TOOLBOX

Maybe have general stuff up above, then primary equations/relations for each topic.

(1) Units & Constants

 Primary psm Units and Conversions Quantity cgs mks psm distance cm m = 102 cm pc    = 3.086 x 1018   cm mass gm kg = 103 gm M = 1.989 x 1033   gm time s s Myr = 3.156 x 1013   s velocity cm s-1 m s-1 = 102 cm s-1 pvu = pc Myr-1   =   9.778 x 104 cm s-1     1 km/s density gm cm-3 kg m-3 = 10-3 gm cm-3 pdu = M pc-3   =   6.77 x 10-23 gm cm-3   =   40.5  mp cm-3 G 6.67 x 10-8 6.67 x 10-11 G = 4.50 x 10-3   pc3 M-1 Myr-2     (km/s)2 pc M-1

 Less Commonly Used psm Units Quantity cgs mks psm energy erg = gm cm2 s-2 J = kg m2 s-2 = 107 erg peu = M pc2 Myr-2  = 1.90 x 1043 erg               M (km/s)2 luminosity erg s-1 W = J s-1 = 107 erg s-1 plu = peu Myr-1           = 6.02 x 1029 erg s-1     = 1.56 x 10-4 L acceleration cm s-2 m s-2 = 102 cm s-2 pau = pc Myr-2              = 3.10 x 10-9 cm s-2     km/s Myr-1 force dyne = gm cm s-2 N = 105 dyne pfu = M pc Myr-2      = 6.16 x 1024 dyne         M km/s Myr-1 momentum gm cm s-1 kg m s-1 = 105 cgs pmu = M pc Myr-1   = 1.94 x 1038 cgs             M km/s angular mom. gm cm2 s-1 kg m2 s-1 = 107 cgs pamu = M pc2 Myr-1 = 6.00 x 1056 cgs             M km/s pc frequency Hz Hz pfru = Myr-1                    = 3.17 x 10-14 Hz         km/s pc-1

 Astronomical Constants Quantity cgs mks psm yr 3.16 x 107 s 3.16 x 107 s 10-6 Myr pc 3.08 x 1018 cm 3.08 x 1016 m 1 pc lyr 9.46 x 1017 cm 9.46 x 1015 m 0.307 = 1 / 3.26 pc AU 1.49 x 1013 cm 1.49 x 1011 m 4.85 x 10-6 = 1 / 206265 pc R 6.96 x 1010 cm 6.96 x 108 m 2.26 x 10-8 pc     [109 R] M 1.99 x 1033 gm 1.99 x 1030 kg 1 M               [3.33 x 105 M] L 3.85 x 1033 erg s-1 3.85 x 1026 W 6400 plu (M/L) 0.516 gm / (erg s-1) 5160 kg / W 1.56 x 10-4 M / plu H 3.24 x 10-18 h Hz 3.24 x 10-18 h Hz 1.02 x 10-4 h   Myr-1   ( 100h / 106) tH = H-1 3.09 x 1017 h-1   s 9.78 h-1   Gyr 9778 h-1  Myr   ( 106 / 100h) rH = c H-1 9.25 x 1027 h-1   cm 9.78 h-1   G lyr 2.99 h-1   Gpc   ( 3 x 105 x 106 / 100h) crit = 3H2/8G 1.88 x 10-29 h2   gm cm-3 1.88 x 10-25 h2   kg m-3 2.77 x 10-7 h2   M pc-3

 Physical Constants Quantity cgs mks other G 6.67 x 10-8 cm3 gm-1 s-2 6.67 x 10-11 4.50 x 10-3   (psm) c 3.00 x 1010 cm s-1 3.00 x 108 m s-1 3.06 x 105   pc Myr-1   (psm) mp 1.67 x 10-24   gm 1.67 x 10-27   kg 938 MeV / c2 me 9.11 x 10-28   gm 9.11 x 10-31   kg 0.511 MeV / c2 h 6.63 x 10-27   erg s 6.62 x 10-34   J s 4.14 x 10-15 eV s eV 1.60 x 10-12   erg 1.60 x 10-19   J 1.78 x 10-33 gm c2 kB 1.38 x 10-16   erg K-1 1.38 x 10-23   J K-1 8.62 x 10-5 eV K-1 5.67 x 10-5   erg cm-2 s-1 K-4 5.67 x 10-8   J m-2 s-1 K-4 3.54 x 107 eV cm-2 s-1 K-4 a = 4/c 7.56 x 10-15   erg cm-3 K-4 7.56 x 10-16   J m-3 K-4 4.72 x 10-3 eV cm-3 K-4

add Wein's constant (and/or have a separate table for the radiation relations, like in the cosmology section).

(2) Cosmology

 density match condition a @ equality z @ equality t @ equality v = m 0.73 = 0.27 a-3 0.72 0.39 9.43 Gyr v = rel 0.73 = 8.4 × 10-5 a-4 0.103 8.3 615 Myr b = 0.04 a-3 = 5.0 × 10-5 a-4 1.25 × 10-3 800 620 kyr m = rel 0.27 a-3 = 8.4 × 10-5 a-4 3.11 × 10-4 3200 57 kyr m = 0.27 a-3 = 5.0 × 10-5 a-4 1.85 × 10-4 5400 22 kyr

Note that here rel refers to the sum of photons and neutrinos (relativistic matter)
Likewise m refers to the sum of baryons and CDM (non-relativistic matter)

 Useful Approximations     [ see image ] Radiation era:   log a < -3.8     t < 15 kyr     E(a)    r,o½   a-2 t   =   tH,o da / a E(a)   (0 to a)     ½ tH,o r,o-½ a2     741 a2 h72-1 Gyr   =   2.34 x 1019 a2 h72-1 sec a     1.16 x 10-6 h72½ tyr½     2.09 x 10-10 h72½ ts½ T   =   2.725 / a   K   =   2.39 x 10-4 / a   eV     1.31 x 1010 h72-½ ts-½  K     1.14 h72-½ ts-½  MeV rH   =   rH,o / E(a)     c tH,o r,o-½ a2     1480 a2 h72-1 Glyr   =   2 c t rph   =   a rH,o da' / a'2 E(a')   (0 to a)     c tH,o r,o-½ a2     1480 a2 h72-1 Glyr   =   2 c t   =   rH Matter era:   0.002 <  a  < 0.8     1 Myr <  t  < 10 Gyr     E(a)    m,o½   a-3/2 t   =   tH,o da / a E(a)   (0 to a)     2/3 tH,o m,o-½ a3/2     17.4 a3/2 h72-1 Gyr a     1.49 x 10-7 h722/3 tyr2/3 rH   =   rH,o / E(a)     c tH,o m,o-½ a3/2     26.1 a3/2 h72-1 Glyr   =   3/2 c t rph   =   a rH,o da' / a'2 E(a')   (0 to a)     2 c tH,o m,o-½ a3/2     52.3 a3/2 h72-1 Glyr   =   3 c t   =   2 rH Dark Energy Era:   a  > 0.8     t  > 10 Gyr     E(a)    v,o½ t - tnow   =   t   =   tH,o da / a E(a)   (1 to a)     tH,o v,o-½ ln(a)     15.9 ln(a) h72-1 Gyr a     exp[ tGyr h72 / 15.9 ]       (tnow = 0.988 tH,o) rH   =   rH,o / E(a)     c tH,o v,o-½     15.9 h72-1 Glyr       (a constant) rph   =   a rH,o da' / a'2 E(a')   (0 to a)   = reh   =   a rH,o da' / a'2 E(a')   (a to )     c tH,o v,o-½     15.9 h72-1 Glyr   =   rH       (a constant)

 Epoch Time Scale Factor Temperature Energy Planck 10-42 s 10-32 1032 K 1019 GeV GUT 10-36 s 10-28 1028 K 1015 GeV Electro-Weak 10-10 s 10-15 1015 K 100 GeV Quark-Hadron 3 × 10-5 s 10-12 2 × 1012 K 200 MeV -decouple 1 s 2 × 10-10 1.3 × 1010 K 1 MeV He4 synthesis 200 s 2.9 × 10-9 9.4 × 108 K 80 keV Equality 57 kyr 3.1 × 10-4 8700 K 0.75 eV Recombination 380 kyr 9.2 × 10-4 2900 K 0.25 eV Today 14 Gyr 1.0 2.72 K 2.35 × 10-4 eV

more robust, concordance cosmology relations (including subroutine for doing the main integral).

redshift conversions -- see peterson AGN p 156

Blackbody curve/constants, Blam & Bnu

photometric conversions, including from UBV etc to Lsuns, zero points, wavelengths, Jansky etc

add Wein's constant (and/or have a separate table for the radiation relations, like in the cosmology section).

spectral regions defined: EUV (13.6 - 100eV = 91-12nm); soft X (0.1-1keV = 12 - 1.2nm); med (1-10keV = 1.2-0.12 nm); hard X (>10keV).

reddening curve

galactic reddening, link to NED calculator

(4) Kinetic Theory

Kinetic relations : pcle velocities vs T; sound speeds; shock velocity & post shock temps; Pressures nT; B2/8pi; radiation; Maxwell Bolzmann relation & expressions for mode(v) = sqrt(2kT/m); ave(v) = 2/sqrt(pi) * mode(v); and ave(v2) = 3kT/m and ave(E) = 1.5kT . (Flowers & Mendoza, p 109

column densities & emission measures; n = ntot = ne + np + nHI + nH2 = ??ne for ionized.

T(K) = 7740 E(eV)... (3/2 kT); lam(nm) = 1240/E(eV); nu(GHz) = 2.42 e5 E(eV)

(5) Coordinates/Sky Relations

All Sky = 4 Steradians = 41,253 deg2 = 5.34 x 1011 arcsec2

coordinate systems : RA/DEC, precession, l,b, and supergalactic L,B. link to NED calculator.

velocity corections: heliocentric; galactocentric; LSR; Local Group; Virgocentric; CMB