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