Radial Oscillations of Dark Matter Stars Admixed with Dark Energy
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper considers radial oscillations of theoretical objects – stable gravitationally bound “stars” made of dark matter with a little dark energy added.
The paper is correct mathematically. The assumptions are spelled clearly, and then a relatively simple circulation follows. My objections to the paper come in several point listed below.
- equations of state. The dark matter equation of state is assumed to be given by equation (4). with the choice of parameters given in Table 1. How does the value of k or l correspond to the laboratory measurements of properties of dark matter? Apart from the core cusp problem mentioned in the text there are many limits on the proprieties of dark matter in the laboratory experiments. This should be addressed.
- equation of state of dark energy. The standard equation of state of dark energy is P=-rho in the cosmological context which corresponds to low P and rho. This does not look like equation 15. Especially in the cosmological context equation 15 would imply that the parameter w has some specific values. How does the choice o parameters correspond to the known constraints on dark energy from cosmology.
- I have an impression that the parameters have been chosen so as to obtain a stellar mass stable object, while the only known dark matter structures are haloes of galaxies. Is the fact that the mass of the objects is close to stellar a coincidence?
- discussing such theoretical structures as dark matter stable objects seems futile without astrophysical context. What are the astrophysical scenarios to form such objects? When and where in the history of the Universe would they form?
- the paper contains no context or motivation. If these theoretical objects exist and if they oscillate how can we detect any of this phenomenology. The paper should contain discussion of why bother with these phenomena.
Currently the paper contains a relatively simple calculation of oscillation modes of theoretical objects. There is no novelty in the calculation itself and just the calculation is not worth publishing. What could make this paper worth publishing is answering to the questions I raised above, especially the astrophysical context of formation and observability. Otherwise this is a simple exercise with little relevance. Therefore I do not recommend the publication of the paper unless all of the above problems are carefully treated.
Comments on the Quality of English LanguageEnglish is fine.
Author Response
Dear Editor,
We wish to thank the referees for valuable comments and suggestions.
We have revised the manuscript taking into account the points raised in the
reports, and we have made the corresponding changes in boldface. What is more, we have made an effort to reduce the similarity rate, changes in red color.
Our detailed response, point-by-point, is as follows:
-Reviewer #1
a) DM EoS: We have included existing bounds on the self-interaction cross-section
sigma.
b) DE EoS: Looking at the equation-of-state it is not obvious, but using the continuity
equation it is possible to obtain the energy density versus scale factor or red-shift,
see eq. (11) of 2012.06869. At late times, or very low red-shift, z << 1, the energy density becomes
a constant, and so it mimicks the cosmological constant.
c) It is not a coincidence, as a matter of fact we intentionally describe objects with mass and
radius comparable to those of neutron stars. We have now motivated the values of M and R assumed
in our work, since there are a few known compact objects with masses and radii around those values,
see e.g. Table 1 of 1906.00063.
d) In the introduction we have added a paragraph about scenarios and mechanisms that may produce
dark stars in the Universe.
e) In the introduction there is now a short discussion on detection of oscillation spectra of stars.
Sincerely,
The authors
Reviewer 2 Report
Comments and Suggestions for AuthorsThis is an interesting manuscript which models dark stars by a mix of dark matter and dark energy, characterized by their respective equations of state, polytropic and Chaplygin, respectively. In particular, the radial perturbation equations about solutions of the TOV equations are studied in a certain approximation, giving rise to a SL boundary value problem, and the first ten excitations are computed numerically, each for three distinct sets of parameter values that describe the TOV solution. There are minor issues that I would like to state later. Apart from those there are a few technical/conceptual problems that the authors need to address before I can recommend the publication of this article in Universe.
1) Eq. (15): How do we obtain the limiting case of a cosmological constant rho=-P if A^2 is positive?
2) l. 128/129: Motivate the values of M and R. Is there any observational evidendence (light deflection, binaries, etc.) that would suggest to tune in on these values?
3) Eqs. (18)-(21): Is rho=rho_E+rho_M and P=P_E+P_M? As in (6) and (7)? This would clash with Eqs. (13) and (14).
4) Boundary conditions in Eqs. (27) - (29) are not explained sufficiently. Why xi(0)=1? Wouldn't this violate the very idea of a (linear) perturbation? This questions also broadly applies to the solution at n=0 for eta(r) in Fig. 1 where |eta|>1 for all r.
5) The comment starting at line 144 literally coincides with what is written on p. 5 of Ref. 65. Hm ... Here, things must be explained better. Namely, the effect of each fluid pressure on the metric functions is not separated in the present approach but only the impact of the total pressure on the metric functions is studied. How good is this approximation? Can it be benchmarked against exact numerical results?
There are some minor points:
i) l.28: judged on a cosmological basis within LCDM we rather would have 90 % -> 85 %
ii) l.13: imposing -> by imposing
iii) l.25: DELETE it
iv) l. 80: NO SLANTING FOR GeV^-1
v) l.109: when the BE condensate of ultralight axions (fuzzy dark matter) is taken as a motivation for the polytropic EoS for DM a brief discussion of newly extracted axion masses (from the PCs of low-surface brightness galaxies) below 5 x 10^(-23) eV, see https://www.aanda.org/articles/aa/full_html/2023/08/aa46686-23/aa46686-23.html and https://www.mdpi.com/2218-1997/7/6/198, violating the 10^(-22) eV bound obtained from linear matter power spectra, should be included.
Comments on the Quality of English Language
English fine.
Author Response
Dear Editor,
We wish to thank the referees for valuable comments and suggestions.
We have revised the manuscript taking into account the points raised in the
reports, and we have made the corresponding changes in boldface. What is more, we have made an effort to reduce the similarity rate, changes in red color.
Our detailed response, point-by-point, is as follows:
-Reviewer #2
A. Major points
a) DE EoS: Looking the equation-of-state it is not obvious, but using the continuity
equation it is possible to obtain the energy density versus scale factor or red-shift,
see eq. (11) of . At late times, or very low red-shift, z << 1, the energy density becomes
a constant, and so it mimicks the cosmological constant.
b) We have now motivated the values of M and R assumed in our work, since there are a few
known compact objects with masses and radii around those values, see e.g. Table 1 of 1906.00063.
c) We apologize for the confusion, p and rho denote total quantities. In the revised version
we have included sub-indices, (p_M, \rho_M) for DM quantities, and (p_E, \rho_E) for DE quantities.
d) The boundary conditions are better discussed now, and it is explained why we have the right to
assume \xi(0)=1.
e) In this work we have not checked, but we did check in our previous work (2309.13161) where we
computed the tidal Love numbers of dark stars made of 2 fluids. In the Riccati equation (21)-(22),
instead of including one term for each fluid, as eq. (28) suggests, we included a single term with
total quantities. A posteriori we checked, and the numerical solution demonstrated that the two expressions perfectly matched.
B. Minor points
We have corrected all of them, and we have cited the 2 articles recommended by the referee.
We thank him/her for bringing them to our attention.
Sincerely,
The authors
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors have revised their ms properly, and so I recommend the publication of this article as is.
Some minor typo errors could be considered in the production process:
l. 81: units m, kg, and s in straight fond
l. 95: don't start the sentence with m(r)
l. 105: the the
Eq. (15) and lines to follow: all units in straight fond
Table 1 and l. 221: km in straight fond
