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ENH: gravitational waves artale rates #474

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c5e1007
initial commit of artale models
itrharrison Jul 19, 2021
075265e
tests pass
itrharrison Jul 19, 2021
1bd53ed
fixed doc example
itrharrison Jul 19, 2021
e8437f9
fixed doc example, MSun units
itrharrison Jul 19, 2021
c2ef42e
added sfr and metallicity model docs and tests
itrharrison Jul 19, 2021
8d23946
put back doctest
itrharrison Jul 19, 2021
7877207
fixed sfr docstring
itrharrison Jul 21, 2021
cc259b9
added metallicity function to docs autosummary
itrharrison Jul 21, 2021
5cfcf4e
Update skypy/gravitational_waves/merger_rate.py
itrharrison Jul 22, 2021
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Update skypy/gravitational_waves/merger_rate.py
itrharrison Jul 22, 2021
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Update skypy/gravitational_waves/tests/test_merger_rate.py
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Update skypy/gravitational_waves/merger_rate.py
itrharrison Jul 22, 2021
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Update skypy/gravitational_waves/merger_rate.py
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removed private functions, doc examples
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3 changes: 3 additions & 0 deletions skypy/gravitational_waves/__init__.py
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Original file line number Diff line number Diff line change
Expand Up @@ -10,6 +10,9 @@
:toctree: ../api/

b_band_merger_rate
m_star_merger_rate
m_star_sfr_merger_rate
m_star_sfr_metallicity_merger_rate

"""

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285 changes: 267 additions & 18 deletions skypy/gravitational_waves/merger_rate.py
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Expand Up @@ -5,11 +5,15 @@

"""

import numpy as np
from astropy import constants, units


__all__ = [
'b_band_merger_rate',
'm_star_merger_rate',
'm_star_sfr_merger_rate',
'm_star_sfr_metallicity_merger_rate'
]


Expand All @@ -29,19 +33,279 @@
'high': 20}
}

artale_tables = {
'NS-NS': {
'redshift': [0.1, 1.0, 2.0, 6.0],
'alpha1': [1.038, 1.109, 1.050, 1.027],
'alpha1_err': [0.001, 0.001, 0.001, 0.003],
'alpha2': [-6.09, -6.214, -5.533, -5.029],
'alpha2_err': [0.010, 0.006, 0.006, 0.021],
'beta1': [0.800, 0.964, 0.977, 1.113],
'beta1_err': [0.002, 0.001, 0.001, 0.003],
'beta2': [0.323, 0.155, 0.068, -0.070],
'beta2_err': [0.002, 0.001, 0.001, 0.002],
'beta3': [-3.555, -4.819, -4.874, -5.764],
'beta3_err': [0.018, 0.013, 0.011, 0.026],
'gamma1': [0.701, 0.896, 1.018, 1.137],
'gamma1_err': [0.002, 0.002, 0.002, 0.004],
'gamma2': [0.356, 0.184, 0.048, -0.082],
'gamma2_err': [0.002, 0.001, 0.001, 0.002],
'gamma3': [0.411, 0.222, -0.103, -0.053],
'gamma3_err': [0.005, 0.003, 0.002, 0.004],
'gamma4': [-1.968, -3.795, -5.451, -6.104],
'gamma4_err': [0.026, 0.019, 0.017, 0.037],
},
'NS-BH': {
'redshift': [0.1, 1.0, 2.0, 6.0],
'alpha1': [0.824, 0.873, 0.913, 0.965],
'alpha1_err': [0.001, 0.001, 0.001, 0.002],
'alpha2': [-4.731, -4.478, -4.401, -4.315],
'alpha2_err': [0.008, 0.008, 0.007, 0.018],
'beta1': [0.711, 0.813, 0.871, 0.985],
'beta1_err': [0.002, 0.002, 0.002, 0.003],
'beta2': [0.150, 0.064, 0.039, -0.017],
'beta2_err': [0.002, 0.002, 0.001, 0.001],
'beta3': [-3.536, -3.900, -4.019, -4.490],
'beta3_err': [0.016, 0.018, 0.014, 0.024],
'gamma1': [0.833, 1.074, 1.084, 0.978],
'gamma1_err': [0.002, 0.002, 0.002, 0.003],
'gamma2': [0.101, -0.058, -0.068, -0.013],
'gamma2_err': [0.002, 0.002, 0.001, 0.002],
'gamma3': [-0.461, -0.788, -0.535, 0.016],
'gamma3_err': [0.004, 0.004, 0.003, 0.004],
'gamma4': [-5.434, -7.733, -7.055, -4.386],
'gamma4_err': [0.022, 0.023, 0.018, 0.034],
},
'BH-BH': {
'redshift': [0.1, 1.0, 2.0, 6.0],
'alpha1': [0.807, 0.813, 0.831, 0.933],
'alpha1_err': [0.001, 0.001, 0.001, 0.004],
'alpha2': [-4.310, -3.845, -3.600, -4.190],
'alpha2_err': [0.006, 0.008, 0.008, 0.026],
'beta1': [0.812, 0.840, 0.858, 1.053],
'beta1_err': [0.001, 0.002, 0.002, 0.004],
'beta2': [-0.006, -0.029, -0.026, -0.098],
'beta2_err': [0.001, 0.002, 0.001, 0.002],
'beta3': [-4.358, -4.109, -3.850, -5.213],
'beta3_err': [0.013, 0.018, 0.015, 0.034],
'gamma1': [0.921, 1.134, 1.135, 1.131],
'gamma1_err': [0.001, 0.002, 0.002, 0.005],
'gamma2': [-0.051, -0.172, -0.167, -0.137],
'gamma2_err': [0.001, 0.002, 0.001, 0.002],
'gamma3': [-0.404, -0.839, -0.681, -0.171],
'gamma3_err': [0.003, 0.004, 0.003, 0.005],
'gamma4': [-6.049, -8.338, -7.758, -6.321],
'gamma4_err': [0.018, 0.024, 0.020, 0.047],
}
}


def m_star_merger_rate(redshift,
m_star,
population):
r"""M_star merger rate.
Model of Artale et al (2020), equation (1) with parameters
from Tables I, II and III.

Compact binary merger rates as a power law function of a galaxy's
stellar mass.

Parameters are redshift dependent, with linear interpolation
between the simulated points of z={0.1, 1, 2, 6}.

Parameters
----------
redshift : (ngal,) array_like
The redshifts of the galaxies to generate merger
rates for.
m_star : (ngal,) astropy.Quantity
The stellar mass of the galaxies to generate merger
rates for, in units of stellar mass.
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population : {'NS-NS', 'NS-BH', 'BH-BH'}
Compact binary population to get rate for.
'NS-NS' is neutron star - neutron star
'NS-BH' is neutron star - black hole
'BH-BH' is black hole - black hole

Returns
-------
merger_rate : (ngal,) astropy.Quantity
Merger rates for the galaxies in units of Gigayear^-1

Notes
-----

References
----------
.. Artale et al. 2020, MNRAS,
Volume 491, Issue 3, p.3419-3434 (2020)
https://arxiv.org/abs/1910.04890

"""

alpha1 = np.interp(redshift,
artale_tables[population]['redshift'],
artale_tables[population]['alpha1'])
alpha2 = np.interp(redshift,
artale_tables[population]['redshift'],
artale_tables[population]['alpha2'])

m_star = m_star.to(units.Msun).value

n_gw = 10.**(alpha1 * np.log10(m_star) + alpha2)

return n_gw / units.Gyr


def m_star_sfr_merger_rate(redshift,
m_star,
sfr,
population):
r"""M_star SFR merger rate.
Model of Artale et al (2020), equation (2) with parameters
from Tables I, II and III.

Compact binary merger rates as a power law function of a galaxy's
stellar mass.

Parameters are redshift dependent, with linear interpolation
between the simulated points of z={0.1, 1, 2, 6}.

Parameters
----------
redshift : (ngal,) array_like
The redshifts of the galaxies to generate merger
rates for.
m_star : (ngal,) astropy.Quantity
The stellar mass of the galaxies to generate merger
rates for, in units of stellar mass.
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Same as above

sfr : (ngal,) astropy.Quantity
The star formation rate of the galaxies to generate
merger rates for, in units of stellar mass per year
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You do a unit transformation for sfr as well. So do we need to specify here?

population : {'NS-NS', 'NS-BH', 'BH-BH'}
Compact binary population to get rate for.
'NS-NS' is neutron star - neutron star
'NS-BH' is neutron star - black hole
'BH-BH' is black hole - black hole

Returns
-------
merger_rate : astropy.Quantity
Merger rates for the galaxies in units of Gigayear^-1

Notes
-----

References
----------
.. Artale et al. 2020, MNRAS,
Volume 491, Issue 3, p.3419-3434 (2020)
https://arxiv.org/abs/1910.04890

"""

beta1 = np.interp(redshift,
artale_tables[population]['redshift'],
artale_tables[population]['beta1'])
beta2 = np.interp(redshift,
artale_tables[population]['redshift'],
artale_tables[population]['beta2'])
beta3 = np.interp(redshift,
artale_tables[population]['redshift'],
artale_tables[population]['beta3'])

m_star = m_star.to(units.Msun).value
sfr = sfr.to(units.Msun / units.year).value

n_gw = 10.**(beta1 * np.log10(m_star) + beta2 * np.log10(sfr) + beta3)

return n_gw / units.Gyr


def m_star_sfr_metallicity_merger_rate(redshift,
m_star,
sfr,
Z,
population):
r"""M_star SFR Metallicity merger rate.
Model of Artale et al (2020), equation (3) with parameters
from Tables I, II and III.

Compact binary merger rates as a power law function of a galaxy's
stellar mass.

Parameters are redshift dependent, with linear interpolation
between the simulated points of z={0.1, 1, 2, 6}.

Parameters
----------
redshift : (ngal,) array_like
The redshifts of the galaxies to generate merger
rates for.
m_star : (ngal,) astropy.Quantity
The stellar mass of the galaxies to generate merger
rates for, in units of stellar mass.
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sfr : (ngal,) astropy.Quantity
The star formation rate of the galaxies to generate
merger rates for, in units of stellar mass per year
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Z : (ngal,) array_like
The metallicity of the galaxies to generate merger
rates for.
population : {'NS-NS', 'NS-BH', 'BH-BH'}
Compact binary population to get rate for.
'NS-NS' is neutron star - neutron star
'NS-BH' is neutron star - black hole
'BH-BH' is black hole - black hole

Returns
-------
merger_rate : (ngal,) astropy.Quantity
Merger rates for the galaxies in units of Gigayear^-1

Notes
-----

References
----------
.. Artale et al. 2020, MNRAS,
Volume 491, Issue 3, p.3419-3434 (2020)
https://arxiv.org/abs/1910.04890

"""

gamma1 = np.interp(redshift,
artale_tables[population]['redshift'],
artale_tables[population]['gamma1'])
gamma2 = np.interp(redshift,
artale_tables[population]['redshift'],
artale_tables[population]['gamma2'])
gamma3 = np.interp(redshift,
artale_tables[population]['redshift'],
artale_tables[population]['gamma3'])
gamma4 = np.interp(redshift,
artale_tables[population]['redshift'],
artale_tables[population]['gamma4'])

m_star = m_star.to(units.Msun).value
sfr = sfr.to(units.Msun / units.year).value

n_gw = 10.**(gamma1 * np.log10(m_star) + gamma2 * np.log10(sfr) + gamma3 * np.log10(Z) + gamma4)

return n_gw / units.Gyr


def b_band_merger_rate(luminosity,
population='NS-NS',
optimism='low'):

r"""Model of Abadie et al (2010), Table III

Compact binary merger rates as a linear function of a galaxies
Compact binary merger rates as a linear function of a galaxy's
B-band luminosity.

Parameters
----------
luminosity : (ngal,) array-like
luminosity : (ngal,) astropy.Quantity
The B-band luminosity of the galaxies to generate merger
rates for, in units of solar luminosity.
population : {'NS-NS', 'NS-BH', 'BH-BH'}
Expand All @@ -55,7 +319,7 @@ def b_band_merger_rate(luminosity,

Returns
-------
merger_rate : array_like
merger_rate : astropy.Quantity
Merger rates for the galaxies in units of year^-1

Notes
Expand All @@ -67,21 +331,6 @@ def b_band_merger_rate(luminosity,
Volume 27, Issue 17, article id. 173001 (2010)
https://arxiv.org/abs/1003.2480

Examples
--------
>>> import numpy as np
>>> from skypy.gravitational_waves import b_band_merger_rate

Sample 100 luminosity values near absolute magnitude -20.5.

>>> luminosities = 10.**(-0.4*(-20.5 + np.random.randn(100)))

Generate merger rates for these luminosities.

>>> rates = b_band_merger_rate(luminosities,
... population='NS-NS',
... optimism='low')

"""

# Convert luminosity to units of L_10 defined in Abadie et. al. 2010
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