Superfluid Phonons in Neutron Star Core

Round 1

Reviewer 1 Report

This paper provides a short review of work on superfluid phonons in neutron stars. While it does not go into depth in the calculations, or show all the relevant results, it does provide an interesting summary of the state of the field, and provides references to more detailed results, and I thus find it to be a valuable contribution.

I have a couple of minor comments

1) In the introduction the author could cite the relevance to phonons in vortex mediated glitches ( e.g. Warszawski, Melatos and Berloff, 2012, Physical Review B, vol. 85, 104503)

2) The author should point out that the superfluid velocity defined after eq. 4 is a rescaled momentum, and differs from the actual velocity of the components when entrainment is present (see e.g. Andersson and Comer Living Reviews in Relativity volume 10, Article number: 1 (2007))

3) It is unclear to me what is happening at eq.8, is it actually linearized as claimed in the previous paragraph? In general the discussion around the linearization should be clarified.

4) Parenthesis error in eq. 10

5) Maybe the author should clarify that 'below' the crust indicates 'at higher densities', i.e. in the core.

6) Eq. 28 is a velocity but is referred to as an energy.

7) In figure 2 and following the author should point to where the spectral functions are defined in the text.

8) In section 7, can the author provide references directly for the relevance to r-modes?

Author Response

I corrected the manuscript following all the points raised by the referee.

In particular for point 3 I have explained in more detail the manipultions of the equations and where the linearization is actually used.

Reviewer 2 Report

 

 

This paper represent a review of collective excitations in neutron
stars, specifically phonons in various phases of nuclear
component. The paper can be published after minor revision according
to the points below.

1. There is no need to capitalize "Neutron Stars"; this can be done in
the acronym, if such is introduced, i.e., neutron stars --> NS.

2. Please check the sentence starting "Unfortunately..." on lines
22-24.

3. Line 37: Ref. 39 is cited out of order

4. Line 47: Th --> The

5. It is not visible if \nabla in Eq. (6) is a vector or not. It
should be.

6. Before equation (7) "...small and long wavelength..." should be
"...small amplitude and long wavelength..." (?)

9. Line 73: "whatever small they can be" ---> "no matter how small
they are"

10. In Eq. (18) a bracket is missing. Why it is important to mention
that the time ordering operator T in (18) is for bosons? It must be
the same for bosons and fermions. For example, in (19) it appears
acting on fermionic fields. Its action is to put the operators in such
an order that the time flows from the left to the right; and this is
independent on the bosonic and fermionic nature of the operators. Only
the commutation properties of the operators are different in these two
cases of statistics.

11 When discussing the pairing patterns it would be useful to refer
the reader to the overviews of the pairing where results from
different calculations are collected.

12. Line 247: been yet explored --> be explored yet.

13. Line 267: NS like oscillations ---> NS oscillations

14. Line 364: at higher ... --> At higher ...

References:

The list of the references that are related to the computations of polarization tensor,
pair-breaking processes associated with it and neutrino and axion emission is not quite
complete. The author might wish to complete the list for the sake of the reader.

Finally, please run a spell-check on the file. Some trivial typos were
not mentioned above.

 

 

 

Author Response

The manuscript has been corrected following all the indications of the referee. As for point 10, the standard form of the time ordering includes a change of sign for each inversion of position of the fermion operators. For operators quadratic in fermion operators of course there is no change of sign, and this is equivalent to the case of boson time ordering, where no change of sign is needed.

Reviewer 3 Report

This review paper discusses phonons in the nuclear matter of neutron stars. I find the first part and also Eqs. (27) and (28) very interesting.

There are some typos:

- In Eq. (10): one closed round bracket must be removed.

- In Eqs. (11) and (12): the partial derivative with respect to \rho must have \mu_0 instead of \mu at the numerator. Moreover, this partial derivative is then calculated at \rho = \rho_0. A more appropriate symbol should be used.

- Just after Eq. (11): "In Eq. (11 the" must be "In Eq. (11) the".

- Row 364: "at higher" must be "At higher".

Other comments:

Just above Eq. (2) it could be better to write "local number density" instead of "local density".

After Eq. (15) one could be also write the formula that relates k_F to \rho_0.

Similarly, after Eqs. (27) and (28) it could be useful to insert the formulas which connect v_F and E_F to \rho_0.

 

Author Response

I followed closely all the observations of the referee in revising the manuscript.