def dust_cont_integrate(dust_mass, dust_temp, dust_beta): """ Integrate over the IR spectral energy distribution. Calculate SFR based on Kennicut relation. Prints output to console. :param dust_mass: in kg :param dust_temp: in K :param dust_beta: dimensionless :return: """ # Total IR is 8 - 1000 microns lum_tir = integrate.quad( lambda x: dust_lum(x, dust_mass, dust_temp, dust_beta), c / (1000e-6), c / (8e-6)) print("Ltir (10^12 Lsol) = ", sigfig(lum_tir[0] * u.W.to(u.solLum) * 1e-12, 3)) # Far IR is 42.5 - 122.5 microns lum_fir = integrate.quad( lambda x: dust_lum(x, dust_mass, dust_temp, dust_beta), c / (122.5e-6), c / (42.5e-6)) print("Lfir (10^12 Lsol) =", sigfig(lum_fir[0] * u.W.to(u.solLum) * 1e-12, 3)) # Kennicutt+98 relation scaled to Chabrier IMF print("SFR_Kennicutt98 (Msol/yr)", sigfig(lum_tir[0] * u.W.to(u.solLum) * 1e-10, 3)) # print("SFR", Ltir[0]*4.5e-37/1.7) # Salpeter to Chabrier is a facotr of 1.7 # Kennicutt+12 relation scaled to Chabrier IMF print( "SFR_Kennicutt12 (Msol/yr)", sigfig(10**(np.log10(lum_tir[0] * u.W.to(u.erg / u.s)) - 43.41) / 1.7, 3))
def spectrum_aperture_paper(): """ Compute residual corrected spectrum. Fit a Gaussian plus a continuum. Generate paper quality plot. """ filename = "./data/Pisco.cube.50kms.image.fits" ra, dec = (205.533741, 9.477317341) # [degrees] we know where the source is radius = 1.3 # [arcsec] we know the size of the aperture we want scale = 1e3 # map units are Jy/beam, will use to scale fluxes to mJy # load the cube and perform residual scaling spectrum extraction mcub = MultiCube(filename) # because the cubes follow a naming convention, will open several present cubes spectrum, err, tab = mcub.spectrum_corrected(ra=ra, dec=dec, radius=radius, calc_error=True) freqs = mcub.freqs # this will be the x-axis # fit the spectrum with a Gaussian on top of a constant continuum, initial fit parameters (p0) must be set manually popt, pcov = curve_fit(iftools.gausscont, freqs, spectrum, p0=(1, 5, 222.5, 0.2), sigma=err, absolute_sigma=True) cont, amp, nu, sigma = popt cont_err, amp_err, nu_err, sigma_err = np.sqrt(np.diagonal(pcov)) # compute some further numbers from the fit sigma_kms = iftools.ghz2kms(sigma, nu) fwhm_kms = iftools.sig2fwhm(sigma_kms) fwhm_err_kms = iftools.sig2fwhm(iftools.ghz2kms(sigma_err, nu)) integral_fit = amp * sigma_kms * np.sqrt(2 * np.pi) integral_err = integral_fit * np.sqrt((sigma_err / sigma) ** 2 + (nu_err / nu) ** 2 + (amp_err / amp) ** 2) txt = "[CII] Flux = " + str(iftools.sigfig(integral_fit, 2)) \ + r" $\pm$ " + str(iftools.sigfig(integral_err, 1)) + " Jy km/s\n" \ + "[CII] FWHM = " + str(iftools.sigfig(int(fwhm_kms), 2)) \ + r" $\pm$ " + str(iftools.sigfig(int(fwhm_err_kms), 1)) + " km/s\n" \ + "Freq = " + str(iftools.sigfig(nu, 6)) \ + r" $\pm$ " + str(iftools.sigfig(nu_err, 1)) + " GHz\n" \ + "Continuum = " + str(iftools.sigfig(cont * scale, 2)) \ + r" $\pm$ " + str(iftools.sigfig(cont_err * scale, 1)) + " mJy\n" # print("Gaussian fit:") # print("Flux = " + str(iftools.sigfig(integral_fit, 2)) + " +- " + str(iftools.sigfig(integral_err, 1)) + " Jy.km/s") # print("FWHM = " + str(iftools.sigfig(fwhm_kms, 2)) + " +- " + str(iftools.sigfig(fwhm_err_kms, 1)) + " km/s") # print("Freq = " + str(iftools.sigfig(nu, 7)) + " +- " + str(iftools.sigfig(nu_err, 1)) + " GHz") # plot the spectrum, fill around the fitted continuum value fig, ax = plt.subplots(figsize=(4.8, 3)) ax.plot(freqs, spectrum * scale, color="black", drawstyle='steps-mid', lw=0.75) ax.fill_between(freqs, spectrum * scale, cont * scale, color="skyblue", step='mid', lw=0, alpha=0.3) ax.text(0.98, 0.95, txt, va='top', ha='right', transform=ax.transAxes) # Plot the uncorrected specturum as well # ax.plot(freqs, tab["flux_image"] * scale, color="black", drawstyle='steps-mid', lw=0.5, ls="--") # plot Gaussian fit x_gauss = np.linspace(freqs[0], freqs[-1], 1000) y_gauss = iftools.gausscont(x_gauss, *popt) ax.plot(x_gauss, y_gauss * scale, color="firebrick") # add velocity axis based around the fitted peak vels = mcub.cubes["image"].vels(nu) ax2 = ax.twiny() # match ranges of the two axes ax.set_xlim(freqs[0], freqs[-1]) ax2.set_xlim(vels[0], vels[-1]) # add axis labels ax.tick_params(direction='in', which="both") ax.set_xlabel("Frequency (GHz)") ax.set_ylabel("Aperture flux density (mJy)") ax2.tick_params(direction='in', which="both") ax2.set_xlabel(r"Velocity (km s$^{-1}$)") # add the zero line ax.axhline(0, color="gray", lw=0.5, ls=":") plt.savefig("./plots/spectrum_aperture_paper.pdf", bbox_inches="tight") # save plot plt.savefig("./thumbnails/spectrum_aperture_paper.png", bbox_inches="tight", dpi=72) # web raster version plt.show()
def dust_cont_fit(): """ Fit a modified black body dust continuum emission to observed flux density data points. File for input flux densities, redshift, and exact fitting method are currently hardcoded. Uses dust_sobs, which takes cmb heating and contrast into account by default. :return: """ # Points to fit, inputs need so to be in SI units t = Table.read("./data/Pisco_continuum_fluxes.txt", format="ascii.commented_header") freqs = t["freq_ghz"] * 1e9 # to Hz fluxes = t["flux_jy"] * 1e-26 # to W/Hz/m2 fluxes_err = t["flux_err_jy"] * 1e-26 # to W/Hz/m2 # Parameters for the black body emission # These are either fixed, or used as intial guess for fitting if chosen to be free parameters z = 7.5413 # redshift dust_mass = 1e37 # in kilograms dust_temp = 47 # T_dust in Kelvins dust_beta = 1.9 # modified black body exponent dust_mass_err = 0 dust_temp_err = 0 dust_beta_err = 0 # several fitting scenarios, choose one # lambdas are used to set non-free parameters, because curve_fit wants only the variable and free params # Parameters are degenerate, so be careful with error interpretation # Fit Mdust only - this could be used if you only have a single point, for example if 0: popt, pcov = curve_fit(lambda freqs, dust_mass: dust_sobs( freqs, z, dust_mass, dust_temp, dust_beta), freqs, fluxes, p0=(dust_mass), sigma=fluxes_err, absolute_sigma=True) dust_mass = popt[0] dust_mass_err = np.diagonal(pcov)[0] # Fit Mdust and T - to constrain the temperature, the black body peak needs to be sampled if 0: popt, pcov = curve_fit(lambda freqs, dust_mass, dust_temp: dust_sobs( freqs, z, dust_mass, dust_temp, dust_beta), freqs, fluxes, p0=(dust_mass, dust_temp), sigma=fluxes_err, absolute_sigma=True) dust_mass, dust_temp = popt dust_mass_err, dust_temp_err = np.sqrt(np.diagonal(pcov)) # Fit Mdust and beta - the best option on the Rayleigh-Jeans tail if 1: popt, pcov = curve_fit(lambda freqs, dust_mass, dust_beta: dust_sobs( freqs, z, dust_mass, dust_temp, dust_beta), freqs, fluxes, p0=(dust_mass, dust_beta), sigma=fluxes_err, absolute_sigma=True) dust_mass, dust_beta = popt dust_mass_err, dust_beta_err = np.sqrt(np.diagonal(pcov)) # Fit Mdust and T and beta - not recommended due to degeneracy if 0: popt, pcov = curve_fit( lambda freqs, dust_mass, dust_temp, dust_beta: dust_sobs( freqs, z, dust_mass, dust_temp, dust_beta), freqs, fluxes, p0=(dust_mass, dust_temp, dust_beta), sigma=fluxes_err, absolute_sigma=True) dust_mass, dust_temp, dust_beta = popt dust_mass_err, dust_temp_err, dust_beta_err = np.sqrt( np.diagonal(pcov)) print("dust_mass (10^8 Msol) = ", sigfig(dust_mass * u.kg.to(u.solMass) * 1e-8, 3), " +- ", sigfig(dust_mass_err * u.kg.to(u.solMass) * 1e-8, 1)) print("dust_temp (K) = ", sigfig(dust_temp, 3), " +- ", sigfig(dust_temp_err, 1)) print("dust_beta = ", sigfig(dust_beta, 3), " +- ", sigfig(dust_beta_err, 1)) return dust_mass, dust_temp, dust_beta