Tom J. Wilson
Postdoctoral Research Fellow at the University of Exeter, working on cross-matching photometric catalogues in crowded fields as part of the LSST:UK Consortium. Also developing PSF photometry codebase in the astropy-affliated photutils package. Astrostatistician, occasional exoplanet dabbler.
t.j.wilson [at] exeter.ac.uk
CV
ADS Publications
ORCID: 0000-0001-6352-9735
Github
Schechter Function Parameterisation for Differential Galaxy Counts
Here I provide the data used to construct the galaxy count model described in Wilson (2022, RNAAS, …). The model assumes galaxy luminosities are described by a Schechter function, where the density of galaxies as a function of absolute magnitude in a given bandpass is given by \(\phi(M) = 0.4 \ln(10) \phi^* [10^{-0.4 (M-M^*)}]^{\alpha+1} \exp(-10^{-0.4 (M - M^*)})\), with \(M^*(z) = M^*_0 - Qz\), \(\phi^* = \phi^*_0 10^{0.4 P z}\) describing the redshift dependency of the characteristic absolute magnitude and normalising density of the luminosity function respectively and \(\alpha\) the slope of the faint end of the distribution.
The observed differential galaxy count is then derived by a conversion from \(\phi\) in units of \(\mathrm{Mpc}^{-3}\,\mathrm{mag}^{-1}\) to sky number densities (\(\mathrm{deg}^{-2}\,\mathrm{mag}^{-1}\)) by consideration of differential comoving volume and an integral over all redshifts. Final observed densities of galaxies in a bandpass are the sum of two Schechter functions, \(\phi_\mathrm{tot} = \phi_b + \phi_r\), for “blue” (star-forming) and “red” (quiescent) galaxies, and hence we require a total of 10 parameters to describe the density of galaxies at a particular redshift.
To derive galaxy counts for an arbitrary bandpass, a parameterisation for these 10 parameters – \(M^*_0\), \(\phi^*_0\), \(P\), \(Q\), and \(\alpha\), for both blue and red galaxy distributions – was found as a function of wavelength, with the exception of \(Q\), which – due to the degeneracy between it and \(P\) – was derived as a function of \(P\). The functions used to describe these parameters are \(y(x) = m \times x + c\) for \(Q(P)\), \(\alpha(\log_{10}(\lambda / \mu\mathrm{m}))\), and \(P(\log_{10}(\lambda / \mu\mathrm{m}))\); \(y(x) = a \exp(-m x) + c\) for \(M^*_0(\log_{10}(\lambda / \mu\mathrm{m}))\) and blue galaxy \(\phi^*_0(\log_{10}(\lambda / \mu\mathrm{m}))\); and \(y(x) = a \exp(-0.5 (x - u)^2 \times m) + c\) for red galaxy \(\phi^*_0(\log_{10}(\lambda / \mu\mathrm{m}))\). Note that \(x \equiv \log_{10}(\lambda / \mu\mathrm{m}))\) in four cases, with \(x \equiv P\) solely for the parameterisation of \(Q\). The table below provides the values derived for each parameter fit for both galaxy types, with a machine-readable version of the data available here. A figure showing the first to the parameters, as well as some example differential galaxy counts (see Wilson 2022, RNAAS, … for more details) is also available.
| Parameter | Galaxy type | c | m | a | u |
|---|---|---|---|---|---|
| \(M^*_0\) | b | -24.2865 | 1.142 | 2.6558 | |
| \(M^*_0\) | r | -23.1925 | 1.779 | 1.6683 | |
| \(\phi^*_0\) | b | 0.0015 | 2.919 | 0.0005 | |
| \(\phi^*_0\) | r | 0.0006 | 7.691 | 0.0033 | -0.066 |
| \(\alpha\) | b | -1.2578 | 0.021 | ||
| \(\alpha\) | r | -0.3091 | -0.067 | ||
| \(P\) | b | -0.3020 | 0.034 | ||
| \(P\) | r | -0.7131 | 0.233 | ||
| \(Q\) | b | 1.2336 | -0.322 | ||
| \(Q\) | r | 1.0689 | -0.386 |
Additionally, the final table provides the values used to calculate these functional forms, also available in machine-readable form here. The machine-readable .csv file also provides the original, un-corrected literature values of \(M^*_0\) and \(\phi^*_0\) – in linear- and log-form where quoted solely in \(\log_{10}(\phi^*)\) – and \(h\) and \(z_0\) when conversion from non-zero redshift or values in arbitrary \(H_0\) values are quoted.
| Citation | Band | Wavelength / nm | Type | \(M^*_0\) / AB mag | \(\phi^*_0\) / Mpc\(^{-3}\)mag\(^{-1}\) | \(\alpha\) | Q / mag \(z^{-1}\) | P / \(z^{-1}\) |
|---|---|---|---|---|---|---|---|---|
| MNRAS 420 1239 | u | 355.0 | b | -18.495±0.117 | 4.493e-03±8.575e-04 | -1.430±0.070 | 5.500±0.600 | -7.100±1.500 |
| MNRAS 420 1239 | u | 355.0 | r | -17.475±0.157 | 1.468e-02±4.939e-03 | -0.140±0.130 | 6.400±1.400 | -8.100±3.400 |
| MNRAS 420 1239 | g | 469.0 | b | -20.045±0.092 | 2.504e-03±1.029e-04 | -1.400±0.030 | 3.100±0.700 | -1.200±1.500 |
| MNRAS 420 1239 | g | 469.0 | r | -19.725±0.152 | 4.322e-03±5.831e-04 | -0.430±0.050 | 3.600±1.400 | -3.900±2.800 |
| MNRAS 420 1239 | r | 617.0 | b | -20.975±0.067 | 1.303e-03±1.715e-04 | -1.490±0.030 | 0.800±0.300 | 2.900±0.600 |
| MNRAS 420 1239 | r | 617.0 | r | -20.875±0.032 | 3.807e-03±5.145e-04 | -0.570±0.030 | 1.800±0.100 | -1.200±0.500 |
| MNRAS 420 1239 | i | 748.0 | b | -21.285±0.072 | 1.441e-03±2.058e-04 | -1.450±0.020 | 1.700±0.400 | 1.200±0.900 |
| MNRAS 420 1239 | i | 748.0 | r | -21.205±0.032 | 3.979e-03±5.145e-04 | -0.540±0.030 | 2.000±0.100 | -1.800±0.500 |
| MNRAS 420 1239 | z | 892.0 | b | -21.675±0.045 | 1.166e-03±1.372e-04 | -1.450±0.030 | 0.900±0.200 | 3.600±0.500 |
| MNRAS 420 1239 | z | 892.0 | r | -21.405±0.067 | 4.528e-03±5.488e-04 | -0.490±0.050 | 2.400±0.300 | -2.700±0.700 |
| MNRAS 451 1540 | r | 617.0 | b | -21.265±0.051 | 1.842e-03±2.121e-04 | -1.380±0.060 | 1.090±0.100 | 1.300±0.250 |
| MNRAS 451 1540 | r | 617.0 | r | -21.610±0.063 | 2.020e-03±2.325e-04 | -0.790±0.110 | 0.580±0.180 | 1.550±0.400 |
| MNRAS 439 1245 | u | 355.0 | b | -18.530±1.250 | 9.640e-03±1.290e-02 | -0.910±7.170 | ||
| MNRAS 439 1245 | u | 355.0 | r | -18.530±1.250 | 1.460e-03±9.390e-03 | 1.250±6.010 | ||
| MNRAS 439 1245 | g | 469.0 | b | -20.280±0.260 | 3.510e-03±1.750e-03 | -1.290±0.140 | ||
| MNRAS 439 1245 | g | 469.0 | r | -20.280±0.260 | 4.880e-03±1.220e-03 | 0.060±0.590 | ||
| MNRAS 439 1245 | r | 617.0 | b | -20.900±0.260 | 4.510e-03±1.030e-03 | -1.130±0.070 | ||
| MNRAS 439 1245 | r | 617.0 | r | -20.900±0.260 | 3.010e-03±8.300e-04 | 0.530±0.560 | ||
| MNRAS 439 1245 | i | 748.0 | b | -21.450±0.200 | 2.200e-03±1.500e-03 | -1.350±0.210 | ||
| MNRAS 439 1245 | i | 748.0 | r | -21.450±0.200 | 4.870e-03±1.340e-03 | -0.090±0.480 | ||
| MNRAS 439 1245 | z | 892.0 | b | -21.780±0.250 | 1.400e-03±1.120e-03 | -1.460±0.210 | ||
| MNRAS 439 1245 | z | 892.0 | r | -21.780±0.250 | 5.050e-03±8.800e-04 | -0.260±0.440 | ||
| MNRAS 439 1245 | Y | 1031.0 | b | -21.760±0.240 | 1.440e-03±1.250e-03 | -1.450±0.230 | ||
| MNRAS 439 1245 | Y | 1031.0 | r | -21.760±0.240 | 4.830e-03±8.400e-04 | -0.100±0.540 | ||
| MNRAS 439 1245 | J | 1248.0 | b | -21.820±0.170 | 1.580e-03±7.600e-04 | -1.380±2.430 | ||
| MNRAS 439 1245 | J | 1248.0 | r | -21.820±0.170 | 4.780e-03±7.200e-04 | 0.080±2.580 | ||
| MNRAS 439 1245 | H | 1631.0 | b | -22.040±0.260 | 1.350e-03±6.330e-03 | -1.460±2.430 | ||
| MNRAS 439 1245 | H | 1631.0 | r | -22.040±0.260 | 5.300e-03±6.690e-03 | 0.080±2.580 | ||
| MNRAS 439 1245 | K | 2201.0 | b | -21.720±0.230 | 1.640e-03±3.130e-03 | -1.390±1.620 | ||
| MNRAS 439 1245 | K | 2201.0 | r | -21.720±0.230 | 5.090e-03±3.180e-03 | 0.240±1.550 | ||
| ApJ 518 533L | U | 366.0 | b | -19.942±0.248 | 3.259e-03±1.338e-03 | -1.140±0.130 | 0.510±0.660 | 2.670±0.920 |
| ApJ 518 533L | U | 366.0 | r | -19.754±0.264 | 3.156e-03±8.918e-04 | -0.510±0.150 | 0.970±0.700 | 0.680±0.690 |
| ApJ 518 533L | B | 435.0 | b | -19.981±0.266 | 2.470e-03±1.132e-03 | -1.230±0.120 | 0.180±0.710 | 3.080±0.990 |
| ApJ 518 533L | B | 435.0 | r | -19.361±0.190 | 6.963e-03±1.235e-02 | 0.080±0.140 | 1.580±0.490 | -1.070±0.490 |
| ApJ 518 533L | Rc | 710.0 | b | -20.852±0.286 | 1.921e-03±1.029e-03 | -1.340±0.120 | 0.110±0.740 | 3.170±1.030 |
| ApJ 518 533L | Rc | 710.0 | r | -21.038±0.284 | 2.744e-03±7.889e-04 | -0.630±0.150 | 0.690±0.760 | 0.890±0.740 |
| ApJ 697 506 | [3.6] | 3544.0 | b | -22.009±0.266 | 2.573e-03±6.860e-05 | -1.400±0.180 | 1.000±0.700 | 0.000±0.000 |
| ApJ 697 506 | [3.6] | 3544.0 | r | -21.819±0.253 | 1.509e-03±1.715e-04 | -0.630±0.290 | 1.400±0.500 | 0.000±0.000 |
| ApJ 697 506 | [4.5] | 4487.0 | b | -21.551±0.273 | 2.470e-03±6.860e-05 | -1.290±0.170 | 0.900±0.700 | 0.000±0.000 |
| ApJ 697 506 | [4.5] | 4487.0 | r | -21.271±0.280 | 1.269e-03±1.372e-04 | -0.600±0.280 | 1.300±0.500 | 0.000±0.000 |
| ApJ 697 506 | [5.8] | 5710.0 | b | -22.884±0.266 | 1.406e-03±3.430e-05 | -1.630±0.150 | 0.400±0.700 | 0.000±0.000 |
| ApJ 697 506 | [5.8] | 5710.0 | r | -21.584±0.336 | 9.947e-04±1.029e-04 | -1.330±0.280 | 1.200±0.800 | 0.000±0.000 |
| ApJ 697 506 | [8.0] | 7841.0 | b | -23.818±0.262 | 1.509e-03±3.430e-05 | -1.350±0.090 | 1.700±0.800 | 0.000±0.000 |
| ApJ 697 506 | [8.0] | 7841.0 | r | -22.793±1.140 | 2.401e-04±3.430e-05 | -2.030±0.470 | 1.800±3.500 | 0.000±0.000 |
| ApJ 560 566 | Ks | 2159.0 | b | -21.920±0.060 | 3.464e-03±4.459e-04 | -0.870±0.090 | ||
| ApJ 560 566 | Ks | 2159.0 | r | -22.470±0.060 | 1.543e-03±2.058e-04 | -0.920±0.100 | ||
| MNRAS 427 3244 | FUV | 152.0 | b | -17.905±0.045 | -1.140±0.015 | |||
| MNRAS 427 3244 | FUV | 152.0 | r | -16.975±0.200 | -0.700±0.195 | |||
| MNRAS 427 3244 | NUV | 227.0 | b | -18.335±0.040 | -1.160±0.015 | |||
| MNRAS 427 3244 | NUV | 227.0 | r | -17.355±0.140 | -0.900±0.115 | |||
| MNRAS 427 3244 | u | 355.0 | b | -19.465±0.035 | -1.140±0.015 | |||
| MNRAS 427 3244 | u | 355.0 | r | -18.635±0.060 | -0.040±0.050 | |||
| MNRAS 427 3244 | g | 469.0 | b | -20.805±0.035 | -1.200±0.025 | |||
| MNRAS 427 3244 | g | 469.0 | r | -20.275±0.060 | -0.070±0.045 | |||
| MNRAS 427 3244 | r | 617.0 | b | -21.455±0.030 | -1.200±0.010 | |||
| MNRAS 427 3244 | r | 617.0 | r | -21.045±0.065 | -0.100±0.045 | |||
| MNRAS 427 3244 | i | 748.0 | b | -21.935±0.040 | -1.280±0.010 | |||
| MNRAS 427 3244 | i | 748.0 | r | -21.485±0.060 | -0.190±0.040 | |||
| MNRAS 427 3244 | z | 892.0 | b | -22.145±0.035 | -1.250±0.010 | |||
| MNRAS 427 3244 | z | 892.0 | r | -21.715±0.060 | -0.170±0.040 | |||
| MNRAS 427 3244 | Y | 1031.0 | b | -22.315±0.040 | -1.250±0.010 | |||
| MNRAS 427 3244 | Y | 1031.0 | r | -21.875±0.060 | -0.250±0.040 | |||
| MNRAS 427 3244 | J | 1248.0 | b | -22.445±0.040 | -1.240±0.015 | |||
| MNRAS 427 3244 | J | 1248.0 | r | -22.015±0.055 | -0.270±0.040 | |||
| MNRAS 427 3244 | H | 1631.0 | b | -22.695±0.040 | -1.210±0.015 | |||
| MNRAS 427 3244 | H | 1631.0 | r | -22.315±0.055 | -0.280±0.035 | |||
| MNRAS 427 3244 | K | 2201.0 | b | -22.325±0.040 | -1.170±0.015 | |||
| MNRAS 427 3244 | K | 2201.0 | r | -22.035±0.065 | -0.310±0.045 | |||
| MNRAS 465 672 | K | 2201.0 | b | -23.590±0.510 | 4.270e-04±1.133e-03 | -1.516±0.230 | 0.249±0.340 | -0.454±0.880 |
| MNRAS 465 672 | K | 2201.0 | r | -23.590±0.510 | 1.386e-03±1.228e-03 | -0.817±0.740 | 0.249±0.340 | -0.725±0.410 |
| A&A 476 137 | K | 2201.0 | b | -23.379±0.055 | 1.195e-03±1.029e-03 | -1.300±0.053 | 0.493±0.044 | -0.543±0.073 |
| A&A 476 137 | K | 2201.0 | r | -23.161±0.450 | 1.651e-03±1.102e-03 | -0.206±0.610 | 0.453±0.400 | -1.859±0.290 |
| MNRAS 380 585 | K | 2201.0 | b | -23.167±0.047 | 6.637e-04±4.065e-04 | -1.232±0.032 | 0.677±0.039 | -0.500±0.074 |
| MNRAS 380 585 | K | 2201.0 | r | -22.921±0.034 | 1.322e-03±6.613e-04 | -0.112±0.061 | 0.416±0.031 | -1.049±0.074 |
| IAUS 306 40 | r | 617.0 | b | -21.305±0.080 | 1.334e-03±1.844e-04 | -1.470±0.060 | 0.580±0.050 | 2.740±0.250 |
| IAUS 306 40 | r | 617.0 | r | -21.345±0.070 | 2.428e-03±2.796e-04 | -0.710±0.140 | 0.790±0.100 | 1.140±0.250 |
| A&A 508 1217 | B | 435.0 | b | -19.961±0.600 | 4.527e-03±3.120e-03 | -1.143±0.360 | ||
| A&A 508 1217 | B | 435.0 | r | -20.500±0.560 | 3.634e-03±1.323e-03 | -0.618±0.410 | ||
| ApJ 647 853 | B | 435.0 | b | -20.113±0.015 | 3.905e-03±3.820e-05 | -1.300±0.500 | 1.232±0.017 | -0.456±0.012 |
| ApJ 647 853 | B | 435.0 | r | -20.799±0.023 | 2.220e-03±4.020e-05 | -0.500±0.500 | 0.459±0.027 | -0.900±0.026 |
| ApJ 748 10 | r | 617.0 | b | -20.919±0.120 | 3.958e-03±6.339e-04 | -1.110±0.500 | 1.660±0.090 | -0.380±0.210 |
| ApJ 748 10 | r | 617.0 | r | -21.092±0.070 | 3.184e-03±4.777e-04 | -0.550±0.500 | 1.730±0.070 | -0.950±0.100 |
| ApJ 873 78 | K | 2201.0 | b | -22.572±0.023 | 2.339e-03±2.090e-05 | -1.200±0.500 | 0.601±0.029 | -0.652±0.014 |
| ApJ 873 78 | K | 2201.0 | r | -22.792±0.019 | 2.906e-03±5.670e-05 | -0.500±0.500 | 0.192±0.022 | -0.459±0.029 |
| ApJ 889 80 | IR | 504000.0 | b | -20.774±0.304 | 9.528e-04±3.281e-04 | -0.540±0.241 | 0.336±0.125 | 0.046±0.156 |
| ApJ 889 80 | IR | 504000.0 | r | -20.774±0.304 | 6.352e-04±2.187e-04 | -0.540±0.241 | 0.336±0.125 | 0.046±0.156 |
| MNRAS 494 1894 | FUV | 154.6 | b | -18.329±0.120 | 5.861e-03±1.376e-03 | -1.391±0.080 | 0.886±0.008 | -0.405±0.010 |
| MNRAS 494 1894 | NUV | 234.5 | b | -18.475±0.090 | 6.067e-03±1.305e-03 | -1.367±0.060 | 0.975±0.006 | -0.419±0.008 |
Notes
Where applicable, relevant information from each literature reference used to calculate the quoted values in the above table is given below.
- In all cases, quoted uncertainties are statistical. These are inflated by adding 5% relative uncertainty and (0, 0.001, 0.1, 0.1, 0.01) systematic uncertainty to (\(M^*_0\), \(\phi^*_0\), \(Q\), \(P\), \(\alpha\)) respectively during the parameterisation fitting process.
Loveday et al. (2012, MNRAS, 420, 1239)
- Table 5
- Conversion from units of \(h^3\,\mathrm{Mpc}^{-3}\) and \(M^* - 5\log_{10}(h)\) using \(h=0.7\)
- \(M^*_0\) translated from \(z_0 = 0.1\) to \(z=0\)
- Colour cut between “blue” and “red” galaxies (equation 3)
Loveday et al. (2015, MNRAS, 451, 1540)
- Tables 3 and 4, Mean Probability Petrosian
- Conversion from units of \(h^3\,\mathrm{Mpc}^{-3}\) and \(M^* - 5\log_{10}(h)\) using \(h=0.7\)
- \(M^*_0\) translated from \(z_0 = 0.1\) to \(z=0\)
- Colour cut between “blue” and “red” galaxies (equation 2)
Kelvin et al. (2014, MNRAS, 439, 1245)
- Table 9
- \(H_0 = 70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{kpc}\) gives \(h=1\) so no conversion of values necessary
- Classification on morphological grounds into spheroid- and disc-dominated primarily
Lin et al. (1999, ApJ, 518, 533)
- Tables 1 and 2, \(Q_0 = 0.5\)
- Conversion from units of \(h^3\,\mathrm{Mpc}^{-3}\) and \(M^* - 5\log_{10}(h)\) using \(h=0.7\)
- \(M^*_0\) translated from \(z_0 = 0.3\) to \(z=0\)
- Classification by “SED type” to early and late
Dai et al. (2009, ApJ, 697, 506)
- Table 2, using “early” and “late” type
- Conversion from units of \(h^3\,\mathrm{Mpc}^{-3}\) and \(M^* - 5\log_{10}(h)\) using \(h=0.7\)
- \(M^*_0\) translated from \(z_0 = 0.25\) to \(z=0\)
- \(P\) and \(Q\) not used in fitting \(P(\log_{10}(\lambda / \mu\mathrm{m}))\) or \(Q(P)\), but has its \(Q\) values represented in Figure 1 of Wilson (2022, RNAAS, …) at \(P = 0\), the value fixed during the derivation for these parameters
- \(M^*\) quoted in the Vega magnitude system, so for self-consistency had its values converted to the AB system using table 4.2, IRAC instrument handbook
- Galaxy classification based on SED fitting, with assignment to “early” type if fit good enough, else “late” are “not early” type objects
Kochanek et al. (2001, ApJ 560 566)
- Table 3
- Conversion from units of \(h^3\,\mathrm{Mpc}^{-3}\) and \(M^* - 5\log_{10}(h)\) using \(h=0.7\)
- \(M^*\) quoted in the Vega magnitude system, so for self-consistency had its values converted to the AB system using the Cohen et al. (2003, AJ, 126, 1090) values
- Early-late type split based on \(T\)-type
Driver et al. (2012, MNRAS, 427, 3244)
- Tables 5 and 6
- Conversion from units of \(M^* - 5\log_{10}(h)\) using \(h=0.7\)
- Split by visual inspection and combined Sersic index, colour cut selection; elliptical vs not-elliptical classification
- Due to an apparent bias towards assigning objects as “blue” galaxies, do not use \(\phi^*\) values; if the values of \(\phi^*\) were used, units are \((0.5\,\mathrm{mag})^{-1}\) and hence would need correcting by a factor two
Mortlock et al. (2017, MNRAS, 465, 672)
- Table 4
- Conversion from units of \(h^3\,\mathrm{Mpc}^{-3}\) and \(M^* - 5\log_{10}(h)\) using \(h=0.7\)
- Parameters quoted as \(M^*\), \(\phi^*\), \(\alpha\) for various \(z\) values; linear slopes fit for using the original bin values
- Both sets of parameters have significant correlation and hence overall uncertainties underestimated, statistical uncertainty padded from least-squared fit quoted values
- No distinction between red and blue, just a simultaneous double Schechter function fit
Arnouts et al. (2007, A&A, 476, 137)
- Table 1
- Conversion from units of \(h^3\,\mathrm{Mpc}^{-3}\) and \(M^* - 5\log_{10}(h)\) using \(h=0.7\)
- Parameters quoted as \(M^*\), \(\phi^*\), \(\alpha\) for various \(z\) values; linear slopes fit for using the original bin values
- Red parameters have significant correlation and hence overall uncertainties underestimated, statistical uncertainty padded from least-squared fit quoted values
- Red/quiescent vs blue/active galaxy split by colour bimodality and SED fitting, ultimately decided by SED fitting
Cirasuolo et al. (2007, MNRAS, 380, 585)
- Table 2
- Conversion from units of \(h^3\,\mathrm{Mpc}^{-3}\) and \(M^* - 5\log_{10}(h)\) using \(h=0.7\)
- Parameters quoted as \(M^*\), \(\phi^*\), \(\alpha\) for various \(z\) values; linear slopes fit for using the original bin values
- “Red” and “blue” galaxies split by a colour cut (equation 2)
Loveday (2014, IAUS, 306, 40)
- Table 1
- Conversion from units of \(h^3\,\mathrm{Mpc}^{-3}\) and \(M^* - 5\log_{10}(h)\) using \(h=0.7\)
- Uncertainties in \(P\) and \(Q\) estimated by eye from two-dimensional \(\chi^2\) contours
- Unspecified blue-red galaxy split, likely from the GAMA-II sample, Driver et al. (2011, MNRAS, 413, 971)
Zucca et al. (2009, A&A, 508, 1217)
- Table 1, “early” and “spiral” morphology types
- \(H_0 = 70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{kpc}\) gives \(h_{70}=1\) so no conversion of values necessary
- Parameters quoted as \(M^*\), \(\phi^*\), \(\alpha\) for various \(z\) values; linear slopes fit for using the original bin values
- Both red and blue parameters have significant correlation and hence overall uncertainties underestimated, statistical uncertainty padded from least-squared fit quoted values
- Galaxy split done by spectrophotometric class through \(\chi^2\) fitting
Willmer et al. (2006, ApJ, 647, 853)
- Tables 4 and 5, “minimal” weights
- \(H_0 = 70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{kpc}\) gives \(h=1\) so no conversion of values necessary
- Uncertainties on \(\alpha\) set manually due to fixed value
- Parameters quoted as \(M^*\), \(\phi^*\), \(\alpha\) for various \(z\) values; linear slopes fit for using the original bin values
- “Red” and “blue” galaxies split by a colour cut (equation 19)
Cool et al. (2012, ApJ, 748, 10)
- Tables 4 and 5
- Conversion from units of \(h^3\,\mathrm{Mpc}^{-3}\) and \(M^* - 5\log_{10}(h)\) using \(h=0.7\)
- \(M^*_0\)translated from \(z_0 = 0.1\) to \(z=0\)
- Uncertainties on \(\alpha\) set manually due to fixed value
- “Red” and “blue” galaxies split by a colour cut (equation 3)
Beare et al. (2019, ApJ, 873, 78)
- Table 4
- \(H_0 = 70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{kpc}\) gives \(h_{70}=1\) so no conversion of values necessary
- Uncertainties on \(\alpha\) set manually due to fixed value
- Parameters quoted as \(M^*\), \(\phi^*\), \(\alpha\) for various \(z\) values; linear slopes fit for using the original bin values
- Quiescent and star-forming galaxies divided by a colour cut (equation 6)
Lim et al. (2020, ApJ, 889, 80)
- Table 9, non-fixed faint-end slope
- Single Schechter slope, but split 60%-40% blue-red galaxies in \(\phi^*\)
- Parameters quoted as \(\log_{10}(L^*/L_\odot)\), \(\phi^*\), \(\alpha\) for various \(z\) values; linear slopes fit for using the original bin values
- Conversion from “IR” luminosity \(\log_{10}(L*/L_\odot)\) in 8-1000\(\mu\,\mathrm{m}\) “bandpass” to absolute AB magnitudes using the Solar spectrum from \(\texttt{calspec}\); value not used in derivation of \(M^*_0(\log_{10}(\lambda / \mu\mathrm{m}))\) but presented for reference in the sub-mm wavelength range
Moutard et al. (2020, MNRAS, 494, 1894)
- Table 2
- \(H_0 = 70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{kpc}\) gives \(h=1\) so no conversion of values necessary
- Assume all galaxies are blue in the UV bands where single Schechter functions are fit; U-band is a simple simultaneous fit with no dataset splitting
- Parameters quoted as \(M^*\), \(\phi^*\), \(\alpha\) for various \(z\) values; linear slopes fit for using the original bin values
- Only take the UV bands due to abnormal red galaxy \(\phi\) normalisation values in double Schechter U-band parameterisation
Page updated October 2024