Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002apj...564.1062s&link_type=abstract
The Astrophysical Journal, Volume 564, Issue 2, pp. 1062-1065.
Astronomy and Astrophysics
Astronomy
7
Errata, Addenda
Scientific paper
We report the results of an error in our previous computations, which resulted in quantitatively significant errors in our r, λ maps of effective temperature Teff and effective heat flux qeff at the boundaries of the polar coronal hole and equatorial regions near the Sun. In our original paper, we attributed high temperatures and negative heat fluxes at the boundary of the polar coronal hole to inaccuracies of the magnetic field model. We also suspected inaccuracies in our density model. The error is important only close to the Sun, so we will show only revised Figures 9a, 10a, and 11a from the original paper. We will also show figures giving the fractional error for Teff and qeff as a function of r and λ. When we correct the problem of a sign error in our code which computes the radial derivative of the mass density, the above-mentioned anomalies go away, and we have well-behaved solutions. So, the discovery of this error has resolved the problem in our two-dimensional maps of Teff and qeff. Correction.-The error can be traced to the radial derivative of the density, which can be expressed as follows: ∂N(z)/∂z=(∂Np(z))/(∂(z)) + [(∂Ncs(z))/(∂z)-(∂Np(z))/(∂z)] exp[-(λ2)/(w2(z))] +2[Ncs(z)-Np(z)][(λ2)/ (w3(z))]∂w(z)/∂z exp[-(λ2)/ (w2(z))], for which z=1/r. The error was in the form of a negative sign for the third term on the right-hand side of the above equation, which is shown here in the correct form as having a positive sign. Combined with the directional derivative ∂N(r,θ)/∂θ we can compute the component of the spatial derivative of N(r,θ) along the magnetic field direction (θ=π/2-λ is the colatitude). This is then used in our computation of Teff via equation (12) in our original publication. The errors in Teff then affect our computation of qeff via equation (15) in our original paper. Results.-In Figures 1 and 2 we plot the normalized errors of Teff and qeff as a function of r,λ. The normalized error is given by the following expressions for Teff and qeff, respectively: δTeff=(2(Told-Tnew))/ (Told+Tnew), δqeff= (2(qnew-qold))/(qnew+qold). If one compares Figure 1 in this paper with Figure 9a in our original paper, one can see that the enhanced temperatures reported in our original paper at the boundary of the polar coronal hole and equatorial regions can be largely explained by the errors displayed in Figure 1. A similar comparison can be made between Figure 2 in this paper and Figure 10a in our original paper, except here the error caused an underestimate of qeff. In Figures 3 and 4 we show revised two-dimensional maps of Teff and qeff, respectively; they should be viewed as the replacement for the corresponding figures, Figure 9a and Figure 10a, respectively, in our original paper. As can be seen from these figures, there is a lack of enhanced temperatures at the boundary of the polar coronal hole and equatorial regions and a lack of suppressed values of the heat flux at corresponding regions. The contours now vary smoothly across the boundary of the polar coronal hole, and none of the anomalies mentioned in our original paper exist now. The absence of the anomalies in the revised calculations reinforces the correctness of the model calculations and the magnetic field model used. The integrations are performed along the magnetic field, which is highly divergent at the polar coronal hole boundary (i.e., octupole term dominates near the Sun), and by properly taking into account latitudinal gradients, we obtain solutions which are free of anomalies. For completeness, we show in Figure 5 the revised two-dimensional map of the plasma beta reported in our original paper (Fig. 11a). In the original paper the plasma beta was overestimated by more than a factor of 2 in the equatorial regions near the Sun. Finally, the error reported here is also present in the papers by E. C. Sittler, Jr., & M. Guhathakurta (in AIP Conf. Proc. 471, Solar Wind 9, ed. S. Habbal [New York: AIP, 1999], 401), and M. Guhathakurta & E. C. Sittler, Jr. (in AIP Conf. Proc. 471, Solar Wind 9, ed. S. Habbal [New York: AIP, 1999], 79). The impact on the Sittler & Guhathakurta paper is marginal at best because the impacted region is occupied by a tilted current sheet for which no solution is given because of the presence of closed field lines. In the paper by Guhathakurta & Sittler, the error shows up for the r=2.5RS curve in Figure 4, which shows Teff.
Guhathakurta Madhulika
Sittler Edward C. Jr.
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