Peer review of: Loss-cone instability modulation due to a magnetohydrodynamic sausage mode oscillation in the (2019)

Reviewer #1

The author present some very interesting observations of a solar radio
pulsation event that exhibits a very fast (2 s) period and interpret
it in terms of a loss-cone instability that is coupled to an MHD sausage
mode oscillation.  The authors perform a wavelet analysis which 
convincingly shows a periodicity during most time of the flare. Although similar events
have been reported earlier, what is unique in this study is that the
authors have high-resolution EUV images from AIA/SDO and the tool of 
magnetic modeling at hand, which helps them to identify an X-point 
geometry that plays a keyrole in the interpretation.
The data quality is very good and the Figures are of highest quality
and very informative. Having said all these positive aspects, I think
that the interpretation could be substantially improved, and therefore
I suggest that the authors do some more in-depth work before the manuscript
is considered for publication.

Essentially there are at least two interpretations: (A) MHD sausage mode,
and (B) nonlinear limit cycles. The authors should discuss these two
models in more detail, otherwise we do not learn anything in this paper.
The first model could be possible if: (A1) the periodicity is very regular
(as expected for a standing wave in an eigen-mode), (A2) if the modulated
radio flux amplitude is sinusoidal with symmetric pulse shapes (as it is
expected for a MHD sausage mode in the linear regime), and (A3) if the
sausage mode period (P_sausage > 2.62 a / v_A ) is consistent with the
observables a and v_a. The loop diameters a could be measured from the
AIA images, and the Alfven velocity v_A can be obtained from the 
magnetic field (using the NLFFF method at the oscillating location)
and the electron densities n_e (using a differential emission measure
analysis, and possibly a hydrostatic density model). The possible 
range of the observables (a, n_e) should be determined and a mean value 
and standard deviation of the predicted sausage mode period P_sausage 
could be derived, including measurement uncertainties.
 
The second model (B) could also be modeled in more detail, which is
completely absent in the present version. The authors mention a
Lotka-Volterra equation system with a limit cycle for the energy
exchange between plasma particle and wave distribution. In such a
model, the wave growth (of the observed radio flux) has an e-folding
growth time t_g and a decay time t_d for empting the loss-cone from
particles, while the limit cycle period has the mathematical solution
of P = square root ( t_g * t_d), which is just the geometric mean
of the growth and decay time. It is also straightforward to 
calculate the modulated wave flux profile W(t) from the Lotka-Volterra
equation and to show whether it can produce the non-symmetric pulse
shapes, which look like sawtooth profiles as shown in Fig. 4.
One can also use the NLFFF magnetic field model to calculate the
mirror ratio of the loss-cone in the X-point region of the magnetic 
field. Together with some simplified transport model for empting
the loss cone, one can derive the decay time t_d. If the authors
interpret the radio flux in terms of electron cyclotron maser emission,
they could use the theoretically calculated growth times for the
various X, O, and W modes. 

Once the authors have quantified the two models by using all the
constraints they have from the (excellent) observations, they should
be able to present a decisive discussion which model fits the data 
better. There are a number of possible criteria which the authors
have not used. For instance, sausage (or kink-mode) mode oscillations
usually exhibit very periodic but strongly damped time profiles, while
limit cycles can be periodic over much longer time intervals, with
occasional intermittent glitches (see Froment et al. 2015 for
instance). In addition, are the saw-tooth pulses more consistent
with sausage modes or with limit cycles ?


Some details:
The text could be shortened in a number of places. For instance the
first half of the abstract says nothing new, the abstract could just
start at: "Here we report on ..."
Introduction, "... but this has never before been achieved ..."
This is an overstatement
Introduction: "... modern challenge ..." 
Not only in modern times !
Results: The acronyms or instruments Orfees and NDA are never
explained
Many other acronyms are not defined or at the wrong places: 
PFSS, NLFFF, 
The term "thorns" should probably be "sawtooth pattern"
The term "pulse crash" probably means "pulse decay phase"
Discussion: "This is not a region where we would expect a loss-cone
instability". Really ?
A magnetic field of B > 39 G is cited. Is this the average field
strength along a loop? The corona is 3-dimensional, a single 
0-dimensional value is useless, unless it is explained over what 
volume this value has been averaged. 



Reviewer #2 (Remarks to the Author):  

This paper reports an intriguing observation of radio oscillations that occurred during a solar flare. 
The radio source is attributed to emission produced by a loss-cone instability modulated by an MHD 
sausage mode oscillation in a compact loop near a magnetic null point. It is a very interesting 
observation but I am not convinced that the authors have demonstrated the proposed physical 
scenario.  

The scenario is complex and involves several steps. A large flare and flux rope eruption occurred in 
AR12036. The radio oscillations were excited ~400 Mm to the east of the flare in AR12035.  

• The authors argue that the EUV wave produced by the flare excited MHD oscillations in a 
compact, hot magnetic loop located near a magnetic null point.  

o It is not clear from Supplementary Fig. 1 that the EUV wave (shown at 13:03 UT) in fact 
excited MHD oscillations at the time in question (1254-1258). The non-pulsating radio emission 
begins in this source at ~1245. The role of the EUV wave as an exciter needs to be shown more 
carefully.  

o While the authors identify an EUV loop near the location of the oscillating radio source that 
could be the oscillator, they cannot show that the loop is in fact oscillating because the SDO cadence 
is too slow.  

• The authors argue that loop oscillations periodically modulate magnetic reconnection and 
electron energization near the null point. This is asserted by the authors but cannot be shown.  

• If the loop is implicated in reconnection, shouldn’t it show some signs of being “activated” in 
radio or EUV emissions because fast electrons have access to the oscillating loop? Here, too, the 
timing and sequence of events is important.  

• The authors claim that electrons are injected into an adjacent coronal loop that acts as a 
magnetic trap, presumably as part of the reconnection process – but it is left unstated.  

• Into which magnetic loops might the electrons be injected based on the location of the null 
and the NLFF extrapolation? What is the mirror ratio of these loops? What is the height of the 
pulsating radio source?  

• Next, a loss cone electron distribution results in the trap that is unstable to the production of 
Langmuir waves.  

o Perhaps, but why would the loss cone be set up near the oscillating loop instead of the 
conjugate magnetic footpoint? Is the adjacent loop/trap itself compact? The authors raise the idea 
that there are electron beam signatures in the spectrum (not obvious to this reader). What is the 
role of electron beams in their scenario? By claiming spectral signatures of electron beams, the 
beams are themselves producing type III-like signatures? And loss-cone driven type IV? Do they 
attribute loss-cone quenching to the purported electron beams? If so, why are the claimed beam-
like signatures in phase with the pulse peaks?  

• The authors claim that the Langmuir wave are then converted to radio waves that escape to 
the observer.  

o The authors argue that the emission is plasma radiation. The Hewitt et al (1985) reference 
they provide is a formal study of the mechanism in an unmagnetized plasma (no polarization). The 
degree of polarization from harmonic plasma emission is expected to be weak (Melrose 1980), not 
the 70% degree of circular polarization reported here. The evidence is by no means “conclusive” that 
the suggested mechanism is operative. If the emission is harmonic plasma radiation the density in 
the source is 1.5x10^8/cm^3. Is that commensurate with the plasma environment at the apparent 
height of the radio source?  

o The authors go on to discuss the spectral index of the radio pulses. The relevance of 
references to work about loss-cone driven electron cyclotron maser emission was not clear to me.  


In summary, each of the steps described in the overall scenario is plausible at some level but by no 
means inevitable. The observational evidence supporting each step is more suggestive than 
conclusive and, in some cases, completely absent. The overall scenario is speculative. Given the fact 
that remote pulsations occurred as part of a large flare, erupting flux rope, and fast halo CME, aren’t 
other means of energizing and distributing electrons over a wide volume, and exciting MHD or other 
periodic phenomena, equally plausible?  

 

 

Reviewer #3 (Remarks to the Author):  


The manuscript presents a detailed study of quasi-periodically pulsating radio emission generated in 
the solar corona, supplemented by the study of the magnetic field and plasma geometry in the 
source region. The phenomenon of quasi-periodic pulsations is now at the forefront of the ongoing 
research effort in solar and stellar physics, which makes the results presented in the paper especially 
timely. The main novel element of the paper is the use of the combination of spatially-resolving 
observations in radio and EUV, and the state-of-the-art theory. It allowed to authors to trace the 
whole physical chain of the induction of the pulsations, and use it for a convincing interpretation of 
the observed phenomenon. In my opinion, the paper is a very solid and timely contribution to the 
research field of solar radio physics and plasma physics, and should be published as soon as possible.  

I would suggest some minor revision of the text.  

Abstract: "In rare cases, ..." - I would suggest to modify this statement, as quasi-periodic pulsations 
of the radio emission intensity are a rather frequent phenomenon.  

 

p. 2: "... known as a Lotka-Volterra system" - better, "modelled by ..."  

 

" Solar radio pulsations usually display periodicities of ~0.3-4 seconds" - those pulsations have much 
longer periods too. I'd suggest to rephrase this statement.  

 

p. 17, the estimation of the sausage mode oscillation period. I would remove the factor of 2.62, as 
recent works (including the cited in this estimations) demonstrated that this factor appears only in 
the case of a loop with a step-function perpendicular profile of the fast speed, while for smoother 
profiles this factor is different. Hence, a more correct estimation would be P less than a/C_F, where 
C_F is the fast speed. But, this modification does not affect the result and conclusions.