AN STIS ATLAS OF Ca ii TRIPLET ABSORPTION LINE KINEMATICS IN GALACTIC NUCLEI^*

The study of supermassive black holes (SBHs) has been one of the most successful areas of Hubble Space Telescope (HST) research. The importance of SBHs was highlighted with the discovery that their masses (M_•) are seen to correlate with many properties of the galaxy bulges that host them, e.g., luminosity (Kormendy & Richstone 1995), stellar velocity dispersion, σ_* (Ferrarese & Merritt 2000; Gebhardt et al. 2000), concentration index (Graham et al. 2001), and potentially the dark matter halo mass (Ferrarese 2002; Baes et al. 2003). As these SBH–galaxy scaling relations intimately link the most basic characteristic of an SBH with the defining properties of the surrounding galaxy, they sparked significant efforts toward understanding the nature of black hole and galaxy formation and evolution (e.g., Ciotti & van Albada 2001; Adams et al. 2003; Heckman et al. 2004; Wyithe & Loeb 2005; Cattaneo et al. 2005; Robertson et al. 2006; Treu et al. 2007; Ciotti 2008).

While the fundamental importance of the SBH scaling relations is clear, their form remains dependent on establishing an unbiased and statistically significant number of high quality direct measurements of M_•. However, there are several fundamental difficulties with obtaining such a sample of M_•. For example, the relations are currently established over only a few orders of magnitude (7 ≲ log  M_• ≲ 9), there are potential selection effects and biases (Lauer et al. 2007; Batcheldor 2010), and there is an increasing population of galaxies that do not seem to follow the same relations defined by nearby early-type galaxies (Graham & Li 2009; Greene et al. 2010; Mathur et al. 2012; Graham et al. 2011). In addition, it is not clear whether the local scaling relations are consistent with each other (Tundo et al. 2007), or whether they may have experienced cosmic evolution (Treu et al. 2007). In addition, at present, the only way to estimate M_• outside of the local universe, and therefore determine if scaling relations have evolved, is to use the reverberation mapping technique (e.g. Peterson 1993) or derivatives thereof (Wandel et al. 1999). However, since about 2004, the geometrical factor in the reverberation-mapping virial relation has been calibrated using the M_•–σ_* relation (Onken et al. 2004), increasing still more the importance of establishing this relation.

There are predominantly two methods for directly estimating M_•: gas kinematics (GK) and stellar dynamics (SD). While not all galaxies contain nuclear gas disks (Tran et al. 2001), the Keplerian kinematics of gas is relatively easy to model (e.g., Ferrarese et al. 1996; Marconi et al. 2001) provided the gas is dominated by the gravitational potential of the SBH and not subject to significant inflow, outflow, or turbulence. In contrast, SD (e.g., van der Marel et al. 1998; Cretton et al. 1999; Verolme et al. 2002; Gebhardt et al. 2003; Valluri et al. 2004; van den Bosch & de Zeeuw 2010), does not suffer from non-gravitational influences and can theoretically be applied to all galaxies. However, unless the root-mean-square (rms) stellar velocities show a clear rise near the center, which is only true for a handful of galaxies, stellar dynamical models require significantly more data in order to constrain M_• and (compared with emission-line data) more observing time must be invested to accurately determine the line-of-sight velocity distributions (LOSVDs), particularly in the low-surface-brightness cores of bright galaxies.

A fundamental step in obtaining more high-accuracy direct estimates of M_• is to compile a list of galaxies that have the greatest potential for success. The Hughes et al. (2003) Space Telescope Imaging Spectrograph (STIS) atlas of nearby spiral galaxies has enabled the identification of nuclear disks ideal for further M_• estimates using GK, however, there does not exist a similar atlas for SD. Consequently, we present such an atlas here. For each of the galaxies in the chosen sample we provide the signal-to-noise (S/N) profile across the STIS slit. In addition, we present the inferred moments of the LOSVDs derived from the highest S/N spectra in each galaxy. Finally, we identify those galaxies in the HST archive that may produce further estimates of M_• from SD. In Section 2 we describe the sample. The details of the data reduction are in Section 3. The results are compiled in Section 6 and discussed in Section 7. Section 8 concludes.

In order to determine the relative suitability of the available data for SBH modeling we use two approaches. First, we calculate the S/N profiles of each galaxy across the STIS slit. Second, we match appropriate stellar templates to the Ca ii absorption features and determine how well the central LOSVDs can be recovered. Therefore, standard stars that have been collected using identical set ups to the galaxies observed must also be recovered from the HST archive. Late-type G, K and M stars are ideal to best match the stellar populations at the centers of galactic bulges. Currently, there are eight stellar templates in the archive that have been observed with the same set up as the galaxy sample. However, as detailed in Section 3, only three of these have the appropriate contemporaneous calibration flat fields necessary to satisfactorily remove near-infrared fringing. The details of these standard stars are presented in Table 1.

Table 1. Available STIS Ca ii Stellar Absorption Line Data for Standard Stars

Name	Type	Vmag	Slit	Binning	Data Sets	Exp.	Fringe Data Set	PID	Date-Obs
						(s)
HD 141680	G8 III	5.23	01	x1	O67117020	2.2	O67117030	8591	2001 Apr 4
			02	x1	O67117040	2.2	O67117050
HR 6770	G8 III	4.65	01	x2	O4AN18010, 20, 30, 40, 50	2.2	O4AN18060	7388	1998Sep 6
			02	x2	O4AN18070, 80, 90, A0, B0	2.2	O4AN180C0
HR 7576	K3 III	5.03	01	x2	O4AN17010, 20, 30, 40, 50	3.2	O4AN17060	7388	1998 May 24
			02	x2	O4AN17070, 80, 90, A0, B0	3.2	O4AN170C0

Notes. Suitable LOSVD late-type template standard stars available in the HST archive that include contemporaneous flat fields necessary for defringing. "Slit" is the width of the STIS long-slit used in arc-seconds. "Binning" is the on-chip binning used in the dispersion direction. "PID" is the HST program during which these observations were taken.

Download table as:  ASCIITypeset image

We have selected all NASA Extra-galactic Database (NED)⁵ identified non-barred galactic bulges in the HST archive that have G750M STIS long-slit spectra (52'' × 01 or 52'' × 02) centered at 8561 Å. The high spatial resolution and sensitivity of HST make it the natural choice from which to compile a sample of galactic bulges suitable for stellar dynamical modeling of the central SBH. Indeed, most M_• estimates to date are a result of HST observations, many of which are included in this sample for comparison purposes. We exclude barred-spirals as dynamical models that can accommodate triaxial potentials are still under development. To avoid any possible selection bias (Batcheldor 2010), we do not discard any galaxy based on spatially resolving the predicted SBH sphere of influence. The G750M grating, centered at 8561 Å, ensures the Ca ii stellar absorption triplet (8500 Å, 8544 Å & 8665 Å vacuum) can be observed at the highest possible spectral resolution. This enables a better determination of the LOSVDs needed for dynamical models. The archive does contain 3 additional galaxies that have been observed at the wavelengths of the Mgb triplet (G430M), however the Ca ii triplet is favored due to a reduced impact from standard star template mismatching. This selection results in 42 galaxies, the details of which are compiled in Table 2.

Table 2. Available STIS Ca ii Stellar Absorption Line Data for Non-barred Galactic Nuclei

Name	Class	D (ref.)	log M• (ref.)	Slit	Binning	Exp. Time	Prop. ID	σ*
		(Mpc)	(M☉)			(s)		(km s−1)
NGC 205	E5 pec	0.82 (1)	<4.34 (s, 7)	01	x1	24132	9448	31 ± 5
NGC 221	cE2	0.81 (2)	$6.40_{-0.10}^{+0.08}$ (s, 8)	01	x1	4899	7566	72 ± 2
NGC 224	SA(s)b	0.79 (1)	$8.15_{-0.11}^{+0.21}$ (s, 9)	01	x1	20790	8018	170 ± 5
NGC 598	SA(s)cd	0.81 (1)	<3.48 (s, 10)	01	x1	7380	8018	37 ± 16
NGC 821	E6	24.10 (2)	$7.93_{-0.23}^{+0.15}$ (s, 11)	01	x2	27478	7388	200 ± 3
NGC 1374	E3	19.77 (2)	...	01	x1	7372	9107	186 ± 4
NGC 1700	E4	44.26 (2)	...	02	x2	7170	7566	239 ± 4
NGC 2434	E0-1	21.58 (2)	...	02	x1	28400	9107	187 ± 7
NGC 2778	E	22.91 (2)	$7.15_{-0.45}^{+0.19}$ (s, 12)	01	x2	15026	7388	162 ± 3
NGC 2784	SA(s)	9.82 (2)	...	01	x1	8740	8591	225 ± 7
NGC 2841	SA(s)b	14.06 (3)	...	02	x2	7990	8022	206 ± 4
NGC 3031	SA(s)ab	3.91 (2)	$7.88_{-0.07}^{+0.11}$ (g, 13)	02	x1	39200	7350	162 ± 3
NGC 3115	S0-	9.68 (2)	$8.96_{-0.16}^{+0.33}$ (s, 14)	01	x1	7360	7566	267 ± 4
NGC 3585*	E7/S0	20.04 (2)	$8.53_{-0.08}^{+0.16}$ (s, 23)	01	x1	12241	9107	206 ± 7
NGC 3593	SA(s)	9.72 (4)	...	01	x1	5990	8591	54 ± 7
NGC 3607	SA(s)	22.80 (2)	$8.08_{-0.18}^{+0.12}$ (s, 23)	02	x1	26616	9107	224 ± 10
NGC 3608	E2	22.91 (2)	$8.28_{-0.17}^{+0.18}$ (s, 12)	02	x2	12950	7388	192 ± 4
NGC 3706*	SA(rs)	38.02 (5)	...	01	x1	15174	8687	270 ± 8
NGC 3998	SA(r)	14.13 (2)	$8.91_{-0.12}^{+0.09}$ (g, 15)	02	x1	21840	7350	280 ± 15
NGC 4026	S0	13.61 (2)	$8.32_{-0.13}^{+0.09}$ (s, 23)	01	x1	9973	9107	178 ± 4
NGC 4278	E1-2	16.07 (2)	...	02	x2	17502	7350	237 ± 5
NGC 4291	E3	26.18 (2)	$8.49_{-0.59}^{+0.10}$ (s, 12)	02	x2	16013	7388	285 ± 6
NGC 4382	SA(s)0+ pec	17.86 (6)	...	02	x1	18794	9107	179 ± 5
NGC 4473	E5	15.70 (2)	$8.04_{-0.56}^{+0.14}$ (s, 12)	02	x2	12840	7388	179 ± 3
NGC 4486	E+0-1 pec	17.22 (6)	$9.81_{-0.04}^{+0.03}$ (g, 16)	02	x2	25300	7567	334 ± 5
NGC 4486A	E2	18.28 (6)	$7.11_{-0.41}^{+0.21}$ (s, 17)	02	x1	21112	8687	135 ± 4
NGC 4486B	cE0	16.29 (6)	$8.78_{-0.18}^{+0.17}$ (s, 18)	02	x2	14530	7566	169 ± 4
NGC 4552	E	15.85 (6)	$8.68_{-0.08}^{+0.07}$ (s, 19)	02	x2	7490	8022	253 ± 3
NGC 4564	E6	15.85 (6)	$7.75_{-0.07}^{+0.02}$ (s, 12)	01	x2	15060	7388	157 ± 3
NGC 4621	E5	14.93 (6)	$8.60_{-0.07}^{+0.06}$ (s, 19)	02	x1	4340	8018	225 ± 3
NGC 4649	E2	17.30 (2)	$9.30_{-0.15}^{+0.08}$ (s, 12)	02	x2	46467	7388	335 ± 5
NGC 4697	E6	11.75 (2)	$8.23_{-0.03}^{+0.05}$ (s, 12)	01	x2	26920	7388	171 ± 2
NGC 4736	(R)SA(r)ab	5.20 (2)	...	01	x1	5769	8591	104 ± 4
NGC 4742	E4	15.49 (2)	$7.15_{-0.20}^{+0.11}$ (s, 20)	02	x1	7130	8018	108 ± 4
NGC 4826	(R)SA(rs)ab	7.48 (2)	...	01	x1	5990	8591	92 ± 4
NGC 5033	SA(s)c	17.22 (5)	...	02	x1	10300	9776	131 ± 7
NGC 5055	SA(rs)bc	8.75 (5)	$8.93_{-0.11}^{+0.09}$ (g, 21)	01	x1	4190	8591	101 ± 3
NGC 5102	SA0-	4.00 (2)	...	01	x1	4592	8591	...
NGC 5576	E3	25.47 (2)	$8.26_{-0.11}^{+0.06}$ (s, 23)	01	x1	7138	9107	171 ± 5
NGC 7213	SA(s)	22.70 (5)	...	01	x1	7603	9107	163 ± 9
NGC 7332	S0 pec sp	24.89 (2)	$7.11_{-0.21}^{+0.19}$ (s, 22)	02	x1	9870	7566	125 ± 3
NGC 7457	SA(rs)0-?	13.24 (2)	$6.54_{-0.22}^{+0.12}$ (s, 12)	01	x2	15282	7388	69 ± 4

Notes. Non-barred galactic bulges with Ca ii stellar dynamics observed by STIS (G750M, 8561 Å). Galaxies marked with * also have 02 slit widths available. Class: NED classifications. Method codes: s, stellar dynamics; g, gas dynamics. The values of σ_* are those listed as central velocity dispersions by Hyperleda (http://leda.univ-lyon1.fr/; Paturel et al. 2003). "Slit" is the width of the STIS slit used. "Binning" is the on-chip binning used in the dispersion direction. "Exp.Time" is the total exposure time. References. (1) McConnachie et al. 2005; (2) Tonry et al. 2001; (3) Macri et al. 2001; (4) Wiklind & Henkel 1992; (5) NED (Virgo+GA+Shapley corrected Hubble flow distances); (6) Mei et al. 2007; (7) Valluri et al. 2005; (8) Joseph et al. 2001; (9) Bender et al. 2005; (10) Merritt et al. 2001; (11) Richstone et al. 2004; (12) Gebhardt et al. 2003; (13) Devereux et al. 2003; (14) Emsellem et al. 1999; (15) Walsh et al. 2012; (16) Gebhardt & Thomas 2009; (17) Nowak et al. 2007; (18) Kormendy et al. 1997; (19) Hu 2008; (20) Tremaine et al. 2002; (21) Blais-Ouellette et al. 2004; (22) Häring & Rix 2004; (23) Gültekin et al. 2009.

Download table as:  ASCIITypeset image

After being passed through the latest CALSTIS pipeline for on-the-fly-recalibration using the best reference files, all data were retrieved from the HST archive. At wavelengths longer than ∼7000 Å, STIS experiences significant fringing from multiple reflections between the two surfaces of its CCD. More extensive details of the issue can be found in several Instrument Science Reports, i.e., ISR 97-16 (Walsh et al. 1997), ISR 98-19 (Goudfrooij et al. 1998), ISR 98-29 (Goudfrooij & Christensen 1998). For the G750M grating centered at 8561 Å the amplitude of the fringes can be between 10%–15% for observations with a S/N > 50; the relative effects of fringing are much more difficult to detect in low S/N data. Thus, fringing will have an impact on the standard star observations, and potentially the galaxy data. In addition, due to the non-repeatability in the position of some of the STIS mechanisms, the fringe patterns are not stationary with time, i.e., a standard fringe flat field cannot be used. Therefore, in every case, the appropriate contemporaneous fringe flats were also retrieved from the HST archive; these are not normally included in the calibration files distributed with archived data. Care must be taken to ensure the most appropriate fringe flat field is used. For example, there are differences in the removal of the fringe pattern when observing point and diffuse sources, and when using different slit widths. This will be more thoroughly detailed in the following sections.

3.1. Standard Stars

All three standards were observed using the 01 and 02 slit widths. The data from the two slit widths are treated separately so that an appropriate template can be generated to match the slit widths used on the galaxies. Contemporaneous fringe flats were recovered that are optimized for these slits widths and for point sources, i.e., fringes observed through the 02 × 006 slit for the 52'' × 01 observations, and 03 × 009 for the 52'' × 02 observations (the use of these short-slit fringe flats better mimic the point spread function than the long-slit flats; Goudfrooij et al. 1998). In addition, the data for HD 141680 was not binned on-chip, whereas the HR 6770 and HR 7576 data was binned by 2 pixels in the dispersion direction. The galaxy sample contains both un-binned and 2 pixel binned data, so the binned and un-binned template stars are also treated separately.

After the pipeline reduced data had been defringed, large amplitude variations were still noted in the central row of the spectra. This is attributed to a small residual misalignment between the dispersion direction of the spectra and the pixel rows. This was confirmed by performing a column-by-column trace of the spectrum peak. The peak positions correlate with the amplitude variation in the central row. This residual misalignment can be removed by re-centering the spectra column-by-column to a common position, or by collapsing the data across the slit width (7 and 9 pixels for the 01 and 02 slits, respectively). There is no significant difference between the resulting spectra produced either way, so the intra-slit collapse was used for the sake of simplicity. The improvement to the template spectra as a result of defringing is demonstrated in Figure 1 for HD 141680. The standard deviation of the residual spectra between the defringed and final spectra is 5%.

Zoom In Zoom Out Reset image size

HD 141680 was only observed at a single spatial slit position. However, in order to map the line profiles across the slit, spatial steps across the positions of HR 6770 and HR 7576 have been performed, thus producing five spectra at different locations for each of these standards. In each visit to these standards, the 01 slit data was gathered first. Therefore, in both cases the brightest spectra come from the slit with zero spatial offset (POSTARG1 = 0.00). However, the brightest spectra are found in the POSTARG1 = 0.04 position for the 02 slits. In both cases it was found that the guide star acquisition had failed, and that the pointing of HST had drifted slightly over the ∼16 minute period between the peak-up and beginning of the 02 slit observations. Only data from the brightest spectra are used to generate the stellar template.

For the galaxy data that is un-binned, to preserve the maximum spectral resolution there is only one choice of template star to estimate the LOSVDs (HD 141680). However, for the galaxy data binned by 2 pixels there is HR 6770 and HR 7576. Plus, the HD 141680 data can be additionally binned by 2 dispersion pixels to create a third useful standard. To reduce the possibility of template mismatching, a composite template is produced by normalizing each individual standard spectra and averaging them together. Thus, we are left with four templates. Templates A and B are the un-binned HD 141680 data using the 01 and 02 data, respectively. Templates C and D are the 2 pixel binned data generated from a composite of all three standards using the 01 and 02 data, respectively. Two templates (B and D) are presented in Figure 1 for the 02 slit. Gaussian fits to the prominent Ca ii triplet shows the centers of the lines to be within 10 km s⁻¹ of the vacuum values expected, indicative to the level of precision in the data reduction techniques and the heliocentric velocity corrections."

3.2. Galaxies

The S/N in a spectrum is one obvious, and frequently used, method for assigning a measure of quality to data. Therefore, in determining the suitability of galaxies for future dynamical modeling aimed at constraining M_•, calculating the S/N in the STIS spectra is a natural first step. However, this seemingly trivial exercise is not necessarily as straightforward as one may think; one cannot simply take the square-root of the detector data number as this would neglect, for example, background counts and read noise. None of the standard post-pipeline data reduction tasks specifically deal with data quality or error propagation. One could consider calculating the ratio of the mean flux and standard deviation along the spectra. However, such calculations would be contaminated by absorption and emission lines at varying wavelengths and widths.

However, to include both the science and reference file errors, the pipeline does propagate through the per pixel statistical errors estimated from the bias subtracted observed data number (counts), the gain and the read noise. These data are assigned to an error array that is included in the second extension of the pipeline provided data files. So, it is possible to assign a per pixel S/N based on the ratio of the science array to the error array. Indeed, this is how the pipeline assigns the header parameters that show the maximum, minimum and mean S/N (〈S/N〉) in a processed data array. Unfortunately, this does not provide the S/N in an individual spectra. Therefore, the error arrays have been extracted, squared, aligned using the same offsets calculated for the science arrays, median combined and then square rooted. The S/N arrays are then created simply by dividing the co-aligned and combined science array by the equivalent error array. This provides an array from which we can extract the S/N in any pixel, or along any spectrum.

Table 3 presents the S/N for the standard stars. The maximum per pixel values from the S/N arrays are consistent with the maximum per pixel S/N calculated by the pipeline. The small differences will be due to the defringing process that is not accounted for in the pipeline calculated S/N. However, these S/N values are based on single pixels so, while they do demonstrate that our S/N array is consistent with the pipeline S/N calculations, they do not provide any information on the S/N present in the spectra. Consequently, the mean and standard deviation of the S/N from the brightest template spectra are also presented in Table 3. These values are lower than the peak per pixel S/N by ≲15%, which can be attributed to including the lower S/N across the absorption lines. In addition, the 〈S/N〉 ratios calculated here are consistent with those expected from the STIS exposure time calculator⁶ (ETC). The spatial 〈S/N〉 profiles for each standard star are presented in Figure 2.

Zoom In Zoom Out Reset image size

Table 3. S/N Tests for the Standard Stars

Name	Slit	SNRMAX	S/Npeak	〈S/N〉
HD 141680	01	93.8	95.6	80 ± 7
	02	96.4	98.2	75 ± 11
HR 6770	01	166.7	169.1	146 ± 9
	02	173.2	185.1	162 ± 10
HR 7576	01	171.8	192.8	169 ± 10
	02	170.5	203.3	176 ± 10

Notes. Signal-to-noise ratios for the standard stars. SNRMAX is the pipeline header parameter for the reduced templates. It is the maximum S/N calculated in a single pixel. S/N_peak is the maximum per pixel S/N calculated from our S/N arrays. 〈S/N〉 is the mean and standard deviation of the S/N along the peak spectra from our S/N array.

Download table as:  ASCIITypeset image

In column 2, Table 4 lists the 〈S/N〉 along the peak galaxy spectra. An interesting check is to compare our calculated S/N values to those predicted by the STIS ETC. Figure 3 presents such a comparison. To be consistent with the S/N arrays, the ETC S/N values were estimated using the peak galaxy flux in a single pixel at 8500 Å, and the median of the S/N values that resulted from the individual (pre-combined) exposure times. Figure 3 shows good agreement between the two methods. Some scatter is expected because the ETC S/N calculations have used updated sensitivity values as the detector has aged. As LOSVDs over a spatially extended region are necessary to constrain M_• models the S/N spatial profiles are also presented for all galaxies in Figure 4.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

View figure set (42 panels)

Tarball of figure set images

Table 4. Results from the MPL Routine

Name	Template	〈S/N〉	ISE	α	vc	σc	h3	h4
1	2	3	4	5	6	7	8	9
NGC 205*	A	4.5	3.82	3.4	$-232^{+3}_{-4}$	$21^{+5 }_{-3}$	$0.03^{+0.03}_{-0.09}$	$0.05^{+0.03}_{-0.04}$
NGC 221*	A	25.2	1.1	5.4	$-195^{+19}_{-6}$	$165^{+21}_{-29}$	$0.03^{+0.06}_{-0.06}$	$0.1^{+0.05}_{-0.06}$
NGC 224*	A	8.6	1.64	6.7	$-175^{+27}_{-14}$	$168^{+25}_{-22}$	$-0.15^{+0.08}_{-0.04}$	$0.03^{+0.06}_{-0.04}$
NGC 598*	A	13.7	1.62	2.9	$-180^{+2}_{-2}$	$19^{+3 }_{-2}$	$0.07^{+0.05}_{-0.08}$	$0.02^{+0.04}_{-0.02}$
NGC 821*	B	8.3	1.81	8.9	$1734^{+27}_{-70}$	$354^{+35}_{-58}$	$0.11^{+0.05}_{-0.11}$	$0.03^{+0.06}_{-0.06}$
NGC 1374	A	3.7	6.84	9	$1244^{+122}_{-44}$	$338^{+31}_{-60}$	$-0.09^{+0.16}_{-0.08}$	$-0.04^{+0.08}_{-0.07}$
NGC 1700	D	14.1	1.42	10.3	$3732^{+82}_{-36}$	$468^{+5 }_{-100}$	$-0.01^{+0.06}_{-0.05}$	$0.01^{+0}_{-0.05}$
NGC 2434	C	6.2	2.6	10	$1496^{+44}_{-25}$	$369^{+7 }_{-18}$	$-0.08^{+0.05}_{-0.02}$	$-0.06^{+0.06}_{0}$
NGC 2778*	B	6.2	2.97	8.1	$2058^{+33}_{-45}$	$191^{+52}_{-20}$	$0^{+0.1}_{-0.11}$	$-0.06^{+0.1}_{-0.03}$
NGC 2784	A	5.1	3.69	8.2	$617 ^{+42}_{-58}$	$265^{+62}_{-48}$	$0^{+0.07}_{-0.08}$	$0.09^{+0.05}_{-0.08}$
NGC 2841	D	13	1.51	9.6	$692 ^{+26}_{-55}$	$327^{+21}_{-52}$	$0.12^{+0}_{-0.11}$	$0.06^{+0.02}_{-0.07}$
NGC 3031	C	26.7	...	...	...	...	...	...
NGC 3115	A	13.3	1.52	11	$674 ^{+43}_{-66}$	$466^{+51}_{-17}$	$0^{+0.03}_{-0.03}$	$-0.02^{+0.02}_{-0}$
NGC 3585*	A	5.5	3.38	8.5	$1434^{+74}_{-46}$	$312^{+36}_{-97}$	$-0.15^{+0.12}_{-0.02}$	$0.05^{+0.05}_{-0.1}$
NGC 3593	A	4.3	11.12	6.5	$636 ^{+7}_{-22}$	$72^{+15}_{-12}$	$0.11^{+0}_{-0.18}$	$0.01^{+0.03}_{-0.03}$
NGC 3607*	C	2.9	3.82	9.6	$899 ^{+30}_{-28}$	$253^{+4 }_{-23}$	$0.02^{+0.01}_{-0.05}$	$-0.03^{+0.03}_{-0.01}$
NGC 3608*	D	9.1	1.45	11.4	$1170^{+38}_{-35}$	$338^{+25}_{-56}$	$0^{+0}_{-0}$	$0^{+0}_{-0.01}$
NGC 3706	A	3.5	4.65	7.8	$3002^{+22}_{-49}$	$173^{+29}_{-21}$	$0.05^{+0}_{-0.12}$	$-0.04^{+0.08}_{-0.03}$
NGC 3998	C	19.9	...	...	...	...	...	...
NGC 4026*	A	8.4	2.36	9.6	$974 ^{+21}_{-42}$	$352^{+26}_{-35}$	$0.01^{+0.02}_{-0.04}$	$-0.01^{+0.01}_{-0.03}$
NGC 4278	D	5.6	...	...	...	...	...	...
NGC 4291*	D	8.3	1.49	12	$1892^{+56}_{-91}$	$515^{+21}_{-67}$	$-0.01^{+0.01}_{-0.01}$	$-0.01^{+0.01}_{-0}$
NGC 4382	C	4.1	3.08	11.6	$693 ^{+6}_{-16}$	$180^{+1}_{-1}$	$0^{+0}_{-0}$	$0^{+0}_{-0}$
NGC 4473*	D	8.8	1.95	8.5	$2305^{+37}_{-40}$	$253^{+17}_{-47}$	$0.05^{+0.08}_{-0.09}$	$-0.06^{+0.13}_{-0}$
NGC 4486	D	16.8	...	...	...	...	...	...
NGC 4486A	C	3.4	3.04	7.3	$798 ^{+25}_{-15}$	$153^{+22}_{-20}$	$0.04^{+0.07}_{-0.09}$	$0.07^{+0.04}_{-0.06}$
NGC 4486B	D	10.8	4.37	8.6	$1542^{+47}_{-99}$	$254^{+66}_{-40}$	$0.04^{+0.11}_{-0.15}$	$-0.04^{+0.11}_{-0.05}$
NGC 4552	D	9.5	2.32	12	$356 ^{+39}_{-50}$	$259^{+1 }_{-9}$	$0^{+0}_{-0}$	$0^{+0}_{-0}$
NGC 4564*	B	10.5	2.94	11.5	$1113^{+18}_{-22}$	$159^{+1}_{-2}$	$0^{+0}_{-0}$	$0^{+0}_{-0}$
NGC 4621	C	13.9	...	...	...	...	...	...
NGC 4649*	D	4.3	2.12	10.4	$822 ^{+136}_{-54}$	$551^{+35}_{-82}$	$-0.1^{+0.1 }_{-0.03}$	$0.01^{+0.03}_{-0.05}$
NGC 4697*	B	9.6	1.34	8.4	$1290^{+17}_{-43}$	$224^{+23}_{-24}$	$0.1^{+0.03}_{-0.09}$	$0.01^{+0.05}_{-0.04}$
NGC 4736	A	9.7	3.42	6.7	$343 ^{+15}_{-13}$	$101^{+12}_{-14}$	$-0.06^{+0.07}_{-0.05}$	$0.05^{+0.02}_{-0.05}$
NGC 4742	C	19.8	1.32	5.8	$1317^{+11}_{-16}$	$107^{+14}_{-11}$	$0.04^{+0.06}_{-0.08}$	$-0.03^{+0.06}_{-0.05}$
NGC 4826	A	4.1	5.92	6.4	$442 ^{+17}_{-121}$	$112^{+5 }_{-35}$	$0.03^{+0.09}_{-0.12}$	$0.09^{+0.01}_{-0.11}$
NGC 5033	C	10	2.49	10.6	$890 ^{+23}_{-19}$	$242^{+2 }_{-24}$	$-0.01^{+0.01}_{-0}$	$0^{+0}_{-0.01}$
NGC 5055	A	12.4	2.39	5.8	$493 ^{+22}_{-13}$	$119^{+18}_{-22}$	$-0.15^{+0.1}_{-0.06}$	$0.02^{+0.08}_{-0.07}$
NGC 5102	A	24.4	1.63	5.6	$496 ^{+8}_{-13}$	$97^{+6 }_{-13}$	$-0.06^{+0.17}_{-0.05}$	$-0.06^{+0.17}_{-0}$
NGC 5576*	A	4	6.83	8.8	$1607^{+31}_{-72}$	$238^{+39}_{-41}$	$0.14^{+0.01}_{-0.15}$	$0.03^{+0.04}_{-0.07}$
NGC 7213	A	11.4	...	...	...	...	...	...
NGC 7332	C	14	1.05	6.9	$1201^{+14}_{-8}$	$123^{+14}_{-6}$	$-0.08^{+0.07}_{-0.04}$	$-0.03^{+0.06}_{-0.01}$
NGC 7457*	B	9.9	1.28	4.5	$660 ^{+27}_{-39}$	$61^{+15}_{-18}$	$0.28^{+0.03}_{-0.08}$	$0.31^{+0.08}_{-0.01}$

Notes. Galaxies marked * are those with M_• presented in the peer reviewed literature. Galaxies without data are those potentially contaminated by LINER [Fe ii] λ8616 emission. The letters associated with the template stars used to make the fits are matched to the observing setups for the galaxies (Table 2). A: 01 slit, x1 binning; B: 01, x2; C: 02, x1; D: 02, x2. The ranges given for the estimated LOSVD parameters are the 95% bootstrap confidence bands.

Download table as:  ASCIITypeset image

S/N alone cannot be used to quantify the quality of an estimated LOSVD. There have been many methods used to recover LOSVDs from galaxies using template spectra (e.g., Simkin 1974; Sargent et al. 1977; Franx et al. 1989; Bender 1990; Rix & White 1992; Kuijken & Merrifield 1993; van der Marel & Franx 1993; Batcheldor et al. 2005). The current trend in inferring the moments of LOSVDs has been to use a maximum penalized likelihood (MPL) method (e.g., Pinkney et al. 2003; Cappellari & Emsellem 2004). As it is known to perform well in the case of low S/N spectra, we use a well established MPL method here (Merritt 1997).

In brief, the MPL approach uses a velocity grid to estimate the true LOSVD based on an optimal fit between a convolved stellar template and the galaxy spectrum. No implicit assumptions are made about the form of the LOSVD, and a penalty is applied to the fit based on the level of smoothness in the estimated LOSVD (where α is the smoothing factor). As α is increased, the estimated LOSVD tends toward a Gaussian, therefore it is desirable to introduce as little smoothing as possible to limit the amount of bias in the estimated LOSVD. While the MPL approach estimates the LOSVD non-parametrically, the LOSVD is parameterized using the Gauss–Hermite series. The h₃ and h₄ coefficients of the Gauss–Hermite series (which are similar to skewness and kurtosis, respectively) can then be used to correct the estimated velocity dispersion, $\sigma _c = \sigma _0(1+\sqrt{6}h_4)$, and radial velocity, $v_c = v_0 + \sqrt{3}\sigma _0h_3$ (van der Marel & Franx 1993; Gerhard 1993).

Our MPL procedure for the STIS spectra was as follows. First, we match the observational setups for the template spectra and the galaxy spectra, i.e., the binning and slit width of the data to the four different templates. The optimum (lowest) value of the smoothing parameters was then determined by progressively increasing α in 0.1 increments until there was only a single stationary point in the estimated LOSVD at the radial velocity, i.e., α was slowly increased until the fluctuations from grid point to grid point disappeared; the estimated LOSVD was smooth, single, and not overly biased. The number of velocity grid points used was then adjusted to ensure the value was large enough to have no influence on the inferred moments of the LOSVD. The confidence in the LOSVD moments was then determined by a bootstrap. If the resulting confidence intervals did not fall either side of the optimal values, α was increased and the bootstrap repeated.

Table 4 presents the values of α used and the outputs from the MPL routine. It includes the integrated square error (ISE) between the estimated LOSVD and the observed spectra (Merritt 1997). Figure 4 presents the estimated LOSVDs with respect to the observed spectra, along with the spatial position of the STIS slit overlaid on the acquisition image. The full figure set also contains radial S/N profiles for each galaxy to demonstrate the spatial extent of the data.

In four cases (NGC 3608, NGC 4382, NGC 4552 and NGC 4564), the values of h₃ and h₄ have been driven to zero by large smoothing parameters (α ⩾ 11.4). This is to be expected in such cases where the required smoothing parameter forces the LOSVD toward a Gaussian. However, there is no relation between α and S/N. For example, NGC 1374, NGC 3607, NGC 3706 and NGC 4486A all have S/N < 4 but α ⩽ 9.6).

In six cases (those with only the S/N presented in Table 4) no estimates of the LOSVD were possible. Each of these galaxies are known to host low-ionization nuclear emission-line regions (LINERs), and we see a clear signature of [Fe ii] λ8616 in NGC 3031 (the highest S/N case) and NGC 3998. However, Fe ii] λ8616 emission is not detected in NGC 4278, NGC 4621 and NGC 7213. The STIS spectrum for NGC 4486 seems to be featureless, despite having a S/N much greater than members of the sample with well defined LOSVD. However, NGC 4486 is the dominant elliptical in the Virgo cluster with the most massive reported SBH in our sample. Compared to a less massive giant elliptical in the Virgo cluster, NGC 4649 where $\sigma _c=551^{35}_{-82}$ km s⁻¹, an intrinsic value of σ_c > 550 km s⁻¹ is expected for NGC 4486. As demonstrated in the online version of Figure 4 for NGC 4649, when σ_c becomes this large the signature of the absorption lines becomes very small—almost negligible. These absorption line signatures would be even less if σ_c in NGC 4486 is intrinsically larger than 550 km s⁻¹. However, it is the low number of constraining data points left in the template spectrum, once it has been broadened to >575 km s⁻¹, that prevents an estimate of the LOSVD to be made.

Of the remaining sample, 15 have peer reviewed M_• estimates made using the spectra presented in Figure 4. The reference for NGC 4742 (Tremaine et al. 2002) leads to an unpublished paper (M. E. Kaiser et al. 2002, in preparation), and the NGC 7332 reference (Häring & Rix 2004) quotes a private communication. As a consequence, both of these galaxies are considered part of the "yet to be modeled" sample. As noted by Graham (2008), the M_• estimates quoted for NGC 4552 and NGC 4621 (Hu 2008) have been extracted from the figures of an IAU Symposium article (Cappellari et al. 2008). Therefore, both of these galaxies are also considered to be part of the "yet to be modeled" sample. NGC 205 and NGC 598 only have upper limits to M_• and are also excluded. These 15 galaxies allow us to examine whether there are any fundamental relationships between the uncertainty of the inferred moments of the LOSVDs and the M_• estimates (Figure 4). The uncertainty in the M_• estimates presented in Table 2, where δM_•(the published range of acceptable values) is compared to the S/N, α, the ISE, and the uncertainty in the inferred moments of the LOSVD, where δσ = (σ_max − σ_min) for example. Figure 5 demonstrates the uncertainty in M_• is independent of the quality of the LOSVDs, and that the S/N ⩽10 in all but one case (NGC 221).

Zoom In Zoom Out Reset image size

To determine the suitability of the 19 remaining STIS spectra for estimates of SBH masses, we can compare the distributions of uncertainty in the inferred moments of the LOSVDs for these galaxies with the 15 galaxies from before (Figure 6). Immediately apparent are two galaxies with high S/N and low uncertainties (NGC 5102 and NGC 4742). As noted for Figure 5, NGC 221 also lies in the same high S/N-low uncertainty region of Figure 6. However, aside from these three cases, there are no statistically significant differences between those data already used to estimate M_• and those that have not.

Zoom In Zoom Out Reset image size

From these data, NGC 5102 and NGC 4742 have the highest potential for new high quality estimates of M_• using SD. Both show high S/N and low uncertainties in their LOSVDS. In addition, they have spatially extended data with good S/N (that may provide excellent constraints on the bulge gravitational potential), and very prominent Ca ii absorption. This is not the case for the majority of the remaining spectra however.

To the unaided eye, many galaxies in the sample do not exhibit obvious absorption-line features, including some galaxies for which estimates of M_• have already been published. The S/N levels are also all very low. This demonstrates the advantages of MPL; even with data such as these relative uncertainties of ∼10% in v_c and ∼20% in σ_c can be recovered. The quality of these spectra will, however, deteriorate as spatial positions either side of the S/N peaks are sampled to constrain the gravitational potential. Regardless, M_• estimates with relative uncertainties of ∼70% ± 30% mostly from Gebhardt et al. (2003) and Gültekin et al. (2009), have been extracted from these data, and there is nothing to indicate that the remaining 19 galaxies would not yield many useful estimates of M_•. It is not unexpected that these galaxies have yet to have M_• estimates attempted; in most cases these data have not be collected with the express purposes of determining M_•.

We find no correlation between S/N and the inferred moments of the LOSVD. Therefore, there is no simple way to determine the relative uncertainty of any LOSVD, and as a consequence M_•, based solely on an estimated S/N from an exposure time calculator. Principle component analysis may reveal a deeper relationship between S/N and the relative uncertainties in the estimated LOSVD, but our aim here is to simply determine the best candidates in the archive for further M_• modeling. However, there are only a very limited number of suitable stellar templates with which to extract the LOSVDs. Consequently, it is possible that some of the scatter seen in the uncertainties may be due to various levels of template mismatching between the galaxy spectra and standard stars. Increasing the variety of standard stars observed with STIS using a multitude of common instrument configurations would be beneficial in this case. In addition, some improvements may result from using the extensive stellar libraries of Cenarro et al. (2001) as kinematic templates, and by using linear combinations of the stellar template spectra currently available that may better match the galaxy spectra.

Non-gravitational kinematics, nuclear star clusters, multiple nuclei, dust, spatially offset SBHs, triaxial potentials, dark matter halos and mathematical degeneracy of solutions (Valluri et al. 2004) may all play non-trivial roles in the complexity of estimating δM_•, so the lack of correlation between δM_• and the estimated LOSVD parameters in Figure 5 is not surprising. Indeed, many of these factors determine the complexity of the observed absorption features and consequently the precision with which the LOSVD can be estimated. As a result, the lack of correlation seen between S/N and the estimated LOSVD parameters in Figure 6 is also not surprising. For example, NGC 205 has a peak S/N of 4.5, a small smoothing parameter (3.4), but easily detected Ca ii absorption. The absolute uncertainty in the radial velocity is 6.8 km s⁻¹(3% relative). Conversely, NGC 221 has a peak S/N of 25.22, α = 5.4, with less easily detected Ca ii absorption. Here the absolute uncertainty in radial velocity is 25 km s⁻¹(8% relative). Both these objects are well known dwarf galaxies, but the differences in the relative uncertainty in the LOSVDs are not unexpected when it is considered that NGC 205 contains a well defined compact nuclear star cluster. However, as expected and as demonstrated by Figure 7, there is a strong correlation between absolute value of σ and the smoothing parameter.

Zoom In Zoom Out Reset image size

As the number of different M_• estimates using different approaches increases, the consistency between M_• techniques can be examined in those galaxies where more than one method has been applied. Table 5 presents 19 galaxies with 2 M_• estimates each; 9 from GK, 9 from megamasers (MM), 20 from SD. NGC 221, NGC 4486 and NGC 5128 have more than 2 M_• estimates; see Bender et al. (2005), Gebhardt et al. (2011) and Neumayer (2010) for more details. NGC 598 only has published upper limits and is excluded from further discussion. Nine galaxies have consistent M_• estimates; four are MM to MM, three are SD to SD, and two are GK to SD comparisons. Nine galaxies have inconsistent M_• estimates; one MM to GK, three SD to SD, one GK to GK, and four GK to SD. Excluding the MMs, only 38% of M_• estimates are consistent; there is a dispersion of 0.3 dex about the one-to-one relation. However, as demonstrated by the differences between galaxies with two separate SD and GK estimates, there still appears to be ample motivation for refining current modeling techniques (e.g., using the CO band-head and adaptive optics to get HST-like spatial resolution; Gebhardt et al. 2011), or perhaps pursuing some new ones like spectroastrometry of nuclear gas disks (Gnerucci et al. 2013) and the kinematics of molecular gas (Davis et al. 2013).

Table 5. Galaxies with Multiple Peer-reviewed M_• Estimates

Name	log M•1	log M•2	Δlog M•		Name	log M•1	log M•2	Δlog M•
IC 1459	$8.54_{-0.30}^{+0.30}$a (g, 1)	$9.41_{-0.23}^{+0.16}$ (s, 1)	i, 0.87		NGC 3998b	$8.34_{-0.64}^{+0.28}$ (g, 19)	$8.91_{-0.12}^{+0.09}$ (s, 20)	i, 0.57
IC 2560	$6.45_{-0.30}^{+0.30}$a (m, 2)	$6.54_{-0.06}^{+0.06}$ (m, 3)	c, 0.09		NGC 4151	$7.48_{-0.57}^{+0.10}$ (g, 13)	7.60 − 7.70 (s, 21)	i, 0.17
NGC 224b	7.54 − 7.93 (s, 4)	$8.15_{-0.11}^{+0.21}$ (s, 5)	i, 0.42		cNGC 4258	$7.591_{-0.001}^{+0.001}$ (m, 22)	$7.52_{-0.04}^{+0.03}$ (g, 23)	i, 0.07
NGC 598b	<3.18 (s, 6)	<3.48 (s, 7)	n/a		NGC 4350	8.18 − 8.99 (s&g, 24)	$8.90_{-0.30}^{+0.30}$a (s, 25)	c, 0.32
NGC 1023	$7.78_{-0.12}^{+0.09}$ (s, 8)	$7.59_{-0.05}^{+0.04}$ (s, 8)	i, 0.19		NGC 4374	$9.18_{-0.23}^{0.23}$ (g, 26)	$8.60_{-0.30}^{0.30}$a (g, 27)	i, 0.58
NGC 2960	$7.04_{-0.14}^{+0.11}$ (m, 9)	$7.06_{-0.02}^{+0.02}$ (m, 10)	c, 0.02		NGC 4486b	$9.53_{-0.15}^{+0.11}$ (g, 28)	$9.82_{-0.03}^{+0.03}$ (s, 29)	i, 0.29
NGC 3079	$6.00_{-0.30}^{+0.30}$a (m, 11)	$6.30_{-0.30}^{+0.30}$a (m, 12)	c, 0.30		NGC 4649b	$9.30_{-0.15}^{+0.08}$ (s, 15)	$9.65_{-0.11}^{+0.09}$ (s, 30)	i, 0.35
NGC 3227	$7.30_{-0.10}^{+0.18}$ (g, 13)	6.85 − 7.30 (s, 14)	c, 0.27		NGC 5128	$7.65_{-0.11}^{+0.14}$ (g, 31)	$7.74_{-0.34}^{+0.19}$ (s, 32)	c, 0.09
NGC 3377	$8.00_{-0.05}^{+0.28}$ (s, 15)	$7.85_{-0.55}^{+0.19}$ (s, 16)	c, 0.15		UGC 3789	$6.95_{-0.30}^{+0.30}$a (m, 33)	$7.02_{-0.02}^{+0.02}$ (m, 34)	c, 0.07
NGC 3379	$8.15_{-0.55}^{+0.55}$ (s, 17)	$8.60_{-0.12}^{+0.10}$ (s, 18)	c, 0.45

Notes. Estimates of M_• from more than one peer reviewed source. The estimated M_• method codes are: g: gas kinematics, m: megamasers, s: stellar dynamics. Δlog M_• is the difference between the two quoted M_• estimates, and the codes reference whether the uncertainties in the two estimates are c: consistent or i: inconsistent. Our consistency criteria is that either dM_•1/Δlog M_• > 1.0 or dM_•2/Δlog M_• > 1.0. Note that there has yet to be a standard M_• uncertainty adopted by the community, and that some authors choose 1σ, some choose 3σ, and some do not state how their uncertainties were estimated. ^aIndicates a factor of two uncertainty has been assumed for M_• because no estimate of the uncertainty could be found in the literature. ^bIndicates galaxies also in the Table 2 sample. References. (1) Cappellari et al. 2002; (2) Ishihara et al. 2001; (3) Yamauchi et al. 2012; (4) Bacon et al. 2001; (5) Bender et al. 2005; (6) Gebhardt et al. 2001; (7) Merritt et al. 2001; (8) Bower et al. 2001; (9) Henkel et al. 2002; (10) Kuo et al. 2011; (11) Yamauchi et al. 2004; (12) Kondratko et al. 2005; (13) Hicks & Malkan 2008; (14) Davies et al. 2006; (15) Gebhardt et al. 2003; (16) Copin et al. 2004; (17) Shapiro et al. 2006; (18) van den Bosch & de Zeeuw 2010; (19) de Francesco et al. 2006; (20) Walsh et al. 2012; (21) Onken et al. 2007; (22) Miyoshi et al. 1995; (23) Siopis et al. 2009; (24) Pignatelli et al. 2001; (25) Loyer et al. 1998; (26) Bower et al. 1998; (27) Maciejewski & Binney 2001; (28) Macchetto et al. 1997; (29) Gebhardt et al. 2011; (30) Shen & Gebhardt 2010; (31) Neumayer et al. 2007; (32) Cappellari et al. 2009; (33) Braatz & Gugliucci 2008; (34) Kuo et al. 2011.

Download table as:  ASCIITypeset image

For the six galaxies in this sample that have active galactic nucleus contamination it may be possible to mask out, or model, the [Fe ii] 8616λ emission. This was achieved by Walsh et al. (2012), for example, with NGC 3998. While the data that dominated the M_• estimate in this case was from Keck adaptive optics measurements of the CO band-heads, the authors were able to successfully recover the LOSVDs of this galaxy from the STIS spectra presented here.

We have identified galaxies in the STIS archive with spectra of sufficient quality that they could be used for stellar-dynamical estimates of M_•. These data were retrieved, co-aligned, combined, and their radial S/N calculated. The LOSVDs were also fitted and the resulting data are presented in this atlas. In addition to the 15 galaxies that have already been modeled in this way, there are another 19 for which the data quality is comparable. Two galaxies are particularly noteworthy: NGC 5102 and NGC 4742 both have spectra of relatively high S/N and correspondingly well-determined LOSVDs. NGC 5055 is also an interesting prospect, since it has already been modeled using GK, and a stellar dynamical model might help explain why gas- and stellar dynamical mass estimates are so often discrepant.

The uncertainties in the inferred moments of the LOSVDs derived from the central STIS spectra show no correlations with S/N, i.e., there appears to be no way to determine the accuracy with which an estimate of M_• can be made simply from S/N. This highlights the difficulty in estimating precise values of M_• because, in addition to the need for intricate data sets, the complicated methods being used give M_• uncertainties that are independent of the measurement errors. However, there may be excessive scatter in the estimated LOSVDs due to template mismatching from the limited number of stellar templates observed using the appropriate instrument configurations. Further STIS observations of a range of stellar templates using slit widths of 01 and 02, un-binned and x2 binned data, and the appropriate contemporaneous fringe flats, may provide a significant improvement to the accuracy of the estimated LOSVDs.

We would like to thank the anonymous referee for excellent comments that improved the quality of this manuscript. D.B. wishes to thank K. Azalee Bostroem, Brian York, Jerry Kriss, and Phil Hodge for their help and patience with the multiple questions regarding the reduction of the STIS spectra. Support for Proposal number HST-AR-10935.01 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We acknowledge the usage of the HyperLeda database (http://leda.univ-lyon1.fr).