|
| 1 | +"""COSMO. |
| 2 | +
|
| 3 | +:Name: cosmo.py |
| 4 | +
|
| 5 | +:Description: This file contains methods for cosmological |
| 6 | + quantities. |
| 7 | +
|
| 8 | +:Author: Martin Kilbinger <martin.kilbinger@cea.fr> |
| 9 | +
|
| 10 | +""" |
| 11 | + |
| 12 | +import numpy as np |
| 13 | + |
| 14 | +from astropy import constants |
| 15 | +from astropy import units |
| 16 | + |
| 17 | + |
| 18 | + |
| 19 | +def sigma_crit(z_lens, z_source, cosmo, d_lens=None, d_source=None): |
| 20 | + """Critical surface mass density. |
| 21 | +
|
| 22 | + Parameters |
| 23 | + ---------- |
| 24 | + z_lens : float |
| 25 | + lens redshift |
| 26 | + z_source : float |
| 27 | + source redshift |
| 28 | + cosmo : pyccl.core.Cosmology |
| 29 | + cosmological parameters |
| 30 | + d_lens : astropy.units.Quantity, optional |
| 31 | + precomputed anguar diameter distance to lens, computed from z_lens |
| 32 | + if ``None`` (default) |
| 33 | + d_source : astropy.units.Quantity, optional |
| 34 | + precomputed anguar diameter distance to sourcce, computed from z_source |
| 35 | + if ``None`` (default) |
| 36 | +
|
| 37 | + Returns |
| 38 | + ------- |
| 39 | + astropy.units.Quantity |
| 40 | + critical surface mass density with units of M_sol / pc^2 |
| 41 | +
|
| 42 | + """ |
| 43 | + unit_return = units.Msun / units.pc**2 |
| 44 | + |
| 45 | + # Return 0 if lens behind source |
| 46 | + if z_lens >= z_source: |
| 47 | + return 0.0 * unit_return |
| 48 | + |
| 49 | + a_lens = 1 / (1 + z_lens) |
| 50 | + a_source = 1 / (1 + z_source) |
| 51 | + if not d_lens: |
| 52 | + d_lens = cosmo.angular_diameter_distance(a_lens) * units.Mpc |
| 53 | + if not d_source: |
| 54 | + d_source = cosmo.angular_diameter_distance(a_source) * units.Mpc |
| 55 | + |
| 56 | + d_lens_source = cosmo.angular_diameter_distance( |
| 57 | + a_lens, |
| 58 | + a_source |
| 59 | + ) * units.Mpc |
| 60 | + |
| 61 | + frac = d_source / (d_lens_source * d_lens) |
| 62 | + pref = constants.c**2 / (4 * np.pi * constants.G) |
| 63 | + |
| 64 | + sigma_cr = (pref * frac).to(unit_return) |
| 65 | + |
| 66 | + return sigma_cr |
| 67 | + |
| 68 | + |
| 69 | +def sigma_crit_eff( |
| 70 | + z_lens, |
| 71 | + z_source_arr, |
| 72 | + nz_source_arr, |
| 73 | + cosmo, |
| 74 | + d_lens=None, |
| 75 | + d_source_arr=None, |
| 76 | +): |
| 77 | + """Effective critical surface mass density, which |
| 78 | + is sigma_crit(z_lens, z_source) weighted by nz_source. |
| 79 | +
|
| 80 | + Parameters |
| 81 | + ---------- |
| 82 | + z_lens : float |
| 83 | + lens redshift |
| 84 | + z_source_arr : list |
| 85 | + source redshifts |
| 86 | + nz_source_arr : list |
| 87 | + number of galaxies at z_source |
| 88 | + cosmo : pyccl.core.Cosmology |
| 89 | + cosmological parameters |
| 90 | + d_lens : astropy.units.Quantity, optional |
| 91 | + precomputed anguar diameter distance to lens; |
| 92 | + computed from z_lens if ``None`` (default) |
| 93 | + d_source_arr : list, optional |
| 94 | + precompuated angular diameter distances to sources; |
| 95 | + computed from z_source_arr if ``None`` (default); |
| 96 | + needs to be list of astropy.units.Quantity |
| 97 | +
|
| 98 | + Raises |
| 99 | + ------ |
| 100 | + IndexError |
| 101 | + If lists ``z_source_arr``, ``nz_source_arr``, and d_source_arr |
| 102 | + do not match |
| 103 | +
|
| 104 | + Returns |
| 105 | + ------- |
| 106 | + astropy.units.Quantity |
| 107 | + effective critical surface mass density with units of M_sol / pc^2 |
| 108 | +
|
| 109 | + """ |
| 110 | + n_source = len(z_source_arr) |
| 111 | + |
| 112 | + if d_source_arr is None: |
| 113 | + d_source_arr = [None] * n_source |
| 114 | + |
| 115 | + if (len(nz_source_arr) != n_source) or (len(d_source_arr) != n_source): |
| 116 | + raise IndexError( |
| 117 | + 'Lists for source z, n(z), and/or d_ang have different lenghts' |
| 118 | + ) |
| 119 | + |
| 120 | + sigma_cr_arr = [] |
| 121 | + for idx in range(n_source): |
| 122 | + sigma_cr = sigma_crit( |
| 123 | + z_lens, |
| 124 | + z_source_arr[idx], |
| 125 | + cosmo, |
| 126 | + d_lens=d_lens, |
| 127 | + d_source=d_source_arr[idx] |
| 128 | + ) |
| 129 | + |
| 130 | + # Get unit |
| 131 | + if len(sigma_cr_arr) == 0: |
| 132 | + unit = sigma_cr.unit |
| 133 | + |
| 134 | + sigma_cr_arr.append(sigma_cr.value) |
| 135 | + |
| 136 | + # Mean sigma_cr weighted by source redshifts. |
| 137 | + # np.average can only deal with unitless quantities. |
| 138 | + sigma_cr_eff = np.average(sigma_cr_arr, weights=nz_source_arr) |
| 139 | + |
| 140 | + return sigma_cr_eff * unit |
| 141 | + |
| 142 | + |
| 143 | +def sigma_crit_m1_eff( |
| 144 | + z_lens, |
| 145 | + z_source_arr, |
| 146 | + nz_source_arr, |
| 147 | + cosmo, |
| 148 | + d_lens=None, |
| 149 | + d_source_arr=None, |
| 150 | +): |
| 151 | + """Effective inverse critical surface mass density, which |
| 152 | + is sigma_crit^{-1}(z_lens, z_source) weighted by nz_source. |
| 153 | + See Eq. (17) in :cite:`2004AJ....127.2544S`. |
| 154 | +
|
| 155 | + Parameters |
| 156 | + ---------- |
| 157 | + z_lens : float |
| 158 | + lens redshift |
| 159 | + z_source_arr : list |
| 160 | + source redshifts |
| 161 | + nz_source_arr : list |
| 162 | + number of galaxies at z_source |
| 163 | + cosmo : pyccl.core.Cosmology |
| 164 | + cosmological parameters |
| 165 | + d_lens : astropy.units.Quantity, optional |
| 166 | + precomputed anguar diameter distance to lens; |
| 167 | + computed from z_lens if ``None`` (default) |
| 168 | + d_source_arr : float, optional |
| 169 | + precomputed anguar diameter distance to sources; |
| 170 | + computed from z_source_arr if ``None`` (default); |
| 171 | + needs to be list of astropy.units.Quantity |
| 172 | +
|
| 173 | + Raises |
| 174 | + ------ |
| 175 | + IndexError |
| 176 | + If lists ``z_source_arr``, ``nz_source_arr``, and ``d_source_arr`` |
| 177 | + do not match |
| 178 | +
|
| 179 | + Returns |
| 180 | + ------- |
| 181 | + astropy.units.Quantity |
| 182 | + effective inverse critical surface mass density with units of |
| 183 | + M_sol / pc^2 |
| 184 | +
|
| 185 | + """ |
| 186 | + n_source = len(z_source_arr) |
| 187 | + |
| 188 | + if d_source_arr is None: |
| 189 | + d_source_arr = [None] * n_source |
| 190 | + |
| 191 | + if (len(nz_source_arr) != n_source) or (len(d_source_arr) != n_source): |
| 192 | + raise IndexError( |
| 193 | + 'Lists for source z, n(z), and/or d_ang have different lenghts' |
| 194 | + ) |
| 195 | + |
| 196 | + sigma_cr_m1_arr = [] |
| 197 | + weights = [] |
| 198 | + |
| 199 | + for idx in range(n_source): |
| 200 | + sigma_cr = sigma_crit( |
| 201 | + z_lens, |
| 202 | + z_source_arr[idx], |
| 203 | + cosmo, |
| 204 | + d_lens=d_lens, |
| 205 | + d_source=d_source_arr[idx] |
| 206 | + ) |
| 207 | + |
| 208 | + # Get unit |
| 209 | + if len(sigma_cr_m1_arr) == 0: |
| 210 | + unit = 1 / sigma_cr.unit |
| 211 | + |
| 212 | + # If lens behind source: continue |
| 213 | + if sigma_cr == 0: |
| 214 | + continue |
| 215 | + |
| 216 | + sigma_cr_m1 = 1 / sigma_cr |
| 217 | + |
| 218 | + sigma_cr_m1_arr.append(sigma_cr_m1.value) |
| 219 | + weights.append(nz_source_arr[idx]) |
| 220 | + |
| 221 | + sigma_cr_m1_eff = np.average(sigma_cr_m1_arr, weights=weights) |
| 222 | + |
| 223 | + return sigma_cr_m1_eff * unit |
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