Modern Solar Facilities – Advanced Solar Science, 139–142
F. Kneer, K. G. Puschmann, A. D. Wittmann (eds.)
c© Universitätsverlag Göttingen 2007
The height dependence of temperature –
velocity correlation in the solar photosphere
J. Koza1,2,*, A. Kučera2, J. Rybák2, and H. Wöhl3
1Sterrekundig Instituut, Utrecht University, The Netherlands
2Astronomical Institute, Slovak Academy of Sciences, Tatranská Lomnica, Slovakia
3 Kiepenheuer-Institut für Sonnenphysik, Freiburg, Germany
*Email: j.koza@astro.uu.nl
Abstract. We derive correlation coefficients between temperature and line-of-sight velocity as a func-
tion of optical depth throughout the solar photosphere for the non-magnetic photosphere and a small
area of enhanced magnetic activity. The maximum anticorrelation of about −0.6 between temperature
and line-of-sight velocity in the non-magnetic photosphere occurs at log τ5 = −0.4. The magnetic field
is another decorrelating factor along with 5-min oscillations and seeing.
1 Introduction
The correlative analysis proves to be an essential tool in disentangling of causal relations
in the solar atmosphere. Recently, Rutten & Krijger (2003) and Rutten et al. (2004) quanti-
fied the correlation of the reversed granulation observed in the low chromosphere and mid-
photosphere with surface granulation in quest for the nature of internetwork background
brightness patterns in these layers. In agreement with these studies Puschmann et al. (2003)
demonstrated that filtering out of the p-modes is inevitable for studying the convective struc-
tures in the solar photosphere because p-modes mostly reduce the correlation between var-
ious line parameters. Odert et al. (2005) showed that correlation coefficients can fluctuate
strongly in time with amplitudes of over 0.4 due to 5-min oscillations and the amplitudes
are larger for higher formed lines. In case of weak lines the situation worsens even more,
because correlations derived from them are influenced stronger by seeing.
In this paper, we address the dissimilarity between non-magnetic and magnetic region seen
in height variations of the correlation between temperature and line-of-sight velocity. We
compare our results with a similar study by Rodrı́guez Hidalgo et al. (1999). Our analysis
follows on the paper Koza et al. (2006, henceforth Paper I) and we invite the reader to have
the paper at hand for further references.
2 Observational data and inversion procedure
We use a time sequence of spectrograms obtained at the German Vacuum Tower Telescope at
the Observatorio del Teide on April 28, 2000. The inversion code SIR (Ruiz Cobo & del Toro Iniesta
1992) was employed in the analysis of this observation. Thorough descriptions of the obser-
vational data, inversion procedure, and spectral lines are given in Paper I.
http://arxiv.org/abs/0704.0603v1
140 J. Koza et al.: Temperature – velocity correlation in the solar photosphere
Figure 1. The height variation of the correlation between line-of-sight velocity and temperature for
the results of Rodrı́guez Hidalgo et al. (1999) (solid) and for the non-magnetic (dashed) and magnetic
(dotted) region defined in Paper I.
3 Results
Figure 1 shows the height variations of the correlation between temperature and line-of-sight
velocity for three different sets of data. The results of Rodrı́guez Hidalgo et al. (1999) in-
dicate the significant anticorrelation between granules and intergranular lanes reaching the
maximum of about −0.7 at log τ5 = −0.2. The subsequent weakening of this anticorrelation
over the log τ5 ∈ 〈−0.2,−1.0〉 range is followed by a rise of correlation up to 0.28 at the
middle photosphere at log τ5 = −1.75. No significant correlation exists in the upper photo-
sphere. In the lower layers of the non-magnetic region (Paper I) the anticorrelation decreases
to −0.63 at log τ5 = −0.4. However, in the middle photosphere temperature and line-of-sight
velocity are almost uncorrelated with a local peak value of 0.08 at log τ5 = −1.7. Higher up at
log τ5 = −2.9 the anticorrelation of about −0.42 is established again. In the sub-photospheric
layers of the magnetic region the anticorrelation of −0.6 was found at log τ5 = 0.5. An
approximately constant value of anticorrelation −0.2 was obtained in the low and middle
photosphere. In the upper photosphere the anticorrelation reaches again −0.6.
Figure 2 compares temperatures and line-of-sight velocities in the form of scatter corre-
lation plots. Each plotted sample represents temperature and line-of-sight velocity specified
along the x and y axes at a given pixel along the slit at a time within the interval of 15 min.
From the top down, the row panels show correlations of the results of Rodrı́guez Hidalgo et al.
(1999) and our results in the non-magnetic and magnetic region in three selected optical
depths log τ5 = −0.3,−1.3, and −1.8. Plot saturation is avoided by showing sample density
contours rather than individual points, except for the extreme outliers. The total distributions
of temperatures and line-of-sight velocities are shown at the top and the left side of each
panel, respectively. The first-moment curves are aligned at large correlation and become
perpendicular in the absence of any correlation (Rutten & Krijger 2003). The first column
in Fig. 2 shows good agreement of correlation coefficients and positions of maxima of ve-
J. Koza et al.: Temperature – velocity correlation in the solar photosphere 141
Figure 2. Height-dependent scatter correlations of the line-of-sight velocity versus temperature. Top
row: data from Rodrı́guez Hidalgo et al. (1999, see p. 315, Fig. 1). Middle and bottom row: our data for
the non-magnetic and magnetic region (Paper I), respectively. The optical depths log τ5 and correlation
coefficients cc are specified at each panel. Negative velocities indicate upflows. The rescaled total
distributions of temperatures and line-of-sight velocities are shown as solid curves at the top and the
left side of each panel, respectively. The dashed curves show the first moments of the sample density
distributions over temperature and velocity bins.
locity distributions in the non-magnetic region with the results of Rodrı́guez Hidalgo et al.
(1999). However, the temperature distributions are dissimilar both in terms of asymme-
try and also the positions of maxima. Our results indicate predominance of higher tem-
peratures in the sample in contrast with lower temperatures prevailing in the results of
Rodrı́guez Hidalgo et al. (1999). In the magnetic region, weak anticorrelation was found.
The temperature distribution in this region is almost symmetric with maximum at higher
temperatures than in the non-magnetic region. The second column of Fig. 2 corresponds to
the layers where granulation is almost erased. While the temperature distributions in the
non-magnetic region and in the results of Rodrı́guez Hidalgo et al. (1999) are symmetric, in
the magnetic region the asymmetry indicates the abundant higher temperatures. The posi-
tive correlation in the results of Rodrı́guez Hidalgo et al. (1999) shown in the third column
suggests reversed granulation. However, this is not seen in our results. In the magnetic re-
gion the asymmetries of temperature and velocity distributions indicate higher abundance of
relatively hotter pixels with faster upflows.
142 J. Koza et al.: Temperature – velocity correlation in the solar photosphere
4 Discussion
Figures 1 and 2 show dissimilarities both in height variations of correlation and distributions,
although we and Rodrı́guez Hidalgo et al. (1999) used VTT observations and the SIR code.
Because the maximum of anticorrelation found at sub-photospheric layers of the magnetic
region is out of the range of sensitivity of the spectral lines (Paper I), we disregard this fea-
ture. Very low anticorrelation found over log τ5 ∈ 〈0.0,−2.0〉 in the magnetic region (Fig. 1)
suggests that magnetic field is another important decorrelating factor along with 5-min os-
cillations and seeing (Puschmann et al. 2003; Odert et al. 2005). In our results, the middle
layers of the non-magnetic and magnetic region lack signatures of reversed granulations
(Fig. 1). The sinusoidal shape of the correlation coefficient in the non-magnetic region over
the log τ5 ∈ 〈−1.2,−3.5〉 range can be explained as a sum of positive correlation typical for
reversed granulation and negative anticorrelation characteristic for 5-min oscillations.
5 Summary
Using a time sequence of high-resolution spectrograms and the SIR inversion code we have
inferred height variation of correlation between the temperature and line-of-sight velocity
throughout the quiet solar photosphere and a small magnetic region. The most important as-
pect is comparison of the results with the akin study by Rodrı́guez Hidalgo et al. (1999). We
found in agreement with Rodrı́guez Hidalgo et al. (1999) that the maximum anticorrelation
−0.6 between the temperature and line-of-sight velocity in the non-magnetic region occurs at
log τ5 = −0.4. The absence of signatures of reversed granulation in the middle layers of the
non-magnetic region is likely to be due to 5-min oscillations, which negative anticorrelation
prevails over weaker positive correlation typical for reversed granulation. Our results show
that magnetic field is another decorrelating factor along with 5-min oscillations and seeing.
Acknowledgements. The VTT is operated by the Kiepenheuer-Institut für Sonnenphysik, Freiburg,
at the Observatorio del Teide of the Instituto de Astrofı́sica de Canarias. We are grateful to B. Ruiz
Cobo (IAC) for kindly providing of the original data used in Figs. 1 and 2. This research is part of
the European Solar Magnetism Network (EC/RTN contract HPRN-CT-2002-00313). This work was
supported by the Slovak grant agency VEGA (2/6195/26) and by the Deutsche Forschungsgemein-
schaft grant (DFG 436 SLK 113/7). J. Koza’s research is supported by a Marie Curie Intra-European
Fellowships within the 6th European Community Framework Programme.
References
Koza, J., Kučera, A., Rybák, J., & Wöhl, H. 2006, A&A, 458, 941, (Paper I)
Odert, P., Hanslmeier, A., Rybák, J., Kučera, A., & Wöhl, H. 2005, A&A, 444, 257
Puschmann, K., Vázquez, M., Bonet, J. A., Ruiz Cobo, B., & Hanslmeier, A. 2003, A&A, 408, 363
Rodrı́guez Hidalgo, I., Ruiz Cobo, B., Collados, M., & del Toro Iniesta, J. C. 1999, in ASP Conf.
Ser. 173: Stellar Structure: Theory and Test of Connective Energy Transport, ed. A. Giménez, E. F.
Guinan, & B. Montesinos, 313
Ruiz Cobo, B. & del Toro Iniesta, J. C. 1992, ApJ, 398, 375
Rutten, R. J., de Wijn, A. G., & Sütterlin, P. 2004, A&A, 416, 333
Rutten, R. J. & Krijger, J. M. 2003, A&A, 407, 735
	Introduction
	Observational data and inversion procedure
	Results
	Discussion
	Summary

  We derive correlation coefficients between temperature and line-of-sight
velocity as a function of optical depth throughout the solar photosphere for
the non-magnetic photosphere and a small area of enhanced magnetic activity.
The maximum anticorrelation of about -0.6 between temperature and line-of-sight
velocity in the non-magnetic photosphere occurs at log tau5 = -0.4. The
magnetic field is another decorrelating factor along with 5-min oscillations
and seeing.

Introduction
The correlative analysis proves to be an essential tool in disentangling of causal relations
in the solar atmosphere. Recently, Rutten & Krijger (2003) and Rutten et al. (2004) quanti-
fied the correlation of the reversed granulation observed in the low chromosphere and mid-
photosphere with surface granulation in quest for the nature of internetwork background
brightness patterns in these layers. In agreement with these studies Puschmann et al. (2003)
demonstrated that filtering out of the p-modes is inevitable for studying the convective struc-
tures in the solar photosphere because p-modes mostly reduce the correlation between var-
ious line parameters. Odert et al. (2005) showed that correlation coefficients can fluctuate
strongly in time with amplitudes of over 0.4 due to 5-min oscillations and the amplitudes
are larger for higher formed lines. In case of weak lines the situation worsens even more,
because correlations derived from them are influenced stronger by seeing.
In this paper, we address the dissimilarity between non-magnetic and magnetic region seen
in height variations of the correlation between temperature and line-of-sight velocity. We
compare our results with a similar study by Rodrı́guez Hidalgo et al. (1999). Our analysis
follows on the paper Koza et al. (2006, henceforth Paper I) and we invite the reader to have
the paper at hand for further references.
2 Observational data and inversion procedure
We use a time sequence of spectrograms obtained at the German Vacuum Tower Telescope at
the Observatorio del Teide on April 28, 2000. The inversion code SIR (Ruiz Cobo & del Toro Iniesta
1992) was employed in the analysis of this observation. Thorough descriptions of the obser-
vational data, inversion procedure, and spectral lines are given in Paper I.
http://arxiv.org/abs/0704.0603v1
140 J. Koza et al.: Temperature – velocity correlation in the solar photosphere
Figure 1. The height variation of the correlation between line-of-sight velocity and temperature for
the results of Rodrı́guez Hidalgo et al. (1999) (solid) and for the non-magnetic (dashed) and magnetic
(dotted) region defined in Paper I.
3 Results
Figure 1 shows the height variations of the correlation between temperature and line-of-sight
velocity for three different sets of data. The results of Rodrı́guez Hidalgo et al. (1999) in-
dicate the significant anticorrelation between granules and intergranular lanes reaching the
maximum of about −0.7 at log τ5 = −0.2. The subsequent weakening of this anticorrelation
over the log τ5 ∈ 〈−0.2,−1.0〉 range is followed by a rise of correlation up to 0.28 at the
middle photosphere at log τ5 = −1.75. No significant correlation exists in the upper photo-
sphere. In the lower layers of the non-magnetic region (Paper I) the anticorrelation decreases
to −0.63 at log τ5 = −0.4. However, in the middle photosphere temperature and line-of-sight
velocity are almost uncorrelated with a local peak value of 0.08 at log τ5 = −1.7. Higher up at
log τ5 = −2.9 the anticorrelation of about −0.42 is established again. In the sub-photospheric
layers of the magnetic region the anticorrelation of −0.6 was found at log τ5 = 0.5. An
approximately constant value of anticorrelation −0.2 was obtained in the low and middle
photosphere. In the upper photosphere the anticorrelation reaches again −0.6.
Figure 2 compares temperatures and line-of-sight velocities in the form of scatter corre-
lation plots. Each plotted sample represents temperature and line-of-sight velocity specified
along the x and y axes at a given pixel along the slit at a time within the interval of 15 min.
From the top down, the row panels show correlations of the results of Rodrı́guez Hidalgo et al.
(1999) and our results in the non-magnetic and magnetic region in three selected optical
depths log τ5 = −0.3,−1.3, and −1.8. Plot saturation is avoided by showing sample density
contours rather than individual points, except for the extreme outliers. The total distributions
of temperatures and line-of-sight velocities are shown at the top and the left side of each
panel, respectively. The first-moment curves are aligned at large correlation and become
perpendicular in the absence of any correlation (Rutten & Krijger 2003). The first column
in Fig. 2 shows good agreement of correlation coefficients and positions of maxima of ve-
J. Koza et al.: Temperature – velocity correlation in the solar photosphere 141
Figure 2. Height-dependent scatter correlations of the line-of-sight velocity versus temperature. Top
row: data from Rodrı́guez Hidalgo et al. (1999, see p. 315, Fig. 1). Middle and bottom row: our data for
the non-magnetic and magnetic region (Paper I), respectively. The optical depths log τ5 and correlation
coefficients cc are specified at each panel. Negative velocities indicate upflows. The rescaled total
distributions of temperatures and line-of-sight velocities are shown as solid curves at the top and the
left side of each panel, respectively. The dashed curves show the first moments of the sample density
distributions over temperature and velocity bins.
locity distributions in the non-magnetic region with the results of Rodrı́guez Hidalgo et al.
(1999). However, the temperature distributions are dissimilar both in terms of asymme-
try and also the positions of maxima. Our results indicate predominance of higher tem-
peratures in the sample in contrast with lower temperatures prevailing in the results of
Rodrı́guez Hidalgo et al. (1999). In the magnetic region, weak anticorrelation was found.
The temperature distribution in this region is almost symmetric with maximum at higher
temperatures than in the non-magnetic region. The second column of Fig. 2 corresponds to
the layers where granulation is almost erased. While the temperature distributions in the
non-magnetic region and in the results of Rodrı́guez Hidalgo et al. (1999) are symmetric, in
the magnetic region the asymmetry indicates the abundant higher temperatures. The posi-
tive correlation in the results of Rodrı́guez Hidalgo et al. (1999) shown in the third column
suggests reversed granulation. However, this is not seen in our results. In the magnetic re-
gion the asymmetries of temperature and velocity distributions indicate higher abundance of
relatively hotter pixels with faster upflows.
142 J. Koza et al.: Temperature – velocity correlation in the solar photosphere
4 Discussion
Figures 1 and 2 show dissimilarities both in height variations of correlation and distributions,
although we and Rodrı́guez Hidalgo et al. (1999) used VTT observations and the SIR code.
Because the maximum of anticorrelation found at sub-photospheric layers of the magnetic
region is out of the range of sensitivity of the spectral lines (Paper I), we disregard this fea-
ture. Very low anticorrelation found over log τ5 ∈ 〈0.0,−2.0〉 in the magnetic region (Fig. 1)
suggests that magnetic field is another important decorrelating factor along with 5-min os-
cillations and seeing (Puschmann et al. 2003; Odert et al. 2005). In our results, the middle
layers of the non-magnetic and magnetic region lack signatures of reversed granulations
(Fig. 1). The sinusoidal shape of the correlation coefficient in the non-magnetic region over
the log τ5 ∈ 〈−1.2,−3.5〉 range can be explained as a sum of positive correlation typical for
reversed granulation and negative anticorrelation characteristic for 5-min oscillations.
5 Summary
Using a time sequence of high-resolution spectrograms and the SIR inversion code we have
inferred height variation of correlation between the temperature and line-of-sight velocity
throughout the quiet solar photosphere and a small magnetic region. The most important as-
pect is comparison of the results with the akin study by Rodrı́guez Hidalgo et al. (1999). We
found in agreement with Rodrı́guez Hidalgo et al. (1999) that the maximum anticorrelation
−0.6 between the temperature and line-of-sight velocity in the non-magnetic region occurs at
log τ5 = −0.4. The absence of signatures of reversed granulation in the middle layers of the
non-magnetic region is likely to be due to 5-min oscillations, which negative anticorrelation
prevails over weaker positive correlation typical for reversed granulation. Our results show
that magnetic field is another decorrelating factor along with 5-min oscillations and seeing.
Acknowledgements. The VTT is operated by the Kiepenheuer-Institut für Sonnenphysik, Freiburg,
at the Observatorio del Teide of the Instituto de Astrofı́sica de Canarias. We are grateful to B. Ruiz
Cobo (IAC) for kindly providing of the original data used in Figs. 1 and 2. This research is part of
the European Solar Magnetism Network (EC/RTN contract HPRN-CT-2002-00313). This work was
supported by the Slovak grant agency VEGA (2/6195/26) and by the Deutsche Forschungsgemein-
schaft grant (DFG 436 SLK 113/7). J. Koza’s research is supported by a Marie Curie Intra-European
Fellowships within the 6th European Community Framework Programme.
References
Koza, J., Kučera, A., Rybák, J., & Wöhl, H. 2006, A&A, 458, 941, (Paper I)
Odert, P., Hanslmeier, A., Rybák, J., Kučera, A., & Wöhl, H. 2005, A&A, 444, 257
Puschmann, K., Vázquez, M., Bonet, J. A., Ruiz Cobo, B., & Hanslmeier, A. 2003, A&A, 408, 363
Rodrı́guez Hidalgo, I., Ruiz Cobo, B., Collados, M., & del Toro Iniesta, J. C. 1999, in ASP Conf.
Ser. 173: Stellar Structure: Theory and Test of Connective Energy Transport, ed. A. Giménez, E. F.
Guinan, & B. Montesinos, 313
Ruiz Cobo, B. & del Toro Iniesta, J. C. 1992, ApJ, 398, 375
Rutten, R. J., de Wijn, A. G., & Sütterlin, P. 2004, A&A, 416, 333
Rutten, R. J. & Krijger, J. M. 2003, A&A, 407, 735
	Introduction
	Observational data and inversion procedure
	Results
	Discussion
	Summary
