physconst_template.h File Reference

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Macros
#define	pow2(a)   ((a)*(a))
#define	pow3(a)   ((a)*(a)*(a))

Functions
	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)
	NEW_CONSTANT (SOLAR_MASS, 1.98848e33)
	NEW_CONSTANT (SOLAR_LUMINOSITY, 3.828e33)
	NEW_CONSTANT (MBOL_ZERO_LUMINOSITY, 3.0128e35)
	NEW_CONSTANT (AU, 1.49597870700e13)
	NEW_CONSTANT (ELECTRON_MASS, 9.1093837015e-28)
	NEW_CONSTANT (ELECTRON_MASS_U, 5.48579909065e-4)
	NEW_CONSTANT (PROTON_MASS, 1.67262192369e-24)
	NEW_CONSTANT (PROTON_MASS_U, 1.007276466621)
	NEW_CONSTANT (ALPHA_MASS_U, 4.001506179127)
	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, 1.0973731568160e5)
	NEW_CONSTANT (HIONPOT, 0.999466508345)
	NEW_CONSTANT (HE2IONPOT, 3.99963199547)
	NEW_CONSTANT (HMINUSIONPOT, 0.055432956)
	NEW_CONSTANT (ATOMIC_MASS_UNIT, 1.66053906660e-24)
	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))
	NEW_CONSTANT (SAHA, 4.1413302848114741e-16)
	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)
	NEW_CONSTANT (MILNE_CONST, 4.1234755895831189e+11)
	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))
	NEW_CONSTANT (FREE_FREE_EMIS, 1.0325265080202923e-11)
	NEW_CONSTANT (FREE_FREE_ABS, 1.0369973575937702e-38)

Detailed Description

* physical constants used by Cloudy, mostly taken from
* >>refer       phys    const   CODATA 2018, https://physics.nist.gov/cuu/Constants/
* <BR><BR>
* NB - these are all printed with the "print constants" command, 
* which is in parse_print.cpp. Using the NEW_CONSTANT macro guarantees
* that any constant added here is printed there as well 

Macro Definition Documentation

#define pow2

(

a

)

((a)*(a))

#define pow3

(

a

)

((a)*(a)*(a))

Function Documentation

NEW_CONSTANT	(	EE	,
		2.	718281828459045235360287
	)

the number e

NEW_CONSTANT	(	EULER	,
		0.	577215664901532860606512090082
	)

the Euler constant (aka Euler-Mascheroni constant or gamma)

NEW_CONSTANT	(	EXPEULER2	,
		0.	74930600128844902360587
	)

the Euler constant parameter exp(-gamma/2)

NEW_CONSTANT	(	PI	,
		3.	141592653589793238462643
	)

pi

NEW_CONSTANT	(	PI2	,
		6.	283185307179586476925287
	)

2*pi

NEW_CONSTANT	(	PI4	,
		12.	56637061435917295385057
	)

4*pi

NEW_CONSTANT	(	PI8	,
		25.	13274122871834590770115
	)

8*pi

NEW_CONSTANT	(	SQRT2	,
		1.	414213562373095048801689
	)

sqrt(2)

NEW_CONSTANT	(	SQRTPI	,
		1.	772453850905516027298167
	)

sqrt(pi)

NEW_CONSTANT	(	SQRTPIBY2	,
		1.	253314137315500251207883
	)

sqrt(pi/2)

NEW_CONSTANT	(	LN_TWO	,
		0.	6931471805599453094172321
	)

ln(2)

NEW_CONSTANT	(	LN_TEN	,
		2.	302585092994045684017991
	)

ln(10)

NEW_CONSTANT	(	LOG10_E	,
		0.	4342944819032518276511289
	)

log(e)

NEW_CONSTANT	(	OPTDEP2EXTIN	,
		1.	085736204758129569127822
	)

factor that converts optical depth into extinction in mags, 2.5 log e

NEW_CONSTANT	(	RADIAN	,
		57.	29577951308232087679815
	)

180/pi

NEW_CONSTANT	(	SOLAR_MASS	,
		1.	98848e33
	)

solar mass in gram >>refer phys const http://pdg.lbl.gov/2019/reviews/rpp2018-rev-astrophysical-constants.pdf

NEW_CONSTANT	(	SOLAR_LUMINOSITY	,
		3.	828e33
	)

solar luminosity erg s-1 >>refer phys const http://pdg.lbl.gov/2019/reviews/rpp2018-rev-astrophysical-constants.pdf

NEW_CONSTANT	(	MBOL_ZERO_LUMINOSITY	,
		3.	0128e35
	)

luminosity of a star with absolute bolometric magnitude 0, in erg s-1 >>refer phys const http://pdg.lbl.gov/2019/reviews/rpp2018-rev-astrophysical-constants.pdf

NEW_CONSTANT	(	AU	,
		1.	49597870700e13
	)

astronomical unit, cm, nearly the length of the semimajor axis of the Earth's elliptical orbit around the sun

NEW_CONSTANT	(	ELECTRON_MASS	,
		9.1093837015e-	28
	)

electron mass, gram

NEW_CONSTANT	(	ELECTRON_MASS_U	,
		5.48579909065e-	4
	)

electron mass, in u

NEW_CONSTANT	(	PROTON_MASS	,
		1.67262192369e-	24
	)

proton mass, gram

NEW_CONSTANT	(	PROTON_MASS_U	,
		1.	007276466621
	)

proton mass, in u

NEW_CONSTANT	(	ALPHA_MASS_U	,
		4.	001506179127
	)

mass of the alpha particle, in u

NEW_CONSTANT	(	BOLTZMANN	,
		1.380649e-	16
	)

this is the Boltzmann factor, erg/K, exact

NEW_CONSTANT	(	SPEEDLIGHT	,
		2.	99792458e10
	)

speed of light, cm/s, exact

NEW_CONSTANT	(	HPLANCK	,
		6.62607015e-	27
	)

Planck's constant, exact

NEW_CONSTANT	(	AVOGADRO	,
		6.	02214076e23
	)

Avogadro constant, exact

NEW_CONSTANT	(	GRAV_CONST	,
		6.67430e-	8
	)

Gravitational constant, cm^3/g/s^2

NEW_CONSTANT	(	ELEM_CHARGE	,
		1.602176634e-	19
	)

elementary charge, in C (SI units), exact, to use this must convert to cgs

NEW_CONSTANT	(	RYD_INF	,
		1.	0973731568160e5
	)

infinite mass rydberg constant, in cm^-1

NEW_CONSTANT	(	HIONPOT	,
		0.	999466508345
	)

ionization potential of real hydrogen atom, in inf mass ryd, based on CODATA 2006, uncertainty 10e-12, calculated by Peter van Hoof

NEW_CONSTANT	(	HE2IONPOT	,
		3.	99963199547
	)

ionization potential of real He^+ ion, in inf mass ryd, based on CODATA 2006, uncertainty 13e-11, calculated by Peter van Hoof

NEW_CONSTANT	(	HMINUSIONPOT	,
		0.	055432956
	)

ionization potential of H- in inf mass ryd, >>refer phys const T. Anderson, 2004, Phys. Reports, 394, 157

NEW_CONSTANT	(	ATOMIC_MASS_UNIT	,
		1.66053906660e-	24
	)

atomic mass unit, gram

NEW_CONSTANT	(	MOL_MASS_CONST	,
		AVOGADRO *	ATOMIC_MASS_UNIT
	)

molar mass constant, g/mol

NEW_CONSTANT	(	AS1RAD	,
		RADIAN *	3600.
	)

number of arcsec in 1 radian, 206264.806

NEW_CONSTANT	(	SQAS1SR	,
		pow2(AS1RAD)
	)

number of square arcsec in 1 steradian, 4.254517e10

NEW_CONSTANT	(	SQAS_SKY	,
		PI4 *	SQAS1SR
	)

number of square arcsec in the whole sky, 5.3463838e11

NEW_CONSTANT	(	PARSEC	,
		AU *	AS1RAD
	)

parsec in cm, 3.085678e18

NEW_CONSTANT	(	MEGAPARSEC	,
		1.e6 *	PARSEC
	)

megaparsec in cm, 3.085678e24

NEW_CONSTANT	(	H_BAR	,
		HPLANCK/	2.*PI
	)

h/2pi, 1.05457e-27

NEW_CONSTANT	(	ELEM_CHARGE_ESU	,
		ELEM_CHARGE *SPEEDLIGHT/	10.
	)

elementary charge, in ESU, 4.8032e-10

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

electric constant, in F/m, 8.854e-12

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

this is the factor that appears in front of Boltzmann factor to get LTE level populations for hydrogenic ions. It is given in the first parts of section 5 of part 2 of hazy, and is actually ( planck^2 / (2 pi m_e k ) )^3/2, but cannot evaluate powers here, must raise this to 3/2 when used, HION_LTE_POP, 5.556e-11 cm^2 K

NEW_CONSTANT	(	SAHA	,
		4.1413302848114741e-	16
	)

SAHA is ( h^2/2/pi/m/k )^3/2, is correct constant for free electron SAHA, 4.14132e-16 cm^3 K^(3/2)

NEW_CONSTANT	(	ERG1CM	,
		HPLANCK *	SPEEDLIGHT
	)

number of ergs per wavenumber, 1.9864e-16

NEW_CONSTANT	(	T1CM	,
		HPLANCK *SPEEDLIGHT/	BOLTZMANN
	)

degrees kelvin per unit wavenumber, 1.4388

NEW_CONSTANT	(	KJMOL1CM	,
		ERG1CM *AVOGADRO/	1e10
	)

kJ/mol per unit wavenumber, 0.01196266

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

ratio of Rydberg constants R_H/R_inf, 0.999456

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

ratio of Rydberg constants R_He/R_inf, 0.999863

NEW_CONSTANT	(	WAVNRYD	,
		1./	RYD_INF
	)

number of Ryd per wavenumber, 9.11267e-6

NEW_CONSTANT	(	RYDLAM	,
		1.e8/	RYD_INF
	)

Angstrom per infinite mass Ryd, 911.2671

NEW_CONSTANT	(	EN1RYD	,
		HPLANCK *SPEEDLIGHT *	RYD_INF
	)

ergs per inf mass Ryd, 2.180e-11

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

the temperature of 1 Rydberg te1ryd is h/k is temp of 1 Rydberg, 1.579e5

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

Kelvins per eV, 1.1604e4

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

eV per inf mass Ryd, 13.606

NEW_CONSTANT	(	EN1EV	,
		EN1RYD/	EVRYD
	)

ergs per eV, 1.602176e-012

NEW_CONSTANT	(	FR1RYD	,
		SPEEDLIGHT *	RYD_INF
	)

frequency of one Ryd for infinite mass nuclei, 3.289842e15

NEW_CONSTANT	(	HNU3C2	,
		2.*HPLANCK *SPEEDLIGHT *	pow3RYD_INF
	)

2 h FR1RYD^3 / c^2 for infinite mass nucleus, 0.5250

NEW_CONSTANT	(	FR1RYDHYD	,
		SPEEDLIGHT *RYD_INF *	HIONPOT
	)

frequency of ionization potential of H (not inf mass), 3.288087e15 - never used

NEW_CONSTANT	(	HBAReV	,
		H_BAR/	EN1EV
	)

H_BAR in eV sec, 6.582e-16

NEW_CONSTANT	(	RYDLAMHYD	,
		RYDLAM/	HIONPOT
	)

wavelength (A) of ionization potential of Hydrogen, 911.7535 - never used

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

Stefan-Boltzmann constant, 5.6704e-5

NEW_CONSTANT	(	FREQ_1EV	,
		SPEEDLIGHT *RYD_INF/	EVRYD
	)

the frequency of one eV, 2.418e14

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

the fine-structure constant a= 2pi e^2/hc 7.297 352 533 x 10-3

NEW_CONSTANT	(	FINE_STRUCTURE2	,
		pow2(FINE_STRUCTURE)
	)

the square of the fine-structure constant

NEW_CONSTANT	(	BOHR_RADIUS_CM	,
		FINE_STRUCTURE/	PI4 *RYD_INF
	)

Bohr radius in cm, 5.29177249e-9

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

the two photon constant as defined by Breit & Teller, as in equation 4 of Spitzer & Greenstein 51, 2.18313

NEW_CONSTANT	(	COLL_CONST	,
		SAHA *BOLTZMANN/	HPLANCK
	)

this is the square of the value roughly equal to 8.629e-6 that appears in converting collision strengths to rates. The constant is h^2/((2PI*me)^3/2 * k^1/2).

NEW_CONSTANT	(	MILNE_CONST	,
		4.1234755895831189e+	11
	)

this is the square of the value roughly equal to 4.123e11 that appears in the integration of photoionization cross-sections to obtain recombination coefficients.

NEW_CONSTANT	(	TRANS_PROB_CONST	,
		PI4 *HPLANCK *FINE_STRUCTURE/	ELECTRON_MASS
	)

This is the constant used in converting oscillator strengths to As. The formula is Aul, TRANS_PROB_CONST * f(u,l) * wavenumber^2. TRANS_PROB_CONST is 0.667025

NEW_CONSTANT	(	ABSOR_COEFF_CONST	,
		SQRTPI *	pow2ELEM_CHARGE_ESU)/(ELECTRON_MASS *SPEEDLIGHT
	)

This is the atomic physics constant that enters the calculation of the absorption coefficient given the energy separation between two levels, and the oscillator strength. Numerical value: 0.01497361235435992 Units: esu^2 / (g cm/s) = cm^2 / s The absorption coefficient is defined as in Eq. (9-33) of Mihalas, Stellar Atmospheres, 2nd Edition

NEW_CONSTANT	(	SIGMA_THOMSON	,
		PI8/3.*	pow2FINE_STRUCTURE *H_BAR/(ELECTRON_MASS *SPEEDLIGHT)
	)

Thomson cross-section, cm^2

NEW_CONSTANT	(	HC_ERG_ANG	,
		HPLANCK *SPEEDLIGHT *	1e8
	)

Express hc in erg Angstroms, approximately equal to 1.9864e-8 Used to get h*nu from wavelength in Angstroms

NEW_CONSTANT	(	JEANS	,
		PI *BOLTZMANN/	GRAV_CONST *ATOMIC_MASS_UNIT
	)

Jeans constant as in Hazy 3 – other constant factors are quoted

NEW_CONSTANT	(	FREE_FREE_EMIS	,
		1.0325265080202923e-	11
	)

NEW_CONSTANT	(	FREE_FREE_ABS	,
		1.0369973575937702e-	38
	)