.. _mockstream-heliocentric: =========================================================================== Generating a mock stellar stream and converting to Heliocentric coordinates =========================================================================== We first need to import some relevant packages:: >>> import astropy.coordinates as coord >>> import astropy.units as u >>> import numpy as np >>> import gala.coordinates as gc >>> import gala.dynamics as gd >>> import gala.potential as gp >>> from gala.units import galactic We will also set the default Astropy Galactocentric frame parameters to the values adopted in Astropy v4.0: >>> _ = coord.galactocentric_frame_defaults.set('v4.0') In the examples below, we will use the galactic ~gala.units.UnitSystem: as I define it, this is: :math:{\rm kpc}, :math:{\rm Myr}, :math:{\rm M}_\odot. We first create a potential object to work with. For this example, we'll use a two-component potential: a Miyamoto-Nagai disk with a spherical NFW potential to represent a dark matter halo. >>> pot = gp.CCompositePotential() >>> pot['disk'] = gp.MiyamotoNagaiPotential(m=6E10*u.Msun, ... a=3.5*u.kpc, b=280*u.pc, ... units=galactic) >>> pot['halo'] = gp.NFWPotential(m=7E11, r_s=15*u.kpc, units=galactic) We'll use the Palomar 5 globular cluster and stream as a motivation for this example. For the position and velocity of the cluster, we'll use :math:(\alpha, \delta) = (229, −0.124)~{\rm deg} [odenkirchen02]_, :math:d = 22.9~{\rm kpc} [bovy16]_, :math:v_r = -58.7~{\rm km}~{\rm s}^{-1} [bovy16]_, and :math:(\mu_{\alpha,*}, \mu_\delta) = (-2.296,-2.257)~{\rm mas}~{\rm yr}^{-1} [fritz15]_:: >>> c = coord.ICRS(ra=229 * u.deg, dec=-0.124 * u.deg, ... distance=22.9 * u.kpc, ... pm_ra_cosdec=-2.296 * u.mas/u.yr, ... pm_dec=-2.257 * u.mas/u.yr, ... radial_velocity=-58.7 * u.km/u.s) We'll first convert this position and velocity to Galactocentric coordinates:: >>> c_gc = c.transform_to(coord.Galactocentric).cartesian >>> c_gc >>> pal5_w0 = gd.PhaseSpacePosition(c_gc) We can now use the position and velocity of the cluster to generate a :ref:mock stellar stream  with a progenitor that ends up at the present-day position of the cluster. We will generate a stream using the prescription defined in [fardal15]_, but including the self-gravity of the cluster mass itself. We will represent the cluster with a Plummer potential, with mass :math:2.5 \times 10^4~{\rm M}_\odot:: >>> pal5_mass = 2.5e4 * u.Msun >>> pal5_pot = gp.PlummerPotential(m=pal5_mass, b=4*u.pc, units=galactic) We now have to specify that we want to use the Fardal method for generating stream particle initial conditions by creating a ~gala.dynamics.mockstream.FardalStreamDF instance:: >>> from gala.dynamics import mockstream as ms >>> df = ms.FardalStreamDF() Finally, we can generate the stream using the ~gala.dynamics.mockstream.MockStreamGenerator:: >>> gen_pal5 = ms.MockStreamGenerator(df, pot, ... progenitor_potential=pal5_pot) >>> pal5_stream, _ = gen_pal5.run(pal5_w0, pal5_mass, ... dt=-1 * u.Myr, n_steps=4000) Here the negative timestep tells the stream generator to first integrate the orbit of the progenitor (the Pal 5 cluster itself) backwards in time, then generate the stream forwards from the past until present day:: >>> pal5_stream.plot(alpha=0.1) # doctest: +SKIP .. plot:: :align: center :context: close-figs import astropy.coordinates as coord import astropy.units as u import numpy as np import gala.coordinates as gc import gala.dynamics as gd import gala.potential as gp from gala.units import galactic from gala.dynamics import mockstream as ms coord.galactocentric_frame_defaults.set('v4.0') pot = gp.CCompositePotential() pot['disk'] = gp.MiyamotoNagaiPotential(m=6E10*u.Msun, a=3.5*u.kpc, b=280*u.pc, units=galactic) pot['halo'] = gp.NFWPotential(m=1E12, r_s=20*u.kpc, units=galactic) c = coord.ICRS(ra=229 * u.deg, dec=-0.124 * u.deg, distance=22.9 * u.kpc, pm_ra_cosdec=-2.296 * u.mas/u.yr, pm_dec=-2.257 * u.mas/u.yr, radial_velocity=-58.7 * u.km/u.s) c_gc = c.transform_to(coord.Galactocentric).cartesian pal5_w0 = gd.PhaseSpacePosition(c_gc) pal5_mass = 2.5e4 * u.Msun pal5_pot = gp.PlummerPotential(m=pal5_mass, b=4*u.pc, units=galactic) df = ms.FardalStreamDF() gen_pal5 = ms.MockStreamGenerator(df, pot, progenitor_potential=pal5_pot) pal5_stream, _ = gen_pal5.run(pal5_w0, pal5_mass, dt=-1 * u.Myr, n_steps=4000) pal5_stream.plot(alpha=0.1) We now have the model stream particle positions and velocities in a Galactocentric coordinate frame. To convert these to observable, Heliocentric coordinates, we have to specify a desired coordinate frame. We'll convert to the ICRS coordinate system and plot some of the Heliocentric kinematic quantities:: >>> stream_c = pal5_stream.to_coord_frame(coord.ICRS) .. plot:: :align: center :context: close-figs stream_c = pal5_stream.to_coord_frame(coord.ICRS) style = dict(marker='.', s=1, alpha=0.5) fig, axes = plt.subplots(1, 2, figsize=(10,5), sharex=True) axes[0].scatter(stream_c.ra.degree, stream_c.dec.degree, **style) axes[0].set_xlim(250, 220) axes[0].set_ylim(-15, 15) axes[1].scatter(stream_c.ra.degree, stream_c.radial_velocity.to(u.km/u.s), **style) axes[1].set_xlim(250, 220) axes[1].set_ylim(-100, 0) axes[0].set_xlabel(r'$\alpha\,[{\rm deg}]$') axes[1].set_xlabel(r'$\alpha\,[{\rm deg}]$') axes[0].set_ylabel(r'$\delta\,[{\rm deg}]$') axes[1].set_ylabel(r'$v_r\,[{\rm km}\,{\rm s}^{-1}]$') fig.tight_layout() References ========== .. [odenkirchen02] Odenkirchen et al. (2002) _ .. [fritz15] Fritz & Kallivayalil (2015) _ .. [bovy16] Bovy et al. (2016) _