© ESO, 2013

1. Introduction

Diffuse interstellar bands (DIBs) and interstellar (IS) absorption lines have been almost exclusively extracted from early-type star spectra, using the fact that stellar lines are broad, shallow, and limited in number, and that they do not contaminate the IS lines. The stellar continua can be easily fitted without any need for stellar models. However, extracting absorption from early-type star spectra is a strong limiting factor since it considerably reduces the number of potential targets, the information that can be obtained on the source regions of the absorptions, and especially the spatial resolution that can be achieved. In the case of the DIBs, it limits studies of the DIB response to the radiation field and to the local physical properties within the IS clouds, while such studies are promising tools in the search for the DIB carriers (e.g., Vos et al. 2011). Moreover, with the advent of stellar spectroscopic surveys at increasing resolution, the use of multi-object spectrographs and the perspective of forthcoming Gaia parallaxes, a large amount of line-of-sight integrated absorption data will become available.

Extracting absorption characteristics towards all targets, including cool stars, would allow better mapping of the galactic ISM, because it would considerably increase the achievable spatial resolution. For such mapping, IS lines of atoms, simple molecules, and DIBs are available, since all three contain information on the amount of IS matter. While the first two are well identified, carriers of the last remain unknown, despite their early discovery (e.g., Herbig 1995; Jenniskens & Desert 1994; Salama et al. 1996; Fulara & Krelowski 2000; Snow & Destree 2011; Friedman et al. 2011; Hobbs et al. 2008, 2009). Still, this lack of carrier identification and the fact that most of them are only weakly correlated with extinction or gas column are not incompatible with their use as tracers of IS clouds in the same way IS lines are used; i.e., the radial gradients of their strengths allow locating IS clouds in distance and building 3D maps. In some respects, DIBs may have advantages as interstellar medium (ISM) tracers, because they are numerous, thus observable at various instrumental settings; they are often broad; and in general they are unsaturated. Recent data analyses suggest that the average ratios between the DIBs and the extinction do not seem to vary significantly within the first kiloparsec (Friedman et al. 2011; Vos et al. 2011). Finally, making use of cooler stars to extract their strengths reduces the dispersion around the average relationship, because extreme ionizing field effects linked to bright and hot targets are avoided (Raimond et al. 2012). For this reason, extracting DIB information from cool stars would be another improvement to the mapping.

Here we present a new method of DIB measurement based on cool star synthetic spectra, and as a test case we applied this technique to three different diffuse bands and 219 targets located in the Galactic bulge that have the advantage of possessing precise determinations of their atmospheric parameters. We selected the 6196.0, 6204.5, and 6283.8 Å DIBs that are the three strongest absorptions contained in the observed spectral interval. Those DIBs have already been widely studied (see e.g., the works of Galazutdinov et al. 2008; Cami et al. 1997; Friedman et al. 2011; Vos et al. 2011). We estimate the statistical and systematic uncertainties on the DIB equivalent widths (EWs) and discuss potential improvements. We compare the measured EW angular pattern over the field with an independent mapping of the reddening based on photometric data of stars close to the Galactic center (GC). We finally use average DIB-reddening empirical relationships previously established in the Sun’s vicinity to derive three independent estimates of the reddening towards all targets, compare the three estimate together, and finally compare with the photometric determination.

This article is organized as follows. Data are presented in Sect. 2. In Sect. 3 we describe the new method of IS absorption band extraction and its ingredients. In Sect. 4, we show the model adjustments for selected target stars and discuss the results. In Sect. 5, we discuss the relations between the DIBs and between the DIBs and the extinction obtained by photometry. Section 6 presents color excess estimates based on the DIBs and nearby star studies. Finally, we summarize the results and discuss the perspectives in the last section.

2. Data

We used the sample of 219 bulge red clump giants of Hill et al. (2011). Those stars were observed with FLAMES/GIRAFFE at the VLT and are located within a 12 arcmin radius field in Baade’s Window (l = 0.8, b = −4). We used here the spectra obtained with the GIRAFFE HR13 setup, leading to a resolution of R = 22   500 and a spectral coverage spanning 6120 to 6405 Å, which contains three well known diffuse bands. The target selection, observations, data reduction, and stellar-parameter determination are described by Hill et al. (2011). Those stellar parameters were determined by these authors from photometric and spectroscopic data. Here we use the effective temperature, gravity, micro-turbulence, and metallicity resulting from their analysis, whose full ranges for the present sample are listed in Table 1. The different exposures were observed within a week interval so that at this resolution we can neglect variations in the radial velocity difference between the telluric and stellar lines and work with the final co-added spectra. Signal-to-noise ratios vary between ≃30 and 77 per pixel. (The Giraffe pixel-size is 0.07 Å.)

This region benefits from a high-resolution differential extinction map that was derived from the OGLE-II red clump giants photometry by Sumi (2004). Assuming a mean reddening-corrected color for the red clump, Sumi (2004) divided each field in small subfields, computed the mean observed color of the red clump in each subfield and derived the reddening E_V − I. The resulting extinction map has a spatial resolution of 33 arcsec in our field. For comparison purposes we have interpolated within the Sumi (2004) reddening grid to infer its value at each target location. Sumi (2004) indicates a potential zero-point offset for A_v that may amount to 0.05. The distribution of the target stars is shown superimposed on the Sumi (2004) extinction map in Fig. 1.

Fig. 1 Target stars used in this study (black crosses) superimposed on the extinction map from Sumi (2004). The map is centered on (l,   b) = (0.8, − 4). Each pixel is 0.6′ × 0.6′. The extinction scale is displayed in Fig. 14. Stars are numbered according to Table 3. Dotted lines link stars in increasing order of their ID number. Only one out of five numbers is indicated for clarity.

3. Fitting procedure

Our approach is to model and adjust the spectrum of the background star, the DIB, and the atmospheric transmission simultaneously in one unique step. In the opposite case of hot stars, extracting the IS absorption was done in two or three steps. The correction for the telluric absorption, if necessary, was done first and independently of the IS absorption fitting. Synthetic transmission spectra were adjusted through computing the mean ratio between observed and modeled EWs of specific lines (Lallement et al. 1993), or by minimizing the length (defined as the sum of flux differences between consecutive points) of the residual spectrum obtained after dividing by the model atmospheric transmission (Raimond et al. 2012). None of those methods is necessary here, since the atmospheric transmission model is adjusted in velocity and airmass during the global adjustment. In a second step the smooth continuum of the hot star was fitted to a function, and in a last step the DIB strength was measured using the normalized spectrum. Characterizing the DIB strength was done in several ways, the two main ones being measurements of the central depth and of the EW. We refer to the detailed discussion of this point by Friedman et al. (2011). We chose here the EW, and, as we will see, this is the quantity that comes directly out from our cool star analysis.

For cool stars, the presence of numerous, deep, and narrow stellar lines precludes applying the simple continuum fitting procedure that is used for stars of earlier spectral types. Identifying and correcting the stellar lines one by one in the IS absorption region is not practical. Furthermore, if the stellar lines and the IS absorption do overlap, it is very difficult or even impossible to separate them, hence our approach using a global adjustment. Our composite model here is the product of a synthetic stellar spectrum, a synthetic telluric transmission, and an empirical model for the DIB absorption. The model allows for wavelength shifts between those three spectra to take the stellar radial velocity, the Earth motion, and the IS radial velocity into account. The giant stars used as background sources in the present investigation do not have measurable projected rotational velocities at this resolution. Sizeable projected rotational velocity in the background star could be modeled as well, if necessary. The combination of the three models is convolved by a Gaussian profile to take the instrumental spectral resolution into account and is adjusted to the data in the DIB region, with the DIB strength, the DIB center location, and an atmospheric transmission scaling (see below) as the free parameters.

The synthetic stellar spectra, S(λ), were computed from an ATLAS 9 model atmosphere using the SYNTHE suite (Kurucz 2005). We used the Linux port of all the codes (Sbordone et al. 2004; Sbordone 2005). Atomic and molecular data were taken from the data base on Kurucz’s website¹ (Kurucz 2005). For each star we computed a synthetic spectrum with the stellar parameters obtained by Hill et al. (2011), i.e. the effective temperatures, gravity, metallicity, and microturbulence, summarized in Table 1. The stellar radial velocity is taken into account by Doppler-shifting the computed spectrum to the appropriate radial velocity.

The synthetic telluric transmissions were computed by means of the LBLRTM code (Line-By-Line Radiative Transfer Model, Clough et al. 2005), using the molecular database HITRAN (HIgh-resolution TRANsmission molecular absorption, Rothman et al. 2009). Here we have used the transmission T₀(λ) computed for a standard atmosphere and for the altitude of the observatory and assumed that airmass variations from star to star simply result in a variable coefficient α for the transmission, with T(λ) = T₀(λ)^α. The projected Earth motion is taken into account by Doppler-shifting the transmission.

Finally, the profiles of the 6196.0, 6204.5, and 6283.8 Å DIBs are derived from a high resolution (R = 48   000), high signal-to-noise survey of early-type stars recorded with the FEROS spectrograph at the 2.2 m ESO/Max Planck Institute Telescope in La Silla. Those profiles do not reveal the fine structure that is known to be present Galazutdinov et al. (2008), but this is not necessary here since we deal with spectra at a resolution that is lower than the one of FEROS. The shape of the 6283.8 Å DIB, which is contaminated by strong telluric molecular oxygen lines, has been derived by Raimond et al. (2012) by averaging a large number of individual shapes obtained after division by an adjusted telluric template. This use of a synthetic atmospheric model is allowed by this DIB being relatively strong and much broader than the telluric lines. In the same way, this DIB is broader here than the stellar lines and thus relatively easy to detect and measure (see Figs. 3−5). The two, much weaker DIBs, 6196.0 and 6204.5 Å, are in regions that are free of contaminating telluric lines. Their shapes were derived by means of an automated fitting method appropriate to early-type stars (Puspitarini et al. 2012, priv. comm.). About ten individual profiles extracted from the best FEROS spectra were averaged to produce those templates. Since those two DIBs are narrower than the 6283.8 Å DIB, here in the case of cool stars they are much more difficult to measure due to the overlap with the similarly narrow stellar lines.

Neglecting emissions from the cloud in comparison with the stellar flux, DIB transmission profiles D(λ) can be expressed as exp(− τ(λ)), where τ(λ) is the optical thickness as a function of wavelength. The value of τ(λ) is proportional to the column N of absorbers and can be expressed as τ(λ) = N/N₀τ₀(λ), τ₀(λ) and N₀ being some related optical thickness and column of reference. Calling β the N/N₀ ratio, a quantity proportional to the column density of the DIB carrier, one has D(λ) = D₀(λ_D)^β, where D₀(λ) = exp(− τ₀(λ)) is the reference profile derived from the FEROS analyses, and λ_D is the wavelength shifted by the radial velocity of the main absorbing medium. The DIB EW is, by definition, (1)where I₀(λ) and I(λ) are the unabsorbed and absorbed intensities. Within the weak absorption regime appropriate here, τ is small, exp( − τ) ≃ 1 − τ and the EW W is approximated by (2)where W₀ is the EW of the line of reference.

We chose to list the results in the form of the product βW₀, which has the advantage of being both truly proportional to the absorbing column and being an equivalent width, i.e., a widely used, meaningful quantity. For the broader DIB, 6284 Å, the relative difference between βW₀ and the actual EW is smaller here than 4.5%, a value reached for EWs on the order of 1.2 Å. For the narrower DIB, 6196 Å, the departure from the linear regime for the EW occurs at a smaller optical thickness; however, the DIB is weak, and finally the relative difference between βW₀ and the actual EW is less than 4%, a value reached for EWs on the order of 70 mÅ.

After adjusting the coefficient β through spectral fitting, the DIB EW is thus simply computed as the product of the EW of the reference profile W₀ by the coefficient β. We also assume here that most of the absorbing medium originates in clouds with a similar radial motion, or equivalently that the DIB is negligibly broadened by the line-of-sight velocity structure. This assumption is legitimated here by the fact that most of the absorption arises within 1500 pc from the Sun, as derived from the extinction model of Marshall et al. (2006) and that for those low l, b coordinates the projection of the gas motions onto the line-of-sight remains small with respect to the DIB spectral width.

Figure 2 illustrates the procedure for this study. The stellar parameters are used as input for the stellar synthetic models, and the stellar radial velocity is taken into account by an appropriate shift. The atmospheric synthetic model of reference is calculated based on the position and altitude of the observatory. While doing the fitting, the program computes the product κS(λ_S) T₀(λ_E)^αD₀(λ_D)^β, with κ being a scaling factor, λ_S is the wavelength shifted by the stellar radial velocity, λ_E by the Earth’s radial velocity and λ_D by the radial velocity of the DIB absorbing medium, and convolves the product of the three models by a Gaussian instrumental function appropriate for the resolution of GIRAFFE.

Telluric absorptions should be identical for all fibers for the same exposure, and we also expect the DIB radial velocity to vary very little over the narrow field. Still, to test the adjustment and allow for small uncertainties in the three wavelength shifts, we started by allowing all parameters κ, α, β, λ_S, λ_E and λ_D to freely vary, and performed a least mean squares adjustment to the data for each star. All the fittings were done in an automated way. The results revealed a large majority of identical or very close values for the λ_E shift (actually a null value for a fit in the earth frame) and for α. As mentioned previously this was expected for both α, which responds to the airmass, and λ_E, a function of the date. We extracted those two parameters and kept them fixed for the second adjustment phase. From this first attempt we could also check that the values found by fitting for λ_S differ from the radial velocities from Hill et al. (2011) by very small velocity intervals (on the order of 1 km s^-1). We kept those very small differences from values in Table 3 and fixed λ_S for the next step. Finally, the coefficient λ_D that represents the DIB shift was also found to be the same or nearly the same for a large majority of the stars. This confirms that the DIB radial velocity variation is very small over such a small field of view, both because most of the absorption originates in the first two kpc, and also because the radial motion of the absorbing gas in this direction is small. We then fixed this shift λ_D at the most frequently found value. For all those four parameters we checked that the outliers correspond to low signal-to-noise spectra or to the presence of a spurious feature. We then proceeded to a second fit of all spectra, this time only for free κ and β coefficients.

Fig. 2 Procedure flowchart of the fitting.

4. Model adjustments

Figures 3−9 illustrate exemplary cases of model adjustments for the three 6196.0, 6204.5, and 6283.8 Å DIBs chosen for this study.

Fig. 3 Model adjustment for Ogle N: 393009 (Teff = 5012 K). The DIB is in a region devoid of strong stellar lines. The upper panel shows the spectrum (red line) and the best-fit model (purple line). The lower panel shows the synthetic stellar model (yellow line), the synthetic atmospheric model (blue line), and the DIB profile (green line), which all correspond to the fit parameters.

Fig. 4 Same as Fig. 3 for Ogle N: 392992 (Teff = 4907 K). The DIB here is in a spectral region characterized by moderately strong stellar lines.

Fig. 5 Same as Fig. 3 for Ogle N: 89667 (Teff = 4516 K). The DIB here is both weak and embedded in strong stellar lines.

What we aim at showing in those figures are the strong differences linked to the target star individual radial velocities, which vary over a very large velocity interval, from −230 to +250 km s^-1. This results in very different locations of the DIBs with respect to the main stellar lines. There are also very large differences between the 6283.8 Å DIB and the two narrow ones, with a much stronger impact of the star radial velocity and of the signal-to-noise on the DIB detection for the last two DIBs. Finally, the higher the metallicity, the stronger the stellar lines and their impact on the DIB measurement, especially again in the case of the two narrow and weak DIBs.

Figures 3 to 5 show three examples of adjustments for the strongest and broadest DIB at 6283.8 Å, The first star (Fig. 3) corresponds to an optimal case: given the star radial velocity, only weak stellar lines are located in the DIB region, and the fitting program could easily adjust the DIB strength. Moreover, the star is metal-poor (Fe/H = −0.68), which helps the fitting procedure further. Figures 4 and 5 correspond to more difficult cases, with one or more strong stellar lines in the DIB region. In those cases, it should be possible to measure the DIB strengths with accuracy, provided the stellar models adequately predict the stellar line depths. However, it can be seen that there are significant and often systematic differences between the observed and modeled lines for some spectral regions. Such departures may have several origins: the oscillator strengths (log (gf)) and other atomic data (wavelengths, damping constants) that we use have an error attached to them; some of the lines are simply not identified and absent from our line list; our spectra are computed assuming local thermodynamic equilibrium (LTE); departures from LTE in the stellar atmosphere may change the line strength, for a given abundance; the model atmospheres we used are one-dimensional static and plane-parallel, hydrodynamic effects (granulation) may also affect both the line strengths and shapes. In practice our computed stellar spectrum differs from the observed spectrum due to a number of shortcomings in our modeling. For example, significant residuals are found at the locations of unidentified lines of the solar spectrum, such as the 6273.949, 6282.816, 6286.142, and 6288.315 Å lines (Moore et al. 1966). Obviously such unidentified lines are not present in our line list. Details on these discrepancies can be found in the Appendix, which aims at estimating the uncertainties on the DIBs EWs and at empirically correcting for systematic effects. Nevertheless, despite the observed departures from the stellar model, the DIB is broad enough here for a reliable DIB estimate. Figure 5 illustrates this property, and shows one of the worst cases of overlapping stellar lines, a metal-rich (although moderately, Fe/H = 0.67) target star, and one of the smallest DIB EWs. The DIB strength could be measured reasonably well despite those conditions, thanks to the good signal-to-noise ratio of the spectrum and the width of the DIB.

Fig. 6 Same as Fig. 3 for the 6196 Å DIB and Ogle N: 412854 (Teff = 5191 K). The narrow DIB is in a region devoid of strong stellar lines.

Fig. 7 Same a Fig. 6 for Ogle N: 234898 (Teff = 4714 K). The DIB and a strong stellar line do overlap.

Fig. 8 Same as Fig. 3 for the 6204 Å DIB and Ogle N: 393033 (Teff = 4914 K). The narrow DIB is in a region devoid of strong stellar lines.

Fig. 9 Same as Fig. 8 for Ogle N: 268068 (Teff = 4837 K). The DIB region corresponds to strong stellar lines.

This is not the case for the two narrow DIBs. Figures 6 to 9 show two examples of determinations for each of the 6196.0 and 6204.0 Å DIBs, a relatively easy one with only weak stellar lines contaminating the DIB region, and a difficult one with stellar lines overlapping the DIB. In the first case, it can be seen that DIB EWs can be safely measured. In the second, it is clear from the figure that the stellar line accuracy is critical and that some of the measurements are very uncertain, at least for the low extinction (and DIB strength) regime that prevails here. In comparison with those uncertainties, additional errors linked to the use of a predefined shape of the DIB, as well as to the telluric model (for the 6284 Å DIB), are negligible. Those systematic departures have been studied in detail and are discussed in the Appendix. Based on them, a first-order empirical correction was devised and was applied to the DIB derivation. In brief, residuals for all spectra were all shifted to the stellar frame, and the resulting spectra were sorted as a function of the stellar metallicity (see Fig. A.1 in the Appendix). At each wavelength an average linear relationship between the residual value and the metallicity was adjusted, providing a systematic offset as a function of metallicity and wavelength (Figs. A.2 and A.3). This offset is maximal at the locations of the over- or underpredicted lines, and nil elsewhere. Such an offset was then applied as a corrective term at all wavelengths to all DIB spectra (Fig. A.4), and a new adjustment of the model and subsequent computation of the DIB EW were performed after those corrections. We compared the DIB-DIB relationships and also the DIB-extinction relationships both before and after the empirical correction, and found a systematically better DIB-DIB relationship, in particular with a factor of two increase in the Pearson correlation coefficient in the case of the 6196 Å vs. 6204 Å DIB comparison. We also found a significant improvement in the DIB-extinction relationship, except for the 6284 Å DIB for which there was no change. We are conscious that a more fundamental approach would be desirable, but, in view of those improvements, we kept the corrected values for the remaining part of the analysis. More improvements are expected in future from elaborated studies of the stellar spectra in the DIB spectral regions, i.e. individual adjustments of the log (gf), studies of the missing lines, non-LTE and granulation effects. Such studies are beyond the scope of this work, which is devoted to testing the new method adapted to cool stars.

5. DIB equivalent widths, DIB-DIB, and DIB-extinction correlations

Table 3 lists the resulting EWs for the three DIBs, both before and after the empirical correction, as well as the associated uncertainty. Uncertainties, whose derivations are also described in detail in the Appendix, are a combination of random errors associated to the noise level and of errors linked to the use of the three models that remain after applying the above-mentioned empirical correction. These quasi-random uncertainties were derived from the whole set of residual vs metallicity curves that were computed for each wavelength and used for correcting of systematics. They were simply taken as the variance of the residuals around the mean relationship (see Figs. A.1 and A.2). This variances includes both the noise and the departure from the empirical ideal relationship between the metallicity and the stellar lines. It is clear that those derived uncertainties provide an order of magnitude of the errors, which has a sense as a mean for all targets, but that individual errors for each target may be larger or smaller. Future work will address this point, once additional studies of the stellar models have been performed.

Fig. 10 Equivalent width (EW) of DIB 6196.0 Å as a function of the EW of DIB 6283.8 Å. The black line is the best linear fit for pure proportionality, using error bars of both DIBs.

Fig. 11 Same as Fig. 10 for DIB 6204 Å.

An immediate test of the reliability of the DIB strengths is the existence of DIB-DIB correlations, because EWs have been measured independently for the three bands. This test is not so easy here owing to the limited range of extinctions (Sumi 2004). Still, the Spearman’s rank correlation statistics allows the absence of two-by-two correlations to be rejected by better than 99.9%. Figures 10 and 11 show the DIBs 6196.0 and 6204.5 EWs as a function of the broad 6283.8 Å EW for the whole sample. The black lines correspond to a pure proportionality. Despite the large uncertainties, especially for the two small DIBs, the correlation between the three bands is clearly visible. Those correlations show that the signal we extracted for the DIBs contains some information on the IS absorption, even for the two small DIBs. A second test of the DIB measurement is obtained from a comparison with the extinction map. Figure 12 displays the star-by-star variations in each DIB EW, as well as the extinction derived from the OGLE photometry obtained by interpolation through the A_v map of Sumi (2004). The four patterns, which represent variations across the field of the four independent quantities, reveal large similarities for the strong DIB and some similarities for the 6204 Å DIB. Large uncertainties make the comparison less obvious for the 6196 Å band. This is reflected in the Spearman’s rank correlation statistics that allow rejecting the absence of correlation at better than 99.9% for the 6284 and 6204 DIBs, and 90% for the 6196 Å DIB.

More precise statistics could have been obtained after rejections of the noisy spectra or particularly poor adjustments. However, our goal here is to provide some idea of the DIB extraction results as a function of the signal quality, the DIB strength, and the reddening for an entire field, with an entirely automated method.

Fig. 12 From bottom to top, EWs of the three DIBs (6196, 6204, and 6284 Å) as a function of the star number and the extinction Av interpolated from the map of Sumi (2004) at each star location.

6. Color excess estimates based on nearby star empirical relationships

Diffuse interstellar bands are moderately or only weakly correlated with the extinction, as shown by a number of studies and the existence of DIB families whose members are internally closely correlated, while distinct families seem to obey different laws (e.g., Krelowski & Walker 1987; Cami et al. 1997). There is no parental link between the three DIBs we study here, and thus we do not expect to find strong correlations between their EWs or very similar dependencies on the extinction. Previous surveys of stars in the solar neighborhood have provided some statistical relationships between the reddening E_B − V derived from spectrophotometry and the EW of each DIB. Best-fit parameters of linear correlations have been established recently by Friedman et al. (2011) for all three DIBs, based on about 130 O-B nearby northern hemisphere stars within 1 kpc. In the case of the 6284 Å DIBs, Raimond et al. (2012) derived slightly different coefficients based on about the same number of southern hemisphere targets, observed with the ESO/La Silla FEROS spectrograph. Using the same FEROS data, Puspitarini et al. (2012, priv. comm.) derived linear fit coefficients for the two other DIBs, again found to be slightly different when compared to the northern survey study. The coefficients for the linear relations between EW and E_B − V are shown in Table 2 for both surveys and for the three DIBs. There are some differences between the relationships as they emerge from the two surveys, which have been discussed by Raimond et al. (2012). Owing to the use of cooler and fainter target stars, the ESO/FEROS DIB strengths are not as influenced by strong radiation fields, and there is significantly less dispersion around the mean DIB-E_B − V relationship. As a matter of fact, DIB strengths may be significantly reduced in case the main dust cloud responsible for the absorption is very close to the UV-bright target star (Friedman et al. 2011; Vos et al. 2011), an effect attributed to the ionization state change of the carriers in the stellar environment. For this reason, the number of outliers with a relatively weak DIB and a large reddening is smaller in the FEROS survey, and the dispersion decreases. In parallel, the mean slope E_B − V/EW(DIB) derived from the sample is also smaller. This was found systematically for the three DIBs. Here we make use of the FEROS-based mean relationships, because the line-of-sight here is not related to hot bright stars and the DIB should correspond better to average conditions. For comparisons we also show both results for the strong 6284 Å band.

Fig. 13 Color excess EB − V derived from the three DIBs as a function of the EV − I value interpolated within the Sumi (2004) map at the locations of the target stars. EB − Vs here are obtained using the Raimond et al. (2012) and Puspitarini et al. (2012, priv. comm.) average relationships based on FEROS data. The blue and pink dotted lines correspond to color excess relationships based on the Fitzpatrick (1999) and Cardelli et al. (1989) extinction curves and Rv = 3.1 (see text). In the case of the DIBs 6283.8 Å we also show the color excess values deduced from the Friedman et al. (2011) average relationships (open triangles).

The measured DIB EWs derived from the global fitting were converted into E_B − V color excess values by application of the three average relationships listed in Table 2.

Figure 13 shows the color excess E_B − V estimate based on the DIB 6283.8 Å and the FEROS relationship, as a function of the color excess E_V − I interpolated from the Sumi (2004) maps (x-axis). The figure is somewhat redundant with the previous one, however it provides a better idea of the EW dispersion and the global relationship. The data point distribution shows a correlation between the DIB-based and photometric determinations, but there is a large dispersion, and also the observed interval for the DIB strength is significantly larger than the range of variation in the photometric determination. (The best fit linear relationship does not go through zero.) The relationship between E_B − V and E_V − I depends on the extinction curve, and to a lesser extent on the stellar spectrum. We have drawn here the relationships based on both classical Cardelli et al. (1989) and Fitzpatrick (1999) extinction curves, for the total-to-selective extinction ratio R_v = 3.1. The value of E_V − I is computed for a typical red-clump giant star, and E_B − V is computed for the A0 star Vega. As far as average absolute values are concerned, the DIB-based E_B − Vs are similar to what one would expect from those classical laws, and in better agreement with the Fitzpatrick relationship. We also show the E_B − V values we would obtain with the empirical Friedman et al. (2011) relationship. Those E_B − V empirical estimates are systematically higher and more difficult to reconcile with the photometric data. We believe that the relationship based on the cooler FEROS targets may be more appropriate here because it probes environmental conditions that are closer to the average conditions encountered here than to the high ionization conditions encountered towards O- and early B-type nearby target stars.

Figure 13 also shows how the 6196 and 6204 Å DIB-based color excess E_B − V compares with the photometric determination of E_V − I. For those two DIBs, the correlation is visible, and the agreement between the measured and the expected ratio between the two color excess values is again better with the Fitzpatrick (1999) reddening law. There appears to be less deviation from average simple proportionality for those DIBs, compared to 6284 Å, especially for the DIB 6196 Å for which the best-fit relationship is compatible with proportionality within the uncertainty range.

An important source of dispersion is the fact that the Sumi color excess is an average over the series of stars contained within the 0.6 × 0.6 arcmin pixel field and located at various distances in the bulge, while the DIB is derived for individual stars. Here the main effect would be angular variability, because, as said above, the quasi-totality of the extinction is generated closer than 2000 pc, thus differences in the distances to the bulge targets have in principle no impact. At 1 kpc, 0.6 acrimony corresponds to a transverse distance of 0.17 pc, thus only very dense, small cloud cores could produce variations as large as those observed. A likely explanation for both the dispersion and also departures from proportionality between the DIB-based color excess and the photometric E_V − I is the existence of intrinsic DIB variations in response to the radiation field and in general to environmental conditions, such as those found at smaller distances. This is favored by the spatial pattern as we discuss below. On the other hand, spatial variations of the DIB-E_V − I ratio may also be related to spatial variability of the extinction curve. Udalski (2003) and Sumi (2004) both consider R_v may vary significantly towards the bulge. A relationship between the extinction curve, the total to selective extinction ratio and the DIB behavior has been first discussed by Krełowski et al. (1999). Environmental effects and dust processing, on one hand, and extinction curve, on the other, are themselves related through the grain distribution and the cloud history, which also influences DIB carriers and strengths.

The spatial variability of the ratio between DIB-based and photometric determinations of the color excess is shown superimposed on the Sumi map in Fig. 14. In this figure the color indicates the ratio and the size of the markers is proportional to the DIB strength. The distribution of colors shows that there are some systematic changes across the field for the 6284 DIB; in particular, the DIB is relatively small compared to the photometric value at larger declinations and right ascensions. Future investigations will hopefully allow those differences to be attributed in variations of the environmental conditions in the encountered clouds, to extinction law spatial variations, or both, as discussed above. The 6204 Å DIB shows the same behavior as the 6284 band, although less clearly, due to large uncertainties and also not as pronounced. At variance with the other two bands, the 6196 Å DIB does not reveal any spatial trend, although there are strong uncertainties on the DIB EW. If confirmed, for the three DIBs the spatial homogeneity of the measured ratio follows the degree of correlation of the DIBs with the color excess, as measured in the solar neighborhood and for widely distributed targets by Friedman et al. (2011). The correlation degree and spatial homogeneity decrease from the 6284 Å DIB to the small 6196 Å DIB.

Finally, we show in Fig. 15 a weighted mean value of E_B − V derived from the three DIBs, again compared with the E_V − I value deduced from the OGLE analysis. This figure allows determining to what extent the combination of those three DIBs can be used here as a first estimator for the reddening, in the absence of photometric measurements. The average linear relationship is E_B − V = (0.72 ± 0.14) E_V − I + (0.06 ± 0.10) and the standard deviation is 0.08, i.e. on the order of 15% of the average value. This should be compared with other conditions and distances.

Fig. 14 Spatial variability of the DIB and the DIB-extinction ratio (from left to right, the 6284, 6204, 6196 Å DIBs). Target stars used in this study are superimposed on the Av extinction map from Sumi (2004) (gray scale). The size of the circle is proportional to the DIB EW, and its color corresponds to the ratio between the DIB EW and the extinction Av obtained by interpolation through the Sumi map (color scale).

Fig. 15 Synthesis of all EB − Vs estimates from the 3 DIBs, in the form of a weighted mean, here compared with the EV − I determination from the OGLE photometry. The blue and pink dotted lines correspond to color excess relationships based on the Fitzpatrick (1999) and Cardelli et al. (1989) extinction curves.

7. Summary and discussion

We have used R = 22   500, S/N = 30 − 77 observations of 219 red clump giants from the galactic bulge in Baade’s Window (A_v ≃ 1.4) as a test case for our newly developed composite model and automated fitting method of IS absorption extraction from cool star spectra. The combination of synthetic stellar models, synthetic atmospheric lines, and DIB profiles allowed us to extract EW values for the three DIBs 6284, 6196, and 6204 Å. The existence of DIB-DIB correlations demonstrates that, even without any adaptation of the stellar model, in the case of a moderate color excess E_B − V ≃ 0.4 and of signal-to-noise ratios above 30, a strong DIB like the 6284 Å band, but also narrow and weaker DIBs like the 6196 or the 6204 Å bands, can be measured for cool stars, provided one takes the velocity shift into account between the star and the absorbing ISM. More precisely, all spectra could be efficiently used in the case of the strong and broad 6284 Å DIB (width ≃3.5 Å, depth ≃20%), while for the two narrow and weaker DIBs (≃0.5 and 1 Å width, 10% depth) the potential extraction of the DIB EW depends on the star’s radial velocity, whose value results in an overlap of stellar lines and DIBs or does not. This is due to the presence of unidentified lines, as well as to over- or underpredicted line strengths. Model improvements are beyond the scope of this work, but should be performed in future, once other analyses confirm the present trends and enough constraints have been obtained. Here we simply performed an empirical correction, independently for each DIB, which is described in the Appendix. Its validity was demonstrated by a strong improvement in the DIB-DIB correlations, as well as improvements in the DIB-extinction correlations. More work is needed on a more fundamental approach to those corrections. Overall, this modeling demonstrates that DIBs can be measured in an automated way for a large number of cool targets during spectroscopic surveys, and be used as any other IS line to locate the IS matter.

For the three DIBs, the spatial pattern generally reflects extinction variations deduced from stellar photometry, which also validates the fitting method. The degree of correlation is, as expected, generally better for the broader and stronger DIB because uncertainties on the EWs are much smaller. DIB strengths are converted into color excesses, using best-fit linear relationships established for early-type star surveys. Mean values of E_B − V over all targets are 0.53, 0.62, and 0.52 for the 6284, 6204, and 6196 Å DIBs, respectively. Discrepancies among the DIBs amount to about 20%, and there is a 15% dispersion of the weighted mean value around its average linear relationship with the photometric reddening (Fig. 15). There were several results from the analysis that call for further studies. The 6284, and to a smaller extent the 6204 Å DIBs amplitude intervals over the field, are found to be larger than the color excess relative variations deduced from OGLE photometric data and their analysis (Sumi 2004, see Fig. 12). This is reflected in the spatial variability of the DIB-based to photometry-based color excess ratio. Those variations are not randomly located, as is especially visible for the 6284 Å DIB: the DIB is systematically weaker around α,δ = 270.95, −30°. One likely explanation for such departures from proportionality is the DIB response to ionization conditions in the clouds and other environmental effects such as shocks.This may be linked to the spatial variability of the extinction law. The grain size distribution influences the shape of the extinction law and the R_v, but it is also linked to the cloud’s physical properties and its history, which in turn influence the quantity of macro-molecules and the DIBs. Such a link between the R_v and the DIBs has been discussed by Krełowski et al. (1999). The excess of amplitude variation and the spatial variability do not seem to exist for the small 6196 Å DIB, although large uncertainties make the comparison with the photometric extinction more difficult. This may relate to this DIB having been found to be better correlated with the extinction than the two others, something again potentially related to its different response to the dust distribution, or the environmental conditions. Moreover, the absolute value of the extinction based on the 6196 Å DIB (again deduced from the average solar neighborhood relationship) seems to agree better with the photometric determination than do the two other DIBs.

More analyses should be performed over various fields and for targets at various distances to confirm unidentified or poorly predicted stellar lines. More data should help in refining the stellar models in the DIB spectral regions and subsequently improve the DIB extraction. On the other hand, extinction estimates would certainly be strongly improved by the use of multiple DIBs and of their ratios, accompanied by better understanding of their specific behavior. Such studies may also provide additional information on the links between the extinction law and the DIBs.

Acknowledgments

We thank the referee for the useful comments on the manuscript. H.-C. C. wants to acknowledge the Taiwanese government for her scholarship NSC100-2917-I-564-057.

References

Appendix A: Error estimates

Fig. A.1 Residuals as a function of wavelength and metallicity for the DIB 6283.8 Å. They form the basis for the EW correction and the error estimate.

Fig. A.2 Example of residuals vs. -metallicity relationships: here the residuals depend on the metallicity and are negative, which corresponds to an under-predicted stellar absorption line.

Fig. A.3 Example of residuals vs. -metallicity relationships: here the residuals do not depend on the metallicity and are negligible.

Fig. A.4 Schematic illustration of the correction applied to the EW measurements. The red curve represents the DIB profile as it comes out from the fitting phase. Hatched surfaces show the offsets applied at each wavelength that are computed for each star, as a function of its metallicity. The dashed line illustrates the corrected DIB.

Estimating uncertainties on the DIB EWs is not straightforward here, as there are different sources of errors. The error linked to measurement uncertainties can in principle be classically estimated. For the 219 spectra of this study, the signal-to-noise ratio varies between from 30 and 77 per pixel. It can be immediately derived that for a broad DIB covering about 6 Å (i.e. defined over more than 100 pixels and of about 10−15% depth, which corresponds to the 6284 Å one), the relative error due to the noise should only be very small. For the shallower and narrower DIBs, this is not the case. The other major source of uncertainties comes from the use of synthetic spectra, which have not been adjusted individually for all targets. As shown by Figs. 6 to 9, those uncertainties may approach the DIB itself depending on the star radial velocity, for the two small DIBs.

We have devised a method for error estimates that has the advantage of providing a corrective term for the DIB EW in addition to the errors. For each target, the (data − model) residuals for the best adjustment are shifted into the stellar frame. Those residuals are then sorted by metallicity. The corresponding 2D residual plot is shown in Fig. A.1 for the 6284 Å DIB. The x-axis is the wavelength in the star frame, and the y-axis is the metallicity. The color scale represents the value of the residuals. Obviously there are some features at specific wavelengths, some quite strong, and they are also obviously related to the metallicity. They correspond to stellar lines that are under- or overpredicted by the synthetic spectra. A large number of lines are simply unidentified. The next step is to use this map in the orthogonal direction, i.e., to extract the residual as a function of the metallicity, for each wavelength in the star frame. Examples of the obtained extracted series are shown in Figs. A.2 and A.3. Each of those metallicity-residual series of points is then fitted to a linear relationship, as shown in the two plots. For the wavelength corresponding to Fig. A.2, the residual is negative, and its absolute value increase strongly with the metallicity. This means that at this location there is a stellar line that is under-predicted and that the higher the metallicity, the greater the data-model discrepancy. At variance with this case, at the wavelength corresponding to Fig. A.3, the residual is on average zero and not related to the metallicity. This means that there is no stellar line at this location, or that the model does predict the line adequately. We then use both the fit coefficients (at each wavelength) to correct the previously computed DIB profile and the standard deviation around the mean relationship (again at each wavelength) to estimate the random (or quasi-random) remaining errors. More precisely, for each star we consider the wavelength interval that contains the entire DIB, and compute for each wavelength the most-probable residual as a function of the star metallicity, based on the linear relationships coefficients. We apply this correction over the whole DIB interval (as shown in Fig. A.4) and recalculate the DIB EW. Table 3 contains both the initial and corrected values for the EW for the three DIBs and all targets. We found that the recalculated EWs provide significantly improved DIB-DIB correlations, which demonstrates that this method provides a partial, but valid correction.

The distribution of data points around the mean residual-metallicity relationship provides an estimate of the combination of unpredictable uncertainties linked to the stellar lines and the actual noise). We then used the standard deviation measured for each relationship to compute the standard deviation at each wavelength, then propagated the errors on the whole DIB interval. In the case of the two narrow DIBs, this estimated uncertainty may be smaller in some cases than the actual errors; however, considering those deviations as systematic and not random leads to errors that are unrealistically large.

All Tables

All Figures

	Fig. 1 Target stars used in this study (black crosses) superimposed on the extinction map from Sumi (2004). The map is centered on (l,   b) = (0.8, − 4). Each pixel is 0.6′ × 0.6′. The extinction scale is displayed in Fig. 14. Stars are numbered according to Table 3. Dotted lines link stars in increasing order of their ID number. Only one out of five numbers is indicated for clarity.
In the text

	Fig. 2 Procedure flowchart of the fitting.
In the text

	Fig. 3 Model adjustment for Ogle N: 393009 (Teff = 5012 K). The DIB is in a region devoid of strong stellar lines. The upper panel shows the spectrum (red line) and the best-fit model (purple line). The lower panel shows the synthetic stellar model (yellow line), the synthetic atmospheric model (blue line), and the DIB profile (green line), which all correspond to the fit parameters.
In the text

	Fig. 4 Same as Fig. 3 for Ogle N: 392992 (Teff = 4907 K). The DIB here is in a spectral region characterized by moderately strong stellar lines.
In the text

	Fig. 5 Same as Fig. 3 for Ogle N: 89667 (Teff = 4516 K). The DIB here is both weak and embedded in strong stellar lines.
In the text

	Fig. 6 Same as Fig. 3 for the 6196 Å DIB and Ogle N: 412854 (Teff = 5191 K). The narrow DIB is in a region devoid of strong stellar lines.
In the text

	Fig. 7 Same a Fig. 6 for Ogle N: 234898 (Teff = 4714 K). The DIB and a strong stellar line do overlap.
In the text

	Fig. 8 Same as Fig. 3 for the 6204 Å DIB and Ogle N: 393033 (Teff = 4914 K). The narrow DIB is in a region devoid of strong stellar lines.
In the text

	Fig. 9 Same as Fig. 8 for Ogle N: 268068 (Teff = 4837 K). The DIB region corresponds to strong stellar lines.
In the text

	Fig. 10 Equivalent width (EW) of DIB 6196.0 Å as a function of the EW of DIB 6283.8 Å. The black line is the best linear fit for pure proportionality, using error bars of both DIBs.
In the text

	Fig. 11 Same as Fig. 10 for DIB 6204 Å.
In the text

	Fig. 12 From bottom to top, EWs of the three DIBs (6196, 6204, and 6284 Å) as a function of the star number and the extinction Av interpolated from the map of Sumi (2004) at each star location.
In the text

Fig. 13 Color excess EB − V derived from the three DIBs as a function of the EV − I value interpolated within the Sumi (2004) map at the locations of the target stars. EB − Vs here are obtained using the Raimond et al. (2012) and Puspitarini et al. (2012, priv. comm.) average relationships based on FEROS data. The blue and pink dotted lines correspond to color excess relationships based on the Fitzpatrick (1999) and Cardelli et al. (1989) extinction curves and Rv = 3.1 (see text). In the case of the DIBs 6283.8 Å we also show the color excess values deduced from the Friedman et al. (2011) average relationships (open triangles).

In the text

Fig. 14 Spatial variability of the DIB and the DIB-extinction ratio (from left to right, the 6284, 6204, 6196 Å DIBs). Target stars used in this study are superimposed on the Av extinction map from Sumi (2004) (gray scale). The size of the circle is proportional to the DIB EW, and its color corresponds to the ratio between the DIB EW and the extinction Av obtained by interpolation through the Sumi map (color scale).

In the text

	Fig. 15 Synthesis of all EB − Vs estimates from the 3 DIBs, in the form of a weighted mean, here compared with the EV − I determination from the OGLE photometry. The blue and pink dotted lines correspond to color excess relationships based on the Fitzpatrick (1999) and Cardelli et al. (1989) extinction curves.
In the text

	Fig. A.1 Residuals as a function of wavelength and metallicity for the DIB 6283.8 Å. They form the basis for the EW correction and the error estimate.
In the text

	Fig. A.2 Example of residuals vs. -metallicity relationships: here the residuals depend on the metallicity and are negative, which corresponds to an under-predicted stellar absorption line.
In the text

	Fig. A.3 Example of residuals vs. -metallicity relationships: here the residuals do not depend on the metallicity and are negligible.
In the text

	Fig. A.4 Schematic illustration of the correction applied to the EW measurements. The red curve represents the DIB profile as it comes out from the fitting phase. Hatched surfaces show the offsets applied at each wavelength that are computed for each star, as a function of its metallicity. The dashed line illustrates the corrected DIB.
In the text