Error analysis for stellar population synthesis as an inverse problem

Stellar population synthesis can be approached as an inverse problem. The physical information is extracted from the observations through an inverse model. The process requires the transformation of the observational errors into model errors. A description is given for the error analysis to obtain objectively the errors in the model. Finding a solution for overdetermined and under-determined case was the purpose of two preceding papers. This new one completes the problem of stellar populations synthesis by means of a data base, by providing practical formul\ae defining the set of acceptable solutions. All solutions within this set are compatible, at a given confidence level, with the observations.Comment: 11 pages, LaTeX, 4 figures, 1 table. M.N.R.A.S.(2000) in pres

Constraining the solutions of an inverse method of stellar population synthesis

In three previous papers (Pelat 1997, 1998 and Moultaka & Pelat 2000), we set out an inverse stellar population synthesis method which uses a database of stellar spectra. Unlike other methods, this one provides a full knowledge of all possible solutions as well as a good estimation of their stability; moreover, it provides the unique approximate solution, when the problem is overdetermined, using a rigorous minimization procedure. In Boisson et al. (2000), this method has been applied to 10 active and 2 normal galaxies. In this paper we analyse the results of the method after constraining the solutions. Adding {\it a priori} physical conditions on the solutions constitutes a good way to regularize the synthesis problem. As an illustration we introduce physical constraints on the relative number of stars taking into account our present knowledge of the initial mass function in galaxies. In order to avoid biases on the solutions due to such constraints, we use constraints involving only inequalities between the number of stars, after dividing the H-R diagram into various groups of stellar masses. We discuss the results for a well-known globular cluster of the galaxy M31 and discuss some of the galaxies studied in Boisson et al. (2000). We find that, given the spectral resolution and the spectral domain, the method is very stable according to such constraints (i.e. the constrained solutions are almost the same as the unconstrained one). However, an additional information can be derived about the evolutionary stage of the last burst of star formation, but the precise age of this particular burst seems to be questionable.Comment: Accepted in A&A. 15 pages, 5 figures and 6 table

The achromatic chessboard, a new concept of phase shifter for Nulling Interferometry - I. theory

Direct detection of a planet around a star in the mid-IR, requires a nulling interferometer featuring an achromatic phase shift of pi on broad range. A new concept for designing such an achromatic phase shifter is presented here. The major interest of this solution is that it allows a simple design, with essentially one device per beam. The heart of the system consists in two cellular mirrors where each cell has a thickness introducing for the central wavelength, a phase shift of (2k+1)pi or of 2k pi on the fraction of the wave it reflects. Each mirror is put in one of the collimated beams of the interferometer. Because of the odd/even distribution, when recombining the two beams, a destructive interference is produced on axis for the central wavelength . If the distribution of cells thickness follows a rather simple law, based on the Pascal's triangle, then the nulling is also efficient for a wavelength not too far from the central wavelength. For instance, with two mirrors of 64x64 cells, one reaches a nulling of 1.e-6 on more than one complete octave. This could satisfy the specifications of space mission as Darwin. We also show the way to distribute the cells in the plane of the pupil for the optimum isolation of the planet image from the residual. We present the nulling performances of those various configurations.Comment: Accepted in Astronomy and Astrophysic

Limits of flexural wave absorption by open lossy resonators: reflection and transmission problems

The limits of flexural wave absorption by open lossy resonators are analytically and numerically reported in this work for both the reflection and transmission problems. An experimental validation for the reflection problem is presented. The reflection and transmission of flexural waves in 1D resonant thin beams are analyzed by means of the transfer matrix method. The hypotheses, on which the analytical model relies, are validated by experimental results. The open lossy resonator, consisting of a finite length beam thinner than the main beam, presents both energy leakage due to the aperture of the resonators to the main beam and inherent losses due to the viscoelastic damping. Wave absorption is found to be limited by the balance between the energy leakage and the inherent losses of the open lossy resonator. The perfect compensation of these two elements is known as the critical coupling condition and can be easily tuned by the geometry of the resonator. On the one hand, the scattering in the reflection problem is represented by the reflection coefficient. A single symmetry of the resonance is used to obtain the critical coupling condition. Therefore the perfect absorption can be obtained in this case. On the other hand, the transmission problem is represented by two eigenvalues of the scattering matrix, representing the symmetric and anti-symmetric parts of the full scattering problem. In the geometry analyzed in this work, only one kind of symmetry can be critically coupled, and therefore, the maximal absorption in the transmission problem is limited to 0.5. The results shown in this work pave the way to the design of resonators for efficient flexural wave absorption

Subaru High-Dispersion Spectroscopy of Narrow-Line Region in the Seyfert Galaxy NGC 4151

We report on a study of forbidden emission-line spectrum of nearby Seyfert 1.5 galaxy NGC 4151 based on the high-resolution (R ~ 45,000) optical spectrum obtained by using the High Dispersion Spectrograph boarded on the Subaru Telescope. The profile parameters such as the emission-line widths, the velocity shifts from the recession velocity of the host galaxy, and the asymmetry indices, for emission lines including very faint ones such as [Ar IV]4712,4740 and [Fe VI]5631,5677 are investigated. Statistically significant correlations between the measured profile parameters and the critical densities of transitions are found while there are no meaningful correlations between the profile parameters and the ionization potentials of ions. By comparing the results with photoionization model calculations, we remark that a simple power-law distribution of the gas density which is independent of the radius from the nucleus cannot explain the observed correlation between the emission-line widths and the critical densities of the transitions. Taking the additional dense gas component expected to exist at the innermost of the narrow-line region into account, the observed correlations between the emission-line width and the critical density of the transitions can be understood since high-critical-density emission lines can arise at such relatively inner regions even if their ionization potentials are low. The observed correlation between the blueshift amounts of emission lines and the critical densities of the ions is also explained if such dense gas clouds located closer to the nucleus have larger outflowing velocities.Comment: 19 pages and 1 separate jpeg figure. Accepted for publication in A