Equivalent width

B. Lam and T.L. Isenhour, Equivalent width criterion for determining frequency domain cutoffs in Fourier transform smoothing. Anal. Chem., 53 (1981) 1179-1182. 

Astronomical Observatory, were used to carry out the calculations of theoretical equivalent widths of lines, synthetic spectra and a set of plane parallel, line-blanketed, flux constant LTE model atmospheres. The effective temperatures of the stars were determined from photometry, the infrared flux method and corrected, if needed, in order to achieve the LTE excitation balance in the iron abundance results. The gravities were found by forcing Fe I and Fe II to yield the same iron abundances. The microturbulent velocities were determined by forcing Fe I line abundances to be independent of the equivalent width. For more details on the method of analysis and atomic data see Tautvaisiene et al. (2001). 

The temperatures of all stars were determined from colour indices, including our own observations and data from the literature. The log g values were derived by fundamental relations using distances from [5], and the metallicities were derived from equivalent widths of Fe II lines. 

Absolute magnitudes, effective temperatures, gravities and metallicities have been estimated, as well as distances and 3D velocities. Abundances of Fe, Si and Ni have been determined from equivalent widths under LTE approximation, whereas abundances of Mg have been determined under NLTE approximation using equivalent widths of 4 lines and profiles of 5 lines. 

We present here the results of abundance measurements of iron, calcium and nickel in four open clusters, from UVES spectra of solar type stars. A code developed by one of the authors (Francois) performs line recognization, equivalent width measurements and finally obtains the abundances by means of OSMARCS LTE model atmosphere [4]. Temperature, gravity and microturbulence velocity have to be input to the program. This is made in an automatic way for a grid of values chosen on photometric basis. Those that best reproduce excitation and ionization equilibria are selected and used, namely when no significant trend of the computed abundances is seen, neither versus the excitation potential of the line nor versus its equivalent width, and for which the abundances obtained with lines of different ionization stages of the same specie give equal results within the errors. This check is made with iron lines, we have in fact at least thirty Fe I lines in each star, and six Fell lines. 

We are therefore developing a set of routines for an automatic or semiautomatic abundance analysis of stellar spectra based on equivalent widths (EW). The first product is DAOSPEC, a code developed by P. B. Stetson for automatic EW measurement (http //cadcwww.hia.nrc. ca/stetson/daospec/). The preliminary abundance analysis presented here is the first step of an iterative and automatic procedure under development at the Bologna Observatory. 

Comparison of our equivalent widths with those of the literature, when available, shows a satisfactory agreement. 

The microturbulent velocity was set by the need of having an iron abundance independent of the equivalent width of the lines. 

The equivalent widths were determined using gaussian fit and the atmospheric models were computed using OSMARCS code improved by [6,3]. When it was not possible to measure equivalent width, the abundance was directly determined by using spectrum synthesis. 

Chemical abundances are inferred from the EW of the lines. Selected lines and atomic data are from our previous paper [5], from [4] and. Stellar parameters were first inferred from Geneva photometry and Hipparcos parallaxes. Then temperatures, microturbulence velocities, gravities and metallicities were iteratively changed in order to i) obey the excitation equilibrium of the Fe I lines ii) require that Fe I and Fe II abundances agree within 0.1-0.15 dex and iii) require that Fe I lines with different equivalent widths (EW) give the same iron abundance. 

The Li equivalent widths show a clear scatter as a function of (B — V)a (Fig. 1). The resulting scatter in Li abundances (Fig. 2) is nearly as large as the one in M 67 except for the fact that the upper limits in Cr 261 are significantly higher than in the latter cluster. The derived maximum Li abundances for solar-... 

Fig. 1. Li equivalent widths vs. magnitude for the M71 stars of Ramirez and Cohen (2002). The RGB-bump magnitude is indicated with a dashed vertical line. Stars brighter (at the left of the line) than the bump show Li upper limits only.

Fig. 2. Li equivalent widths vs. Na abundance for TO stars in NGC6752, showing a clear Li-Na anticorrelation (Pasquini et al. 2005, in preparation).

Compare the convolved synthetic spectrum with the observed spectrum, line profiles or equivalent widths. 

We now consider in somewhat more detail a simplified approach based on the curve of growth . For this, we ignore fine details of the observed line profile and use the equivalent width (EW) defined in Fig. 3.4, WA = f RdX or Wv = f Rdv, where R(AX) or R(Av) is the relative depression below the continuum at some part of the line. The curve of growth is a relationship between the equivalent width of a line and some measure of the effective number of absorbing atoms. Equivalent... 

Fig. 3.12. Simple (exponential) curve of growth for low-excitation Fe I lines with wavelengths between 4000 and 8700 A at the centre of the solar disk, with 6>ex = 1.00, b = lkms-1 (assuming Roo = 1), a = 0.02. Equivalent widths are from Moore, Minnaert and Houtgast (1966). gf -values are from furnace measurements by the Oxford group (Blackwell et al. 1986 and references therein).

The Na I D-lines have wavelengths and oscillator strengths A,i = 5896 A, /i = 1 /3, and X2 = 5889 A, f2 — 2/3. In a certain interstellar cloud, their equivalent widths are measured to be 230 mA and 370 mA respectively, with a maximum error of 30 mA in each case. Assuming a single cloud with a Gaussian velocity dispersion, use the exponential curve of growth to find preferred values of Na I column density and b, and approximate error limits for each of these two parameters. (Doublet ratio method.)... 

H. N. Russell analyzes solar spectrum with theoretical transition probabilities and eye estimates of line intensities. Notes predominance of hydrogen (also deduced independently by Bengt Stromgren from stellar structure considerations) and otherwise similarity to meteorites rather than Earth s crust. M. Minnaert et al. introduce quantitative measurements of equivalent width, interpreted by the curve of growth developed by M. Minnaert, D. H. Menzel and A. Unsold. 

This is best done graphically, using Table 3.3 (a = 0.001). The data are just barely compatible with the lines being on the linear part of the curve of growth, in which case the EW of Di is 200 mA and the column density is 2.0 x 1012cm-2 from Eq. (3.38). In this case, the equivalent width of D2 could be at most about 1 Doppler width,... 

FIGURE 14-8 (a) Meaning of equivalent width, W (b) Doppler and Lorentzian line-shapes for equivalent half-widths (c) transmission curves for an absorption line for a weak and strong absorber, respectively (adapted from Lenoble, 1993). 

The three parameters C, D, and K can be obtained by empirical fits to the data and p is the partial pressure of nonabsorbing gases present. Since this total absorption band area is directly related to the equivalent width and hence to the absorbed irradi-ance, there is a logarithmic dependence of the net absorption on (M), which is the case for the strong absorption bands of both water vapor and carbon... 

If b and g are peaked functions (such as in a spectral line), the area under their convolution product is the product of their individual areas. Thus, if b represents instrumental spreading, the area under the spectral line is preserved through the convolution operation. In spectroscopy, we know this phenomenon as the invariance of the equivalent width of a spectral line when it is subjected to instrumental distortion. This property is again referred to in Section II.F of Chapter 2 and used in our discussion of a method to determine the instrument response function (Chapter 2, Section II.G). 

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