jesterTOV.eos.spectral.SpectralDecomposition_EOS_model

class SpectralDecomposition_EOS_model(

crust_name='SLy',

n_points_high=500,

reparametrized=False,

sigma_scale=1.0,

)

Bases: Interpolate_EOS_model

Spectral decomposition equation of state model.

This class implements the spectral decomposition EOS parametrization following Lindblom (2010) PRD 82, 103011 and Lackey & Wade (2018) PRD 98, 063004. The implementation matches LALSuite’s XLALSimNeutronStarEOS4ParameterSpectralDecomposition exactly.

The adiabatic index is parametrized as:

\[\log \Gamma(x) = \gamma_0 + \gamma_1 x + \gamma_2 x^2 + \gamma_3 x^3\]

where \(x = \log(p/p_0)\) is the dimensionless log-pressure.

Reference values (geometric units):

\(\varepsilon_0 = 9.54629006 \times 10^{-11} \, \mathrm{m}^{-2}\) \(p_0 = 4.43784199 \times 10^{-13} \, \mathrm{m}^{-2}\)

Thermodynamic relations from PRD 82, 103011 (2010):

\[\begin{split}\mu(x) &= \exp\left[-\int_0^x \frac{1}{\Gamma(x')} \, dx'\right] \\ \varepsilon(x) &= \varepsilon_0 \cdot \exp\left[\int_0^x \frac{\mu(x')}{1+\mu(x')} \, dx'\right] \\ p(x) &= p_0 \cdot \exp(x)\end{split}\]

Reparametrization (reparametrized=True):

When this flag is set the model expects tilde parameters \(\tilde\gamma = [\tilde\gamma_0, \tilde\gamma_1, \tilde\gamma_2, \tilde\gamma_3]\) drawn from a 4-D unit normal, and maps them to physical spectral coefficients via:

\[\boldsymbol{\gamma} = \boldsymbol{\mu}_\text{radio} + L_\text{wide}\,\tilde{\boldsymbol{\gamma}}\]

where \(\boldsymbol{\mu}_\text{radio}\) is the posterior mean from a radio-timing inference run and \(L_\text{wide} = \sigma_\text{scale}\,L\) is the Cholesky factor of the radio posterior covariance scaled by sigma_scale (default 1.0). Increasing sigma_scale broadens the reparametrized prior around the radio posterior. This concentrates the sampler around physically reasonable EOS.

__init__(

crust_name='SLy',

n_points_high=500,

reparametrized=False,

sigma_scale=1.0,

)

Initialize spectral decomposition EOS model.

Parameters:

• crust_name (str) – Name of crust model to use (‘SLy’, ‘DH’, ‘BPS’). Default ‘SLy’ for LALSuite compatibility.

• n_points_high (int) – Number of high-density points to generate. Default 500 to match LALSuite although this is a bit high.

• reparametrized (bool) – If True, expect tilde parameters \(\tilde\gamma_i\) drawn from a 4-D unit normal and apply the affine map \(\gamma = \mu_\text{radio} + L_\text{wide}\,\tilde\gamma\) inside construct_eos(). The _tilde suffix in the parameter names signals to the inference system that the whitened parametrization is active. Default False (original parametrization).

• sigma_scale (float) – Multiplicative factor applied directly to the base Cholesky factor \(L\) to form \(L_\text{wide} = \sigma_\text{scale}\,L\). This scales the standard deviation of the reparametrized distribution. Only used when reparametrized=True. Values greater than 1 broaden the reparametrized prior around the radio posterior; the default 1.0 uses the posterior standard deviation exactly. Must be strictly positive.

Methods

__init__([crust_name, n_points_high, ...])	Initialize spectral decomposition EOS model.
construct_eos(params)	Construct full EOS from spectral parameters.
get_required_parameters()	Return list of spectral parameters required for this EOS.
interpolate_eos(n, p, e)	Convert physical EOS quantities to geometric units and compute auxiliary quantities.

Attributes

REPARAM_L_BASE	Lower-triangular Cholesky factor \(L\) of the radio posterior covariance (\(\Sigma_\text{radio} = L\,L^\top\)).
REPARAM_MEAN	Posterior mean \(\boldsymbol{\mu}_\text{radio}\) of the spectral coefficients.
e0_geom
p0_geom
xmax

REPARAM_L_BASE: Float[Array, '4 4'] = Array([[ 3.41174267e-01,  0.00000000e+00,  0.00000000e+00,          0.00000000e+00],        [-2.12029883e-01,  1.15271551e-01,  0.00000000e+00,          0.00000000e+00],        [ 3.18696840e-02, -3.73794902e-02,  8.27531880e-03,          0.00000000e+00],        [-1.38603940e-03,  2.39274018e-03, -7.76593593e-04,          1.86425321e-04]], dtype=float64)

Lower-triangular Cholesky factor \(L\) of the radio posterior covariance (\(\Sigma_\text{radio} = L\,L^\top\)). The effective transform uses \(L_\text{wide} = \sigma_\text{scale}\,L\) where sigma_scale is set at initialisation time.

REPARAM_MEAN: Float[Array, '4'] = Array([ 0.92232738,  0.34177628, -0.08307007,  0.00413816], dtype=float64)

Posterior mean \(\boldsymbol{\mu}_\text{radio}\) of the spectral coefficients.

construct_eos(params)

Construct full EOS from spectral parameters.

This method: 1. Validates parameters and checks gamma bounds 2. Loads low-density crust (preprocessed via Crust class) 3. Generates high-density spectral region (500 points by default) 4. Stitches them together 5. Converts to geometric units and computes auxiliary quantities

Parameters:

params (dict[str, float]) – Dictionary containing: - gamma_0, gamma_1, gamma_2, gamma_3: Spectral coefficients

Return type:

EOSData

Returns:

EOSData –

Complete EOS with all required arrays in geometric units.

If gamma bounds are violated, extra_constraints contains the violation count.

e0_geom = 9.54629006e-11

get_required_parameters()

Return list of spectral parameters required for this EOS.

Return type:

list[str]

Returns:

list[str] – ["gamma_0", "gamma_1", "gamma_2", "gamma_3"] in the original parametrization, or ["gamma_0_tilde", "gamma_1_tilde", "gamma_2_tilde", "gamma_3_tilde"] when reparametrized=True.

p0_geom = 4.43784199e-13

xmax = 12.3081