!23456789a123456789b123456789c123456789d123456789e123456789f123456789g12 ! 2017_10_28oct28: Copyright D.J. Jeffery ! ! constant.f is a set of module setting numerical, physical, ! and astronomical constants. ! !23456789a123456789b123456789c123456789d123456789e123456789f123456789g12 ! module contants include '/module_precision_set_implicit.f' ! !23456789a123456789b123456789c123456789d123456789e123456789f123456789g12 ! ! Numerical constants ! integer, parameter :: & & iprecision_nd=precision(1.0_nd), & ! See MRC-167 for precision function. ! Standard precision significant decimal digits and standard range of exponents. ! Standard precision is set to double precision. ! 18 2020jan19 Jeffery machine & iprecision_np=precision(1.0_np), & ! 18 & iminexponent_np=minexponent(1.0_np), & ! -16381 & imaxexponent_np=maxexponent(1.0_np), & ! 16384 ! Single precision significant decimal digits and standard range of exponents. & iprecision_ns=precision(1.0_ns), & ! 15 & iminexponent_ns=minexponent(1.0_ns), & ! -1021 & imaxexponent_ns=maxexponent(1.0_ns), & ! 1024 & itc_numerical=1 & ! ! The last line is just so all the real lines end in commas for uniformity. ! real (kind=np), parameter :: & ! & exp1=2.71828182845904523536028747135266249775724709369995_np, & ! !!23456789a123456789b123456789c123456789d123456789e123456789f123456789g12 ! !https://en.wikipedia.org/wiki/E_(mathematical_constant) AKA Euler constant 51 digits & exp1_inverse=1.0_np/exp1, & ! & f_1_2=0.5_np, & ! Needs that zero to compile. & f_1_4=0.25_np, & & f_1_3=1.0_np/3.0_np, & & f_2_3=2.0_np*f_1_3, & & f_4_3=4.0_np*f_1_3, & & f_1_6=1.0_np/6.0_np, & ! & f_1_8=0.125_np, & & f_1_16=(0.5_np)**4, & & f_1_32=(0.5_np)**5, & & f_1_64=(0.5_np)**6, & & f_1_128=(0.5_np)**7, & & f_1_256=(0.5_np)**8, & & f_1_512=(0.5_np)**9, & & f_1_1024=(0.5_np)**10, & ! & xln2=0.693147180559945309417232121458_np, & ! !!123456789a123456789b123456789c123456789d123456789e123456789f123456789g12 ! ! https://en.wikipedia.org/wiki/Natural_logarithm_of_2 30 digits ! & phi_0_golden_ratio=1.618033988749894848204586834365638117720_np, & & phi_1_golden_ratio=0.618033988749894848204586834365638117720_np, & ! !1!23456789a123456789b123456789c123456789d123456789e123456789f123456789g12 ! ! phi_0=(1+sqrt(5))/2 , phi_1=phi-1=(sqrt(5)-1)/2 ! ! https://en.wikipedia.org/wiki/Golden_ratio ! ! http://mathworld.wolfram.com/GoldenRatio.html for value to 40 decimal digits. ! & pi=3.14159265358979323846264338327950288419716939937510_np, & ! !!23456789a123456789b123456789c123456789d123456789e123456789f123456789g12 ! ! https://en.wikipedia.org/wiki/Pi#Approximate_value_and_digits 51 digits & pi_1_2=pi*0.5_np, & & pi_2=pi*2.0_np, & & pi_sqroot=sqrt(pi), & ! & sqroot_2= & & 1.4142 & & 1356237309504880168872420969807856967187537694807317667973799_np, & ! !23456789a123456789b123456789c123456789d123456789e123456789f123456789g12 ! ! From https://en.wikipedia.org/wiki/Square_root_of_2 . 66 digits ! ! Spaces in numbers ! ! are not allowed by some compilers. & xprecision=10.0_np**(-iprecision_np+1), & ! ! Relative machine precision almost. ! & etc_numerical_np=1.0_np ! !23456789a123456789b123456789c123456789d123456789e123456789f123456789g12 ! ! See https://physics.nist.gov/cuu/Constants/Table/allascii.txt generally ! ! Physical constants: fundamental ! real (kind=np), parameter :: & ! & amu =1.660 539 066 60 e-24_np, & & amu_mks=1.660 539 066 60 e-27_np, & ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt error (50) ! & clight= 2.99792458e10_np, & & clight_mks=2.99792458e8_np, & & ckms=clight_mks*1.e-3_np, & ! https://en.wikipedia.org/wiki/Speed_of_light ! https://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%93second_system_of_units#Physical_constants_in_CGS_units ! & ev_electronvolt =1.602 176 634 e-12_np, & & ev_electronvolt_mks=1.602 176 634 e-19_np, & ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt exact ! The electron-volt = eV. Units of erg or erg/eV ! & alpha_fine_structure=7.297 352 5693 e-3_np, & & alpha_fine_structure_inverse=137.035 999 084_np, & ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt ! Error: 11 digits: (11) ! The fine structure constant which is dimensionless. ! One often gives 1/137. ! & g_grav= 6.67430e-8_np, & & g_grav_mks=6.67430e-11_np, & ! http://en.wikipedia.org/wiki/Gravitational_constant MKS error (15): ! Wik says this 2018 Codata recomended. ! So 4 digit accurate, but there may still be controversy beyond. ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt ! & h_planck= 6.626 070 15e-27_np, & & h_planck_mks=6.626 070 15e-34_np, & ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt exact ! https://en.wikipedia.org/wiki/Planck_constant & h_bar=h_planck/pi_2, ! 1.054 571 817e-27_np NIST & h_bar_mks=h_planck_mks/pi_2, ! 1.054 571 817e-34_np NIST ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt ! & xk_boltzmann= 1.380 649e-16_np, & & xk_boltzmann_mks=1.380 649e-23_np, & & xk_boltzmann_ev= 8.617 333 262e-5_np, & ! approx 10e-4 & xk_boltzmann_mev=8.617 333 262e-11_np, & ! approx 10e-10 ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt exact in MKS, not eV ! https://en.wikipedia.org/wiki/Boltzmann_constant for CGS ! ! Electron mass: & xm_e= 9.109 383 7015e-28_np, & & xm_e_mks=9.109 383 7015e-31_np, & ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt ! error 11 digits: (28 cgs,mks) ! https://en.wikipedia.org/wiki/Electron_rest_mass ! & xm_hyd=1.00782505_np*amu, & ! https://en.wikipedia.org/wiki/Atomic_mass#Mass_defects_in_atomic_masses for H-1 ! ! Proton mass: & xm_p= 1.672 621 923 69e-24_np, & & xm_p_mks=1.672 621 923 69e-27_np, & ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt ! error 12 digits: (51 cgs,mks) ! https://en.wikipedia.org/wiki/Proton & xm_e_reduced=xm_e/(1.0_np+xm_e/xm_p), & ! ! & xm_planck=sqrt(h_bar*clight/g_grav), ! https://en.wikipedia.org/wiki/Planck_mass ! & xna_avogadro=6.022 140 76 e23_np, & ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt ! https://en.wikipedia.org/wiki/Avogadro_constant = number of particles per mole ! m_i=A_i*u_amu and xna approx 1 g/u_amu to 3.5e-10 relative accuracy. ! So m = A_i*u_amu = approx A_i*(1 g) is a molar mass to high accuracy. ! ! Physical constants: derived ! ! Rydberg energy: & e_rydberg_ev=13.605 693 122 994_np, & & e_rydberg=2.179 872 361 1035d-11, & ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt ! error: 14 digits both: (26 eV),(42 cgs) ! https://en.wikipedia.org/wiki/Rydberg_constant & e_rydberg_ev_reduced=e_rydberg_ev*(xm_e_reduced/xm_e), & ! =13.598 287 264 286831241 ! =13.598 287 264 287 ! https://en.wikipedia.org/wiki/Rydberg_constant#Rydberg_constant ! & etc_physical_np=1.0_np ! ! !23456789a123456789b123456789c123456789d123456789e123456789f123456789g12 ! ! Astronomical constants ! real (kind=np), parameter :: & ! ! Distances ! & pc_m=(1.49597870700e11_np/(pi/(180.0_np*3600.0_np))), & & pc_m=9.6939420213600000e+16_np/pi, & ! https://en.wikipedia.org/wiki/Parsec#Calculating_the_value_of_a_parsec ! http://en.wikipedia.org/wiki/Astronomical_unit ! r_pc * pc_m = b_AU *au_m /(theta_arcs * pi/(180*3600)) defines pc_m & xly_m=9.460730472580800e15_np, & ! exact value by definition, ! light distance traveled in 1 Jyr ! https://en.wikipedia.org/wiki/Light-year#Definitions & pc_ly=pc_m/xly_m, & ! x m * factor of unity = x_m (1 ly/ly_m) & xmpc_km=pc_m*1.e+6_np*1.e-3_np, & ! xmpc_km/xmpc = 1 Converts Mpc to km ! inverse converts H_0 (km/s)/Mpc in standard to inverse seconds & gpc_m=pc_m*1.e+9_np, & ! ! Also the conversion Gpc to m ! ! Times & daysec=86400.0_np, & & xjy=365.25_np, & ! Julian year in days & xjy_s=xjy*daysec, & ! Julian year in seconds & gjy_s=xjy_s*1.0e9_np, & ! Gigayear in seconds & ! ! Radiative transfer (radtran) & saha_con=0.5_np*(h_planck**2/(pi_2*xm_e*xk_boltzmann))**1.5_np, & ! Saha constant & saha_con_inverse=1.0_np/saha_con, & ! Saha constant inverse & saha_con_inverse_natural=2.0_np* & ! in natural units & (pi_2*xm_e*e_rydberg/h_planck**2)**1.5_np, & ! 1st formula ! & (pi_sqroot*alpha_fine_structure*xm_e*clight/h_planck)**3, & ! 2nd formula ! ! Mihalas-1978-113: his value is 2.07e-16 cm**3 K**3/2 ! The above expresion evaluates to saha_con=2.070 665 142 40573681148E-0016 ! Planck constant exact, pi exact, xm_e 11 digits, xk_b 7 exact ! The above expresion evaluates to saha_con_inverse=4.829 366 079 143 929 688 0e+15 ! saha_con_inverse_natural is for kT=rydberg ! 3.029 784 927 54121276948E+0023 1st formula ! 3.029 784 927 53254453019E+0023 2nd formula ! They agree to 11 digits. Since the Rydberg has 14 digits and ! the fine structure constant only 11, one guesses the first formula ! maybe better. ! ! Thomson cross-section & sigma_e= 6.652 458 7321 e-25_np, & ! Thomson cross-section & sigma_e_mks=6.652 458 7321 e-29_np, & ! Thomson cross-section ! https://physics.nist.gov/cuu/Constants/Table/allascii.txt error (60) ! Mihalas-1978-106 ! ! Rydberg temperature & temperature_rydberg=e_rydberg_ev/xk_boltzmann_ev, & ! =157887.5124 0469316319 K ! 14 digits for e_rydberg_ev ,10 digits for xk_boltzmann_ev, so 10 digits ! ! Solar units & xm_sun= 1.98847e33_np, & ! grams & xm_sun_mks=1.98847e30_np, & ! kilograms ! https://en.wikipedia.org/wiki/Solar_mass revised 2019 ! ! Supernovae units & w3_lane_emden=2.018236_np, ! approximate ! & xmue=1.0_np/(0.5_np*6.0_np/12.0_np+0.5_np*8.0_np/16.0_np), & ! https://en.wikipedia.org/wiki/Chandrasekhar_limit#Physics ! Pure carbon-oxygen fully ionized, default atomic weights & xmue=2.0_np, & ! default fully ionized above hydroge & xm_chan=w3_lane_emden*sqrt(3.0_np*pi)*0.5_np*xm_planck**3 & /(xmue*amu)**2, & & xm_chan_xm_sun=xm_chan/xm_sun, & & xm_wd_explosion=1.38_np, & ! 1.456 Msun ! https://arxiv.org/pdf/1010.5292.pdf woosley & kasen 2010 ! https://arxiv.org/pdf/1710.04254.pdf Leung and nomoto 2017 ! https://astro.uni-bonn.de/~nlanger/thesis/rudy.pdf p. 5 ! gives 1.38 Msun which must mean ! either finite temperature or some non-fiducial mix of isotopes? ! This is the explosion mass which is only near the Chandrasekhar mass, ! not actually at it. ! ! & etc_astronomical_np=1.0_np ! ! !23456789a123456789b123456789c123456789d123456789e123456789f123456789g12 ! end module contants ! !23456789a123456789b123456789c123456789d123456789e123456789f123456789g12