GWForge.population.pdb_external¶
Power Law + Dip + Break models. None are reviewed.
Classes¶
2D "Power Law + Dip + Break" Model with a pairing function that depends on m2. |
Functions¶
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The one-dimensional mass distribution considered in Fishbach, Essick, Holz. Does |
Module Contents¶
- GWForge.population.pdb_external.power_law_dip_break_1d(mass, A, A2, NSmin, NSmax, BHmin, BHmax, UPPERmin, UPPERmax, n0, n1, n2, n3, n4, n5, alpha_1, alpha_2, alpha_dip, mu1, sig1, mix1, mu2, sig2, mix2, absolute_mmin, absolute_mmax)[source]¶
The one-dimensional mass distribution considered in Fishbach, Essick, Holz. Does Matter Matter? ApJ Lett 899, 1 (2020) : arXiv:2006.13178
\[\begin{split}p(m|\lambda) = n(m|\gamma_{\text{low}}, \gamma_{\text{high}}, A) \times l(m|m_{\text{max}}, \eta) \\ \times \begin{cases} & m^{\alpha_1} \text{ if } m < \gamma_{\text{low}} \\ & m^{\alpha_2} \text{ if } m > \gamma_{\text{low}} \\ & 0 \text{ otherwise } \end{cases}.\end{split}\]where $l(m|m_{text{max}}, eta)$ is the low pass filter with powerlaw $eta$ applied at mass $m_{text{max}}$, $n(m|gamma_{text{low}}, gamma_{text{high}}, A)$ is the notch filter with depth $A$ applied between $gamma_{text{low}}$ and $gamma_{text{high}}$, and $lambda$ is the subset of hyperparameters ${ gamma_{text{low}}, gamma_{text{high}}, A, alpha_1, alpha_2, m_{text{min}}, m_{text{max}}}$.
- Parameters:
mass (array-like) – Mass to evaluate probability at (\(m\)).
alpha_1 (float) – Powerlaw exponent for compact objects below NSmax (\(\alpha_1\)).
alpha_2 (float) – Powerlaw exponent for compact objects above BHmin (\(\alpha_2\)).
alpha_dip (float) – Powerlaw exponent for compact objects between NSmax and BHmin (:math: alpha_d).
NSmin (float) – Minimum compact object mass (\(m_\min\)).
NSmax (float) – Mass at which the notch filter starts for the lower mass gap (\(\gamma_{low1}\)).
BHmin (float) – Mass at which the notch filter ends for the lower mass gap (\(\gamma_{high1}\)).
BHmax (float) – Maximum mass in the powerlaw distributed component (\(m_\max\)).
A (float) – depth of the dip between NSmax and BHmin (A).
UPPERmin (float) – Mass at which the notch filter starts for the upper mass gap (\(\gamma_{low2}\)).
UPPERmax (float) – Mass at which the notch filter ends for the upper mass gap (\(\gamma_{high2}\)).
mu1 (float) – Location of the upper peak where an overdensity of merging compact objects is observed (\(\mu_{peak1}\))..
sig1 (float) – Width of the upper peak where an overdensity of merging compact objects is observed (\(\sigma_{peak1}\))..
mix1 (float) – Mixing fraction of the first gaussian peak with the powerlaw + notches (:math: c_1)
mu2 (float) – Location of the lower peak where an overdensity of merging compact objects is observed (\(\mu_{peak2}\))..
sig2 (float) – Width of the lower peak where an overdensity of merging compact objects is observed (\(\mu_{peak2}\))..
mix2 (float) – Mixing fraction of the second gaussian peak with the powerlaw + notches (:math: c_2)
absolute_mmin (float) – The minimum limit for the truncated normal distribution.
absolute_mmax (float) – The maximum limit for the truncated normal distribution.
n{0 (float) – Exponents to set the sharpness of the low mass cutoff and high mass cutoff, respectively (\(\eta_i\)).
5} (float) – Exponents to set the sharpness of the low mass cutoff and high mass cutoff, respectively (\(\eta_i\)).
n{1 (float) – Exponents to set the sharpness of the lower edge and upper edge of the lower mass gap, respectively (\(\eta_i\)).
2} (float) – Exponents to set the sharpness of the lower edge and upper edge of the lower mass gap, respectively (\(\eta_i\)).
n{3 (float) – Exponents to set the sharpness of the lower edge and upper edge of the upper mass gap, respectively (\(\eta_i\)).
4} (float) – Exponents to set the sharpness of the lower edge and upper edge of the upper mass gap, respectively (\(\eta_i\)).