Planetary isotopologue ratios ============================= ========== 1) General ========== Files with adapted planetary isotopologue ratios have been created and can be found in the planets folders in arts-xml-data package. Isotopic ratios of planets (Mars, Venus, Jupiter) differ from Earth only for D/H (all planets) and 15N/14N (Mars and Jupiter, not Venus), while 13C/12C as well as 18O/16O and 17O/16O are within 5% of Earth's values. That is, only species containing H (all 3 planets) and N (Mars, Jupiter) need adaptation. Applied planetary isotopic ratios were provided by L. Rezac under ESA planetary toolbox study (see TN1). Earth values were derived from ARTS built-in isotopologue ratios separately per molecular species (hence only an approximate value given here): -------------------------------- Planet D/H 15N/14N -------------------------------- Earth (~1.5e-4) (~3.7e-3) Venus 1.9e-2 as Earth Mars 8.1e-4 5.7e-3 Jupiter 2.6e-5 2.25e-3 -------------------------------- =========== 2) Approach =========== Isotopologue ratios of species for those planets are derived from modifying the ARTS built-in Earth values for the above listed ratio changes (i.e., we do NOT calculate them from scratch from the isotopic ratios of all atomic species involved!). That is, we (1a) derive molecule-specific isotope ratios D/H and 15N/14N from the built-in Earth isotopologue ratios of the individual molecules (1b) or where molecule-specific isotope ratios are not available set them from N2 and H2 (2) modify those to the above listed values. Isotopologue ratio is the product of the relative isotopic abundances of all the individual atoms in a molecule (times the number of positional permutations). example: IR(CH4) = ia(C) * ia(H)**4 #1C atom, 4H IR(CH3D) = ia(C) * ia(H)**3 * ia(D) * 4 #1C atom, 3H aoms, 1D atom IR(CH3D) has a factor 4 since D can be in place of any of the 4H, i.e., for us CH3D stands for CHHHD and CHHDH and CHDHH and CDHHH, hence their abundances have to be summed up. The isotopic abundance ia can be expressed in terms of the isotopic ratios ir (i.e., abundance of an isotope in relation to the main or another isotope): ia(i) = ir(i) / ( sum_j=1^N ir(j) ) i.e., as the relation of the individual isotope's abundance in relation to a fixed (usually the main) isotope to the sum of the relative abundances of all isotopes to the fixed (main) isotope. example: ia(H) = 1 / (1+D/H) ia(D) = D/H / (1+D/H) ia(O-18) = O-18/O-16 / (1 + O-18/O-16 + O-17/O-16) #for O we have 3 common isotopes with this the isotopologue ratios can be rewritten as: IR(CH4) = ia(C) * 1/(1+D/H)**4 #we don't rewrite C as we do not change C-ir here (but in general those can be handled in the exact same way) IR(CH3D) = ia(C) * 1/(1+D/H)**3 * (D/H)/(1+D/H) * 4 = ia(C) * (D/H) / (1+D/H)**4 * 4 STEP (1a) --------- molecule-specific isotopic ratios can be derived from ratios of isotopologues that apart from the two isotopes we want to derive the ratio of are identical (but we need to be a bit careful with positional permutation factors and when more than one atom of the species is replaced at once, e.g. two D occuring in a molecule) examples: IR(CH3D) / IR(CH4) = [ia(C) * 1/(1+D/H)**3 * (D/H)/(1+D/H) * 4] / [ia(C) * 1/(1+D/H)**4] = (D/H) * 4 => D/H = IR(CH3D) / IR(CH4) / 4 IR(D2O) / IR(H2O) = [ia(O) * [(D/H)/(1+D/H)]**2] / [ia(O) * 1/(1+D/H)**2] = (D/H)**2 => D/H = sqrt( IR(D2O) / IR(H2O) ) simple when only one atom of the species of question occurs, e.g., D/H = IR(O-16D) / IR(O-16H) In case there are more than one possibility to derive molecul-internal isotopic ratios, we take the mean of those. for example , D/H for H2O is derived from IR(HDO-16)/IR(H2O-16), IR(HDO-18)/IR(H2O-18), and IR(D2O-16)/IR(H2O-16). STEP (1b) --------- For cases, where molecule-specific D/H and 15N/14N can not be derived, we take: IR(H2) = 1 / (1+D/H)**2 and IR(N2) = 1 / (1+15N/14N)**2 => D/H = 1/sqrt(IR(H2)) - 1 and 15N/14N = 1/sqrt(IR(N2)) - 1 STEP (2) -------- In the IR formula derived above we now replace (D/H)_earth by (D/H)_planet by dividing through its factoral contribution in IR_e and multiplying by its planetary replacement: IR(CH4_p) = IR(CH4_e) / [1/(1+D/H_e)**4] * [1/(1+D/H_p)**4] = IR(CH4_e) * [(1+D/H_e) / (1+D/H_p)]**4 IR(CH3D_p) = IR(CH3D_e) / [(D/H_e) / (1+D/H_e)**4] * [(D/H_p) / (1+D/H_p)**4] = IR(CH3D_e) * [(1+D/H_e) / (1+D/H_p)]**4 * [(D/H_p) / (D/H_e)] That is, all IR_e get rescaled by [(1+D/H_e) / (1+D/H_p)]**N, where N is the number of atoms of the specific species in this molecule (here: atom=H and N=4). This is the planetary rescaling factor (rp). Isotopologues with other than the main isotope furthermore get refactored by [(D/H_p) / (D/H_e)]**M, where M is the number of atoms of the isotope replacing the main one (here: D and M=1; CD4 would have M=4). This is isotopologue rescaling factor (fac). Note: using this refactoring method, we do not need to care about the positional permutation factors. As they occur in both the Earth and the planet IR, they factor out. =================== 3) Species Overview =================== Below is a list of species implemented in ARTS including tags showing what isotopes for (and combinations thereof) the isotopologue ratios were adapted: * species with both H and N ** species with N *** species with H * replaced by x, if only main isotope of the respective species in the molecule (e.g., only H, but no D). that is, we can't derive the molecule-internal Earth isotopic ratios for them. therefore we fix these from the N2 and H2 values. ############################# *** H2O CO2 O3 ** N2O CO *** CH4 O2 ** NO SO2 xx NO2 * NH3 */x HNO3 (no internal calc of D/H, only of N14/15) *** OH *** HF *** HCl *** HBr *** HI ClO OCS *** H2CO xxx HOCl ** N2 * HCN xxx CH3Cl xxx H2O2 *** C2H2 xxx C2H6 xxx PH3 COF2 SF6 *** H2S *** HCOOH xxx HO2 O xx ClONO2 xx NO+ OClO BrO xxx H2SO4 Cl2O2 xxx HOBr xxx C2H4 xxx CH3OH xxx CH3Br * CH3CN CF4 * HC3N CS * HNC SO xxx C3H8 *** H2 He Ar x C4H2 SO3 #############################