The Astrophysical Journal, 576:89-100, 2002 September 1
© 2002. The American Astronomical Society. All rights reserved. Printed in U.S.A.
Light-Element Nucleosynthesis From Jet-Cloud Interactions in Active Galactic Nuclei
M. A. Famiano 1
The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako-shi, Saitama 351-0198 Japan; famiano@postman.riken.go.jp
R. N. Boyd
Department of Physics and Department of Astronomy, Ohio State University, Columbus, OH 43212; boyd@mps.ohio-state.edu
and
T. Kajino
National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan; kajino@nao.ac.jp
Received 2002 March 17; accepted 2002 May 2
ABSTRACT
The production of light nuclei via the interactions of jets from the central engines of active galactic nuclei and the surrounding medium is studied. Several environments ranging from hot, dense knots of gas near the central engine to the cold broad-line region clouds are simulated by a nuclear reaction network that couples the thermonuclear processes in the cloud to the reactions between the jet particles and the cloud. Reaction products from the jet-cloud interactions are followed until they react or are thermalized, which may involve several subsequent reactions. The effects of nucleosynthesis from the introduction of a jet into the cloud can result in enhanced production of light nuclei well above their primordial abundances, and enhancement of CNO nuclei is also predicted above thermally produced abundances. In these scenarios, the jets can enhance abundances of CNO nuclei by first producing excess amounts of nuclei with A < 8, then by increasing the cloud density to the point at which the thermonuclear reaction rates become important. The comparison to observed abundances in quasars leads to the conclusion that the interactions of ejected matter from AGNs may be responsible for large observed abundances of light nuclei in addition to significant abundances of nuclei in the CNO region.
Subject headings: galaxies: active; galaxies: jets; nuclear reactions, nucleosynthesis, abundances; quasars: general1 STA Fellow.
1. INTRODUCTION
Recent observations of absorption lines from clouds along the line of sight from a quasar to the Earth reveal 2H abundance up to an order of magnitude higher than the expected primordial abundance (Burles & Tytler 1998), while other observations are consistent with a lower primordial value (Carswell et al. 1994; Songaila et al. 1994; Rugers & Hogan 1996). This suggests that postprimordial processing may be responsible for the observed high abundance of 2H (Burles, Kirkman, & Tytler 1999), but the issue is not completely resolved (Tosi et al. 1998). Two possibilities include stochastic and anomolous chemical evolution in Lyman limit systems (Jedamzik & Fuller 1997) and photoerosion reactions on light elements in the region surrounding a black hole (Boyd, Ferland, & Schramm 1989). Black holes formed from the collapses of an early generation of massive stars may provide a source of photons that could process the light elements (Gnedin & Ostriker 1992; Gnedin, Ostriker, & Rees 1995), although some difficulties have been shown with this scenario (Balbes et al. 1996).
There is also interest in an overabundance of Li and B in galactic centers as a possible result of interactions between jets from active galactic nuclei (AGNs) and surrounding clouds (Famiano et al. 2001). Photon spallation reactions in the surrounding medium may also provide these high abundances in the light elements, but many of the processes that produce a high deuterium abundance overproduce Li and B by factors of up to 10,000 (Lubowich et al. 2000).
Besides an overabundance of the primordial elements, some observations of the broad-line regions (BLRs) of quasars have indicated abundances of the CNO elements that are nearly solar or supersolar (Shields 1976; Uomoto 1984; Osmer 1980). Closely associated with this are observations of the damped Ly
systems (DLAs), which produce (high column density; N
2 × 1020 cm-2) absorption features in the QSO spectra (Ellison et al. 2001). Observations of these early galactic systems have resulted in an unexplained enrichment of some elements of higher mass, particularly nitrogen (Molaro et al. 2000; Ellison et al. 2001; Centuriòn et al. 1998), which presents a challenge to models of chemical evolution.
Perhaps another source of nucleosynthesis lies in the interaction of quasar outflows (jets and winds) with the surrounding gas. A nuclear reaction network is used, in the present study, in a one-zone model to test this mechanism. The network includes the possibility for reactions between both the (nonthermal) jet and the particles in the medium and for thermonuclear reactions. Environmental parameters can be changed over several orders of magnitude to simulate various regions of the AGN. Particular attention is given to the BLR and extreme regions in the neighborhood of the central engine. For a single AGN, about 105 clouds in the BLR are believed to exist at temperatures of about 104 K with densities around 1011 cm-3 (Peterson 1997), although some may exist at densities as high as 1013 cm-3 (Fromerth & Melia 2001; Marziani et al. 1996). The average cloud size in this region is about 400 R
, corresponding to a mass of about 10-5 M. At a radius of 1
10 pc from the central engine, the total covering factor of the BLR is estimated at around 10%25% (Peterson 1997; Fromerth & Melia 2001; Hook, Schreier, & Miley 2000).
Gas densities closer to the central engine may be as high as 1018 cm-3 (Kuncic, Blackman, & Rees 1996; Baldwin et al. 1995; Ferland & Rees 1988), with temperatures approaching T9 
1 (where T9 is the temperature in units of a billion kelvin; Peterson 1997). These knots may come from the accretion disk (Bednarck & Protheroe 1997b) or the intersection of the outgoing jet with surfaces of nearby stars (Bednarck & Protheroe 1996a). They are assumed to range in size from 1011 to 1014 cm. The mechanism that confines the BLR clouds and the central knots of gas has not been clearly established, although magnetic confinement has been proposed (Emmering, Blandford, & Shlosman 1992; Rees 1987).
Outflow of material from the AGN can take many forms. Calculations have resulted in the production of roughly azimuthally symmetric winds from the accretion disk and central engine. Such winds can launch about 0.5 M yr-1 to a distance of about 0.1 pc (Proga, Stone, & Kallman 2000). These winds can be highly collimated, with nearly 100% of the matter passing through a small angle relative to the galactic plane. Jets of varying geometry can also be formed as a result of the interaction of the accretion disk with a polar magnetic field (Ogilvie & Livio 2001). Observations have shown these jets to be cone-shaped with an opening angle on the order of a degree and a radius of about 0.010.1 pc (Lobanov 1998; Peterson 1997). The jet is forced out of the cloud to distances ranging from 0.1 pc to several kiloparsecs (Gómez et al. 2000). The mass-loss rate carried by these jets is typically 110 M yr-1 (Norman & Scoville 1988; Peterson 1997) but can have extreme values as low as 0.01 M yr-1 or as high as 100 M yr-1 (Falcke 1996). While radio lobes are often associated with outflows with bulk Lorentz factors 
50, these structures are on the megeparsec scale
much larger than the collimated jets thought to exist within the BLR (Urry & Padovani 1995). The smaller scale jets impinging on BLR clouds closer toward the central engine are believed to be closely associated with the accretion process, during which particles can acquire an energy as high as 10% of their rest energy (Contopoulos & Kazanas 1995; Blandford et al. 1990, p. 161), or about 100A MeV (
= 0.4). This is in good agreement with recent estimations of particle velocities of about 0.1c0.4c (Perucho & Martí 2002). For this reason, jet energies in this model are assumed to vary between 50A and 250A MeV (0.3 < < 0.6).
Given the rather extreme range of physical characteristics for the BLR clouds and the central knots of gas, one can imagine several scenarios for jet interactions in the regions surrounding the central engine of an AGN. The temperature is low enough in BLR clouds that thermonuclear reactions proceed very slowly or not at all, while thermonuclear reactions triggered by mass deposition in the dense clumps may have a large effect. Temperatures can also range from the values of the cold BLR clouds to the hot central clumps depending on the formation of the gas knots and their location relative to the central engine. Gas knots ejected from the accretion disk into the corona can cool very quickly to equilibrium temperatures ranging from 104 to 108 K (Williams 2002). It is also possible for knots of gas near the central engine to reach temperatures as high as 109 K (Krolik 1998). Heating mechanisms of these clouds include viscous dissipation, radiative heating by the disk, and heating by the hot corona surrounding the disk (Kurpiewski, Kuraszkiewicz, & Czerny 1997).
The present study focuses on the nuclear reactions and possible concomitant nucleosynthesis that can occur in the jet-cloud interactions and the extreme environments of the jets themselves. In § 2 the parameters of the jet-cloud interaction, and of the jets themselves, are discussed. In § 3 the nucleosynthesis calculations via an extensive nuclear reaction network are presented. The effects of density increases on thermonuclear reactions are also shown. The various models and results of the network calculation are shown in § 4, and these are discussed in § 5.
2. AGN JET INTERACTION MODEL
Since nuclear abundances are the primary concern, the structure of the clouds in the BLR and surrounding the central engine of an AGN was simulated in a single-zone model. Jet material introduced into the cloud was assumed to be well mixed following thermalization. The mass change rate of the cloud
is the product of the mass outflow rate of the jet and the fraction of its cross-sectional area intersecting the cloud. Given the parameters for the jet and cloud size described in the previous section, this value can range from about 10-6 M yr-1 for BLR clouds up to roughly 10 M yr-1 for clumps surrounding the central engine. This value is assumed constant throughout the simulation, and the simulation is allowed to run until the cloud increases in size (volume, density, or both) to several times its original size. The cloud may only spend a fraction of this time in the region of the jet. However, with covering factors described in § 1, the probability that a cloud is interacting with the jet at any time is nonnegligible, so nucleosynthesis may occur at any time.
As mentioned previously, it is not completely clear how clouds surrounding the central engine in an AGN are confined. In the current calculation, as mass is added to the cloud from the jet, three possibilities for cloud size are simulated: constant volume (d
/dt = /V0), constant density (dV/dt = /0), and the case in which both the volume and the density change:
Thus, these three situations span the entire spectrum of possible geometry evolutions of the cloudtwo extreme situations and a midpoint.
The parameters used to describe the cloud are the initial particle number density, the length and diameter (assuming a cylindrical cloud), the cloud temperature, and the initial number fractions of the elements included in the reaction network. The cloud temperature is assumed constant. Most simulations assume a cloud with primordial initial number fractions, but some assumed that the cloud was "seeded" with an initial abundance of heavier nuclei.
The jet-cloud interaction process is characterized by the introduction of material into the cloud at a preset rate. The particles are assumed to be evenly distributed throughout the cloud and initially to have the same energy per nucleon, although the particle energy distribution some time after introduction into the cloud is altered by the energy loss of the jet and the energy distributions of daughter products. The jets were modeled to have primordial abundances of either 1H,2H, 3He, 4He, 6Li, and 7Li or simply 1H and 4He (number fractions for 1H and 4He of 0.93 and 0.07, respectively). Of course, the jet nuclei do not follow a Boltzmann energy distribution, so their reaction rates are treated separately from those of the cloud thermonuclear reactions.
Because jet particles and jet-cloud reaction products do not have thermal energy distributions, it is necessary to follow the evolution of energy distributions of these particles. Number abundances of particles were divided into abundances for specific discrete energies Yi(Ej). The energy bin width Ej+1 - Ej was taken to be a reasonably small number with respect to the initial jet energytypically 5 MeV for a jet with 4He energy of 400 MeV. As jet particles hit the cloud, slow, and produce reaction products, Yi(Ej) will evolve accordingly. This is described in the next section.
The energy loss of jet particles is given by the fast and slow ion formulas of Ginzburg & Syrovatskii (1964). For high-energy jets, it is possible that a portion of the jet will pass through the cloud. For example, a 4He jet of energy 400 MeV has a range of roughly 1011 cm in a medium with an electron density of 1011 cm-3. This corresponds to a small cloud of low density. This situation is discussed in the next section.
3. NUCLEAR REACTION NETWORK
Integration of the reaction network was done via the first-order Euler method (Timmes 1999). That is, for an isotopic species i with abundance Yi, the vector of abundances for each species in the network is given by Y, and the vector corresponding to the time rate of change of each species is denoted by f(Y), which is given by the sum of reactions that create and destroy each species. For a discrete time step h, at a time t, the vector of the abundance change for each species 
=
(t + h) -
(t) is given by
where
is the Jacobian matrix corresponding to the rate equations f(Y):
The time step h is calculated at each time step n to be sufficiently small that the change in abundance is small for each species:
where 
is a value much less than 1. For = 0.01, the time step is never more than 1% of the total elapsed time.
In the process of thermalization, jet particles react with cloud particles, which are assumed to be at rest with respect to the jet particles. The relationship between the reaction product energy distribution and the initial jet energy distribution in a medium with a nonzero stopping power is described in Mukhin (1987). A reaction from a particle in the jet may produce particles that further react, and so on. For simplicity, only particles with A < 8 are treated as energetic projectiles in the network, while heavier reaction products are assumed to thermalize immediately in the cloud; their more rapid energy loss and higher Coulomb barriers validate this assumption. Reactions from daughter products are followed until all the jet particles and their daughters are thermalized, with products of the jet-cloud reactions treated as source terms in equation (2). For a species i in the jet with an initial energy E0, the fraction of particles surviving to energy E (via thermalization), the survival fraction Si(E, E0), is given by the recursive relationship (Mukhin 1987):
where the sum is over all the reactions that destroy the particle i and Nm is the abundance of cloud target particles for the reaction m. The quantity 
i is the stopping power of the incident particle in the medium. In the current calculations, particle energies are discrete and evenly spaced up to the maximum jet energy. The survival fraction must be calculated for all projectiles and all energy values. The products of reactions of jet particles will emerge with energies less than E0, so the survival fractions were normalized to the product energy by dividing the values calculated in equation (5) by the initial fraction at this energy. That is, if a particle has an initial energy E1 < E0, the survival fraction of this particle to an energy E2 < E1 is
where the survival fractions on the right-hand side of the equation are calculated for an initial energy of E0.
The yield for a particle k produced in all reactions between the cloud and particles i (those from the jet and their reaction products) that slow to an energy E1 < E < E2 from an initial energy E0 while accounting for losses due to previous reactions is
Equation (7) can be adapted for discrete energy values by first casting equation (6) into an appropriate form. For a particle i with a discrete energy En-1 < E < En, the form of the survival fraction (eq. [6]) is written as
where the value of E0 is sufficiently high (e.g., the jet energy) so that all survival fractions, i.e., the fraction of particles that slow to E 
Ei before being destroyed, can be calculated. The fraction of particle j that slows to energy Ei-1 < E Ei without reacting, but is destroyed before slowing to E Ei-1, is given by the survival fraction in an individual energy bin i (energy Ei) in the computation
Since the lowest energy bin is E1, then 
Sj1 = Sj(E1,E0) by definition. The destruction fraction 
is defined as the fraction of reacting jet particles with a discrete energy Ek destroyed via a reaction i:
with the abundance of target particles given by Ni. The value of the cross section 
ik for a reaction i and projectile energy Ek is taken to be the average cross section for Ek-1 < E < Ek. The energy distribution tensor 
is defined to be the fraction of products p with an energy Eq from a reaction i in which the projectile has an energy Ek. For a constant i, k, and p, this tensor as a function of q is the energy distribution of the product p and is normalized to unity:
= 1. Equation (7) can then be rewritten for the yield of particles p with discrete energy Eq per incident projectile with an initial energy En in a reaction i between the energetic particles and the cloud:
(In this equation, the superscript "i" serves the dual, but unambiguous, purpose of defining the reaction and its projectile.) The survival fraction factor in this equation defines the fraction of incident projectiles that slow to energy Ek without being destroyed. Equation (11) can also result in a negative value if the cloud particle is a target in the reaction. Reaction products falling into the lowest energy bin (corresponding to = 
) are assumed to have zero energy and do not react further, becoming part of the thermonuclear reaction network. As was mentioned previously, only the light products are treated as secondary projectiles, so that particles with A 8 are automatically assigned = 1.
Using equation (11), the source terms in equation (2) can be calculated. For jet particles incident on the cloud, the production of cloud particles of species i is
The first term represents particles of species i in the jet that thermalize before reacting. The second term represents the products of species i resulting from jet-cloud interactions. These particles either are produced with zero energy (q = 1) or thermalize before reacting (q > 1). The third term corresponds to the products of species i resulting from the secondary reactions between jet-cloud products (the abundances of which are given in the square brackets) and cloud particles (hence, k > 1), and the fourth term corresponds to tertiary reactions from the products of the reactions described in the third term. In equation (12), the survival fraction factors account for the slowing of reaction products. The slowing of incident projectiles is already accounted for in the yield terms (eq. [11]). The sum over j1,k1, 
,jn,kn is meant to indicate all combinations of j and k values in the product. In this manner, a jet of primordial composition incident on a cloud of similar composition can produce source terms for particles with A > 8, two prominent reactions being reactions on 6Li and 7Li. In practice, only the first two terms of equation (12) are used. The nonthermalized products of the initial reactions Njk are summed in the computation, and the second term is recalculated, adding its results to the source term. This is done until a negligible fraction of the initial jet number density remains (
1%). Typically, this iteration needs to be done less than about five times for a jet with an initial 4He energy of 400 MeV and about seven times for an initial energy of 700 MeV.
Equation (12) can be used to simulate scenarios in which the particles can completely penetrate the cloud. If the range of particles with energy Ek is greater than the dimensions of the cloud, then the first term in equation (12) becomes zero. If the reaction products have a range greater than the cloud dimensions, the second term becomes zero. However, it has been assumed that the energy distribution of the products is low enough that a negligible percentage of these particles is expected to penetrate the cloud.
The nuclear reaction network spans 47 nuclei from the neutron to 20Ne. It consists of 261 reactions divided into four groupsthe thermonuclear reactions, the jet-cloud reactions for which the cloud components have A < 8 (the group I reactions), the jet-cloud reactions for which the cloud components have A > 9 (the group II reactions), and weak decays. The reaction network is shown in Figure 1. Many of the 171 thermonuclear reactions used were taken from the NACRE database (Angulo et al. 1999).2 Reaction rates not found in the NACRE database were found in Caughlin & Fowler (1988). Radiative neutron capture rates were taken primarily from the compilations of Bao et al. (2000) and Rauscher & Thielemann (2000). Nine radiative neutron capture rates not listed in these references or involving isomeric states were taken from Wagoner (1969) and Malaney & Fowler (1989). These were radiative captures on 1H, 6Li, 8Li, 7Be, 9Be, 10Be, 10B, 11B, 11C, and 17O. A total of 29 reactions not found on the NACRE database or in Caughlin & Fowler (1988) were taken from other sources listed in Table 1. Updated reaction cross sections for the 45 group II reactions were taken from the National Nuclear Data Center (NNDC) experimental nuclear reaction data file,3 while the 21 group I cross sections were found in the literature (Famiano et al. 2001). The remaining 24 reactions are -decays or delayed particle emissions. Group I and II reactions are listed in Table 2 along with the references for group I reaction cross sections. For many reactions, the cross section data do not exist at higher energies. In many of these cases, however, the cross section either changes very slowly with energy or is insignificant. Thus, the accuracy of the calculation may suffer at higher jet energies, but it is still instructive to attempt calculations by extrapolating to high energies. In such cases, the extrapolation was done by fitting existing data at the highest energies to a 1/E relationship.
 | Fig. 1 Nuclear reaction network used in this jet-cloud interaction model. Arrows connect targets and residual nuclei in each reaction. Not all reactions are shown nor are reverse reactions. |
 | Table 1 Thermonuclear Reaction Rate References |
 | Table 2 Jet-Cloud Reactions |
In order to calculate secondary reaction rates, the energy distributions of products from the primary reactions are necessary. However, these data [(Ep, Er), where Ep(r) corresponds to the projectile (product) energy] are greatly limited. For the group II reactions, the product angular distribution was assumed to be isotropic in the center of mass, and the product energy distributions were determined from kinematics. However, since the group I reactions are more prominent, a higher degree of accuracy is desired, so the angular, hence energy, distributions were calculated based on the distorted wave-Born approximation (DWBA) code DWUCK (P. D. Kunz 1984, unpublished). In such calculations, for a reaction A(a, b)B, the Schrödinger equation is solved for the wave functions that describe the elastic scattering of the incident projectile+target nucleus (entrance channel A + a) and the elastic scattering of the reaction products (exit channel B + b), giving the "distorted waves" 
and , respectively. The optical model potential provides the potential energy terms V that are used in the Schrödinger equation in each channel. A matrix element 
b, B|V|a, A
is then calculated that, in the present case, contains the internal structure of the nuclei a, A, b, and B and contains the operator V that describes particle transfer reaction (which contains the wave function of the transferred particles in the nucleus in which they are bound). The scattering amplitude T is then given as an integral over the scattering wave functions and the matrix element that describe the direct reaction of interest:
The differential cross section is then given by
where Fsp is a spin statistics factor. (For an introduction to DWBA calculations, the reader is referred to Satchler 1990 and Wong 1998.) For p + 4He reactions, optical model parameters input into DWUCK for volume, surface, and spin-orbit potentials were taken from Perey & Perey (1976) and Schwandt et al. (1982) for protons using the general fit presented in Menet et al. (1971), while Perey & Perey (1976) was used for determining the scattering potential of -particles. Perey & Perey (1976) was also used for reactions involving deuterons, with spin-orbit potentials of Lohr & Haeberli (1974). The results closely matched the data of Rogers et al. (1969). The DWUCK output consisted of calculated differential cross sections d/d
in 1° steps in the center-of-mass frame for several projectile energies. These were then converted into lab frame cross sections as a function of energy (Er) based on the reaction kinematics. Since data for the total cross sections exist (Table 2), it was possible to normalize the differential cross section output from DWUCK to the exact values taken from the literature, reducing the dependence on DWUCK so that it was used only to find the product energy distributions. The final result was then a distribution as a function of product energy and projectile energy for each reaction.
Little information exists for the three-body final state reactions, although one study (Brinkmöller et al. 1990) indicates that the three-body final states tend to smear out the structure seen in the angular distributions of the two-body final state reactions. Some peaking toward forward angles, hence higher laboratory energies, is suggested by the one existing data set. Thus, we assumed two possibilities as extreme cases: (1) one in which the distributions of the reaction products were constant with energy and (2) one in which the distributions were enhanced by a factor of 2 for the particles in the top quarter of the energy distributions. This change produced effects in our results only at the 1% level. However, this procedure did allow a test of the sensitivity of the results to the shape of these poorly known cross sections. The magnitudes of the cross sections for the three-body final states are unknown. Thus, we assumed that they scaled with energy as does the 1H(4He,3He)d cross section; their ratio was then fixed at the one energy at which the three-body final state reaction, 1H(4He, np)3He, was studied (Brinkmöller et al. 1990).
For each time step, the vector f(Y) was calculated along with the Jacobian matrix . The solution vector was calculated using the numerical routine LAPACK (Anderson et al. 1999).4 This network is numerically tractable in that the simulation of environments covering a wide range of particle number densities (n 
1011 up to n > 1025), temperatures (0 < T9 < 5), and mass input rates (0 M < < 100 M) is possible. Therefore, the network could be tested against others in simulations for which it was not originally intended. For example, results of a network calculation for the warm CNO cycle were found to agree with those of Wiescher & Kettner (1982).
2 The NACRE on-line database is available at http://pntpm.ulb.ac.be/Nacre/nacre.htm.
3 The NNDC on-line database is available at http://www.nndc.bnl.gov.
4 LAPACK, Version, 3.0, is available at http://www.cs.colorado.edu/~lapack.
4. RESULTS
Several models were examined to evaluate the effects of jet interactions in BLR clouds and the dense gas knots described in § 1. However, only three representative models, the parameters for which are given in Table 3, are discussed in detail. These were chosen to reflect environments thought to be typical of BLR clouds and the higher density regions near the central engine. Both the effects of different densities and temperatures and of the dynamics of the mass increase have been examined. In the table,
is listed as 0, constant, or a function of t [(t)], which increases according to equation (1). In other models the cloud is "seeded" with an initial abundance of CNO elements. In another set of models, the jet is stopped after a set time, while nucleosynthesis is allowed to continue, which would simulate a cloud being ejected from the jet region after some interaction.
 | Table 3 Models Used in the Nucleosynthesis Calculations |
The results of models A and B are shown in Figures 2 and 3, respectively, in which abundances are plotted with respect to the hydrogen abundance. Thus, although the abundance relative to H decreases, because of input from the jet, the total number abundance does not. For 2H, the decrease seems especially dramatic, suggesting that it is also being destroyed. While the calculations were run for a sufficiently long time to produce a large change in cloud density, the actual overlap of the cloud with the jet, the rate of mass transfer, and the time spent in the jet might be quite different for a realistic cloud. Nonetheless, it may be possible for some clouds to increase in mass many times their original size.
 | Fig. 2 Abundance evolution for model A, simulating a hot (T9 = 0.6) central clump of matter with an initial primordial abundance near the central engine of the AGN. The top axis shows the fractional mass change in the cloud, while the lower axis is the time. |
 | Fig. 3 Abundance evolution for model B, simulating a lower density (n0 = 1011 cm-3), cold (T = 104 K) BLR cloud with an initial primordial abundance. The top axis shows the fractional mass change in the cloud, while the lower axis is the time. |
Model A is a calculation for the dense central knots of gas. In this model, a distinct gap exists between nuclei with A < 8 and A > 8, primarily because the thermonuclear reactions produce CNO nuclides only when the density has risen to sufficiently high values (at large t). The lighter nuclei, produced by jet-cloud interactions, are destroyed by the thermonuclear reactions as the density becomes high; this is seen most dramatically for 6Li, which declines rapidly from its initial primordial value because of the 6Li(p, )3He reaction.
The effect of thermonuclear reactions on the dense clumps can be determined using model C, which simulates nucleosynthesis in a dense knot of gas in the absence of the jet. In this model, the results of which are shown in Figure 4, 6Li destruction continues even without the jet, confirming that thermonuclear reactions and not jet reactions are responsible for its destruction. The CNO elements are produced, although their abundances seem to be 24 orders of magnitude lower than in model B because of the density increase from the jet.
 | Fig. 4 Abundance evolution for model C. The initial conditions are identical to model A, except that no jet interacts with the cloud. The top axis shows the fractional mass change in the cloud, while the lower axis is the time. |
It was found that in both models A and B, the D/H reaches a peak of nearly 10-3. As expected, this peak occurs at later times for a lower mass input rate but at roughly the same mass change in the cloud (
M/M0 
0.8) occurring at a slightly later time (mass increase) for = 1 M yr-1. In either case, the evolution of the low-mass elements is similar. Also, the production of the CNO elements is appreciable at late times in both models. From an initial abundance of zero, 10B/H reaches a value of 10-10 in model A because of the 7Li(, n)10B reaction, when the cloud density has increased by 8. Similarly, the production of 11B is relatively strong in this model. At later times, the 10B abundance drops because of thermonuclear processing via the 10B(p, )7Be reaction.
Model B is a simulation for the low-density, low-temperature BLR clouds, corresponding to a 10-6 M object. Here the temperature is low enough that thermonuclear reactions are negligible. In fact, the evolution as a function of the cloud mass (density) varies little with changes in the other parameters (although an increase in mass input rate results in an increase in production rates, as expected). The results of model B are shown in Figure 3. Most apparent is the complete absence of the CNO elements. However, the presence of the small initial abundance of 7Li enables the production of 10B due to reactions with -particles in the jet. The production of A = 3 and A = 7 nuclei via the reactions of subsequent jet-cloud products is also significant, with the possibility that 2H/H can reach values as high as 10-2 for very large amounts of mass added to the cloud. These results are consistent with a previous study on light-element AGN nucleosynthesis (Famiano et al. 2001), with the additional reactions of the present study also producing 10B. It was found that little or no thermal nucleosynthesis takes place at T < 107 K, as would be expected. For higher temperatures, as in model C, it was found that the thermonuclear reactions are responsible for a small amount of CNO production and the destruction of the light elements with A < 8. However, the presence of the jet enhances the production of all elements. It was also found that the effect of the jet in hot clumps is to enhance the production of the boron and CNO elements by as much as 4 orders of magnitude over several thousand seconds while adding mass to the cloudincreasing the density by a factor of about 4via the thermalized jet products.
The abundances as a function of cloud temperature were also studied at various stages in the cloud evolution and are shown in Figure 5. Plots are shown for when the cloud mass has increased by 12%, 120%, and 1200%. The 2H abundance drops to subprimordial abundances via thermonuclear reactions early in the evolution at temperatures T9 > 0.7 as well as for longer times. The abundances of A = 7 nuclei are similarly sensitive, while A = 3 nuclei seem to be enhanced at higher temperatures. The abundances of the heaviest nuclei are enhanced at higher temperatures due to increased thermonuclear reactions at high density. These abundances reach a peak at late times when T9 0.7 and 1.40. Results of one (constant-volume) model calculation, in which the jet was run for 105 s, then was shut off but the thermonuclear reactions proceeded for 109 s, produced somewhat more CNO nuclides. Another calculation, in which both the jets and the thermonuclear processing continued for 109 s, produced a huge abundance of CNO nuclides. However, the density in this calculation became so high that carbon and oxygen were being produced by helium burning. Since it is far from obvious that such an environment could be produced in any interactions between jets and their surrounding environment, we mention this result only for completeness.
 | Fig. 5 Abundances of light elements at various times as a function of cloud temperature. In this figure, the cloud temperature in model A is varied. Each plot is indicated by the percent increase in the initial cloud mass. |
In the calculations discussed above, the dependence on jet energy was found to be minimal. Abundance evolutions as a function of the jet energy are shown in Figure 6. It must be kept in mind that the reaction cross sections in this network are less accurate at higher jet energies because of a lack of data. However, at lower energies, the abundances seem to vary little as a function of jet energy. As expected, the abundances are lower at the lowest jet energies because the reaction product energies are closer to thresholds for subsequent reactions.
 | Fig. 6 Abundances of light elements at various times as a function of cloud temperature. In this figure, the jet energy in model A is varied. Each plot is indicated by the percent increase in the initial cloud mass. |
From this study, one may conclude that jet-cloud interactions and thermonuclear reactions operate essentially independently of each other, except that the jets can result in a sufficiently large mass deposition to increase the density enough for thermonuclear reactions to proceed rapidly (they proceed as the square of the density). The jets could serve another function as well: they could impart sufficient momentum to the "cloud" with which they interact to allow it to move through other clouds and/or gas, sweeping up additional matter, thereby further increasing the density of the environment on which the jets impinge. In our simulations, the jet interactions produce light elements, while production of heavier nuclides results from thermonuclear reactions. Thus, the jet interactions in BLR clouds would only produce the lighter elements in nonnegligible abundances, while the hot, dense central clumps would produce abundances of nuclei in the CNO region via thermonuclear reactions. The dominance of nonthermal (jet-cloud) reactions or thermonuclear reactions in producing or destroying a particular species is examined by comparing the rates for jet reactions to the total rates, fJ(Y ) and ftot(Y ). These are shown for several representative nuclei in model A in Figure 7. If the jet reaction rate is equal (or nearly equal) to the total rate, then the rate of production (or destruction) is dominated by jet reactions. If the total rate is equal to zero for a nonzero jet reaction rate, then the thermonuclear reaction rates cancel the jet reaction rates. Rates less than zero indicate that destruction via thermonuclear reactions exceeds creation by the jet. An interesting feature of this diagram is the local peak in total production of 2H at around 10 s. At short times, the neutrons produced in the jet-cloud interactions decay to protons before they can be captured in the lower density environment. As the density increases, the 2H is destroyed by thermonuclear reactions, as is also seen to be the case for 3He. As the density increases further, the neutron captures on protons produce the secondary peak seen for 2H, which then subsides as the thermonuclear proton captures again dominate at still higher density. This was tested by removing neutron capture reactions, resulting in the disappearance of the peak. It is also seen that production of the higher mass nuclei is due almost solely to thermonuclear reactions. The production of 10B is initially due to jet-cloud interactions but, as time proceeds and the density increases, its production eventually becomes dominated by thermonuclear reactions.
 | Fig. 7 Comparison of reaction rates from jet interactions only fJ to total reaction rates ftot. The scales on the left correspond to the entire row of plots. In general, synthesis of elements in the CNO region is dominated by thermonuclear reactions, while light-element nucleosynthesis reaches an equilibrium between jet-cloud reactions and thermonuclear reactions. |
5. DISCUSSION
The present study extends a previous work, in which the enhanced production of primordial elements was examined (Famiano et al. 2001), to nuclides of higher mass. Some line-of-sight quasar observations have indicated enhanced metallicity, with results showing CNO abundances up to a few orders of magnitude higher than solar values (Shields 1976; Molaro et al. 2000). High metal abundances have also been observed for elements in the Si and Fe group (Molaro et al. 2000). Thus, it was thought to be worthwhile to extend this sort of calculation into those regions of the isotopic chart. In the present study, however, the resulting abundances are about 23 orders of magnitude below solar values after a plausible density growth of the region of exposure to the jet, and they only achieve high CNO abundances in situations in which huge density growth is achieved.
The range of parameters studied in this model is comparable to those mentioned in § 1. Thus, various stages of nucleosynthesis can be present in jet-cloud interactions. The dependence of the nucleosynthesis on the cloud temperature and density explored herein can be applied to what is known about the surrounding regions of AGNs. In particular, the astrophysical sites corresponding to the parameters in this paper can range from the hot, dense knots of gas surrounding the central engine to the cold, low-density BLR clouds.
The interactions of jets with hot dense matter surrounding the AGN central engine, followed by the ejection of this matter into the IGM, can enhance the metallicity of the systems involved, and the momentum gained from the jet would be a possible mode of cloud ejection. However, in order to produce masses similar to those of the DLAs, either several clouds must be ejected into a localized region of space (i.e., within the jet diameter) or the cloud must collect matter from the jet for a long time.
It is also interesting to note that the most robust light-element (A < 11) production is due to jet interactions in the low-mass, low-temperature BLR clouds, while the higher metallicity production comes from the hot, high-density central clumps of gas via thermonuclear reactions. This indicates that a spectrum of environments ranging from the central engine of a quasar to the BLR could produce a variety of nucleosynthesis outcomes. Furthermore, they would be distinct since the production of the CNO elements was found to be concurrent with the destruction of the light elements in these models.
The single-zone model used here should provide a good representation of the jet-cloud nucleosynthesis scenario, but further improvements can be made. These would incorporate the dynamics of a jet impinging on a cloud of comparable size. Diffusion processes may alter the nucleosynthesis by creating localized high-density regions resulting in temporary accelerated nucleosynthesis as well as processes near the surface of the cloud, which eject jet particles other than penetration of the cloud by the jet. Most important is an understanding of the confinement mechanism of the cloud since it was shown that the abundance evolution of the cloud depends heavily on how the cloud is confined.
This work was supported in part by NSF grants INT 0101488 and PHY 9901241 and by the Science and Technology Agency (STA) of Japan Fellowship program. The authors wish to thank P. Osmer for useful discussions on AGN cloud dynamics.
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