.. SPDX-FileCopyrightText: 1992-2026 NWO-I/SRON Space Research Organisation Netherlands .. .. SPDX-License-Identifier: CC-BY-4.0 .. _sec:amolmodel: Amol: interstellar dust absorption model ============================================ This model calculates the transmission of various molecules considering both absorption and scattering. The extinction models are evaluated for grains with a standard MRN size distribution (`Mathis & Rumpl & Nordsieck, 1977 `_): :math:`n(a) \propto a^{-3.5}` with *a* the grain size and :math:`a_{\mathrm{min}}=0.005\ \mu m` and :math:`a_{\mathrm{max}}=0.25\ \mu m`. All the extinction profiles are based on laboratory measurements. For further details on the lab processing see `Zeegers et al. (2017) `_, `Rogantini et al. (2018) `_, `Costantini et al. (2019) `_, `Zeegers et al. (2019) `_ and `Rogantini et al. (2019) `_. The following compounds are presently taken into account (see Table :ref:`tab:xride-table`). .. _tab:xride-table: .. table:: Compounds list ========= ===================== ============================================================= ============= ==================== =============================================== index Name formula Form Edge Source ========= ===================== ============================================================= ============= ==================== =============================================== 115 c-silicon :math:`\mathrm{Si}` crystalline Si 1s `[1] `_ 127 metallic iron :math:`\mathrm{Fe}` crystalline Fe 1s `[2] `_ 129 metallic nickel :math:`\mathrm{Ni}` crystalline Ni 1s `[3] `_ 130 a-carbon :math:`\mathrm{C}` amorphous C 1s `[4] `_ 131 diamond :math:`\mathrm{C}` crystalline C 1s `[4] `_ 132 graphite :math:`\mathrm{C}` crystalline C 1s `[4] `_ 2111 c-silicon carbide :math:`\mathrm{SiC}` crystalline Si 1s `[1] `_ 2230 troilite :math:`\mathrm{FeS}` crystalline S 1s; Fe 1s `[5] `_, `[6] `_ 2231 pyrrhotite :math:`\mathrm{Fe_7 S_8}` crystalline S 1s; Fe 1s `[5] `_, `[6] `_ 2232 a-quartz :math:`\mathrm{Si O_2}` amorphous Si 1s `[7] `_ 2233 c-quartz :math:`\mathrm{Si O_2}` crystalline Si 1s `[7] `_ 2234 a-quartz :math:`\mathrm{Si O_2}` disorder Si 1s `[7] `_ 2235 c-silicon nitride :math:`\mathrm{Si_3 N_4}` crystalline Si 1s `[1] `_ 2236 magnesia :math:`\mathrm{MgO}` crystalline Si 1s `[8] `_ 2237 aluminium oxide :math:`\mathrm{Al_2 O_3}` crystalline Al 1s `[9] `_ 2238 alabandite :math:`\mathrm{MnS}` crystalline S 1s `[5] `_ 2239 pyrite :math:`\mathrm{FeS_2}` crystalline S 1s `[5] `_ 2240 titanium dioxide :math:`\mathrm{TiO_2}` crystalline Ti 1s `[10] `_ 2241 a-hydrocarbon :math:`\mathrm{CH}` amorhpous C 1s `[11] `_ 3230 c-forsterite :math:`\mathrm{Mg_2 Si O_4}` crystalline Mg 1s; Si 1s `[12] `_, `[7] `_ 3231 a-enstatite :math:`\mathrm{Mg Si O_3}` amorphous Mg 1s; Si 1s `[12] `_, `[7] `_ 3232 c-enstatite :math:`\mathrm{Mg Si O_3}` crystalline Mg 1s; Si 1s `[12] `_, `[7] `_ 3233 c-spinel :math:`\mathrm{Mg Al_2 O_4}` crystalline Mg 1s; Al 1s `[12] `_, `[9] `_ 3270 calcium aluminate :math:`\mathrm{Ca Al_2 O_4}` crystalline Ca 1s `[13] `_ 3271 tri-Ca aluminate :math:`\mathrm{Ca_3 Al_2 O_6}` crystalline Ca 1s `[13] `_ 3302 c-fayalite :math:`\mathrm{Fe_2 Si O_4}` crystalline Si 1s; Fe 1s; Fe 2p `[7] `_, `[14] `_, `[15] `_ 4230 a-olivine :math:`\mathrm{Mg Fe Si O_4}` amorphous Mg 1s; Si 1s `[12] `_, `[7] `_ 4231 c-olivine :math:`\mathrm{Mg_{1.56} Fe_{0.4} Si_{0.91} O_4}` crystalline Mg 1s; Si 1s; Fe 1s `[12] `_, `[7] `_, `[6] `_ 4232 c-En60Fe40 :math:`\mathrm{Mg_{0.6} Fe_{0.4} Si O_3}` crystalline Mg 1s; Si 1s; Fe 1s `[12] `_, `[7] `_, `[6] `_ 4233 a-En60Fe40 :math:`\mathrm{Mg_{0.6} Fe_{0.4} Si O_3}` amorphous Mg 1s; Si 1s; Fe 1s `[12] `_, `[7] `_, `[6] `_ 4234 a-En75Fe25 :math:`\mathrm{Mg_{0.75} Fe_{0.25} Si O_3}` amorphous Mg 1s; Si 1s `[12] `_, `[7] `_ 4235 a-En90Fe10 :math:`\mathrm{Mg_{0.9} Fe_{0.1} Si O_3}` amorphous Mg 1s; Si 1s; Fe 1s `[12] `_, `[7] `_, `[6] `_ 4236 c-En90Fe10 :math:`\mathrm{Mg_{0.9} Fe_{0.1} Si O_3}` crystalline Mg 1s; Si 1s; Fe 1s `[12] `_, `[7] `_, `[6] `_ 4237 c-hypersthene :math:`\mathrm{Mg_{1.502} Fe_{0.498} Si_2 O_6}` crystalline Mg 1s; Si 1s; Fe 1s `[12] `_, `[7] `_, `[6] `_ 4270 c-diopside :math:`\mathrm{Mg Ca Si_2 O_6}` crystalline Ca 1s `[13] `_ 4271 a-diopside :math:`\mathrm{Mg Ca Si_2 O_6}` amorphous Ca 1s `[13] `_ 4272 c-anorthite :math:`\mathrm{Ca Al_2 Si_2 O_8}` crystalline Ca 1s `[13] `_ ========= ===================== ============================================================= ============= ==================== =============================================== [1] `Chang et al. (1999) `_, [2] `exafsmaterials.com `_, [3] `Van Loon et al. (2015) `_, [4] `Albella et al. (1998) `_, [5] `esrf.eu `_, [6] `Rogantini et al. (2018) `_, [7] `Zeegers et al. (2019) `_, [8] `Fukushi et al. (2017) `_, [9] `Costantini et al. (2019) `_, [10] `Shin et al. (2013) `_, [11] `Bonnin-Mosbah et al. (2002) `_, [12] `Rogantini et al. (2019) `_, [13] `Neuville et al. (2007) `_, [14] `Lee et al. (2005) `_, [15] `Lee et al. (2009) `_. Additional molecules are listed in Table :ref:`tab:additional_compounds`. These models do not include scattering and were not integrated over a size distribution. They will be updated in future versions. .. _tab:additional_compounds: .. table:: Additional compounds list ========== =================== ====================================================================================== =============== ===== 108 molecular oxygen :math:`\mathrm{O_2}` O 1s `[16] `_ 126 metallic iron :math:`\mathrm{Fe}` Fe 2p `[17] `_ 2001 water :math:`\mathrm{H_2 O}` O 1s `[18] `_ 2002 crystalline ice :math:`\mathrm{H_2 O}` O 1s `[19] `_ 2003 amorphous ice :math:`\mathrm{H_2 O}` O 1s `[19] `_ 2010 carbon monoxide :math:`\mathrm{CO}` O 1s `[16] `_ 2011 carbon dioxide :math:`\mathrm{CO_2}` O 1s `[16] `_ 2020 laughing gas :math:`\mathrm{N_2 O}` O 1s `[16] `_, `[21] `_ 2102 silicon monoxide :math:`\mathrm{SiO}` Si 1s `[20] `_ 2200 eskolaite :math:`\mathrm{Cr_2 O_3}` O 1s `[22] `_ 2300 iron monoxide :math:`\mathrm{FeO}` Fe 1s `[23] `_ 2301 iron oxide :math:`\mathrm{Fe_{1-x} O}` O 1s `[22] `_ 2302 magnetite :math:`\mathrm{Fe_3 O_4}` O, Fe 1s `[22] `_, `[23] `_ 2303 hematite :math:`\mathrm{Fe_2 O_3}` O, Fe 1s; Fe 2p `[22] `_, `[23] `_, `[17] `_ 2304 iron sulfite :math:`\mathrm{Fe S_2}` Fe 1s `[23] `_ 2400 nickel monoxide :math:`\mathrm{NiO}` O 1s `[22] `_ 2500 cupric oxide :math:`\mathrm{CuO}` O 1s `[22] `_ 3001 adenine :math:`\mathrm{C_5 H_5 N_5}` O 1s `[24] `_ 3103 pyroxene :math:`\mathrm{Mg Si O_3}` O 1s `[25] `_ 3200 calcite :math:`\mathrm{Ca C O_3}` Ca 1s `[26] `_ 3201 aragonite :math:`\mathrm{Ca C O_3}` Ca 1s `[26] `_ 3202 vaterite :math:`\mathrm{Ca C O_3}` Ca 1s `[26] `_ 3203 perovskite :math:`\mathrm{Ca Ti O_3}` O 1s `[22] `_ 3300 hercynite :math:`\mathrm{Fe Al_2 O_4}` O 1s `[22] `_ 3301 lepidocrocite :math:`\mathrm{Fe O (OH)}` Fe 2p `[17] `_ 3303 iron sulfate :math:`\mathrm{Fe S O_4}` Fe 2p `[17] `_ 3304 ilmenite :math:`\mathrm{Fe Ti O_3}` O 1s `[22] `_ 3305 chromite :math:`\mathrm{Fe Cr_2 O_4}` O 1s `[22] `_ 4001 guanine :math:`\mathrm{C_5 H_5 N_5 O}` O,N 1s `[24] `_ 4002 cytosine :math:`\mathrm{C_4 H_5 N_3 O}` O,N 1s `[24] `_ 4003 thymine :math:`\mathrm{C_5 H_6 N_2 O_2}` O,N 1s `[24] `_ 4004 uracil :math:`\mathrm{C_4 H_4 N_2 O_2}` O,N 1s `[24] `_ 4100 andradite :math:`\mathrm{Ca_3 Fe_2 Si_3 O_{12}}` O 1s `[22] `_ 4101 acmite :math:`\mathrm{Na Fe Si_2 O_6}` O 1s `[22] `_ 4102 franklinite :math:`\mathrm{Zn_{0.6} Mn_{0.8} Fe_{1.6} O_4}` O 1s `[22] `_ 4103 olivine :math:`\mathrm{Mg_{1.6} Fe_{0.4} SiO_4}` O 1s `[22] `_ 4104 almandine :math:`\mathrm{Fe_3 Al_2 (Si O_4)_3}` O 1s `[22] `_ 4105 hedenbergite :math:`\mathrm{Ca Fe Si_2 O_6}` O 1s `[22] `_ 5001 dna (herring sperm) :math:`\mathrm{C_{39} H_{61} N_{15} O_{36} P_{4}}` O,N 1s `[24] `_ 6001 montmorillonite :math:`\mathrm{Na_{0.2} Ca_{0.1} Al_2 Si_4 O_{10} (O H_2)(H_2 O)_{10}}` Si 1s `[20] `_ 6002 nontronite :math:`\mathrm{Na_{0.3} Fe_2^{3+} Si_3 Al O_{10} (OH)_2 \bullet (H_2 O)}` Si 1s `[20] `_ 7001 enstatite_paulite :math:`\mathrm{Ca_2 Mg_4 Al_{0.75} Fe_{0.25} Si_7 Al O_{22} (OH)_2}` Si 1s `[20] `_ ========== =================== ====================================================================================== =============== ===== [16] `Barrus et al. (1979) `_, [17] `Lee et al. (2009) `_, [18] `Hiraya et al. (2001) `_, [19] `Parent et al. (2002) `_, [20] `Lee et al. (2010) `_, [21] `Wight et al. (1974) `_, [22] `Van Aken et al. (1998) `_, [23] `Lee et al. (2005) `_, [24] `Fujii et al. (2003) `_, [25] `Lee et al. (2008) `_, [26] `Hayakawa et al. (2008) `_. The chemical composition of these minerals was mainly taken from the `Mineralogy Database of David Barthelmy `_. For DNA we assume equal contributions of adenine, cytosine, guanine and thymine, plus for each of these on average one phosphate and one 2-deoxyribose molecule. We take the cross-sections from the references as listed in :ref:`tab:additional_compounds` in the energy interval where these are given. Outside this range, the cross sections for free atoms `Verner & Yakovlev (1995) `_ :math:`var pixsec 1` or `Badnell et al. (2005) `_ :math:`var pixsec 2` are used. `Van Aken et al. (1998) `_ do not list the precise composition of iron oxide. We assume here that :math:`x=0.5`. Some remarks about the data from `Barrus et al. (1979) `_: not all lines are given in their tables, because they suffered from instrumental effects (finite thickness absorber combined with finite spectral resolution). However, `Barrus et al. (1979) `_ have estimated the peak intensities of the lines based on measurements with different column densities, and they also list the FWHM of these transitions. We have included these lines in the table of cross sections and joined smoothly with the tabulated values. For :math:`\mathrm{N_2 O}`, the fine structure lines are not well resolved by `Barrus et al. (1979) `_. Instead we take here the relative peaks from `Wight et al. (1974) `_, that have a relative ratio of 1.00 : 0.23 : 0.38 : 0.15 for peaks 1, 2, 3, and 4, respectively. We adopted equal FWHMs of 1.2 eV for these lines, as measured typically for line 1 from the plot of Wight. We scale the intensities to the peak listed by `Barrus et al. (1979) `_. Further, we subtract the C and N parts of the cross section as well as the oxygen 2s/2p part, using the cross sections of `Verner & Yakovlev (1995) `_. At low energy, a very small residual remains, that we corrected for by subtracting a constant fitted to the 510–520 eV range of the residuals. The remaining cross section at 600 eV is about 10 % above the Verner cross section; it rapidly decreases; we approximate the high-E behaviour by extrapolating linearly the average slope of the ratio between 580 and 600 eV to the point where it becomes 1. The remaining cross section at 600 eV is about 10% above the `Verner & Yakovlev (1995) `_ cross section; it rapidly decreases; we approximate the high-E behaviour therefore by extrapolating linearly the average slope of the ratio between 580 and 600 eV to the point where it becomes 1. .. Warning:: The normalisation is the total *molecular* column density. Thus, a value of :math:`10^{-7}` for :math:`\mathrm{CO_2}` means :math:`10^{21}` :math:`\mathrm{CO_2}` molecules :math:`\mathrm{m}^{-2}`, but of course :math:`2\times 10^{21}` atoms :math:`\mathrm{m}^{-2}`, because each :math:`\mathrm{CO_2}` molecule contains 2 oxygen atoms. .. Warning:: The Tables above shows for which edges and atoms the XAFS are taken into account. For all other edges and atoms not listed there, we simply use the pure atomic cross-section (without absorption lines). Note that for almost all constituents this may give completely wrong cross sections in the optical/UV band, as at these low energies the effects of chemical binding, crystal structure etc. are very important for the optical transmission constants. This is contrary to the SPEX models for pure atomic or ionised gas, where our models can be used in the optical band. .. Warning:: It is possible to change the values of the output atomic column densities of H–Zn, that are shown when you issue the "show par" command of SPEX. However, SPEX completely ignores this and when you issue the ``calc`` or ``fit`` commands, they will be reset to the proper values. Morale: just read of those parameters, don’t touch them! The parameters of the model are: | ``n1--n4`` : Molecular column density in :math:`10^{28}` :math:`\mathrm{m}^{-2}` for molecules 1–4. Default value: :math:`10^{-6}` for molecule 1, and zero for the others. | ``i1--i4`` : the molecule numbers for molecules 1–4 in the list (:ref:`tab:xride-table` and :ref:`tab:additional_compounds`). Default value: 108 (:math:`\mathrm{O_2}`) for molecule 1, zero for the others. A value of zero indicates that for that number no molecule will be taken into account. Thus, for only 1 molecule, keep *i2–i4* :math:`=0`. | The following parameters are common to all our absorption models: - ``f`` : The covering factor of the absorber. Default value: 1 (full covering) - ``zv`` : Average systematic velocity :math:`v` of the absorber (using relativistic Doppler shift) | The following parameters are *only* output parameters: - ``h--zn`` : The column densities in :math:`10^{28}` :math:`\mathrm{m}^{-2}` for all *atoms* added together for the all molecules that are present in this component. | *Recommended citation:* `Pinto et al. (2010) `_.