Defining equations#

The equation definition information is held in the EQN_DEFINITIONS dictionary. This is created from a set of YAML files containing the information for each individual equation. To define a new equation a new YAML file must be created. The file name (preceding the YAML extension) is used to define the equation’s name with which it must be referred to.

The file should contain the following information:

“description (required)”:

a string giving a brief description of the equation

“variable (required)”:

the variable that the equation is defining (this must be from the names in ALLOWED_VARIABLES). This may be the same as the equation name, but it doesn’t have to be. For example, the equation named “h0spindown” defines a “h0” variable.

“latex_string (required)”:

a LaTeX math string (excluding $ symbols) with which to represent the left-hand-side of the equation.

“parts (required or chain)”:

pairs of values containing the all parts of the equation (constants and variables) and their exponents. These should both be string values. For variables the parameter names (the first value in the tuple) must be consistent with the names in the ALLOWED_VARIABLES dictionary. Constants can be number value strings or the strings containing “G”, “c” or “pi”.

“chain (required or parts)”:

instead of providing the parts of the equation, it can be constructed from other equations that are already defined. To do this the chain of equations, rearrangments and substitutions needs to be set. This value should be a list with the first entry being the starting equation name. Subsequent entries are strings containing the words “equals”, “rearrange”, or “substitute” followed by an equation or variable name. “equals” should be followed by an equation name which will be set as equal to the current equation for the next “rearrangement”; “rearrange” should be followed by a variable name, for which the current equation should be solved for; and, “substitute” should be followed by the equation name into which the current equation will be substituted.

“default_fiducial_values (required)”:

pairs of keys and values all variable parameters in the equation. Each value gives the default value of that variable (the astropy.units.Unit can be set be giving a unit string wrapped in the word “Unit”, e.g., Unit(“Hz”)). The variable parameter names must be consistent with the names in the ALLOWED_VARIABLES dictionary and those given in parts.

“alternative_variables”:

a list of variable names that can be used to derive a subset of the variables in the “default_fiducial_values”, i.e., if the equation requires the “rotationfrequency” then this could contain “rotationperiod”, which can instead be used to derive the rotation frequency. The variable parameter names must be consistent with the names in the ALLOWED_VARIABLES dictionary.

“converters”:

a set of pairs of variable names and conversion functions to convert the additional values into the required values.

“reference”:

information about the a reference for the equation, containing:

“short”:

a short string version of the reference

“adsurl”:

the URL of the NASA ADS entry for the paper

“eqno”:

the equation number in the given reference

“bibtex”:

the NASA ADS BibTeX entry for the paper

An example YAML file for an equation is:

description: Gravitational wave amplitude
variable: h0
latex_string: h_0
default_fiducial_values:
  ellipticity: 1e-6
  momentofinertia: 1e38 * Unit("kg m^2")
  rotationfrequency: 100 * Unit("Hz")
  distance: 1 * Unit("kpc")
parts:
  "16": "1"
  "pi": "2"
  "G": "1"
  "c": "-4"
  "ellipticity": "1"
  "momentofinertia": "1"
  "rotationfrequency": "2"
  "distance": "-1"
alternative_variables: ["gwfrequency", "rotationperiod"]
converters:
  rotationfrequency: convert_to_rotation_frequency
reference:
  short: Jaranowski, P., Krolak, A., & Schutz, B. F. 1998, PhRvD, 58, 063001
  adsurl: https://ui.adsabs.harvard.edu/abs/1998PhRvD..58f3001J/abstract
  eqno: 23
  bibtex: |
    @ARTICLE{1998PhRvD..58f3001J,
           author = {{Jaranowski}, Piotr and {Kr{\\'o}lak}, Andrzej and {Schutz}, Bernard F.},
            title = "{Data analysis of gravitational-wave signals from spinning neutron stars: The signal and its detection}",
          journal = {\\prd},
         keywords = {95.55.Ym, 04.80.Nn, 95.75.Pq, 97.60.Gb, Gravitational radiation detectors, mass spectrometers, and other instrumentation and techniques, Gravitational wave detectors and experiments, Mathematical procedures and computer techniques, Pulsars, General Relativity and Quantum Cosmology},
             year = 1998,
            month = sep,
           volume = {58},
           number = {6},
              eid = {063001},
            pages = {063001},
              doi = {10.1103/PhysRevD.58.063001},
    archivePrefix = {arXiv},
           eprint = {gr-qc/9804014},
     primaryClass = {gr-qc},
           adsurl = {https://ui.adsabs.harvard.edu/abs/1998PhRvD..58f3001J},
          adsnote = {Provided by the SAO/NASA Astrophysics Data System}
    }
ALLOWED_VARIABLES = {   'angulargwfdot': {   'aliases': [   'angulargwfdot',                                         'omgwdot',                                         'om1gw'],                          'description': 'Gravitational-wave '                                         'angular frequency '                                         'derivative',                          'latex_string': '\\dot{\\Omega}_{\\rm '                                          'gw}',                          'sign': None,                          'units': 'rad / s^2'},     'angulargwfrequency': {   'aliases': [   'angulargwfrequency',                                              'omegagw',                                              'omgw',                                              'omega0gw',                                              'om0gw',                                              'Ωgw',                                              'Ω0gw'],                               'description': 'Angular '                                              'gravitational-wave '                                              'frequency',                               'latex_string': '\\Omega_{\\rm '                                               'gw}',                               'sign': '>= 0',                               'units': 'rad / s'},     'angularrotationfdot': {   'aliases': [   'angularrotationfdot',                                               'omrotdot',                                               'om1rot',                                               'om1spin'],                                'description': 'Source '                                               'angular '                                               'rotational '                                               'frequency '                                               'derivative',                                'latex_string': '\\dot{\\Omega}_{\\rm '                                                'rot}',                                'sign': None,                                'units': 'rad / s^2'},     'angularrotationfrequency': {   'aliases': [   'angularrotationfrequency',                                                    'omegarot',                                                    'omrot',                                                    'omega0rot',                                                    'om0rot',                                                    'Ω',                                                    'Ωrot',                                                    'Ω0rot'],                                     'description': 'Source '                                                    'angular '                                                    'rotational '                                                    'frequency',                                     'latex_string': '\\Omega_{\\rm '                                                     'rot}',                                     'sign': '>= 0',                                     'units': 'rad / s'},     'brakingindex': {   'aliases': ['brakingindex', 'n'],                         'description': 'The braking index '                                        'of a pulsar',                         'latex_string': 'n',                         'sign': None,                         'units': None},     'characteristicage': {   'aliases': [   'characteristicage',                                             'tau',                                             '𝜏'],                              'description': 'The '                                             'characteristic '                                             'age of a '                                             'pulsar',                              'latex_string': '\\tau',                              'sign': None,                              'units': 'yr'},     'distance': {   'aliases': [   'distance',                                    'dist',                                    'd',                                    'r'],                     'description': 'Distance to the source',                     'latex_string': 'd',                     'sign': '>= 0',                     'units': 'kpc'},     'ellipticity': {   'aliases': [   'ellipticity',                                       'ell',                                       'eps',                                       'epsilon',                                       '𝜀'],                        'description': 'Neutron star '                                       'ellipticity',                        'latex_string': '\\varepsilon',                        'sign': '>= 0',                        'units': None},     'gwfddot': {   'aliases': [   'gwfddot',                                   'fddotgw',                                   'f2gw'],                    'description': 'Gravitational-wave '                                   'second frequency '                                   'derivative',                    'latex_string': '\\dot{f}_{\\rm gw}',                    'sign': None,                    'units': 'Hz / s '},     'gwfdot': {   'aliases': ['gwfdot', 'fdotgw', 'f1gw'],                   'description': 'Gravitational-wave '                                  'frequency derivative',                   'latex_string': '\\dot{f}_{\\rm gw}',                   'sign': None,                   'units': 'Hz / s'},     'gwfrequency': {   'aliases': [   'gwfrequency',                                       'fgw',                                       'f0gw'],                        'description': 'Gravitational-wave '                                       'frequency',                        'latex_string': 'f_{\\rm gw}',                        'sign': '>= 0',                        'units': 'Hz'},     'h0': {   'aliases': ['h0', 'h_0'],               'description': 'Gravitational wave amplitude',               'latex_string': 'h_0',               'sign': '>= 0',               'units': None},     'luminosity': {   'aliases': [   'luminosity',                                      'l',                                      'spindownluminosity',                                      'gwluminosity',                                      'lgw',                                      'lsd'],                       'description': 'The luminosity of a '                                      'source',                       'latex_string': 'L',                       'sign': '>= 0',                       'units': 'W'},     'massquadrupole': {   'aliases': [   'massquadrupole',                                          'q22',                                          'q_22'],                           'description': 'Mass quadrupole '                                          'moment (l=m=2)',                           'latex_string': 'Q_{22}',                           'sign': '>= 0',                           'units': 'kg m^2'},     'momentofinertia': {   'aliases': [   'momentofinertia',                                           'izz',                                           'i38'],                            'description': 'Principal '                                           'moment of '                                           'inertia about '                                           'the rotation '                                           'axis',                            'latex_string': 'I_{zz}',                            'sign': '>= 0',                            'units': 'kg m^2'},     'rotationfddot': {   'aliases': [   'rotationfddot',                                         'frotddot',                                         'f2rot',                                         'f2spin'],                          'description': 'Source rotational '                                         'frequency second '                                         'derivative',                          'latex_string': '\\ddot{f}_{\\rm '                                          'rot}',                          'sign': None,                          'units': 'Hz / s^2'},     'rotationfdot': {   'aliases': [   'rotationfdot',                                        'frotdot',                                        'f1rot',                                        'f1spin'],                         'description': 'Source rotational '                                        'frequency '                                        'derivative',                         'latex_string': '\\dot{f}_{\\rm '                                         'rot}',                         'sign': None,                         'units': 'Hz / s'},     'rotationfrequency': {   'aliases': [   'rotationfrequency',                                             'frot',                                             'spinfrequency',                                             'fspin',                                             'f0rot',                                             'f0spin'],                              'description': 'Source '                                             'rotational '                                             'frequency',                              'latex_string': 'f_{\\rm rot}',                              'sign': '>= 0',                              'units': 'Hz'},     'rotationpdot': {   'aliases': [   'pdot',                                        'p0dot',                                        'rotationpdot'],                         'description': 'Source rotational '                                        'period derivative',                         'latex_string': '\\dot{P}',                         'sign': None,                         'units': 's / s'},     'rotationperiod': {   'aliases': [   'rotationperiod',                                          'prot',                                          'p0rot'],                           'description': 'Source '                                          'rotational '                                          'period',                           'latex_string': 'P',                           'sign': '>= 0',                           'units': 's'}}#

allowed variables for equations

EQN_DEFINITIONS = {   'brakingindex': {   'alternative_variables': [   'gwfrequency',                                                      'rotationperiod',                                                      'gwfdot',                                                      'rotationpdot'],                         'converters': {   'rotationfdot': 'convert_to_rotation_fdot',                                           'rotationfrequency': 'convert_to_rotation_frequency'},                         'default_fiducial_values': {   'rotationfddot': <Quantity 1.e-23 Hz / s2>,                                                        'rotationfdot': <Quantity -1.e-11 Hz / s>,                                                        'rotationfrequency': <Quantity 50. Hz>},                         'description': 'The braking index '                                        'of a pulsar',                         'latex_string': 'n',                         'parts': {   'rotationfddot': '1',                                      'rotationfdot': '-2',                                      'rotationfrequency': '1'},                         'reference': {   'adsurl': 'https://ui.adsabs.harvard.edu/abs/2016era..book.....C/abstract',                                          'bibtex': '@BOOK{2016era..book.....C,\n'                                                    '       '                                                    'author '                                                    '= '                                                    '{{Condon}, '                                                    'James '                                                    'J. and '                                                    '{Ransom}, '                                                    'Scott '                                                    'M.},\n'                                                    '        '                                                    'title '                                                    '= '                                                    '"{Essential '                                                    'Radio '                                                    'Astronomy}",\n'                                                    '         '                                                    'year = '                                                    '2016,\n'                                                    '       '                                                    'adsurl '                                                    '= '                                                    '{https://ui.adsabs.harvard.edu/abs/2016era..book.....C},\n'                                                    '      '                                                    'adsnote '                                                    '= '                                                    '{Provided '                                                    'by the '                                                    'SAO/NASA '                                                    'Astrophysics '                                                    'Data '                                                    'System}\n'                                                    '}\n',                                          'eqno': '6.35',                                          'short': 'Condon, '                                                   'J. J. '                                                   'and '                                                   'Ransom, '                                                   'S. M., '                                                   '2016, '                                                   'Essential '                                                   'Radio '                                                   'Astronomy'},                         'variable': 'brakingindex'},     'characteristicage': {   'alternative_variables': [   'gwfrequency',                                                           'rotationfrequency',                                                           'rotationfdot'],                              'converters': {   'rotationpdot': 'convert_to_rotation_pdot',                                                'rotationperiod': 'convert_to_rotation_period'},                              'default_fiducial_values': {   'brakingindex': 3,                                                             'rotationpdot': <Quantity 1.e-15>,                                                             'rotationperiod': <Quantity 0.01 s>},                              'description': 'The '                                             'characteristic '                                             'age of a '                                             'pulsar',                              'latex_string': '\\tau',                              'parts': {   'brakingindex - 1': '-1',                                           'rotationpdot': '-1',                                           'rotationperiod': '1'},                              'reference': {   'adsurl': 'https://ui.adsabs.harvard.edu/abs/2016era..book.....C/abstract',                                               'bibtex': '@BOOK{2016era..book.....C,\n'                                                         '       '                                                         'author '                                                         '= '                                                         '{{Condon}, '                                                         'James '                                                         'J. '                                                         'and '                                                         '{Ransom}, '                                                         'Scott '                                                         'M.},\n'                                                         '        '                                                         'title '                                                         '= '                                                         '"{Essential '                                                         'Radio '                                                         'Astronomy}",\n'                                                         '         '                                                         'year '                                                         '= '                                                         '2016,\n'                                                         '       '                                                         'adsurl '                                                         '= '                                                         '{https://ui.adsabs.harvard.edu/abs/2016era..book.....C},\n'                                                         '      '                                                         'adsnote '                                                         '= '                                                         '{Provided '                                                         'by '                                                         'the '                                                         'SAO/NASA '                                                         'Astrophysics '                                                         'Data '                                                         'System}\n'                                                         '}\n',                                               'eqno': '6.31',                                               'short': 'Condon, '                                                        'J. '                                                        'J. '                                                        'and '                                                        'Ransom, '                                                        'S. '                                                        'M., '                                                        '2016, '                                                        'Essential '                                                        'Radio '                                                        'Astronomy'},                              'variable': 'characteristicage'},     'ellipticityspindown': {   'alternative_variables': [   'gwfrequency',                                                             'rotationperiod',                                                             'gwfdot',                                                             'rotationpdot'],                                'chain': [   'gwluminosity',                                             'equals '                                             'spindownluminosity',                                             'rearrange '                                             'ellipticity'],                                'converters': {   'rotationfdot': 'convert_to_rotation_fdot',                                                  'rotationfrequency': 'convert_to_rotation_frequency'},                                'default_fiducial_values': {   'momentofinertia': <Quantity 1.e+38 kg m2>,                                                               'rotationfdot': <Quantity -1.e-11 Hz / s>,                                                               'rotationfrequency': <Quantity 100. Hz>},                                'description': 'Spin-down '                                               'limit for '                                               'neutron '                                               'star '                                               'ellipticity',                                'latex_string': '\\varepsilon^{\\rm '                                                'sd}',                                'reference': {   'adsurl': 'https://ui.adsabs.harvard.edu/abs/2019ApJ...879...10A/abstract',                                                 'bibtex': '@ARTICLE{2019ApJ...879...10A,\n'                                                           '       '                                                           'author '                                                           '= '                                                           '{{Aasi}, '                                                           'J. '                                                           'and '                                                           'others},\n'                                                           '        '                                                           'title '                                                           '= '                                                           '"{Searches '                                                           'for '                                                           'Gravitational '                                                           'Waves '                                                           'from '                                                           'Known '                                                           'Pulsars '                                                           'at '                                                           'Two '                                                           'Harmonics '                                                           'in '                                                           '2015-2017 '                                                           'LIGO '                                                           'Data}",\n'                                                           '      '                                                           'journal '                                                           '= '                                                           '{\\\\apj},\n'                                                           '     '                                                           'keywords '                                                           '= '                                                           '{gravitational '                                                           'waves, '                                                           'pulsars: '                                                           'general, '                                                           'stars: '                                                           'neutron, '                                                           'Astrophysics '                                                           '- '                                                           'High '                                                           'Energy '                                                           'Astrophysical '                                                           'Phenomena, '                                                           'General '                                                           'Relativity '                                                           'and '                                                           'Quantum '                                                           'Cosmology},\n'                                                           '         '                                                           'year '                                                           '= '                                                           '2019,\n'                                                           '        '                                                           'month '                                                           '= '                                                           'jul,\n'                                                           '       '                                                           'volume '                                                           '= '                                                           '{879},\n'                                                           '       '                                                           'number '                                                           '= '                                                           '{1},\n'                                                           '          '                                                           'eid '                                                           '= '                                                           '{10},\n'                                                           '        '                                                           'pages '                                                           '= '                                                           '{10},\n'                                                           '          '                                                           'doi '                                                           '= '                                                           '{10.3847/1538-4357/ab20cb},\n'                                                           'archivePrefix '                                                           '= '                                                           '{arXiv},\n'                                                           '       '                                                           'eprint '                                                           '= '                                                           '{1902.08507},\n'                                                           ' '                                                           'primaryClass '                                                           '= '                                                           '{astro-ph.HE},\n'                                                           '       '                                                           'adsurl '                                                           '= '                                                           '{https://ui.adsabs.harvard.edu/abs/2019ApJ...879...10A},\n'                                                           '      '                                                           'adsnote '                                                           '= '                                                           '{Provided '                                                           'by '                                                           'the '                                                           'SAO/NASA '                                                           'Astrophysics '                                                           'Data '                                                           'System}\n'                                                           '}\n',                                                 'eqno': 'A9',                                                 'short': 'Abbott, '                                                          'B. '                                                          'P., '                                                          'et '                                                          'al. '                                                          '2019, '                                                          'ApJ, '                                                          '879, '                                                          '10'},                                'variable': 'ellipticity'},     'gwluminosity': {   'alternative_variables': [   'gwfrequency',                                                      'rotationperiod'],                         'converters': {   'rotationfrequency': 'convert_to_rotation_frequency'},                         'default_fiducial_values': {   'ellipticity': 1e-06,                                                        'momentofinertia': <Quantity 1.e+38 kg m2>,                                                        'rotationfrequency': <Quantity 100. Hz>},                         'description': 'The '                                        'gravitational-wave '                                        'luminosity of a '                                        'pulsar',                         'latex_string': 'L_{\\rm gw}',                         'parts': {   '2048/5': '1',                                      'G': '1',                                      'c': '-5',                                      'ellipticity': '2',                                      'momentofinertia': '2',                                      'pi': '6',                                      'rotationfrequency': '6'},                         'reference': {   'adsurl': 'https://ui.adsabs.harvard.edu/abs/1969ApJ...157.1395O/abstract',                                          'bibtex': '@ARTICLE{1969ApJ...157.1395O,\n'                                                    '       '                                                    'author '                                                    '= '                                                    '{{Ostriker}, '                                                    'J.~P. '                                                    'and '                                                    '{Gunn}, '                                                    'J.~E.},\n'                                                    '        '                                                    'title '                                                    '= "{On '                                                    'the '                                                    'Nature '                                                    'of '                                                    'Pulsars. '                                                    'I. '                                                    'Theory}",\n'                                                    '      '                                                    'journal '                                                    '= '                                                    '{\\\\apj},\n'                                                    '         '                                                    'year = '                                                    '1969,\n'                                                    '        '                                                    'month '                                                    '= '                                                    'sep,\n'                                                    '       '                                                    'volume '                                                    '= '                                                    '{157},\n'                                                    '        '                                                    'pages '                                                    '= '                                                    '{1395},\n'                                                    '          '                                                    'doi = '                                                    '{10.1086/150160},\n'                                                    '       '                                                    'adsurl '                                                    '= '                                                    '{https://ui.adsabs.harvard.edu/abs/1969ApJ...157.1395O},\n'                                                    '      '                                                    'adsnote '                                                    '= '                                                    '{Provided '                                                    'by the '                                                    'SAO/NASA '                                                    'Astrophysics '                                                    'Data '                                                    'System}\n'                                                    '}\n',                                          'eqno': '7',                                          'short': 'Ostriker, '                                                   'J. P. '                                                   'and '                                                   'Gunn, '                                                   'J. E., '                                                   '1969, '                                                   'ApJ, '                                                   '157, '                                                   '1395'},                         'variable': 'luminosity'},     'h0': {   'alternative_variables': [   'gwfrequency',                                            'rotationperiod'],               'converters': {   'rotationfrequency': 'convert_to_rotation_frequency'},               'default_fiducial_values': {   'distance': <Quantity 1. kpc>,                                              'ellipticity': 1e-06,                                              'momentofinertia': <Quantity 1.e+38 kg m2>,                                              'rotationfrequency': <Quantity 100. Hz>},               'description': 'Gravitational wave amplitude',               'latex_string': 'h_0',               'parts': {   '16': '1',                            'G': '1',                            'c': '-4',                            'distance': '-1',                            'ellipticity': '1',                            'momentofinertia': '1',                            'pi': '2',                            'rotationfrequency': '2'},               'reference': {   'adsurl': 'https://ui.adsabs.harvard.edu/abs/1998PhRvD..58f3001J/abstract',                                'bibtex': '@ARTICLE{1998PhRvD..58f3001J,\n'                                          '       author = '                                          '{{Jaranowski}, '                                          'Piotr and '                                          "{Kr{\\\\'o}lak}, "                                          'Andrzej and '                                          '{Schutz}, '                                          'Bernard F.},\n'                                          '        title = '                                          '"{Data analysis '                                          'of '                                          'gravitational-wave '                                          'signals from '                                          'spinning neutron '                                          'stars: The '                                          'signal and its '                                          'detection}",\n'                                          '      journal = '                                          '{\\\\prd},\n'                                          '     keywords = '                                          '{95.55.Ym, '                                          '04.80.Nn, '                                          '95.75.Pq, '                                          '97.60.Gb, '                                          'Gravitational '                                          'radiation '                                          'detectors, mass '                                          'spectrometers, '                                          'and other '                                          'instrumentation '                                          'and techniques, '                                          'Gravitational '                                          'wave detectors '                                          'and experiments, '                                          'Mathematical '                                          'procedures and '                                          'computer '                                          'techniques, '                                          'Pulsars, General '                                          'Relativity and '                                          'Quantum '                                          'Cosmology},\n'                                          '         year = '                                          '1998,\n'                                          '        month = '                                          'sep,\n'                                          '       volume = '                                          '{58},\n'                                          '       number = '                                          '{6},\n'                                          '          eid = '                                          '{063001},\n'                                          '        pages = '                                          '{063001},\n'                                          '          doi = '                                          '{10.1103/PhysRevD.58.063001},\n'                                          'archivePrefix = '                                          '{arXiv},\n'                                          '       eprint = '                                          '{gr-qc/9804014},\n'                                          ' primaryClass = '                                          '{gr-qc},\n'                                          '       adsurl = '                                          '{https://ui.adsabs.harvard.edu/abs/1998PhRvD..58f3001J},\n'                                          '      adsnote = '                                          '{Provided by the '                                          'SAO/NASA '                                          'Astrophysics '                                          'Data System}\n'                                          '}\n',                                'eqno': 23,                                'short': 'Jaranowski, P., '                                         'Krolak, A., & '                                         'Schutz, B. F. '                                         '1998, PhRvD, 58, '                                         '063001'},               'variable': 'h0'},     'h0spindown': {   'alternative_variables': [   'gwfrequency',                                                    'rotationperiod',                                                    'gwfdot',                                                    'rotationpdot'],                       'chain': [   'ellipticityspindown',                                    'substitute h0'],                       'converters': {   'rotationfdot': 'convert_to_rotation_fdot',                                         'rotationfrequency': 'convert_to_rotation_frequency'},                       'default_fiducial_values': {   'distance': <Quantity 1. kpc>,                                                      'momentofinertia': <Quantity 1.e+38 kg m2>,                                                      'rotationfdot': <Quantity -1.e-11 Hz / s>,                                                      'rotationfrequency': <Quantity 100. Hz>},                       'description': 'Gravitational-wave '                                      'amplitude spin-down '                                      'limit',                       'latex_string': 'h_0^{\\rm sd}',                       'reference': {   'adsurl': 'https://ui.adsabs.harvard.edu/abs/2014ApJ...785..119A/abstract',                                        'bibtex': '@ARTICLE{2014ApJ...785..119A,\n'                                                  '       '                                                  'author = '                                                  '{{Aasi}, '                                                  'J. and '                                                  'others},\n'                                                  '        '                                                  'title = '                                                  '"{Gravitational '                                                  'Waves '                                                  'from '                                                  'Known '                                                  'Pulsars: '                                                  'Results '                                                  'from the '                                                  'Initial '                                                  'Detector '                                                  'Era}",\n'                                                  '      '                                                  'journal '                                                  '= '                                                  '{\\\\apj},\n'                                                  '     '                                                  'keywords '                                                  '= '                                                  '{gravitational '                                                  'waves, '                                                  'pulsars: '                                                  'general, '                                                  'Astrophysics '                                                  '- High '                                                  'Energy '                                                  'Astrophysical '                                                  'Phenomena, '                                                  'General '                                                  'Relativity '                                                  'and '                                                  'Quantum '                                                  'Cosmology},\n'                                                  '         '                                                  'year = '                                                  '2014,\n'                                                  '        '                                                  'month = '                                                  'apr,\n'                                                  '       '                                                  'volume = '                                                  '{785},\n'                                                  '       '                                                  'number = '                                                  '{2},\n'                                                  '          '                                                  'eid = '                                                  '{119},\n'                                                  '        '                                                  'pages = '                                                  '{119},\n'                                                  '          '                                                  'doi = '                                                  '{10.1088/0004-637X/785/2/119},\n'                                                  'archivePrefix '                                                  '= '                                                  '{arXiv},\n'                                                  '       '                                                  'eprint = '                                                  '{1309.4027},\n'                                                  ' '                                                  'primaryClass '                                                  '= '                                                  '{astro-ph.HE},\n'                                                  '       '                                                  'adsurl = '                                                  '{https://ui.adsabs.harvard.edu/abs/2014ApJ...785..119A},\n'                                                  '      '                                                  'adsnote '                                                  '= '                                                  '{Provided '                                                  'by the '                                                  'SAO/NASA '                                                  'Astrophysics '                                                  'Data '                                                  'System}\n'                                                  '}\n',                                        'eqno': '5',                                        'short': 'Aasi, A., '                                                 'et al. '                                                 '2014, '                                                 'ApJ, 785, '                                                 '119'},                       'variable': 'h0'},     'massquadrupole': {   'alternative_variables': [],                           'converters': {},                           'default_fiducial_values': {   'ellipticity': 1e-06,                                                          'momentofinertia': <Quantity 1.e+38 kg m2>},                           'description': 'Mass quadrupole',                           'latex_string': 'Q_{22}',                           'parts': {   '15': '1/2',                                        '8': '-1/2',                                        'ellipticity': '1',                                        'momentofinertia': '1',                                        'pi': '-1/2'},                           'reference': {   'adsurl': 'https://ui.adsabs.harvard.edu/abs/2005PhRvL..95u1101O/abstract',                                            'bibtex': '@ARTICLE{2005PhRvL..95u1101O,\n'                                                      '       '                                                      'author '                                                      '= '                                                      '{{Owen}, '                                                      'Benjamin '                                                      'J.},\n'                                                      '        '                                                      'title '                                                      '= '                                                      '"{Maximum '                                                      'Elastic '                                                      'Deformations '                                                      'of '                                                      'Compact '                                                      'Stars '                                                      'with '                                                      'Exotic '                                                      'Equations '                                                      'of '                                                      'State}",\n'                                                      '      '                                                      'journal '                                                      '= '                                                      '{\\\\prl},\n'                                                      '     '                                                      'keywords '                                                      '= '                                                      '{04.30.Db, '                                                      '04.40.Dg, '                                                      '26.60.+c, '                                                      '97.60.Jd, '                                                      'Wave '                                                      'generation '                                                      'and '                                                      'sources, '                                                      'Relativistic '                                                      'stars: '                                                      'structure '                                                      'stability '                                                      'and '                                                      'oscillations, '                                                      'Nuclear '                                                      'matter '                                                      'aspects '                                                      'of '                                                      'neutron '                                                      'stars, '                                                      'Neutron '                                                      'stars, '                                                      'Astrophysics, '                                                      'General '                                                      'Relativity '                                                      'and '                                                      'Quantum '                                                      'Cosmology},\n'                                                      '         '                                                      'year '                                                      '= '                                                      '2005,\n'                                                      '        '                                                      'month '                                                      '= '                                                      'nov,\n'                                                      '       '                                                      'volume '                                                      '= '                                                      '{95},\n'                                                      '       '                                                      'number '                                                      '= '                                                      '{21},\n'                                                      '          '                                                      'eid '                                                      '= '                                                      '{211101},\n'                                                      '        '                                                      'pages '                                                      '= '                                                      '{211101},\n'                                                      '          '                                                      'doi '                                                      '= '                                                      '{10.1103/PhysRevLett.95.211101},\n'                                                      'archivePrefix '                                                      '= '                                                      '{arXiv},\n'                                                      '       '                                                      'eprint '                                                      '= '                                                      '{astro-ph/0503399},\n'                                                      ' '                                                      'primaryClass '                                                      '= '                                                      '{astro-ph},\n'                                                      '       '                                                      'adsurl '                                                      '= '                                                      '{https://ui.adsabs.harvard.edu/abs/2005PhRvL..95u1101O},\n'                                                      '      '                                                      'adsnote '                                                      '= '                                                      '{Provided '                                                      'by '                                                      'the '                                                      'SAO/NASA '                                                      'Astrophysics '                                                      'Data '                                                      'System}\n'                                                      '}\n',                                            'eqno': 2,                                            'short': 'Owen. '                                                     'B. '                                                     '2005, '                                                     'PhRvL, '                                                     '95, '                                                     '211101'},                           'variable': 'massquadrupole'},     'spindownluminosity': {   'alternative_variables': [   'gwfrequency',                                                            'rotationperiod',                                                            'gwfdot',                                                            'rotationpdot'],                               'converters': {   'rotationfdot': 'convert_to_rotation_fdot',                                                 'rotationfrequency': 'convert_to_rotation_frequency'},                               'default_fiducial_values': {   'momentofinertia': <Quantity 1.e+38 kg m2>,                                                              'rotationfdot': <Quantity -1.e-11 Hz / s>,                                                              'rotationfrequency': <Quantity 100. Hz>},                               'description': 'The '                                              'spin-down '                                              'luminosity '                                              'of a pulsar',                               'latex_string': 'L_{\\rm sd}',                               'parts': {   '4': '1',                                            'momentofinertia': '1',                                            'pi': '2',                                            'rotationfdot': '1',                                            'rotationfrequency': '1'},                               'reference': {   'adsurl': 'https://ui.adsabs.harvard.edu/abs/2016era..book.....C/abstract',                                                'bibtex': '@BOOK{2016era..book.....C,\n'                                                          '       '                                                          'author '                                                          '= '                                                          '{{Condon}, '                                                          'James '                                                          'J. '                                                          'and '                                                          '{Ransom}, '                                                          'Scott '                                                          'M.},\n'                                                          '        '                                                          'title '                                                          '= '                                                          '"{Essential '                                                          'Radio '                                                          'Astronomy}",\n'                                                          '         '                                                          'year '                                                          '= '                                                          '2016,\n'                                                          '       '                                                          'adsurl '                                                          '= '                                                          '{https://ui.adsabs.harvard.edu/abs/2016era..book.....C},\n'                                                          '      '                                                          'adsnote '                                                          '= '                                                          '{Provided '                                                          'by '                                                          'the '                                                          'SAO/NASA '                                                          'Astrophysics '                                                          'Data '                                                          'System}\n'                                                          '}\n',                                                'eqno': '6.35',                                                'short': 'Condon, '                                                         'J. '                                                         'J. '                                                         'and '                                                         'Ransom, '                                                         'S. '                                                         'M., '                                                         '2016, '                                                         'Essential '                                                         'Radio '                                                         'Astronomy'},                               'variable': 'luminosity'}}#

equation definitions

class EqDict#

Bases: dict

Dictionary class to hold equation definitions.

get_defaults(key)#

Get the default values for a given equation.

Parameters

key (str) – The equation name.

Returns

defaults – A dictionary of default values.

Return type

dict