6.4.2 External Comparison and Applied Offsets

The spectroscopic parameters were compared with data from JFK95b, J97, Davies et al. (1987) [D87], Faber (1994) [F94], Lucey & Carter (1988) [LC88], and Richter (1989) [R89]. The comparisons are shown in Fig. - and summarized in Table  (p. ).

Comparisons of ${\log\sigma}$ are shown in Figure . All literature data have been aperture corrected, and the individual values from D87 and F94 have been averaged, cf. JFK95b. The mean differences $\Delta \log \sigma \equiv \log \sigma_{\rm DFOSC} - \log \sigma_{\rm literature}$ are given in Table . From these, the following offset was adopted to reach the system of JFK95b, which is also the system of D87 (cf. JFK95b):

$$\log \sigma_{\rm JFK95b/D87} = \log \sigma_{\rm DFOSC} - 0.014 \enspace .$$ (6.7)

This gives consistency within 0.010 with D87 and JFK95b. It also gives consistency within 0.010 with LC88 when applying the offset found by JFK95b: $\log \sigma_{\rm JFK95b/D87} = \log \sigma_{\rm LC88} - 0.020$.

 

Comparisons of $cz_{\rm hel}$ are shown in Figure . The consistency is good. In the case of JFK95b, Fig. (c), we can compute the total error on $\Delta {cz_{\rm hel}}$ expected from the internal uncertainties on our and their measurements. This error is 17 km/s, which is far less than the observed rms scatter of 48 km/s. Thus, other sources of error, such as the wavelength calibration, dominate. If the observed scatter in the comparison with JFK95b is divided equally on our and their data, the found external accuracy is 34 km/s. JFK95b find their external accuracy to be $\approx$ 35 km/s, in good agreement with this.

 

 

J97 presents various line indices calibrated to the Lick/IDS system. Figure (a) shows the comparison for ${ <{\rm Fe}>}$. The mean difference is zero, and therefore the DFOSC ${ <{\rm Fe}>}$ values are already on the Lick/IDS system,

$${ <{\rm Fe}>}_{\rm Lick/IDS} = { <{\rm Fe}>}_{\rm DFOSC} \enspace .$$ (6.8)

Figure (b) shows the comparison for Mgb. The mean difference is used to transform the DFOSC data to the Lick/IDS system:

$${\rm Mgb}_{\rm Lick/IDS} = {\rm Mgb}_{\rm DFOSC} + 0.16 \enspace .$$ (6.9)

${ {\rm Mg}_2}$ could not be measured from all the DFOSC spectra since the blue pseudocontinuum of ${ {\rm Mg}_2}$ was not fully included in the observed wavelength range for galaxies redshifted less than $cz_{\rm observed} \approx 3600$ km/s. Therefore, Mgb was used instead for the calibration of ${ {\rm Mg}_2}$ to the Lick/IDS system. A transformation from Mgb to ${ {\rm Mg}_2}$ has been established by J97 as

$$\arraycolsep=2pt % \begin{array}{lllll} { {\rm Mg}_2}= & & 0.... ...\quad & N=159 \enspace . \\ & \pm & 0.044 & & \\ \end{array}$$ (6.10)

${\sigma_{\rm fit}}$ is the rms scatter and N is the number of galaxies used in the fit. The author reports that the relation has no significant intrinsic scatter. The right hand side of Eq. () is what we referred to as ${\widehat{{ {\rm Mg}_2}}}$ in Sect. .

In Figure , real DFOSC ${ {\rm Mg}_2}$ values are compared with fiducial ${ {\rm Mg}_2}$ values calculated from Mgb using Eq. (). In panel (a) the Mgb data are from the DFOSC itself (thus being a sort of an internal comparison). The mean difference is $\Delta {\rm Mg}_{2} = -0.031 \pm 0.004$. In panel (b) the Mgb data are from J97. The mean difference is $\Delta {\rm Mg}_{2} = -0.024 \pm 0.007$.

The real DFOSC ${ {\rm Mg}_2}$ values were also compared with real ${ {\rm Mg}_2}$ values from the literature. In comparison with D87, F94, and J97, mean differences $\Delta {\rm Mg}_{2} \equiv {\rm Mg}_{\rm 2,DFOSC} - {\rm Mg}_{\rm 2,literature}$ of -0.029, -0.014, and -0.013 were found for 2, 1, and 2 galaxies in common, respectively. It was concluded, that the best transformation to the Lick/IDS system was

$${ {\rm Mg}_2}_{\rm Lick/IDS} = { {\rm Mg}_2}_{\rm DFOSC} + 0.024 \enspace .$$ (6.11)

The uncertainty on the offset was estimated from the consistencies to be 0.010.

 

 

Table: External Comparison of the Spectroscopy

Parameter	Source	N	mean		rms	With offset(s)	Comments
$cz_{\rm hel}$	D87	8	-16.2	$$	22.5	63.5
$cz_{\rm hel}$	LC88	11	-0.7	$$	7.1	23.4
$cz_{\rm hel}$	JFK95b	17	-1.8	$$	11.6	48.0
$cz_{\rm hel}$	R89	20	-4.4	$$	14.0	62.6
${\log\sigma}$	D87	8	0.011	$$	0.019	0.055	$-0.003\pm$0.019
${\log\sigma}$	LC88	11	-0.010	$$	0.010	0.032	$-0.004\pm$0.010
${\log\sigma}$	JFK95b	17	0.023	$$	0.013	0.054	$0.009\pm$0.013
${\log\sigma}$	JFK95b	16	0.015	$$	0.011	0.042	$0.001\pm$0.011	R283/E437G11 omitted
${ {\rm Mg}_2}$	D87	2	-0.029	$$	0.002	0.002	$-0.005\pm$0.002
${ {\rm Mg}_2}$	F94	1	-0.014	$$			$0.010\quad\quad\quad$
${ {\rm Mg}_2}$	JFK95b	2	-0.013	$$	0.007	0.010	$0.011\pm$0.007
Mgb	F94	2	-0.037	$$	0.034	0.049	$0.123\pm$0.034
Mgb	J97	17	-0.159	$$	0.084	0.346	$0.001\pm$0.084
${ <{\rm Fe}>}$	F94	2	-0.147	$$	0.212	0.300
${ <{\rm Fe}>}$	J97	17	-0.002	$$	0.060	0.249

 

Notes: All differences have been calculated as ``DFOSC''-``literature''. ``rms'' is the root mean square standard deviation. The uncertainty on the mean has been calculated as rms/$\sqrt{N}$. The column ``With offset(s)'' gives the mean difference after the following offsets have been applied to the DFOSC data
$\log \sigma_{\rm JFK95b/D87} = \log \sigma_{\rm DFOSC} - 0.014$
${ {\rm Mg}_2}_{\rm Lick/IDS} = { {\rm Mg}_2}_{\rm DFOSC} + 0.024$
${\rm Mgb}_{\rm Lick/IDS} = {\rm Mgb}_{\rm DFOSC} + 0.16$
${ <{\rm Fe}>}_{\rm Lick/IDS} = { <{\rm Fe}>}_{\rm DFOSC}$
and the following offset has been applied to the LC88 data (cf. JFK95b)
$\log \sigma_{\rm JFK95b/D87} = \log \sigma_{\rm LC88} - 0.020$ .