## RESEARCH STATEMENT

My research interests are in theoretical spectroscopy for astrophysical modeling and observations. During the past two decades astronomy has acquired unprecedented theoretical capability for sophisticated and large-scale calculations of fundamental parameters, to successfully complement the immense investment made in observational capabilities of large ground based telescopes and space based observatories aimed at high-resolution spectroscopy.

My work involves development of basic theory and computations on atomic parameters for diagnostics and modeling of astrophysical plasmas. My particular areas of expertise are: dominant radiative processes in astrophysical objects such as stars, AGN, stellar atmospheres, planetary nebulae etc. Typical results from large-scale ab initio quantum mechanical calculations have been applied mainly to astrophysical problems. They have also been utilized to benchmark highly accurate measurements carried out at several laboratories in the US and Europe.

Some of the highlights and major accomplishments are mentioned, followed by a more detailed exposition.

{\bf Highlights}

$\bullet$ {\it Theory of Photoionization and Recombination in Astrophysics:}

I have developed a new method for self-consistent unified treatment of {\it total} recombination and photoionization in astrophysical sources, such as nebulae, active galactic nuclei, stars, and supernovae. For the first time, this general method enables large-scale ab initio quantum mechanical calculations using for all atomic species of interest in astronomy. I am reporting this work in a continuing series of papers in the {\it Astrophysical Journal Supplement Series}, with myself as the sole or the first author in all 13 papers thus far, resulting a total of 28 papers on the subject. The unified recombination rates are in use for applications, such as for determination of velocities, velocity widths, column densities for ions in interstellar clouds by E.L. Fitzpatrick and L. Spitzer (1996)

$\bullet$ {\it X-Ray Astronomy:}

My work has been instrumental in the discovery and analysis of oxygen K$_{\alpha}$ resonance lines in the {\it Chandra} and {\it XMM-Newton} spectra, as signatures of black hole activity in AGN and the missing 'warm/hot' baryonic matter in the Universe. I gave an invited talk on the new radiative atomic data available currently at the day and a half Joint Discussion (JD) session on "ATOMIC DATA FOR X-RAY ASTRONOMY" of the General Assembly of International Astronomical Union (IAU) in Sydney, Australia in 2003.

$\bullet$ {\it Active Galactic Nuclei:}

In order to solve the long-standing "Fe II problem" in AGN spectra, the Iron data that I computed have recently been used to compute theoretical iron emission line strengths for physical conditions typical of AGN with Broad Line Regions. Sigut, Pradhan, and I (ApJ, 2004) have published theoretical line strengths, from heretofore the most extensive non-LTE model involving nearly 1000 levels, that satisfactorily reproduce the empirical UV Fe~III emission line template of Vestergaard \& Wilkes (2001) for the prototypical narrow-line Seyfert 1 galaxy I~Zw~1, both in terms of the Fe~III flux distribution and the relative strength of the Fe~III and Fe~II emission.

$\bullet$ {\it H~II Regions and Stellar Atmospheres:}

In recent years my work has provided the basic physical parameters for the new generation of powerful computational codes in (i) spectral analysis of H~II regions in general, and (ii) numerical simulations of stellar atmospheres (e.g. for O-type stars by Lanz and Hubeny 2003. These contributions were particularly highlighted at some recent invited conference talks, one in 2001 at the "IAU Symposium on PLANETARY NEBULAE" at Stromlo Observatory in Australia, and the other in 2002 at the "Workshop on STELLAR ATMOSPHERES" in Tuebingen, Germany.

In their recent book {\it Astrophysics of the Diffuse Universe}, M.A. Dopita and R.S. Sutherland (2003) remark: "The calculations of Nahar and Pradhan (1997) represent the first such fully self-consistent computations using the R-matrix method developed for the Opacity Project and the Iron Project, and extended by Nahar and Pradhan (1994) .... When such calculations become available for more ions, then theoretical models of the ionization state of the interstellar medium will ....include them in tabular form for each ion of each element."

$\bullet$ {\it Laboratory Astrophysics:}

Based on the features I predicted in photoionization cross sections of astrophysically important ions such as C~II, O~II, O~III, O~IV, O~V and Fe~II, Fe~IV, experimentalists, using accelerator based light sources, were able to benchmark absolute measurements state-of-the-art theory for the first time. I have collaborated for theoretical calculations with all three groups, ALS (Berkely)-Nevada in the US, Synchrotron radiation source in France, and Synchrotron with a new modulator in Denmark, engaged in these measurements.

$\bullet$ {\it The Iron Project:}

Employing the state-of-the-art theoretical and computational method, known as the R-matrix method, I have developed a number of large codes for the calculation of atomic data in astronomy, especially in theoretical spectroscopy for idenitifying large number of levels, primarily for the iron-peak elements. I have been the leading contributor of the radiative atomic processes to the Iron Project (IP) series which has published over 50 papers in {\it Astronomy and Astrophysics} by approximately 20 researchers from six countries (mainly UK and US). In an application of the data recently, Hartigan, Morse, Tumlinson, Raymond, Heathcote (1999) uncovered a number of Fe~II weak lines in the UV spectra of HH 47A from HST and found no significant depletion of Fe using the results of my work on Fe~II transitions (1995).

Being the prime researcher on these above projects, I carried out study in collaboration with Anil Pradhan and others. A more detailed description, including collaborative efforts directed at varied astrophysical applications, is as follows.

{\bf I. PHOTOIONIZATION AND ELECTRON-ION RECOMBINATION}

Accurate determination of ionization fraction or abundances in photoionized plasmas, such as in emission nebulae, requires self-consistent set of parameters for the inverse processes of photoionization and electron-ion recombination. Uncertainties and errors may be introduced in use of the parameters obtained using different approximations valid for different temperature ranges. Our new unified method of self-consistent treatment of both processes implements same wavefunction expansion in an ab initio manner using the close coupling (CC) approximation.

{\it \bf i) Photoionization:}

{\it The Opacity Project (OP)}, an international collaboration of about 25 researchers, was initiated in 1981 in response to a plea for accurate atomic data to calculate stellar opacities which would be able to solve several longstanding astrophysical problems, especially for pulsating stars. Twelve years of work under the OP resulted in a huge amount of radiative data for energy levels, photoionization cross sections, and oscillator strengths for all astrophysically abundant atoms and ions, from hydrogen to iron. These data are available at NASA-Goddard and at CDS in France through a database, called TOPbase.

As a member of the OP collaboration, I carried out some of the most extensive {\it ab initio} atomic calculations in the CC approximation. In particular, the most elaborate of the OP calculations has been for singly ionized iron, Fe II, using 83 LS terms in the eigenfunction expansion. This has been the largest atomic calculation carried out to date, involving about 500 CPU hours on the Cray Y-MP. I have published the most of the up-to-date photoionization cross sections many atoms and ions including C, N, O throgh all ionization stages, Si, S, Fe ions etc.

One of the main aims is to benchmark the state-of-the-art theoretical methods that we have developed against the sophistated experiments that have become possible only in the past 5 years or so using accelerator based photon sources. To that end, I have been collaborating with all three existing experimental groups in the world. The principal collaborators are: Prof. Ron Phaneuf of the University of Nevada using the Advanced Light Source at Berkeley, Dr. Henrik Kjeldsen of University of Aarhus, Denmark, and Dr. Francois Wuilleumier at University of Paris-Sud, France. The comparison provides a stringent accuracy check for large-scale applications of photoionization cross sections, such from the Opacity Project.

\noindent {\it \bf ii) Electron-Ion Recombination:}

Electron-ion recombination is commom to all ionized astrophysical systems, at a wide range of density, temperature, and mode of ionization (photoionization or collisional). Calculation of the total recombination rates becomes complex since recombination may proceed either through radiative (non-resonant) or dielectronic (resonant) recombinations. {\it The two ways are, however, inseparable in nature}, although one may dominate the other at different temperatures or energies. Existing methods deal with radiative recombinaton (RR) and dielectronic recombination (DR) separately, and employ approximations that are valid for different temperature regions; the total recombination rates are then obtained from summing the individual RR and DR rates. This can result in over- or under-estimation, especially at temperatures where both the RR and DR may dominate. In photoionized plasmas ionic states exist at lower temperatures than in collisional plasmas. Therefore, in photoionized H~II regions and AGN, our unified scheme is particularly useful and accurate.

We first reported the computationally unified method in a {\it Physical Review Letter} (Nahar and Pradhan, 1992). The method yields the {\it total} electron-ion recombination cross section, and rate coefficient, incorporating both the RR and DR processes in an ab initio close coupling approxmiation, valid over the entire range of temperatures in astrophysical and laboratory plasmas [Phys. Rev. Lett 1992, Phys. Rev. A 1994, ApJ 1995]. The method also provides the level specific electron-ion recombination rate coefficients of hundreds of excited levels, not obtained from existing methods. Since both the photoionization and recombinatoin calculations employ the same eigenfunction expansion, we obtain self-consistent sets of data for both (inverse) processes, and thereby more accurate ionization fractions of elements.

Thus far I have carried out and reported these extensive calculations for over 50 ions in the second and third row of elements [e.g. ApJ. Suppl 1996]. These include ions along isonuclear sequences of astrophysical importance, e.g., carbon, nitrogen (ApJS 1997), oxygen ions (ApJS, 1999), Si-like ions, carbon like ions, etc.

Possibly the most useful application of the unified treatment has been for heavy and complex ions with strong electronic coupling, and hundreds of resulting channels, such as the Fe ions. Work is complete or in progress for Fe I (ApJ 1997), Fe II (Phys Rev A 1997), Fe III (Phys Rev A 1996), Fe IV (Phys Rev A 1998), Fe V (ApJS 1999), Fe XIII (ApJS 2000), Fe XVII (2001), Fe XX, Fe XXI, Fe XXIV, Fe XXV, F XXVI (2001), and Ni II (ApJS 2001). I should like to note that often the calculations for a complex ion, such as the Fe ions, take up to one or two years to complete.

The accuracy of the unified method has been benchmarked with high resolution experiments on ion storage rings: the Test Storage Ring at Heidelberg, Germany, and CRYRING at Stockholm, Sweden (e.g. J. Phys.B 1999, ApJL 2001).

{\it \bf II. X-RAY ASTRONOMY}

Atomic spectroscopy is the foundation of X-ray astronomy. My recent work includes calculations of atomic parameters for X-ray spectral analysis, as described below.

The emission and absorption lines in a spectra correspond mainly to the radiative bound-bound transitions. However, absorption of a photon at a resonance energy during photoionization can also appear as absorption 'lines', as was predicted for the X-ray KLL photoabsorption in O~VI (Pradhan 2000), and subsequently observed by {\it Chandra} (Lee \etal 2001). In addition, and earlier than the Pradhan's calculation, I had calculated the photoionization cross sections on oxygen ions, including the K-edges, that were used to analyze the 'warm absorber' spectra of the AGN MCG6--30-15 to resolve an outstanding problem of relativistic broadening vs. atomic features in a hot, ionized gas. Later, I also carried out K-shell X-ray photoabsorption calculations in C IV, O VI, and Fe XXIV (PRA Rapid Commun., 2001). These data have recently been used to analyze the \chan and \xmm observations of photoionised gas in AGN (e.g. Bianchi \etal 2004, astro-ph/0411603).

I reported the oscillator strengths for a large number of fine structure transitions, going up to very high n = 10 levels, for Li-like ions from carbon to nickel, C~IV, N~V, O~VI, F~VII, Ne~VIII, Na~IX, Mg~X, Al~XI, Si~XII, S~XIV, Ar~XVI, Ca~XVIII. Ti~XX, Cr~XXII, Fe XXIV, Fe XXV, Ni~XXVI. Work is in progress for He-like ions. Results have been used to simulate time-dependent X-ray spectra of He-like ions to study transient plasmas such as in flares in accretion discs, stellar coronae, comets (Dalgarno 2003).

We have investigated the L-shell photoionization and recombination of Ne-like Fe XVII (APJL 2001, Phys Rev A, 2001). This ion is a prime constituent in the high temperature astrophysical plasmas and emits strong X-rays. We benchmarked the unified recombination method by comparing the calculated DR spectra, with excellent and detailed agreement with the measured DR spectra (ApJL 2001). Work is in progress for Fe XVII with a much larger wavefunction expansion. The work should provide definitive results for this ion.

The R-matrix method has been extended under the Iron Project to include relativistic effects in the Breit-Pauli (BPRM) approximation which have been implemented for the total unified electorn-ion recombination. This enables calculations of recombination rates of fine structure levels of atoms and ions needed for modeling of X-ray lines, such as the diagnostics {\it w, x, y, z} lines of He-like ions. I have calculated such rates for ions like C IV and C V (ApJS 2000), O VI and O VII, Fe XXIV and Fe XXV, Ni XXVI and Ni XXVII. and continuing on similar ions. The complete theoretical recombination spectra of Li-like ions include the DR satellite lines alongwith radiative, dielectronic recombinations. The spectra of most of these highly charged He- and Li-like ions are in the UV and X-ray region as have been observed by {\it Chandra}, {\it XMM-Newton}. My results for photoionization and recombination for these ions are being used in various X-ray astrophyscial models.

{\it \bf IV. THE IRON PROJECT}

Numerical simulations of synthetic spectra require extensive sets of collisional and radiative data. The Opacity Project data did not consider collisional processes, mainly electron impact excitation. Furthermore, relativistic fine structure was not included since the opacities calculations would have been prohibitive in computational terms, and in any case not needed for mean Rosseland or Planck opacities. Following the OP, another international collaboration for the Iron Project (IP) was initiated in 1991 with the aim of calculating collision strengths and radiative data, mainly for the iron group elements. The IP extended the theoretical consideration by including the relativistic effects in Breit-Pauli approximation, and thus extended the computations considerably.

My work under the IP has focused mainly on the oscillator strengths, line strengths and transition probabilities for fine structure transitions using the relativistic BPRM method. The advantage of the BPRM approximation is that (i) both the dipole-allowed and intercombination transitions are considered, and (ii) results for a large number of transitions, as needed in astrophysical models, can be obtained with consistent accuracy (other methods of comparable accuracy such as the relativistic multi-configuraion Hartree-Fock method are applicable to a relatively few transitions).

One of the major problems in the theoretical calculations that I solved was to develop a procedure for spectroscopic identification of the large number of energy levels. Only a small fraction of these levels is available from the NIST (National Institute for Standards and Technology) compilation. I have written a new code, based on the quantum defect analysis, channel contributions, and LS to fine structure level correspondence (Phys. Scr. 2000) to identify these levels. The method was first applied on a large-scale to the very complex spectra of Fe V involving the identification of thousands of levels, resulting in about 1.5 million transition probabilities.

I also carried out the first large-scale BPRM calculations for fine structure transition probabilities for Fe XXIV and Fe XXVI (A\&AS 1999). The total number of transitions exceeded considerably all previous data, and agreed very well (less than 1\% to a few percent) with the measured values and other equally elaborate (but far less numerous) calculations.

In total, I have worked on transition probabilities for Fe II, Fe III, Fe IV, Fe V, Fe XIII, Fe XVII, Fe XVIII, Fe XX, Fe XXI, Fe XXIII, Fe XXIV, and Fe XXV alongwith many other atoms and ions, such as, C~II, C~III, O~I, O~II, O~III, O~IV, O~V, O~VI, F~IV, F~VII, Ne~IV, Ne~V, Ne~VIII, Na~VI, Na~IX, Mg~VII. Mg~X, Al~VIII, Al~XI, Si~I, Si~II, Si~XII, S~II, S~III, S~XIV, Ar~V, Ar~XIII, Ar~XVI, Ca~VII, Ca~XV, Ca~XVIII. Ca~XIX, Ti~XX, Ti~XXI, Cr~XXII, Cr~XXIII, Ni~XXVI, Ni~XXVIII.

{\it \bf V. ATOMIC DATABASES: TOPBASE AND TIPTOPBASE and OPSERVER}

With a few other members of the OP/IP group, I am involved in the continuing development of a comprehensive electronic database, TIPTOPbase, for collisional and radiative data for nearly all astrophysically abundant elements. TIPTOPbase is being installed at the Ohio Supercomputer Center (OSC) and at Center de Donnees Astronomiques de Strasbourg (CDS) in France. By far the largest part of the new data, particularly for the important iron ions, will be from Ohio State group.

In addition, the new stellar opacities from the Opacity Project, recently computed by M.J. Seaton and collaborators, will be available from an on-line database called OPSERVER at the OSC and CDS -- the two nodes, one in the US and the other in Europe, for worldwide dissemination of these datasets.

\centerline{\bf RESEARCH PLAN}

$\bullet$ {\it Astrophysical Spectroscopy:} The OSU Atomic Astrophysics group has been the world leader in bringing about the paradigm change towards high-precision astronomy. The availability of large-scale atomic data is one of the twin drivers for this far-reaching change. The other, of course, is the huge investment in high-resolution instruments on the next generation of large telescopes and space missions. The calculations that I have described in the Research Statement are the underpinnings of astrophysical spectroscopy, and form the basis for the end result --- a precise understanding of astrophysical systems and phenomena. It is noteworhy that the period of transition of to high-precision/high-resolution astronomy in the past two decades, largely coincides with the formation of the OSU group, which I joined 16 years ago.

Therefore, the next logical step in my research is to interface directly with observations and analysis of astrophsical spectra. With particular reference to the OSU department of astronomy, this could entail joint collaborative efforts with the observers in the department (nearly all of whom are spectroscopists!) on the one hand, and spectral modeling researchers on the othe hand. In particular, and aimed at utilizing the great departmental asset, the Large Binocular Telescope, I envisage such programs on the observation and analysis of O/IR Iron spectra of H~II regions and AGN, involving Rick Pogge, Darren Depoy, Kris Sellgren, Anil Pradhan, and others.

The OSU group has also made substative contributions to X-ray astrophysics --- an area of space astronomy likely to remain active for decades to come with the advent of Astro-2E and Constellation-X, after Chandra and XMM. I believe that together with Anil Pradhan and others in Astronomy we can establish an unparalleled X-ray astronomy program at OSU, again spanning the entire range from observations to analysis to basic theory.

$\bullet$ {\it High-Performance Computing:} The OSU Atomic Astrophysics group is one of the largest users of the Ohio Supercomputer Center in the state of Ohio. In the past 15 years, we have utilized roughly 25,000 hours of Cray-equivalent CPU time. This represents a tremendous investment in our program of about \$20M. As the person in charge of most of the high-performance computing, I have been the prime beneficiary of this investment. Indeed, this has been one of the major reasons for my choosing to stay at OSU (just as proximity to, and availability of, large telescope time might be attractive to many observers). The OSC has now expanded (and is expanding) considerably into new areas, with the latest computing platforms, such as the recently acquired Cray X1 and Cray XD, and a number of massively parallel platforms such a Itanium-64, IBM-SP2, etc. One of my tasks in future will be to coordinate the trials of the next generation of R-matrix codes to be developed partly in our group and in collaboration with the larger Iron Project collaboration.$\bullet${\it Nanoscience and Nanospectroscopy:} After a university-wide competition under the {\it Large Interdisciplinary Grant Program}, instituted by the Office of Research, we were recently awarded a grant for {\it Computational Nanoscience on Fundamental Atomic and Molecular Scales} (PI: Anil Pradhan, total amount with matching from CMPS and Astronomy, is \$235 K for 2 years). The aim is to initiate a program on spectroscopy as applied to major areas in nanoscience, such as biomedical research. My work on X-ray spectroscopy is considered crucial in this multi-disciplinary endeavor. Future plans include coordination with several national and international groups on theoretical atomic and molecular physics and chemistry, computational methods and tools, biomedical engineering, and clinical research.