pint.models.binary_ell1.BinaryELL1

class pint.models.binary_ell1.BinaryELL1[source]

Bases: PulsarBinary

ELL1 binary model.

This binary model uses a rectangular representation for the eccentricity of an orbit, resolving complexities that arise with periastron-based parameters in nearly-circular orbits. It also makes certain approximations (up to O(e^3)) that are invalid when the eccentricity is “large”; what qualifies as “large” depends on your data quality. A formula exists to determine when the approximations this model makes are sufficiently accurate.

The actual calculations for this are done in pint.models.stand_alone_psr_binaries.ELL1_model.ELL1model.

It supports all the parameters defined in pint.models.pulsar_binary.PulsarBinary except that it removes ECC, OM, and T0:

Parameters supported:

Name / Aliases	Description	Kind
PB	Orbital period	d
PBDOT	Orbital period derivative respect to time	number
A1	Projected semi-major axis of pulsar orbit, ap*sin(i)	ls
A1DOT / XDOT	Derivative of projected semi-major axis, d[ap*sin(i)]/dt	ls / s
EDOT	Eccentricity derivative respect to time	1 / s
OMDOT	Rate of advance of periastron	deg / yr
M2	Companion mass	solMass
SINI	Sine of inclination angle	number
FB{number}	0th time derivative of frequency of orbit	1 / s
TASC	Epoch of ascending node	d
EPS1	First Laplace-Lagrange parameter, ECC*sin(OM)	number
EPS2	Second Laplace-Lagrange parameter, ECC*cos(OM)	number
EPS1DOT	First derivative of first Laplace-Lagrange parameter	1e-12 / s
EPS2DOT	Second derivative of first Laplace-Lagrange parameter	1e-12 / s
ECC / E	Eccentricity	number
OM	Longitude of periastron	deg

References

Lange et al. (2001), MNRAS, 326 (1), 274–282 [1]
Zhu et al. (2019), MNRAS, 482 (3), 3249-3260 [2]
Fiore et al. (2023), arXiv:2305.13624 [astro-ph.HE] [3]

Notes

This includes o(e^2) expression for Roemer delay from Norbert Wex and Weiwei Zhu This is equation (1) of Zhu et al (2019) but with a corrected typo:

In the first line of that equation, ex->e1 and ey->e2 In the other lines, ex->e2 and ey->e1

See Email from NW and WZ to David Nice on 2019-Aug-08 The dre expression comes from NW and WZ; the derivatives were calculated by hand for PINT

Also includes o(e^3) expression from equation (4) of Fiore et al. (2023) (derivatives also calculated by hand)

Methods

`FBX_description`(n)
`FBX_unit`(n)
`add_param`(param[, deriv_func, setup])	Add a parameter to the Component.
`apply_units`()	Apply units to parameter value.
`binarymodel_delay`(toas[, acc_delay])	Return the binary model independent delay call.
`change_binary_epoch`(new_epoch)	Change the epoch for this binary model.
`check_required_params`(required_params)
`d_binary_delay_d_xxxx`(toas, param, acc_delay)	Return the binary model delay derivatives.
`get_params_of_type`(param_type)	Get all the parameters in timing model for one specific type.
`get_prefix_mapping_component`(prefix)	Get the index mapping for the prefix parameters.
`is_in_parfile`(para_dict)	Check if this subclass included in parfile.
`match_param_aliases`(alias)	Return the parameter corresponding to this alias.
`param_help`()	Print help lines for all available parameters in model.
`pb`([t])	Return binary period and uncertainty (optionally evaluated at different times) regardless of binary model
`print_par`([format])	param format: Parfile output format. PINT outputs the 'tempo', 'tempo2' and 'pint'
`register_deriv_funcs`(func, param)	Register the derivative function in to the deriv_func dictionaries.
`remove_param`(param)	Remove a parameter from the Component.
`set_special_params`(spcl_params)
`setup`()	Finalize construction loaded values.
`update_binary_object`(toas[, acc_delay])	Update stand alone binary's parameters and toas from PINT-facing object.
`validate`()	Validate parameters.
`validate_toas`(toas)	Check that this model component has TOAs where needed.

Attributes

`aliases_map`	Return all the aliases and map to the PINT parameter name.
`category`
`component_types`
`free_params_component`	Return the free parameters in the component.
`param_prefixs`
`register`

validate()[source]: Validate parameters.

change_binary_epoch(new_epoch)[source]

Change the epoch for this binary model.

TASC will be changed to the epoch of the ascending node closest to the supplied epoch, and the Laplace parameters (EPS1, EPS2) and projected semi-major axis (A1 or X) will be updated according to the specified EPS1DOT, EPS2DOT, and A1DOT or XDOT, if present.

Note that derivatives of binary orbital frequency higher than the first (FB2, FB3, etc.) are ignored in computing the new T0, even if present in the model. If high-precision results are necessary, especially for models containing higher derivatives of orbital frequency, consider re-fitting the model to a set of TOAs.

Parameters:: new_epoch (float MJD (in TDB) or astropy.Time object) – The new epoch value.

add_param(param, deriv_func=None, setup=False)

Add a parameter to the Component.

The parameter is stored in an attribute on the Component object. Its name is also recorded in a list, self.params.

Parameters:

param (pint.models.Parameter) – The parameter to be added.
deriv_func (function) – Derivative function for parameter.

property aliases_map

Return all the aliases and map to the PINT parameter name.

This property returns a dictionary from the current in timing model parameters’ aliase to the pint defined parameter names. For the aliases of a prefixed parameter, the aliase with an existing prefix index maps to the PINT defined parameter name with the same index. Behind the scenes, the indexed parameter adds the indexed aliase to its aliase list.

apply_units(): Apply units to parameter value.

binarymodel_delay(toas, acc_delay=None): Return the binary model independent delay call.

d_binary_delay_d_xxxx(toas, param, acc_delay): Return the binary model delay derivatives.

property free_params_component

Return the free parameters in the component.

This function collects the non-frozen parameters.

Return type:: A list of free parameters.

get_params_of_type(param_type): Get all the parameters in timing model for one specific type.

get_prefix_mapping_component(prefix)

Get the index mapping for the prefix parameters.

Parameters:: prefix (str) – Name of prefix.
Returns:: A dictionary with prefix parameter real index as key and parameter name as value.
Return type:: dict

is_in_parfile(para_dict)

Check if this subclass included in parfile.

Parameters:: para_dict (dictionary) – A dictionary contain all the parameters with values in string from one parfile
Returns:: Whether the subclass is included in the parfile.
Return type:: bool

match_param_aliases(alias)

Return the parameter corresponding to this alias.

Parameters:: alias (str) – Alias name.

Note

This function only searches the parameter aliases within the current component. If one wants to search the aliases in the scope of TimingModel, please use TimingModel.match_param_aliase().

param_help(): Print help lines for all available parameters in model.

pb(t=None)

Return binary period and uncertainty (optionally evaluated at different times) regardless of binary model

Parameters:

t (astropy.time.Time, astropy.units.Quantity, numpy.ndarray, float, int, str, optional) – Time(s) to evaluate period

Returns:

astropy.units.Quantity – Binary period
astropy.units.Quantity – Binary period uncertainty

print_par(format='pint')

Parameters:: format (str, optional) – Parfile output format. PINT outputs the ‘tempo’, ‘tempo2’ and ‘pint’ format. The defaul format is pint. Actual formatting done elsewhere.
Returns:: str
Return type:: formatted line for par file

register_deriv_funcs(func, param)

Register the derivative function in to the deriv_func dictionaries.

Parameters:

func (callable) – Calculates the derivative
param (str) – Name of parameter the derivative is with respect to

remove_param(param)

Remove a parameter from the Component.

Parameters:: param (str or pint.models.Parameter) – The parameter to remove.

setup(): Finalize construction loaded values.

update_binary_object(toas, acc_delay=None)

Update stand alone binary’s parameters and toas from PINT-facing object.

This function passes the PINT-facing object’s parameter values and TOAs to the stand-alone binary object. If the TOAs are not provided, it only updates the parameters not the TOAs.

Parameters:

toas (pint.toa.TOAs) – The TOAs that need to pass to the stand alone model.Default value is None. If toas is None, this function only updates the parameter value. If ‘acc_delay’ is not provided, the stand alone binary receives the standard barycentered TOAs.
acc_delay (numpy.ndarray) – If provided, TOAs will be corrected by provided acc_delay instead of the standard barycentering. The stand alone binary receives the input TOAs - acc_delay.

Notes

The values for obs_pos (the observatory position wrt the Solar System Barycenter) and psr_pos (the pulsar position wrt the Solar System Barycenter) are both computed in the same reference frame, ICRS or ECL depending on the model.

Warns:

If passing ‘None’ to ‘toa’ argument, the stand alone binary model will use
the TOAs were passed to it from last iteration (i.e. last barycentered
TOAs) or no TOAs for stand alone binary model at all. This behavior will
cause incorrect answers. Allowing the passing None to ‘toa’ argument is
for some lower level functions and tests. We do not recommend PINT
user to use it.

validate_toas(toas): Check that this model component has TOAs where needed.