.. SPDX-FileCopyrightText: 1992-2026 NWO-I/SRON Space Research Organisation Netherlands .. .. SPDX-License-Identifier: CC-BY-4.0 Fitting interstellar dust absorption ==================================== *By: Daniele Rogantini* .. highlight :: none Goal ---- Characterise the extinction of the interstellar dust along the line of sight of a bright low-mass X-ray binary observed with Chandra HETG. .. Note:: This thread merely intends to show the fit of the magnesium and silicon K edges using the ``amol`` model. The simulated dataset with 250 ks exposure time is based on the model used to fit the source GX 3+1 in `Rogantini et al. 2019 `_. Preparation ----------- To follow this thread, it is necessary to download the simulated spectrum and its responsive matrix: :download:`data_sim.spo` and :download:`data_sim.res`. Starting SPEX ------------- Start SPEX in a linux terminal window:: user@linux:~> spex Welcome user to SPEX version 3.05.00 SPEX> Loading data ------------ A command file tailored for this thread to load data is available here :download:`data_gx.com`:: user@linux:~> cat data_gx.com # Simulated data #--------------- # HETG DATA data data_sim data_sim bin inst 1 reg 1:2 0:10000 2 unit ang ignore inst 1 reg 1:2 0:3 unit ang ignore inst 1 reg 1:2 11:1000 unit ang Load the above command file into SPEX:: SPEX> log exe data_gx Plotting data ------------- A command file tailored for this thread to plot the data is available here :download:`plot_edges.com`:: user@linux:~> cat plot_edges.com # plot setting plot dev xw plot type data plot x lin plot y lin plot ux a plot uy fa plot rx 6:10 plot ry 0:900 plot set 1 # HEG color blue plot data col 11 plot mod lw 3 plot fill disp f plot back disp f plot cap id disp f plot cap ut disp f plot cap lt disp f plot Load the above command file into SPEX:: SPEX> log exe plot_edges .. figure:: /_static/data_display.png :width: 600 Defining the broadband model ---------------------------- We are studying the interstellar dust along the line of sight of a bright low-mass X-ray binary located near the Galactic bulge (distance 6.1 kpc). Setting the distance of the source """""""""""""""""""""""""""""""""" :: SPEX> distance 6.1 kpc Distances assuming H0 = 70.0 km/s/Mpc, Omega_m = 0.300 Omega_Lambda = 0.700 Omega_r = 0.000 Sector m A.U. ly pc kpc Mpc redshift cz age(yr) ---------------------------------------------------------------------------------------------- 1 1.882E+20 1.258E+09 1.990E+04 6100.0000 6.1000 6.100E-03 0.0000 0.4 1.990E+04 ---------------------------------------------------------------------------------------------- Setting the SED """"""""""""""" Set the intrinsic spectral-energy-distribution (SED) of the low-mass X-ray binary. For a typical X-ray binary, the SED between 0.1 and 10 keV is described by two components (`Mitsuda et al. 1984 `_): a thermal component, e.g. a black-body (:ref:`sect:bb`), and a non-thermal component, e.g. a power-law (:ref:`sect:pow`):: SPEX> com pow You have defined 1 component. SPEX> par 1 1 norm value 30 SPEX> par 1 1 gamm value 1.1 SPEX> com bb You have defined 2 components. SPEX> par 1 2 norm value 3.e-7 SPEX> par 1 2 t value 0.8 Setting the Galactic cold neutral absorption """""""""""""""""""""""""""""""""""""""""""" :: SPEX> com hot You have defined 3 components. SPEX> par 1 3 nh value 1.9e-2 SPEX> par 1 3 t value 8e-6 SPEX> par 1 3 t status frozen Defining the dust absorption ---------------------------- Here we introduce the ``amol`` components (:ref:`sec:amolmodel`) to characterise the interstellar dust extinction. In this example we add four arbitrary dust compounds: a-olivine (index=4230, :math:`\mathrm{Mg Fe Si O_4}`), a-quartz (index=2234, :math:`\mathrm{Si O_2}`), c-forsterite (index=3230, :math:`\mathrm{Mg_2 Si O_4}`), and a-enstatite (index=3231, :math:`\mathrm{Mg Si O_3}`). The full list of all compounds is reported in Table :ref:`tab:xride-table` and Table :ref:`tab:additional_compounds` in the :ref:`sec:amolmodel` section of the manual. Setting the interstellar dust models """""""""""""""""""""""""""""""""""" Defining ``amol`` with the initial guess for the column densities of the dust compounds:: SPEX> com amol You have defined 4 components. SPEX> par 1 4 i1 value 4230 SPEX> par 1 4 i2 value 2234 SPEX> par 1 4 i3 value 3230 SPEX> par 1 4 i4 value 3231 SPEX> par 1 4 n1 value 1e-7 SPEX> par 1 4 n2 value 1e-7 SPEX> par 1 4 n3 value 1e-7 SPEX> par 1 4 n4 value 1e-7 SPEX> par 1 4 n1 status thawn SPEX> par 1 4 n2 status thawn SPEX> par 1 4 n3 status thawn SPEX> par 1 4 n4 status thawn .. warning:: It is necessary to change and let free to vary the relative abundances of the cold gas elements (:ref:`sect:hot` in this case) which are also contained in the dust compounds. In this example, the dust models contain oxygen (``08``), magnesium (``12``), silicon (``14``) and iron (``26``). We let them to vary within a limited range according to the depletion intervals defined by `Whittet et al. (2002) `_ and `Jenkins et al. (2009) `_. :: SPEX> par 1 3 08 value 0.7 SPEX> par 1 3 12 value 0.10 SPEX> par 1 3 14 value 0.10 SPEX> par 1 3 26 value 0.05 SPEX> par 1 3 08 range 0.4 1 SPEX> par 1 3 12 range 0 0.4 SPEX> par 1 3 14 range 0 0.4 SPEX> par 1 3 26 range 0 0.2 SPEX> par 1 3 08 status thawn SPEX> par 1 3 12 status thawn SPEX> par 1 3 14 status thawn SPEX> par 1 3 26 status thawn Setting the component relations """"""""""""""""""""""""""""""" Adding the multiplicative components ``hot`` and ``amol`` to the broad-band model:: SPEX> com rel 1:2 4,3 SPEX> model show -------------------------------------------------------------------------------- Number of sectors : 1 Sector: 1 Number of model components: 4 Nr. 1: pow [4,3 ] Nr. 2: bb [4,3 ] Nr. 3: hot Nr. 4: amol Fitting ------- We fit the model to the data and print the free parameters:: SPEX> calc SPEX> fit print 1 SPEX> fit SPEX> fit SPEX> plot SPEX> par show free -------------------------------------------------------------------------------------------------- sect comp mod acro parameter with unit value status minimum maximum lsec lcom lpar 1 1 pow norm Norm (1E44 ph/s/keV) 23.14066 thawn 0.0 1.00E+20 1 1 pow gamm Photon index 0.9320605 thawn -10. 10. 1 2 bb norm Area (1E16 m**2) 3.5883755E-07 thawn 0.0 1.00E+20 1 2 bb t Temperature (keV) 0.7793768 thawn 1.00E-04 1.00E+03 1 3 hot nh X-Column (1E28/m**2) 2.0304110E-02 thawn 0.0 1.00E+20 1 3 hot 08 Abundance O 0.5010648 thawn 0.40 1.0 1 3 hot 12 Abundance Mg 0.1016048 thawn 0.0 0.40 1 3 hot 14 Abundance Si 0.1060375 thawn 0.0 0.40 1 3 hot 26 Abundance Fe 0.000000 thawn 0.0 0.20 1 4 amol n1 Column 1 (1E28/m**2) 5.6286910E-07 thawn 0.0 1.00E+20 1 4 amol n2 Column 1 (1E28/m**2) 1.1466740E-07 thawn 0.0 1.00E+20 1 4 amol n3 Column 1 (1E28/m**2) 1.3037014E-07 thawn 0.0 1.00E+20 1 4 amol n4 Column 1 (1E28/m**2) 9.8849377E-08 thawn 0.0 1.00E+20 Instrument 1 region 1 has norm 1.00000E+00 and is frozen Instrument 1 region 2 has norm 1.00000E+00 and is frozen -------------------------------------------------------------------------------- Fluxes and restframe luminosities between 2.0000 and 10.000 keV sect comp mod photon flux energy flux nr of photons luminosity (phot/m**2/s) (W/m**2) (photons/s) (W) 1 1 pow 7877.93 6.754451E-12 4.125361E+45 3.331746E+30 1 2 bb 3030.35 1.681985E-12 1.818740E+45 9.538203E+29 -------------------------------------------------------------------------------- Fit method : Classical Levenberg-Marquardt Fit statistic : C-statistic C-statistic : 2388.02 Expected C-stat : 2402.60 +/- 69.35 Chi-squared value : 2406.15 Degrees of freedom: 2388 W-statistic : 0.00 .. figure:: /_static/data_model.png :width: 600 Final remarks ------------- This is the end of this analysis thread. If you want, you can save the parameters and quit SPEX:: SPEX> par write parameters SPEX> log out fit_result SPEX> par show SPEX> log close output SPEX> quit Thank you for using SPEX!