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The AtomDB Charge Exchange Model
Randall Smith, Adam Foster
April 8, 2014
The ACX package includes two primary tools: the XSPEC package ACX,
which includes a number of related charge exchange models described below,
and a program ‘dacx’, which displays line strengths from ACX models based
on parameters identical to those in the XSPEC models.
Version History
April 8th 2014: version 1.0.0
Initial Release
June 26th 2015: version 1.0.1
Bugfix for dacx.
Intallation
The acx package makes an honest, but limited, attempt to be installable
on multiple platforms. It should work on any modern Linux system and on
Macs running OSX 10.6 or later. It may work on other machines; if it fails,
however, please consider how much you paid for this before complaining too
loudly. Complaining politely, however, may prove useful, especially if you’re
willing to work with us to see how to fix it.
Since the primary purpose of ACX is to create a model usable in XSPEC,
it is important to have XSPEC (and, in fact, the entire HEASOFT pack-
age) available on the computer you’re going to install it on. HEASOFT is
available at http://heasarc.gsfc.nasa.gov/docs/software/lheasoft/,
in case you do not have it already installed. If you plan to use acx, I strongly
recommend you use the ‘build-from-source’ option, as you’re going to want
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to make sure the C compiler you used to build HEASOFT is the same as the
one you built acx with. This may not be absolutely necessary, but I’ve found
that the XSPEC model creation tool is a bit fragile so it’s best to humor
it. The following procedure should work so long as you have HEASOFT
installed and ready when you run the compilation step. That means you
should be able to type ‘xspec’ at the command line and have xspec start
before you begin the compilation process. If you don’t, acx will not com-
pile the xspec module. The installation procedure is as follows, for version
1.0.1:
unix>source $HEADAS/headas-init.csh
unix>tar zxf acx-1.0.1.tar.gz
unix>cd acx-1.0.1
unix>./configure
unix>make
This should compile all the necessary libraries, along with the dacx code
(in the src/ directory) and the XSPEC models in the xspec/ directory. Note
that the installation is done in place; if you really want to use the ‘make
install’ option, you can try it but there are no guarantees.
If the above does not work and all you really want is the xspec module,
I recommend restarting from the beginning and just trying to compile the
XSPEC module thusly:
unix>source $HEADAS/headas-init.csh
unix>tar zxf acx-1.0.1.tar.gz
unix>cd acx-1.0.1/xspec
unix>cp acx.h.in acx.h
...edit acx.h to put in the full path to the acx-1.0.1directory
...
unix>initpackage acx model.dat .
unix>hmake
This will compile just the XSPEC model. It’s important that when you
edit the acx.h file you define the DIRECTORY variable to just point to
the top level directory, ending in acx-1.0.1, not the data/ subdirectory. The
code tacks on the /data/ part itself.
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The XSPEC module
Installing into XSPEC
If the installation worked out ok, you should now be able to install the acx
model into your running copy of XSPEC. acx requires a fairly large chunk of
memory to install, and seems to work best if you load it right after starting
XSPEC. Not ‘working best’ translates into unexpected core dumps, losing
all of your fits, so I urge you to install acx immediately upon starting XSPEC
if you plan to use it.
Installing acx into XSPEC is simple:
XSPEC>lmod acx /path/to/acx-1.0.1/xspec
If this completes without an error message, you should be ready to go.
The basic acx / vacx models
For more information about the physics in the acx models, please see the
Smith et al. (2014, ApJ) and Smith et al. (2012, AN) papers in this directory.
These instructions provide only a how-to guide. The acx model takes seven
parameters, defined here:
kT The equilibrium ion population distribution “temperature”, in keV.
Note that this does not a true Maxwellian velocity distribution; in-
stead, it sets the ion population as though it were in collisional ioniza-
tion equilibrium created by electrons at this temperature. In practice,
ion population distributions involved in charge exchange may not be
represented by a single temperature or even multiple temperatures.
However, this is a necessary simplification to make an XSPEC model
practicable.
FracHe0 The fraction of neutral Helium (relative to the total neutral pop-
ulation, assumed to be H and He) in the plasma. By default set to a
cosmic value of 1/10th He, or 0.090909.
Abundanc The relative (to Anders & Greveese 1989 solar values) abun-
dance of metals in the plasma. Note: This should be kept frozen in
almost all cases, because a change in the overall metal abundance will
act as a change in the normalization value. In a pure charge exchange
spectrum there is no way to measure the absolute abundances since
Hydrogen, the typical astronomical normalizing abundance, does not
create any detectable charge exchange emission. Users strongly urged
to ensure they understand why this is so before using acx.
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redshift The redshift of the emitting plasma.
swcx For most cases, this should be 0; set it to 1 for modeling solar wind
charge exchange (SWCX). See §for more details.
model The assumed model for the distribution of nand lin the charge
exchanging ions. See §for more details.
norm A scaling for the emissivity of the plasma. In concept, this should
depend upon the densities of the charge exchanging ions and neutrals
and their distance from Earth. However, the acx model is an approx-
imation that does not include the actual cross section of the charge
exchange process itself, and so the norm has no physical use except
as a relative scaling. Users strongly urged to ensure they understand
what this means before using acx.
The corresponding variable-abundance version vacx takes similar pa-
rameters except it allows for the relative abundances of individual elements
to be varied. At least one of these elements should be frozen, however, to
avoid problematic interactions with the XSPEC norm.
The swcx flag
The sole difference between the swcx=0 and the swcx=1 models is in how
the charge exchange model is implemented. In the standard model, suitable
for sources galactic or extragalactic sources, the assumption is made that
once an ion interacts via charge exchange with a neutral atom, it will then
immediately find another neutral and will repeat the charge exchange pro-
cess until the ion is fully neutralized. Thus a fully-stripped O+8 ion will emit
not only O VIII lines, it will also emit O VII, O VI, and on down until the
oxygen can no longer undergo charge exchange. Physically, the picture is
that of a hot ion from some source – a supernova shock, galactic superwind,
etc – has run into a dense neutral cloud. In this case, the CX cross section
is so large that the process will neutralize the ion in a very short distance,
certainly smaller than can be resolved with an X-ray telescope.
The only time this statement is not true is if we are actually within the
cloud of ions – in this case, coming from the solar wind and interacting with
neutral matter in the heliosphere. In this case, it’s entirely possible the ion
will not interact again within the field of view of the telescope. One way to
imagine this process is to consider following the progress of a large coronal
mass ejection (CME) as it travels through the heliosphere. At early times,
while the CME is just leaving the Sun, it will have mostly highly-ionized
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gas, so any CX will only show high ions. After it crosses one AU and heads
out into the more distant reaches of the solar system, it will show lower
ions with a lower temperature. This would be clearly require swcx=1, as
just because an O+8 ion undergoes CX and emits a O VIII photon does not
imply we will also see an equal number of O VII and O VI photons in the
same observation. Instead, a O+7 ion will travel further from the Sun and
eventually undergo more CX reactions.
As a practical matter, then, these models will have far less emission for
a given temperature and normalization value than the standard models.
The acxion model
This model is useful largely as a diagnostic of charge exchange patterns from
particular ions. The model takes 5 parameters, listed here:
FracHe0 Same as the acx model.
El Z for the ion, or the number of protons in the ion
rmJ The ionization stage; 0 for neutral, Z for fully-stripped.
redshift Same as the acx model.
model Same as the acx model.
norm Same as the acx model.
Thus, to find out what the spectral shape of charge exchange emission
from Ne10 is, use El=10, rmJ=10.
The meaning of the ’model’ parameter
The model parameter sets how the code assumes electrons from the neutral
participant in the charge exchange land on the ion. Essentially, there are
two primary questions: which (1) principal quantum number nstate and
(2) total angular momentum lstate will be populated? The spin state could
also vary (and does, in some cases, as a function of impact velocity), but we
assume this distribution is done equally in all cases. This latter assumption
is based on a lack of available data, however, and not out of any physical
principle.
There are 16 different models included in the initial distribution. These
come about as we have two different versions of how the nstate is dis-
tributed, and eight different cases for l.
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Predicting the actual line emission following charge exchange thus re-
quires first determining the exact atomic level (or distribution of levels) of
the charge-exchanged ion. We follow the approximation described by Janev
& Winter (1985), who found that the peak of the principal quantum number
ndistribution is at
n0=qsIH
Ip1 + q−1
√2q−1/2(1)
where again qis the charge of the ion, IHis the ionization energy of the
neutral ion (assumed here to be hydrogen), and Ipis the ionization potential
in atomic units. In the case of the ACX model parameter, models 1-4 and
9-12 assume all the ions ended up in this level, while models 5-8 and 13-16
use a weighted distribution between, so that if n0is equal to (say) 4.7, then
30% of the ions would populate n= 4 while 70% would be in n= 5. In
practice, then, models 5-8 and 13-16 should be a more accurate depiction
of the real distribution, although a comparison between related models (e.g.
3 & 7, or 4 & 8) shows that there is relatively little difference in the final
spectrum in practice.
The primary uncertainty in the process, however, is the angular mo-
mentum (l) of the exchanged electron. The correct result will be velocity-
dependent, which is problematic since in most cases the input ion velocity
(or position) will not be known. Following the approximate nature of this
model, we address this uncertainty by simply providing a range of options
for the model.
By default we use orbital angular momentum distributions based on the
nl of the captured electron, creating the 1-8 model cases. This approach best
handles the intermediate weight ions where LS coupling is inappropriate and
Lis not a reliable quantum number. However, it does present a different
set of problems with heavier ions where there is significant configuration
mixing. For example, defining which levels truly represent a captured 11f
electron is not exact.
For reasons of convenience, we initally developed methods that replaced
the orbital angular momentum lwith the total orbital angular momentum
L. This was used for the fits presented in Smith et al (2012, 2014) because
there is no practical difference between the two for the Li-, He- and H-like
ions which dominate X-ray spectra, and Lis stored explicitly in AtomDB.
These no longer our default models, however, and are now labeled the 9-16
models. They may be removed in future releases.
Given the qualitative nature of these distributions, we currently include
both approaches in the distributed ACX model. Regardless of these dif-
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ferences, within all the levels which can be created by each capture with
varying L,S, and Jquantum numbers, we distribute the population using
statistical weighting (2J+ 1).
The four different distributions considered based on either orbital (1-8)
or total (9-16) angular momemtum are:
1. “Even:” weighted evenly by angular momentum, models 1, 5, 9, and
13.
2. “Statistical:” weighted by the relative statistical weight of each level,
models 2, 6, 10, and 14.
3. “Landau-Zener:”, models 3, 7, 11, and 15, weighted by the function
W(l) = l(l+ 1)(2l+ 1) ×(n−1)! ×(n−2)!
(n+l)! ×(n−l−1)! (2)
4. “Separable:”, models 4, 8, 12, and 16, weighted by the function
W(l) = (2l+ 1)
Z×exp h−l×(l+ 1)
zi(3)
The latter two methods in this list are from Janev & Winter (1985). The
separable is the default, preferably with the second ndistribution model
using the orbital angular approach, making the standard starting method
model 8. We hope that providing the alternative models we will allow users
to test the sensitivity of their data to the model approximation. Despite
the simple nature of these models, we expect they will be useful to check
if charge exchange could or could not be responsible for some or all of an
observed spectrum.
For convenience, Table 1 lists each case and the assumptions involved.
For slow winds (v < 1000 km/s), either model 7 or 8 is recommended, along
with tests for sensitivity using other values. The statistical model would
only be applicable for high-velocity CX, while the even distribution would
be a good test for sensitivity.
The dacx program
The dacx program is designed to output the line strengths from a charge
exchange model using the values obtained from an XSPEC fit. The code
outputs the line id’s, their wavelengths, and the line strengths in units of
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photons cm−2s−1. It uses the ever-popular IRAF interface, which should be
familiar to all HEASOFT users via the pset,punlearn and other commands.
To run dacx, first set the environment variable PFILES to ../pfiles and then
just type dacx:
unix> setenv PFILES ../pfiles
unix> bin/dacx
The code will prompt you for all the necessary options, which are for
convenience also listed here:
OutputFileName The name of the optional output file; set to STDOUT
if you want screen output
Wavelength Set this to yes if you want to work in wavelength units (=˚
A).
Otherwise, the code assumes Energy units (=keV)”
LambdaMin The minimum wavelength (or energy) to output
LambdaMax The maximum wavelength (or energy) to output
MinEmiss The minimum emissivity (in photons cm−2s−1) to still output
kT Equilibrium ion balance temperature
FracHe Fraction by number of Neutral He
Abundance Abundance relative to solar (Anders and Grevesse)
Model Model number (1-8)
Norm XSPEC Normalization
redshift Redshift (hidden; must be actively set with pset )
swcx Standard model (if no) or Solar Wind Charge Exchange (if yes). (hid-
den; must be actively set with pset )
CRelative abundance of Carbon (hidden; must be actively set with pset )
NRelative abundance of Nitrogen (hidden; must be actively set with pset
)
O, Relative abundance of Oxygen (hidden; must be actively set with pset )
Ne Relative abundance of Neon (hidden; must be actively set with pset )
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Mg Relative abundance of Magnesium (hidden; must be actively set with
pset )
Al Relative abundance of Aluminum (hidden; must be actively set with
pset )
Si Relative abundance of Silicon (hidden; must be actively set with pset )
SRelative abundance of Sulfur (hidden; must be actively set with pset )
Ar Relative abundance of Argon(hidden; must be actively set with pset )
Ca Relative abundance of Calcium (hidden; must be actively set with pset
)
Fe Relative abundance of Iron (hidden; must be actively set with pset )
Ni Relative abundance of Nickel (hidden; must be actively set with pset )
clobber If yes, can overwrite existing output file. (hidden; must be actively
set with pset )
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Table 1: Meanings of the (v)acx model value
Value Assumptions
1 All CX into one nshell, even distribution by orbital angular momentum l.
2 All CX into one nshell, statistical distribution by orbital angular momentum l.
3 All CX into one nshell, Landau-Zener distribution by orbital angular momentum l.
4 All CX into one nshell, Separable distribution by orbital angular momentum l.
5 CX distributed by weight into neighboring nshells, even distribution
by orbital angular momentum l.
6 CX distributed by weight into neighboring nshells, statistical distribution
by orbital angular momentum l.
7 CX distributed by weight into neighboring nshells, Landau-Zener distribution
by orbital angular momentum l.
8 CX distributed by weight into neighboring nshells, Separable distribution
by orbital angular momentum l.
9 All CX into one nshell, even distribution by total angular momentum L.
10 All CX into one nshell, statistical distribution by total angular momentum L.
11 All CX into one nshell, Landau-Zener distribution by total angular momentum L.
12 All CX into one nshell, Separable distribution by total angular momentum L.
13 CX distributed by weight into neighboring nshells, even distribution
by total angular momentum L.
14 CX distributed by weight into neighboring nshells, statistical distribution
by total angular momentum L.
15 CX distributed by weight into neighboring nshells, Landau-Zener distribution
by total angular momentum L.
16 CX distributed by weight into neighboring nshells, Separable distribution
by total angular momentum L.
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