7.3 The Fundamental Plane in Other Passbands

For the HydraI sample of 45 galaxies photometry is also available in Johnson B, and for a subsample of 19 galaxies also in Johnson U. A fit to the Johnson B data gives ( ${r_{\rm e}}$ in kpc)

$$\arraycolsep=2pt % \begin{array}{lllllllll} {\rm HydraI,\;JB... ...d & N=45 \\ & & & \pm & 0.14 & \pm & 0.04 & & \\ \end{array}$$ (7.10)

The scatter is the same as in Gunn r (Eq. ).

A fit to the Johnson U data gives ( ${r_{\rm e}}$ in kpc)

$$\arraycolsep=2pt % \begin{array}{lllllllll} {\rm HydraI,\;JU... ...d & N=19 \\ & & & \pm & 0.21 & \pm & 0.07 & & \\ \end{array}$$ (7.11)

For the same 19 galaxies, the result in Gunn r is

$$\arraycolsep=2pt % \begin{array}{lllllllll} {\rm HydraI,\;GR... ...d & N=19 \\ & & & \pm & 0.29 & \pm & 0.06 & & \\ \end{array}$$ (7.12)

The scatter in those two passbands is also not significantly different. Figure  shows the Fundamental Plane seen edge-on in Johnson B and Johnson U.

 

We assume that the contribution to the scatter from the measurement errors is the same in the different passbands. This is supported by the internal comparison of the photometry: we found an rms scatter of $0\hbox{$.\!\!^{\rm m}$ }012$ for Gunn r and $0\hbox{$.\!\!^{\rm m}$ }011$ for Johnson B (Table , p. ). This implies that the intrinsic scatter in the three passbands is approximately the same. This is also what JFK96 found for the passbands Gunn r, Gunn g, Johnson B, and Johnson U. As JFK96 noted, one consequence of this is that intrinsic dust absorption in the galaxies cannot be a major source of the intrinsic FP scatter, since dust absorption depends on wavelength.

Another consequence is related to the question whether the intrinsic FP scatter is produced by an age scatter or a metallicity scatter. If the galaxies have similar structure, we can translate the FP scatter into a scatter in the ${\left( M/L \right)}\propto M^b$ relation (cf. Sect. ), where b can be calculated from $\alpha$ as $b = (2-\alpha)/(2+\alpha)$. The scatter in the quantity $[{\log(M/L)}- b \, {\log(M)}]$ (i.e. the zero point in the ${\left( M/L \right)}\propto M^b$ relation) is 0.127 dex in Gunn r and Johnson B, 0.075 dex in Johnson U, and 0.103 dex in Gunn r selected as Johnson U. This includes scatter from the measurement errors. The typical measurement error on $\log(M/L)$ is 0.074 for the 45 HydraI galaxies with Gunn r and Johnson B photometry, and 0.068 for the 19 HydraI galaxies with Johnson U photometry. This is based on the values in Table , p. , and corrected for the fact that the 19 galaxies have lower ${\log\sigma}$ uncertainties than all the 45 galaxies. As an approximation, we estimate the intrinsic scatter in the ${\left( M/L \right)}\propto M^b$ relation by subtracting in quadrature the typical measurement error on $\log(M/L)$ only. We get 0.103 dex (24%) in Gunn r and Johnson B, 0.020 dex (5%) in Johnson U, and 0.078 dex (18%) in Gunn r selected as Johnson U. By means of stellar population models, we can translate the scatter in ${\left( M/L \right)}$ into a scatter in age or metallicity. Specifically, the models by Vazdekis et al. (1996) with a bi-modal IMF with high mass slope $\mu = 1.35$ can for ages > 5 Gyr be well approximated by

   

$${\log(M/L_{\rm r})} \approx 0.63 \, {\log {\rm age}}+ 0.26 \, {{\rm [M/H]}}- 0.16$$ (7.13)

$${\log(M/L_{\rm B})} \approx 0.78 \,{\log {\rm age}}+ 0.41 \,{{\rm [M/H]}}- 0.05$$ (7.14)

$${\log(M/L_{\rm U})} \approx 0.97 \,{\log {\rm age}}+ 0.58 \,{{\rm [M/H]}}- 0.07$$ (7.15)

If we consider Gunn r, the scatter in ${\log(M/L_{\rm r})}$ of 0.10 dex (i.e. 24% in ${(M/L_{\rm r})}$) can be translated into a scatter in ${\log {\rm age}}$ of 0.16 dex (38% in age) or a scatter in ${{\rm [M/H]}}$ of 0.40 dex (90% in Z). However, since the scatter is approximately constant for the three passbands (when comparing the same galaxies), and since neither the ${\log {\rm age}}$ coefficients nor the ${{\rm [M/H]}}$ coefficients are the same, variations in both age and metallicity are needed. We revisit this issue in Sect.  (p. ) in the light of the age-metallicity-sigma relation.