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Investigating the Schwarzschild precession of S2 using galpy
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"import numpy\n",
"import astropy.units as u\n",
"import rebound\n",
"from galpy.orbit import Orbit\n",
"from galpy.util import bovy_coords\n",
"from galpy.potential import KeplerPotential\n",
"import matplotlib.animation as animation\n",
"from IPython.display import HTML\n",
"%pylab inline\n",
"from galpy.util import bovy_plot\n",
"bovy_plot.bovy_print(axes_labelsize=17.,text_fontsize=12.,\n",
" xtick_labelsize=15.,ytick_labelsize=15.)\n",
"_SAVE_GIFS= False"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# The orbit of S2 and its Schwarzschild precession with ``galpy``\n",
"\n",
"[Gravity Collaboration et al. (2020)](https://arxiv.org/pdf/2004.07187.pdf) announced the detection of the Schwarzschild precession of the star S2 that is orbiting the supermassive black hole at the Milky Way's center. Let's see whether we can reproduce its orbit, both with and without taking into account Schwarzschild precession, using ``galpy``\n",
"\n",
"## Getting the initial conditions using ``rebound``\n",
"\n",
"The initial conditions in Gravity Collaboration et al. (2020) are given in terms of orbital elements, so we need to convert these to cartesian coordinates. To do this, we use ``rebound``. We set up a simulation with the orbital elements given by Gravity Collaboration et al.:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"R0= 8246.7*u.pc\n",
"vo= 220.*u.km/u.s\n",
"MSgrA= 4.261*10**6*u.Msun\n",
"sim= rebound.Simulation()\n",
"sim.units= ('AU', 'yr', 'Msun')\n",
"# GC\n",
"sim.add(m=MSgrA.to_value(u.Msun))\n",
"# S2\n",
"sim.add(m=0.,\n",
" a=(125.058*u.mas*R0).to_value(u.AU,equivalencies=u.dimensionless_angles()),\n",
" e=0.884649,\n",
" inc=(134.567*u.deg).to_value(u.rad),\n",
" omega=(66.263*u.deg).to_value(u.rad),\n",
" Omega=(228.171*u.deg).to_value(u.rad),\n",
" T=(8.37900*u.yr).to_value(u.yr)-0.35653101) # time since 2010's apocenter (calculated: 2010+0.35653101)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we convert to cylindrical cartesian coordinates and initialize a ``galpy`` orbit. The cartesian frame used by Gravity Collaboration et al. is that with the $X-Y$ being the plane of the sky and $Z$ being the line-of-sight direction. The $Y$ component corresponds to RA and the $X$ component to Dec (apparently). Thus, we initialize the orbit in ``galpy`` using ``radec=True`` in ``galpy`` and calculate the initial RA,Dec, etc. coordinates using the position of Sgr A* as reference:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"ogc= Orbit([0.,0.,0.,0.,0.,0.],ro=R0,vo=vo)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"pt= sim.particles[1]\n",
"o= Orbit([(ogc.ra()+(pt.y*u.AU/R0).to(u.deg,equivalencies=u.dimensionless_angles())).to_value(u.deg),\n",
" (ogc.dec()+(pt.x*u.AU/R0).to(u.deg,equivalencies=u.dimensionless_angles())).to_value(u.deg),\n",
" (ogc.dist()+pt.z*u.AU).to_value(u.kpc),\n",
" (ogc.pmra()+(pt.vy*u.AU/u.yr/R0).to(u.mas/u.yr,equivalencies=u.dimensionless_angles())).to_value(u.mas/u.yr),\n",
" (ogc.pmdec()+(pt.vx*u.AU/u.yr/R0).to(u.mas/u.yr,equivalencies=u.dimensionless_angles())).to_value(u.mas/u.yr),\n",
" (ogc.vlos()+pt.vz*u.AU/u.yr).to_value(u.km/u.s)],\n",
" radec=True,ro=R0,vo=vo)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Integrate the orbit with ``galpy``\n",
"\n",
"Next, we integrate the orbit and compare to the literature:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"times= numpy.linspace(0.,2.*16.0455,100001)*u.yr # 2 periods\n",
"kp= KeplerPotential(amp=MSgrA,ro=R0)\n",
"o.integrate(times,kp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The orbit in RA and Dec relative to Sgr A* looks similar to what's in all S2 papers:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 360x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figsize(5,10)\n",
"o.plot(d1='(ra-{})*{}'.format(ogc.ra().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" d2='(dec-{})*{}'.format(ogc.dec().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" xlabel=r'$\\Delta \\mathrm{RA}\\,(\\mathrm{arcsec})$',\n",
" ylabel=r'$\\Delta \\mathrm{Dec}\\,(\\mathrm{arcsec})$')\n",
"plot([0.],[0.],'k+',ms=30.)\n",
"xlim(0.055,-0.075)\n",
"ylim(-0.03,0.21);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also look at RA, Dec, and $v_{\\mathrm{los}}$ as a function of time:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figsize(8,5)\n",
"o.plot(d1='t*1e9',\n",
" d2='(ra-{})*{}'.format(ogc.ra().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" xlabel=r'$t\\ (\\mathrm{year\\ since\\ 2010})$',\n",
" ylabel=r'$\\Delta \\mathrm{RA}\\,(\\mathrm{arcsec})$');"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figsize(8,5)\n",
"o.plot(d1='t*1e9',\n",
" d2='(dec-{})*{}'.format(ogc.dec().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" xlabel=r'$t\\ (\\mathrm{year\\ since\\ 2010})$',\n",
" ylabel=r'$\\Delta \\mathrm{Dec}\\,(\\mathrm{arcsec})$');"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot(o.time().to(u.yr),o.vlos(times))\n",
"xlabel(r'$t\\ (\\mathrm{year\\ since\\ 2010})$')\n",
"ylabel(r'$V_{\\mathrm{los}}\\,(\\mathrm{km\\,s}^{-1})$');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Modeling Schwarzschild precession with ``galpy``\n",
"\n",
"To compute the Schwarzschild precession, we implement the approximate GR force as class that inherits from ``DissipativeForce`` in ``galpy``, which can take velocity input. We implement the following form\n",
"\n",
"\\begin{equation}\n",
" \\vec{a}_{\\mathrm{SP}} = f_\\mathrm{SP}\\,\\frac{GM}{c^2r^2}\\left[\\left(2(\\gamma+\\beta)\\,\\frac{GM}{r}-\\gamma\\,v^2\\right)\\frac{\\vec{r}}{r}+2(1+\\gamma)\\,v_r\\,\\vec{v}\\right]\\,.\n",
"\\end{equation}\n",
"\n",
"This form includes both the overall 'GR' factor that Gravity Collaboration et al. (2020) use to detect the GR effect as $f_\\mathrm{SP} = 1$ and the PPN parameters $\\gamma$ and $\\beta$, which are useful for checking for example that there is no GR precession when $\\beta = 2(1+\\gamma)$."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"from galpy.potential.DissipativeForce import DissipativeForce\n",
"from astropy.constants import c\n",
"c= c.to_value(u.km/u.s)\n",
"class SchwarzschildPrecessionForce(DissipativeForce):\n",
" def __init__(self,amp=1.,fsp=1.,gamma=1.,beta=1.,ro=None,vo=None):\n",
" DissipativeForce.__init__(self,amp=amp,ro=ro,vo=vo,\n",
" amp_units='mass')\n",
" self._fsp= fsp\n",
" self._gamma= gamma\n",
" self._beta= beta\n",
" # Following functions implement the vec{r}/r and \\vec{v} parts, respectively\n",
" def _force_firstterm(self,r,v):\n",
" return 1./(c/self._vo)**2./r**3.*(2.*(self._gamma+self._beta)*self._amp/r-self._gamma*v**2.)\n",
" def _force_secondterm(self,r,vr):\n",
" return 2.*(1.+self._gamma)/(c/self._vo)**2./r**2.*vr\n",
" # Now compute the three projections of the forve\n",
" def _Rforce(self,R,z,phi=0.,t=0.,v=None):\n",
" r= numpy.sqrt(R**2.+z**2.)\n",
" vr= R/r*v[0]+z/r*v[2]\n",
" vmag= numpy.sqrt(v[0]**2.+v[1]**2.+v[2]**2.)\n",
" return self._fsp*(self._force_firstterm(r,vmag)*R+self._force_secondterm(r,vr)*v[0])\n",
" def _zforce(self,R,z,phi=0.,t=0.,v=None):\n",
" r= numpy.sqrt(R**2.+z**2.)\n",
" vr= R/r*v[0]+z/r*v[2]\n",
" vmag= numpy.sqrt(v[0]**2.+v[1]**2.+v[2]**2.)\n",
" return self._fsp*(self._force_firstterm(r,vmag)*z+self._force_secondterm(r,vr)*v[2])\n",
" def _phiforce(self,R,z,phi=0.,t=0.,v=None):\n",
" r= numpy.sqrt(R**2.+z**2.)\n",
" vr= R/r*v[0]+z/r*v[2]\n",
" return self._fsp*(self._force_secondterm(r,vr)*v[1]*R)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can now integrate the orbit of S2 including the effect of Schwarzschild precession. To see the effect clearly, we first multiply the expected for by 5 (``fsp=5``):"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"sp= SchwarzschildPrecessionForce(amp=MSgrA,ro=R0,fsp=5.)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"galpyWarning: Cannot use C integration because some of the potentials are not implemented in C (using leapfrog instead)\n",
"galpyWarning: Cannot use symplectic integration because some of the included forces are dissipative (using non-symplectic integrator odeint instead)\n"
]
}
],
"source": [
"times= numpy.linspace(0.,4.*16.0455,1001)*u.yr # 4 periods\n",
"o.integrate(times,kp)\n",
"osp= o()\n",
"osp.integrate(times,kp+sp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The radius is not that affected:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figsize(8,5)\n",
"plot(o.time().to(u.yr),o.r(times).to_value(u.AU))\n",
"plot(osp.time().to(u.yr),osp.r(times).to_value(u.AU))\n",
"xlabel(r'$t\\ (\\mathrm{year\\ since\\ 2010})$')\n",
"ylabel(r'$r\\,(\\mathrm{AU})$')\n",
"ylim(0.,2000.);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But the orbit in (RA,Dec) is:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figsize(5,10)\n",
"o.plot(d1='(ra-{})*{}'.format(ogc.ra().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" d2='(dec-{})*{}'.format(ogc.dec().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" xlabel=r'$\\Delta \\mathrm{RA}\\,(\\mathrm{arcsec})$',\n",
" ylabel=r'$\\Delta \\mathrm{Dec}\\,(\\mathrm{arcsec})$')\n",
"osp.plot(d1='(ra-{})*{}'.format(ogc.ra().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" d2='(dec-{})*{}'.format(ogc.dec().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" overplot=True)\n",
"plot([0.],[0.],'k+',ms=30.)\n",
"xlim(0.075,-0.095)\n",
"ylim(-0.03,0.21);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's look at the actual expected signature (``fsp=1``):"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"sp= SchwarzschildPrecessionForce(amp=MSgrA,ro=R0,fsp=1.)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"times= numpy.linspace(0.,4.*16.0455,1001)*u.yr # 4 periods\n",
"o.integrate(times,kp)\n",
"osp= o()\n",
"osp.integrate(times,kp+sp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The precession is now much smaller, but still noticeable:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x792 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figsize(5,11)\n",
"o.plot(d1='(ra-{})*{}'.format(ogc.ra().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" d2='(dec-{})*{}'.format(ogc.dec().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" xlabel=r'$\\Delta \\mathrm{RA}\\,(\\mathrm{arcsec})$',\n",
" ylabel=r'$\\Delta \\mathrm{Dec}\\,(\\mathrm{arcsec})$')\n",
"osp.plot(d1='(ra-{})*{}'.format(ogc.ra().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" d2='(dec-{})*{}'.format(ogc.dec().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" overplot=True)\n",
"plot([0.],[0.],'k+',ms=30.)\n",
"xlim(0.075,-0.095)\n",
"ylim(-0.03,0.21);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The signatures in $v_\\mathrm{los}$, RA, and Dec are similar to that shown in Gravity Collaboration et al. (2020):"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figsize(8,5)\n",
"plot(o.time().to(u.yr),osp.vlos(times)-o.vlos(times))\n",
"xlabel(r'$t\\ (\\mathrm{year\\ since\\ 2010})$')\n",
"ylabel(r'$\\delta V_{\\mathrm{los}}\\,(\\mathrm{km\\,s}^{-1})$');"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Xn5F/h0Aqb+ggK9FKYnQkidERdPQO0jpiqqa+Lfx+/kxHKCQDjwGlrg6EW12P3UqBx0c8fs7VpfBJnM2JvC5BFP4RaTHzzQeW0dU/xP/ZdiTslr59/81KXj1ex5b3KlYV+vdToruIUOoGfM9TfwG3kSMD7sfp8VbON8vywkCqbOgcLp6NibLQ0z9E36CdvGTnMtBLbZKcTUawrybAtRLAPfz/wqjntng495kAhSa8mJuVwD/dvYh/eOkY3329nM9tnH6jnVDwxukGvvFHzfuX5fLY9cV+f715WQlEmE0cv9QWtlMy/rK3uoXE6AiUa+vokUaODLjlp8ZQ0yrJQKA4HA4qG7u4d6WzHicuKoKu/kH6B+3Mz0ngoq2HSzZJBiYjFEYGRAh6cG0+m1bm8e1d5bypG4wOx+/O1Hfw2V8dYkF2IlvvXRqQOfzoSAtzsxI4flGKCH1tb7VzPwKz+ep/x9EjA4Cz8ZAkAwFT195LZ9+gx5GBwjRnwackA5MjyYDwC5PJxJfvWYLKSuBzZYdndLvW2rYePvbTvcREWnju4VUebxb+sjg3kROX2nA4wms6xp8aOnqpauryOEUAXkYGUmK5ZOuVrYwDpMK1WqAk0zlyExtlobt/iL7BIZJjIkmNixreP0JMjCQDwm9ioiw8+9FVmE0mHvnZXpo7Z15BT1vPAI/8dB8dvYP87ONrmOUqJguURbmJNHX2D1dRi+nbV90KwNoizy1Nor1MEwzZHcNbGwv/upwMXB4Z6OobZGDIgTXCQk5S9PDOkmJiJBkQflWYFsePHl5NXVsvj/3nfnoHhowOyWc6egf4+M/2UtXUybMfXcWi3KSAx7DYtWueFBH6zp7qZmKjLMNbRY+WGhcFwOc2zh0+NnJ5ofC/ioZOkmIiSY93/lvERllodTU7i4owk5UYLQnyJEkyIPxuVWEK3ypdzqEaG5/67wP0DYZ+QtDZN8gjP9vH0QttfPfBlVxb4rXlt18tyEnEZELqBnxob3ULqwpTiLR4/vGYGhfFkf97G397y4hkIOVy4yHhf+WulQTu2py4qAh6XB80rBFmMhOs1LdLMjAZkgyIgLhjSQ5f+eAS3tCN/PV/H6R/MHTnVp1TA3s5XGPjuw+u4L2Lsw2LJc4aQXF6HMcvyciAL7R29XO6ruOq/QhGS4qNvKJINCcpGovZJEWEAVLZ0ElJxuU9Oa5oBBVpJjMxmuauPqnhmARJBkTAPLi2gH+9ZzG7Tjfw1784EJJTBrVtPTzww3c5csGZCATDkr7FeUkcvWCTIkIfeLeqGYBrS7xugeJRhMVMXnIMNS0yT+1vrV39NHf1X7FB18g6DmuEhcwEKw4HNHXKfhETJcmACKiH1hfyL66E4CM/3oOtO3T+s56ua+fe77/DRVsPz398Le8LgkQAnNMw9e19XJSCqWnbXdFEXJSFpbM8bYkytvzUGJkmCICKxiuLB8E5NeDmrhkAhvcqEOOTZEAE3EfXF/IfD67k2IU27v3BOyGxF/wrR2vZ9P13GLQ7+NXm9VxjUI2AJ6sLnUPa+8+2GhxJ6Hunoon1xWle6wXGkp8SywWZJvC70SsJwJkAuLlrBgCpG5gESQaEIe5cmsN/PbqWps5+7vrubnadqjc6JI/6B+185Q+n+Jv/Ocj87AR+95nrhiv4g4XKTiDBGsG+s552/BYTdaG1m7PN3VMuBs1PjaWps5/u/kEfRyZGqmjoJCbSMtx2GCDKcmUyICMDkyfJgDDMuuI0fv+Z6yhMi+XR5/fztVdPB9VKgzP1Hdzzvbd57k9VPLS+gF9t3jD8QyaYWMwmVhSmcOCcjAxMxzsV7nqBqScDgNQN+FlFQyfFGXFXdIe8cmTAQnp8FCaTjAxMhiQDwlD5qbG88MlreHBtAT98q5K7v7uboxdshsbUOzDEd3aVc9d3d1Pf3suPHl7Nv96z5IofOMFmTWEKur6DNtdaazF5uyuaSI+3Mi8rfvyTPchPcX5SlV4D/lUxYoMit9E1AxEWM2lxVhplZGDCgvenmwgb0ZEWvrppCT97ZA1tPQPc8723+cJLx2gKcMdCh8PBjpP1vPdbf+KbO85w64Is/vdz7+HWhVkBjWMqVs1OweGAg+dldGAqHA4H71Q2cW1J2pT3lShwjwxI3YDfdPUNctHWc8WyQnCOBlz+2nlbk14DkxP0uxaK8HHT/Ez++Hc38O87zvBffznHy4cv8Ynri/nYNYUkx0b57XUdDgdvnWnk33eWc6TGRnF6HP/16Fqun5vht9f0teX5yUSYTew728JN8zONDifk6PoOmjr7p9U8KjUuitgoi0wT+FFVo7PYePTIwMhRu+hI59dZiVbq22VkYKIkGRBBJSkmkn96/yIeWl/I1149zb/vPMOzf6rkgdX5lK7JZ0GO5xaxU9HeO8BvD13k+XfPUdHQSV5yDFvvXcKmlbOmVE1upNioCBblJcmKginaXd4ETL1eAJybc+WnxMryQj+qaOwAxk4G3KMEmQnRHL8knTknSpIBEZRKMuP58cdWc7qunefequIXe87x83fOsjAnkTsWZ3ODymBxbpLHLWbHUtPSzbtVzbx2vI4/lzfRP2RnSV4S37h/Ge9flhvUdQHjWTs7heffPUfvwJDHzXSEd2+daaQkM/6KCvWpyE+V5YX+VNHQSYTZNLxNsdvI1QTu/8NZiVaaOp1dCCNCLLk3giQDIqjNz07km6XL+eJdC3n58EVeOnyJf9txhn/bcYYEawQLchNZmJPIrJQYshKjSYyJxOKa823rGaC1u5+a1m4qG7o4Vds+3JgnNymaj24o5O5luSyblTTleeJgcs2cdH7052oOnGs1bK+EUNTVN8ieqhY+dk3htK+VnxrDu5VNOByOGfE9FWwqGjopTIu9Kmm3Rl65tBAgMzEahwOau/qDchVQsJFkQISE1LgoHrm2iEeuLaKps4/d5U3sP9fCiUvtlO2rGd6kxJNIi4mi9DiWFySz+T3FrC1KRWUlTHpUIditKUolwmzi7YomSQYm4Z3KZvqH7Nykpl9rkZ8SS1f/EC1d/aTFW30QnRipvKGTuZlXr/a4ss+Ae5rA3XioV5KBCZBkQISc9Hgr96zI454VeYCzALC9Z5C69l46+wYYsjuPJcZEkhIbRXp8VFgME8ZbI1iWn8w7lc1GhxJS3tANxEVZWD3O5kQTcXlFQY8kAz7WP2jnfHM3d3jYGCwqwtM0gavxkKwomBBJBkTIM5lMJMVGkhQbaXQohrtmThrfe6OC9t4BEqPl72M8DoeDN083cN3cdJ/Ui1xuPNTN8vzJ728gvDvX3MWg3cHczISrnhv5b2dxjfhlJrpGBqTXwITM/I9LQoSRa+akY3fA3ippTTwRZ+o7udTW65MpAoBZrsZDsqLA98o97EngFuOhYDY93orJJCMDEyXJgBAzyIqCZKwRZpkqmKA3dAMAN/ooGYizRpAeHyUrCvygvL4TkwnmZFydDMRbrx7kjrSYSYuLkv0JJkiSASFmkOhIC2tmp/JOZZPRoYSEN043sCAnkewk3xWYzUqJlcZDflDe0EF+SiwxUVePAnhbuZGZEC0jAxMkyYAQM8x1c9M5XddBXZt8IhpLa1c/+8+1cvN833aazE+VxkP+UOFlJcFYMhOtUjMwQSGTDCiltiqlNk7gvCeVUve5fl8ZiNiECCY3KufN7a0zDQZHEtx2nqpnyO7g9kVXV6dPR0FqDJdsPQzZHT69bjgbHLJT1dhFyRibSH3+tnk8sHrWFceyZGRgwoJ+NYErAVgJ3AfsGOfcbcBXtdYHXY93ALf6PUghgojKSiAnKZo3dSOlawqMDidovXaijtykaJbkJfn0uvkpsQzaHdS29TArJdan1w5X51u66R+ye1xJ4Pbpm+dedSzT1YVwyO4YXmUgPAv6kQGt9U6t9TNA1QRO3+hOBFyqJjKaIMRMYjKZuFFl8ufyJgaG7EaHE5S6+gb5U3kTty3K9nmnQPfyQpkq8B33SoLJTxNEY3dAc4B3QA1FQZ8MTJTrpj86YbAhIwMiDN2oMujsG5SNi7x4UzfSP2jnvR4a2ExXvms04IIUEfpMhSsZmDPZZGC4C6EkA+MJ+mmCSfDU4aMZWOPp5NbWVjZt2jT8uLS0lNLSUj+FJkRgXVuSTqTFxJtnGtgwJ83ocILO/56oIzUuijU+6Do4Wk5yNBaziXMtXT6/drgqr+8gLznG4xLCsQx3IezoBXw7HRQKysrKKCsrG3nIa5/ymZQMTOp/dUpKCtu3b/dXLEIYKt4awdqiVN443cDTdywwOpyg0jc4xBunG7hzSY5f5pEjLWYKUmOpbpJkwFfKGzo9NhsaT7iPDIz+kKuU8rrmeMZMEwCeWq7JRyIRtm5SmZyp7+Rcs9yURnq7oonOvkG/TBG4FafHUdUof+++MGR3TGlZIUCGKxmQxkPjC/jIgFJqM7BqnNO2aq0nUjA4kg3PUwWTvY4QM8Lti7L511dO8dqJOja/Z47R4QSN3x2pJTE6gmtK/PdZoTgjjt0VTdjtjhm3O2agXWztoW/QztwxlhV64+5CGK4jA5MR8GRAa/2cn667Uyk1eqqgGHjWH68nRLDLT41lUW4ir52ol2TApad/iNdO1PH+ZbnDW936Q3FGPH2Ddi7aeoZXF4ipKW/oAKBkjGWFY8lMjKahXUYGxhPS0wRKqZWjGgvtHPW4WGu9M9BxCREsbl+UzcHzrfLD0GXnqXq6+4d4//Jcv75OcXocAFVSNzBtut6ZDExlZACcdQMNHTIyMJ6gTwZcN/ytwEZgq1LqyRFPlwKPj3j8GFDq6kC41fVYiLB1+6JsHA7448l6o0MJCr89fInsxGjWFfm3nKjYtZlOVWOnX18nHJyuda4kmOqW3FmJVuolGR5X0K8mcDUROghs8fDcllGPbSPOe8H/0QkR3OZlxVOUHsdrJ+p4aH2h0eEYytbdz1tnGnjkmtl+70aXHh9FQnSEFBH6gK7rYH721KYIwLm8ULoQji/oRwaEEFNnMpm4fVE271Y209LVb3Q4hnr1eB0DQw4+sDzP769lMpkozoinqklGBqajb3CIysZO5udMPRnITLBKF8IJkGRAiBnu7mU5DNodvHKs1uhQDPXSoYsUp8exKDcxIK83R5YXTltlQxeDdgfzs6f+b5Y53HhIkoGxSDIgxAy3MCeRuZnxvHz4otGhGOZsUxd7q1u4d9Usn+9F4E1Rehy1bb109w8G5PVmotN17QAsmObIACB1A+OQZECIGc5kMnHPijz2nW3lQmt4bp7z6/01mE1w36pZ45/sI5eLCGV0YKp0XQdREWZmp8VN+RpZMjIwIZIMCBEG3r/MuZTut4cvGRxJ4A0O2XnhwAVuUpnDN4ZAKM5w3sCkLfHUnarrYG5mPBGWqd+q0uNlZGAiJBkQIgzkp8ayujCFl8MwGXhTN9LQ0ccDa/ID+rpF6XGYTFApywun7HRt+7TqBQCiIpxdCGVkYGySDAgRJj6wPBdd38Gp2najQwmoX+2rIT3eys3zMwP6utGRFvJTYilvkGRgKlq6+mno6JtWvYBbRoJVGm+NQ5IBIcLEnUtzibSY2Lb/gtGhBExDey9v6AbuXZVH5DSGmqdqXlY85a4OemJy3MWDaho9BtyyEqNlZGAckgwIESZS46K4bVE22w9doHdgyOhwAuIXe84zZHfwoTUFhrz+3KwEqpu6GBiyG/L6oex0rTOJmu40AThXFEjNwNgm3YFQKbUcSOXyDoE2oEprfdaHcQkh/ODDawt45Wgt/3u8jntW+L/5jpH6Bof4xZ7z3KQyKEqfejX6dMzLimdgyMHZpi7mZk3/E244OV3XTnp81PA2xNPh7ELYL10IxzChZEApdS9wK+AATEAlziQAYA7wgFIK1/M7tNbbfR+qEGK6NhSnUZgWy//sPT/jk4E/HKulqbOPj19bZFgM81wJgK7vkGRgkk7XdfhkigAgM9HKkN1Bc1cfmQmBW1ESSsZMBpRSK3BuEHRAa/3JiVxQKXWLUurzwE6t9WEfxCiE8BGz2cSDawv42qunqWjopCRzajvBBTuHw8HP3j7LnIw4rp+bblgcczLiMZvgTL0UEU7GwJCd03UdPHLNbJ9cz50ANLRLMuCN1wKqTcUAACAASURBVJoB12iAQ2v9da316xO9oNZ6l9b6G4BJKXWzL4IUQvjOfatmEWkx8cu9540OxW8O1dg4eqGNR66ZHbCOg55ER1ooTIuTIsJJqmjopH/Q7rPW0ZmJzqmGhg6pG/DG68iA1vrF6VxYa31oOn9eCOEf6fFWbluYzbb9Nfz9rfOIswb95qWT9pPd1SRER7BpZeA6DnozNzOeM5IMTMqxi20ALM5L8sn1hrsQtsuKAm8mtZpAKTXb9SvR9Xi5UuprSqlP+Cc8IYQ//NV1RbT3DrJtf43RofhcVWMnfzhWy0PrC4Mi0ZmXlcDZ5m76BsNjBYcvnLjYRlyUhaJptCEeKWO4C6EkA95MdmnhJ3HWEKS66gm2Ab8CDkhCIEToWFWYwsqCZH769lmG7A6jw/GpH7xZiTXCzKPXGVc4ONK87ASG7A7Zo2ASjl9qZ1FuEmYfVf5HRZhJjYuiXqYJvJpsMrBDa/1j1zLCp4DntNaHXVMC1T6PTgjhN5vfU8z5lm7+eKLO6FB85qKth5cOXeRDawqGe9IbbV6Ws0hTpgomZsju4OSldhbl+Xar6cwEq0wTjGGyyUDziK83As+OeDyzPl4IMcPdujCbwrRYnvtzldGh+Mxzb1ViMjkTnWBRlB6HxWySZGCCqho76RkYYnGub+oF3DITo6WAcAyTTQbmKKUSlVJP4Fxu2A4gqwaECD0Ws4m/uraIQ+dt7DvbYnQ401bf3suv9tWwacUscpNjjA5nmDXCwpyMuOGOemJsxy85iweXzPJtMpAlIwNjmlQy4Fph8Ljr4f0ASqmvub4OnlRcCDEhD6zOJz0+im/tPGN0KNP27V3l2B0O/uamEqNDucrCnEROhtkGUVN1/GI70ZFmin3cNTIz0UpjZ9+Mq5HxlUnvTeDqO/B1rXWb61AZsBPY79PIhBB+FxNl4ZM3zOHtimb2VDWP/weCVGVjJ2X7avjw2gIK0mKNDucqC3MTqW3rpaWr3+hQgt6xi20syEkkwscbS2UlRjNkd8i/gRfT/tt2FQ/uwFlDIIQIMR9ZV0hGgpV/D+HRgX/7o8YaYebTN881OhSPFuY4h7zDbfvoybK7igeX+Ki/wEiZCe7lhVI34MmkFuEqpZJwLicsBlJch004iwcf821oQohAiImy8Kkb5vDPvz/J2xVNXFtiXPveqThSY+MPx+r47C1zfbKpjT8syHH22D95qT3k/n4D6VxLN519gz4vHgRnASFAo2xl7NFkRwaeAh7XWpcAD2it07TWqcBqYOaUJAsRZj68roC85Bi+/MqpkJpTtdsd/L/fnSAtLorHrg+OvgKepMVbyU6MlrqBcRy94Nz/zledB0dydyGsbZORAU8mmwzs11q7+wkM/2uNOOY3SqmtSqkxpyKUUptdv5KVUsVKqa3+jkuImSA60sKWO+ZzsradFw9eMDqcCXvh4AUOnrfx1B3zSYiONDqcMS3MTeTkJUkGxnLovI2YSMtwbwZfykqwYjGbqG3r8fm1Z4Ip1QwopZYDh5RSXx1x2C81A0qpjUqpJ4H7JnB6Ms7eB6046xieHft0IYTb3UtzWFGQzDde03T1DRodzrjaugf42qunWV2Ywr1BsAfBeBbmJFLR2EnvgLQl9uZQjY2ls5J8XjwIEGExk50YzcVWSQY8mezf+E7XboY/wtmAqFopVaGUKgfSfB4doLXeqbV+holNQ9hw1jKkaK3naK1l6kKICTKZTHzxzoU0dPTx7V3lRoczrq//8TS27n7++QOLfda21p8W5iYyZHdQLtsZe9Q3OMSpS+0sL0j222vkJkdz0SbJgCeTKiB0LSd80fUL4Dml1A4gOVh2KdRa24yOQYhQtaowhQ+tyecnu6t5/7Jcv8zd+sKeqmZ+sec8j1wzm4U+2ubW3xbmOOM8Vdvu84Y6M8GJS+30D9lZke/PZCCGA+da/Xb9UOaLpYXVWutDrqkDw7lqBu5z1RisNDoeIULN03csICU2iqe3HwvKYsKuvkE+/8IRClJj+fxtyuhwJqwgNZa4KMtwhz1xpcPnnZ/jVhSkjHPm1OUlx1DX1huU39dGm/T+nkqp2XjuNrgFuH26AU3TzhFTAy8opSqVUqs8jRa0trayadOm4celpaWUlpYGKk4hglZSbCT/9+6FfPaXh3juT1V86sY5Rod0ha/84RQXWnv49eMbgmKL4okym00syk3i6AVJBjw5XGMjJyl6uOrfH3KTYxi0O2js6CM7yX+vEyzKysooKysbecjrutbJ9hn4GrASz/P3hrcj9lAjYAMeAJ4bfW5KSgrbt28PSFxChJq7l+bw6rFa/u2PmutK0oNmWPvVY7X8Ys95Hru+iDWzU40OZ9KWzkriP/9yjv5BO1ERvi+SC2WHalpZ4cd6AXCODABctHWHRTIw+kOuUqrJ27mTTav3aa2f8vSEq7BwXEqpzcCqcU7bOtniP6VUMc7Nk0aOMVUBwfWxRogQYDKZ+OqmJRyusfG3vzrE7z5zneGfws82dfHkC0dZlp/ME7fPNzSWqVqan0z/7mrO1HcEbT2GEZo6+6hp6eGj6wv9+jp5Ke5koJdV/n2pkDPZ/91ei/NcmxiNS2t91ad0H9oy6nEyUOnH1xNixkqOjeKbDyznwz/+C1tePMp3H1yByWRM1X5X3yCf+sVBzGYT3/vwipD9VL3MNcJy9EKbJAMjuOsFluf7r14AGN7N8pKsKLjKZP9HVXkrFBzVcyAglFIr3UWCrpGE5BHPJQPFfk4+hJjRNsxJ44nbFb8/Wsv33zQmrx6yO/jbXx1C17XzrQ8tZ1ZK8G1ENFEFqbEkx0YOd9oTTodrbFjMJr/sSTBSvDWCpJhI6TXgwWRHBoqBZ5VSRVw5SmDC2ZHwaV8F5ua62ZfibGqUqpQqc/UdwHU8mcvbKj/nalAEzumBW30djxDh5lM3zOF0bQff+KNmTkYc712cE7DXdjgc/PPvTrDzVAP//IFF3KQyA/ba/mAyOW94R6SI8AoHz7cyPzuBmCiL318rNzlGRgY8mGwysBJYNWL74mGu4kKf01ofBA5y9RQAWustox7bgGdGnyeEmDqTycQz9y2lprWbz/7yMD/+WATvmZfh99d1OBw885rm+XfP8Ynrinh4w2y/v2YgLJuVzA/eqqSnfyggN79gNzBk59B5G6Vr8gPyennJ0VyQkYGrTHaa4KCnRADAW2GhECL0RUda+Pkja5mTGc/m/9rPO5Vei5J9wuFw8PXXND94s5IPryvgH963wK+vF0hLZyUxZHdwslZGBwCOX2yjZ2CItUWBWR2SlxwjXQg9mGwy4FBKeWz3pZTa5Om4EGJmSIqN5L8eXUt+SiyP/HQfrxyt9cvr9A/aeeKFo3z/zUoeXFvAv4ZIu+GJWubqsHekRpIBgH1nWwACtlQ0NzmGjt5B2nsHAvJ6oWKy0wS3AVuUUjagZcRxE3ALIAv3hZjB0uOtbPvkBj7x/H4+/cuDVDfN41M3lmDx0c26ob2Xz/zyEHuqW/jbW+byuY1zDVvB4C9ZidFkJ0ZzuEaKCAH2VrdSlB5HRoI1IK/nXlFQa+slMTu4d7oMpMkmAxsBb6sGDG86JITwv+TYKP77E+t48oWjfOOPZ3i3qpl/u3/5tJu4/O/xOp7efpSegSH+vXQZH1wR/DsRTtXKwmQOnpce+Xa7g/3nWrhtYVbAXvNyr4FuVHZCwF432E02GXjM24ZESinZIVCIMBEdaeHbH1rOtSVpfOnlE9z8b2/yNzeV8Oh1RURHTq4o7kx9B19+5RRvnWlkcV4i3ypdQUmm7/ezDyarClP5w7E66tt7/dp+N9hVNHZi6x4IaDfJ4S6EUkR4hcnuWuh1Z8Jg2bVQCBEYJpOJ0jUFbChO5yt/OMXXX9P8ZHc1D67N596VsyjO8H5D7x0YYnd5E7/Yc443zzSSYI3gi3cu4OENs0O2odBkrCp0Ntc5cK6V9y0J3FLNYLOn2jnbvK4oLWCvmRFvxRphpkaSgSt4TQZc7YUPaK3PTuXCrl4EK7TWUkcgxAxWkBbLDz+6ij1VzfxkdzU/eLOS771RSWFaLEvykihMiyUxOpL+QTvNXf2cqe/g0HkbPQNDZCRY+czNc/n4NbNJiYsy+q0EzMKcRKwRZvafDe9kYF91C1mJVvJTYwL2mmazifzUWM43dwfsNUOB12RAa/2iUuoWpdRGnLsBnp3IBV27Gt4PVEoiIET4WFecxrriNC7Zethxsp4/lzdxuMbGH47V4t4xNi7KQklmPA+snsWNKpPr5qYTaZn5IwGjRUWYWZafzIFzLeOfPEM5HA72nW1hzezUgBeJ5qfEcL5FkoGRxpwm0FrvAlBKPeHaCMgGNOPcAMhdCpuMs3gw3fV1hdb6636LWAgR1HKTY/jYNbP52DWzAecP/e7+ISIt5rCYApioVYUp/OhPVWHbfOhCaw+1bb0B6y8wUkFqLPvPtuJwOGbcapWpmlDNgPvmrpRKAlbjvPm7dwO0AYfciYMQQoxkMpkM3/EwGK0uTOEHdgdHLthYXxy4OfNg8XaFs3HVNXMC/97zU2Pp6BukrWeA5NjwmZ4ay2QLCNuAXa5fQgghpmhlweUiwnBMBnZXNJGVaGXOGIWm/pKf6tzs6nxLtyQDLjJmJ4QQBkiJi2JORtxwB75wYrc7eLeymWvnpBsyTF/gSgZqWmRFgZskA0IIYZD1xWnsq25hcMhudCgBdbqug+aufq4tSTfk9UeODAgnnyUD3vYsEEII4dmGOWl09Q9x7GJ47VPgrhcwKhmIt0aQGhclycAIvhwZeNqH1xJCiBnP3WznL1XhNVWwu6KJORlx025hPR35qbFcaJVkwG3ayYBS6mal1K+BJ30QjxBChI2MBCtzM+N5t6rZ6FACpn/Qzt7qFq4zaFTArSA1VkYGRpjSeh+l1HLgcaAUZ9+BF5EVBkIIMWkb5qTxwoELDAzZw6IB06HzrfQMDBk2ReCWnxLDq8dqGbI7fLbrZiibcDLg6iz4SWAzzu2LK4FVWutq1/NF/ghQCCFmsvXFafznu+c4eqFteM+CmWx3RRNmE6w3oL/ASAWpsQzaHdS29TArJdbQWILBmGmoUmq2UurzSqkKYBvOUYBVWusSnC2Kq93njvxaCCHExLh7DPwlTKYK3tSNrChIITE60tA4CmRFwRXGGxn4JM4Ww7d6uNk7/BOSEEKEj9S4KOZnJ/BOZRN/c1OJ0eH4VUN7L8cutvHE7croUIaXF9a0dF/upxvGxhwZ0Fo/pbX+JJCslFruqhUQQgjhQ9fPTWdfdSvd/YNGh+JXb+pGAG5SmQZHAjlJ0URaTJyV3QuBie9NcMj9tVJqBZAKXJHCKqUStdbtvg1PCCFmvhvmZfKjP1fzl6pmbp6fZXQ4fvP66QZykqJZkJNgdChEWMzkp8ZS3dhldChBYdKrCUYkBruUUrcASYAJeApY48PYhBAiLKyenUJ0pJk/nWmasclA/6Cd3RVN3L0sN2h2CixOj+NssyQDMMWlhW4jtjguAmZ+GawQQvhBdKSF9cVp/OlMo9Gh+M2+sy109g1y83zjpwjcZqfFsbuiCbvdgTnMlxf6ZFGrq7hwiy+uJYQQ4eiGeRlUNXU5C9pmoNdPNxAVYebakuDZoXF2ehy9A3bq2nuNDsVwPtlk3FVHsMMX1/Jw7WScvQ3AOQ3xVa31wTHOfxKoAopxLn/0eq4QQgSL98zLAOCtM408tL7Q4Gh8743TDawvTiM2yie3HZ8oSo8D4GxTF7nJMQZHYyxfjQwcAh7wxbU82Kq1fkZr/QzO0YddSqliTycqpbbhTABecJ2/1U8xCSGETxWnxzErJWa44n4mqWjooKqpi1uCaIoALicD1VI3MLFkQCm1SSn1iXFO8/lKTddNv9L9WGtdhfNT/31e/sjGUSMBVUqpjb6OSwghfM1kMnHz/Ex2VzTS0z9kdDg+9eqxOgBuX5RtcCRXyk6Mxhph5myTJAPjJgNKqf3Aj4FnlFLlI44/oZR6TSnVrJQaYsRN24eS8fzp/qpJJ9dNv2rUYRtwqx/iEkIIn7t1YRa9A86q+5nk1eN1rCpMMXSXQk/MZhOz0+KolmRg7JoBpdTngS0jVg08qZT6quvpFuAF4DngoD/aEWutDyqlVo06vBLPxYrJHo4142W5Y2trK5s2bRp+XFpaSmlp6VRDFUKIaVtXlEaCNYIdJ+u4deHMWGJ4rrmLk7XtfPHOBUaH4lFRehzlDR1Gh+EXZWVllJWVjTzkdXeo8So50t2JAIDW+hml1B+B+wLVYGjksL9SajPOmoCdHk5Nncx1U1JS2L59+3TDE0IIn4mKMHPj/Ex2nWqYMbvpvXrcOUXw3sXBNUXgNjs9jtdPz5y/75FGf8hVSnkdchpvmsDTzhnbjOg06FpVcL/W2tuwf4uHY8GzhkUIISbg1oVZNHf1c+h8q9Gh+MSrx2pZNispaHcGLEqPpX/IziVbj9GhGGq8kQFPmxF5rA1QSt2stX59vBd0fbofPfQ/2lZXseAVx4D7x/gzNjxPFYy+jhBCBK0bVQaRFhM7TtazevakBjyDzoXWbo5caOOpO+YbHYpXs9OcKwqqmrqGNy8KR+MlA7cqpUav01+plMcdp7YA4yYDWuvnJhjbMFfvgK1aa5vr8crR/QO01juVUqP/5xQDz0729YQQwiiJ0ZGsL07j1eN1PHXH/KBp3TsV7lUEdwTpFAFAUYZreWFjJze4ej2Eo3GTAZxz8aO/Gz/k4dwVPoloFKXUfcBBoMU1VVAMrAYOKqVWwhV1BTtHJQrFXuoLhBAiaN29NJcnXzzKsYttLJ3lacAzNLx06CLLZiVR6Pr0HYwy4q0kWCOoDPMNi8ZLBp7RWj81kQsppb7mg3hGX7MY2ObhKXfdQCnOqYHHXY8fA552/bk1rsdCCBFSbl+UzRd+c4zfHbkUssmAruvgZG07/3T3QqNDGZPJZKIkK56Khk6jQzHUeMnAV8d5fthEk4bJcNUNeB0j01pvGfXYxuVlhy/4Oh4hhAiEpNhI3jM3g1eO1vL0HQtCchOdlw5dxGI2cdeyXKNDGVdJRjxvzuBNoiZivNUEq5RSiQGJRAghxLC7l+Vyqa2XgyG4qsBud/Dbwxe5YV4G6fFWo8MZV0lmPI0dfbT1DBgdimHGGxl4FueQ/PBSQqXUcmAjzmV7lcCvjVhqKIQQM9nGhVlYI8z87silkFtV8JfqZmrbenn6fcHZaGi0ksx4ACoaOllVmGJwNMYYb2SgTWt9FkAplaiU+jXOFQNrcQ7f34azkG/C0wlCCCHGF2+N4JYFmfzuaC39g3ajw5mUbfsvkGCN4NYFodFF8XIyMDM7EU7EeMlAGYBS6l7gAPArrXWq1voBrfVTrt9LgP2u1sVCCCF85P5V+bR09fP66XqjQ5kwW3c/rxyr5Z4VecREWYwOZ0JmpcRijTCHdRHheMnAC0qpJ4AUnMv5dnk6SWv9ItDm49iEECKsXT83naxEK7/ef8HoUCbsxYMX6R+08+DaAqNDmTCL2URxRnivKBizZsC1+dDXRx5TSt0CJGmtRzf2D831L0IIEaQiLGbuXTmLH75VSX17L1mJwbXr32gOh4Nf7j3P8vxkFuaGVu15SWY8h2tCr1jTV8bdwng018ZFJqVUhVJqn2sb4304pxGEEEL40P2r87E7YPvBi0aHMq7951qpaOjkwyE0KuBWkhHPhdYeevqHjA7FEJNOBsA5LeCqFdgMPANsnMi+BEIIISanKD2OtbNT+dW+89jtnraLCR7Pv3OWBGsEdy3LMTqUSSvJjMfhgMrG8JwqmFIy4Ka1PqS13qW1lnoBIYTwk4c2FHKuuZs3zzQYHYpXF209vHq8jgfXFRAbNd6q9eAzN8u5okCSASGEEEHpjsXZZCVa+fk754wOxavn3zkLwMeumW1oHFM1Oy0Oi9lEeb0kA0IIIYJQpMXMQ+sK+dOZxqCseO/sG+SXe87zviU55CXHGB3OlERFmClOj+N0XXj2GpBkQAghQsCD6wqIspiHP4EHk7J9NXT0DfLodUVGhzIt83MSOV0Xng11JRkQQogQkB5v5f3Lc9l2oIamzj6jwxnWOzDEs29Vsr44leX5ob3CfH52Ahdae+joDb89CiQZEEKIEPGpG+fQN2jnJ7urjQ5l2K/2nqeho4+/vWWe0aFM2/zsBADO1IffVIEkA0IIESLmZMRz55Ic/vOds9i6+40Oh96BIb7/ZiVri1LZMCfN6HCmTbmSgXCsG5BkQAghQsinby6hq3+In7591uhQ+KVrVOBzG+caHYpP5CXHkGCN4HStJANCCCGC2PzsRG5flMXPdlfTbGDtQFvPAN/ZVc6G4jQ2FIf+qACAyWRCZSegZWRACCFEsHvidkX3wBDf3lVuWAz/8Xo5tp4BvnDnAkwmk2Fx+Nr8nARO1bXjcAR3t0dfk2RACCFCTElmAg+uzecXe84b0jHvXHMXP3/nLPetnMXivKSAv74/qexEOnoHqW3rNTqUgJJkQAghQtDnNs4jJtLCV145FdDXdTgc/L/fnSTSYubzt6uAvnYgzB8uIgyvfgOSDAghRAhKj7fymZtL2HW6gVeP1QbsdV8+conXTzfwf25TQb+l8lS4VxScCrMiQkkGhBAiRD16XRGL8xL5x9+eCMhSw6bOPv7p5RMsz0/mkRDdg2A8idGR5KfGcLJWRgaEEEKEgAiLma33LqW1u59/+b1/pwscDgdfeOkYnX2DPHPfUizmmVM0ONri3CSOXwyvzXglGRBCiBC2KDeJv75xDi8evMBvD1/02+s8/85ZXjtRzxO3K+ZlJfjtdYLB4rwkzjV309YTPm2JJRkQQogQ99lb5rK6MIWntx/zy66GB8618pU/nGbjgkweu77Y59cPNu4VEicvhc9UQYTRAYxHKZUMbHY9XAN8VWt90Mu57vN+DaQCj2utt/g/SiGEME6kxcx3P7yCO7+zm0ef38f2T11DWrzVJ9c+19zFY/+5n9zkaL5x/7IZ1VPAm0W5iQCcuNQ2I9osT0QojAxs1Vo/o7V+BtgC7FJKeUtNk4FngVZgh+trIYSY8XKSYvjRw6upa+vl0ef309k3OO1r1rb18LGf7sXucPCzj68lOTbKB5EGv/R4KzlJ0WFVNxDUyYDrpl/pfqy1rgKqgPu8/BEbkAKkaK3nuM4XQoiwsKowhe88uIJjF9t46Md7aOue+pz3hdZuSp/9C02d/fzkY2soSo/zYaTBb1FuEsckGQgaycBWD8e9jttorW1aa5v/QhJCiOB1+6Jsvv+RlZy81M69P3yHiobJr5ffU9XMB/7jbVq7+/nvT6xjVWGKHyINbovzEqlq6qLLByMsoSCoawa01geVUqtGHV6Jc7rAI1fdQAvO+oIyb/UFra2tbNq0afhxaWkppaWl0w9aCCEMdvuibH7+V2v4zP8c4v3/8TZP3TGfD68tIMIy9ue/nv4hvrXzDD/eXc3stFiee3g1czLiAxR1cFmSl4TDAadq21k9O9XocKakrKyMsrKykYfSvZ1rCqXNGFw3+vu11rd6eb545NSAUqoSWOVppGDTpk2O7du3+y9YIYQwWG1bD5/fdoS3K5qZlxXPx66ZzV1LckmKjbzivJqWbl4+comfvX2Wps4+Hlybz9PvW0BidKSXK8989e29rPvKLr5090I+fm2R0eH4hFLqgNZ6tafngnpkYCTXqgKviQAM1xSMZAMeAJ7zZ2xCCBGMcpJi+O9H1/Hq8Tq+s6ucL7x0nC/+5jhzMuLJTLBidzi4aOuhpqUHgPfMy+CzN5eE7CdhX8pMsJKRYOXYhfCoGwh4MuD6dD966H+0rR5u7FuB+8e4bjFwQGs9cnKrCpgzpUCFEGIGMJlMvG9JDncszuZQjY3d5U0cvWCj1VVcuGxWMh/bMJub52dSHKZTAp6YTCaW5ydzqCY8StACngxorSf9KV0p9STOBMHmerzSSy3A6FqCZEasRhBCiHBlMplYWZDCyoLwKwacqhUFyew4WY+tu3/GL6sM9tUEKKXuAw4CLUqpZKXUSmC167mVrsfuKYLkEX8uGSieSvIhhBBCLM933lIOh8HoQFDXDLiG/rd5eMpdN1CKMwF43PX4OdcoAjinB7zWFwghhBBjWTorGbMJDp23caPKNDocvwrqZMD1ad9r78vRrYZd0wjP+DsuIYQQM1+8NYJ5WQlhMTIQ9NMEQgghhFGW5ydzuMZGKC3DnwpJBoQQQggvVhQk09YzQHVTl9Gh+JUkA0IIIYQXy/Odqy9m+lSBJANCCCGEFyWZ8cRbIzh4vtXoUPxKkgEhhBDCC4vZxMrCFPZVSzIghBBChK11Rano+g5au/qNDsVvJBkQQgghxrDGtVfD/nMzd3RAkgEhhBBiDEtnJREVYWZvdbPRofiNJANCCCHEGKIjLSyflczeszIyIIQQQoSttUWpHL/YRlffoNGh+IUkA0IIIcQ41hSlMmR3cOj8zOw3IMmAEEIIMY5VhSmYTbBnhtYNSDIghBBCjCPeGsGSWcm8WynJgBBCCBG2ritJ41CNjY7eAaND8TlJBoQQQogJuLYknSG7gz1VLUaH4nOSDAghhBATsKowhehIM7srmowOxeckGRBCCCEmwBphYW1RmiQDQgghRDi7riSNioZO6tp6jQ7FpyQZEEIIISbo2pJ0AN6eYaMDkgwIIYQQE7QgO5G0uCj+VN5odCg+JcmAEEIIMUFms4kbVAZvnWlkcMhudDg+I8mAEEIIMQm3zM/C1j3AwRnUmliSASGEEGIS3jMvnQiziV2n640OxWckGRBCCCEmISE6knXFqew61WB0KD4TYXQA41FKJQObARtwK/Cs1nrnGOc/CVQBxcBOrfXBgAQqhBAibNwyP4t//v1JzjV3UZgWZ3Q40xYKIwNPa62f0Vo/B2wBdrgShKsopbbhTABe0Fo/A2wNZKBCCCHCwy0LImzghQAADy9JREFUMgFmzOhAKCQDm5VSGwG01lWuY8Vezt04aiSgyv1nhRBCCF8pTItjbmY8fzxZZ3QoPhEKycAq97SAUsqdBFSNPsl10x993D21IIQQQvjUHUty2FvdQkNH6HcjDPqagRGjAQCPA1u01p7Wc3iaOmgG1ni6bmtrK5s2bRp+XFpaSmlp6XRCFUIIEUbuWprDd3aV87/H63h4w2yjw7lKWVkZZWVlIw+lezs36JMBGB4RuA/n9MBXvZyWOplrpqSksH379umGJoQQIkzNy0pgbmY8vz9aG5TJwOgPuUoprz2UQ2GaAK11lasgcAtwwEsBoacNptP8G5kQQohwdufSHPadbaG+PbSnCgI+MqCU2gysGue0re7pAaVUsntaQGtdpZSyAU/jTAxGsuF5quCq+gIhhBDCF+5cksO3dpbz6rFaHrm2yOhwpizgyYBrieCEuIoCdwCmUU9dddPXWu9USo2eKigGnp10kEIIIcQEzM1KYH52Ar85fCmkk4Fgnyao4uoRgGJgG4BSaqVSauWI53aOelw8VoMiIYQQYrruWzWLwzU2yus7jA5lyoI6GXBNFRxUSj2plNqslHoWeGzEDb4U5woDt8eAUqXUfUqpra7HQgghhN/csyKPCLOJbQcuGB3KlAX9agLXjd/jp3ut9ZZRj21cHkl4wc+hCSGEEKTHW7l5fibbD17kidsVkZag/pztUehFLIQQQgSZB1bn09TZx5u60ehQpkSSASGEEGKablQZZCRY+dXe80aHMiWSDAghhBDTFGEx8+CafF7XDVQ3dRkdzqRJMiCEEEL4wEMbCokwm/j529VGhzJpkgwIIYQQPpCZEM3dy3LZduACbT0DRoczKZIMCCGEED7yV9cW0d0/FHK1A5IMCCGEED6yOC+J9cWp/GR3Nb0DQ0aHM2GSDAghhBA+9Le3zKOho4//2RM6owOSDAghhBA+tGFOGhuK0/jBW5X09IfG6IAkA0IIIYSP/f1t82js6OOnIbKyQJIBIYQQwsfWzE7ltoVZfO+NCuraeo0OZ1ySDAghhBB+8MU7FzJod/C1V08ZHcq4JBkQQggh/KAgLZbN1xfzm8OXeEM3GB3OmCQZEEIIIfzk0zeXMC8rni0vHMXW3W90OF5JMiCEEEL4SXSkhW8+sJyWrn62vHgUu91hdEgeSTIghBBC+NHivCSeumM+r52o59u7yo0Ox6MIowMQQgghZrpHryvidF0H395VTmailY+sKzQ6pCtIMiCEEEL4mclk4ssfXExLVz9feOk4Pf1DPHpdESaTyejQAJkmEEIIIQLCGmHhhw+t4r2LsvnXV07xubLDtHQFR1GhjAwIIYQQARIVYeb7H1nJf7xRwbd3lfPG6QY+vK6QOxZnMzcrHhMmKhs7eetMI3Mz47ltUXZA4pJkQAghhAggs9nEZ2+Zy3sXZ/ON1zTP/amSH75VedV5n71lriQDQgghxEw2LyuB5x5eTWNHH3uqm6lp6cHucDArJYYNc9LITIgOWCySDAghhBAGykiwctfSXENjkAJCIYQQIsxJMiCEEEKEuaCfJlBKJQObARtwK/Cs1nqnl3M3u778NZAKPK613hKQQIUQQogQFfTJAPC0+4aulNoJVCqlUrTWNg/nJgNbgWeBKpzJgxBCCCHGEArTBJuVUhsBtNZVrmPFXs61ASlAitZ6zojzhRBCCOFFKIwMrHLf1JVS7iTA603ey4jBVVpbW9m0adPw49LSUkpLS6cTpxBCCBE0ysrKKCsrG3ko3du5QT8yMOrT/ePAlrFu+EqpzUqp+5RSW5VSK72dl5KSwvbt24d/TTcRGPUXHlbC+b1DeL9/ee/hKZzfO4TO+y8tLb3iPgc0eTs36JMBcI4IKKWexDk98NwYp+7UWj+ntX7BVWewzVWA6Heh8s3hD+H83iG837+89/AUzu8dZub7D4lkQGtdpbV+BtgCHPB2g/dQI2ADHvB3fEIIIUQoC3jNgGv536pxTts6ok4g2T0toLWuUkrZgKdxJgYjr1sMHNBap4w4XAXM8VnwQgghxAwU8GRAaz3WMP8VXKsIdgCjN3z2NvQ/uqdAMnD17g/AiRMnmpRS5yYaywSkK6W8zsfMcOH83iG837+89/AUzu8dQvf9F3p7IthXE1Rx9Q2+2H3MXSCotT7oGjUYThJcXxd7Sz601hn+CVkIIYQILUGdDLhu8AddxYM2nNMLj43oQFiK89P/467Hz7nOBef0gDQdEkIIIcZhcjgcRscgQohSaiuwY3RLaFcSVoVz5Gan1vqgEfEJ4U+uqctkrfULI47J974IeUE9MhAqwuGHgeuH4ErgPpx1HCOf2wZ81f2+lVI7mGGjMiP2yABYw4j363p+Rn8PjLdHyEx//yO4250DM/97f7z9Xmb6v7urMP0+nN/3V9S8zbT3LsnANM30HwZurh/8O5VSnt7bRq31/SMeVymlNnrbUCpEbdVaPw6XV64opVa5prLC4XvA6x4hYfL+3Qnx6OXLM/173+t+LzP93931/3yr+99XKXVAKbVfa31wJr73kOgzEOQ2jsoIq9x7KYQDLz8g3Z8eZwTXD4XhVSmuZa9VOD8xQHh8D4y1R0g4vH9w3hhb3A/C4Xufsfd7men/7s8yYhQIuGXE+51x712SgWkIkx8G4/n/7Z3fdRo7EMa/2wGHdEAe5p3YFQQ6wHEFiTuA4wp8oAOcCnxNB+ZWEId3PUAH4dJB7oNGIMvaZQnX3l3p+53jY9i/Gq+8M9KMZmLLPH+huJhUG3Gjo5APGfWBT26069cIyUV+ERn5cQJKDn0fxphdmAI+9eeubrEXMzzub5Cq7HQTnEfRy+DyvRtSI926G/DW6LRgmCirD7vENYs+UFQjpCAbaFLyq4yxeijJ931gHzewhX2mDzoiTv259wDsXMCofl+pcZCk7DQGziOLl8ERtpFtH969FW9MECz4DTZgaOkFWCWPF0zVA3Cnm3P4H/hSkK8kh76/9AzBhYis1TBO/bm72Z2tNyP2U0SukKjsNAbOI4eXwTF2iFvKhWWm24yOEq+MMW5KMJs+oEph5gdQInH5Vdbngt3J9/2Sei9JP3fosw3jAmBnxX5Ejm+97IwZOI/kXwbHUKs5tJR7CJYfJsQUgB89nkUf8N0BqiBcjZDU5e8DGIjIWJeSXQAYisi31Pu+Vov9N9js6r2k/txdHw+39ZCo7DQGziD1l8EJLF1qaKWX0NKqPaoMpl4gUT+HPqB+01ApAHbklLT8Wg595n5gX/hPntsg9b4frfeSwXPf4LXC7wDYpCo7jYHzSf1lAMAqPs0+OAAw9dI+A8BXANciMtJjvtbSyDdEREYAVgC2ItLRZ36hu1PvA0U1Qh71c+ryA9gbgwMAN9ofgIT7fqgQI/VeUn/us2C54AUOSw2Tk53piM9E/0FuYf1IfrQtSYQwz4DHUIMIk+8DXgZKVyPkyS21y0H+XAkyb35EUF4eiT93NfDWsLLv5UtRdhoDhBBCSObQTUAIIYRkDo0BQgghJHNoDBBCCCGZQ2OAEEIIyRwaA4QQQkjm0BggpGV4a9xJg+FzIm2CtQkIqRldw/8cloktObY165lFZA7gZ0Ghn/e4fwc2l34Hdj34U9gWTSa0TyUbKVXsilMhJkfJ+RvNUtma50XyhTMDhNTPKWlMe5HiMU1mDqDOzGxfjDH3mk74CjZ74L7SpCrypaYdXgC41CRTbv9AE88MEclHX3a+GgGD8BxCmgiNAUJqRFOa7irOCoxRr2I9GWPMqi7jRZVyeO872Mpzjutg5P7k7zfGLI0xE8Qr1R09H8CK7gLSBmgMEFIvF6iu4D+2bFagbjo41E9wuMpzzlgIR/tbVBzNVzlf89UPQUjDYcwAITWgvv8hgBGsb3kKYF6k7NX3vQu2jWFLKi+NMUPd1gfwD4B7Y8zEyy2/gq0tsAzyqzvFdQngzqvIOICd4p/DKtBLAD9i/nQ9fqTHdVWuOayi/K73nGjbvsMaP841MoT14y+D64296z0HbY7KE2KMWYnI52CzP1vgytH67PS6VTj3fEIaA2cGCKkBb/q5C+DGGDM5Muq/APAruMYMwAze6FcV40SvDd13r/ebwSpjx8Dzdc+D6yxhDY2h7n9AQb12z2++0vPWXlvuoKNn73sfVsEv9fs0uN4jDn74e+hIvoI8r4gYCjd6T2i7tsH+8HsZlc8PKtwR0jhoDBBSE26aueLUf8z/DVglvvdR68j5WT8PACCIR3j2fNi3TklpG3ylC1jFttP9qyNR8d+8z0sclGIsFmIfI6G//YC9HoAwAn8qIr0K8pTiZi+KZjfekDWs0UdIY6GbgJD6GKB6vEAHEWPAGLMREYiIW2Uw8JRdH8AuqMm+xkFBfwbQVSW5Q1xhVTFU7gE8isgtrDx3RwycstF3H6+XTg5VzhHK5SlEjaShMcYP7ovJfIrSrnr+DpGVCIQ0CRoDhNTHJ5y2rLAINzswiezbBP54//MX2KDECQCIyB/dXEfqQ8+f/ygiV3+4vr6LQHEGhkWZPGXcBoYAYA2dUElHja4Czj2fkMZANwEh9bGfGQhGuzHKRpd/AxjpFLuvgF2Q3QtEpKPH+rEF/v6T/Nsa/AhjzE79+FcArk+5hscSr90VjkJ5jrRvjEOcgO8+iSntLioaGCec/yr4k5CmQWOAkPro4mVkexkxnz6A/ch8AxuI6GfCc4aG75N3yvSFAnXHqGI91paQTsSYWZ94DQB7Bbvyr6fxAr0j8kRR18LCWyXRwUuDYhHEHFwhCGhUPhTcosr5H8HZAtJw/vr9+3fdbSAkS3TECtiAuqPpekVkGhvJ674RgG5ButwprHLewk6zr7ztv3AYyfb0x33/Dms0TMvapxn9fGXXM8bcq6Ke6jVv9P7u+8QYs9A2jAHMfNmCNu9810CRPJF29QH8jOxaaDZCd9wYdtahB2DrBxjqNa5hl4ACwALAg3/PsvN1/zzioiCkUdAYIKQllCmVU+obkPeFxgBpA3QTENIe1v4UeUCHhkDzUCPt/wgSJeRNoTFASEvQ4Ly9f1pE5upPZwR7c+nXkNeAkJOhMUBIu9h4swNPsH7qAcvkNg+NN2hVYSmSL4wZIKRliMiIo83mIyKDsOYCIU2FxgAhhBCSOXQTEEIIIZlDY4AQQgjJHBoDhBBCSObQGCCEEEIyh8YAIYQQkjn/AerBVUZlHAaUAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figsize(8,5)\n",
"plot(o.time().to(u.yr),(osp.ra(times)-o.ra(times))\n",
" *(u.deg/u.mas).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles()))\n",
"xlabel(r'$t\\ (\\mathrm{year\\ since\\ 2010})$')\n",
"ylabel(r'$\\delta \\mathrm{RA}\\,(\\mathrm{mas})$');"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figsize(8,5)\n",
"plot(o.time().to(u.yr),(osp.dec(times)-o.dec(times))\n",
" *(u.deg/u.mas).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles()))\n",
"xlabel(r'$t\\ (\\mathrm{year\\ since\\ 2010})$')\n",
"ylabel(r'$\\delta \\mathrm{Dec}\\,(\\mathrm{mas})$');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, let's check that when setting $\\beta = 2(1+\\gamma) = 4$ for $\\gamma=1$ we get zero precession:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"spzero= SchwarzschildPrecessionForce(amp=MSgrA,ro=R0,fsp=1.,beta=4.,gamma=1.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We integrate for 20 orbits to clearly show the difference:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"times= numpy.linspace(0.,20.*16.0455,10001)*u.yr # 4 periods\n",
"o.integrate(times,kp)\n",
"osp= o()\n",
"osp.integrate(times,kp+sp)\n",
"ospz= o()\n",
"ospz.integrate(times,kp+spzero)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the next figure, blue is the Keplerian orbit, orange the GR orbit, and green the PPN orbit with $\\beta = 2(1+\\gamma)$:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x792 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figsize(5,11)\n",
"o.plot(d1='(ra-{})*{}'.format(ogc.ra().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" d2='(dec-{})*{}'.format(ogc.dec().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" xlabel=r'$\\Delta \\mathrm{RA}\\,(\\mathrm{arcsec})$',\n",
" ylabel=r'$\\Delta \\mathrm{Dec}\\,(\\mathrm{arcsec})$')\n",
"osp.plot(d1='(ra-{})*{}'.format(ogc.ra().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" d2='(dec-{})*{}'.format(ogc.dec().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" overplot=True,zorder=0)\n",
"ospz.plot(d1='(ra-{})*{}'.format(ogc.ra().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" d2='(dec-{})*{}'.format(ogc.dec().to_value(u.deg),\n",
" (u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())),\n",
" overplot=True,zorder=2)\n",
"plot([0.],[0.],'k+',ms=30.)\n",
"xlim(0.075,-0.095)\n",
"ylim(-0.03,0.21);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Indeed, the green curve does not have any Schwarzschild precession."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Animation of the Schwarzschild precession of S2\n",
"\n",
"Next, we make a quick animation of the precession of the orbit of S2. For this, we integrate for a *long time* and then plot successive frames of a single orbit:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"nperiods= 600.\n",
"times= numpy.linspace(0.,nperiods*16.0455,1000001)*u.yr # 4 periods\n",
"o.integrate(times[times < 16.0455*u.yr],kp)\n",
"osp= o()\n",
"osp.integrate(times,kp+sp)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
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"\">\n",
" Your browser does not support the video tag.\n",
"</video>"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def delta_ra(ra):\n",
" return (ra.to_value(u.deg)-ogc.ra().to_value(u.deg))\\\n",
" *(u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())\n",
"def delta_dec(dec):\n",
" return (dec.to_value(u.deg)-ogc.dec().to_value(u.deg))\\\n",
" *(u.deg/u.arcsec).to(u.dimensionless_unscaled,equivalencies=u.dimensionless_angles())\n",
"figsize(6,7)\n",
"fig, ax= subplots()\n",
"line1= plot(delta_ra(o.ra(o.time())),delta_dec(o.dec(o.time())),\n",
" label=r'$\\mathrm{without\\ Schwarzschild\\ precession}$')\n",
"line2= plot([0.],[0.],'k+',ms=30.)\n",
"xlabel(r'$\\Delta \\mathrm{RA}\\,(\\mathrm{arcsec})$')\n",
"ylabel(r'$\\Delta \\mathrm{Dec}\\,(\\mathrm{arcsec})$')\n",
"xlim(0.075,-0.25)\n",
"ylim(-0.19,0.26)\n",
"nstride= round(len(times)/nperiods)+1\n",
"line,= ax.plot(delta_ra(osp.ra(times[:nstride])),delta_dec(osp.dec(times[:nstride])),'-',\n",
" label=r'$\\mathrm{with\\ Schwarzschild\\ precession}$')\n",
"txt= ax.annotate(r'$\\mathrm{year}=%.0f$' % (round(2010.35653101,-1)),\n",
" (0.05,0.05),xycoords='axes fraction',\n",
" horizontalalignment='left',verticalalignment='bottom',size=18.)\n",
"legend(frameon=False,fontsize=18.,loc='upper right')\n",
"def animate(ii):\n",
" minii= int(round((ii+0.5)*nstride))\n",
" maxii= int(round((ii+1.5)*nstride))\n",
" line.set_xdata(delta_ra(osp.ra(times[minii:maxii])))\n",
" line.set_ydata(delta_dec(osp.dec(times[minii:maxii])))\n",
" txt.set_text(r'$\\mathrm{year}=%.0f$' % (round(2010.35653101+times[ii*nstride].to_value(u.yr),-1)))\n",
" return (line,)\n",
"anim = animation.FuncAnimation(fig,animate,#init_func=init_anim_frame,\n",
" frames=len(times)//nstride,interval=40,blit=True,repeat=True)\n",
"tight_layout()\n",
"if _SAVE_GIFS:\n",
" anim.save('gravity-sp.gif',writer='imagemagick',dpi=80)\n",
"# The following is necessary to just get the movie, and not an additional initial frame\n",
"plt.close()\n",
"out= HTML(anim.to_html5_video())\n",
"plt.close()\n",
"out"
]
},
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