pttools.models.sm

Standard Model equation of state

Classes

class pttools.models.sm.StandardModel(g_mult_s=1, g_mult_b=1, V_s=0, V_b=0, name=None, T_min=None, T_max=None, restrict_to_valid=True, label_latex=None, label_unicode=None, gen_cs2=True, silence_temp=False)

Bases: ThermoModel

Standard Model equation of state

Based on cubic spline interpolation for the effective degrees of freedom of the Standard Model. Data range \(0 - 10^{5.45}\) MeV from the table S2 of Borsanyi et al., 2016. Units are in MeV.

Parameters:

  • g_mult_s (float)

  • g_mult_b (float)

  • V_s (float)

  • V_b (float)

  • name (str)

  • T_min (float)

  • T_max (float)

  • restrict_to_valid (bool)

  • label_latex (str)

  • label_unicode (str)

  • gen_cs2 (bool)

  • silence_temp (bool)

DEFAULT_LABEL_LATEX: str = 'Standard Model'
DEFAULT_LABEL_UNICODE: str = 'Standard Model'
DEFAULT_NAME: str = 'standard_model'
DEFAULT_T_MAX: float = np.float64(281838.2931264455)
DEFAULT_T_MIN: float = np.float64(1.0)
GEFF_DATA = array([[  0.     ,   0.5    ,   1.     ,   1.25   ,   1.6    ,   2.     ,           2.15   ,   2.2    ,   2.4    ,   2.5    ,   3.     ,   4.     ,           4.3    ,   4.6    ,   5.     ,   5.45   ],        [ 10.71   ,  10.74   ,  10.76   ,  11.09   ,  13.68   ,  17.61   ,          24.07   ,  29.84   ,  47.83   ,  53.04   ,  73.48   ,  83.1    ,          85.56   ,  91.97   , 102.17   , 104.98   ],        [  1.00228,   1.00029,   1.00048,   1.00505,   1.02159,   1.02324,           1.05423,   1.07578,   1.06118,   1.0469 ,   1.01778,   1.00123,           1.00389,   1.00887,   1.0075 ,   1.00023]])
GEFF_DATA_GE = array([ 10.71,  10.74,  10.76,  11.09,  13.68,  17.61,  24.07,  29.84,         47.83,  53.04,  73.48,  83.1 ,  85.56,  91.97, 102.17, 104.98])
GEFF_DATA_GE_GS_RATIO = array([1.00228, 1.00029, 1.00048, 1.00505, 1.02159, 1.02324, 1.05423,        1.07578, 1.06118, 1.0469 , 1.01778, 1.00123, 1.00389, 1.00887,        1.0075 , 1.00023])
GEFF_DATA_GS = array([ 10.68563675,  10.7368863 ,  10.75483768,  11.0342769 ,         13.39089067,  17.2100387 ,  22.83182987,  27.73801335,         45.0724665 ,  50.66386474,  72.19634892,  82.99791257,         85.22846129,  91.1613984 , 101.40942928, 104.95586015])
GEFF_DATA_LOG_TEMP: ndarray = array([0.  , 0.5 , 1.  , 1.25, 1.6 , 2.  , 2.15, 2.2 , 2.4 , 2.5 , 3.  ,        4.  , 4.3 , 4.6 , 5.  , 5.45])

Container for the log10 temperatures of \(g_\text{eff}\) data

GEFF_DATA_TEMP: ndarray = array([1.00000000e+00, 3.16227766e+00, 1.00000000e+01, 1.77827941e+01,        3.98107171e+01, 1.00000000e+02, 1.41253754e+02, 1.58489319e+02,        2.51188643e+02, 3.16227766e+02, 1.00000000e+03, 1.00000000e+04,        1.99526231e+04, 3.98107171e+04, 1.00000000e+05, 2.81838293e+05])

Container for the temperatures of \(g_\text{eff}\) data

GE_GS_RATIO_SPLINE = (array([0.  , 0.  , 0.  , 0.  , 1.  , 1.25, 1.6 , 2.  , 2.15, 2.2 , 2.4 ,        2.5 , 3.  , 4.  , 4.3 , 4.6 , 5.45, 5.45, 5.45, 5.45]), array([1.00228   , 1.00111734, 0.99814066, 1.0025812 , 1.03172131,        1.01015023, 1.03512559, 1.1049024 , 1.06249373, 1.03037781,        1.01071172, 0.99855174, 1.00314972, 1.01447269, 1.00423606,        1.00023   , 0.        , 0.        , 0.        , 0.        ]), 3)
GE_SPLINE = (array([0.  , 0.  , 0.  , 0.  , 1.  , 1.25, 1.6 , 2.  , 2.15, 2.2 , 2.4 ,        2.5 , 3.  , 4.  , 4.3 , 4.6 , 5.45, 5.45, 5.45, 5.45]), array([ 10.71      ,  10.72147224,  10.77195831,  10.75208058,         13.97175682,  16.14887948,  19.3665458 ,  36.32828416,         46.70267551,  59.39484605,  83.93815179,  81.43498826,         84.6979596 ,  95.98808458, 108.82718917, 104.98      ,          0.        ,   0.        ,   0.        ,   0.        ]), 3)
GS_SPLINE = (array([0.  , 0.  , 0.  , 0.  , 1.  , 1.25, 1.6 , 2.  , 2.15, 2.2 , 2.4 ,        2.5 , 3.  , 4.  , 4.3 , 4.6 , 5.45, 5.45, 5.45, 5.45]), array([ 10.68563675,  10.71155646,  10.78875531,  10.72709596,         13.60050033,  15.82322449,  18.89190919,  33.12782602,         43.78721812,  57.58978961,  82.82957709,  81.56975649,         84.43953549,  94.66655542, 108.27420634, 104.95586015,          0.        ,   0.        ,   0.        ,   0.        ]), 3)
TEMPERATURE_IS_PHYSICAL: bool = True

Whether the temperature is in proper physics units

V(phase)
Parameters:

phase (ndarray)

Return type:

ndarray

dge_dT(temp, phase)

\(\frac{dg_e}{dT}\)

Parameters:
Return type:

float | float64 | ndarray

dgs_dT(temp, phase)

\(\frac{dg_s}{dT}\)

Parameters:
Return type:

float | float64 | ndarray

g_mult(phase)
Parameters:

phase (float | float64 | ndarray)

Return type:

float | float64 | ndarray

ge(temp, phase)

Effective degrees of freedom for the energy density \(g_{\text{eff},e}(T)\)

Parameters:

  • temp (float | float64 | ndarray) – temperature \(T\) (MeV)

  • phase (float | float64 | ndarray) – phase \(\phi\)

Returns:

\(g_{\text{eff},e}\)

Return type:

float | float64 | ndarray

ge_gs_ratio(temp, phase)
Parameters:
Return type:

float | float64 | ndarray

gs(temp, phase)

Effective degrees of freedom for the entropy density, \(g_{\text{eff},s}(T)\)

Parameters:

  • temp (float | float64 | ndarray) – temperature \(T\) (MeV)

  • phase (float | float64 | ndarray) – phase \(\phi\)

Returns:

\(g_{\text{eff},s}\)

Return type:

float | float64 | ndarray