Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.astro.spbu.ru/staff/afk/AtDatCentre/AtDatCat/Chapter4.pdf Дата изменения: Fri Nov 19 16:06:58 2010 Дата индексирования: Tue Oct 2 04:13:19 2012 Кодировка: Поисковые слова: corona

Chapter 4 Sp ectra of the gaseous nebulae and their interpretation The sp ectrum of a gaseous nebula consists of weak continuous emission sp ectrum sup erp osed by numerous emission lines. Several thousands of sp ectral lines have b een recognized but only ab out 200 of them can b e measured with sufficient exactness and used for analysis of physical conditions in nebulae. The sp ectral lines of atoms and ions of almost all chemical elements from H to Ni and more heavy elements (see Balateau et al. (1995), Pequignot & Balateau (1994)) have b een detected. Intensity of the continuous sp ectrum has b een measured for comparatively small numb er of nebulae. The emission lines observed in nebulae dep ending on the mechanism of their formation can b e divided in two main typ es: 1) the recombinational and 2) the collisional lines. The list of main sp ectral lines sp ecified in the ultraviolet, visible and infrared sp ectral regions, is given in Table 25. The values of wavelengths and transition probabilities for these lines are also presented in Table 25. 4.1 Recombination line intensities In the sp ectra of nebulae there are observed the sp ectral lines of allowed transitions b etween excited states of H, He, C, N and O. Some lines of such typ es are detected for the ions having lower abundances (see Table 25), say for Ne, Si and Mg. The main mechanism of formation of these lines is recombination: the photorecombination or (and) dielectronic recombination (for He, C, N, O) of the excited states of ion Xi+1 followed by the cascade transitions to the ground state of ion Xi . Definite contribution to the formation of some recombination lines give also the collisional excitation processes. At the present time only the recombination sp ectra of H and He have b een investigated in detail. The most complete data concerning the theoretical recombination line intensities of H, HeI and HeI I are given in the pap ers by Brocklehurst (1971, 1972), Hummer & Storey (1987), Martin (1988) and Ilmas & Nugis (1982). Somewhat less have b een studied the recombinational sp ectra of C, N and O. The difficulties of these calculations are caused by the complicity of the structure of their atomic energy levels and by inaccuracy of the values of transition probabilities, which determine the state p opulations. The references on the recombination sp ectra of C, N and O ions have b een compiled by Nikitin et al. (1988), Hummer & Storey (1987) and Escalante & Victor (1990, 1992). In the most cases gaseous nebulae are transparent for the emission in the recombination lines. Thus, the energy irradiated by a nebula in recombination line with wavelength jk is E () = 4j ( ) = nj n(X i )Ajk hjk dV = ne n(X
i+1

)ef f ()hjk dV ,

(4.1)

where nj is the p opulation of the level j of ion Xi , the quantity Ajk is the corresp onding sp ontaneous transition probability, further, hjk is the photon energy of the transition, ne is 43


the electron numb er density, n(Xi+1 ) is the numb er density of recombining ion and ef f is the effective coefficient of recombination, which has b een defined as the total recombination coefficient due to all recombination acts plus the contribution of the cascade processes. The integration covers whole volume of a nebula. The p opulations of levels nj can b e found from the equation of statistical equilibrium
m-1

n

m k =1

Amk = ne n(X

i+1

k

max

)m (Te )+
k =m+1

nk Akm

(m = 2, 3, 4...)

(4.2)

for the Menzel A case if the optical depth in the resonance line series (1n 1). Here kmax is 1) we have the index of the highest state considered. For Menzel B case (1n
m-1

n

m k =2

Amk = ne n(X

i+1

k

max

)m (Te )+
k =m+1

nk Akm

(m = 3, 4, 5...).

(4.3)

In these equations am (Te ) is the total electron recombination rate onto level n of ion Xi+1 . It must b e mentioned that models A and B simplify essentially the problem of radiative transfer in recombination sp ectral lines. For intermediate case if at different values of n the optical depth 1n is in the range of b etween the Menzel A and B cases, we have to use some approximations to solve the transfer problem for the first series lines. In gaseous nebulae the optical depth in resonance line series of most abundant elements (H, He, C, N, O) is 10 -105 . The calculation of recombination sp ectra for HI in the case of the finite optical depth in the L for the stationary nebulae presented by the plane-parallel layers has b een carried out by Grinin (1969). In the most cases one can use the standard Sob olev (1947) approximation. This approximation has b een used by several authors (see, e.g., Rublev (1969), Ilmas (1986), Ilmas & Nugis (1982)). The level p opulations of atoms and ions practically in all nebulae can b e treated as the time indep endent quantities. Only in the case if there happ ens a rapid change of ionizing radiation it is inevitable to use the equations describing the time dep endency of level p opulations. The level p opulation of atoms and ions having low excitation p otentials can also b e influenced by collisions with electrons or other particles. In this case to the right-hand part of Eq.(4.2) and Eq.(4.3) must b e added the term n1 ne q1n which takes into account the excitation processes from the ground state. їFrom Eq.(4.2) or Eq.(4.3) we can find the quantities nk /(n1 (Xi+1 ) ne ) and thereafter to calculate the recombination line intensities Ikj nk Akj hjk . Due to large numb ers of quantum states and of corresp onding equations for nebulae the system of equations turns out to b e very bulky one (ab out 10000 states for planetary nebulae). The needed values of Akj and an are often badly known. Therefore it is reasonable to simplify the problem considering moderate numb er of states (ab out 100) and to take the contribution of higher states into account by correction coefficients (e.g., Nikitin et al. (1986)). Using the

44


Menzel parameters bm the level p opulations n n
m

m

can b e expressed in the form
16 gn

=

gn h3 ne n(Xi+1 ) bm (Te ) eI g+ 2(2mkTe )3/2

m

/k T e

= 2.071 10-

ne n(Xi+1 ) bm (Te ) eI g+ (Te )3/2

m

/k T e

,

(4.4)

where level n, g+ is the statistical weight for the ground state of ion Xi+1 . The coefficients bm , express the deviations of the level p opulation nm of ion Xi from its value at the local thermodynamical equilibrium, and the quantity Im is the ionization p otential for level m. The system of statistical equilibrium equations for atoms and ions of H, He, C, N and O has b een solved by numerous authors, who have taken into account the transition probabilities due to different processes p opulating and dep opulating the levels. Here we shall refer to the results of most complete computations. For hydrogen levels the values of parameters Bn = bn exn = bn exp(In /kTe ) , which are indisp ensable for calculation of E (H ) and the intensity ratios of HI, HeI and HeI I recombination lines have b een computed by Brocklehurst (1971, 1972) for different values of ne and Te with due account of most imp ortant processes. The results we reproduce in our Tables 26 - 28. In these tables there are given also the numerical values of expressions Q = E ()/n(XI +1 )ne and ef f (). The theoretical values of the recombination line intensities of HeI and HeI I for the Menzel B model can b e taken from a pap er by Hummer & Storey (1987). These line intensities have b een computed taking into account the collisions with electrons for wide range of values for ne , Te and for the principal quantum numb er n. The logarithms of total line intensities have b een stored on microfiches in the same journal as the main pap er, where also the effective collision strengths (HeI I) for quantum levels n=1, 2, 3 have b een tabulated. Martin (1988) has calculated the HI recombination sp ectra in the case of extremely low temp erature Te 500 K. Sp ecial interest presents the transitions b etween higlyexcited states of atoms (Rydb erg states) forming the radiolines. Short review of the problem and numerous references have b een presents by Gulaev (1990). Ferland (1980) has approximated the radiation coefficient of the H line (in erg cm3 /s) with an error less than 10% by the expression 4j (H ) = 2.53 · 10- 1.12 · 10-
22 22 - Te - Te 0.833 1.20

,

, for Te 2600 K, . for Te > 2600 K.

(4.5)

In Table 29 are given the relative intensities of recombination lines of some C, N and O ions, computed by Nikitin & Kholtygin (1986), Bogdanovich et al. (1985b) and Nikitin et al. (1994) for Menzel A and B cases at Te =10 000K and Te =20 000K. For many recombination lines the contribution of dielectronic recombination in the total line intensity is imp ortant. Its contribution (Nussbaumer & Storey (1984, 1986, 1987)) at low electron temp eratures has b een presented by a (4.6) di (Te ) = ( + b + ct + dt2 ) t-3/2 exp (-f/t)10-12 cm3 /s . ik t The numerical values of parameters a, b, c, d and f are given in Table 30. The value of total recombination coefficient includes the contribution of b oth the photorecombination and the dielectronic recombination: R = ef f + di . ik ik ik 45


In Table 31 we have compiled the values of aeff ,adi and aR for main sp ectral lines of ions of ik ik ik C, N and O, which have b een taken from the pap er by Nikitin et al. (1994). Many values of ef f for recombination lines of C, N and O ions were calculated in hydrogen-like approximation ik by Pequignot et al. (1991). Most of the given in this pap er values are close to those presented in table 31. The observed intensities of sp ectral lines in nebulae are usually expressed in duly calibrated units of Balmer lines as shown ab ove - usually of H , but sometimes also of H , H or H . The effect of electron collision processes on intensities of recombination lines of H and He has b een discussed by Ferland (1986), Hummer & Storey (1987), Peimb ert & Torres-Peimb ert (1987a,b), Clegg (1987), Giovanardi et al. (1987), Storey & Hummer (1988). The effect of electron collisions for the recombination lines is low. 4.2 Collision-excited lines In the sp ectra of gaseous nebulae a large numb er of forbidden lines of atoms and ions of C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Ar, Ca, K and of some other elements have b een observed. These lines are generated due to transitions from the metastable states of corresp onding ions Xi . The lines of highest intensity among them b elong to the visible sp ectral region. During the last decade a lot of forbidden sp ectral lines in the ultraviolet and infrared sp ectral regions have b een detected. The term structure and the typ es of forbidden transitions for configurations with the external shell p, p2 , p3 , p4 and p5 are shown in Fig. 2.1. Drawn values of wavelenghts are given for ions OI - OI I I. The ground term of configurations p1 and p5 is splitted, the transitions b etween its levels give sp ectral lines observed in the infrared sp ectral region. The transitions b etween two higher terms of configurations p2 , p3 and p4 are named the auroral (A), the transitions b etween the middle and the lowest terms give nebular (N) lines and the transitions b etween the highest and the lowest terms give the transauroral (TA) sp ectral lines. Thus, the transitions D ­P in configurations p2 and p4 give the nebular lines, but to transitions S ­D and S ­P corresp ond the auroral and the transauroral sp ectral lines, resp ectively. In configuration P 3 the nebular lines corresp ond to transitions D­S , the auroral lines to P ­D transitions and the transauroral ones to P ­S transitions. The intercombination lines (I) are forming in dip ole transitions b etween the levels of different multiplicity (s = 0). They are observed mainly in the ultraviolet sp ectral region of nebulae. The list of the sp ectral lines, included the intercombinational ones observed in the ultraviolet, visible and infrared sp ectral regions is given in Table 25. The main mechanism of the formation of the forbidden and intercombinational lines is the collision with protons and electrons. The collisions with the neutral atoms (atoms H et al.) are less effective. In most cases contribution of recombination processes into the intensities of forbidden and intercombinational sp ectral lines of nebulae is negligible. The energy, emitted in a forbidden or intercombinational line in nebulae is expressed by Eq.(4.1). In order to determine the level p opulations nj we must solve the equations of statistical 46


equilibrium nj ne qji +
j =i j>i

nj Aji =
j =i

ni ne qij +
i>j

ni Aij .

(4.7)

where the quantities qij are the coefficients of collisional excitation if i < j and of collisional deactivation if i > j . The quantities qij can b e expressed via the effective collision strengths (see Eq.(3.8)). For finding the level p opulations of atoms and ions we need the large numb er of transition probabilities Aij and effective collision strengths ij (Te ). These values, which are taken basically from compilation (Mendoza (1983)), are given in Tables 16,17 and 25. 4.3 Selective mechanisms of the line excitation Recombination and collisional excitation are the main mechanisms preceding to the line formation in the sp ectra of low-density plasma targets such as the gaseous nebulae and stellar coronae. Besides that there are the selective line excitation mechanisms which are resp onsible for enhancement of intensity of the selective lines in the sp ectra. The most imp ortant selective mechanisms are: photoionization, excitation in the result of Auger ionization, photoexcitation by the continous sp ectrum, excitation by the light emited in the selective lines (Bowen fluorescence), excitation in charge transfer reaction. These excitation mechanisms have b een treated in detail by Rudzikas et al. (1990). First of the mentioned mechanisms leads mainly to the enhancement of the resonance or forbidden and intercombination line intensities in the sp ectra of the gaseous nebulae relative to the intensities determined by electron impacts (see, for example, Ferland (1986)). The photoinization mechanism app ears to b e effective for relatively low electron temp eratures (Te 8 · 103 K). The Auger ionization is accompanied by formation of the auotoionization states. The radiative stabilization of such states results in generation of the excited states of the high-stripp ed ions and of numerous lines due to the cascade transitions from these states. Photoexcitation by the continuous radiation (non-resonant fluorescence) has b een discussed by Nikitin et al. (1990). This kind of excitation can increase the intensity of the weak recombination lines of C, N and O ions (see, e.g. Grandi (1976)). The increase is commonly not high. On the contrary, the Bowen (resonance) fluorescence (often treated as the laser action) enhances significantly the intensity of the selective lines. The most famous example of the Bowen fluorescence is the pumping of the 2p3d 3 P1,2 of OIII by the HeI I L photons (Aller (1984), Harrington et al. (1982), O'Dell et al. (1992), Liu & Danziger (1994)). Florescent excitation of the OI and NeI I lines has b een considered by Sarazin (1986). Charge transfer process also leads to the additional p opulation of the excited levels. An example of such process is the charge transfer OIV + HOIII (2p3d) + H+ . 47


The excited states 1D, 3 P and 1 D of ions OI I I are formed in the result of this process (see, for example, Dalgarno & Sternb erg (1982)). 4.4 Plasma diagnostics for ne and Te In the first approximation the emission p ower of the plasma dep ends on the mean values of electron temp erature T e and on the mean electron numb er density ne . The intensities of the emission lines excited by electron collisions are strongly sensitive to the values of T e and ne . The ratio of the intensities of such lines dep ends on T e and ne : R
ki; mn

=

I (ki ) = R(T e , ne ) . I (mn )

(4.8)

If the upp er levels of transitions k i and m n in Eq.(4.8) have a great energy difference then the ratio R(T e , ne ) dep ends mainly on T e (see, for example, Fig 4.1). So, if ne is approximately known, the mean electron temp erature T e can b e found by using the function R(T e , ne ) and the observed line intensity ratio. On the contrary, for lines with small energy difference of the upp er levels (mostly for the lines of the same multiplet) the ratio of their intensities predominantly dep ends on the value of ne , see Fig.4.2. Lines of such typ e are often used for the mean electron numb er density determinations. Numerous references on the recent calculations of the collision line intensities can b e found in b ook by Rudzikas et al. (1990) and in review by Kholtygin (1990). In general case the line ratios dep end on b oth ne and T e . For determination of b oth the values, not less than two observed line ratios must b e known. The method of line pairs (see, for detail, Aller (1984), Pottash (1984)) can b e used. Different pairs of lines in the sp ectra of a nebula give slightly different values of b oth ne and T e . This difference gives evidence ab out the temp erature and density fluctuations (or clumps) in the nebulae. The method of diagnostics of the temp erature fluctuations following Peimb ert (1967) has b een prop osed by Kholtygin and Feklistova (1992 a,b). Joint study of b oth the temp erature and the electron numb er density fluctuations has b een carried out by Kholtygin (1996). The recombination line intensities do not show significant dep endence neither on ne nor T e and thus they cannot b e used for ne and Te diagnostics. Paschen lines can b e an exception of the rule. The intensities of these lines dep end significantly on the mean electron numb er density (see Table 26). In the presence of the strong external X-ray radiation field the intensity of the collisionlly excited lines can b e strongly distorted by the p ost-Auger ionization and excitation (Aldrovandi & Gruenwald (1985)) and thus they cannot b e used for ne and Te diagnostics. 4.5 Chemical abundance determination The total flux emitted by a nebula in a sp ectral line can b e found if we know the distance

48


to the nebulae. The relative ion abundancies can b e found from observed line intensities by (Xi ) ef f (H ) I () I () n(Xi ) = = X(Te ) . +) ef f () I (H ) n(H (H ) I (H ) (4.8)

This formula follows from (4.1) if we make use of averaged effective recombination coefficients. Using the effective recombination coefficients found by Brocklehurst (1971, 1972) for HeI and HeI I lines we can write the following formula for finding the relative ion numb er densities


I (i HeI) n(HeI I) = (ai + bi t + ci t2 ) · = n(HI I) I (H )

(3.98 + 0.33t - 0.01t2 ) I (4026 HeI )/I(H ), (98.3 - 58.0t - 14.0t2 ) I (4120 HeI )/I(H ), (27.6+ 2.13t - 0.068t2 ) I (4123 HeI )/I(H ), (14.8+ 1.8t - 0.16t2 ) I (4388 HeI )/I(H ), (274 - 153t - 36.7t2 ) I (4437 HeI )/I(H ), (1.73 + 0.37t - 0.06t2 ) I (4471 HeI )/I(H ), (6.36 - 1.54t - 0.23t2 ) I (4921 HeI )/I(H ), (0.493 + 0.305t - 0.059t2 ) I (5876 HeI )/I(H ), (5.64 + 2.13t - 0.35t2 ) I (6678 HeI )/I(H ), (31.3 - 18.0t +4.38t2 ) I (7065 HeI )/I(H ), (148 - 93.4t +23.4t2 ) I (7281 HeI )/I(H ),

and

n(HeIII) = (0.0653 + 0.0238t - 0.052t2 ) I (4686 HeI I )/I (H ), n(HI I)

where t = Te /104 K. The coefficient X(Te ) in Eq.(4.8) for many ion sp ecies can b e expressed by X(Te ) = 0 (t) . (4.9)

The numerical values of the fitting parameters 0 and for the C, N and O ion sp ectral lines are given in Table 32. They were derived based on the effective recombination coefficients, given in Table 31. In monograph by Aller (1984) there are given the expressions, connecting the relative abundances of ions with corresp onding ratios of ultraviolet line intensities: N (Xi ) 0 = Ai E4,2 t N (HI I)
1/2 -d/t

e

I () , I (H )

(4.10)

0 where the coefficient E4,2 for line H has for the Menzel B case the following form 0 E4,2 = eff (H )1025 = 1.387t- 0.983

· 10-

0.0424/t

erg/cm3 s

(4.11)

The needed values of Ai and d are given in Table 33. 4.6 The continuous sp ectrum of nebulae Gaseous nebulae emit the weak continuous sp ectrum, which is observed in ultraviolet, visible, infrared and radio wave regions. The continuous sp ectrum of nebulae has b een caused by the free-free, free-b ound and two-quantum transitions 2s­1s of H, He atoms and of the ion He+ . 49


The computations of the two-quantum transitions have b een first carried out by Kipp er (1950, 1952) and by Spitzer & Greenstein (1951). In the far infrared sp ectral region the main contribution in the total continuum emission is provided by the emission of dust and by the HI free-free transitions. The energy emitted by gas in the unit volume is E d = N (Xi+1 )ne d, where the emission coefficient = (HI) + (2q, HI) + (HeI) N(HeI I I) N(HeI I) + (HeI I) , N(HI I) N(HI I) (4.13) (4.12)

In this expression (Xi ) is the emission coefficient due to free-free and free-b ound electron transitions in HI, HeI or HeI I, the quantity (2q ,HI) is the two-photon emission coefficient of H atoms. The values of these coefficients are given in Table 34. The values of (2q ,HeI) can b e found in the monograph by Pottash (1984). Two-photon transitions from singlet and triplet metastable states of helium-like ions have b een studied in the pap er by Drake et al. (1969), where the corresp onding values of (2q, Xi ) have b een given. Due to relatively low helium abundance in nebulae the processes, however, can b e neglected. Delivery of the catalogue and additional information The electronic copy of the catalogue will b e available by anonymous ftp via ftp-server IP 193.125.206.230 in the directory /usr/home/afk under the name CatAda.tex. The data included into the Catalogue will b e up dated and completed at least twice a year. Any user is invited to contact with A.F. Kholtygin to get additional information or with any other problems via e-mail afk@aispbu.spb.su. We will greatly appreciate your comments and information ab out any recent review pap ers, catalogues or atomic data bases not duly referred in the catalogue.

50