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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): \(n(a) \propto a^{-3.5}\) with a the grain size and \(a_{\mathrm{min}}=0.005\ \mu m\) and \(a_{\mathrm{max}}=0.25\ \mu m\). 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 Compounds list).

Compounds list

index	Name	formula	Form	Edge	Source
115	c-silicon	\(\mathrm{Si}\)	crystalline	Si 1s	[1]
127	metallic iron	\(\mathrm{Fe}\)	crystalline	Fe 1s	[2]
129	metallic nickel	\(\mathrm{Ni}\)	crystalline	Ni 1s	[3]
130	a-carbon	\(\mathrm{C}\)	amorphous	C 1s	[4]
131	diamond	\(\mathrm{C}\)	crystalline	C 1s	[4]
132	graphite	\(\mathrm{C}\)	crystalline	C 1s	[4]
2111	c-silicon carbide	\(\mathrm{SiC}\)	crystalline	Si 1s	[1]
2230	troilite	\(\mathrm{FeS}\)	crystalline	S 1s; Fe 1s	[5], [6]
2231	pyrrhotite	\(\mathrm{Fe_7 S_8}\)	crystalline	S 1s; Fe 1s	[5], [6]
2232	a-quartz	\(\mathrm{Si O_2}\)	amorphous	Si 1s	[7]
2233	c-quartz	\(\mathrm{Si O_2}\)	crystalline	Si 1s	[7]
2234	a-quartz	\(\mathrm{Si O_2}\)	disorder	Si 1s	[7]
2235	c-silicon nitride	\(\mathrm{Si_3 N_4}\)	crystalline	Si 1s	[1]
2236	magnesia	\(\mathrm{MgO}\)	crystalline	Si 1s	[8]
2237	aluminium oxide	\(\mathrm{Al_2 O_3}\)	crystalline	Al 1s	[9]
2238	alabandite	\(\mathrm{MnS}\)	crystalline	S 1s	[5]
2239	pyrite	\(\mathrm{FeS_2}\)	crystalline	S 1s	[5]
2240	titanium dioxide	\(\mathrm{TiO_2}\)	crystalline	Ti 1s	[10]
2241	a-hydrocarbon	\(\mathrm{CH}\)	amorhpous	C 1s	[11]
3230	c-forsterite	\(\mathrm{Mg_2 Si O_4}\)	crystalline	Mg 1s; Si 1s	[12], [7]
3231	a-enstatite	\(\mathrm{Mg Si O_3}\)	amorphous	Mg 1s; Si 1s	[12], [7]
3232	c-enstatite	\(\mathrm{Mg Si O_3}\)	crystalline	Mg 1s; Si 1s	[12], [7]
3233	c-spinel	\(\mathrm{Mg Al_2 O_4}\)	crystalline	Mg 1s; Al 1s	[12], [9]
3270	calcium aluminate	\(\mathrm{Ca Al_2 O_4}\)	crystalline	Ca 1s	[13]
3271	tri-Ca aluminate	\(\mathrm{Ca_3 Al_2 O_6}\)	crystalline	Ca 1s	[13]
3302	c-fayalite	\(\mathrm{Fe_2 Si O_4}\)	crystalline	Si 1s; Fe 1s; Fe 2p	[7], [14], [15]
4230	a-olivine	\(\mathrm{Mg Fe Si O_4}\)	amorphous	Mg 1s; Si 1s	[12], [7]
4231	c-olivine	\(\mathrm{Mg_{1.56} Fe_{0.4} Si_{0.91} O_4}\)	crystalline	Mg 1s; Si 1s; Fe 1s	[12], [7], [6]
4232	c-En60Fe40	\(\mathrm{Mg_{0.6} Fe_{0.4} Si O_3}\)	crystalline	Mg 1s; Si 1s; Fe 1s	[12], [7], [6]
4233	a-En60Fe40	\(\mathrm{Mg_{0.6} Fe_{0.4} Si O_3}\)	amorphous	Mg 1s; Si 1s; Fe 1s	[12], [7], [6]
4234	a-En75Fe25	\(\mathrm{Mg_{0.75} Fe_{0.25} Si O_3}\)	amorphous	Mg 1s; Si 1s	[12], [7]
4235	a-En90Fe10	\(\mathrm{Mg_{0.9} Fe_{0.1} Si O_3}\)	amorphous	Mg 1s; Si 1s; Fe 1s	[12], [7], [6]
4236	c-En90Fe10	\(\mathrm{Mg_{0.9} Fe_{0.1} Si O_3}\)	crystalline	Mg 1s; Si 1s; Fe 1s	[12], [7], [6]
4237	c-hypersthene	\(\mathrm{Mg_{1.502} Fe_{0.498} Si_2 O_6}\)	crystalline	Mg 1s; Si 1s; Fe 1s	[12], [7], [6]
4270	c-diopside	\(\mathrm{Mg Ca Si_2 O_6}\)	crystalline	Ca 1s	[13]
4271	a-diopside	\(\mathrm{Mg Ca Si_2 O_6}\)	amorphous	Ca 1s	[13]
4272	c-anorthite	\(\mathrm{Ca Al_2 Si_2 O_8}\)	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 Additional compounds list. These models do not include scattering and were not integrated over a size distribution. They will be updated in future versions.

Additional compounds list

108	molecular oxygen	\(\mathrm{O_2}\)	O 1s	[16]
126	metallic iron	\(\mathrm{Fe}\)	Fe 2p	[17]
2001	water	\(\mathrm{H_2 O}\)	O 1s	[18]
2002	crystalline ice	\(\mathrm{H_2 O}\)	O 1s	[19]
2003	amorphous ice	\(\mathrm{H_2 O}\)	O 1s	[19]
2010	carbon monoxide	\(\mathrm{CO}\)	O 1s	[16]
2011	carbon dioxide	\(\mathrm{CO_2}\)	O 1s	[16]
2020	laughing gas	\(\mathrm{N_2 O}\)	O 1s	[16], [21]
2102	silicon monoxide	\(\mathrm{SiO}\)	Si 1s	[20]
2200	eskolaite	\(\mathrm{Cr_2 O_3}\)	O 1s	[22]
2300	iron monoxide	\(\mathrm{FeO}\)	Fe 1s	[23]
2301	iron oxide	\(\mathrm{Fe_{1-x} O}\)	O 1s	[22]
2302	magnetite	\(\mathrm{Fe_3 O_4}\)	O, Fe 1s	[22], [23]
2303	hematite	\(\mathrm{Fe_2 O_3}\)	O, Fe 1s; Fe 2p	[22], [23], [17]
2304	iron sulfite	\(\mathrm{Fe S_2}\)	Fe 1s	[23]
2400	nickel monoxide	\(\mathrm{NiO}\)	O 1s	[22]
2500	cupric oxide	\(\mathrm{CuO}\)	O 1s	[22]
3001	adenine	\(\mathrm{C_5 H_5 N_5}\)	O 1s	[24]
3103	pyroxene	\(\mathrm{Mg Si O_3}\)	O 1s	[25]
3200	calcite	\(\mathrm{Ca C O_3}\)	Ca 1s	[26]
3201	aragonite	\(\mathrm{Ca C O_3}\)	Ca 1s	[26]
3202	vaterite	\(\mathrm{Ca C O_3}\)	Ca 1s	[26]
3203	perovskite	\(\mathrm{Ca Ti O_3}\)	O 1s	[22]
3300	hercynite	\(\mathrm{Fe Al_2 O_4}\)	O 1s	[22]
3301	lepidocrocite	\(\mathrm{Fe O (OH)}\)	Fe 2p	[17]
3303	iron sulfate	\(\mathrm{Fe S O_4}\)	Fe 2p	[17]
3304	ilmenite	\(\mathrm{Fe Ti O_3}\)	O 1s	[22]
3305	chromite	\(\mathrm{Fe Cr_2 O_4}\)	O 1s	[22]
4001	guanine	\(\mathrm{C_5 H_5 N_5 O}\)	O,N 1s	[24]
4002	cytosine	\(\mathrm{C_4 H_5 N_3 O}\)	O,N 1s	[24]
4003	thymine	\(\mathrm{C_5 H_6 N_2 O_2}\)	O,N 1s	[24]
4004	uracil	\(\mathrm{C_4 H_4 N_2 O_2}\)	O,N 1s	[24]
4100	andradite	\(\mathrm{Ca_3 Fe_2 Si_3 O_{12}}\)	O 1s	[22]
4101	acmite	\(\mathrm{Na Fe Si_2 O_6}\)	O 1s	[22]
4102	franklinite	\(\mathrm{Zn_{0.6} Mn_{0.8} Fe_{1.6} O_4}\)	O 1s	[22]
4103	olivine	\(\mathrm{Mg_{1.6} Fe_{0.4} SiO_4}\)	O 1s	[22]
4104	almandine	\(\mathrm{Fe_3 Al_2 (Si O_4)_3}\)	O 1s	[22]
4105	hedenbergite	\(\mathrm{Ca Fe Si_2 O_6}\)	O 1s	[22]
5001	dna (herring sperm)	\(\mathrm{C_{39} H_{61} N_{15} O_{36} P_{4}}\)	O,N 1s	[24]
6001	montmorillonite	\(\mathrm{Na_{0.2} Ca_{0.1} Al_2 Si_4 O_{10} (O H_2)(H_2 O)_{10}}\)	Si 1s	[20]
6002	nontronite	\(\mathrm{Na_{0.3} Fe_2^{3+} Si_3 Al O_{10} (OH)_2 \bullet (H_2 O)}\)	Si 1s	[20]
7001	enstatite_paulite	\(\mathrm{Ca_2 Mg_4 Al_{0.75} Fe_{0.25} Si_7 Al O_{22} (OH)_2}\)	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 Additional compounds list in the energy interval where these are given. Outside this range, the cross sections for free atoms Verner & Yakovlev (1995) \(var pixsec 1\) or Badnell et al. (2005) \(var pixsec 2\) are used.

Van Aken et al. (1998) do not list the precise composition of iron oxide. We assume here that \(x=0.5\).

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 \(\mathrm{N_2 O}\), 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 \(10^{-7}\) for \(\mathrm{CO_2}\) means \(10^{21}\) \(\mathrm{CO_2}\) molecules \(\mathrm{m}^{-2}\), but of course \(2\times 10^{21}\) atoms \(\mathrm{m}^{-2}\), because each \(\mathrm{CO_2}\) 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 \(10^{28}\) \(\mathrm{m}^{-2}\) for molecules 1–4. Default value: \(10^{-6}\) for molecule 1, and zero for the others.

i1--i4 : the molecule numbers for molecules 1–4 in the list (Compounds list and Additional compounds list). Default value: 108 (\(\mathrm{O_2}\)) 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 \(=0\).

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 \(v\) of the absorber (using relativistic Doppler shift)

The following parameters are only output parameters:

• h--zn : The column densities in \(10^{28}\) \(\mathrm{m}^{-2}\) for all atoms added together for the all molecules that are present in this component.

Recommended citation: Pinto et al. (2010).

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