{"id":"ae2086b0-fc11-4d00-abf1-9fc73b3d1af3","arxiv_id":"2505.21047","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In Bifrost simulations of the quiet Sun and coronal hole, acoustic waves near the cut-off frequency dissipate most of their energy as viscous heating at the plasma-beta=1 interface.","lead":"The authors analyzed two 3D simulations of the quiet solar atmosphere and found that acoustic waves steepen into shocks near the height where gas pressure equals magnetic pressure, depositing heat in the lower chromosphere. The result matters because it identifies a concrete channel by which sound waves from the solar surface could help balance the energy losses of the chromosphere.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The acoustic flux proxy in Eq. (8) is unsigned (ρ0 v_z² c_s), so upward and downward waves both add positively and its height gradient need not measure energy lost to heating; a signed pressure–velocity flux check is needed before the flux-dissipation comparison can support the central claim.","rationale":"The reader's weakest assumption (isothermal dispersion relation) is real and is acknowledged by the authors, but the more fundamental issue is that the quantity in Eq. (8) is not a signed net flux. The paper computes Fm from the power spectrum of uz only; at a fixed height, a downward reflected acoustic wave and an upward one produce identical positive contributions. The dispersion-relation filter can exclude evanescent p-modes, but it cannot distinguish propagation direction, and the paper's own Section 6 documents reflection off the transition region. Consequently the 'acoustic flux' in Fig. 4 is an upper bound on the net upward energy flux, and the gradient in Fig. 5 mixes genuine dissipation with changes in reflection and conversion. The central statement that acoustic energy loss is 'more than enough' to account for viscous dissipation is exactly the kind of quantitative claim that this proxy cannot establish without a signed check. This is not an accusation; the authors repeatedly disclaim accuracy and call the flux a proxy, but the strength of the abstract and conclusions still leans on Fig. 5. A signed flux computation with pressure and vertical velocity is straightforward from Bifrost output and would settle the issue. If the signed divergence remains above q_visc, the paper's conclusion is robust; if not, the claim should be softened to 'coherent with' rather than 'more than enough.' I therefore keep the reader's CONDITIONAL verdict rather than rejecting: the concern is concrete and testable, not a demonstrated error.","tokens_in":14696,"tokens_out":9726,"duration_ms":125235,"concrete_test":"Recompute the vertical acoustic energy flux from the same simulation snapshots using the signed quantity F_net(k_h,ν,z) = Re[\\hat{p}^*(k_h,ν,z) \\hat{v}_z(k_h,ν,z)] (or the filtered p′ v_z correlation), integrate it over exactly the same propagating region used for Figs. 3–4, and compare −∂F_net/∂z with the averaged q_visc in Fig. 5. If the signed-flux divergence is substantially smaller than the proxy gradient, or no longer exceeds q_visc in 0.75–1.7 Mm, the central claim that acoustic-wave energy loss is 'more than enough' to account for viscous dissipation is not supported by the present analysis.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing assumption is not just the dispersion-relation boundary, but that Eq. (8), Fm = ρ0 û² cs with û the Fourier power of uz, is a vertical energy flux whose height gradient measures wave-energy loss. Because only uz² is used and no vertical Fourier transform or pressure–velocity phase is taken, upward and downward propagating waves contribute with the same positive sign. The dispersion-relation filter excludes the evanescent region, but it cannot remove reflected propagating waves: Section 6 explicitly shows shocks reflecting downward off the transition region, and mode conversion at β≈1 also creates downward or re-directed signals. Thus Fm is an upper bound on the net upward acoustic flux, not a signed flux, and ∂Fac/∂z in Fig. 5 is not necessarily the acoustic energy lost to heating. The Section 7 statement that 'the energy lost by acoustic waves is more than enough to account for the heat generated by viscous dissipation' therefore rests on a flux proxy that has not been validated as a divergence of net energy flux. The authors acknowledge reflection and conversion as alternative loss channels, but they never quantify them, so the central energy-balance comparison is underdetermined.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper analyzes two 3D radiative MHD Bifrost simulations, one of the quiet Sun and one of a coronal hole, to study acoustic-wave heating in the chromosphere. The authors use an isothermal acoustic-gravity dispersion relation to separate vertical-velocity power into propagating acoustic flux, internal gravity-wave flux, and evanescent power, and then integrate the acoustic contribution to obtain a height-dependent acoustic flux (Eq. 8, Fig. 4). They compare the height gradient of this flux with the average viscous dissipation in the simulations (Fig. 5), compute the coherence between the flux proxy and viscous heating (Fig. 6), and examine one individual shock event in detail (Figs. 7-8). The central claim is that acoustic waves with frequencies near the acoustic cut-off dissipate much of their energy by shock formation near the plasma-β = 1 layer, making acoustic-wave heating an important component of the chromospheric energy balance in the quiet Sun and coronal holes.","tokens_in":14887,"tokens_out":12803,"duration_ms":142048,"significance":"If the quantitative comparison is valid, the paper would provide a strong simulation-based case that acoustic waves from the convection zone can supply a significant fraction of the energy required to heat the quiet-Sun chromosphere, complementing ongoing observational debates. The study is transparent about many of its limitations, uses no parameters fitted to the target result, and combines independent diagnostics (flux gradients, viscous dissipation, coherence, and a single-shock case study). The qualitative picture and the shock event analysis are plausible and valuable. However, as detailed below, the central quantitative claim rests on interpreting the height derivative of an unsigned velocity-power proxy as the divergence of net acoustic energy flux, and that interpretation is not currently justified.","major_comments":[{"comment":"The proxy F_m = ρ0 û_z² c_s is an unsigned power spectrum of vertical velocity, not a signed vertical energy flux. Upward and downward propagating waves both contribute with the same positive sign, and the paper itself shows shocks reflecting off the transition region (§6) and discusses mode conversion at β≈1 (§7). Therefore ∂F_ac/∂z is not the energy lost by the upward-propagating acoustic wave field. In a standing wave produced by reflection, |u_z|² can increase with height even with zero dissipation, so the inequality '∂F_ac/∂z > acoustic wave heating' stated in §5 is not guaranteed. The comparison in Fig. 5, and the Section 8 statement that 'the energy lost by acoustic waves is more than enough to account for the heat generated by viscous dissipation', rest on a flux measure that has not been validated as a divergence of net energy flux. I recommend computing a signed flux (e.g., the horizontal average of p' v_z, or a decomposition into upward and downward vertical wavenumber components) and comparing its divergence with q_visc. This is a necessary check for the central claim.","section":"§4–§5, Eq. (8), Fig. 5"},{"comment":"Even setting aside the sign issue, F_m = ρ0 c_s û_z² varies with height through the background quantities ρ0(z) and c_s(z). The derivative plotted in Fig. 5 therefore contains the term (d/dz)(ρ0 c_s) û_z², which is not a wave-energy loss and can be significant in a stratified atmosphere. The authors acknowledge this effect for the transition-region spike at 2 Mm, but the same background term may contaminate the 0.7–1.7 Mm range where the comparison is made. I ask that the authors either compute the divergence of the actual energy flux, or estimate and subtract this stratification term, or show explicitly that it is negligible in the region of interest.","section":"§5, Fig. 5"},{"comment":"The isothermal, adiabatic dispersion relation evaluated with time- and horizontally-averaged c_s is used to define the propagating acoustic region. The authors state in §7 that 'an accurate dispersion relation for wave propagation is not feasible' and that the fluxes should be taken as proxies. However, the quantitative conclusion in Section 8 depends on the integrated acoustic flux and its gradient; if the filter misclassifies part of the evanescent p-mode ridge (visible below the cut-off in Fig. 3) as propagating, the values of F_ac and ∂F_ac/∂z will be biased. Please add a sensitivity test (e.g., varying the cut-off frequency within the range spanned by local temperature fluctuations, or using the local c_s field) to show that the height range and magnitude of the dissipation peak are robust. Without such a test, the energy-budget comparison is not established.","section":"§3, Eq. (1), Figs. 3–6"}],"minor_comments":[{"comment":"Equation (6) and the definitions below it appear to have lost complex conjugates and averaging brackets. As written, K² uses F(k,ω)G(k,ω) without conjugation and S_{f,f}=⟨F(k,ω)⟩², which is not the standard coherence and can exceed one. Please check against Vigeesh et al. (2017) and correct the expression.","section":"§3, Eq. (6)"},{"comment":"The phrase 'the amplitude of the wave with frequency k' should read 'frequency f' (or 'angular frequency ω'), since k is used for wavenumber.","section":"§3, DFT paragraph"},{"comment":"The sentence 'Both simulation boxes have 7683 grid points' should read '768³ grid points' if that is the intended meaning.","section":"§2"},{"comment":"The axis label 2Hk_x uses H, which is not defined in the text or caption; please define the pressure scale height.","section":"Fig. 2"},{"comment":"Please clarify the normalization of û². If û is the Fourier amplitude of a harmonic component, a factor of 1/2 may be needed for the time-averaged acoustic energy flux (ρ0⟨u²⟩c_s). The current text does not make this factor explicit.","section":"§4, Eq. (8)"},{"comment":"The statement 'our flux estimates are a lower bound' should be qualified. Because Eq. (8) is unsigned, it is an upper bound on the net upward flux for the measured vertical component; the 'lower bound' wording presumably refers to the neglect of inclined propagation or other wave modes. Please clarify which meaning is intended.","section":"§7"}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid simulation study from a well-established group and the qualitative conclusions are plausible. The main obstacle to acceptance is the unsigned flux proxy used for the quantitative energy-budget comparison; this is fixable with a signed flux calculation or an explicit upward/downward decomposition. The sensitivity test for the dispersion-relation cut-off would also materially strengthen the paper. I would be willing to review a revised version."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Udnæs and Pereira do something useful: they take two long Bifrost runs, one quiet Sun and one coronal hole, and map where acoustic wave power actually turns into viscous heating. The headline result — that 3–8 mHz waves steepen into shocks around the β=1 layer near 1 Mm, and that the acoustic-flux gradient is comparable to or exceeds the time-averaged viscous dissipation there — is specific and new for these simulations. The individual shock event in the coronal hole gives a concrete, physical illustration, and the paper is unusually upfront about its own assumptions: isothermal dispersion relation, horizontal averaging, vertical-only propagation, numerical smearing of shocks.\n\nThe soft spot is the flux diagnostic. Equation (8) is ρ0 ⟨u_z²⟩ c_s, an unsigned proxy. It sums upward and downward power, so its vertical gradient is not cleanly the energy lost by the waves. The authors acknowledge reflection and mode conversion as loss channels, but because the flux is unsigned, those channels can bias the gradient in either direction depending on how the downward component changes with height. The stress-test note worried this is a load-bearing issue; I think it is a genuine limitation but not a dealbreaker. In the region below the transition region where the paper sees the strongest gradient, the reflected downward component probably increases with height, which would make the unsigned-gradient a conservative estimate of total loss. Still, a signed pressure–velocity flux or even a two-direction decomposition would remove the ambiguity, and it should not be hard to compute.\n\nThe paper also reports no uncertainties on the main comparisons, does not provide code or data, and leans on a coronal-hole simulation described in a sibling paper. Those are minor to moderate. The coherence analysis between flux proxy and viscous heating is a useful diagnostic on its own, and the shock event gives direct evidence of chromospheric dissipation. The central conclusion — acoustic heating matters in the chromospheric energy balance in these simulations — holds up, but it is a statement about Bifrost, not about the Sun.\n\nThis is for people working on chromospheric heating and wave diagnostics. It deserves peer review; a good referee should push for the signed flux check and for a statement about how reflection affects the gradient before accepting the quantitative claim. I would take it.","headline":"A transparent analysis of Bifrost runs that credibly localizes acoustic heating near the beta=1 layer, with an unsigned flux proxy that a referee should ask them to tighten.","tokens_in":15446,"tokens_out":6396,"would_cite":true,"duration_ms":71485,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In two 3D radiative MHD simulations, the energy lost by upward-propagating acoustic waves exceeds the viscous dissipation above 0.75 Mm, placing a major part of chromospheric heating at the beta=1 layer where waves steepen into shocks.","keywords":["quiet Sun chromosphere","acoustic waves","chromospheric heating","shock dissipation","acoustic cut-off frequency","radiative MHD simulations","wave flux","coronal hole"],"falsifier":"Compute the acoustic flux gradient using a fully 3D, non-isothermal dispersion relation that includes local temperature fluctuations and magnetic-field effects; if the corrected gradient no longer exceeds the viscous dissipation above 0.75 Mm, the central claim fails. A simpler check is to map where shocks actually form in the simulations and compare those heights with the beta=1 layer; if most shocks dissipate well above or below that layer, the localization claim is wrong.","tokens_in":1820,"feed_emoji":"🌞","tokens_out":2243,"duration_ms":91860,"temperature":0.7,"pith_summary":"The paper's aim is to show that acoustic waves do not merely pass through the quiet Sun chromosphere but deposit a significant fraction of their energy there. Using two long 3D radiative magnetohydrodynamic simulations, one of the quiet Sun and one of a coronal hole, the authors find that upward-propagating acoustic waves near the acoustic cut-off frequency steepen into shocks around the height where plasma $\\beta$ equals one, and that the height gradient of the acoustic flux exceeds the simulated viscous dissipation above 0.75 Mm. They identify frequencies of about 3 to 6 mHz and horizontal scales larger than about 1 Mm as the main carriers, and one tracked shock deposits a peak heating rate of about 4 kW $m^{-2}$. If correct, acoustic-wave heating is an important mechanism in the chromospheric energy balance, complementing magnetic heating rather than being a negligible leftover.","feed_headline":"Sound waves can heat the Sun's chromosphere, simulations show","feed_subtitle":"Energy lost by upward sound waves exceeds viscous heating above 0.75 Mm in quiet Sun and coronal hole models.","key_machinery":"The central object is the isothermal acoustic-gravity dispersion relation, $k_z^2 = c_s^{-2}(\\omega^2 - \\omega_a^2) - (\\omega^2 - \\omega_g^2) k_h^2/\\omega^2$, with the acoustic and gravity cut-off frequencies $\\omega_a = \\gamma g/(2 c_s)$ and $\\omega_g = \\sqrt{\\gamma-1}\\, g/c_s$. It separates the Fourier power of measured vertical velocity into propagating acoustic waves, evanescent p-mode ridges, and internal gravity waves, and thereby defines which part of the measured flux counts as acoustic. The vertical mechanical flux is then $F_m = \\rho_0 u_z^2 c_s$ from the azimuthally averaged power spectrum, and the height derivative of the acoustic flux is compared with the simulated viscous dissipation. Coherence between the flux and the dissipation term, computed with the paper's Eq. (6), identifies the frequencies and heights where wave energy actually becomes heat. The simulations themselves provide the velocity, density, sound speed, and dissipation fields, and one tracked shock front shows the same heating in physical space.","core_discovery":"In two long-duration 3D radiative magnetohydrodynamic simulations of the quiet Sun and a coronal hole, vertically propagating acoustic waves near the acoustic cut-off frequency carry a mechanical flux of about 6 kW $m^{-2}$ at 0.5 Mm. As this flux rises through the chromosphere it declines steeply, and its height gradient closely matches the time-averaged viscous dissipation between about 0.75 and 1.7 Mm. The dissipation is concentrated around 1 Mm, the height where the plasma $\\beta$ equals one and the sound speed roughly equals the Alfvén speed; there the authors find coherence between the mechanical flux and viscous heating for frequencies of 3 to 6 mHz and horizontal wavenumbers below about 1 $Mm^{-1}$. Following one individual shock shows a peak integrated heating rate of about 4 kW $m^{-2}$, with viscous dissipation 6.3 times the Ohmic dissipation. The authors conclude that the energy lost by acoustic waves is more than enough to account for the heat generated by viscous dissipation above 0.75 Mm, making acoustic-wave heating an important mechanism in the chromospheric energy balance of the quiet Sun and coronal holes.","pith_inferences":["A direct follow-up would be to count and integrate every shock front in the two simulations; the authors note they did not do this systematic accounting, and it would bridge the gap between per-event heating of 4 to 10 kW m^-2 and the mean viscous dissipation profile.","The same flux-gradient method could be applied to high-cadence chromospheric observations, with the expectation that unresolved spatial scales would make observed acoustic fluxes lower than simulated ones; the paper's numbers provide a target for resolution-corrected estimates.","If the beta=1 localization is real, chromospheric heating models should treat the beta=1 surface as a preferred dissipation site, a prediction testable by comparing shock emission locations with magnetic field inversions.","The coronal hole result hints that some p-mode energy is converted to other MHD modes and escapes the chromosphere; tracking wave energy across the beta=1 layer in the simulations would quantify that loss."],"forward_implications":["The acoustic flux at 0.5 Mm is about 6 kW m^-2, large enough to compete with the canonical 4.6 kW m^-2 radiative loss of the chromosphere, so wave heating cannot be dismissed on energy grounds.","Above roughly 0.75 Mm, the loss of acoustic flux exceeds the simulated viscous heating, meaning acoustic shocks can supply the mid and upper chromospheric heating in these simulations without invoking magnetic dissipation.","The dissipative region lies near the beta=1 layer at frequencies of 3 to 6 mHz, giving a concrete prediction for where shock heating should be concentrated.","Internal gravity waves carry little flux in the chromosphere, so acoustic waves dominate mechanical energy transport above the temperature minimum.","In a coronal hole, the magnetic field alters the wave mode and reduces the acoustic-heating coherence, so the local magnetic geometry controls how much p-mode energy is deposited versus converted and lost."],"supporting_citations":[{"why":"Supplies the Bifrost code and numerical dissipation scheme that produced the quiet Sun and coronal hole atmospheres studied here.","marker":"Gudiksen et al. 2011"},{"why":"Source of the isothermal acoustic-gravity dispersion-relation diagram used to separate propagating acoustic waves from evanescent and internal-gravity waves.","marker":"Mihalas & Mihalas 1984"},{"why":"Provides the mechanical flux expression I = rho u^2 c_s used to estimate the vertical wave energy flux from vertical velocity power.","marker":"Lighthill 1978"},{"why":"Gives the canonical chromospheric radiative loss of 4.6 kW m^-2 against which the simulated acoustic fluxes are compared.","marker":"Vernazza et al. 1981"},{"why":"Earlier estimate of low acoustic flux around 0.4 kW m^-2 that this paper's simulation values challenge and must be reconciled with.","marker":"Fossum & Carlsson 2005"},{"why":"Shows how vertical temperature gradients and radiative effects modify the propagation boundaries, justifying the adiabatic isothermal approximation and the internal-gravity-wave damping interpretation.","marker":"Vigeesh et al. 2017"},{"why":"Establishes mode conversion at the cs = cA, beta=1 layer, which the paper invokes to explain where acoustic heating is strong and where it stops.","marker":"Bogdan et al. 2003"},{"why":"Describes the artificial 450 s p-mode in Bifrost simulations that the flux integration removes, a correction that affects the low-frequency flux values.","marker":"Carlsson et al. 2016"}],"fun_headline_variants":["Acoustic wave flux matches viscous heating in chromosphere simulations","Sound waves near cut-off heat chromosphere in 3D rMHD simulations","Acoustic waves near cut-off carry flux that heats chromosphere","Sound-wave energy dissipation explains chromospheric heating","Viscous dissipation of acoustic waves heats quiet Sun chromosphere"],"cache_read_input_tokens":17664,"weakest_assumption_plain":"The load-bearing premise is that a simple isothermal wave theory, using horizontally averaged sound speed and density, correctly identifies which measured oscillations are genuinely propagating acoustic waves rather than non-propagating p-mode ridges; if that identification is wrong, the inferred flux, dissipation heights, and the beta=1 heating claim weaken.","fun_headline_variants_meta":{"raw":{"variants":["Acoustic wave flux matches viscous heating in chromosphere simulations","Sound waves near cut-off heat chromosphere in 3D rMHD simulations","Acoustic waves near cut-off carry flux that heats chromosphere","Sound-wave energy dissipation explains chromospheric heating","Viscous dissipation of acoustic waves heats quiet Sun chromosphere"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000967,"raw_usage":{"total_tokens":4115,"prompt_tokens":945,"completion_tokens":3170,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":561,"completion_tokens_details":{"reasoning_tokens":3085}},"tokens_in":561,"tokens_out":3170,"duration_ms":21882,"temperature":1.0,"reasoning_tokens":3085,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T13:38:25.366476+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the acoustic flux gradient using a fully 3D, non-isothermal dispersion relation that includes local temperature fluctuations and magnetic-field effects; if the corrected gradient no longer exceeds the viscous dissipation above 0.75 Mm, the central claim fails. A simpler check is to map where shocks actually form in the simulations and compare those heights with the beta=1 layer; if most shocks dissipate well above or below that layer, the localization claim is wrong.","supporting_citations":[{"cited_title":"& Mihalas, B","cited_arxiv_id":null,"evidence_quote":"Source of the isothermal acoustic-gravity dispersion-relation diagram used to separate propagating acoustic waves from evanescent and internal-gravity waves."},{"cited_title":"1978, Waves in fluids (Cambridge University Press)","cited_arxiv_id":null,"evidence_quote":"Provides the mechanical flux expression I = rho u^2 c_s used to estimate the vertical wave energy flux from vertical velocity power."},{"cited_title":"& Carlsson, M","cited_arxiv_id":null,"evidence_quote":"Earlier estimate of low acoustic flux around 0.4 kW m^-2 that this paper's simulation values challenge and must be reconciled with."},{"cited_title":"2017, ApJ, 835, 148 Wedemeyer-Böhm, S., Steiner, O., Bruls, J., & Rammacher, W","cited_arxiv_id":null,"evidence_quote":"Shows how vertical temperature gradients and radiative effects modify the propagation boundaries, justifying the adiabatic isothermal approximation and the internal-gravity-wave damping interpretation."}],"review_version":1}