analysis

analysis.py is a Python routine that contains functions used in the analyses of potential detection of GW signals by space-based GW detectors (LISA or Taiji).

Currently part of the cosmoGW code:

https://github.com/cosmoGW/cosmoGW/ https://github.com/cosmoGW/cosmoGW/blob/main/src/cosmoGW/analysis.py

Note

For full documentation, visit Read the Docs.

To use it, first install cosmoGW:

pip install cosmoGW

Author

Dates

References

  • [RoperPol:2022iel]: A. Roper Pol, C. Caprini, A. Neronov, D. Semikoz, “The gravitational wave signal from primordial magnetic fields in the Pulsar Timing Array frequency band,” Phys. Rev. D 105, 123502 (2022), arXiv:2201.05630.

  • [RoperPol:2023bqa]: A. Roper Pol, A. Neronov, C. Caprini, T. Boyer, D. Semikoz, “LISA and γ-ray telescopes as multi-messenger probes of a first-order cosmological phase transition,” arXiv:2307.10744 (2023).

cosmoGW.analysis.analysis_LISA_alphabeta(s, alphas, betas, vws, TTs, eps_turb=1.0, turb=True, cs2=0.3333333333333333, quiet=True, a_sw=3, b_sw=1, c_sw=3, alp1_sw=0, alp2_sw=0, corrRs=True, expansion=True, Nsh=1.0, model_efficiency='fixed_value', OmGW_tilde=0.01, bs_HL_eff=20, model_K0='Espinosa', bs_k1HL=40, model_decay='sound_waves', interpolate_HL_decay=True, b=0, model_shape='sw_LISA', strength='weak', interpolate_HL_shape=False, interpolate_HL_n3=False, N_turb=2, a_turb=5, b_turb=0.6666666666666666, alp_turb=0.35294117647058826, tdecay='eddy', tp='both', alpPi_turb=2.15, fPi_turb=2.2, bPi_turb=3, h0=1.0, Neff=3, interf='LISA', Tobs=4)

Compute the signal-to-noise ratio (SNR) for gravitational wave backgrounds from sound waves and turbulence in a first-order cosmological phase transition, for a range of phase transition and detector parameters, comparing the sensitivity of LISA with 4 years of observations (and no foregrounds).

This function calculates the GW spectrum for sound waves and turbulence, redshifts it to today, and computes the SNR for a given detector sensitivity. It supports vectorized input for all physical parameters, automatically adapting the output shape to match scalar or array inputs.

Parameters

sarray_like

Array of normalized wave numbers, \(s = f R_\ast\).

alphasfloat or array_like

Strength of the phase transition \(\alpha\) (latent heat fraction).

betasfloat or array_like

Nucleation rate of the phase transition \(\beta/H_\ast\).

vwsfloat or array_like

Bubble wall velocity \(v_w\).

TTsfloat, array_like, or astropy.units.Quantity

Temperature(s) of the phase transition (can be MeV, GeV, etc).

eps_turbfloat or array_like, optional

Fraction of kinetic energy converted to turbulence (default: 1).

turbbool, optional

If True, include turbulence contribution (default: True).

cs2float, optional

Square of the speed of sound (default: 1/3).

quietbool, optional

Suppress verbose output (default: True).

a_sw, b_sw, c_swfloat, optional

Spectral slopes for spectral shape of GWs from sound waves (default 3, 1, 3).

alp1_sw, alp2_swfloat, optional

Additional shape parameters for sound waves (default are the reference values for model_shape=`sw_LISA`, see GW_templates.OmGW_spec_sw).

corrRsbool, optional

Correct Rstar beta with \(\max(v_w, c_s)\) (default: True).

expansionbool, optional

Include Universe expansion (default: True).

Nshfloat, optional

Duration of the sound waves sourcing in number of shock formation times (default: 1).

model_efficiencystr, optional

Model for GW production efficiency (default: ‘fixed_value’, other option is ‘higgsless’).

OmGW_tildefloat, optional

Reference amplitude for GW spectrum (default: 1e-2).

bs_HL_eff, bs_k1HLint, optional

Box size parameters for Higgsless simulation interpolation for UV and IR quantities (default: 20, 40), used if model_efficiency=’higgsless’, model_decay=’decay’ with interpolate_HL_decay True, or model_shape=’sw_HL_new with interpolate_HL_shape True.

model_K0str, optional

Model for kinetic energy ratio (‘Espinosa’ or ‘higgsless’).

model_decaystr, optional

Model for decay of the source (‘sound_waves’, ‘decay’).

interpolate_HL_decaybool, optional

Interpolate decay parameter from HL simulations if model_decay=’decay’ (default: True).

bfloat, optional

Decay parameter (default: 0).

model_shapestr, optional

Spectral shape model for sound waves (default: ‘sw_LISA’).

strengthstr, optional

Strength regime for HL shape interpolation (default: ‘weak’, used when model_shape=’sw_HL_new’ and interpolate_HL_shape False).

interpolate_HL_shapebool, optional

Interpolate HL shape (default: False, used when model_shape=’sw_HL_new’).

interpolate_HL_n3bool, optional

Interpolate HL n3 slope parameter (default: False, used when model_shape=’sw_HL_new’).

N_turbint, optional

Ratio between decay time and effective source duration for turbulence production of GWs.

a_turb, b_turb, alp_turbfloat, optional

Spectral fit parameters (slopes and smoothness) for turbulence (default 5, 2/3, 2).

tdecaystr, optional

Determines finite duration in the turbulence model (default ‘eddy’).

tpstr, optional

Type of turbulence source (‘both’, ‘magnetic’, ‘kinetic’).

alpPi_turb, fPi_turb, bPi_turbfloat, optional

Parameters for the anisotropic stress fit for turbulence.

h0float, optional

Hubble rate at present time (default 1), such that \(H_0 = 100\) km/s/Mpc.

Neffint, optional

Effective number of neutrino species (default: 3).

interfstr, optional

Detector/interferometer name (default: ‘LISA’).

Tobsfloat, optional

Observation time in years (default: 4 years).

Returns

SNRndarray

Signal-to-noise ratio for each parameter combination. The output shape adapts to the input: axes corresponding to scalar inputs are squeezed. For example, if all inputs are arrays, shape is (len(eps_turb), len(TTs), len(vws), len(alphas), len(betas)). If some inputs are scalars, those axes are removed.

References

RoperPol:2022iel, RoperPol:2023bqa