Observationally quantified reconnection providing a viable mechanism for active region coronal heating

The heating of the Sun’s corona has been explained by several different mechanisms including wave dissipation and magnetic reconnection. While both have been shown capable of supplying the requisite power, neither has been used in a quantitative model of observations fed by measured inputs. Here we show that impulsive reconnection is capable of producing an active region corona agreeing both qualitatively and quantitatively with extreme-ultraviolet observations. We calculate the heating power proportional to the velocity difference between magnetic footpoints and the photospheric plasma, called the non-ideal velocity. The length scale of flux elements reconnected in the corona is found to be around 160 km. The differential emission measure of the model corona agrees with that derived using multi-wavelength images. Synthesized extreme-ultraviolet images resemble observations both in their loop-dominated appearance and their intensity histograms. This work provides compelling evidence that impulsive reconnection events are a viable mechanism for heating the corona.

General: Unfortunately I do not find the work contained in the manuscript terribly novel. Also, I do not think that the outcomes are unique, largely as a result of the model-observation metric applied. As a result it is very difficult to assess if the rather obvious claim being made in the title and abstract is indeed the case. I will provide some examples below, but cannot see how anything other than a radically different approach could be used to back the claim made above.
Are they novel and will they be of interest to others in the community and the wider field? I [opinion] think it is widely believed that magnetic reconnection at small-scales (nanoflares; as discussed originally by Parker) is important for the transport of mass and energy throughout the outer solar atmosphere, so the questions that I ask myself are: does the present work unambiguously highlight reconnection being the majority component of the possibly competing heating events? and, do the diagnostics presented even permit such a discernment being made? In both situations I cannot answer in the affirmative.
There is a statement in the opening paragraph that wave energy [Alfvenic, Torsional, etc] is not sufficient to heat the active corona. I believe that this statement may be true but McIntosh et al follow with a statement that their assessment regarding wave energy is impeded by the patiotemporal resolution of the observations and there could be considerable amounts of "hidden energy". That's ok. There is a different issue however that, at the smallest spatial scales there is NO difference between the processes of wave dissipation and nano flare heating. The braiding, twisting, jostling of the field lines [which are invisible] induced by magneto-convection is really a wave process and the dissipation of induced small-angle differences in the magnetic field are "nanoflares." I refer the authors to two recent and popular reviews: http://adsabs.harvard.edu/abs/2012RSPTA.370.3193D and http://adsabs.harvard.edu/abs/2012RSPTA.370.3217P My issues with the bulk of the manuscript can be broken into those two categories, 1) the modeling approach and 2) the diagnostics applied to. I will address these separately, as follows: Modeling Methodology: The model is static, there is no flux emergence -can the authors comment on the validity of excluding flux emergence as driving heating, surely the impact could/would be "nanoflares" too. I am to believe that the driving velocities are easily discernible from observations. That is likely not the case. The driving velocities must be subject to noise characterisics in the methodology applied. Can the "field lines" be resolved at BBSO/NST resolution, can they demonstrate -I'm highly skeptical that the resolution of HMI is extremely out of range. Are chromospheric diagnostics [imaging or otherwise] used to help clarify? This approach is a theoretical toy. Also, what is the statistical range of alpha parameters in the NLFF extrapolations and how do they vary locally and globally over the modeled field of view as well as over time. I am VERY concerned that the noise induced by forcing a NLFF solution is actually what you're seeing the impact of and not any physical transport. What is the velocity spectrum applied? Is it an observational one? There's simply no completeness here to establish the applicability of the method. Diagnostic Methodology -DEM is a blunt knife. It is a measure of density square weighted emission of plasmas at a given temperature. It is a function of density and temperature as the authors identify. But as used it can characterize the apparent distribution of temperatures of the emitting plasma in a pixel of code/observation from relatively broad (in temperature) transmission functions. it ohs not a unique method The broadband transmission profiles are nowhere near as exact as the state-of-the art approach of reproducing line intensities, widths and Doppler velocities that are required to back up claims made that go beyond the "well nanoflares must be important" presumption in the community.
-While qualitatively giving the appearance of reproducing the observations, depending on the colorable and range chosen, critical elements are missing indicating that the final temperature distribution in the active region modeled is not correct and the thermodynamics are incorrectthere are extensive regions of "moss" in the filed of view. Moss lies in the transition region of hot, high pressure loops. What does the lack of moss being reproduced tell us about the modeling and/or diagnostic methodology applied? Do you feel that the paper will influence thinking in the field? > No. Too many simplistic approximations made in analysis and methodology.
We would also be grateful if you could comment on the appropriateness and validity of any statistical analysis, as well the ability of a researcher to reproduce the work, given the level of detail provided. > See above.

REFEREE REPORT
I consider the work of extreme interest not only for physics of the solar corona, but for stellar coronae in general and possibly also for other applications in magnetized plasmas.
The slipping reconnection is an important energy release mechanism known to be present in solar flares, both predicted theoretically and later confirmed observationally. The idea to apply the slipping reconnection mechanism to coronal heating and modeling of coronal emission is novel; as is the finding that the slipping velocity is structured on small spatial scales. The observational paper of Aulanier et al. (2007, Sci 318, 1588) and a short comment in Testa et al. (2013, Astrophys. J., 770, 1) represent the only clues I am aware of that the slipping reconnection could be important in coronal physics as well.
The authors succeed in generating a coronal emission that both contains coronal loops and requires no fudge (filling) factor to scale the modeled emission to the observed one. Both these points are important, given that some of the previous attempts failed in either or both accounts.
However, the coronal emission synthesis employed ought to be improved upon, as there are a number of difficulties that must be addressed.

COMMENTS AND SUGGESTIONS
[1] The synthesis of temperature and density (from which the DEM(T) and AIA emission is calculated) is simplistic, and in turn may not be entirely realistic, since it i] disregards the loop geometry as calculated from the NLFFF extrapolation of the HMI vector magnetograms; both assuming semi-circular geometry (Eq. M2) and no expansion of the magnetic flux tubes. The latter is not even commented upon.
ii] assumes equilibrium solutions, i.e., no time derivative in Eq. (M1). This perhaps could be justified by public unavailability of the 1D hydrodynamic codes. However, the manuscript finds that the value of R, representing a ratio of the heating scale-length to loop half-length L/2, is optimally chosen at R=0.3. This finding is problematic, since short heating scale-lengths could prevent equilibrium solutions, a well-known fact already noted by Serio et al. (1981, Astrophys. J., 243, 288) and subsequently by Aschwanden et al. (2001, Astrophys. J., 550, 1036. observations and the model. [5] The authors cite articles from The Astrophysical Journal (13) and Solar Physics (6), but only two articles from Astronomy & Astrophysics. The authors should consider whether there might be an unconscious bias.
[6] The reference #3 (Zou et al. 2017) does not seem to be appropriate on page 1, line 19. This paper concerns observations of an active region filament rather than a coronal structure.
[7] The reference #23 (Viall & Klimchuk 2012) does not seem to be appropriate on page 4, line 103. These authors do not build a model of active region corona.
[8] The CHIANTI 8.1 atomic database and software is not properly referenced, although it is essential to building the model of coronal emission. The proper references (see www.chiantidatabase.org/referencing.html) are Dere et al. 1997, Astron. Astrophys. Suppl., 125, 149 Del Zanna et al. 2015, Astron. Astrophys., 582, A56 [9] Please note that the "latest" (page 8, line 204) 'hybrid' abundances Schmelz et al. (2012) are not necessarily the 'correct' coronal abundance values, as the FIP bias in corona may depend e.g. on age or individual structure. Using a different set of abundances (photospheric or coronal) would change the total radiative losses Lambda(T), by a factor of about 2, but will not influence the visualization process of AIA images itself, since in coronal conditions the AIA images are dominated only by Fe ions.

Jaroslav Dudik referee
Reviewer #3 (Remarks to the Author): Here is my review for the manuscript entitled Observationally quantified reconnection providing a viable mechanism for active region coronal heating Yang et al.
The manuscript addresses the relevant issue of seeking for observational support for the nanoflare scenario for coronal heating in active regions. The paper is very well written and the authors make a compelling case using a schematic theoretical model and the observational data at their disposal. However, I think a few words of caution should be added to the text, before I can recommend publication of this manuscript.
I agree with their back-of-the-envelope calculation to estimate the heating rate, and I understand that the authors do their best to come up with constrains for the free parameters in this calculation. However, for the benefit of the readers, I think the authors should stress that these are crude estimates at best. I am referring for instance to the diameter L for the flux elements being reconnected. Based on Big Bear data, 160 km would definitely be an upper limit rather than a typical value. Chances are that there is a whole range of values of L for the very many reconnection events consistent with the nanoflare scenario. There is no reason to believe that the events that Big Bear managed to resolve just barely, happen to be typical dissipation events. Also, the authors assume that the heating time $\tau_r$ is much longer than typical cooling times, but that is based on the same assumption that 160 km is the typical size and not an upper limit. I urge the authors to take these considerations into account and warn the reader in this direction.
We thank the reviewers very much for a careful reading and constructive comments on the paper.
Based on these comments, we have made a substantial revision of the paper. We hope this revision can meet the requirements and answer the questions by the reviewers. Our revisions in the paper are in cyan color. The replies to the reviewers' questions are listed as follows. With a recent discussion on the terms, we have changed the term 'slipping velocity' to 'non-ideal velocity'.
Reviewer 1, Reviewer's general comments: Q: Unfortunately I do not find the work contained in the manuscript terribly novel. Also, I do not think that the outcomes are unique, largely as a result of the model-observation metric applied. As a result it is very difficult to assess if the rather obvious claim being made in the title and abstract is indeed the case. I will provide some examples below, but cannot see how anything other than a radically different approach could be used to back the claim made above.
A: Thanks for the comments. We would express our point of view on the novelty of the paper. We think that our results are novel in the following aspects. We consider the effect of 3D reconnection of magnetic fields in a novel way that the conjugate footpoints show a departure from the ideal plasma flow. And we do NOT use the velocity spectrum as the input to the model. We do not drive the system with an imposed motions with specified spectral properties, as the referee implies. Instead we use a novel form of heating expression which incorporates measured quantities and only a single free parameter, R.
The most important is that the parameter, L, could be constrained by the high resolution observations instead of an artificial high resistivity, which can not be measured directly. Even the coronal model (we use the equilibrium state as the approximation of the plasma response to the heating) is simple, however, its predictions are remarkably similar to the observations. As shown in the main text, we calculate the non-ideal velocity by combining the techniques of DAVE4VM and the optimization method of the NLFFF. These techniques offer a reasonable way to infer the physical parameters from the observations, V and B, which are used to test our heating expression. The diagnostic methodology uses not only the intensity histogram but also the DEM inversion technique. Although the DEM method is an ill-posed problem, if we vary the input data and try different codes as shown in Figure   R5, we could still trust the region where the solution is stable. Considering that there are no other more accurate and practical methods at present, we think we have done our best in performing such an investigation. We have also estimated the errors by 50 Monte-Carlo realizations ( Figure 5 in the main text). The result shows that our calculation is trustable with acceptable errors.
Q: Are they novel and will they be of interest to others in the community and the wider field?  Q: I am to believe that the driving velocities are easily discernible from observations. That is likely not the case. The driving velocities must be subject to noise characterisics in the methodology applied.

I [opinion] think it is widely believed that magnetic reconnection at small-scales (nanoflares; as discussed originally by Parker) is important for the transport of mass and energy throughout
A: Thanks for the comments. We agree that it is difficult to calculate the driving velocities, but we are here making the best attempt with state-of-the-art observations, namely from HMI. We agree that noise is a limitation and thus we have now attempted to estimate the level of errors in our computation of the heating (shown in Figure R2).
Among all the features, we note that those locations with the largest values of the plasma velocity, non-ideal velocity and heating flux, have the smallest errors ( Figure R2 a, b, and   c). In those locations with magnetic field strength greater than 100 G, the relative errors of the plasma velocity and non-ideal velocity are less than 0.6 ( Figure R2 d and e). Moreover, when the non-ideal velocity and heating flux increase, the relative errors decrease ( Figure   2R g, h, and i). In addition, the non-ideal velocity is larger than the plasma velocity, but it does not matter, since it is only an apparent motion, not a physical motion. A figure of these errors has been added in the revised manuscript as Figure 5, and a discussion on the errors has been added in the first paragraph of the Discussion section (Line 155-160 Page 6).  Figure R3, which shows that during 2 hours, it changes very little. A Monte Carlo test has been conducted by adding random, normally distributed errors to the photospheric magnetogram, and repeating our analysis 50 times. The reduced plasma velocity, non-ideal velocity, heating, and the corresponding errors are shown in Figure R2. We are not imposing a velocity spectrum, but are deducing the footpoint velocities from observations, and then combining the magnetic field to measure the non-ideal velocity. However, as the reviewer requested, we show the plasma velocity spectrum and the non-ideal velocity spectrum in Figure. R4.    ii] assumes equilibrium solutions,i.e.,no time derivative in Eq. (M1). This perhaps could be justified by public unavailability of the 1D hydrodynamic codes. However, the manuscript finds that the value of R, representing a ratio of the heating scale-length to loop half-length L/2, is optimally chosen at R=0.3. This finding is problematic, since short heating scale-lengths could prevent equilibrium solutions, a well-known fact already noted by Serio et al. (1981, Astrophys. J., 243, 288) and subsequently by Aschwanden et al. (2001, Astrophys. J., 550, 1036. The importance of geometric effects and their connection to departures from thermal equilibrium in coronal loops are discussed in works of Dudik et al. (2011, Astron. Astrophys., 531, A115) andMikic et al. (2013, Astrophys. J., 773, 94). In particular, combinations of expanding cross-sections and short heating scale-lenghts could produce thermal non-equilibrium in coronal loops; evidence of which has been detected in the solar corona (e.g., Froment et al. 2015, Astrophys. J., 807, 158;Froment et al. 2017, Astrophys. J., 835, 272; see also Mok et al. 2016;Astrophys. J., 817, 15).
A: i] Thanks for the comments. We agree with the referee that our approach may not be 'entirely realistic'. We have two reasons for not using the real geometry from the NLFFF.
• Since we populate every coronal point independently rather than superposing distinct loops, in our data we have 341 × 501 × 501 points. If we use the real geometry of the field lines from the NLFFF, we would need to solve the equilibrium equations for 8 × 10 7 separate loops. This seems impractical at present, and would take an undue amount of time and computer resources.

• The way the assumed axis geometry enters our model is actually a rather subtle issue.
Every volume element is populated independently using a single point taken from an equilibrium loop. We just use the physical parameters at this single point but not the whole loop; thus semi-circular loops are not evident in any of our model results. We use the true distance along the real (non-semi-circular) field line to determine which point along the equilibrium loop to draw the physical parameters from.
The majority of every loop is at high enough temperature that thermal conduction is extremely effective and the pressure scale height is comparable or larger than the loop's full length. This means that our assumed geometry has very little effect on the precise values of density and temperature, which we find and use for the vast majority of the coronal volume. The only place where this reasoning breaks down is near the feet where temperature is low.
The loop's feet will not be affected by the detailed shape we adopt for the entire axis, but they will be affected by the angle from vertical the axis makes at the foopoint: the inclination angle of the legs. We had assumed that the legs were perfectly vertical, which is admittedly a singular case. Under that assumption density and pressure fell off with the small length scale along the axis. In point of fact, the loops found in the NLFFF have a distribution of inclination angles, which will lead to a distribution of density scale distances: all systematically larger than ours. We have therefore chosen to quantify how the distribution of inclination angles will affect our results. We Figure   R7. We can see that the loops with a lower height usually have a large inclination angle, while the higher one is nearly perpendicular to the bottom (close to the semi-circular structure). And we make a comparison between the oblique loop and the semi-circular geometry with a typical heating value ( Figure R8)

measure the inclination of the loop footpoint at the bottom and show them in
where Γ is the expansion factor and L is the loop length. The value of parameter R in our fitting results can be treated as the one that has been modified with the expansion factor. If we only consider the case s H < L, then the parameter R without expansion effect can be found in Figure R10. Thus the expansion effect here is only changing the optimal value of parameter R to a large one, e.g., R(R Γ = 0.3, Γ = 30) ≈ 1. Some discussions have been added in the 3rd and 4th paragraphs in the Discussion section (Line 178-186 Page 6-7).      ' (page 4, line 93). This statement appears to be at odds with the equilibrium assumption.
A: We thank the referee for this comment. It seems that we had written this incorrectly.  (2004, Astrophys. J., 615, 512), while an entirety of newer literature on the subject is ignored. This is a large omission. An incomplete list some of the papers dealing with synthesis of coronal emission is provided below, and I request that authors cite at least several of these papers: Mok et al. 2005, Astrophys. J., 621, 1098Mok et al. 2008, Astrophys. J., 679, 161 Mok et al. 2016, Astrophys. J., 817, 15 Warren & Winebarger 2006, Astrophys. J., 645, 711 Warren & Winebarger 2007, Astrophys. J., 666, 1245Winebarger et al. 2008, Astrophys. J., 676, 672 Lundquist et al. 2008, Astrophys. J. Suppl. Ser., 179, 509 Lundquist et al. 2008, Astrophys. J., 689, 138 Martinez-Sykora et al. 2011, Astrophys. J., 743, 23 Dudik et al. 2011, Astron. Astrophys., 531, A115 Peter & Bingert 2012, Astron. Astrophys., 548, A1 Lionello et al. 2013, Astrophys. J., 773, 134 Bourdin et al. 2013 Figure   2c. Omitting the intensity histograms precludes further quantitative comparison among the observations and the model.  (13) and Solar Physics (6) There is no reason to believe that the events that Big Bear managed to resolve just barely, happen to be typical dissipation events. Also, the authors assume that the heating time τ r is much longer than typical cooling times, but that is based on the same assumption that 160 km is the typical size and not an upper limit. I urge the authors to take these considerations into account and warn the reader in this direction.

From our analysis, the nano-flare frequency is about 5 km s
A: We thank the reviewer for this comment. We agree that 160 km is an upper limit rather than a typical value. We have emphasized that 160 km is an