1 Introduction

The results from the Goddard High Resolution Spectrograph (GHRS) onboard the Hubble Space Telescope (HST) supersede the recordings of the International Ultraviolet Explorer (IUE) both in range and resolution, as expected. At the same time, however, this illustrates the increased necessity for accurate atomic parameters for spectrum synthesis and diagnostics.

In this work, we present atomic data on Co II, i.e. calculated log(gf) values of the ultraviolet transitions. Stellar spectra in the ultraviolet region show a wealth of lines from second spectra of transition elements: Fe-group, Pd-group and Pt-group elements occur predominantly in their "singly ionized" stage in the stellar atmospheres (specifically the photospheres) of B- to G-type stars. Moreover, the class of chemically peculiar (CP) stars is known to display enhanced abundances for these heavy elements, in serious deviation from the solar abundance pattern. Being an odd-Z element, cobalt is not as abundant as chromium, iron or nickel; on the other hand, its appearance in specific astrophysical objects like Co-stars and supernovae certainly makes a study worthwhile.

The present work is part of a series of transition probability calculations in the Fe-group transition elements using orthogonal operators (Raassen & Uylings 1997; Uylings & Raassen 1997). Computational details of the method can be found in the above references.

The spectrum of Co II has been recorded using the Imperial College Fourier transform spectrometer (Thorne et al. 1987), which is operational down to 1400 Å. Experimental details and results will be published in another paper (Pickering et al. 1997).

With its appreciable nuclear dipole moment, ⁵⁹Co (similar to ⁵⁵Mn in the Fe-group) displays a sizeable hyperfine structure. To some degree, this has already been studied in Co I (Dembczynski et al. 1993; Dembczynski 1996; Pickering 1996). As it obviously affects abundance determinations (the line profiles will appear "too broad", Biémont 1978), we plan to give A and B hyperfine structure constants in the near future; this work will include both the FTS obtained experimental values as the calculated eigenvector composition.

1.1 Astrophysical applications

Cobalt stars constitute a subgroup of CP stars for which the cobalt abundance justifies the special peculiarity label "Co"; they are mostly Ap-type, sometimes Bp-type. Co-stars often have strong magnetic fields (5 kG or more) which, in combination with the hyperfine structure, makes abundance determination a challenging task (Matthys 1995) in which accurate atomic data like transition probabilities are indispensable. Given the scarcity of large scale hfs measurements, hfs calculations are particularly important in this. Examples of Co-stars are the Bp star HR 1094 (Sadakane 1992), the Ap stars HD 200311 (Adelman 1974) and HD 203932 (Gelbmann et al. 1997) and possibly HD 208217 (Adelman et al. 1993) and HR 4059.

Stellar iron, nickel and cobalt are products of nuclear burning in a supernova event. Strong absorption lines can be found in supernovae of types Ia and II (Jaschek & Jaschek 1995) as a result of explosive nucleosynthesis. The strong Co II emission in late-type SN II may at early epochs be due to radioactive ⁵⁶Co which is, like ²⁶Fe, a beta-decay product of ⁵⁶Ni (Rank et al. 1998); at later times, ⁵⁷Co and the stable isotope ⁵⁹Co become more important. Especially the supernova SN 1987 A has been studied in this respect. Transition probabilities of forbidden lines in the infra-red (like the features at 10.52 $\mu$m, 1.547 $\mu$m and 18.8 $\mu$m) have been calculated (Nussbaumer & Storey 1988) and observed (Jennings et al. 1993), but many M1 and E2 transitions are uncertain though needed (Li et al. 1993).

Absorption resonance lines of Co II are seen in the Interstellar Medium (ISM). The advantage of Co II (compared to Fe II e.g.) is that its lines are weaker which is more apt for ISM studies of abundances and depletions.

Widths of Co II lines have apparently been used to determine the chromospheric turbulent velocity of the supergiant $\alpha$ Orionis (M2 Iab) (Carpenter & Robinson 1997).

1.2 Orthogonal operators

Transition probability calculations of such complex systems as transition metals with their many closely lying energy levels, require highly accurate eigenvectors. A semi-empirical approach, in which parameters of a model Hamiltonian are adjusted to yield eigenvalues as closely as possible to the experimental energies, is an obvious tool for this purpose.

Orthogonal operators (Hansen et al. 1988), have the marked advantage that the parameters are stabilized in the fit. As a result, several smaller (higher order or relativistic) effects can meaningfully be added to raise the accuracy of both eigenvalues and eigenvectors.

First, the angular coefficients of the transition matrix in pure LS coupling are found from straightforward Racah algebra. They are multiplied with the transition integrals (given in Table 1) obtained from a relativistic Hartree-Fock program (MCDF from Parpia et al. 1996) and corrected for core polarization (Hameed 1972; Laughlin 1992). The result of core polarization is a decrease of $5-10\%$ of the absolute values of the transition integrals from Parpia et al.

Second, the pure but unphysical LS transition matrix is transformed into the actual intermediate coupling by the eigenvectors obtained from the orthogonal operator approach. The squared matrix elements of this final transition matrix yield the line strengths and thereby the log(gf) or the A-values.

For details on the method and parameter values, we refer to our overview article on d^N-1p configurations (Uylings & Raassen 1996). Those interested in orthogonal operators are invited to contact the authors or to visit our Internet address ftp://nucleus.phys.uva.nl in the directory pub/orth.

  

Table 1: Values for the electric dipole transition integrals in Co II calculated by means of MCDF including core polarization