pttools.omgw0.omgw0_ssm

Calculate the physical gravitational wave power spectrum \(\Omega_{\rm gw}(f)\) as a function of physical frequency \(f\) in the Sound shell model.

Classes

class pttools.omgw0.omgw0_ssm.Spectrum(bubble, y=None, z_st_thresh=ssm.Z_ST_THRESH, nuc_type=ssm.DEFAULT_NUC_TYPE, nt=NTDEFAULT, n_z_lookup=N_Z_LOOKUP_DEFAULT, r_star=None, lifetime_multiplier=1, compute=True, label_latex=None, label_unicode=None, Tn=None, g_star=None, gs_star=None)

Bases: SSMSpectrum

A spectrum object that includes \(\Omega_{\text{gw},0}\)

Parameters:

  • bubble (Bubble)

  • y (ndarray)

  • z_st_thresh (float)

  • nuc_type (NucType)

  • nt (int)

  • n_z_lookup (int)

  • r_star (float)

  • lifetime_multiplier (float)

  • compute (bool)

  • label_latex (str)

  • label_unicode (str)

  • Tn (float)

  • g_star (float)

  • gs_star (float)

F_gw0(g0=const.G0, gs0=const.GS0)
Parameters:

  • g0 (float)

  • gs0 (float)

Return type:

float

property Tn: float
f(z=None)
Parameters:

z (ndarray)

Return type:

float | float64 | ndarray

property f_star0: float
property g_star: float
property g_star_computed
property gs_star: float
property gs_star_computed: float
noise()
Return type:

ndarray

noise_ins()
Return type:

ndarray

omgw0(g0=const.G0, gs0=const.GS0, suppression=sup.SuppressionMethod.DEFAULT)
Parameters:

  • g0 (float)

  • gs0 (float)

  • suppression (SuppressionMethod)

Return type:

ndarray

omgw0_peak(g0=const.G0, gs0=const.GS0, suppression=sup.SuppressionMethod.DEFAULT)
Parameters:

  • g0 (float)

  • gs0 (float)

  • suppression (SuppressionMethod)

signal_to_noise_ratio()
Return type:

float

signal_to_noise_ratio_instrument()
Return type:

float

suppression_factor(method=sup.SuppressionMethod.DEFAULT)
Parameters:

method (SuppressionMethod)

Return type:

float

Functions

pttools.omgw0.omgw0_ssm.F_gw0(g_star, g0=const.G0, gs0=const.GS0, gs_star=None, om_gamma0=const.OMEGA_RADIATION)

Power attenuation following the end of the radiation era

\[F_{\text{gw},0} = \Omega_{\gamma,0} \left( \frac{g_{s0}}{g_{s*}} \right)^{4/9} \frac{g_*}{g_0} = (3.57 \pm 0.05) \cdot 10^{-5} \left( \frac{100}{g_*} \right)^{1/3}\]
There is a typo in Gowling & Hindmarsh, 2021 eq. 2.11: the \(\frac{4}{9}\) should be \(\frac{4}{3}\).

Parameters:
Return type:

float | float64 | ndarray

pttools.omgw0.omgw0_ssm.J(r_star, K_frac, nu=0)

Pre-factor to convert power_gw_scaled to predicted spectrum approximation of \((H_n R_*)(H_n \tau_v)\) updating to properly convert from flow time to source time

\[J = H_n R_* H_n \tau_v = r_* \left(1 - \frac{1}{\sqrt{1 + 2x}} \right)\]
Gowling & Hindmarsh, 2021 eq. 2.8

Parameters:

  • r_star (float | float64 | ndarray)

  • K_frac (float | float64 | ndarray)

  • nu (float)

Return type:

float | float64 | ndarray

pttools.omgw0.omgw0_ssm.f(z, r_star, f_star0)

Convert the dimensionless wavenumber \(z\) to frequency today by taking into account the redshift. $$f = \frac{z}{r_*} f_{*,0}$$, Gowling & Hindmarsh, 2021 eq. 2.12

Parameters:

  • z (float | float64 | ndarray) – dimensionless wavenumber \(z\)

  • r_star (float | float64 | ndarray) – Hubble-scaled mean bubble spacing

  • f_star0 (float | float64 | ndarray)

Returns:

frequency \(f\) today

Return type:

float | float64 | ndarray

pttools.omgw0.omgw0_ssm.f0(rs, T_n=const.T_default, g_star=100)

Factor required to take into account the redshift of the frequency scale

Parameters:

  • rs (float | float64 | ndarray)

  • T_n (float | float64 | ndarray)

  • g_star (float)

Return type:

float | float64 | ndarray

pttools.omgw0.omgw0_ssm.f_star0(Tn, g_star=100)

Conversion factor between the frequencies at the time of the nucleation and frequencies today. $$f_{,0} = 2.6 cdot 10^{-6} text{Hz} left( frac{T_n}{100 text{GeV}} right) left( frac{g_}{100} right)^{frac{1}{6}}$$, Gowling & Hindmarsh, 2021 eq. 2.13 :param Tn: Nucleation temperature :param g_star: Degrees of freedom at the time the GWs were produced. The default value is from the article. :return:

Parameters:
Return type:

float | float64 | ndarray

pttools.omgw0.omgw0_ssm.omgw0_bag(freqs, vw, alpha, r_star, T=const.T_default, npt=NPTDEFAULT, suppression=sup.SuppressionMethod.DEFAULT)

For given set of thermodynamic parameters vw, alpha, rs and Tn calculates the power spectrum using the SSM as encoded in the PTtools module (omgwi) Gowling & Hindmarsh, 2021 eq. 2.14

Parameters:

  • freqs (ndarray)

  • vw (float)

  • alpha (float)

  • r_star (float)

  • T (float)

  • npt (ndarray | Tuple[int, int, int])

  • suppression (SuppressionMethod)

pttools.omgw0.omgw0_ssm.r_star(H_n, R_star)

\[r_* = H_n R_*\]
Gowling & Hindmarsh, 2021 eq. 2.2

Parameters:
Return type:

float | float64 | ndarray