMz0JCxsmZdl1TDeF9arc\nTnk+P6PJpySe32IwA2mnTavdyxNTca6uaHJJQa3lM7OiWC4LToz4xGMO9bbeTm2e7DfWTzYBmbjm\nhTfNkLljQ7BcMQ09TwzDD99me+zBd9+A3/uEeXx20iK1okjHxU3fi/uF1prNhkn5vl0h8cedSOFE\nHAxuEuoVsByEE0NISTy713gjQ6tZxwpr6BDKZUl/fz9r1ZC3r/skrbZpUokR7GP9RlEcG5QslU3j\nypFbHxqA5VKbuVWT/hyrrzPQnmU58QxaSBwrJAg1QaiwLMm7s21WNl1cKdC6yuszCa4sGVfOHz5j\nBN9OpBScGjMD1fzQIttp22JJE8dA7FQSRqhvNqDtG6ksBUwkVphvDeHIgISrWFcJetLQbCscu3Mc\nCWnXtHSptsAPBIm4YHYdMklFEJqU4d6MwrKMO3GLnRaI1povnjWza8Z6jcXQbHe3haFJSJA7+rKB\nUX/ZZEgQSipNvV2To5Sg7RlLaLgX3pvtphu325rXr0JfNg8I0k6T6bhJ2y6Mmv2Wy4K3rsZo+4Ja\nS7PWCBECPnnSoi8jeGYaTo+buM+VJXiv43pbqWhyacGvrmquLAWUmxKwOn+T7ud1HaPMr66YY/Tu\nMaSt7YWcn20hhWBqKEYmae2r1fPKFdP9OunCbz2uTVueX0MihRNxILhf/BNj3QxMIOK3Hni2hWXb\nNz1eLIUoDRl/lbpreqfUqzXeb1bpySYZ603x+08Z4SJvEA5+oFgu+6Tikp60s0vgWgTk1AbnGj9k\nNnMWN5kilXCp1FtktMtKx9/fVjFcV1NeNe8z82luVjgAS2XNLy4aBdKXNqm7Wgk2qkbyZZMhCXd3\noeJw3mKzHpKKC0RD0ueUGIqX6csnsbIJWr7izasBsxsObc8ogXQ84OQoNJptXr6SxGsJai0bS2pG\newOODwvOzwLC1MlYUtHy4cSIBATvzGrenjEjqb9wGoY6rsEzR0zHgbgLSVcRKkHLM1M+kwlTyOo6\nRnFKoVjekHiBoD+rGMxp2r5gckCSiMHxYc3lRaPwbNt0g95y37VVAtveHS8byjuA0Y7JhHmfEKa/\nW18n3rJlveZTbNfwbMVypOhYZhlF3JHEbMGTJ0xs0LYEGzX45WWzb7kBv/vEzX+/87Me7c74gtff\nVwzlLR6a2L/puYsl83+jbVLX+7P7duhDRaRwIg4EkUhjP/TUB94/k05362ESSWZW2tjC5GMlwirJ\ndoNQWLRkD0EIi6ubeDqxLTDnV+usbbbpy7qMD6a4vNCi3EmBfuSYZKjHRWOaV24yQpV1WsRJ9eQZ\n6oszs7DBptaslxsM5nKsbCpySZgczhJPmqB1f6Y7OtkLYLUCuaRGoKi1uppkowblhiYMu7fZ1aZE\nac0TU2bYl5Tg2pCIOQzlNN99exCtBRtBngEpGbVNdX0rsIjZAq0gHgvZbMJr72t6EhrXVjQ8I7xD\nJVgq24z0QK2p6c12rCcJaVcxs2q6Pjc67f2VFrx6JeSfnRNIIZjfgFhMMJALO3UxGi+wCBTEYxo3\nJsgmjUDWuluLYwnJHzwjePOa5q0Z89ojR2BxA0o1kx3n2npbiVhCUGmYBIU3r5vr+dRx+JPPCb77\nmkml9jvXrelplNK7Gm4O5QV/8hlNrQm1luDSkiIZMxZRqASfOyO4sqT45WXIxOGZacFKOUAKB6UF\nttTMroUM5Kwbugd0/1aBEpTrXfNwbrVFvRUy1u+STtydSD07aQqDB7LQ+2s8VTRSOBGHlrZvWrzY\nnVvVeCJBrd7i+kqL5bL5wU/2SmxrimB1hkA6WJZEKUUrsPlJET5T0AxmYblkCkdWyi0G8i5+uDU3\n0ygxKQWjfZ071uEE8Gm01gSh5rUrVZLSFBwqpTk+5iDwSbgmhXY4D7/zhIlxvDOjSLr/P3tvFiTZ\nmd33/b7vLrkvte/d1V3dnd1obA1gelbMhhkORWooShRlUnqQHSFRcpgMP1hWiC9+dFBhhh9MRngJ\nh8IKb7K4yFyCoslZOQBmMNiBRqOzl+qq7tqrsir37d77fX44WZlV6ALQwCwABnVeKrPuvV/em8s5\n95zzP/9/xKvLDo2OxnMsc0NNxnOahSHDbjdBpSmObH6813+qQCYpjf96W3FhVlNuiLSAZb8c2MsA\nQodbm5r13ZDz020UPlo7JOKAVexUHZSy+E7EiaE6NzbT1Foaz5WA8eqyrNVoWxK+9HgaLc1YXmF7\nmUAY7SuKSj+pG8hd99ENdYXrWhIxC1aRTSiaHZlpaXYhGY/48+c0t7cV+d7k/iu3FXOjlp9/DHbq\nUGloSjXLbl2xFyr+3+clU2p1BQSwMAGNjkZ5Ft+zfWbqpW1DEEY8dloodVZ3BR03mhGoc6NjsECz\n6/Cpc4rxrIA4nrshx9facG2lQ61lGM9EjGZjlBsdbq7D+m7I5XMDqYEHT/p8/7qi2hLqoJkR+f5V\nmyFrJak3hpHl4vwR9bj7sIUJxcLE+zr0I2Uf24DzQTIN/CyYDbqE119C5UZwZ8/+2Nff2muxst3E\n0YrzJ3LEfIeVjV2arQ7tKAYI/LjSaDE9nGA7Ng3AieEEy9uW5apsb3alh5JOuNRbIQnHcHWpggXi\nrmJ6NE3mbe5KlVKExmKMomVjxJyI+ekMNzdCtiuSIaTiDuM5h7VSyGvLIVYJ43OjI2sGkcYaS6py\nnbztciI9xDOdBdqBAAQm8sKajJKgurRtyaciMgndd/DrZVH5zCYt7V7mkE106HQ6TGW66Mhj1tug\nWJ+jRRxrFWNZj7NTDre2NO2uqIPmnUE2sFORuZxu19LuqWaODkkpap9tYCIvkOed6mC2p9kypGOG\nlZKPjP9YhtLCsqw1rJZkIDXmW0ZzIe2uongHwGKMIZcVkIPIBMC1dVl3dlhRbsj1dkMYy+wrdQq6\nTAg+FZUGnJqw1FoRcdf0j/n2FcvyjkIry9yooRVYXG3IxKXU2ew43C0Jb935acXNTUs6JlmW6wig\n4eSY7a8ns00D811Fwncp1eW553n9/+9T7MS8owEHB9m7P6p2zDTwI9oHyTTws2Cdp/+E6OargEL9\n0prrykkAACAASURBVG/gTMzd97HWWpY3atSaXSZHkozl7x0GrTR6TAzGUm+HxHyHIOgJr+kO2nEI\nQ4OnIvJpn0zSx1grjX8bMZuHiBhxJyIyPmdns9TX7lBfX2I9K3IJxlomhg5z2Rlre/0IcR4JX3Nq\nIk65ETI17JNOuri629/fdaDVNdzc6JCMSbnFosklQ7qhw0gqJO4EeEaO2agpXB1grcvqrmZmSGh2\n6h051nNFWjqX0syNCKXN3R4tTaMjqDDPsaQODEYmaVENUxSSy7zePEs+pZkb1SK//ZY5xX1UXxRJ\nj0Mg1JCICWlnsy3BZTJv+eRZOXg0azkzEbFdiZjKNtmoZtkpA0iQ+YXH4KUlWddzIipNB2thbVfe\n21wqotKQ12q0IJNUGKsprg+oIu72eNpGM3BqXCQI/u+n5fq/8dqBC1CwMGFZ25UyXC6peXXJcLfH\nSmCsYq8hEO199+5o2Cgbyk0Jdl98wGFhUvMXLxtaHY9ULCSXcPnD72viXoyHToScmrx37ur8tHDt\neQ4sb1veXLF8YkFz8WSaZidiOHPvUOhu3fD8TcmGLp9xGEp/MCi4H9WOmQaO7YO1zr7giR0ofd6n\ntbsRZRnWYHO32Q841loq9S5Kw/hQnFYnJOY55FLyQ54aH6K0VyOZiJFJJVhcq6O1h+s6JFxNoxX2\ndenjwS4za89yK3yKVjfJwlQSP2qQCqsQhRjtknyLN46M5bXbbRodQy6lmRnxGE67TA77TA4PAtPZ\naY90XBP3FcNph3Zg+ne5IHxvI2nLWtkSWpedTh6fMeJOl1XmcB3IxkOqHZ+lHYeH5ySzeGNFHGaj\nqyn17rR/7iEo16EdDs7TdSyBiTGV17x+16XckeuYj6/xa59osFxN88x1yUk+WVCM5cTxNQMIegOs\nIznJJBIxTblqiPk92eo4OMrwpYsD+pvvXBWEW4TH0l4e37PEfYFNTw7J4GU3lDKYUnD5DLy+pPv0\nN/NTinany/J2DBXCfigwRhi0b270hlddKTM+Mn94cikycHLMslmxzA7D1ZUeUymKSgu6kcF3Nd1A\npLYdbXE15FMiNDeW1WxVZS1j4XvXIqaGNBM5uLWpCYzPdlXRDaX35Hse+dS92Ug2qfjiRZFFeO6m\nnN21NcsXHnBIxo8eDN4oD+QSNiuSDX6c7TjgHNv7Mv8zf5vgpW+hcqM4c+fe27GeQ8xz6ATRIX6y\n7XKLtZ0GYBnN+Jw/kcX3Bl/RVCJGqsfDtrnXptGxQMjiyh7DuRjD2aSUzpoBw+WbpDq7pFubhNl5\ned2pM9hui/N2DWYeIJEYBBFjLFuVkEZHvEO5btird7g4ByPZwz8TRytmRhyWd6Cza5kZ1jx0Mk65\nETGRc0jEHP70hd46Tbgwo7i5MU/ODfpRyfeAjgSYzYphr7GvOEpfLE4p2S+ThHbPYSoUxhgqDUOx\n61FquH00Vio/jJeMs9fLHPaZnU+OW25u7nOP2d7Mj5S0jFWcnnQwkekHOa3ltb/5OqyXReIgCKHV\n3Se0VCST4rxHs3B9zeI4mmzS9KQdFM9dHyDPskndkwS1hJGi0zWkEhJErJWGvlJy7a1B8sjPPQLX\n12TOprgOvtfjKestba0g0LqBJggVriOkpM2uyGw/fBL2k+fpYbi5YdgoW1pdxeKm5fPnYWFC2Btu\nrov8ddyDmXcY8gWBTe/PKb2bXs70kGJFFMaZGvpoZjc/TjsOOMf2vkxnh4l98e+/r2MdrSicGKIb\nRsQ8B2stO5UO1WbA0O51WrkZqvWQRqvNufkJlFIEQYDWGqdHGLavO+/pUCDOpYCY71KYyxLcfJlo\n7xqRnyIxNsn0hIABlOcTP3ME5hW4cqdLqRb1aW7276474dGt8qurcHVFtj1+yjKZV4xlNeulJo2u\nZirvs1xymMjBA7OK89PwypKm3orIJBQnxjxeXJSSXBgZXG3pRhprhb1ZK8XnZst4W5s8MTnD/1fN\nEllwVEQ2IQHFVSHdjiayMD2iuHQ2jrUi2RxFlpGMOOvnris8FdAxHrZHLxNzLbW2kIBWW5aJLKxu\nGYYyiqQPKyURfVNKU2tZPG0O0bv4bkTMtbQCMNZhPldnfqROtePx7LURTH8+R7G4YZgZgamRkFLF\no9VRtNpwckTxw+sWFGRSAjqYG1F8/7phtWSZHzN8puDS6kL1liDUml3wHI2jTE+NFdpBLxAacHrU\nO0rBtRV4Y1nO45c+CY+fdvjr1yKqTXnf//BZxT/8vPRhHpiT7Mp1eNcZmExC8bcuCQ/cUVLYew3L\nzXXLaFZmwb76sOxzzFbwIwScQqHwKDAM7I/UlYHFYrG49GM4r2P7GbcgCNja3sVxNLipPopsOqjR\n7GndR5E4uUq1xs5OCa01szNT+L7PcMZHzyhK5RqtttwWO71pPu/MJdzZc+DFOOWI/kqzHRHzFddW\nhADz3LTL8IGp8kpTyjRBpLh02mN9NxQZ64zD9dUmO1VLhMfChMP0sNOXqga4ud5lvRSS9ru0Ak09\n8ADDgzOWwoyUuzbKticM5pBOSHD6+Ufl+Ds7muJqRNoPUVrTCRUqinj2asiw4/BY9vv82me/xrfe\nUNR6+jggkymJuKHV1jRbAgh4465luyrObWNPnOedbUup5mCxJBPCORYYMIElQpx2qaHIpDUrW4bh\njOKPnrGMDfccJdBqGcJIo5T0kOoN2GwpUgnLSNYwlWtSbvncKA3hOpCMS1YURpIZLe/EAUUmZajU\nZd0Xbw0yG0dHVJqKP3teXlFrTasLE/mQ1V3nkEZQJ5QgNzdsuXRK8+cvCYrO2UcS9hDLYUS/nLW0\nBWC5uiyfubUi4bC+B2cTsLghwnLz4/DYwrt/f+Oeuqc/tm8v3DLU27CyCyMZSzZxHGj27T0FnEKh\n8CvAV+kntdxCAg3AAvAPCoUCve1/XSwW//jHd6rH9lZrvf4CNgxIPPqpj9zd0265SrsjgUIfYJ6M\ndIzxzVfYzS+QmzmJ1ppmQ3pExhja7Q6+L6WwfNojk8yzV2nhew6pgyUyPyn8a9byxnKdVseQjDus\nV+S1rq+HfCoj+1trmRpy2a4Iv1o+5ZJPyU/j7nabUjVEAUGgeGVJMoIwDPFdRySNraLW8Uh6XbqR\ny34p6c6OZavSxnFgYdLvDyTmEhCUt1gseeyGKc5OOXz5Idl+5Y7Mn9SamsiMs8I4U7EKZxQ89SC8\nsaK5s21QygprQUqxT8C9uisw5oM0OS8uRjTaCpDsachv8PXHk6zswjPXoBtYkj1G6rivODurudOT\nn67ULBPDloRvUAnDnR3JFlwXUklNJm3Z2LaMDsFeO8HybhaUQqnBjI/Q9gzKa5ERbjmLDJ7mezMn\n1brCWkVk6TMYONoSRIqlnR6zgbJMDVlWe0OSQ2nNmyuKektKa59YgHNTUG3JexBFIo9gLVycg5XS\n4PuXTkImYfE9WNwUYEInEGj1wpQ9MnO5X4u5UEfOyT2uoh2y+wo4hULhEvAV4MVisfjP7/OYpwqF\nwr8AvlEsFl/5Ec7x2I6wxnPfZfff/g8A5H/lPyXz1Nc/4DN6bxaP+dTqEkgmhxP49RClFGNjD9LZ\n3WF28hSJHnujOKweCsp9az9FMzo0YCqw1nJ9pU6tGTKWjzE5HKfV68u0OhEWjzBSh0g7b25ELG8b\ntFJMD8v6Iv5l+6U7WbsXSLYjQYr5YW/4Ue7SrZOia0z/XFUvwJgQ2l3DkxdcOqEltXuNzrWbTKEo\nxT/FzY0cF+d0j94mYjLbpRvEaHbEyeYXCnS6AbWOi6M1l89oiusRuz1Ib7cHKNipCZGlUkIjk4xF\nXFvTdCON58k1JZN+nw9utybHJXywClxtGM8L11mzLQ6z2rD4rmU02WZFexij+jIISslsjbWKrUYa\niwSTTk8sLpswVAJB3JWaEkiiUEpr2rF0ug77A5XZpKFU0z0oAMR9YSh4dVkTcw2dUDORV3z6nGan\navnhLXhlCUYzgzKf7dHt5Htfh52qZXoIJodhLKfIpSwv3JImfi4t79Pzi4cpfhI+b5u53K998qzm\nbskynBYV2WMb2LsGnF5Wc6tYLP5372XhYrH4TeCbhULhUqFQ+HKxWPzW+z3JY7vXor2d/uPwwOOP\nig3ls8TjMRyt8X2PZrfNna0Wu47HhZMFfE8TBCHGGKwx7E+lGGvecd1uYKg1xQPvVDqcnEgylvfZ\nqwWMZH02VoTCZbs6WKfaNL21od62xDzLi4tt2l3L9JDL6ck4t7cM2nFIOBas6ZVu1CHtmdGMS7XZ\nIbIKhcVzIiKr0UoxknFIxRUpFK27FUBEzRKmwVYzy1++Kv2D6UxHCD4nWmTTSaaGFN1WyI3lHa7u\nTGIsDKXgSw86dAPJAt5cFecZBJaoJz2tlEUFDtEBZ5pJWOYnNJERtFTck8b3uSlx8OvliG4IubQm\nHlNU6hC2FVjDg6MVdvIJEjEPrKIbicDayVHN00WoNBRRL5uJeZZ0vFdydKAZmF6vTomuDjIY6mlD\nsyvBbyLbIZOwdEIHY+HBOcW1Nd3/XKIIHj8lSwaRZDEg5bUHZiWTOHdYRom/elmGaq+twtSQJRvv\ncn6iyVo9y37GtY8szKXh0ryUG2PejxYkYp7izKTiyh34fhEuzMLpj8FQ5/3YuwacYrH4Rz/KCxSL\nxZd/lOOP7WhLf/EXCEtb2CAg+/O/8kGfzvuyRHyAUNuryW1xEFlqrZBkZFlZ3cQCw726i+/7JJP3\nzuyYVo3Ole+BNfgPfJZs0qXaDBnLxcS5ZnxmR+O9vot44DAyRD0yzoVJl2urIamY9FbqbUO7K55o\nt96l0wmZyLnMT8TYqRqurkQ4GlqBRivQGHJJQ62liDkBkdW42pB0OqIfA6Tjg6l1/8QFOrdDymGc\nXTV+AP0FRgk8txV6VEqWfAo6rTamJ9Us5wT/zzPwpYswO6Kod6RvM5SUAGQM+I44ac8V6hnPsYzl\nQjYrkEtCtekSGglU1RacmlCs94rjqZgBq0RWAEU+GXFzJ0ep5qHq8KmCSAEkfRjJKD5XsPzHV0Bm\nIRWpxIAccyQnap/7UtWOIwEJBOjwwIzihVuQSaQ4kbC8fsfiaaG0KTeFY6wTKLqhME7HEZRY0hcA\nQa1pOTtpOTN5QKWzI+vHexVWraTMtV1q8sd/uMhuM8YXv3aGdMbnwsyAzWB2ZBBouqHM29xvqVok\nselzuzU7QsgJsHvtOODs2zFK7SNqOp5g+B/95x/0afzYbGwoRqM34JlLudRq9T5SLAgjpmdmjjwu\nMpbu2m1sU3DDlaVbbLqPMp5VnJhweHWpRaVhiHmKJ84kmM21qbQUY+kQrSXg5VOaT50b9H/SCc1I\nxmG3HhF3QjqBoRN0Gc3GGMt5fD4bRynF6q5htWQwJqLVtWxVLDPDPp0gYiIfp7QXEISGuH+YWdhJ\n5Uk++CTteoR7JyDnWuptcZBbtTiRGeRNxTXLEyezXF+LSPkR9bamXNekEpYrd2U+Zrsqe+81hSIn\n4zRIxw2RzlBuKs5MKFZKYZ+Rersm6DVXC7JrZhjGsoqHTrhUmoab64pqUwLERN7y9csx/q+nY7iu\nMBZ893XIpGBls8sbNwISGZ+zEy7X1g6zMFsLnS6EYW/IFLAGQqOJukLjs7QdUW5aqm343LjDUw8p\nfEfg4I/OK06OKq6uCFQ5k5Dy4UZZ4ep97Di8sChB45NnYatiePl2iAWeOONyakIxnoN8WvEf/qzC\n8y/XgTrZnM8/+8dneHDu3ibLC7cMa3uWiRx88uxgvqbetqztwuQQh4AA62XLczfkfB6dV8yPSXl0\nPyjm3p2b9mNj7yvg/CyUyI6pbT5cNpwR5Nm+ZTIp6o0WUWQYyh+mzm12DLWWIRVTvH6nQ7yZ45zS\nKGu51R6nokW4bG7EUmuJI+gEwiDwyOk0nSAk5qX6QSAylpWdLlrBzKiPVorAuFTbDgk3QmNQShH3\nxfnUW4b1vZChtMPlsy7X1wyrpUiOH4mRiosTG057NNoBqcTRTYHhtMOnz2rqHUM+qbhTgpduS5jd\nBxhM5hXZTJrddojrQD5l2KkoOh1her6xAWMZh1JdMTsM1WqdM9kNAK5tB9zeGSETt1RaDnt1KV9t\nVxSnxi2//nlFq2OJe/C/fxcabcUXLjqcm4Ibq3KOW2X4d89IX8b3RF4aoFIz/PCZDS5/doZY16VU\ni/jly4rimiUZU2Tiiu+9KaCNpNel1fUwVjM3ammF0utxgL95Q/o2w9mIp98UePm5afg33xSU2/So\nZXbE0gngjTuKH94StoV2V5FOyAAqFl65Lbo3ew3Tv1FpdA2XTrvs1gwv3IpIZCXLTGdjfP5ShgdP\nDILN3Z2IOzshoxmHtT35XmxWIAhtX5/mm1ckc4ndhb/zCdunqqk2B4jFSm8G2nXg60/AVvXdpTE+\nCvYTp7YpFAqngLer1XwV+EgHnGNqmw+3uY7D3My9dYhuaHl5sUVkIOELLX7gj7I0/RUuzMYI7sSg\nTp8qf2HSZ3WnTcq3WGvYq4XCNO3HuDAbw9Fw/W6VejsiMC6Oo5ga8ljdFSeyWY+jrEdoHE62FCMZ\nIXzshDIomoorFiZcRjMOcV8RRorlHcNUXuG7mlw6ds817FsYWV5cbNENYTitOT8TY3kbtmvCGfbA\njDAif+uKIRUT6eVWV8ALQ5lBDyoTl2l3gOXVCNvrb8TdEMeB4qoijAY6NkpbvnPVEteW4ipkUxCL\nSSns6p2QrzyqiHsO7UAyk1rPiSr2FUXB14ZYwiMWExfSDjRPXxOm5wdPSEnssdOKZqPJiLuOtRCq\nBCdPzPDmiuX5W5adsiDnLFBrOuwEirs7cHszotubrdku9+ZrtKUbDOZZHC2oRWMUtabCd0UhNBV3\nKNXkszsxKu/Jq8sRrS5kp0b47d9+gs12ipYjpcl97Zsb6yHGwt1SxPSQy9qeDG3uBxtjbR8M0e3B\nrfcHbufHFLt12/ufUNmcmRQam/mx+/u+f9jtp0FtswtcBv76iG3H0Itj+0AsjAZUIZGBlG9oBZqJ\n0RRKWy4vOJTqlmzcQnmdsUSaHd2l07XcuNsRJmTl0G3VWNt1Sfkh7W7Qg6+GPe0UGUC8W7J4jqLZ\nEaiztZJdtUOIIulwfP96iAYeW/DQWvH01YjIwGoJPlN45wJCq2sIQosGqq2IyApvmkB6Fat79ITl\npLxVbmg6oZSzTk3A6q54vOsbmodPirbL3FSO0k7A0o5P1aSJ+4dRWL5n+yWeUhPSSUUiLq85nGgx\nl6uyugG//uQQLy/5lBuS3WxXZJ9cBjIx8LTLG0mPne0W+bzPZKbJTjVFMma5tQkbZXjqQU0Yeqze\nVShl2ax6XH3ZkkmIPpFR4khivsV1LdqBVls44/YDm+NAu6uJexFaGfbh3VjLydEuTz4gaqsjaREv\nA8VnCoczyrinaHUtjgadSkJb3pONPUGSgdDg7NYtSV/x2CnNpVOHyTa1UnzuvGVxU8qRB4dDY57i\n0+cc1nYjXl2WL2c7iHjywjEm+q32tr+IYrFYKRQK/3MPbXbICoXC4k/2tI7t2I62ZExzasJjrx6R\ninbwTY3MSI7Ec39Np1HBffBzjJ99jM6V79GpbIPr4eQvETkJrLHYHgxXW0MiNpA+AMil3J7YFzxy\n0uHBOZFSvrFuySZgNKsorgYEkZBPKoQq3yC9g8m80w+GreDweVtrWd2VzGssq+gEUFy1fcG1uKu4\nsWb6QmLJmGFhQnNnR+7wG539GRVFJg5ru4OGdsyFnZrFWMtYVnGnPs6b2xKsPFdKhp4L00P0JQig\nNyNy4Hna7/Ydfaka8PmLPp4jJaxSHb59RVBh43mZJTp1doRW21KuWc6OtIlsEos481pbMoFO6PFm\nZZ5q01JvO2STlmrLMpKFuKt57DR896ql06OmyaYMWmvGfMkgtFI0O4ZEzNLq6D5f27nJDoUZD9eB\nU+NHf1c6gfR8pocdhtKWmWHJHNf3TG/GJ0BgCPDovEe1ZUnH1SF9ncFahm4QcmFGM5IZuM03Vizl\nhuXirGK9PJg3+oiNxf3U7B1vwY4KNu/0/2M7tp+GzY36jKdbbN2VQZJmrUq8IVDj6G4Rq4GtZTRg\nSDA35FJWcXK+oX3rdWpOjvTIKGNZB3BYmM4SRAZfWzZ3quSzSeIxD0crEj48fHLgPTIJjbX7XGXC\nPqy1Je5KP+HirGalJLLPe3XLUO8O+o0Vy7U1WePJ83B9TbFSErZogGsrDtulNqdPigN0NIxnLfW2\nZasq/GVKKRwF2URE3LPsNuRuvxvBd98ERwnlTNztdUiswJ1jHiQ8w/kZzbPXNTFPAlC1IRDjmCcO\nshkmGXcCGl3F3W2fvbbh8hmH9T3F6q5wr63twqu3YX4MUjFLqw2g2OnmcHtw4k6vR9MNFW+uWsrN\n/Z6W9DiqDU0qbvm7n4L1vf0ZKxkHVUqT6MG1L5+BkQz84Lql3ulJWhsJlJfPxd+RgqbcgL98RYKO\nzAcpvv64MFfPjwmrRbt7IIPR6kjCzn27ttLpsVHA4wuaVFyzVbG8cdf21rKcnlB9NdjC9NFknh93\nO0apHdtH0nw/RiyepNNuksoPoXJj2OoOzqmHMBVpmivAyY2RHJ8i07vlzDz2WcZ6jm3fsimfMIy4\nvrQJwF61xYWFyUOvt9cwOAqmh126IdzeikjFFA/PO7x2u8PtrYjNSsADJxK8sSLH/PBWxNcekZ9Y\nozNYq9kRQEAQaRY342SSlhderVKrG5otQ2EhTjalePm2NMBjLrha0e5lTa1OwHS6QWF6iOduKXSv\nZGYRBFi1Y7FWAuDsiOkDJ15ZUhgjAml+JNmb50owA8ilfCbGRnm6GBEaxVZVaPj/8mXp/cQ8SzwG\n6QTsNuDUpGKvvi9MR78fY4y8+7t1KXUtbspncek0/Olz8lr1lqDRhjOisrlVNYRGMZyzfPHiYecv\n0t3yXCsjs1uuzFLd3rKM5wQZdtC2KhK09tv5Fri1CU8saCaHXCqNiPnxw9IU72QHJcj3JR7i3qCn\nlfDh1LhDLqnwHEXmmM7mSHuv1Db/olgs/u5P6mSO7dju15TWjM/NDwgln/qHWGNQWmMqkwRBF5XM\n4F347CFIsjy+1xkEkZWZGQWhsf11o8hyc73FetkSWYeHT3rMj7vMj8tPJ4ws7R6vWrNjwRh8JxLF\nzEh6H5GxpHzDRNYjFYeJ3D56TrFd1rSCgTDa7TsdTszG8H3JWEAc2xcual6+DeulDpPpBmFkSMUs\nQ0nVZ1iWqRmLMVoklluKIHSYHpYGebXpMDUkMN2zU3BzDVb39udWREfmD76vSMUc4jFL1wrVy77t\nzwFZC6GF7bri3AlFu2uJx1yshZ0y+L6wb88Mi/O9vWXYa8CVuzCUht2aXNj/9i34e5+G0bTiRi9I\nl6sDRof993SrKmJx+9aNLI225eUlQzeEraplPHt4qn9uFG5syHV3AkH9jefk8z83fTSQIwgtd0sy\nWJuKw+vLkQyhnnAozMZYLQVkEg7phGQv2aTiyxclazsxKmsM34fezUY5ohNYZkecj7Qo2/ux95rh\nfLzenWP7wK370rcIrzyLM3cO/4u/es8g3qFg0hsC0bkxYpd/8cj12p2A9e0qnquZHs/3HX3Mdwh1\niigMiMVj/XVvbzSpNgKSLjRCkWYeywpqCSuSxQuTPlsV0e556XZI3JOUw1hLeXuPzW6mp6QJ6ZjL\nm6u2N2Rp+eQ5zWtLiscezrB4p0M262G1h1IRcV9o8B8+6aCV4vHTUB6DpQ3NZj3O4usOCc/S6kg5\n6sQo/TLb/k+12YGxLKyUXFIJaAaWEceSTylOTcDdPSHaDCPLSkmAEfW2wvcsjiMDi0Eo1P1JH9BQ\n6aHFjBHpgn0FCaWkt1NuiqTCzQ24MCP9HKUEYZdLR1QaDpFRRAZeX4bCzD67msglLG3R142ptwfX\nIiaDrc9ctSSS0qPxHIEhH7SED1+6aPnW63B3R0p8ybcHDALwgxvyuWgF56ctW1U5p9tbhgdmHc5M\nxai3LX/zpsFz4PHTipGMIBeP/K51pXR5MKjsVCOu3Al7n43lwuyPyKPzEbP3GnCO5mo/tmP7ES1s\nt1gtB5TrXcbyCaZHBUoVvvkcWEN05xq2tofKDv9Ir7O1W6fZY5dOJVsM9br0WikePJXtkXwO7lLD\naMCLlk8qZoYdqk3D87cERvvovMNo1mVq2OWvXglwHdOXOADF3WYWXwe0wzih0dzcMP2+Dkj/5Bef\nUHRDlz92HbqhIuZKT6jeFqqaZgd813BlOaAbaTYreZq9/oNCpvBBUe71GFwHUnFDFMH0cAdjHcay\nls0ei/TyNoBkBfvx2tH7XRTZduk0jKQV9bZidgSefEDeo1eXYEfaZXgOfOmi4dtv0M8Op4YV5Zai\n3oYXb1laHUvCt1gjGV+j6zCUhd2K7Xdu3lhRTI9Bow2+ozh5AEo8loV0DCoti6OEOmevarnRhH/0\nJc3annCnvbWfE4SWb1yxbJX3edYkeI0dHuk6ZM1epmgs+AfobQ6Wx4rrlp0eB93S9r10Ond3IlZK\nEb4Lu3WZcbp81u/T5UQDNPuhxx8XO+7hHNsHbvX1Jeq7O+z68wBs7jYYef3P8T/zdZyTDxDdehU9\nOoNK5frH1JohKztt0nGH2bH421KQWGtZ2W7SDQ0zo0nivkutJzQWOyDutlMzvLYc9WCxlqWtFtVG\nxOSwh+8pkjGHyWFp6C9tRwQRZN0aa2sdrgZZ8mkf1xGOtajXw5BEQzHJOitmghC5bT8xYtE2IOZa\nsskEV+4aqj3G41RctHE6ISR9QxhZ9hqwtBXRCcRDSVPdYywLj50Sws6hlJR43lixIgtgJIIY6/Hs\nVaHv1womRoWzTWuYzgfEHUs78gkjmSGJuRJIFjfAnYLvXBXWg52K4dJpy0MnHBY3Le1A8YUHZFhU\nKdnHGLix0XPwVkAFK7v7pKuw1xQqoJhvme4hy6yGvSpYq0nE4OyUZXU34vU7lnPTDnd2FNtVYzpi\ndwAAIABJREFUCYh+D/Yc9yEes7ywaCk35fU+c9YyPTz4DixuSSktlRBgw/kZ9a4zMZ9YUFxdsYxk\nFOemFGNZuY6DZbJ8UrHcC8u5xL3ftetrYT+4gUhkV1uGsd5dyHhOc2bSoR1YTk98/Nzvx++Ke/ZB\nMQ10blzBRob4+Yd/qq/7YbZOrYwmwjdtujpOpnIHu32XcOkq5Ytfxcx/irGJEZQzqJssb7aotw3l\nuiEecxjLHd0A3qt12SpLx97aJgvTaZIJH9fRxGODcsbtTUO7K2WQlVJEqSplj829gMfPHq6ZTOQ0\nG6U2M3EhTY2pDnerU71sQRFEmnbgMBRrkNF1MqpOnDQjI1kmhxStVoOYboOBV257rJXlZ6g0eE6v\nCW8lYHmOZbUkJTqBCUMqrvhbjw2c65MX5G+laRhNB9TaDlsVcZIjGcX1u7LdWDgxIn2ukZTl5nrA\ng6NbRAaMk2a9McJOXfZtdGB5mz5se2knIs4Ozy9P0uxKkHn+Jlw+O8iLgkjkBxwtJbHhtNDtaDXo\nR9kDoDRHGxqdwz01BdwtyXrXViJubbm9sqcENd+DeM4K87QZHLfXHAScK3fg+9cVMQ9Gs5Ynz8Ps\n26h4droh1UaXTNJnOO3yufODNT1H8cqSwXMiHjut8RzFiR7Fju/ci2pTSpFJKqpNS8yV9yOTUAyl\n9KF99vt/HyX7iTMN/KzbB8E00HzxGcr/x+8DkPvVf0LqM0/9VF//gzBrLbXtNaIgIDM+jevdGxiS\no1M0Nu8yE2vgBbvo298BranHR1jbaQIO4V6bufGBILzriNIlKO7uBIzlfKyJUPpwMd/3NPSb6UJR\nkz6imJ9PKbar4g13G1Ki6YaWXOren0g2qbl81mV1WeQD6AERjLEERtMJpUcxllYMd3eIiDM3N87M\nmJzbVjQ4R/dAfd8YyIdbVNxRxoI1dDyP8ZLUWuKAa02XREzx+YtHQ26XNkMabYsmZCyrKdUcwkhx\nYjxgs+ySTlhqHSkT7tah2U4wm8kwmmqTdJpcGFM82xgmshB32uzWfZK+JRULCUPDYinTCxBSHru1\nCptlUV8dz1mqTcWj84PzqbcVyxtS4rPWks9YlIaE1yWXCNAKmoHL3EiMbEJ6HbMjPZ2eEIYyiomO\nYrMiZbNfviz7bJQ19V4v7ZUlydZOj8PdksFRikpTmKsboSIbV/1gs74n2efB4HNrpUwYGTaU4sL8\nCO4BOYprq0KKCjC6LSXAV5YtqRh8+eKRHwGPn/aoNCyZxICl4GfBfhpMA0fZz847+AFYuL1+5OOP\ngkWlNcIr30Ml0niXvoo6InAcZa3qHo3d7f7zoZn5e/ZJDE+QGB7Q2JixSXB9miZOam2VbLQHtTTB\n8FmWNxqExjIxlKBU7xXdLQRvPE20dhM9MY//8Bf7a6UTHtmkS70V0GgHvH67xtmZZJ8Xbd8ycdGD\niayQYWbjMR6ZVzR2Vlm51WZobJJUNk+7G1FvRSxvO7y5eZahRMBXHtaMtBS1tiU0mrslODmqODOZ\nBR4ZvIfGslGGbCLB6WkXRytKdZcbm/Sn5x8Jf4hfKaGA56OvMH8+y+puyE5VEViX6bQS5oAjes2Z\nhCDNTK/xrzXc2tRkEg5zEwZrFQdBUcbCrb0RJtJ3iMKQVlgh68XIJbsk3IClvSyT+UCQexG8sTpo\ngFgrx4eRZGPDacUvPi4qnj+8Ifu4WhBnQSiMBlEkTXSLYjBvqzg9oRjNqP7zT59zuLUJoxl46ATs\n1eWGYP+YyfwgK/rCA/K/mxumJ/ltOT+tsFZ2FrZpQdt95w3Z91PnRNLAWkvYa6QYY1kvB8yNDm5G\nskmgNHhvr/QkxRsd0R6aGZY1bG8gFyQgDmeO3eTb2XsKOO9VE+d+rVAo5IDf6D19Avidg7IGhULh\nv0bURU8D37zfbR82Sz/584Sbq2AM6S//7Q/6dN6TRbdfw7Zq2FYNs7WMM3P2vo5zXO/Ix+9kOi8F\n/iFrieweEEG7ws5ug2pThlEq9Q4zw46Uy6KAaO0mAGZzCRt0UN7AcbjOwAG0OyFXlxs8spA5hB7K\npbRM5fdmXQKjcEyHbluIxGrlXfxUlteX6kRGWJAhy17Lo9kVga+xXovprY3kfXtpUXoajoYvXXRw\ntGE0KxQ5QaSI+5ZF9QDn2t+n6g6zygwr1xSO4+JoIYl88ZbizRXLly5GTL8FVnty3OOF25LViLKm\nZSJv6QTi9FFACGAJI0upqvFchXaTEFbRWpNJx3FsqyfiFvYb+6BxHEUybglDiMUFXXZrS7YGEfzJ\nDyHhD44wJgJEFVUpAW1HxlJreZTKmlTc8IufcO8RKXtjBZZ3oLguSLPR7Ns78CCyLG8bdmuHp/yn\nh2VIdTwnnHrV5uCY/cdKKdLpFHvVNqF18JzDr3NuSpNPWnxXAt6pjgzzpuMCPqi3Ld+8IgHtswWB\ngR/bO9uHpaT2r/eVRHukoS8WCoXHisXiUqFQ+PfAf7uvGlooFP4K+Lne47fd9mE0nUoz/I//yw/6\nNN6X6ZFpzM4KOB4qN3rfx8VSGYbnFojCgER2qP//qFqidf2HKNcncf7T6Pi9OjdKKWKZPJ1KCceP\nE0vFoCwRIRl36QQhviOetDs0h793Fz06C+7h7GtuPE2pXsNGBosmjCzG2EPOOuErnrzgs1IyVFuW\nk2Ma34/juC5RGJJIpQ/xuMWUnMdYlj4dzVHW6toebFcyIABrDXfX9zDGMJxL8suXM3zriqDeNtQ8\njdkZml2HoOqQikUYA0rp/h1+swM3NwIaHcP52cG1lmqKTiB8NRN5Szpm2OqVhGZGFN0A9nqACWMU\noAlC6OhRTk2n8TyPeddlrz6Kpw2V0KXdDTk1HqK0x+KOIMUePgepuOaZIiRikoV854qsG/eg2TJ4\nruHLhU06kUO55bO4O4y7LzWtoB067Gw5h2ZuQOQP6m0Rk1vbsvyHPfhPvuCQfRvJ56t3oz7R6kRO\nZnFOjStOTwjbQD4lAejCrFx7ZODhk4Pj5yeTJGKezOnk770hGs8NXvfUuOLk6CCbWd62/Rmo21uS\n8RzbO9v7lSeY7z3cLRaL1UKh8Cjwa8DNYrH4v77HtU4hGQoAxWLxdo+r7e8Dvwt8pVgs/oMDhywe\nkEd46h22HduP0dxTD6NH51B+DBV7Bw97hMVS9w4qBFtLEAbYMCDcXcOfPnPksZmZBZKj0zheDOU4\nXDjpYIwllfDoBBGdboTWiuTpL+GYAFz/HsSa62guLWRZ3w2otwJGMt4h6ejBfor58YOlNs3kyTOY\nKOz3nqaGfHbvrDB952/IOxOcf1Iy1f4A6gFb3DRcuSt3yE9e0DxyUnN1xZBPRJhQIle92WF6LMuD\nc5ordw2ZWEhctzGuTzbh9MXKwgjOTyu2KiFKGcpNF6UgFe9SaRhmRz3agcP+Xb7niGOPjDAJzAyJ\nVMBuXdgL8inFTkUa4PPjkIgl+tfRDS0to3l9GSLj0gpcfvFx2S+MLFsVw5W7Gmtl6PSNOweyGguf\nvQC71QjHgaQTEfRkt8NIsg3XgbgLD19QpOKD96zRgT95XihxOm1Dsw3NNvywaPjKJYc3VyzPXZce\nzFMPyw3JQWjx/JhiIj/4XA/Ox8Q8+NKD936/tFJMDd8/48BBnrXJIYivSL/p5M8IK/RP2t5vhvPP\ngZvANwqFwgLw74FfBVShUPgn7zHo5IHfAd5arhspFApPcSAY9awMfLVQKCjgrSSiZX4GpBM+rKYz\nQ+++032aOzRFuLMGjoOTO/xrtdayWaoTRoaJkTTegewnERt8ZWOew5nZA2IjzttP9jlaMTvqAz67\ntYDNcpexnIc+ECSsMYSLr0CnibvwGCqeRGuN1gOHdHIiQcgCi4kZTs4kCCPL1TsNmh3DwmScsfxg\n342yBItuKDMZcyOaJy84WKu5uxFjraLpdBPEdwwKCQ7llsdUusFwvEHMj7HXK/9cPiNcaqW6MBS4\nyEDl8pZkWq2u4YkzSR46AZWGlJKySc2tDemxvLhoeXR+H+slgmX/2VP3yinfXI9Y3hFUnO96tLqa\nWmuw/fmbAbU2RCZC3MeAcgcEgNYIFL9wOcZLN3LsNh0io3liweI6mrOT+0qc92Ysez1WAFDEfGHC\nA1EGBXjuumQ/11bh4Xm5xotzDnHPkIzRDzavLUtm98CsYnroJ1fmysQVv/S4ELi6znE57X7s/Qac\nv94n8CwUCv8a+F8OlLXeU2JZLBZfLhQKj7/l348B/xI4ysOVkD7PUbJG+9uO7UNu7sg0yewItBrY\nZhWbzBBFwhRcrrXZKTf6+85O5OgGhmsrTcLIcm4m2acXea+2Wwu4vtoELK1GxORwgnhCAprZuE10\n+zUAut2Q1KUvYq2luG5Z3zOkY5YHT7gsTGgWJpL99RptcYwbe91DAWc2WqRs50g4XcazaaLI8Npy\nl05gODOVYaeHG3n9jmGi1/+xKNqhR9yJqLZEbhrglSXDQyecvjAbSCAxVmDHcU+GOB+dF9LKH9wQ\n6O7+vpUmPHeTvupnGEnJaeItv6JmV2ZsdmsOQ2kY1ZaRNFxbgbPTqj9f4mhhtO6GDklfeinGQD4V\n9ATSPPxYDNs0aA35pOHUxDvTvkwNCUWMqHdqYo9KljbZCxozI1BchXRcZo2EeFTxwNzgu7DXGJCk\nvnTb/kQDDkjG815ECKy1NDrChPBxo7WB9x9wSgcefwX4pweev2c2gv1gBVAoFH4D+KtisfitQqHw\nT9/hsOOK6YfY6k//Fc3vf4vEpU+T+crfOXqnbofu9/4QsJhYkr2xs3Rzk+SHBj2iffmA7ephx34m\nkThqxXe1feaAtG5Aq8HGKkxMzZBIpfYnCwHYabm0qiH1jubaqpSMGm1LajPigbnBzyadcPoQ6pHs\noAdgjWG4do3Pcw0M+HyNGxuWWkuyhzfvdnG1T2iEcuXUuGavYfAcy2yyycZKlU0zhuvtu7OIasvy\nuQsupZrl5obIUidiMU6OWiwOf/FyhO+Ibg4ouhE8floyrZ1ajzA0lCwi4UmG8FY7M+Xw8qKi0VHU\nWnB+xvJSr47w9JuW6WGD62oRRAs1xkqgeGQenilamoFLMgq4tRkylnXY2JOAM5w52i032pZni9L7\n+cx5eOqhg074sEP+ysPw0AnLy0vwzHUYSlm++vBgn9eWDZsVGVwNIsi/t8rvT8VevxOxtieCep8p\neB+7oPN+A85Cr8/yz4AXi8ViFUR6+kc5mUKhkAd+pVgsfq33r90jdhu5j23H9gGa7Xap/MG/ASzB\nym28fJ74E1+4d79GGUwIno8OO+R2brKZGcfRlhNTecLIMJSRwJJNOn1m3lzq/VO/j+Y82oEhbNR6\niC0IwgCv26bqDtOY+xzNWpNScp4TXYNWhx1lOn7YQfiu5tJCmtBYfFcTllYhinDG5nDHThBu38Ed\nnkZ5Pq5u949zabNZSeC7ls+cFSjtVx/W2G6b9tPfZiIKaPhJtpgDZNYkFYNrqxFDKcVTDx1+D15c\njAgjyVxOT1h2qorpYWmQX5yD71yF7arCdSy5JHz6nD6SnSEV0+RT0k85mE2BOPET6R1QGkdFbFen\nMNZhqT8gKut1Qo3nWO6WNI7r8/AJyB3R9DfG8jdX4dbG/ucA5+dEt+coU0oxnKEPvhAQgIA/Kk3L\nTSH7Ju7BJ8+qftb4ThZGllfvWKJIZCji3k82AGxX5aap0REutY8bq/T7CjjFYvGPenBkkN4NhULh\nd5Ay1wu8/x7K7+yv17MyR5fOFt9l27vaU08Nhi5/8zd/k9/6rd+6/7M8tnc218XJ5YkqeyhH0735\n+pEBR4/NomfOYrbuAJYgnsP3fVLJJI7zljmZhMtjC2kiCwn//SspaqU4MRYnzE9Q2tnCcVwStS2C\nF36A58SpTX4aNTFFMlTc2eqSS0U8fMKnvlNirnuNtJ0HThxeUyt8rQi3luleew4Ar9MgfvoR7KmH\n+lII08OKWq0KKHzVxtphOsGAzwzABm1UD5v9UPAiP0jNMj8uvYpnr4XU2rBdFfqVfG+CvdqyrOzS\nIxOFwrTi8gEMhqMVT56HP33BUqo5nJ6AuBdijEb3CE/v7MCrSzA3Ij0gkDmaT50TeYTQwEoJIqtJ\nuCGRUT2SUIvvKs5Nw1ZVCEsfnFF0I6cfAF5aDLg012F0+DB45Nnrhs3KYKZmcQvu7MKnzlrOzxzt\niCMDvtvrm2j4wXXFqXEYzcp5dkKh+bnfUtriFj1uOYh5lkdO/mQDwMKEw63NiNGMvufm5cNov/d7\nv8fv//7v/9jWe9+w6LfO5BSLxX/1o5xIL4D9zoFs6VKxWPzmET2h08D/WCwWv/022/6n+3m9b37z\nmz91poGPiymtGf0v/hvK//Z3UaZL/PF7gw0I1Nd/7KvYThNTLxMbmmRIazrVPWqldTw/hl/bw5k7\nh05le6wB92+20yR44RugFN4TX0X58f421/OYmJoBoPvSqyjAi9rE27uMTeW4uhph8Sg3Ik4Md1F7\nRb7XKTBW3ePTBxQmb653WdsLmcg5zEeD7nrUbuH1rnHfYr7PVN6h2WrhJ4Y5HUhZaygNq9stqs2A\nqZEU6bNP0N1e5UrnIu0QNivw0AlF3BdotVaHySrX9qATCP3LeO7obGKnCuWG/H9vr8pSuIfjaOZm\npvA8l+++IXDrtd2BJHU3kmD6+d5UvbEQBOO8cKNBpR0j5glK7RMLA/RZN1Ss7DkUVyGVEEiytm22\nSxW+v5jAWpfPnpdy2HYVskmL61g8R9MK9uHGhrNTGgX3qG/u1iX4uVrOZ6NiuL3l8HcvK778IFRb\nUKpZ/t0zlokcfP6Bd+6VJA4A1JL+Tz4AzI87b0FCfrjtt37rt/o34ysrK4du1N+PfSjmcAqFwq8A\nLwF7vSHQBQQ48DKChHv0QJ/nVLFY/Hbv8VHbjhFqHwJzJ6YZ/Zf//X3tq2JJnANQ69raIjYKCZo1\nzAvfwHn5uyR//b96z+cQXn2O6LYMiKhUDu+Rzx+5nzN9hqi8ReQm0Plx7mzX8XEI8UjogEQizg/a\nl6hEadbCCRYqEiiMtazuSl1uoxzh5OfBq+EQEsULvBXorZRiJOEyFEU4Q4k+gWW1EfLmGljr0e62\nuHT2QVoTF9l5VUpH+/M3j847bJQt2cRh7ZfpIWmmB5FibgSurRp8V+ZGlFLS0LdyV71T00xmBPoW\nRYZ2p4PnuWTilmZHONLivgQOUfUcnL8Qb7qMDWXYWRUF0IdOCqv01ZUBDUy1KTxnjZbl3ESNiUSZ\nzXqKzYq4m5cW4ey0BAyFQIrPTsG3rxiMFQ62//iywLcfO6UPDVSOZyGXhHqLe4TfwsiSSyieLQpY\nYr0swIi3kw8AmBtReI5kTm9XyusEIlUwmlEkfgpB6WfZPvCA05vD+QMGYIN9NsCv9p7/BvCvCoXC\naeATHAYovNO2Y7sPa377T+hee5nEp3+O2KOf+aBPBwAnliBs1iDooIIuNuj2xdX2rRtamh1xPm/H\nFH2QXfrgY2Mstza6dALLwqRPYvI08fF5lNbcXZSGgu8bJutXGJ4/g+u6ZPMJKiVwte07Ha0Uw2lN\nuRGQSbh4vsubCaGyOeffexdrGlU6r34LrKW7+AqJR59Cp3KslRXNQG616727/ExC8dlzls1KxOke\numun0mW73MVEHtnkIFvLJkQ+2QJXVyy3t3oMzQ7MjSpeX+pSaRqGU/C1R+JEYZbNrR08zyPZA19c\nPGlp3bJ4jszLhA3N+h7c3FCcOSx+ynZVoN5RqPC15bXbTcotB+HbkaBXXIWxrOL8XIqbK4a2cVHK\nYq3oxzQ6grJTQDouQ5taQaurWNqO2OdVfe6G5e998gChpqt4cFbzvWvCzO258Oi85XvXIrqBMESM\nZxQru4pc8p2HcvdtMq9odiyv34HhtGV25PD36XtvGmptiHuWn3tEf+wa/T9O+7EHnLdkHO9qxWLx\nNrw9srBYLFaA3+49/eP73XZs725RuUTru38GQP0v/s8PTcDJnThHUK/AxjJ2ZgH3/OP3BJvvXo3o\nhHKH+sjJo0sU7rnHUIk0KIUzO6Di2aqErO9JZqK3ujwwF++vn0sn2Ks2iXua0cJDeIkUrXbA5YWA\nhcnE/8/eewfZdd13np9zw8vdr3MO6Ea4iAQIEARJgUEESVGWbMmkRO96bdPlsmyXZzi7MztOWzXe\n2pmyLY9dtVuma9eyxjNLjV1jc0YeybP2SCQhWlkQSQCMwENsNLobjc7h5RvO/nFeJ/TrnLvvpwqF\n+95Np1/3O797zvn9vl+q44JCHgOelJikKTFdSgImLVUhNE2tbTRVzvyTllIyMpohNOFV7HkM9g1z\nLR8tHKE6sXh0KtOtbzTHeNrj0m3ByT1hbvVnkRJ6hnLUlQdmTDFOTD153lQl5MTieiav3nM9kEhi\n0QixtpnrUNUlgnCgsKCdFUipUrK/8yHsqVPtz+U9RrOC/nGlidY3LnmvIw946HhoUkM3dQ61CB47\nOHFlnZoytdQ6klKeM/Vlkt7BNGVBwbgdYjQNfaPqAQIgm9cwDQ8kuO7szr0krERPHQ/qy9Tfg1Ow\nk9aFSo1+9piaWlxscPjhFSZVGR4/MKU8PZHGDMpqQNk4LOqSPkVYdsApqA20F9n1W8Anirzvs8nQ\nIjG0eAXe6BBGfevCJ6wTmm4QjFdCvBKs47P2J7NqcRhUQeW9eJ4kk5eEgwK9ed+s/aFpSQf3JiA0\n1MSpqYih6yqLK5d3uNk1gARKYzkqpxW/Oo5HNq8WPJIZGyEEzZXFg9/5m3C1t4YD2n7a5DV00+Ba\nto7hghJ0ZUzQNwbX7kJt3KO2TJtMA887krGMhys1NDwChjZZaCilxMln8aQkEAwXnugL6tIZdcyB\npgCdAw4VMY2LNzX6RuGBPWrdpTSsCjHLooKDTYIfXIZsfqqTLotKbvbmGBiz6RoJo2tqlDIxqCyL\nCUaSanosm9epCCvDtMvdqgM/0qIW8dW11L++wSRDI0kaSqB7HLJ2iHAADAMcR+JKGE2piY6mSpvX\n31NrH3vr1GcbCwmeOaoSHS7cVNeOhgRSTriGKtHQpYxEJrLxhIAfXIFPHVcjWSEEJ9oFN/vUyOfe\nQlmfpbFcaZsvotZYimWEFQtCPutA+rv/QObH/0jo6ENEn3puweNFIEj8V/4Vzp1OzJbi0jKbkYks\npOGUxKrXkHYeDFMJRErJxZuZyZTTo22z51TKojpH20LkHUlVyewAYUzzK3Zcd3Ku17bdGccFTJ2q\nsjCjyRzVZfPXBU24RF4Sh6k5cJC6coG4qiRfpIScI5GoKaaPuiW1ZbCvIUjXoE1liU7ngGQ0E0DX\nPOrDxuSIZvTOLbJjw9jSwCipJC3r0ITK4qqJq8+jc1AwlDIwdI33bql2vPGeSnOOBOD5h1Sm20dd\nEI/B8RpVxGnoAp0svcM2Y1lT6dB50Fwh6R8TxMtgJBVkOG0wkhQ0VgoeP6wC3Q+vqPuMpuAn7ynF\ndqbp0VREPVrrBKURwQPtklsDE3pvgpDpMfGRf3TbIxbUqC9kn8VCgmx+KlA0lGs0lEuu3pFUxAQV\nMebk7qjkYoekJAyn9qjAdKLN49uXVEq34zFZnAlqtDqXn85qcavfoXPApSauYzVs+ErHmrHcn+yt\nubLSCgkAPuuMdB1Sr/0XkJL0P/43wo88gxaZ51tXQIuWENgzh7nHJkUIwfE2FRTyH32f7LsdaBUN\nBO57orC2M/GE7+G6HnqROZCAIUhlPXK2JDTPQnA0HKS6PEYmZ1NTMXv1uak6RlP1wp/zkRa40KGC\nZW3ZRKcmsN2CGkDOK4QbZQKXykmq4wbVcfUVvdmfRwiBJ3VK5Ah2bxKjqonsuJoHMoXDtaEwQ3lV\npNpSpYpJB8an1nRytoep69huwQ4BNcV1qUtiFFKN1ecLx9oEngc/vqqRsTVChkPKDqAXLAd6hjWE\nmJheMjjSoopM1X2YrJkKTOthsrbkzjBURGNIJLqmUVMZnZQXOtAksBolf3tOBUPPU/I2UoLtapMW\n0BO01yqbZ4C9dYLymPK+cT2J7c6893Q+6pKMZ5U0UO8ImCJHx90sTXEYy0epiOlULvwrXVWu9bpI\nqSyqW6v1Na8H2iiWG3BG5tqRSCS+usxr+qwAoRsYTe04t6+j1zUjiqgvrwe2KxkccygJ6wQ1m+TA\nHXQzSKyqbs7F/cXgjQ4w1HuXAaOS8niE2qpSpOfh3u1Q+4d6wM4RMIOYmovtaZiaW/SeUkre68hi\nO5IuQ3Byb3jettXMl+Z0D056nPGbH4DQKGk/jBFS80kN5WJGFtS1Ox6pXCFtGKmsCiIa6ZxEIvnO\nRw5HWvTJtaDKmEbXkEeMFFV3f0ROSpyRPrSSFpyxuyRldIaW3ETadDSoUogdT2VrPbIPhlKQzkq+\nd1llef3gMvzc49A1pFaSWqrUuT+8Ape7g3heAFOHJ+9TmVyXe2Z/VtPTi+MRePaoGtXtKVg1uJ7k\na2+pNRBT13j+VFwFOKlGNJqm6nyytuCRfZK7o9BUKQgYBu91qqSCtnsEMsui8Nw9hr2prOTblzzy\nDhxvE7RUzX7YqCyBwaT6XOIRuDOg5melhMNNLrXl6z/CKI8KhpKSaEhQJN9k27DcT/bGXMkBlmX9\nQSKR+J1iJ/msLWW/9Js4dzoxaptmLLKvJx91ZhlNe+ga7I3246WHATBDYUIlxep0p0jnPC52KC2u\n+1oDlITVz+AN9ZJ77RWinke+/ggDzSeorihB0zT0+t24d66jVTXTNZRlLD1GY0UYiaAsFplVxwET\nxmETtshqSuveeCPzOfA8Mt/6L+DahD7+PFpsdul6Jq8Wt8NB1dbc8F2kqzqw/Eg/PUaYZFayu1ab\nnP+XUhI2lAgnQED3CAXgRLvG3VGvIKUDg+PeZMA51KxTX64RcSRuomBzYGepaaynJ1yNlpOcrNLp\nGVajg/ZCyrXtQN6bGtHEo+qf7cD3L0HeVh33UEqjNg77G5TUDqiaFqRKcXY9dfz/+Chf9Yq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OYxKRMLVMOvFOfyD3G7rwJgHHkcdBNcG7GAtcBcuJ0JvIFu9H0nVi01Ox4L0j+SQdhZ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\nRK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11c485c50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figsize(6,4)\n",
"bovy_plot.bovy_plot(aprc['FE_H'],vRvTvZ[:,1],c=aprc['ALPHAFE'],\n",
" edgecolors='none',s=10.,cmap='coolwarm',\n",
" scatter=True,\n",
" xrange=[-1.,0.6],\n",
" yrange=[80.,300.],\n",
" xlabel=r'$[\\mathrm{Fe/H}]\\,(\\mathrm{dex})$',\n",
" ylabel=r'$v_\\phi\\,(\\mathrm{km\\,s}^{-1})$')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's compute the actions and look at the action distribution:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"aA= actionAngleStaeckel(pot=MWPotential2014,delta=0.45)\n",
"jr,jp,jz= aA(aprc['RC_GALR']/_REFR0,vRvTvZ[:,0]/_REFV0,vRvTvZ[:,1]/_REFV0,\n",
" aprc['RC_GALZ']/_REFR0,vRvTvZ[:,2]/_REFV0,aprc['RC_GALPHI'],\n",
" ro=_REFR0,vo=_REFV0)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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TceoUHHQKCgogSRIAoFu3bvjoo4/ippq2P4KJt1FZQugRKIRdoFHCJGVmA7ifc94E99k5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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1044217d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figsize(8,4)\n",
"subplot(1,2,1)\n",
"bovy_plot.scatterplot(jp,jr,'k.',ms=7.,gcf=True,bins=51,\n",
" levels=[0.68,0.9],\n",
" xrange=[0.,3000.],yrange=[0.,400.],\n",
" xlabel=r'$L_z\\,(\\mathrm{kpc\\,km\\,s}^{-1})$',\n",
" ylabel=r'$J_R\\,(\\mathrm{kpc\\,km\\,s}^{-1})$')\n",
"kindx= (numpy.fabs(aprc['GLON']-76.5) < 10.)*(numpy.fabs(aprc['GLAT']-13.3) < 10.)\n",
"bovy_plot.bovy_plot(jp[kindx],jr[kindx],'r,',ms=7.,overplot=True,alpha=0.4)\n",
"subplot(1,2,2)\n",
"bovy_plot.scatterplot(jr,jz,'k.',ms=7.,gcf=True,bins=51,\n",
" levels=[0.68,0.9],\n",
" xrange=[0.,400.],yrange=[0.,100.],\n",
" xlabel=r'$J_R\\,(\\mathrm{kpc\\,km\\,s}^{-1})$',\n",
" ylabel=r'$J_Z\\,(\\mathrm{kpc\\,km\\,s}^{-1})$')\n",
"tight_layout()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An apparent feature in the $(L_Z,J_R)$ distribution is simply the location of the Kepler field (red), not an interesting dynamical feature... What about the frequencies?"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"jr,jp,jz,Or,Op,Oz= aA.actionsFreqs(aprc['RC_GALR']/_REFR0,vRvTvZ[:,0]/_REFV0,vRvTvZ[:,1]/_REFV0,\n",
" aprc['RC_GALZ']/_REFR0,vRvTvZ[:,2]/_REFV0,aprc['RC_GALPHI'],\n",
" ro=_REFR0,vo=_REFV0)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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dvr6+rFy5ktGjR7NmzRratGnDp59+SrNmzdi6datDYTwtYfjbb7/FZDIxbNiw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fPmmjGjoaGhYeMU27cuSdIR4AGj4ZJs1GMADErBgJckSZWuG61R/C8F6ACsMy0916hc1KtXj507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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11e6e8150>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figsize(8,4)\n",
"subplot(1,2,1)\n",
"bovy_plot.scatterplot(Op,Or/numpy.sqrt(2.)-Op,'k.',ms=7.,gcf=True,bins=51,\n",
" levels=[0.68,0.9],\n",
" xrange=[0.,50.],yrange=[-2.,2.],\n",
" xlabel=r'$\\Omega_\\phi\\,(\\mathrm{Gyr}^{-1})$',\n",
" ylabel=r'$\\Omega_R/\\sqrt{2}-\\Omega_\\phi\\,(\\mathrm{Gyr}^{-1})$')\n",
"kindx= (numpy.fabs(aprc['GLON']-76.5) < 10.)*(numpy.fabs(aprc['GLAT']-13.3) < 10.)\n",
"bovy_plot.bovy_plot(Op[kindx],Or[kindx]/numpy.sqrt(2.)-Op[kindx],\n",
" 'r,',ms=7.,overplot=True,alpha=0.4)\n",
"subplot(1,2,2)\n",
"bovy_plot.scatterplot(Or,Oz,'k.',ms=7.,gcf=True,bins=51,\n",
" levels=[0.68,0.9],\n",
" xrange=[0.,60.],yrange=[0.,100.],\n",
" xlabel=r'$\\Omega_R\\,(\\mathrm{Gyr}^{-1})$',\n",
" ylabel=r'$\\Omega_Z\\,(\\mathrm{Gyr}^{-1})$')\n",
"tight_layout()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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