Source code for pyspeckit.spectrum.models.hydrogen

# -*- coding: latin-1 -*-
"""
Hydrogen Models
---------------

Hydrogen in HII regions is typically assumed to follow Case B recombination
theory.

The values for the Case B recombination coefficients are given by `Hummer &
Storey (1987)
<http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1987MNRAS.224..801H&db_key=AST>`_.
They are also computed in `Hummer (1994)
<http://adsabs.harvard.edu/abs/1994MNRAS.268..109H>`_ and tabulated at a `wiki
<http://wiki.hmet.net/index.php/HII_Case_B_Recombination_Coefficients>`_.  I
had to OCR and pull out by hand some of the coefficients.

.. Hummer & Storey 1987: Recombination-line intensities for hydrogenic ions.  I - Case B calculations for H I and He II


However, Storey & Hummer 1995 might be a better resource now?
https://cdsarc.unistra.fr/viz-bin/cat/VI/64


Module API
^^^^^^^^^^

"""
import numpy as np
from six import iteritems
from . import model
from .. import units

# log(temperature), alphaBalphaB = [[1.0,9.283],
alphaB=[[1.2,8.823],
    [1.4,8.361],
    [1.6,7.898],
    [1.8,7.435],
    [2.0,6.973],
    [2.2,6.512],
    [2.4,6.054],
    [2.6,5.599],
    [2.8,5.147],
    [3.0,4.700],
    [3.2,4.258],
    [3.4,3.823],
    [3.6,3.397],
    [3.8,2.983],
    [4.0,2.584],
    [4.2,2.204],
    [4.4,1.847],
    [4.6,1.520],
    [4.8,1.226],
    [5.0,0.9696],
    [5.2,0.7514],
    [5.4,0.5710],
    [5.6,0.4257],
    [5.8,0.3117],
    [6.0,0.2244],
    [6.2,0.1590],
    [6.4,0.1110],
    [6.6,0.07642],
    [6.8,0.05199],
    [7.0,0.03498]]

# beta is 946 / H 03b2 / oct 1662


# the command to make this:
# %s/\v.*\n?([0-9]\.[0-9]+).*jH(.+\n?|[^β]\n?[0-9]\.[0-9]+) ?([0-9]\.[0-9]+) ([0-9]\.[0-9]+) ([0-9]\.[0-9]+)/[\1, \3, \4, \5]\r/
# from this:
# http://www.scribd.com/doc/70881169/Physics-of-the-Interstellar-and-Intergalactic-Medium
# with some by-hand editing too
# vacuum wavelengths computed by:
#  [(ii,1.0/10973731.6 * 1./(1/2.**2 - 1/float(ii)**2) * 1e6 * (1+1/1836.15266) ) for ii in range(10,20)]

# Table 14.2 in Draine 2001
temperatures = {5000:0,10000:1,20000:2}
table14dot2 = {
#Balmer-line intensities relative to Hβ 0.48627 µm
'balmer':[["a" ,0.65646, 3.03, 2.86, 2.74],
          ["b" ,0.48627, 1., 1., 1.,],
          ["g" ,0.43418, 0.459, 0.469, 0.475],
          ["d" ,0.41030, 0.252, 0.259, 0.264],
          ["e" ,0.39713, 0.154, 0.159, 0.163],
          ["8" ,0.38902, 0.102, 0.105, 0.106],
          ["9" ,0.38365, 0.0711, 0.0732, 0.0746],
          ["10",0.37990, 0.0517, 0.0531, 0.0540],
          ["11",0.377174, 0.0000, 0.0398, 0.0000],
          ["12",0.375125, 0.0000, 0.0306, 0.0000],
          ["13",0.373547, 0.0000, 0.0240, 0.0000],
          ["14",0.372303, 0.0000, 0.0193, 0.0000],
          ["15",0.371306, 0.0000, 0.0157, 0.0000],
          ["16",0.370494, 0.0000, 0.0130, 0.0000],
          ["17",0.369824, 0.0000, 0.0108, 0.0000],
          ["18",0.369264, 0.0000, 0.00918, 0.0000],
          ["19",0.368792, 0.0000, 0.00785, 0.0000],
          ["20",0.368389,0.0000,0.006790,0.0000] ,
          ["21",0.368044,0.0000,0.005920,0.0000] ,
          ["22",0.367745,0.0000,0.005210,0.0000] ,
          ["23",0.367484,0.0000,0.004610,0.0000] ,
          ["24",0.367256,0.0000,0.004120,0.0000] ,
          ["25",0.367054,0.0000,0.003700,0.0000] ,
          ["26",0.366876,0.0000,0.003350,0.0000] ,
          ["27",0.366718,0.0000,0.003040,0.0000] ,
          ["28",0.366576,0.0000,0.002780,0.0000] ,
          ["29",0.366448,0.0000,0.002550,0.0000] ,
          ["30",0.366333,0.0000,0.002350,0.0000] ,
          ["31",0.366230,0.0000,0.001650,0.0000] ,
          ["32",0.366136,0.0000,0.001220,0.0000] ,
          ["33",0.366050,0.0000,0.000919,0.0000] ,
          ["34",0.365972,0.0000,0.000708,0.0000]],

#Paschen (n→3) line intensities relative to corresponding Balmer lines
'paschen':[["a", 1.8756, 0.405, 0.336, 0.283],
           ["b", 1.2821, 0.399, 0.347, 0.305],
           ["g", 1.0941, 0.391, 0.348, 0.311],
           ["d", 1.0052, 0.386, 0.348, 0.314],
           ["e", 0.95487, 0.382, 0.348, 0.316],
           ["9", 0.92317, 0.380, 0.347, 0.317],
           ["10",0.90175, 0.380, 0.347, 0.317]],


#Brackett (n→4) line intensities relative to corresponding Balmer lines
'brackett':[["a", 4.0523, 0.223, 0.169, 0.131],
            ["b", 2.6259, 0.219, 0.174, 0.141],
            ["g", 2.1661, 0.212, 0.174, 0.144],
            ["d", 1.9451, 0.208, 0.173, 0.145],
            ["e", 1.8179, 0.204, 0.173, 0.146],
            ["10",1.7367, 0.202, 0.172, 0.146]],

#Pfundt (n→5) line intensities relative to corresponding Balmer lines
'pfundt':[["d", 7.4599, 0.134, 0.0969, 0.0719],
          ["e", 4.6538, 0.134, 0.101, 0.0774] ,
          ["8", 3.7406, 0.130, 0.101, 0.0790] ,
          ["9", 3.2970, 0.127, 0.100, 0.0797] ,
          ["10",3.0392, 0.125, 0.0997, 0.0801],
          ["11",2.873004,0.00, 0.084171, 0.0000],
          ["12",2.758276,0.00, 0.098693, 0.0000],
          ["13",2.675139,0.00, 0.098333, 0.0000],
          ["14",2.612655,0.00, 0.097927, 0.0000],
          ["15",2.564334,0.00, 0.097452, 0.0000],
          ["16",2.526098,0.00, 0.096923, 0.0000],
          ["17",2.495261,0.00, 0.097222, 0.0000],
          ["18",2.469994,0.00, 0.096187, 0.0000],
          ["19",2.449007,0.00, 0.095541, 0.0000],
          ["20",2.431369,0.00, 0.094551, 0.0000],
          ["21",2.416392,0.00, 0.093750, 0.0000],
          ["22",2.403559,0.00, 0.092514, 0.0000],
          ["23",2.392474,0.00, 0.091540, 0.0000],
          ["24",2.382830,0.00, 0.075728, 0.0000],
          ["25",2.374384,0.00, 0.083784, 0.0000],
          ["26",2.366943,0.00, 0.087761, 0.0000],
          ["27",2.360353,0.00, 0.086513, 0.0000],
          ["28",2.354488,0.00, 0.083094, 0.0000],
          ["29",2.349243,0.00, 0.083922, 0.0000],
          ["30",2.344534,0.00, 0.082979, 0.0000],
          ["31",2.340290,0.00, 0.077576, 0.0000],
          ["32",2.336451,0.00, 0.073197, 0.0000],
          ["33",2.332966,0.00, 0.071055, 0.0000],
          ["34",2.329793,0.00, 0.069774, 0.0000]],


#Humphreys (n→6) line intensities relative to corresponding Balmer lines
'humphreys':[["e", 6.12372, 0.0855, 0.0601, 0.0435],
             ["8", 7.5026, 0.0867, 0.0632, 0.0471],
             ["9", 5.9083, 0.0850, 0.0634, 0.0481],
             ["10",5.1287, 0.0833, 0.0632, 0.0486]]
}

r_to_hbeta = {}
wavelength = {}

for line in table14dot2['balmer']:
    r_to_hbeta["balmer"+line[0]] = np.array(line[2:])
    wavelength["balmer"+line[0]] = line[1]

for series,values in iteritems(table14dot2):
    if series == 'balmer':
        continue
    for line in values:
        r_to_hbeta[series+line[0]] = np.array(line[2:]) * r_to_hbeta['balmer'+line[0]]
        wavelength[series+line[0]] = line[1]


# not used right now, but it could be so I'm listing it here
[docs]def rrl(n,dn=1,amu=1.007825,Z=1): """ compute Radio Recomb Line freqs in GHz from Brown, Lockman & Knapp ARAA 1978 16 445 UPDATED: Gordon & Sorochenko 2009, eqn A6 Parameters ---------- n : int The number of the lower level of the recombination line (H1a is Lyman alpha, for example) dn : int The delta-N of the transition. alpha=1, beta=2, etc. amu : float The mass of the central atom Z : int The ionization parameter for the atom. Z=1 is neutral, Z=2 is singly ionized, etc. For hydrogen, only z=1 makes sense, since ionized hydrogen has no electrons and therefore cannot have recombination lines. Returns ------- frequency in GHz """ nu = 3.289842e6*(1-5.48593e-4/amu)*(1/float(n)**2 - 1/float(n+dn)**2) nu = 3.28984196e6 * Z**2 * (amu-5.48579911e-4*(Z+1))/(amu-5.48579911e-4*Z) * (1/float(n)**2 - 1/float(n+dn)**2) return nu
[docs]def find_lines(xarr): """ Given a :class:`pyspeckit.units.SpectrosopicAxis` instance, finds all the lines that are in bounds. Returns a list of line names. """ return [linename for (linename, lam) in iteritems(wavelength) if xarr.as_unit('micron').in_range(lam)]
[docs]def hydrogen_fitter(sp, temperature=10000, tiedwidth=False): """ Generate a set of parameters identifying the hydrogen lines in your spectrum. These come in groups of 3 assuming you're fitting a gaussian to each. You can tie the widths or choose not to. *temperature* [ 5000, 10000, 20000 ] The case B coefficients are computed for 3 temperatures *tiedwidth* [ bool ] Should the widths be tied? Returns a list of `tied` and `guesses` in the xarr's units """ tnum = temperatures[temperature] lines = find_lines(sp.xarr) reference_line = lines[0] subtied = [ ['p[0]*%f' % (r_to_hbeta[line][tnum]/r_to_hbeta[reference_line][tnum]), 'p[1]+%f' % (wavelength[line]-wavelength[reference_line]), 'p[2]' if tiedwidth else ''] for line in lines[1:]] tied = ['','',''] + [t for sublist in subtied for t in sublist] dx = np.median(sp.xarr.dxarr) subguesses = [[sp.data[sp.xarr.as_unit('micron').x_to_pix(wavelength[line])], sp.xarr.x_to_coord(wavelength[line], 'micron'), dx*2.0] for line in lines] guesses = [g for sublist in subguesses for g in sublist] return tied, guesses
[docs]def hydrogen_model(xarr, amplitude=1.0, width=0.0, velocity=0.0, a_k=0.0, temperature=10000): """ Generate a set of parameters identifying the hydrogen lines in your spectrum. These come in groups of 3 assuming you're fitting a gaussian to each. You can tie the widths or choose not to. Parameters ---------- sp : pyspeckit.Spectrum The spectrum to fit temperature : [ 5000, 10000, 20000 ] The case B coefficients are computed for 3 temperatures a_k : float The K-band extinction normalized to 2.2 microns. Simple exponential. width : float Line width in km/s velocity : float Line center in km/s amplitude : float arbitrary amplitude of the first line (all other lines will be scaled to this value) Returns ------- np.ndarray with same shape as sp.xarr """ tnum = temperatures[temperature] lines = find_lines(xarr) reference_line = lines[0] model = np.array(xarr * 0) xarr = xarr.as_unit('micron') lw = width / units.speedoflight_kms * wavelength[reference_line] center = wavelength[reference_line] model += amplitude * np.exp(-(xarr-center)**2 / (2.0*lw)**2) for line in lines[1:]: relamp = (r_to_hbeta[line][tnum]/r_to_hbeta[reference_line][tnum]) lw = width / units.speedoflight_kms * wavelength[line] center = wavelength[line] model += amplitude * relamp * np.exp(-(xarr-center)**2 / (2.0*lw)**2) if a_k > 0: # alpha=1.8 comes from Martin & Whittet 1990. alpha=1.75 from Rieke and Lebofsky 1985 Al = a_k * (xarr/2.2)**(-1.75) model *= np.exp(-Al) return model
[docs]def add_to_registry(sp): """ Add the Hydrogen model to the Spectrum's fitter registry """ # can't have absorption in recombination case extincted_hydrogen_emission = model.SpectralModel(hydrogen_model, 4, shortvarnames=('A','\\sigma','\\Delta x','A_K'), parnames=['amplitude','width','velocity','extinction'], parlimited=[(True,False),(True,False),(False,False), (True,False)], parlimits=[(0,0), (0,0), (0,0), (0,0)], fitunit='micron') sp.Registry.add_fitter('hydrogen', extincted_hydrogen_emission, extincted_hydrogen_emission.npars)