Construction and Evolution of Equilibrium Configurations of the Schrödinger–Poisson System in the Madelung Frame
Round 1
Reviewer 1 Report
The article assumes a description of Dark Matter (DM) in terms of a self-gravitating quantum field. It aims to compare the direct use of the coupled equations of Schroedinger and Poisson with the corresponding hydrodynamical representation (Madelung fluid). The methods
used to calculate the "ground state" of a spherically symmetrical distribution of DM according to these approaches are first exposed.
The results obtained with these different methods are shown and compared and the differences found are exhaustively discussed.
These results, referenced in a three-dimensional grid, are then used as an initial condition for the time-dependent problem, and the
stability of the different algorithms is tested by examining the deviations of the calculated quantities from the expected stationary
behavior. Finally, the evolution of a velocity field perturbation in the different approaches is examined, again comparing the results obtained.
The present referee has double checked the exposed theory finding only two trivial typographical errors reported below. The work appears
well written and understandable. The authors are, moreover, well-known researchers in the field. I recommend the publication of this paper
in its current form.
Typos
1) Line 125; m' intead of m for the radial derivative of internal mass (as in eq. 16)
2) Line 148; "quasilinear" instead of "cuasilinear"
3) I assume that in eq. 11 the 4*pi factor at the right hand is absorbed in psi.
Author Response
We appreciate the referee report and the comments in it. We appreciate pointing out the errors that we have now fixed.
Reviewer 2 Report
In the draft for review, the authors have studied equilibrium configurations as well as their time evolution of the Schroedinger-Poisson (SP) system in the Madelung frame (fluid equations of hydrodynamics). A comparison is made between the two frames, while the numerical methods employed are described in some detail as well. The manuscript is well structured and clearly presented, and the main numerical results are summarized in 5 figures. Although the SP system is well-known and extensively studied in the literature, I find the results obtained in this submission new. In conclusion, I feel that the submitted manuscript is suitable for publication, and therefore I recommend publication in the Universe in its current form.
Author Response
We appreciate the referee report and the comments in it.
Reviewer 3 Report
The authors study ground state equilibrium configurations of the Schrödinger- Poisson (SP) system in the Madelung frame and analyze their solutions using numerical techniques based on finite volume methods. They also analyze the behavior of these ground states in both Madelung and Schroedinger Poisson frames, in terms of mass and energy conservation. The whole analysis is implemented with numerical plots of solutions. The article is a consice treatment of the issues mentioned, well written and deserves publication. I have only one comment for the authors, perhaps they could seek deeper in the mathematical structures constructed by the ground states, perhaps some sort of a non-trivial susy algebra lies there, as in many quantum systems, as in 1308.2085,1001.2433. A comment in the conclusions would suffice on this.
Author Response
We appreciate the referee report and the comments in it.
Regarding the references mentioned in the report, we do not see a direct connection between the interesting results in there, and either our system of equations or our eigenvalue problem. Therefore we decided not to include such references.
