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This would make the kinematical major axis roughly perpendicular to the major axis obtaiue from ellipse fitting o the IIT disk.
This would make the kinematical major axis roughly perpendicular to the major axis obtained from ellipse fitting to the HI disk.
The kinematical major axis is also substantially uusalened with the major axis obtained by eclipse fitting to the optical isophotes.
The kinematical major axis is also substantially misaligned with the major axis obtained by ellipse fitting to the optical isophotes.
Iu addition to this nisalieument. the kinematical ceuter of the velocity field is offse (to the north. as can be seen by comparing Fies.
In addition to this misalignment, the kinematical center of the velocity field is offset (to the north, as can be seen by comparing Figs.
and 2)) from the ceuter (as determined by ellipse fitting) of the III disk.
\ref{fig:mom1} and \ref{fig:ov}) ) from the center (as determined by ellipse fitting) of the HI disk.
Apart from the iisalemmentsOo mentioned above. the velocity field of CTS also shows clear departures ποια what would be expected fron) an axisviunuetric rotating disk.
Apart from the misalignments mentioned above, the velocity field of GR8 also shows clear departures from what would be expected from an axisymmetric rotating disk.
The most important departure is that the isovelocity coutotrs in the outer regions of the ealaxy show large scale kinks.
The most important departure is that the isovelocity contours in the outer regions of the galaxy show large scale kinks.
In addition. the velocity field shows several asvinunetries.
In addition, the velocity field shows several asymmetries.
The most prominent asvuunetry is between the northern aud southern half of the galaxy.
The most prominent asymmetry is between the northern and southern half of the galaxy.
The closed dovelocitv contours in the sothern half are more clongated than those iu the northern halt.
The closed isovelocity contours in the southern half are more elongated than those in the northern half.
Further. the kinks noted above are uch more prominent in the western part of the disk than iu the caster half.
Further, the kinks noted above are much more prominent in the western part of the disk than in the eastern half.
Since our velocity feld is better sampled compared to the velocity fields derived bv Loetal.(1993) ancl Carignanetal.(1990) these kinematical peculiarities are more clearly seen.
Since our velocity field is better sampled compared to the velocity fields derived by \cite{lo93} and \cite{carignan90} these kinematical peculiarities are more clearly seen.
Iu particular. the offset between the morphological aud kinematical ceuter. which is appareut in our velocity field. is not seen im velocity fields derived earlier.
In particular, the offset between the morphological and kinematical center, which is apparent in our velocity field is not seen in velocity fields derived earlier.
Further. because of the lower seusitivitv. the kiuks in the isovelocity contours seen towards the edges of the ealaxy are nof seen that clearly iu the earlier velocity fields.
Further, because of the lower sensitivity, the kinks in the isovelocity contours seen towards the edges of the galaxy are not seen that clearly in the earlier velocity fields.
Following Carignanctal.(1990) we could try to fit GRea’s velocity fieldto that expected from a rotating disk.
Following \cite{carignan90} we could try to fit GR8's velocity fieldto that expected from a rotating disk.
A verv comprehensive work in this field was published by Rutledgeetal.(1997a).. based on 52 Galactic globular clusters covering a metallicity range of —2€ [Fe/Il] €—0.7.
A very comprehensive work in this field was published by \citet{r97a}, based on 52 Galactic globular clusters covering a metallicity range of $-2\leq$ [Fe/H] $\leq-0.7$.
They compared the resulting calibration in (he Zinn&West(L984) and Carretta&Gratton metallicity scales.
They compared the resulting calibration in the \citet{zw84} and \citet{cg97} metallicity scales.
While in the Carretta&Gratton(1997) scale a linear correlation between metallicity and equivalent width of the CaT lines at the level of the (IIB) j,5—0 (known as reduced equivalent width) was found for all clusters. this relationship was not linear when the Zinn&West(1984) scale was used.
While in the \citet{cg97} scale a linear correlation between metallicity and equivalent width of the CaT lines at the level of the horizontal-branch (HB) $_{HB}$ =0 (known as reduced equivalent width) was found for all clusters, this relationship was not linear when the \citet{zw84} scale was used.
In most studies. the run of CaT lines with metallicity has been investigated in globular clusters only. which have all similar ages.
In most studies, the run of CaT lines with metallicity has been investigated in globular clusters only, which have all similar ages.
If we wish to derive stellar metallicities in svstems in which star formation has taken place in the last few Gyr. such as clwart irregular galaxies or open clusters. it is necessary to address the role of age on the CaT strength.
If we wish to derive stellar metallicities in systems in which star formation has taken place in the last few Gyr, such as dwarf irregular galaxies or open clusters, it is necessary to address the role of age on the CaT strength.
Some authors have used (a few) voung open clusters to study the behaviour of the CaT with metallicity (e.g.Suntzelletal. 1992).. using the Zinn&West(1984) metallicity scale as reference.
Some authors have used (a few) young open clusters to study the behaviour of the CaT with metallicity \citep[e.g.][]{sunt92}, using the \citet{zw84} metallicity scale as reference.
Coleetal.(2004). very recently obtained a new relationship. using open and globular clusters covering —2< [Fe/II| <—0.2 and 2.5 € (age/Gvr) < 13 in the Carretta&Gratton(1997). scale.
\citet{c04} very recently obtained a new relationship, using open and globular clusters covering $-2\leq$ [Fe/H] $\leq-0.2$ and 2.5 $\leq$ (age/Gyr) $\leq$ 13 in the \citet{cg97} scale.
They. found a linear correlation among (he reduced equivalent width and metallicity.
They found a linear correlation among the reduced equivalent width and metallicity.
This indicates a weak influence of age in the range of ages investigated (age > 2.5 (αντ),
This indicates a weak influence of age in the range of ages investigated (age $\geq$ 2.5 Gyr).
However. to apply (his relationship (o svstems wilh star formation over the last Gyr and/or wilh stars more metal-rich than the solar metallicity. it is necessary (ο investigate its behaviour further lor vounger ages and higher metallicities.
However, to apply this relationship to systems with star formation over the last Gyr and/or with stars more metal-rich than the solar metallicity, it is necessary to investigate its behaviour further for younger ages and higher metallicities.
The purpose of this paper is to obtain a new relationship between the equivalent width of the CaT lines aud metallicity. covering a range as wide as possible of age aud metallicity.
The purpose of this paper is to obtain a new relationship between the equivalent width of the CaT lines and metallicity, covering a range as wide as possible of age and metallicity.
Our sample covers —2.2< |Fe/1l] <+047 and 0.25 < Age/Gvr < 13.
Our sample covers $-2.2\leq$ [Fe/H] $\leq$ +0.47 and 0.25 $\leq$ Age/Gyr $\leq$ 13.
The influence of age and (he variation of the CaT lines along the RGB are investigated.
The influence of age and the variation of the CaT lines along the RGB are investigated.
In Section 2.. we present the cluster sample.
In Section \ref{sample}, we present the cluster sample.
In Section 3.. the observations and data reduction are described.
In Section \ref{obsdata}, the observations and data reduction are described.
The wav in which (he equivalent width of the the CaT lines has been computed is described in Section 4.. where the behaviour of the CaT with luminosity is also investigated.
The way in which the equivalent width of the the CaT lines has been computed is described in Section \ref{catriplet}, where the behaviour of the CaT with luminosity is also investigated.
In Section 5. we obtain the relationship between the equivalent width of the CaT lines aud metallicity. aud we discuss the influence of age and the [Ca/Fe] ratio in them.
In Section \ref{catmetallicityscale} we obtain the relationship between the equivalent width of the CaT lines and metallicity, and we discuss the influence of age and the [Ca/Fe] ratio in them.
Finally. the derived relationships are used in Section G (to obtain the metallicities of the open clusters Berkeley 39. Drumpler 5 and Collinder 110.
Finally, the derived relationships are used in Section \ref{derivedmetallicities} to obtain the metallicities of the open clusters Berkeley 39, Trumpler 5 and Collinder 110.
To study (he behasiour of the CaT lines with metallicity. we have observed individual stars.with available V magnitudes. in 29 stellar clusters (15 open and 14 globular).
To study the behaviour of the CaT lines with metallicity, we have observed individual stars,with available V magnitudes, in 29 stellar clusters (15 open and 14 globular).
OF the
Of the
package.
package.
The I baud frames were obtained with exposure times iusufficieut for detailed photoimetrv. aud we used these frames for iutegral photometry ο].
The $I$ band frames were obtained with exposure times insufficient for detailed photometry, and we used these frames for integral photometry only.
The galaxy was observed iu he 21 cm Hine at the LOOm-class delecimetric radio telescope on 23. 25 aud 28 August 2001. for a total of lL hour per day.
The galaxy was observed in the 21 cm line at the 100m-class decimetric radio telescope on 23, 25 and 28 August 2004, for a total of 1 hour per day.
For further details ou the telescope. data acquisition and data reduction iiethods. iucludiug the ofi-line clinunation of radio frequency interference (RET). see Mounicr Ragaigue et al. (
For further details on the telescope, data acquisition and data reduction methods, including the off-line elimination of radio frequency interference (RFI), see Monnier Ragaigne et al. (
2001).
2001).
The halfpower beam width of he telescope. of 42: fa d). is expected to cover the cutive dadistribution of the galaxy.
The half-power beam width of the telescope, of $\times$ $'$ $\alpha$$\times$$\delta$ ), is expected to cover the entire distribution of the galaxy.
Tn each daily observation a sufficiently wide velocity range around the galaxy profile was fouud to be free of REL m which the galaxys pprofile was detected in both polarizations.
In each daily observation a sufficiently wide velocity range around the galaxy profile was found to be free of RFI, in which the galaxy's profile was detected in both polarizations.
Residual RFI causes the jogative dip in the 15 500 - 15 800 rrange i he averaged data (Fig.
Residual RFI causes the negative dip in the 15 500 - 15 800 range in the averaged data (Fig.
2).
2).
The average of the three spectra (see Fig.
The average of the three spectra (see Fig.
2). smioothed o a velocity resolution of 18L|. has an ris noise evel of 1.6 mJy
2), smoothed to a velocity resolution of 18, has an rms noise level of 1.6 mJy.
The ealaxy profile has a peak fiux density of 10 uta a ceuter velocity ιο 219415 Ll. oa velocity width at of peak maxim Wy =206430 a velocity width at of peak uaxiuun Woy=25 L416 ον, and an integrated line &ux 1.80.21.
The galaxy profile has a peak flux density of 10 mJy, a center velocity 16 $\pm$ 15, a velocity width at of peak maximum $W_{50}$ $\pm$ 30, a velocity width at of peak maximum $W_{20}$ $\pm$ 46, and an integrated line flux $\pm$ 0.2.
Those η. line piuranueters are directly measured values: no corrections have been applied to them for. Ce. lustrimental resolution.
These global line parameters are directly measured values; no corrections have been applied to them for, e.g., instrumental resolution.
We estimated the uncertainties iuIp; aand the line widths following Schneider et al. (
We estimated the uncertainties in, and the line widths following Schneider et al. (
1986. 1990).
1986, 1990).
A comparison with the stmuned CO(1-0) spectra of CGalletta et al. (
A comparison with the summed CO(1-0) spectra of Galletta et al. (
1997) shows that the widths of the profiles are comparable.
1997) shows that the widths of the profiles are comparable.
The 170 ddifference with the published central velocity of the CO profile could be to be due to the application of the relativistic Doppler shift formmla to the CO data velocity. without the autlors cine aware ofthis correction converting to the conveutional optical definition we use (V= e(A-Ay)/Ay) raises the CO center velocity. to 16 233211|... consistent with our vvalue and the published optical racia velocitics.
The 470 difference with the published central velocity of the CO profile could be to be due to the application of the relativistic Doppler shift formula to the CO data velocity, without the authors being aware of this correction – converting to the conventional optical definition we use $V=c$ $\lambda$ $\lambda_0$ $\lambda_0$ ) raises the CO center velocity to 16 $\pm$ 11, consistent with our value and the published optical radial velocities.
ESO 171-C26 is a lavee syste even the central galaxy Qvithout the rugs) is significantly larger aud much more DIuuinuous than the Milkv. Way (Table 2).
ESO 474-G26 is a large system – even the central galaxy (without the rings) is significantly larger and much more luminous than the Milky Way (Table 2).
The V-baud nuage ids cdisplaved in Fig.
The $V$ -band image is displayed in Fig.
l and represented as au isophotal plot in Fig.
1 and represented as an isophotal plot in Fig.
3.
3.
The overall optical morphology of ESO 17-C26 is very intercsting and intriguing: a nearly spherical central body is
The overall optical morphology of ESO 474-G26 is very interesting and intriguing: a nearly spherical central body is
If. following Faber et al. (
If, following Faber et al. (
1987). e» is constant elliptical galaxies would be structurally homologous systems aud the tilt would have to be explained as a systematic variation of masstolight (ML) ratio with huuinositv: M/Lx L. with συ
1987), $c_2$ is constant elliptical galaxies would be structurally homologous systems and the tilt would have to be explained as a systematic variation of mass–to–light (M/L) ratio with luminosity: $M/L\propto L^{\beta}$ , with $\beta$ $\pm$ 0.08.
As discussed in the Introduction it is uulikelv hat this tilt cau be explained by stellar population effects. alone.
As discussed in the Introduction it is unlikely that this tilt can be explained by stellar population effects alone.
One needs to combine two well shown observations: the svstematic variation of stellar populations with huninosity aud the change of observed structural properties along the carly-ype sequence from dwarf to giant ellipticals.
One needs to combine two well known observations: the systematic variation of stellar populations with luminosity and the change of observed structural properties along the early-type sequence from dwarf to giant ellipticals.
Ideally both effects in combination would he able o account for the full tilt of the FP.
Ideally both effects in combination would be able to account for the full tilt of the FP.
It has been shown (see e.g. Trujillo. Graham Caon 2001 and references therein) that elliptical ealaxies do not form a homologous structural aly aud that the huninositv.dependent departures youn the rb/! daw can be described by the ri Séórrsic model.
It has been shown (see e.g. Trujillo, Graham Caon 2001 and references therein) that elliptical galaxies do not form a homologous structural family and that the luminosity–dependent departures from the $^{1/4}$ law can be described by the $^{1/n}$ Sérrsic model.
The nonhomoloey is also reflected in the strong correlations between the shape xuwanmeter pj aud photometriciudepeudoeut galaxy xoperties as. for exaiuple. the central velocity dispersion (Graham. Trujillo Caon. 2001).
The nonhomology is also reflected in the strong correlations between the shape parameter $n$ and photometric–independent galaxy properties as, for example, the central velocity dispersion (Graham, Trujillo Caon, 2001).
In Fig.
In Fig.
5bb. we show the relation between he shape index » and the absolute Dbaud (iiodelindepeudent) magnitude for 200 elliptical ealaxies.
\ref{nohomo}b b, we show the relation between the shape index $n$ and the absolute B–band (model–independent) magnitude for 200 elliptical galaxies.
The galaxies used iu this plot correspond o ellipticals from the Virgo. Foruax aud Coma Clusters (Caon ot al.
The galaxies used in this plot correspond to ellipticals from the Virgo, Fornax and Coma Clusters (Caon et al.
1990: Caou. Capaccioli D'Onofrio 1991: Diugeeli Jerjeu 1998: Cutiórirez et al
1990; Caon, Capaccioli D'Onofrio 1994; Binggeli Jerjen 1998; Gutiérrrez et al.
2001)
2004).
Those galaxies classified as SO were removed from our sample to avoid possible luissineasurements of the iudex » due to the disk conrponeut of these galaxies.
Those galaxies classified as S0 were removed from our sample to avoid possible missmeasurements of the index $n$ due to the disk component of these galaxies.
Error estinates for n are found to have a typical uncertainty of (Caon. Capaccioli D'Onofrio 1993).
Error estimates for $n$ are found to have a typical uncertainty of (Caon, Capaccioli D'Onofrio 1993).
The high statistical significance of this correlation has been studied in previous papers (see. e.g. Gral ct al.
The high statistical significance of this correlation has been studied in previous papers (see, e.g. Graham et al.
2001).
2001).
To check that the robustness of the above relation is not affected by the large unuber of faint galaxies. we have evaluated the Spearma- correlation coefficient for those galaxies brighter than Mp=-16.5 (υγτο kin s+ +) and we find ry, =0.72.
To check that the robustness of the above relation is not affected by the large number of faint galaxies, we have evaluated the Spearman correlation coefficient for those galaxies brighter than $_B$ =-16.5 $_0$ =70 km $^{-1}$ $^{-1}$ ) and we find $_s$ =0.72.
Using the Sérrsic inodel. it is possible to relate he structural parameter eo with ». leading also o a relation between » aud £L. or between e» aud L.
Using the Sérrsic model, it is possible to relate the structural parameter $c_2$ with $n$, leading also to a relation between $n$ and $L$, or between $c_2$ and $L$.
To estimate ο fora Sérrsic mocdol we need to evaluate the velocity dispersion. profile o,(rc).
To estimate $c_2$ for a Sérrsic model we need to evaluate the velocity dispersion profile $\sigma_r(r)$.
In 1e ost simple case this cam be done by assuming spherical. nonrotating. isotropic 11"Hu model aud ien evaluating c,(0) using the Jeans equatiou (sec. e.g.. Binney Tremaine 1987).
In the most simple case this can be done by assuming a spherical, nonrotating, isotropic $^{1/n}$ model and then evaluating $\sigma_r(r)$ using the Jeans equation (see, e.g., Binney Tremaine 1987).
Towever. i6 observed central velocity dispersion oy that irs dm Eq.
However, the observed central velocity dispersion $\sigma_0$ that enters in Eq.
2 does not correspond to 6,(0). nt rather to the observed projected. velocity dispersion co,CR).. Inminosity averaged over the Hoverture used for the spectrographliic observations TapRap}.
\ref{cdos} does not correspond to $\sigma_r(0)$ , but rather to the observed projected velocity dispersion $\sigma_p(R)$, luminosity averaged over the aperture used for the spectrographic observations $\sigma_{ap}(R_{ap})$.
Cousequeutly. to evaluate properly e». we need to switch from 0,(r0) to o,(P) aud from this to σαν) (see a detailed explaiation c.g. in Sec.
Consequently, to evaluate properly $c_2$, we need to switch from $\sigma_r(r)$ to $\sigma_p(R)$ and from this to $\sigma_{ap}(R_{ap})$ (see a detailed explanation e.g. in Sec.
2.2 of Ciotti et al.
2.2 of Ciotti et al.
1996).
1996).
To illustrate how c» changes depending onu which estimate of the velocity dispersion is used we show in Fig.
To illustrate how $c_2$ changes depending on which estimate of the velocity dispersion is used we show in Fig.
L the relation between e» aud n clerived from σης/δ). στο) aud mutefm).
\ref{cdosplot} the relation between $c_2$ and $n$ derived from $\sigma_r(r_e/8)$, $\sigma_p(r_e/8)$ and $\sigma_{ap}(r_e/8)$.
We show e» for r—r./8 because this is one of the most usual aperture radii to measure dy recusen. Frans Kjewreaard 1993).
We show $c_2$ for $r=r_e/8$ because this is one of the most usual aperture radii to measure $\sigma_0$ rgensen, Franx rgaard 1993).
Our value of c9 is in good aerecment with the estimates of this quantity by other authors (c.g. Prugniel Simicu (1997). Bertin. Ciotti Del Principe. 2002).
Our value of $c_2$ is in good agreement with the estimates of this quantity by other authors (e.g. Prugniel Simien (1997), Bertin, Ciotti Del Principe, 2002).
Since the sizes of galaxies differ from one another aud because galaxies are observed at differeut distances. the estimation of the ceutral velocity dispersion using a fixed augular aperture sanrples different fractious of the total light (or the effective radii)
Since the sizes of galaxies differ from one another and because galaxies are observed at different distances, the estimation of the central velocity dispersion using a fixed angular aperture samples different fractions of the total light (or the effective radii).
Consequently. when dealing with samples that extend over a large rauge of sizes. it is not the best approximation to estimate co from the observations by using a fixed aperture related to the effective radius (0.8. 7/8).
Consequently, when dealing with samples that extend over a large range of sizes, it is not the best approximation to estimate $c_2$ from the observations by using a fixed aperture related to the effective radius (e.g. $r_e$ /8).
Iustead oue should use typical angular apertures (e.g. 1.76afHg or 2,72),
Instead one should use typical angular apertures (e.g. $''$ 6 or $''$ 2).
Iu order to evaluate the influence of nonhomology iu the FP. we have selected frou the sample of elliptical galaxies presented above those galaxiesthat have a measured central velocity dispersion.
In order to evaluate the influence of nonhomology in the FP, we have selected from the sample of elliptical galaxies presented above those galaxiesthat have a measured central velocity dispersion.
The velocity dispersions are obtained from Uvpercat.
The velocity dispersions are obtained from Hypercat.
This leaves us with a total of 15 galaxies ranging from -15 to-22 in the Dbaud.
This leaves us with a total of 45 galaxies ranging from -15 to-22 in the B–band.
Iu Fig.
In Fig.
| we show the ο values for the galaxies of this subsainple estimated using two different fixed
\ref{cdosplot} we show the $c_2$ values for the galaxies of this subsample estimated using two different fixed
the probability distribution function.L(Q,.p.h). following. e.g.. ROL or Podariu Ratra (2000).
the probability distribution function$L^S (\Omega_M, p, h)$, following, e.g., R04 or Podariu Ratra (2000).
The joint likelihood lor the SNIa and galaxy cluster data is the product of the two individual likelihoods.
The joint likelihood for the SNIa and galaxy cluster data is the product of the two individual likelihoods.
The two-dimensional probability distribution function for O4, aud p. L(Q3.p). is determined by marginalizing (his product over .
The two-dimensional probability distribution function for $\Omega_M$ and $p$, $L(\Omega_M, p)$, is determined by marginalizing this product over $h$.
For each of the three models mentioned above. we compute L(£3,.p) on the Gwvo-limensional (Qa;.p) grid.
For each of the three models mentioned above, we compute $L(\Omega_M, p)$ on the two-dimensional $(\Omega_M, p)$ grid.
The 1. 2. and 3. c confidence: contours are the set of: points: where the likelihood: is. e.2772,80/2 e4"ERE. and eHN? of (he maximum likelihood value.
The 1, 2, and 3 $\sigma$ confidence contours are the set of points where the likelihood is $e^{-2.30/2}$, $e^{-6.17/2}$, and $e^{-11.8/2}$ of the maximum likelihood value.
Figure | shows the RO4 gold SNla constraints on the 9CDM model with V(ó)x©a determined by marginalizing L(GQ4,.0.h) over h.
Figure 1 shows the R04 gold SNIa constraints on the $\phi$ CDM model with $V(\phi) \propto \phi^{-\alpha}$, determined by marginalizing $L^S(\Omega_M, \alpha, h)$ over $h$.