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 theALLOWED_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:
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