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"Free electron density model" |
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import os |
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import numpy as np |
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from astropy.table import Table |
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from numpy import cos |
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from numpy import cosh |
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from numpy import exp |
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from numpy import pi |
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from numpy import sin |
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from numpy import sqrt |
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from numpy import tan |
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# import astropy.units as us |
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# from astropy.coordinates import SkyCoord |
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# Configuration |
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# TODO: use to config file |
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# input parameters for large-scale components of NE2001 30 June '02 |
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# flags = {'wg1': 1, |
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# 'wg2': 1, |
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# 'wga': 1, |
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# 'wggc': 1, |
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# 'wglism': 1, |
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# 'wgcN': 1, |
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# 'wgvN': 1} |
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# solar_params = {'Rsun': 8.3} |
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# thick_disk_params = {'n1h1': 0.033, |
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# 'h1': 0.97, |
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# 'A1': 17.5, |
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# 'F1': 0.18} |
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# thin_disk_params = {'n2': 0.08, |
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# 'h2': 0.15, |
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# 'A2': 3.8, |
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# 'F2': 120} |
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# galactic_center_params = {'xgc': -0.01, |
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# 'ygc': 0.0, |
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# 'zgc': -0.020, |
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# 'rgc': 0.145, |
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# 'hgc': 0.026, |
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# 'negc0': 10.0, |
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# 'Fgc0': 0.6e5} |
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# spiral_arms_params = {'na': 0.028, |
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# 'ha': 0.23, |
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# 'wa': 0.65, |
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# 'Aa': 10.5, |
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# 'Fa': 5, |
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# 'narm1': 0.5, |
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# 'narm2': 1.2, |
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# 'narm3': 1.3, |
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# 'narm4': 1.0, |
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# 'narm5': 0.25, |
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# 'warm1': 1.0, |
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# 'warm2': 1.5, |
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# 'warm3': 1.0, |
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# 'warm4': 0.8, |
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# 'warm5': 1.0, |
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# 'harm1': 1.0, |
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# 'harm2': 0.8, |
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# 'harm3': 1.3, |
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# 'harm4': 1.5, |
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# 'harm5': 1.0, |
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# 'farm1': 1.1, |
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# 'farm2': 0.3, |
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# 'farm3': 0.4, |
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# 'farm4': 1.5, |
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# 'farm5': 0.3} |
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ldr_params = {'abc': np.array([1.50, .750, .50]), |
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'center': np.array([1.36, 8.06, 0.0]), |
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'theta': -24.2*pi/180, |
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'ne': 0.012, |
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'F': 0.1} |
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lsb_params = {'abc': np.array([1.050, .4250, .3250]), |
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'center': np.array([-0.75, 9.0, -0.05]), |
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'theta': 139.*pi/180, |
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'ne': 0.016, |
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'F': 0.01} |
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lhb_params = {'abc': np.array([.0850, .1000, .330]), |
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'center': np.array([0.01, 8.45, 0.17]), |
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'theta': 15*pi/180, |
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'ne': 0.005, |
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'F': 0.01} |
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loop_params = {'center': np.array([-0.045, 8.40, 0.07]), |
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'r': 0.120, |
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'dr': 0.060, |
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'ne1': 0.0125, |
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'ne2': 0.0125, |
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'F1': 0.2, |
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'F2': 0.01} |
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def ne_thick_disk(xyz, ne_disk, rdisk, hdisk, r_sun): |
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""" |
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Calculate the contribution of the thick disk to the free electron density |
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at x, y, z = `xyz` |
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""" |
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r2d = sqrt(xyz[0]**2 + xyz[1]**2) |
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k = pi/2/rdisk |
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return ne_disk * (cos(r2d*k)/cos(r_sun*k) / |
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cosh(xyz[-1]/hdisk)**2 * |
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(r2d < rdisk)) |
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def ne_thin_disk(xyz, ne_disk, rdisk, hdisk): |
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""" |
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Calculate the contribution of the thin disk to the free electron density |
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at x, y, z = `xyz` |
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""" |
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r2d = sqrt(xyz[0]**2 + xyz[1]**2) |
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return ne_disk * (exp(-(r2d - rdisk)**2/1.8**2) / |
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cosh(xyz[-1]/hdisk)**2) # Why 1.8? |
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def ne_gc(xyz, ne_gc0, rgc, hgc, xyz_gc): |
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""" |
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Calculate the contribution of the Galactic center to the free |
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electron density at x, y, z = `xyz` |
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""" |
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# Here I'm using the expression in the NE2001 code which is inconsistent |
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# with Cordes and Lazio 2011 (0207156v3) (See Table 2) |
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try: |
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xyz = xyz - xyz_gc |
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except ValueError: |
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xyz = xyz - xyz_gc[:, None] |
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r2d = sqrt(xyz[0]**2 + xyz[1]**2) |
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# ???? |
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# Cordes and Lazio 2011 (0207156v3) (Table 2) |
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# return ne_gc0*exp(-(r2d/rgc)**2 - (xyz[-1]/hgc)**2) |
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# ???? |
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# Constant ne (form NE2001 code) |
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return ne_gc0*((r2d/rgc)**2 + (xyz[-1]/hgc)**2 < 1)*(r2d < rgc) |
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def ne_local_ism(xyz, ldr_params, lsb_params, lhb_params, loop_params): |
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""" |
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Calculate the contribution of the local ISM to the free |
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electron density at x, y, z = `xyz` |
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""" |
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# low density region in Q1 |
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neldr = ldr_params['ne']*in_ellisoid(xyz, ldr_params['center'], |
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ldr_params['abc'], |
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ldr_params['theta']) |
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# Local Super Bubble |
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nelsb = lsb_params['ne']*in_ellisoid(xyz, lsb_params['center'], |
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lsb_params['abc'], |
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lsb_params['theta']) |
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# Local Hot Bubble |
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nelhb = lhb_params['ne']*in_cylinder(xyz, lhb_params['center'], |
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lhb_params['abc'], |
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lhb_params['theta']) |
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# Loop I |
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irr1 = in_half_sphere(xyz, loop_params['center'], loop_params['r']) |
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irr2 = in_half_sphere(xyz, loop_params['center'], |
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loop_params['r'] + loop_params['dr']) |
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neloop = loop_params['ne1'] * irr1 + loop_params['ne2'] * irr2*(~irr1) |
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wlhb, wloop, wlsb, wldr = (nelhb > 0, |
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neloop > 0, |
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nelsb > 0, |
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neldr > 0) |
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ne_lism = ((1 - wlhb) * |
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((1 - wloop) * (wlsb*nelsb + (1-wlsb) * neldr) + |
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wloop*neloop) + |
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wlhb*nelhb) |
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wlism = np.maximum(wloop, np.maximum(wldr, np.maximum(wlsb, wlhb))) |
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return ne_lism, wlism |
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def in_ellisoid(xyz, xyz_center, abc_ellipsoid, theta): |
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""" |
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Test if xyz in the ellipsoid |
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Theta in radians |
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""" |
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try: |
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xyz = xyz - xyz_center |
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except ValueError: |
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xyz = xyz - xyz_center[:, None] |
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abc_ellipsoid = abc_ellipsoid[:, None] |
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rot = np.array([[cos(theta), sin(theta)], |
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[-sin(theta), cos(theta)]]) |
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xyz[:2] = (xyz[:2].T.dot(rot)).T |
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xyz_p = xyz/abc_ellipsoid |
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return np.sum(xyz_p**2, axis=0) <= 1 |
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def in_cylinder(xyz, xyz_center, abc_cylinder, theta): |
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""" |
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Test if xyz in the cylinder |
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Theta in radians |
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""" |
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try: |
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xyz = xyz - xyz_center |
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except ValueError: |
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xyz = xyz - xyz_center[:, None] |
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abc_cylinder = np.vstack([abc_cylinder]*xyz.shape[-1]).T |
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xyz[2] -= tan(theta)*xyz[-1] |
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abc_cylinder_p = abc_cylinder.copy() |
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z_c = (xyz_center[-1] - abc_cylinder[-1]) |
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izz = (xyz[-1] <= 0)*(xyz[-1] <= z_c) |
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abc_cylinder_p[0] = (0.001 + |
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(abc_cylinder[0] - 0.001) * |
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(1 - xyz[-1]/z_c))*izz + abc_cylinder[0]*(~izz) |
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xyz_p = xyz/abc_cylinder_p |
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return (xyz_p[0]**2 + xyz_p[1]**2 <= 1) * (xyz_p[-1]**2 <= 1) |
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def in_half_sphere(xyz, xyz_center, r_sphere): |
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"Test if `xyz` in the sphere with radius r_sphere centerd at `xyz_center`" |
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try: |
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xyz = xyz - xyz_center |
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except ValueError: |
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xyz = xyz - xyz_center[:, None] |
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distance = sqrt(np.sum(xyz**2, axis=0)) |
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return (distance <= r_sphere)*(xyz[-1] >= 0) |
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class Clumps(object): |
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""" |
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""" |
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def __init__(self, clumps_file=None): |
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""" |
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""" |
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if not clumps_file: |
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this_dir, _ = os.path.split(__file__) |
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clumps_file = os.path.join(this_dir, "data", "neclumpN.NE2001.dat") |
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self._data = Table.read(clumps_file, format='ascii') |
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@property |
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def use_clump(self): |
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""" |
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""" |
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return self._data['flag'] == 0 |
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@property |
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def xyz(self): |
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""" |
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""" |
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try: |
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return self._xyz |
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except AttributeError: |
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self._xyz = self.get_xyz() |
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return self._xyz |
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@property |
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def gl(self): |
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""" |
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Galactic longitude (deg) |
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""" |
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return self._data['l'] |
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@property |
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def gb(self): |
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""" |
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Galactic latitude (deg) |
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""" |
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return self._data['b'] |
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@property |
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def distance(self): |
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""" |
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Distance from the sun (kpc) |
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""" |
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return self._data['dc'] |
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@property |
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def radius(self): |
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""" |
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Radius of the clump (kpc) |
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""" |
293
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return self._data['rc'] |
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@property |
296
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def ne(self): |
297
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""" |
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Electron density of each clump (cm^{-3}) |
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""" |
300
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return self._data['nec'] |
301
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302
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@property |
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def edge(self): |
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""" |
305
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Clump edge |
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0 => use exponential rolloff out to 5 clump radii |
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1 => uniform and truncated at 1/e clump radius |
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""" |
309
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return self._data['edge'] |
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311
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def get_xyz(self, z_sun=0, rsun=8.5): |
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""" |
313
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""" |
314
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# xyz = SkyCoord(frame="galactic", l=self.gl, b=self.gb, |
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# distance=self.distance, |
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# z_sun = z_sun*us.kpc, |
317
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# unit="deg, deg, kpc").galactocentric.cartesian.xyz.value |
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# return xyz |
319
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320
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slc = sin(self.gl/180*pi) |
321
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clc = cos(self.gl/180*pi) |
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sbc = sin(self.gb/180*pi) |
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cbc = cos(self.gb/180*pi) |
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rgalc = self.distance*cbc |
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xc = rgalc*slc |
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yc = rsun-rgalc*clc |
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zc = self.distance*sbc |
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return np.array([xc, yc, zc]) |
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330
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def clump_factor(self, xyz): |
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""" |
332
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Clump edge |
333
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0 => use exponential rolloff out to 5 clump radii |
334
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1 => uniform and truncated at 1/e clump radius |
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""" |
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try: |
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xyz = xyz[:, None] - self.xyz |
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except ValueError: |
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xyz = xyz[:, :, None] - self.xyz[:, None, :] |
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341
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q2 = (np.sum(xyz**2, axis=0) / |
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self.radius**2) |
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# NOTE: In the original NE2001 code q2 <= 5 is used instead of q <= 5. |
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# TODO: check this |
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return (q2 <= 1)*(self.edge == 1) + (q2 <= 5)*(self.edge == 0)*exp(-q2) |
346
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347
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def ne_clumps(self, xyz): |
348
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""" |
349
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|
|
The contribution of the clumps to the free |
350
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electron density at x, y, z = `xyz` |
351
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""" |
352
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return np.sum(self.clump_factor(xyz)*self.ne*self.use_clump, axis=-1) |
353
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