physconst_template.h

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/* This file is part of Cloudy and is copyright (C)1978-2025 by Gary J. Ferland and
 * others.  For conditions of distribution and use see copyright notice in license.txt */
 
// >>>>>>>> WARNING: do not #define PHYSCONST_TEMPLATE_H_
 
// >>>>>>>> WARNING: This is a header template file, designed to be included
// on more than one occasion, with the macro NEW_CONSTANT defined to achieve
// different actions on each include, and no include guard
//
// Do not include anything here which isn't required for this single purpose

 
/*********************************************************************
 * first come math constants                                         *
 *********************************************************************/
 
// Define macros for mathematical operations, undefined at foot of file
// Can be converted back when constexpr can be relied on to accept sqrt()
 
#define pow2(a) ((a)*(a))
#define pow3(a) ((a)*(a)*(a))

NEW_CONSTANT( EE, 2.718281828459045235360287 );

NEW_CONSTANT( EULER, 0.577215664901532860606512090082 );

NEW_CONSTANT( EXPEULER2, 0.74930600128844902360587 );

NEW_CONSTANT( PI, 3.141592653589793238462643 );

NEW_CONSTANT( PI2, 6.283185307179586476925287 );

NEW_CONSTANT( PI4, 12.56637061435917295385057 );

NEW_CONSTANT( PI8, 25.13274122871834590770115 );

NEW_CONSTANT( SQRT2, 1.414213562373095048801689 );

NEW_CONSTANT( SQRTPI, 1.772453850905516027298167 );

NEW_CONSTANT( SQRTPIBY2, 1.253314137315500251207883 );

NEW_CONSTANT( LN_TWO, 0.6931471805599453094172321 );

NEW_CONSTANT( LN_TEN, 2.302585092994045684017991 );

NEW_CONSTANT( LOG10_E, 0.4342944819032518276511289 );

NEW_CONSTANT( OPTDEP2EXTIN, 1.085736204758129569127822 );

NEW_CONSTANT( RADIAN, 57.29577951308232087679815 );
 
/*********************************************************************
 * astronomical constants go here                                    *
 *********************************************************************/

NEW_CONSTANT( SOLAR_MASS, 1.98841e33 );

NEW_CONSTANT( SOLAR_LUMINOSITY, 3.828e33 );

NEW_CONSTANT( MBOL_ZERO_LUMINOSITY, 3.0128e35 );

/* >>refer      phys    const   https://pdg.lbl.gov/2021/reviews/rpp2021-rev-astrophysical-constants.pdf */
NEW_CONSTANT( AU, 1.49597870700e13 );
 
/*********************************************************************
 * fundamental constants go next, eventually rest should be defined  *
 * in terms of these, these are CODATA 2022 values.                  *
 *********************************************************************/

NEW_CONSTANT( ELECTRON_MASS, 9.1093837139e-28 );

NEW_CONSTANT( ELECTRON_MASS_U, 5.485799090441e-4 );

NEW_CONSTANT( PROTON_MASS, 1.67262192595e-24 );

NEW_CONSTANT( PROTON_MASS_U, 1.0072764665789 );

NEW_CONSTANT( ALPHA_MASS_U, 4.001506179129 );

NEW_CONSTANT( BOLTZMANN, 1.380649e-16 );

NEW_CONSTANT( SPEEDLIGHT, 2.99792458e10 );

NEW_CONSTANT( HPLANCK, 6.62607015e-27 );

NEW_CONSTANT( AVOGADRO, 6.02214076e23 );

NEW_CONSTANT( GRAV_CONST, 6.67430e-8 );

NEW_CONSTANT( ELEM_CHARGE, 1.602176634e-19 );

NEW_CONSTANT( RYD_INF, 1.0973731568157e5 );

NEW_CONSTANT( HIONPOT, 0.999466508345 );

NEW_CONSTANT( HE2IONPOT, 3.99963199547 );

NEW_CONSTANT( HMINUSIONPOT, 0.055432956 );

NEW_CONSTANT( ATOMIC_MASS_UNIT, 1.66053906892e-24 );
 
/*********************************************************************
 * below here should be derived constants                            *
 *                                                                   *
 * NB - explicit values in comments are approximate                  *
 *      and are not maintained !                                     *
 *                                                                   *
 * use the PRINT CONSTANTS command to get precise values             *
 *********************************************************************/

NEW_CONSTANT( MOL_MASS_CONST, AVOGADRO*ATOMIC_MASS_UNIT );

NEW_CONSTANT( AS1RAD, RADIAN*3600. );

NEW_CONSTANT( SQAS1SR, pow2(AS1RAD) );

NEW_CONSTANT( SQAS_SKY, PI4*SQAS1SR );

NEW_CONSTANT( PARSEC, AU*AS1RAD );

NEW_CONSTANT( MEGAPARSEC, 1.e6*PARSEC );

NEW_CONSTANT( H_BAR, HPLANCK/(2.*PI) );

NEW_CONSTANT( ELEM_CHARGE_ESU, ELEM_CHARGE*SPEEDLIGHT/10. );

NEW_CONSTANT( ELECTRIC_CONST, 1.e11/(PI4*pow2(SPEEDLIGHT)) );

NEW_CONSTANT( HION_LTE_POP, pow2(HPLANCK)/(PI2*BOLTZMANN*ELECTRON_MASS) );

#ifdef HAVE_CONSTEXPR
NEW_CONSTANT( SAHA, sqrt(pow3(HION_LTE_POP)) );
#else
// Need to use explicit constant rather than formula as sqrt() isn't
// guaranteed to be evaluated at compile-time.  Checked by an ASSERT
// in t_physconst::t_physconst() in physconst.cpp
NEW_CONSTANT( SAHA, 4.141330276355497e-16 );
#endif

NEW_CONSTANT( ERG1CM, HPLANCK*SPEEDLIGHT );

NEW_CONSTANT( T1CM, HPLANCK*SPEEDLIGHT/BOLTZMANN );

NEW_CONSTANT( KJMOL1CM, ERG1CM*AVOGADRO/1e10 );

NEW_CONSTANT( H_RYD_FACTOR, 1./(1.+ELECTRON_MASS_U/PROTON_MASS_U) );

NEW_CONSTANT( HE_RYD_FACTOR, 1./(1.+ELECTRON_MASS_U/ALPHA_MASS_U) );

NEW_CONSTANT( WAVNRYD, 1./RYD_INF );

NEW_CONSTANT( RYDLAM, 1.e8/RYD_INF );

NEW_CONSTANT( EN1RYD, HPLANCK*SPEEDLIGHT*RYD_INF );

NEW_CONSTANT( TE1RYD, HPLANCK*SPEEDLIGHT*RYD_INF/BOLTZMANN );

NEW_CONSTANT( EVDEGK, ELEM_CHARGE*1.e7/BOLTZMANN );

NEW_CONSTANT( EVRYD, HPLANCK*SPEEDLIGHT*RYD_INF/ELEM_CHARGE*1.e-7 );

NEW_CONSTANT( EN1EV, EN1RYD/EVRYD );

NEW_CONSTANT( FR1RYD, SPEEDLIGHT*RYD_INF );

NEW_CONSTANT( HNU3C2, 2.*HPLANCK*SPEEDLIGHT*pow3(RYD_INF) );

NEW_CONSTANT( FR1RYDHYD, SPEEDLIGHT*RYD_INF*HIONPOT );

NEW_CONSTANT( HBAReV, H_BAR/EN1EV );  

NEW_CONSTANT( RYDLAMHYD, RYDLAM/HIONPOT );

NEW_CONSTANT( STEFAN_BOLTZ, pow2(PI*pow2(BOLTZMANN))/(60.*pow3(H_BAR)*pow2(SPEEDLIGHT)) );

NEW_CONSTANT( FREQ_1EV, SPEEDLIGHT*RYD_INF/EVRYD );

NEW_CONSTANT( FINE_STRUCTURE, pow2(ELEM_CHARGE_ESU)/SPEEDLIGHT/H_BAR );

NEW_CONSTANT( FINE_STRUCTURE2, pow2(FINE_STRUCTURE) );

NEW_CONSTANT( BOHR_RADIUS_CM, FINE_STRUCTURE/(PI4*RYD_INF) );

NEW_CONSTANT( TWO_PHOT_CONST, 9.*pow3(FINE_STRUCTURE2)*FR1RYD/2048. );

NEW_CONSTANT( COLL_CONST, SAHA*BOLTZMANN/HPLANCK );

#ifdef HAVE_CONSTEXPR
NEW_CONSTANT( MILNE_CONST, SPEEDLIGHT*sqrt(pow3(FINE_STRUCTURE2)*pow3(TE1RYD)/PI) );
#else
// Need to use explicit constant rather than formula as sqrt() isn't
// guaranteed to be evaluated at compile-time.  Checked by an ASSERT
// in t_physconst::t_physconst() in physconst.cpp
NEW_CONSTANT( MILNE_CONST, 4.123475589581428e+11 );
#endif
 
NEW_CONSTANT( TRANS_PROB_CONST, PI4*HPLANCK*FINE_STRUCTURE/ELECTRON_MASS );

NEW_CONSTANT( ABSOR_COEFF_CONST, SQRTPI*pow2(ELEM_CHARGE_ESU)/(ELECTRON_MASS*SPEEDLIGHT) );

NEW_CONSTANT( SIGMA_THOMSON, PI8/3.*pow2(FINE_STRUCTURE*H_BAR/(ELECTRON_MASS*SPEEDLIGHT)) );

NEW_CONSTANT( HC_ERG_ANG, HPLANCK*SPEEDLIGHT*1e8 );

NEW_CONSTANT( JEANS, PI*BOLTZMANN/(GRAV_CONST*ATOMIC_MASS_UNIT) );
 
/* Free-free emission constant.
 * This is defined as the constant in the FF cooling equation (5.14a) in Rybicki & Lightman
 * divided by the Planck constant.  This is obtained by integrating equation (5.14a) over
 * frequency and changing variables to energy in units of R_inf.  A factor R_inf*c comes out
 * of the integral, which is accounted for by multiplying the constant by EN1RYD = R_inf * h * c,
 * but we need to correct for the extra h.
 * The exact equation is:
 *     32*pi * e^6 / (3 * h * m_e * c^3) * sqrt(2*pi / (3 * k_Boltzmann * m_e))
 */
#ifdef HAVE_CONSTEXPR
NEW_CONSTANT( FREE_FREE_EMIS,
                          32. * PI * pow2(pow3(ELEM_CHARGE_ESU)) /
                          (3. * pow3(SPEEDLIGHT) * ELECTRON_MASS * HPLANCK ) *
                          sqrt(2. * PI / (3. * BOLTZMANN * ELECTRON_MASS ) ) );
#else
// Need to use explicit constant rather than formula as sqrt() isn't
// guaranteed to be evaluated at compile-time.  Checked by an ASSERT
// in t_physconst::t_physconst() in physconst.cpp
NEW_CONSTANT( FREE_FREE_EMIS, 1.032526505912028e-11 );
#endif
 
/* Free-free absorption constant.
 * The constant is obtained by considering the integral of absorption over frequency
 * to compute the total heating rate.  The logic is similar to that for the emission
 * constant above.  NB  The radiation field is already expressed as dnu*Inu, so that
 * leaves 3 powers of (R_inf * c) in the denominator, from the nu^-3 dependence --
 * see Rybicki & Lightman eqn (5.18a).
 *
 * The exact constant is:
 *     4 * e^6 / (3 * h * m * c) * sqrt(2*pi / (3 * k_Boltzmann * m_e)) / (R_inf * c)^3
 */
#ifdef HAVE_CONSTEXPR
NEW_CONSTANT( FREE_FREE_ABS,
                          4. * pow2(pow3(ELEM_CHARGE_ESU)) /
                          (3. * HPLANCK * ELECTRON_MASS * SPEEDLIGHT ) *
                          sqrt(2. * PI / (3. * BOLTZMANN * ELECTRON_MASS ) ) /
                          pow3(SPEEDLIGHT * RYD_INF) );
#else
// Need to use explicit constant rather than formula as sqrt() isn't
// guaranteed to be evaluated at compile-time.  Checked by an ASSERT
// in t_physconst::t_physconst() in physconst.cpp
NEW_CONSTANT( FREE_FREE_ABS, 1.036997355477227e-38 );
#endif