4 Results

4.1 Velocity maps

The CH-line is suitable for both methods of line shift determination as described in the previous section. The calculated error map gives a rms-value of 25 m s^-1 for the map based on Fourier method and a maximum deviation of 215 m s^-1 (peak-to-peak). The corresponding values for the map based on the line-core shift are 45 m s^-1 and 260 m s^-1. The maps do not differ significantly from each other.

Figure 4 shows the calculated velocity maps for the CH-line based on the Fourier method to the left, for the Fe II-line based on the polynomial fit in the middle and the corresponding error map to the right. In the maps upflows (blue-shifts) are always represented by bright areas and related to positive velocities. The CH-map shows the same flow pattern as the Fe II-map, but it is more diffuse. This can be explained by the inferior seeing quality during the CH-line scan. The correlation coefficient of the two maps is 0.94. The rms-value of the normalized difference of the maps $(v_{{\rm CH}}-v_{{\rm Fe}})/(v_{{\rm CH}}+v_{{\rm Fe}})$ is about 0.05.

The velocity maps reproduce well the granulation pattern outside the pore in regions of normal granulation. For comparison between the velocity map and broadband or continuum filtergrams see also Fig. 5. There is a conspicuous downflow pattern in regions of abnormal granulation, which clearly differs from the downflows of the intergranular lanes in regions of normal granulation in the upper right corner of the image. These downflows form a connected area which coincides with the region of abnormal granulation and which contains most of the structures that are related to enhanced intensity in the G-band image.

4.2 Intensity maps

Figure 5: Intensity and velocity maps. The circles mark the examples, that are described in Sect. 4.4.

Figure 5, panels d and e show the line core intensity of the CH respective the Fe II-line, normalized to the local continuum. The values for the local continuum are taken from the average of the two filtergrams positioned in the neighborhood of the continuum at 430.33 nm (see Fig. 2 or Fig. 3). The line core intensities for each position are given by the minimum value of the polynomial fit, fitted around the profile minimum.

In both maps, regions of enhanced line core intensity outline the intergranular lanes. However, the line core intensity of CH behaves slightly differently. The line core intensity of the CH-line is partially much more enhanced than the line core intensity of the Fe II-line. Away from the pore, the increased line core intensity of the CH-line is restricted to the intergranular lanes. Close to the pore, the brightenings expand in space and cover larger areas that do not show any structure.

In the following we use the term "G-band brightness'' (see Berger et al. 1998) for the normalized intensity of the broadband channel at 431.1 nm. The G-band contrast is then defined by

$$\begin{eqnarray*}C_{G{\rm -band}}=\frac{I_{{\rm bb}}}{\left\langle I_{{\rm bb}}\right\rangle}-1 . \end{eqnarray*}$$

   
4.3 Bright point index

Langhans et al. (2001) show that bright points can be characterized spectroscopically by a decreased line depression of the CH absorption lines, whereby the line depression of the atomic lines within the observed spectral range (430.24 nm to 430.78 nm) remain almost unchanged.

To distinguish regions where CH-line depression dominates from regions where both lines or only the Fe II-line is depressed, we introduce the "Bright Point Index'' (BPI). The index is defined as the ratio of the relative line depression of the Fe II and the CH-line, minus one:

$$\begin{eqnarray*}\mbox{BPI}=\frac{I_{{\rm cont}}-I_{{\rm lc}}^{{\rm Fe}}}{\left\... ... CH}} \right\rangle}{I_{{\rm cont}}-I_{{\rm lc}}^{{\rm CH}}}-1 . \end{eqnarray*}$$

For this calculation all intensities are normalized to $I_{\rm atlas}$. $I_{\rm cont}$corresponds to the "continuum'' intensity at 430.33 nm.

Through the use of a low-excitation majority-stage ionic iron line in combination with a CH-line of similar strength, the BPI provides a measure of CH-abundance variations; it is nearly free of direct temperature effects on the line source functions. (A large BPI corresponds to low CH-abundance.) The BPI map is shown in Fig. 5d. The regions of increased CH-line core intensity and unchanged Fe II-line core intensity are emphasized. Regions where both lines are depressed in the same way make a smaller contribution to the BPI map compared to the contribution to the maps of line core intensity.

Figure 6: Relation between BPI and change in line depression. For clarity only data points for a threshold G-band contrast ${\geq }10$% are taken into account. The error ellipsoids indicate the 2$\sigma$-level for each data point. Left CH-line, Right: Fe II-line, the inclined line in the plot indicates the expected effect on the BPI and line depression of the Fe II-line by the CH-blend.

The correlation diagrams in Fig. 6 show the BPI versus the line depression of both absorption lines. The error ellipsoids in one of the lower corners of the diagrams (and in all following correlation diagrams) represent the 2$\sigma$-confidence level for each data point, which results from the calculation of the rms-values of the concerning error maps as discussed in Sect. 3.2. For clarity in Fig. 6 only data points for a threshold G-band contrast ${\geq }10$% are considered. Thus, the large contribution from granules with a brightness ${\leq} 1.1 \left\langle I_{{\rm bb}}\right\rangle$ are excluded in the correlation diagrams of Fig. 6 and some following figures. To estimate how the CH-blend in the blue wing of the Fe II-line affects the BPI, we vary the strength of the blend in the double Gaussian representing the blended Fe II-line as described in Sect. 2.1. The resulting values for the BPI are represented by the inclined line in the Fe II-diagram. In the case of a decreased CH-abundance the corrected BPI is higher than the BPI for the uncorrected case. Therefore we do not correct the BPI for the CH-blend in the following calculations.

   
4.4 G-band bright structures?

We use the BPI to separate G-band bright structures in two classes: (a) structures which are bright, due to a significant difference in CH and Fe II line depression; (b) structures which are bright due to an increase of the local continuum intensity. Examples of these structures are marked by circles in Fig. 5.

All features appear bright in the G-band image (TESOS broadband channel). Examples 2a and 2b are not conspicuous neither in the narrowband continuum image nor in the line core intensity map of Fe II. The line core intensity of CH is high, which leads to a high BPI-value as well. The dopplergram shows that the selected structures are located in downflow regions. In contrast thereto, the G-band structure of the examples 1a and 1b coincides with high intensity in the narrowband continuum image and low line core intensities in Fe II and CH as well. The BPI is accordingly low. The flow map shows a slight upflow. The spectra of the examples (1b, 2a) are plotted in Fig. 1.

Figure 7: Correlation diagrams: G-band contrast vs. flow velocity. Left: Criterion of data point selection is a BPI above 0.2. Right: center-of-gravity plot. The small numbers indicate BPI intervals to the corresponding center-of-gravity, indicated by "$\Diamond$''.

Figure 8: Correlation diagrams: change in line depression vs. flow velocity. Criterion of data point selection is an enhanced G-band brightness ( $C_{G{\rm -band}}\geq 0.1)$. Left: CH-line, G1 and G2 are explained in Sect. 4.5. Right: Fe II-line.

   
4.5 Correlations

In Sect. 4.4 we described the relation between the G-band brightness, the Doppler velocity and the BPI for different structures. In this Section we follow a quantitative approach using correlation diagrams. Data points from the pores are excluded by requiring $I\geq 0.58\cdot\left\langle I_{G-{\rm band}}\right\rangle$; the mask is marked by contour lines in all but the continuum maps.

In the left diagram of Fig. 7 all data are plotted with a $\mbox{BPI}\geq 0.2$. All points are related to relatively high G-band brightness ( $-0.1\leq C_{G-{\rm band}}\leq 0.3$) and downflows. Next we sort the data into bins of 0.02 BPI units and calculate the center-of-gravity for each bin. (Only intervals with more than 200 data points were used.) The result is shown in the right panel of Fig. 7: The BPI is directly correlated with the downflow velocity of the corresponding areas (pixels).

We also use a different approach starting from the G-band brightness to investigate the relation of the percentage change of line depression and the Doppler velocity. The "change of line depression'' $(I_{{\rm cont}}-I_{{\rm lc}})/\left\langle I_{{\rm cont}}-I_{{\rm lc}} \right\rangle$is equivalent to the later defined line core contrast. Due to the different line strength the "change of line depression'' is a more suitable measure to compare the CH- and Fe II-line. Figure 8 displays the correlation diagram for the CH-line (left) and for the Fe II line (right). In both figures all data points with an enhanced G-band brightness ( $C_{G{\rm -band}}\geq 0.1$) are plotted. In the diagram for the CH-line the points are spread over a large range of velocity and over a large range in the line depression as well. As indicated in the diagram, two groups become apparent: one related to slightly increased line depression and weak upflows (G1), the second one related to downflows and a large decrease in the line depression (G2). The latter one is consequently related to higher BPI values. The corresponding diagram for the Fe II-line shows a different behavior for the same data points. The distribution of velocity is the same, but there is virtually no variation of the line depression. The examples 1a, 1b, 2a and 2b, as described in Sect. 4.4, belong to G1 and G2 respectively.

The G-band brightness is obviously caused by different effects. The brightness of G2 is clearly a line effect while the brightness of G1 is caused by an enhanced continuum intensity. The BPI for points in G1 is close to zero.

Figure 9: Correlation diagrams. Criterion of data point selection is a G-band contrast $\geq 0.1$. a) Continuum contrast vs. BPI. b) CH-line core contrast vs. BPI. c) flow velocity vs. BPI.

Figure 9 shows the relation of the BPI to the narrowband continuum contrast $C_{{\rm nb-cont}}$ and the CH-line core contrast $C_{{\rm CH}}$. Analogous to the G-band contrast $C_{G{\rm -band}}$ we define the narrowband continuum contrast

$$\begin{eqnarray*}C_{{\rm nb-cont}}=\frac{I_{{\rm cont}}}{\left\langle I_{{\rm cont}}\right\rangle}-1 , \end{eqnarray*}$$

where $I_{\rm cont}$ refers to the continuum at 430.33 nm. Additionally we define the CH-line core contrast by

$$\begin{eqnarray*}C_{{\rm CH}}=\frac{I_{{\rm lc}}^{{\rm CH}}}{\left\langle I_{{\rm lc}}^{{\rm CH}}\right\rangle}-1. \end{eqnarray*}$$

For all correlation diagrams in Fig. 9 only data points are plotted that are related to enhanced broadband intensity ( $C_{G{\rm -band}}\geq 0.1$). The correlation diagram in Fig. 9a shows $C_{{\rm nb-cont}}$ versus BPI, Fig. 9b $C_{{\rm CH}}$ versus BPI and Fig. 9c the velocity versus BPI. All diagrams show a concentration of data points for BPI values around zero. For these points the ratio of line depression is more or less the ratio calculated for the mean profiles of the reference region. They belong to G1 as indicated in Fig. 8, because they show a CH line core contrast around zero. Moreover, they show an enhanced continuum contrast and are related to flow velocities around 0 m s^-1 or slight upflows. Towards higher values of BPI the diagrams show different correlations: The continuum contrast decreases slightly, the CH-line core contrast increases and the flow velocity changes toward downflows.