Quantification of Sub-Solar Star Ages from the Symmetry of Conjugate Histograms of Spin Period and Angular Velocity

Round 1

Reviewer 1 Report

This paper develops the method of histogram analysis to correlate rotational changes to star age. It compiles  a large amount of data and finds, for me, the rather surprising result that there is an exponential spin decay as the star ages.

The presentation is very well done.

In the abstract, line 5: to explai n the fact that a variable...

line 11: for the spin period... 

Author Response

Dear Reviewer, Thank you for your supportive critical comments on our paper.

We directly addressed your comments as follows:

Abstract L5.  We changed the wording “exploit that a variable and its reciprocal…” 

to read    “utilize the fact that a variable and its reciprocal…” 

Abstract L11.  We added the wording “the” as was suggested.

We also spell checked the manuscript and made a few other improvements.  Thanks again for your timely and helpful review.

Reviewer 2 Report

This paper extracts, in a  beautifully researched way, a statement that the rate of spin decrease in a wide range of star types over a large number of clusters is governed by a power law compatible with the exponent n=1 (exponential-in-time decay constant in agreement with viscous dissipation). The authors base their analysis on an inverse method using histograms of spin and its reciprocal (period), selfconsistently assuming a constant rate for star formation.  Using data from 15 clusters with hundreds of stars in each, they show that this method delivers robust results on n against variations in initial spin and underpopulated measurements at short and long periods. 

Their result is important because it allows to calibrate statistically the mean age of a star population. Applied to sun-like stars, it addresses Fermi's paradox on the rarity of intelligent life in our universe.

Therefore, I recommend that the paper be published in Symmetry after two minor changes have been performed by the authors.

1) pls explain blue dotted curve together with open circles more exhaustively in Fig. 1

2) on p. 7, l. 221 and p. 5, l. 185 the first author's name in ref. should be changed as: Hartmann -> Hartman

 

Author Response

Dear Reviewer, Thank you for your kind and supportive critical comments on our paper.  We directly addressed your requests for clarification and correction as follows:

Figure 1 blue line.  We made several changes to the Figure 1 caption to remove ambiguities, and specifically describe what the blue line represents.

We corrected the spelling of Hartman throughout.

We also spell checked the manuscript and made a few other improvements.  Thanks again for your timely and helpful review.

Reviewer 3 Report

Title :”Quantification of Sub-solar Star Ages from the Symmetry of Conjugate Histograms of Spin Period and Angular Velocity ”

Authors: R.E. Criss and A. M. Hofmeister

Manuscript type: Article, ID: 1278054

In this work the authors use the symmetry of conjugate Histograms of spin period and angular velocity to quantify sub-solar star ages. In their approach it seems that the power law for the loss of stellar spin as given by eqn (7), plays a fundamental role. Notable results of their analysis of histogram conjugates for each of the 15 clusters studied, give for the exponent in eqn(7) the value: n = 1.16 ± 0.21. Thus it appears that only exponential decay (n = 1) explains the symmetrical shapes of the conjugate histograms for spin period and angular velocity. Another interesting result of their analysis is that the Sun numbers among the oldest type-G stars, and it is not being a middle-aged star as commonly assumed. Therefore the paper is interesting and brings new results that in principle are worth of publication in Symmetry.

However, I recommend some amendments before publication:

1) The authors should define precisely all quantities on the LHS of equation (22).

2)The authors should provide some general comments as to whether their approach (perhaps enriched in general principle) could be used to study more complex problems such as the so called paradox of youth for the observed S-stars in the central arcsecond of SgrA* region which are in orbit around the Milky-Way’s galactic centre supermassive black hole. Some references that outline the problem and discuss some partial solutions to the paradox of youth as well as for the related problem of the observed distribution of orbital planes of the S-stars that the authors should cite are:

a) Ghez A M et al, THE FIRST MEASUREMENT OF SPECTRAL LINES IN A SHORT-PERIOD STAR BOUND TO THE GALAXY'S CENTRAL BLACK HOLE: A PARADOX OF YOUTH, 2003 Astrophys. J. 586 L127-L131

b)  G V Kraniotis, Periapsis and gravitomagnetic precessions of stellar orbits in Kerr and Kerr-de Sitter black hole spacetimes, 2007 Class. Quantum Grav. 24 1775

After these amendments take place the paper may be published in Symmetry.

Author Response

Dear Reviewer, Thank you for your critical comments on our paper.  We directly addressed your recommended corrections as follows:

We added the words “rotational kinetic” and did minor rewriting to clarify Eq. 22, which is now expressed in terms of the Virial equation. We also made sure that all other variables used in the manuscript are clearly defined.

We clarified this section.

Thank you for noticing that our method applies to other situations. We feel that the additions are best placed in the conclusions. So, we added discussion in Section 7 of the “paradox of youth” that you mention in a new paragraph in the Conclusions section, where we cite the first of your two suggested references.  Note that the second reference does not utilize a statistical approach nor does it conform to a power law, which were stated to be requirements for the application of our model.

We also spell checked the manuscript and made a few other improvements.  Thanks again for your helpful review.