CEVMKL MODEL (kTmax = 20 keV)
s/
9
Toe
r
g R
g E
9 -8 6d
-o/
-8
"o'
-co
N NeFe-L Mg Si
s Ar
Ca Fe
12
Energy (keV)
5 10
Ji
e
T.
9g z
29
pt
9 -g 6d 8 -8 -g
-O.2 05
C NO
NeFe-L Mg si
S Ar ca
Fe
O.2 O.5
12
Energy (keV)
5 10
Figure 5.2: Calculated spectra of the emission from an optically thin thermal plasma with maximum temperatures of 1.0 keV (left) and 20.0 keV (right). The plasma metallicity is assumed to be equal to that of the sun.
sirn-refiection.qdp
g
s T NMiH o :
Rs
"
-g 6 e
9
9
r
9
Total Spectrum
• Plasma emission Refleetion
N
t tt
t
"--'l-"s•"' ;iiLas.,`'i,.X.•i..r:•,",'L•`:'""
Iron fiuorescence 1ine (6.4 keV) ->
Z,x:,;,,-..xx('
NS.k Ns•-s
<•`
t
1 to
Energy (keV)
Figure 5.3: An example spectra of the plasma emission (dashed line) and its reflection (dotted line), and the iron Ka fluorescence line (solid line). Absorption edges of oxygen (O.5431 keV) and iron (7.112 keV) are clearly visible in the reflected spectrum. Compton reflection hump dominates the spectra above 10 keV. The spectrum we can observe is
solid line.
emission. The reflected emission consists of the Compton down-scattering of the incident X-rays, photoe}ectric absorption by cold matter, and the iron K fluorescence line. The iron fluorescence line is produced via innershell ionization by X-ray illumination. Figure 10.1 shows an example spectrum of the plasma emission and its reflection, and the iron Kor fiuorescence line. The shape and intensity of the reflected emission essentially depend on an incident ray spectrum, solid angle of the refiecting matter subtending the X-ray source, metal composition of the reflecting material, and the orientation of our view with respect to the normal of the reflecting surface. We adopt such a model of reflect available in XSPEC.
5.3. ACCRETION COLUMN SPECTRUM MODELS
5.3 Accretion Column Spectrum Models
55
Some spectral model taking into account the accretion column structure calculated by analyticallY or numerically (see chap.4) was constructed and fitted to observed spectra (Wu et al. 1994, Cropper et al. 1998, Cropper et al. 1999, Ramsay 2000 Suleimanov et al.
2005, Brunschweiger et al. 2009, Yuasa et al. 2010, Hayashi et al. 2011). For construction their models, they divided the accretion column into small components where the physical
parameter such as the temperature and density may be constant, and summed up the
emissions from the components. Fig.(5.4) is the model presented by Cropper et al. 1999 which used the numerically solved accretion column structure considering the varying gravity along the column (Cropper model), comparing with that not considering the gravity (Aizu model). This figure shows the spectrum based on the Cropper model is harder that based on the Aizu model, because the heatup of the accreting gas occurs by the release of the gravity potential.10
1
>A S 10•i. .NE
g
g lo.,
Es
1cr'
lo4 a 2,5 'k 2.og g' IIg
tzg glg
vnyint
ptvimat
potetsial (tlO)
zero.
grivay (Aizv)
O.1 1.0
Energy aeV)
to.o
Figure 5.4: Upper panel: the photon spectrum from the Aizu model (above), and, dis-placed downwards by a factor of 10 for clarity, that for the case when the effects of gravity are included (Cropper model). Lower plot: the ratio of the Aizu spectrum to the spectrum from the varying gravitational potential.
Assuming the accretion column structure along the accretion column characterized by
T.Tax - (1ÅíI)a, (s s)
p.P. =: (1Åí)b, (s6)
56
CHAPTER 5. SPECTRUM MODELS OF THE ACCRETIOIV COLUMN
Table 5.1: Best fit parameters with accretion column spectral models.
Model
a br
Frank et al. (2002) O.4 -O.4 0.5
Suleimanov et aL (2005) O.312 -O.433 O.430
Falanga et al. (2005) compared some of the models and showed that the emission measure is defined as
EM=(T.T..)or W'th or=(2bi1) (5 7)
They fitted' with the equations to the published accretion column structure and obtained the result as table.(5.1). The model of Frank et al. (2002) is the analytically solved
acctetion column structure model with assumption of the constant pressure. Suleimanov et al. (2005) used the Cropper model. The result show that the Cropper numerical model which better represents reality is softer than analytical one.
5e4 Definition of Solar Abundances
In order to evaluate intensities of line emission of various elements originated from the optically thin thermal plasma, elemental abundances of the plasma should be determined accurately. The relative abundance of each element depends on an abundance table we adopt. Six solar-abundance'tables is available in XSPEC, as listed in ']]able 5.2.
Anders & Ebihara (1982) compiled abundances from Cl type chondrite,• which is de-fined as those including more than 3,5% C and no chondrules. Feldman (1992) performed
spectroscopic abundance measurements from high temperature solar plasmas. Anders
& Grevesse (1989) compiled the abundances of chondrite and solar photosphere and
corona. They found significant difference between Sun and meteorites in composition of Fe,, Mg, Ge, Pb, and W; other well-determined elements agree within Å}9oro on -the average. Grevesse & Sauval (1998) confirmed the solar abundance, essentially derived from the solar photospheric spectrum, is in good agreement with the meteoritic abun-dances. Lodders (2003) summarized the results of these abundance determinations for all elements, and selected the best currently available photospheric abundances. On the other hand, Wilms et al. (2000) presented abundances of the interstellar medium, which is systematically lower abundances than the others.We utilize the abundance table of Anders & Grevesse (1989) as the default solar abun-dance in this thesis. We must recognize that most elemental abunabun-dances are consistent with those of the other definitions, but only Fe abundance (4.68 Å~ 10-5) is higher about
1.5 times than others (rv 3.2 Å~ 10-5).
5.5 SPEXpackage
SPEX (Kaastra et al., 1996) is a software package developed at SRON for the analysis and interpretation of cosmic X-ray spectra. It encompasses options for spectral modelling, fitting, graphical display and output. The widely used Mewe-Kaastra-Liedahl (MEKAL;
see sec.(5.1) plasma model constitutes a part of the package, however many updates have
since been made. SPEX is a software package optimized for the analysis and interpretation of high-resolution cosmic X-ray spectra. The software is especially suited for fitting spectra
obtained by current X-ray observatories like XMM-Newton, Chandra, and Suzaku. SPEX will be continuously improved to handle spectra from high-resolution X-ray instruments on future missions like ASTRO-H and IXO.
We use the cooling function with radiative losses of up-to-date transition lines calcu-lated by SPEX (Schure et al., 2009) to calculate the accretion column structure, and the SPEX package version 2.02.04 to calculate the accretion column spectrum model. This code can calculate the spectra of a given emission measure for plasmas at different tem-peratures and different choices of electron and ion temtem-peratures, and therefore is used as a spectral analysis code tailored to EUV and X-ray observations, in which energy band it is one of the most complete packages currently available. Because it includes a very complete prescription of line emission, cooling rates predicted by SPEX are higher than those of cooling curves available until now as shown in fig.(5.5). The 15 elements presently included are H, He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Fe, and Ni.
For our purpose, we use SPEX to calculate the spectra of a plasma in collisional ionization equilibrium (CIE) and non-equilibrium ionization (NEI). It is very useful for construction of our accretion column spectral model that the plasma temperature range of SPEX being calculated is wide, O.OO05 - 1000 keV comparing with the thin thermal
plasma models in XSPEC package, MEKALof O.0808 - 79.9 keV, CEMEKL and cevmkl
of O.Ol - 100 keV and APEC of O.O08 - 64 keV.nA
s Toua ooNÅë
z v <
oop
---
2O
--
22
-24
--
26
'
ttt " r. !" "' tt ""
tt .. .t .. N
s
s".. s
.N.. ---. .s. "- ,",t-- ,
N
NS- -- -- -h
.
this work
r.--T i".t.hDe.r.ia.nidd&&BD.oi?aSa,69,3
45678
lpg T (K)
Figure 5.5: Cooling curves compared: the higher cooling rates calculated with SPEX are mainly due to a more complete coverage of the line transitions, including Fe L and EUV
lin'es 5.5.