5.4 Internal Comparison of Global Photometric Parameters

We performed an internal comparison of the global photometric parameters. The result is shown in Table . The comparisons are also shown in Fig. -. The data symbols are as follows: boxes - Gunn r; triangles - Johnson B; crosses - Johnson U. Each figure has two panels. In the left panel we plot the difference versus the first observation value. In the right panel we plot the difference versus the seeing difference, in order to check for seeing dependence. $\Delta \log {r_{\rm e}}$, $\Delta {{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$, and $\Delta {m_{\rm T}}$ are correlated with $\Delta({\rm seeing})$, see the right panels of Fig. , , and . Our r^1/4 fits did take the seeing into account, so perhaps the real PSF of our data has larger wings than the model PSF that we used. As a result, the individual error estimates for ${\log{r_{\rm e}}}$, ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$, and ${\varepsilon_{\rm e}}$ are too low. This can be seen in the left panels of Fig. , , and - the scatter is larger than what the individual error bars can account for.

The errors in ${\log{r_{\rm e}}}$ and ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$ are highly correlated, cf. Fig. , with a linear correlation coefficient of r = 0.99. This is because ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$ is the mean surface brightness within ${r_{\rm e}}$, so if ${r_{\rm e}}$ due to random errors is determined too large, ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$ will correspondingly become too faint. This has the effect that the combination of ${\log{r_{\rm e}}}$ and ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$ that enters the fundamental plane, approximately ${\log{r_{\rm e}}}- 0.328 {{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$, has a much lower uncertainty than ${\log{r_{\rm e}}}$ and ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$ individually, cf. Table  and Fig. . The rms scatter for this combination is 0.012 in Gunn r, implying a typical internal uncertainty of only 0.008.

c₄ is also seeing dependent, in the expected sense that larger seeing makes |c₄| smaller. See Fig. . Recall that |c₄| is the amplitude of the observed extremum in the c₄(r)-profile. We found ${< \hspace{-4pt} c_4 \hspace{-4pt}>}$ and ${< \hspace{-4pt} c_6 \hspace{-4pt}>}$ not to be seeing dependent.

 

Table: Internal Comparison of Global Photometric Parameters

Gunn r
Parameter	N	mean	rms
${\log{r_{\rm e}}}$	53	$-0.037 \pm 0.007$	0.051
${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$	53	$-0.128 \pm 0.023$	0.170
``FP''	53	$0.005 \pm 0.002$	0.012
${m_{\rm T}}$	53	$0.058 \pm 0.013$	0.095
${\varepsilon_{\rm e}}$	53	$-0.016 \pm 0.006$	0.047
${\varepsilon_{21.85}}$	53	$-0.015 \pm 0.003$	0.025
c4	47	$(-3.2 \pm 12 ) \cdot 10^{-4}$	0.008
|c4|	47	$(-28 \pm 11 ) \cdot 10^{-4}$	0.007
${< \hspace{-4pt} c_4 \hspace{-4pt}>}$	53	$( 7.9 \pm 8.3) \cdot 10^{-4}$	0.006
${< \hspace{-4pt} c_6 \hspace{-4pt}>}$	53	$( 4.9 \pm 5.5) \cdot 10^{-4}$	0.004
Johnson B
Parameter	N	mean	rms
${\log{r_{\rm e}}}$	42	$-0.053 \pm 0.009$	0.061
${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$	42	$-0.199 \pm 0.033$	0.214
``FP''	42	$0.012 \pm 0.002$	0.014
${m_{\rm T}}$	42	$0.061 \pm 0.016$	0.102
${\varepsilon_{\rm e}}$	42	$-0.011 \pm 0.008$	0.050

 

Notes: ``FP'' = ${\log{r_{\rm e}}}- 0.328 {{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$.

  

Figure: Internal comparison, ${\log{r_{\rm e}}}$

  

Figure: Internal comparison, ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$

  

Figure: Internal comparison, ``FP'' = ${\log{r_{\rm e}}}- 0.328 {{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$

  

Figure: Internal comparison, ${m_{\rm T}}$

  

Figure: Internal comparison, ${\varepsilon_{\rm e}}$

  

Figure: Internal comparison, ${\varepsilon_{21.85}}$

 

  

Figure: Internal comparison, ${< \hspace{-4pt} c_4 \hspace{-4pt}>}$

  

Figure: Internal comparison, ${< \hspace{-4pt} c_6 \hspace{-4pt}>}$