Ammonia Models

The Ammonia modeling tools include a set of constants in the ammonia_constants module and the following ammonia modeling tools listed below.

There is also an ammonia fitter wrapper; see Wrappers.

Note that there are two modules described here: the multi-rotational-transition fitter, which has its own set of custom functions, and a generic hyperfine-line fitting module meant to fit a single metastable (or non-metastable) transition.

Ammonia inversion transition TROT fitter translated from Erik Rosolowsky’s http://svn.ok.ubc.ca/svn/signals/nh3fit/

Module API

pyspeckit.spectrum.models.ammonia.ammonia(xarr, trot=20, tex=None, ntot=14, width=1, xoff_v=0.0, fortho=0.0, tau=None, fillingfraction=None, return_tau=False, return_tau_profile=False, background_tb=2.7315, verbose=False, return_components=False, debug=False, line_names=['oneone', 'twotwo', 'threethree', 'fourfour', 'fivefive', 'sixsix', 'sevenseven', 'eighteight', 'ninenine'])

Generate a model Ammonia spectrum based on input temperatures, column, and gaussian parameters

Parameters:

xarr: `pyspeckit.spectrum.units.SpectroscopicAxis`

Array of wavelength/frequency values

trot: float

The rotational temperature of the lines. This is the excitation temperature that governs the relative populations of the rotational states.

tex: float or None

Excitation temperature. Assumed LTE if unspecified (None) or if tex>trot. This is the excitation temperature for all of the modeled lines, which means we are explicitly assuming T_ex is the same for all lines.

ntot: float

Total log column density of NH3. Can be specified as a float in the range 5-25

width: float

Line width in km/s

xoff_v: float

Line offset in km/s

fortho: float

Fraction of NH3 molecules in ortho state. Default assumes all para (fortho=0).

tau: None or float

If tau (optical depth in the 1-1 line) is specified, ntot is NOT fit but is set to a fixed value. The optical depths of the other lines are fixed relative to tau_oneone

fillingfraction: None or float

fillingfraction is an arbitrary scaling factor to apply to the model

return_tau: bool

Return a dictionary of the optical depths in each line instead of a synthetic spectrum

return_tau_profile: bool

Return a dictionary of the optical depth profiles in each line, i.e., the optical depths that will be used in conjunction with T_ex to produce the synthetic spectrum

return_components: bool

Return a list of arrays, one for each hyperfine component, instead of just one array

background_tb : float

The background brightness temperature. Defaults to TCMB.

verbose: bool

More messages

debug: bool

For debugging.

Returns:

spectrum: `numpy.ndarray`

Synthetic spectrum with same shape as xarr

component_list: list

List of numpy.ndarray’s, one for each hyperfine component

tau_dict: dict

Dictionary of optical depth values for the various lines (if return_tau is set)

class pyspeckit.spectrum.models.ammonia.ammonia_model(npeaks=1, npars=6, parnames=['trot', 'tex', 'ntot', 'width', 'xoff_v', 'fortho'], **kwargs)

The basic Ammonia (NH3) model with 6 free parameters:

Trot, Tex, ntot, width, xoff_v, and fortho

Trot is the rotational temperature. It governs the relative populations of the rotational states, i.e., the relative strength of different transitions

Tex is the excitation temperature. It is assumed constant across all states, which is not always a good assumption - a radiative transfer and excitation model is required to constrain this, though.

ntot is the total column density of p-NH3 integrated over all states.

width is the linewidth

xoff_v is the velocity offset / line of sight velocity

fortho is the ortho fraction (northo / (northo+npara))

annotations()

Return a list of TeX-formatted labels

The values and errors are formatted so that only the significant digits are displayed. Rounding is performed using the decimal package.

Parameters:

shortvarnames : list

A list of variable names (tex is allowed) to include in the annotations. Defaults to self.shortvarnames

Examples

>>> # Annotate a Gaussian
>>> sp.specfit.annotate(shortvarnames=['A','\Delta x','\sigma'])

components(xarr, pars, hyperfine=False, return_hyperfine_components=False, **kwargs)

Ammonia components don’t follow the default, since in Galactic astronomy the hyperfine components should be well-separated. If you want to see the individual components overlaid, you’ll need to pass hyperfine to the plot_fit call

moments(Xax, data, negamp=None, veryverbose=False, **kwargs)

Returns a very simple and likely incorrect guess

multinh3fit(xax, data, err=None, parinfo=None, quiet=True, shh=True, debug=False, maxiter=200, use_lmfit=False, veryverbose=False, **kwargs)

Fit multiple nh3 profiles (multiple can be 1)

Parameters:

xax : array

x axis

data : array

y axis

npeaks : int

How many nh3 profiles to fit? Default 1 (this could supersede onedgaussfit)

err : array

error corresponding to data

params : list

Fit parameters: [trot, tex, ntot (or tau), width, offset, ortho fraction] * npeaks If len(params) % 6 == 0, npeaks will be set to len(params) / 6. These parameters (and the related fixed, limited, min/max, names below) need to have length = 6*npeaks. If npeaks > 1 and length = 6, they will be replicated npeaks times, otherwise they will be reset to defaults:

fixed : list

Is parameter fixed?

limitedmin : list

minpars : list

set lower limits on each parameter (default: width>0, Tex and trot > Tcmb)

limitedmax : list

maxpars : list

set upper limits on each parameter

parnames : list

default parameter names, important for setting kwargs in model [‘trot’,’tex’,’ntot’,’width’,’xoff_v’,’fortho’]

quiet : bool

should MPFIT output each iteration?

shh : bool

output final parameters?

Returns:

mpp : model parameter object

Fit parameters

model : array

The model array

errors : array

the fit errors

chi2 : float

the chi^2 value of the fit

n_ammonia(pars=None, parnames=None, **kwargs)

Returns a function that sums over N ammonia line profiles, where N is the length of trot,tex,ntot,width,xoff_v,fortho OR N = len(pars) / 6

The background “height” is assumed to be zero (you must “baseline” your spectrum before fitting)

pars [ list ]

a list with len(pars) = (6-nfixed)n, assuming trot,tex,ntot,width,xoff_v,fortho repeated

parnames [ list ]

len(parnames) must = len(pars). parnames determine how the ammonia function parses the arguments

parse_3par_guesses(guesses)

Try to convert a set of interactive guesses (peak, center, width) into guesses appropriate to the model.

For NH3 models, we add in several extra parameters:

tex = 2.73 * peak trot = tex * 2 fortho = 0.5 ntot = 15

ntot is set to a constant ~10^15 because this results in optical depths near 1, so it forces the emission to be approximately significant. trot > tex so that we’re in a physical regime to begin with.

We assume tex = peak + 2.73 because most spectra are shown background-subtracted (single dish are always that way, interferometric data are intrinsically that way…) and otherwise the guessing will crash if you guess a number < 2.73.

class pyspeckit.spectrum.models.ammonia.ammonia_model_background(**kwargs)

moments(Xax, data, negamp=None, veryverbose=False, **kwargs)

Returns a very simple and likely incorrect guess

multinh3fit(xax, data, npeaks=1, err=None, params=(20, 20, 14, 1.0, 0.0, 0.5, 2.7315), parnames=None, fixed=(False, False, False, False, False, False, True), limitedmin=(True, True, True, True, False, True, True), limitedmax=(False, False, False, False, False, True, True), minpars=(2.7315, 2.7315, 0, 0, 0, 0, 2.7315), parinfo=None, maxpars=(0, 0, 0, 0, 0, 1, 2.7315), tied=('', '', '', '', '', '', ''), quiet=True, shh=True, veryverbose=False, **kwargs)

Fit multiple nh3 profiles (multiple can be 1)

Parameters:

xax : array

x axis

data : array

y axis

npeaks : int

How many nh3 profiles to fit? Default 1 (this could supersede onedgaussfit)

err : array

error corresponding to data

params : list

Fit parameters: [trot, tex, ntot (or tau), width, offset, ortho fraction] * npeaks If len(params) % 6 == 0, npeaks will be set to len(params) / 6. These parameters (and the related fixed, limited, min/max, names below) need to have length = 6*npeaks. If npeaks > 1 and length = 6, they will be replicated npeaks times, otherwise they will be reset to defaults:

fixed : list

Is parameter fixed?

limitedmin : list

minpars : list

set lower limits on each parameter (default: width>0, Tex and trot > Tcmb)

limitedmax : list

maxpars : list

set upper limits on each parameter

parnames : list

default parameter names, important for setting kwargs in model [‘trot’,’tex’,’ntot’,’width’,’xoff_v’,’fortho’]

quiet : bool

should MPFIT output each iteration?

shh : bool

output final parameters?

Returns:

mpp : model parameter object

Fit parameters

model : array

The model array

errors : array

the fit errors

chi2 : float

the chi^2 value of the fit

class pyspeckit.spectrum.models.ammonia.ammonia_model_restricted_tex(parnames=['trot', 'tex', 'ntot', 'width', 'xoff_v', 'fortho', 'delta'], **kwargs)

make_parinfo(params=(20, 20, 0.5, 1.0, 0.0, 0.5, 0), fixed=(False, False, False, False, False, False, False), limitedmin=(True, True, True, True, False, True, True), limitedmax=(False, False, False, False, False, True, False), minpars=(2.7315, 2.7315, 0, 0, 0, 0, 0), maxpars=(0, 0, 0, 0, 0, 1, 0), tied=('', 'p[0]-p[6]', '', '', '', '', ''), **kwargs)

parnames=[‘trot’, ‘tex’, ‘ntot’, ‘width’, ‘xoff_v’, ‘fortho’, ‘delta’]

‘delta’ is the difference between tex and trot

n_ammonia(pars=None, parnames=None, **kwargs)

Returns a function that sums over N ammonia line profiles, where N is the length of trot,tex,ntot,width,xoff_v,fortho OR N = len(pars) / 6

The background “height” is assumed to be zero (you must “baseline” your spectrum before fitting)

pars [ list ]

a list with len(pars) = (6-nfixed)n, assuming trot,tex,ntot,width,xoff_v,fortho repeated

parnames [ list ]

len(parnames) must = len(pars). parnames determine how the ammonia function parses the arguments

class pyspeckit.spectrum.models.ammonia.ammonia_model_vtau(parnames=['trot', 'tex', 'tau', 'width', 'xoff_v', 'fortho'], **kwargs)

make_parinfo(params=(20, 14, 0.5, 1.0, 0.0, 0.5), fixed=(False, False, False, False, False, False), limitedmin=(True, True, True, True, False, True), limitedmax=(False, False, False, False, False, True), minpars=(2.7315, 2.7315, 0, 0, 0, 0), maxpars=(0, 0, 0, 0, 0, 1), tied=('', '', '', '', '', ''), **kwargs)

parnames=[‘trot’, ‘tex’, ‘tau’, ‘width’, ‘xoff_v’, ‘fortho’]

moments(Xax, data, negamp=None, veryverbose=False, **kwargs)

Returns a very simple and likely incorrect guess

class pyspeckit.spectrum.models.ammonia.ammonia_model_vtau_thin(parnames=['tkin', 'tau', 'width', 'xoff_v', 'fortho'], **kwargs)

make_parinfo(params=(20, 14, 1.0, 0.0, 0.5), fixed=(False, False, False, False, False), limitedmin=(True, True, True, False, True), limitedmax=(False, False, False, False, True), minpars=(2.7315, 0, 0, 0, 0), maxpars=(0, 0, 0, 0, 1), tied=('', '', '', '', ''), **kwargs)

parnames=[‘trot’, ‘tex’, ‘tau’, ‘width’, ‘xoff_v’, ‘fortho’]

moments(Xax, data, negamp=None, veryverbose=False, **kwargs)

Returns a very simple and likely incorrect guess

pyspeckit.spectrum.models.ammonia.ammonia_thin(xarr, tkin=20, tex=None, ntot=14, width=1, xoff_v=0.0, fortho=0.0, tau=None, return_tau=False, **kwargs)

Use optical depth in the 1-1 line as a free parameter The optical depths of the other lines are then set by the kinetic temperature

tkin is used to compute trot assuming a 3-level system consisting of (1,1), (2,1), and (2,2) as in Swift et al, 2005 [2005ApJ…620..823S]

pyspeckit.spectrum.models.ammonia.cold_ammonia(xarr, tkin, **kwargs)

Generate a model Ammonia spectrum based on input temperatures, column, and gaussian parameters

Parameters:

xarr: `pyspeckit.spectrum.units.SpectroscopicAxis`

Array of wavelength/frequency values

tkin: float

The kinetic temperature of the lines in K. Will be converted to rotational temperature following the scheme of Swift et al 2005 (http://esoads.eso.org/abs/2005ApJ…620..823S, eqn A6) and further discussed in Equation 7 of Rosolowsky et al 2008 (http://adsabs.harvard.edu/abs/2008ApJS..175..509R)

class pyspeckit.spectrum.models.ammonia.cold_ammonia_model(parnames=['tkin', 'tex', 'ntot', 'width', 'xoff_v', 'fortho'], **kwargs)

Ammonia inversion transition: Hyperfine-only fitter

Module API

pyspeckit.spectrum.models.ammonia_hf.nh3_vtau_multimodel_generator(linenames)

If you want to use multiple hyperfines for the same spectrum, use this generator. It is useful if you want N independent tau/tex values but the same velocity and linewidth

Parameters:

linenames : list

A list of line names from the set (‘oneone’, …, ‘eighteight’)

Returns:

model : model.SpectralModel

A SpectralModel class build from N different metastable inversion hyperfine models

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