Added READMEs to 'cooling halo' and 'cooling halo with spin'.

examples/CoolingHalo/README

+;
+;To make the initial conditions we distribute gas particles randomly in a cube
+;with a side length twice that of the virial radius. The density profile
+;of the gas is proportional to r^(-2) where r is the distance from the centre
+;of the cube. 
+;
+;The parameter v_rot (in makeIC.py and cooling.yml) sets the circular velocity
+;of the halo, and by extension, the viral radius, viral mass, and the 
+;internal energy of the gas such that hydrostatic equilibrium is achieved.
+;
+;While the system is initially in hydrostatic equilibrium, the cooling of the
+;gas means that the halo will collapse.
+;
+;To run this example, make such that the code is compiled with either the
+;isothermal potential or softened isothermal potential, and 'const_lambda' 
+;cooling, set in src/const.h. In
+;the latter case, a (small) value of epsilon needs to be set in cooling.yml.
+;0.1 kpc should work well.
+;
+;The plotting scripts produce a plot of the density, internal energy and radial
+;velocity profile for each snapshot. test_energy_conservation.py shows the 
+;evolution of energy with time. These can be used to check if the example
+;has run properly.
+;
+;
\ No newline at end of file

examples/CoolingHalo/velocity_profile.py

+import numpy as np
+import h5py as h5
+import matplotlib.pyplot as plt
+import sys
+
+def do_binning(x,y,x_bin_edges):
+
+    #x and y are arrays, where y = f(x)
+    #returns number of elements of x in each bin, and the total of the y elements corresponding to those x values
+
+    n_bins = x_bin_edges.size - 1
+    count = np.zeros(n_bins)
+    y_totals = np.zeros(n_bins)
+    
+    for i in range(n_bins):
+        ind = np.intersect1d(np.where(x > bin_edges[i])[0],np.where(x <= bin_edges[i+1])[0])
+        count[i] = ind.size
+        binned_y = y[ind]
+        y_totals[i] = np.sum(binned_y)
+
+    return(count,y_totals)
+
+
+#for the plotting
+max_r = float(sys.argv[1])
+n_radial_bins = int(sys.argv[2])
+n_snaps = int(sys.argv[3])
+
+#some constants
+OMEGA = 0.3 # Cosmological matter fraction at z = 0
+PARSEC_IN_CGS = 3.0856776e18
+KM_PER_SEC_IN_CGS = 1.0e5
+CONST_G_CGS = 6.672e-8
+CONST_m_H_CGS = 1.67e-24
+h = 0.67777 # hubble parameter
+gamma = 5./3.
+eta = 1.2349
+H_0_cgs = 100. * h * KM_PER_SEC_IN_CGS / (1.0e6 * PARSEC_IN_CGS)
+
+#read some header/parameter information from the first snapshot
+
+filename = "CoolingHalo_000.hdf5"
+f = h5.File(filename,'r')
+params = f["Parameters"]
+unit_mass_cgs = float(params.attrs["InternalUnitSystem:UnitMass_in_cgs"])
+unit_length_cgs = float(params.attrs["InternalUnitSystem:UnitLength_in_cgs"])
+unit_velocity_cgs = float(params.attrs["InternalUnitSystem:UnitVelocity_in_cgs"])
+unit_time_cgs = unit_length_cgs / unit_velocity_cgs
+v_c = float(params.attrs["SoftenedIsothermalPotential:vrot"])
+v_c_cgs = v_c * unit_velocity_cgs
+header = f["Header"]
+N = header.attrs["NumPart_Total"][0]
+box_centre = np.array(header.attrs["BoxSize"])
+
+#calculate r_vir and M_vir from v_c
+r_vir_cgs = v_c_cgs / (10. * H_0_cgs * np.sqrt(OMEGA))
+M_vir_cgs = r_vir_cgs * v_c_cgs**2 / CONST_G_CGS
+
+for i in range(n_snaps):
+
+    filename = "CoolingHalo_%03d.hdf5" %i
+    f = h5.File(filename,'r')
+    coords_dset = f["PartType0/Coordinates"]
+    coords = np.array(coords_dset)
+#translate coords by centre of box
+    header = f["Header"]
+    snap_time = header.attrs["Time"]
+    snap_time_cgs = snap_time * unit_time_cgs
+    coords[:,0] -= box_centre[0]/2.
+    coords[:,1] -= box_centre[1]/2.
+    coords[:,2] -= box_centre[2]/2.
+    radius = np.sqrt(coords[:,0]**2 + coords[:,1]**2 + coords[:,2]**2)
+    radius_cgs = radius*unit_length_cgs
+    radius_over_virial_radius = radius_cgs / r_vir_cgs
+
+#get the internal energies
+    vel_dset = f["PartType0/Velocities"]
+    vel = np.array(vel_dset)
+
+#make dimensionless
+    vel /= v_c
+    r = radius_over_virial_radius
+
+    #find radial component of velocity
+
+    v_r = np.zeros(r.size)
+    for j in range(r.size):
+        v_r[j] = -np.dot(coords[j,:],vel[j,:])/radius[j]
+
+    bin_edges = np.linspace(0,max_r,n_radial_bins + 1)
+    (hist,v_r_totals) = do_binning(r,v_r,bin_edges)
+    
+    bin_widths = bin_edges[1] - bin_edges[0]
+    radial_bin_mids = np.linspace(bin_widths / 2. , max_r - bin_widths / 2. , n_radial_bins) 
+    binned_v_r = v_r_totals / hist
+
+    #calculate cooling radius
+
+    #r_cool_over_r_vir = np.sqrt((2.*(gamma - 1.)*lambda_cgs*M_vir_cgs*X_H**2)/(4.*np.pi*CONST_m_H_CGS**2*v_c_cgs**2*r_vir_cgs**3))*np.sqrt(snap_time_cgs)
+
+    plt.plot(radial_bin_mids,binned_v_r,'ko',label = "Average radial velocity in shell")
+    #plt.plot((0,1),(1,1),label = "Analytic Solution")
+    #plt.plot((r_cool_over_r_vir,r_cool_over_r_vir),(0,2),'r',label = "Cooling radius")
+    plt.legend(loc = "upper right")
+    plt.xlabel(r"$r / r_{vir}$")
+    plt.ylabel(r"$v_r / v_c$")
+    plt.title(r"$\mathrm{Time}= %.3g \, s \, , \, %d \, \, \mathrm{particles} \,,\, v_c = %.1f \, \mathrm{km / s}$" %(snap_time_cgs,N,v_c))
+    plt.ylim((0,2))
+    plot_filename = "./plots/radial_velocity_profile/velocity_profile_%03d.png" %i
+    plt.savefig(plot_filename,format = "png")
+    plt.close()

examples/CoolingHaloWithSpin/README

+;
+;To make the initial conditions we distribute gas particles randomly in a cube
+;with a side length twice that of the virial radius. The density profile
+;of the gas is proportional to r^(-2) where r is the distance from the centre
+;of the cube. 
+;
+;The parameter v_rot (in makeIC.py and cooling.yml) sets the circular velocity
+;of the halo, and by extension, the viral radius, viral mass, and the 
+;internal energy of the gas such that hydrostatic equilibrium is achieved.
+;
+;The gas is given some angular momentum about the z-axis. This is defined by
+;the 'spin_lambda' variable in makeIC.py
+;
+;While the system is initially in hydrostatic equilibrium, the cooling of the
+;gas and the non-zero angular momentum means that the halo will collapse into
+;a spinning disc.
+;
+;To run this example, make such that the code is compiled with either the
+;isothermal potential or softened isothermal potential, and 'const_lambda' 
+;cooling, set in src/const.h. In
+;the latter case, a (small) value of epsilon needs to be set in cooling.yml.
+;0.1 kpc should work well.
+;
+;The plotting scripts produce a plot of the density, internal energy and radial
+;velocity profile for each snapshot. test_energy_conservation.py shows the 
+;evolution of energy with time. These can be used to check if the example
+;has run properly.
+;
+;
\ No newline at end of file

examples/CoolingHaloWithSpin/velocity_profile.py

+import numpy as np
+import h5py as h5
+import matplotlib.pyplot as plt
+import sys
+
+def do_binning(x,y,x_bin_edges):
+
+    #x and y are arrays, where y = f(x)
+    #returns number of elements of x in each bin, and the total of the y elements corresponding to those x values
+
+    n_bins = x_bin_edges.size - 1
+    count = np.zeros(n_bins)
+    y_totals = np.zeros(n_bins)
+    
+    for i in range(n_bins):
+        ind = np.intersect1d(np.where(x > bin_edges[i])[0],np.where(x <= bin_edges[i+1])[0])
+        count[i] = ind.size
+        binned_y = y[ind]
+        y_totals[i] = np.sum(binned_y)
+
+    return(count,y_totals)
+
+
+#for the plotting
+max_r = float(sys.argv[1])
+n_radial_bins = int(sys.argv[2])
+n_snaps = int(sys.argv[3])
+
+#some constants
+OMEGA = 0.3 # Cosmological matter fraction at z = 0
+PARSEC_IN_CGS = 3.0856776e18
+KM_PER_SEC_IN_CGS = 1.0e5
+CONST_G_CGS = 6.672e-8
+CONST_m_H_CGS = 1.67e-24
+h = 0.67777 # hubble parameter
+gamma = 5./3.
+eta = 1.2349
+H_0_cgs = 100. * h * KM_PER_SEC_IN_CGS / (1.0e6 * PARSEC_IN_CGS)
+
+#read some header/parameter information from the first snapshot
+
+filename = "CoolingHalo_000.hdf5"
+f = h5.File(filename,'r')
+params = f["Parameters"]
+unit_mass_cgs = float(params.attrs["InternalUnitSystem:UnitMass_in_cgs"])
+unit_length_cgs = float(params.attrs["InternalUnitSystem:UnitLength_in_cgs"])
+unit_velocity_cgs = float(params.attrs["InternalUnitSystem:UnitVelocity_in_cgs"])
+unit_time_cgs = unit_length_cgs / unit_velocity_cgs
+v_c = float(params.attrs["SoftenedIsothermalPotential:vrot"])
+v_c_cgs = v_c * unit_velocity_cgs
+header = f["Header"]
+N = header.attrs["NumPart_Total"][0]
+box_centre = np.array(header.attrs["BoxSize"])
+
+#calculate r_vir and M_vir from v_c
+r_vir_cgs = v_c_cgs / (10. * H_0_cgs * np.sqrt(OMEGA))
+M_vir_cgs = r_vir_cgs * v_c_cgs**2 / CONST_G_CGS
+
+for i in range(n_snaps):
+
+    filename = "CoolingHalo_%03d.hdf5" %i
+    f = h5.File(filename,'r')
+    coords_dset = f["PartType0/Coordinates"]
+    coords = np.array(coords_dset)
+#translate coords by centre of box
+    header = f["Header"]
+    snap_time = header.attrs["Time"]
+    snap_time_cgs = snap_time * unit_time_cgs
+    coords[:,0] -= box_centre[0]/2.
+    coords[:,1] -= box_centre[1]/2.
+    coords[:,2] -= box_centre[2]/2.
+    radius = np.sqrt(coords[:,0]**2 + coords[:,1]**2 + coords[:,2]**2)
+    radius_cgs = radius*unit_length_cgs
+    radius_over_virial_radius = radius_cgs / r_vir_cgs
+
+#get the internal energies
+    vel_dset = f["PartType0/Velocities"]
+    vel = np.array(vel_dset)
+
+#make dimensionless
+    vel /= v_c
+    r = radius_over_virial_radius
+
+    #find radial component of velocity
+
+    v_r = np.zeros(r.size)
+    for j in range(r.size):
+        v_r[j] = -np.dot(coords[j,:],vel[j,:])/radius[j]
+
+    bin_edges = np.linspace(0,max_r,n_radial_bins + 1)
+    (hist,v_r_totals) = do_binning(r,v_r,bin_edges)
+    
+    bin_widths = bin_edges[1] - bin_edges[0]
+    radial_bin_mids = np.linspace(bin_widths / 2. , max_r - bin_widths / 2. , n_radial_bins) 
+    binned_v_r = v_r_totals / hist
+
+    #calculate cooling radius
+
+    #r_cool_over_r_vir = np.sqrt((2.*(gamma - 1.)*lambda_cgs*M_vir_cgs*X_H**2)/(4.*np.pi*CONST_m_H_CGS**2*v_c_cgs**2*r_vir_cgs**3))*np.sqrt(snap_time_cgs)
+
+    plt.plot(radial_bin_mids,binned_v_r,'ko',label = "Average radial velocity in shell")
+    #plt.plot((0,1),(1,1),label = "Analytic Solution")
+    #plt.plot((r_cool_over_r_vir,r_cool_over_r_vir),(0,2),'r',label = "Cooling radius")
+    plt.legend(loc = "upper right")
+    plt.xlabel(r"$r / r_{vir}$")
+    plt.ylabel(r"$v_r / v_c$")
+    plt.title(r"$\mathrm{Time}= %.3g \, s \, , \, %d \, \, \mathrm{particles} \,,\, v_c = %.1f \, \mathrm{km / s}$" %(snap_time_cgs,N,v_c))
+    plt.ylim((0,2))
+    plot_filename = "./plots/radial_velocity_profile/velocity_profile_%03d.png" %i
+    plt.savefig(plot_filename,format = "png")
+    plt.close()