Column Densities with AbsComponent

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%matplotlib inline

# suppress warnings for these examples
import warnings
warnings.filterwarnings('ignore')

# imports
try:
    import seaborn as sns; sns.set(context="notebook",font_scale=2)
except:
    pass

from scipy import integrate
import astropy.units as u

from linetools.isgm import abscomponent as lt_abscomp
from linetools.spectralline import AbsLine
from linetools.spectra.xspectrum1d import XSpectrum1D
#
import imp
lt_path = imp.find_module('linetools')[1]

Read Spec

xspec = XSpectrum1D.from_file(lt_path+'/spectra/tests/files/UM184_nF.fits')

Generate a few AbsLines

SiIItrans = ['SiII 1260', 'SiII 1304', 'SiII 1526', 'SiII 1808']

abslines = []
for trans in SiIItrans:
    iline = AbsLine(trans)
    iline.attrib['z'] = 2.92939
    iline.analy['vlim'] = [-250.,80.]*u.km/u.s
    iline.analy['spec'] = xspec
    abslines.append(iline)
#
abslines

[<AbsLine: SiII 1260, wrest=1260.4221 Angstrom>,
 <AbsLine: SiII 1304, wrest=1304.3702 Angstrom>,
 <AbsLine: SiII 1526, wrest=1526.7070 Angstrom>,
 <AbsLine: SiII 1808, wrest=1808.0129 Angstrom>]

Generate the Component

abscomp = lt_abscomp.AbsComponent.from_abslines(abslines)

try:
    sns.set(context="notebook",font_scale=2)
except:
    pass
abscomp.stack_plot()

---

Synthesize/Measure AODM Column Densities

abscomp.synthesize_colm(redo_aodm=True)

abscomp.logN

13.594445560856554

for iline in abscomp._abslines:
    print(iline.wrest, iline.attrib['flag_N'], iline.attrib['logN'], iline.attrib['sig_logN'])

1260.4221 Angstrom 1 13.5883729709 0.0150745701489
1304.3702 Angstrom 1 13.7708705955 0.0862006463782
1526.707 Angstrom 1 13.6707360009 0.0640855113383
1808.0129 Angstrom 3 0.0 0.50976387151

---

Apparent Column Density Plot

abscomp.plot_Na()

---

COG

\(F(\tau_0)\)

Definition \(F(\tau_0) = \int_0^\infty dx \, [1- \rm e^{-\tau_0 \rm e^{-x^2}}]\)

def ftau_intgrnd(x,tau0=0.1):
    return 1 - np.exp(-tau0 * np.exp(-x**2))

neval = 10000
lgt = np.linspace(-3, 9, neval)
all_tau0 = 10.**lgt
Ftau = np.zeros(neval)
for jj,tau0 in enumerate(all_tau0):
    Ftau[jj], ferr = integrate.quad(ftau_intgrnd, 0, np.inf, args=(tau0,))

# Damped limit (not accurate enough)
damp_lgt = np.linspace(6, 10, 100)
damp_tau0 = 10.**damp_lgt
damp_Ftau = np.sqrt(np.log(damp_tau0))

import matplotlib.pyplot as plt
plt.plot(lgt, Ftau, damp_lgt, 1.015*damp_Ftau)

[<matplotlib.lines.Line2D at 0x10c48b5c0>,
 <matplotlib.lines.Line2D at 0x10c464e10>]

Perform and Plot

abscomp = lt_abscomp.AbsComponent.from_abslines(abslines)
COG_dict = abscomp.cog(redo_EW=True, show_plot=True)

# Output
COG_dict

{'EW': <Quantity [ 0.43129915, 0.06810455, 0.11137664,-0.01950807] Angstrom>,
 'b': <Quantity 49.22868767597288 km / s>,
 'f': array([ 1.18   ,  0.0863 ,  0.127  ,  0.00208]),
 'logN': 13.693355878125537,
 'parm': <single_cog_model(logN=13.693355878125537, b=49.22868767597288)>,
 'redEW': array([  3.42186280e-04,   5.22125891e-05,   7.29522068e-05,
         -1.07897867e-05]),
 'sig_EW': <Quantity [ 0.0129661 , 0.01440996, 0.01686854, 0.02102034] Angstrom>,
 'sig_b': <Quantity 6.356381185059458 km / s>,
 'sig_logN': 0.054323725737309987,
 'wrest': <Quantity [ 1260.4221, 1304.3702, 1526.707 , 1808.0129] Angstrom>}