On the Origin of Persistent Radio and X-ray Emission from Brown Dwarf TVLM 513-46546

Round 1

Reviewer 1 Report

The article by A.V. Stepanov and V.V. Zaitsev is devoted to the analysis of physical conditions in the coldest substellar objects of our Galaxy - brown dwarfs. Apparently, they represent the missing link between red dwarfs and gas giant planets. Discovered in the mid-1990s, they still remain the field of many unsolved problems in the physics of low-mass stars. Particularly, significant differences in the global characteristics of brown dwarf stars lead to differences in the structures of the coronal plasma and magnetic fields from those of the solar corona. Therefore, research aimed at understanding the physics of phenomena in the outer atmospheres of these stars is welcome.

     Although available observations are scarce and provide mainly the only upper limits of soft X-ray fluxes from the brown dwarf out-of-flares, the authors tried to consider the model of their corona.  Besides discussion of problem of coronal heating in low-mass stars, the authors consider the origin of the permanent microwave and X-ray radiation. The authors propose not only the heating mechanism of coronal loop plasma driven by dissipation of electric current generated by photosphere convection, but also the mechanism of long-term particle acceleration in the atmosphere of a brown dwarf supporting the persistent nature of the radio flux. They argue that the sources of radio and X-ray emission of TVLM 513–46546 consist of a few hundreds of coronal magnetic loops quasi-uniformly distributed over the dwarf’s surface. Electric currents required for the heating of the loop up to Т ≈ 10^7 K are determined. Thereby, the magnetic loops responsible for the persistent microwave emission can also be the sources of the “soft” X-ray component.

Thus, the authors show that photosphere convection not only forms numerous magnetic loops in the corona of TVLM 513–46546, but also generates an electric current leading to heating of the loop plasma and acceleration of electrons. As a result, two populations of loops distributed over the dwarf’s surface are formed, one of which is a source of “hard” X-ray radiation, and the other is simultaneously a source of microwave and “soft” X-ray radiation.

A thorough analysis of the parameters of the corona, loops and heating mechanisms carried out by methods adequate for this approach. The estimates of the coronal loop densities agree with accepted values for coronae of low-mass late-type stars.

An approach using an equivalent RLC-circuit, developed earlier by the authors, allow them to substantiate their explanation of the microwave and X-ray radiation of the brown dwarf  TVLM 513–46546.

I recommend to accept this article for publication.

Author Response

Dear referee, thank you for positine opinion.

Reviewer 2 Report

This paper presents a model for the radio emission that has been observed from a well-studied ultra-cool dwarf star. The authors present an alternative explanation for the topology of the radio emitting regions in the corona of the star as compared to the standard and predominant view in the literature. I commend the authors for their effort to provide a consistent physical model for the origin of the accelerated charges that emit in the radio and the thermal bremsstrahlung in the X-ray band. I list some concerns I have in no particular order of importance.


1. ABSTRACT: RLC circuits --> RLC ciruit

 

2. Line 104: The 15% CP values can be converted to a magnetic field only when we assume a consistent magnetic geometry. In case of a large scale field this may be ok but for hundreds of smaller loops the polarisation is further reduced due to cancellation of Stokes V emission from regions of different magnetic polarity. Can the authors therefore establish the validity of their assumptions leading to the estimate of the 100G field strength.

 

3. L108 and in several other places: When the authors mean to show a range they use the "divided by" symbol which is very confusing. Can they adopt a different notation ?

 

4. Eqn 6: Can the authors re-check the units at the end of the equation.

 

5. L141: Looks like the high temperature limit for the plasma conductivity has been assumed in the expression for Qt. This is fine for the coronal temperature considered here, but it is worth providing a reference for the expression for thermal conductivity used here.

 

6. L145: Regarding the reference to solar spicules. Solar type II spicules are also transient phenomena. So for this to work it shold be mentioned that the spicules must cover the dwarfs surface at any given moment in time.

 

7. Eqn 8: There seems to be an implicit assumption here that the energy is deposited into to the corona primarily via thermal conduction. We dont know if this is the case in the star being studied. So please considering mentioning that this is being assumed.

8. In Section 5 the loss timescale of the accelerated particles is considered. The authors compute the loss rate due to diffusion into the loss cone which is fine. However the charges will also loose energy via other mechanisms. For example via Cerkenkov emission of Langmuir waves via the beam instability (initially spontaneous and eventually stimulated). the growth rate for which can be quite large as the authors are well aware. Can the authors comment on why the loss mechanisms considered here are the relevant ones?

9. Please make sure that all symbols used are defined in the text.

 

10. In equations 19 and 20, the authors compute the accelerating electric field in the loop. Fro their own calculations, it seems that the accelerated electron energies are approximately 160 keV which is comfortably below the rest-mass energy of 500keV; hence the electrons are sub relativistic. Are the approximations in equation 1 though 4 even valid in this regime? I don't think so. At such low energies the emission from a single charge will be a monotone at the gyro-frequency and with very little energy in the higher harmonics that are necessary to establish a power-law radio spectrum. Am I missing something here?

11. One thing conspicuously lacking in Sec5 and 6 are falsifiable predictions of the many-small-loops-model. I would have thought that the lack of any detectable polarisation is one of the predictions which is actually a problem for the model presented here (see my comment 3 above). Apart from that, can the authors make any falsifiable predictions, or at least make some predictions that can distinguish between their many-loops model and the large-scale-geometry model that is prevalent in the literature?

Author Response

Dear reviewer, thank you very much for your attention on multi-loop problem.

Author Response File: Author Response.docx