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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": [ | |
"%pylab is deprecated, use %matplotlib inline and import the required libraries.\n", | |
"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 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 plot as galpy_plot\n", | |
"galpy_plot.start_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", | |
"Note that this notebook has been tested with ``galpy`` version 1.9.2 and that it requires ``astropy-units = True`` in the [galpy configuration file](https://docs.galpy.org/en/v1.9.2/installation.html#configuration-file).\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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", | |
"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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", | |
"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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", | |
"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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", | |
"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 _phitorque(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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", | |
"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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", | |
"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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", | |
"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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", | |
"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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", | |
"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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", | |
"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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", | |
"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": { | |
"text/html": [ | |
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"</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= int(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" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.10.6" | |
}, | |
"toc": { | |
"base_numbering": 1, | |
"nav_menu": {}, | |
"number_sections": false, | |
"sideBar": true, | |
"skip_h1_title": false, | |
"title_cell": "Table of Contents", | |
"title_sidebar": "Contents", | |
"toc_cell": false, | |
"toc_position": {}, | |
"toc_section_display": true, | |
"toc_window_display": false | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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