#!/usr/bin/env python3 # # Aaron LI # Created: 2016-06-30 # Updated: 2016-07-04 # # Change logs: # 2016-07-04: # * Fix a bug with wrong variable # * Update radii to unit "kpc" and mass to unit "Msun" # """ Calculate the overdensity profile, and from which to calculate the R_{500} (defined as the radius of the sphere that encloses a mean total mass density of 500 times the critical density at the cluster's redshift) and M_gas_{500}/M_{500} (the enclosed gas/total mass by a sphere of radius R_{500}). References: [1] Ettori et al., 2013, Space Science Review, 177, 119-154 Sample configuration file: ------------------------------------------------------------ ## Configuration for `calc_overdensity.py` ## Date: 2016-06-30 # redshift of the source (critical density) redshift = # gas mass profile m_gas_profile = mass_gas_profile.txt # output total (gravitational) mass profile m_total_profile = mass_total_profile.txt # number of times w.r.t the critical density delta = 1500, 500, 200 # output results in JSON format outfile = overdensity.json # output overdensity profile overdensity_profile = overdensity_profile.txt ------------------------------------------------------------ """ import argparse import json from collections import OrderedDict import numpy as np import scipy.optimize as optimize import astropy.units as au from astropy.cosmology import FlatLambdaCDM from configobj import ConfigObj import rpy2.robjects as ro from rpy2.robjects.packages import importr from astro_params import AstroParams class MassProfile: """ Cluster's gas/total integrated mass profile. The total/gravitational mass profile is required to calculate the overdensity profile, from which the R_{delta} is then determined. """ # supported types of mass profile MASS_TYPES = ["total", "gas"] # available splines SPLINES = ["mass", "overdensity"] # input mass data: [r, r_err, m] r = None r_err = None m = None # redshift of the object redshift = None # fitted smoothing spline m_spline = None m_spline_log10 = None od_spline = None od_spline_log10 = None # call R through `rpy2` mgcv = importr("mgcv") def __init__(self, mass, mass_type="total"): self.load_data(data=mass, mass_type=mass_type) def load_data(self, data, mass_type="total"): if mass_type not in self.MASS_TYPES: raise ValueError("invalid mass_types: %s" % mass_type) # 3-column mass profile: r[kpc], r_err[kpc], mass[Msun] self.r = data[:, 0].copy() self.r_err = data[:, 1].copy() self.m = data[:, 2].copy() self.mass_type = mass_type def calc_overdensity(self, z, verbose=True): """ Calculate the overdensity profile from the total/gravitational mass profile. The overdensity is the ratio of the enclosed mean total mass density to the critical density at the source's redshift. """ if self.mass_type != "total": raise ValueError("total mass profile is required") # if verbose: print("Calculating the overdensity profile ...") overdensity = np.zeros(self.r.shape) # critical density cosmo = FlatLambdaCDM(H0=AstroParams.H0, Om0=AstroParams.OmegaM0) d_crit = cosmo.critical_density(z).cgs.value # [ g/cm^3 ] for i, r in enumerate(self.r): volume = (4.0/3.0) * np.pi * (r*au.kpc.to(au.cm))**3 mass = self.m[i] * au.solMass.to(au.g) overdensity[i] = mass / volume / d_crit self.overdensity = overdensity return overdensity def calc_radius_delta(self, delta): """ Calculate the radius at which the overdensity is delta. """ if self.od_spline is None: self.fit_spline(spline="overdensity", log10=True) if min(self.overdensity) > delta: raise ValueError("min(overdensity) > %d" % delta) r = optimize.newton( lambda x: self.eval_spline("overdensity", x) - delta, x0=500.0, tol=1e-2) return r def calc_mass_delta(self, r_delta): if self.m_spline is None: self.fit_spline(spline="mass", log10=True) return self.eval_spline(spline="mass", x=r_delta) def save(self, outfile): """ Save calculated overdensity profile. """ data = np.column_stack([self.r, self.r_err, self.overdensity]) header = "radius[kpc] radius_err[kpc] overdensity" np.savetxt(outfile, data, header=header) def fit_spline(self, spline, log10): """ Fit a smoothing line to the specified spline data, by utilizing the R `mgcv::gam()` function. If 'log10' is True, the input data are first applied the log-scale transform, and then fitted by the smoothing spline. The fitted spline allows extrapolation. """ if spline not in self.SPLINES: raise ValueError("invalid spline: %s" % spline) # if spline == "mass": # input gas/total mass profile if log10: x = ro.FloatVector(np.log10(self.r)) y = ro.FloatVector(np.log10(self.m)) self.m_spline_log10 = True else: x = ro.FloatVector(self.r) y = ro.FloatVector(self.m) self.m_spline_log10 = False self.m_spline = self.mgcv.gam( ro.Formula("y ~ s(x, bs='ps')"), data=ro.DataFrame({"x": x, "y": y}), method="REML") elif spline == "overdensity": # calculated overdensity profile if log10: x = ro.FloatVector(np.log10(self.r)) y = ro.FloatVector(np.log10(self.overdensity)) self.od_spline_log10 = True else: x = ro.FloatVector(self.radius) y = ro.FloatVector(self.rho_total) self.od_spline_log10 = False self.od_spline = self.mgcv.gam( ro.Formula("y ~ s(x, bs='ps')"), data=ro.DataFrame({"x": x, "y": y}), method="REML") else: raise ValueError("invalid spline: %s" % spline) def eval_spline(self, spline, x): """ Evaluate the specified spline at the supplied positions. Also check whether the spline was fitted in the log-scale space, and transform the evaluated values if necessary. """ x = np.array(x) if x.shape == (): x = x.reshape((1,)) if spline == "mass": spl = self.m_spline log10 = self.m_spline_log10 elif spline == "overdensity": spl = self.od_spline log10 = self.od_spline_log10 else: raise ValueError("invalid spline: %s" % spline) # if log10: x_new = ro.ListVector({"x": ro.FloatVector(np.log10(x))}) y_pred = self.mgcv.predict_gam(spl, newdata=x_new) y_pred = 10 ** np.array(y_pred) else: x_new = ro.ListVector({"x": ro.FloatVector(x)}) y_pred = self.mgcv.predict_gam(spl, newdata=x_new) y_pred = np.array(y_pred) # if len(y_pred) == 1: return y_pred[0] else: return y_pred def main(): parser = argparse.ArgumentParser( description="Calculate overdensity profile and R_{500} etc.") parser.add_argument("config", nargs="?", default="overdensity.conf", help="config for overdensity profile and R_{500} " + "etc. calculation (default: overdensity.conf)") args = parser.parse_args() config = ConfigObj(args.config) redshift = config.as_float("redshift") m_gas_data = np.loadtxt(config["m_gas_profile"]) m_total_data = np.loadtxt(config["m_total_profile"]) delta = list(map(int, config.as_list("delta"))) m_total_profile = MassProfile(mass=m_total_data, mass_type="total") m_total_profile.calc_overdensity(z=redshift, verbose=True) m_total_profile.save(outfile=config["overdensity_profile"]) m_gas_profile = MassProfile(mass=m_gas_data, mass_type="gas") results = OrderedDict() results["redshift"] = redshift for d in delta: r_delta = m_total_profile.calc_radius_delta(delta=d) m_total_delta = m_total_profile.calc_mass_delta(r_delta) m_gas_delta = m_gas_profile.calc_mass_delta(r_delta) results["R%d[kpc]" % d] = r_delta results["Mtotal%d[Msun]" % d] = m_total_delta results["Mgas%d[Msun]" % d] = m_gas_delta results_json = json.dumps(results, indent=2) print(results_json) open(config["outfile"], "w").write(results_json+"\n") if __name__ == "__main__": main()