3 10
lll l•. •L• ll, ...•
l .•.
Sb, ockHe},ght / i, .,.• ...
'''''''
i' i
ilholi''i//lij'ii'li'i-ii'`'"'/tt tt--- -- -It "-t--- -t- ltttny-t- tti:--tt - -ttv-v
'
5;
,g.
10
e,
E g
loi EO.,
E'o ua
10 .
02 O.4 O.6 O.8 1 1.2 1.4
' MwDeq.un) '
Figure 3.4: Results of the numerical solu,tions (Yuasa et al., 2010) for the shock height from the WD surface (thick solid line) and the shock temperature (thin solid line), shown against the WD ntass. For comparison, the dashed line shows the shock temperature calculated by assuming no-gravity in the accretion column.
' '
Mo ) systems comparing to the shock temperature without gravitational attraction. For example, at MwD == l.2 Mo, n6-graviky distribution overestimates a shock temperature and following MwD by rtvlO% compared with the present result.
1oO
Chapter 4
X-ray Emission from
Thermal Plasma
Optically Thin
X-ray emission from thermal plasma involves many atomic processes listed in Table 4.1, Some processes produce photons with a continuous energy distribution and the resultant spectra become continuum, while other processes produce photons of characteristic ener-gies, and are observed as line spectra. In the case of optically thick plasma which bptical depth is larger than 1 enough (T >> 1), detailed features due to interaction in the plasma between the gas and photons are lost and the emission approaches blackbody radiation.
In this chapter, we describe the details of the X-ray emission mechanisms from optically thin thermal plasma, to understand the observed X-ray spectra of non-Magnetic CVs.
First we consider the balance between collisional ionization and recombination pro-cesses, which determines the ionization distribution of atoms in the plasma in the colli-sional ionization equilibrium. It is shown that the helium-like and hydrogenic ions are important for our analysis. Then, line emission mechanisms and selection rules are de-scribed. Density effects are .also examined, because we treat the plasma of n tv 10i6 cm-3.
4.1 IonizationBalance
Ionization structure of a plasma is determined by the balance between ionization and recombination processes. The rate equation to the number density Nz,. of ion Z+Z, where Z is the atomic number and z is the charge number, is given by
'
.t
'
' ldNz,z
ilg dt = Nz,z-i Cz,z-i ' Nz,z(Cz,z + or z,z) + Nz,z+, ,i orz,.+i? (4.1)
'
Table 4.1 : Atomic Radiation Processes
'Ilrransition Type Atomic Process Spectral Shape
free- fre' e
free-bound
bound-bound
bremsstrahlung radiative recombination
innershell ionization - fluorescence line excitation line
innershell excitation satellite line radiative recombination - cascade line dielectronic recombination satellite line two-photon decay
continuum continuum
line line line line line ,
continuuin
39
40CErAPTER 4. X-RAYEMISSION FROM OPTICALLY THIN THERMAL PLASMA
where Cz,. denotes the total electron collisional ionization rate coefficient (cm3 s-i) for the process of ZZ - ZZ+i-, and dvz,. is the total recombination rate coeflicient for the process of ZZ . ZZ-i. Equation (4.1) is transformed into the equation of the fraction of
' '
.'
'
lons asil;dndZt'Z F= cz,.-inz,.Li -- (cz,. ri- orz,?)nz,z + dvz,z+inz,z+i) ' (4•2)
'
where nz,. ii Nz,./nHAz is the fraction of ions from element Z in ionization stage z, nH is ,,the hydrogen density, and Az is the relative abundance of element Z to hydrogen.4.1.1 IonizationProcess
The following two types of ionization processes contribute to the collisional ionization rate coefficient Cz,. (Table 4.2).
Direct ionization - Ion ZZ is directly ionized to ZZ+i by electron impact.
Autoionization - This process requires an intermediate state of an inner electron excited (ZZ*). If the excitation energy exceeds the ionization energy of any of the other electrons present, the excited atom (ion) will eject an electron and become singly ionized (Zz+i).i
Using the electron-impact ionization cross section, the rate coeMcient from state i to state
' (1•Ii,• 'L <gijov,>= ./ aijvk(v,T,)dv, (4.3)
' Jt ,••
tt
where f(v, T.) is the Maxwellian distribution function and oij• is the electron-impact ion-ization cross section, which is given by experiments and/or quantum mechanical calcula-tions.
4.1.2 RecombinationProcess
The following two types of recombination processes contribute to the radiative recombi-nation rate coefficient az,. (Table 4.2).
Radiative recombination - This is an inverse process of photo--ionization. A free electron is captured by an ion, and the excess energy is eMitted as a photon. The rate coeflEicient of radiative recombination is a monotonically decreasing function of temperature.
Dielectronic recombination - This is a two-electron process. The resonance tion simultaneously occurred with the electron capture to a higher state produces a doubly excited state Z•Z-i*. The ion will be rearranged to the ground state, emitting one of the excited electrons (autoionization), or a photon (dielectronic tion). The dielectronic recombination coefficient has a maximum value at around the characteristic temperature corresponding to the excitation energy, and at that temperature. This effect is usually more important than the direct radiative combination. Note that this process contributes to a line emission, whose energy is slightly different from that of the excitation line of ZZ, and is called the dielectronic recombination satellite line. It must be emphasized that the dielectronic nation satellite lines of ZZ7i" emerge just •beside the resonance line of ZZ".
iThis process resembles Auger effect, in which the initial step is the ionization of an inner electron (ZZ+i') rather than the excitation to a higher level, and the final state is the doubly ionized ion (Z"+2).
4.2. LINEEMISSION
41Tab!e 4.2: Ionjzation and Recombination Process Atomic Process Ionization State
(direct) ionization autoionization
radiative recombination dielectronic recombination
ZZ - zz+1
ZZ - zz" -> zz+1 ZZ -. zz-1 zz - zz-1* =, zz-14.1.3 Ionization Equilibrium and Ionization Fractions
The collisionally ionizing plasma ev61ves according to equation (4.2) and reaches the equilibrium state. The final state is called collisional ionization equilibrium (CIE) while the ionizing stage is called non-equilibrium ionization (NEI). According to Masai (1994), it takes about t k 10i2(n. [cm-3])-i s for abundant ions to establish ionization equilibrium.
In the ionization equilibrium, equation (4.1) becomes a set of equations
Cz,z-iopz,z-i=cuz,znz,x• (4•4)
By solving these (Z + 1) dimensional simultaneous equations for each element, fractional abundance nz,, of ion ZZ are determined. Note that eiectron density does not appear in equation (4.4), because it is a common factor of all the ionization and recombination proc'esses, and the ion fractions are functions only of temperature. At high electron densities, however, the dielectronic recombination rate coeflicients depend on density and dielectronic recombination will be suppressed (g 4.2.3). For the details of the calculations of ionization equilibrium fractions, see e.g., Shull & van Steenberg (1982), Arnaud &
Rothenflug (1985), and Amaud & Raymond (1992).
Figure 4.1 is' a result of the ionization balance calculations for iron (McCray 1987;
Shull & van Steenberg 1982). It is remarkable that closed-shell ions like helium-like Fe XXV and neon-like Fe XVII are very durable and exist for large temperature ranges. This is because it requires a large energy to excite or ionize the electron in the closed-shell, which makes the possibility of ionization and dielectronic recombination small.
Note that helium-like, hydrogenic, and fu11-ionized ions are dominant over the tem-perature range T k 1.8 Å~ 107 K, and fractions of Iithium-like or less ionized ions are srpall for the iron.
4.2 Line Emission
4.2.1 Hydrogenic and Helium-like Kcu Lines
Due to,spin-orbit interaction, n == 2 state of the hydrogenic ion is split into 2P3/2, 2Pi/2, and 2Si/2. Transition from 2P312, 2Pi/2 to the ground state 2Si/2 is possible within the electric dipole approximation, and the resultant emission line is called resonance line, while from 2Si/2 to the ground state is ppssible only via two photon decay.
On the other hand, n = 2 state of the helium-like ion is split into 3P2,3Pi, 3Po, 3Si, iPi, and iSo due to Coulomb interaction, exchange interaction, and spin-orbit interaction.
Here the emission line due to the transition from iPi, 3Si, and 3Pi to the ground state iSo is called resonance iine, forbidden line, and inter-combination line, respectively.