We are grateful to the reviewers for their constructive and useful comments that led us to improve the paper in several points.  There occurred a few issues where Reviewer 1 asked for elaborating them more, while Reviewer 2 suggested that they could be presented more concisely, some parts could be shortened (or moved to appendix).  We saw they both had some good reasons for their suggestions, yet they suggested contradicting actions as each reviewer emphasized different aspects in their comments.  We considered the issues case by case.  We elaborated some points more as requested by Reviewer 1 as we believe that presenting a few more details there will be appreciated by interested readers.  We shortened the paper in some other parts following the comments by Reviewer 2.  Overally, the main text part of the manuscript was shortened by 2 and half pages, i.e., by 12%.

Author responses to specific comments by the reviewers:

R1: I will state my main concern first, and then go through a number of smaller issues in detail. The entire statistical argument is predicated on the fact that the probability of observing a binary with obliquity away from the extremes (what I call a non-eclipsing binary) is much lower than observing a binary whose orbit pole has an obliquity near 0 or 180 degrees (what I call an eclipsing binary in the following). I agree with their derivation of p_mut, the probability of observing a mutual event, but wonder whether their application of the same p_mut function for the second observation is wholly justified. There are a few issues that the authors should clearly address, and which I am not sure they currently do. First, the probability of observing a mutual event for an eclipsing binary is much higher than observing a mutual event for a non-eclipsing binary. Thus it is to be expected that a potential majority of first detected mutual event binaries are indeed eclipsing
binaries. To better understand this effect, it would be useful for the authors to provide more details about their simulations of initial detections to find the characteristics (i.e., the obliquities) of those initial positive detections and total number of initial detections for that given distribution. It could be that for uniformly distributed poles there just aren't as many initial detections as for the anisotropic distributions -- given the lower number of samples of the high p_mut objects that cluster at the extreme obliquity values for the isotropic distributions. In other words, since the probability of observing a mutual event for eclipsing binaries is so much higher, that these are the binaries that you preferentially detect. A related statistic would be the total number of MBAs in these size scales that have been observed, the overall detection rate of binaries out of that whole group, and whether there may be a population of non-eclipsing binaries which just
aren't being discovered. 

A: This was the case where the reviewers‘ suggestions contradicted: Reviewer 1 asked for elaborating on these points more, while Reviewer 2 wrote „The principal conclusions of this section are well-known and straightforward so I don't think we need all this discussion here“ and suggested that the section could be moved to appendix.  Though we agree with Reviewer 2 that the theory is straightforward, we don’t think that it is well-known to most potentially interested readers and therefore we accepted most of the suggestions by Reviewer 1 and elaborated on it more.  In particular, we made following additions: 
In Section 2: A discussion of the p_me function put below Eq. 2, and added new Fig. 1 with the p_me function plotted for three values of sin i_c.  New Eq. 7 added and the brief discussion below it slightly more elaborated.  
In Section 4: We added the values of sin i_c and the solar phase as columns 2 and 3 to Table 3 and another three columns with values of n_1stapp, n_2ndapp and the probability (n_2ndapp/n_1stapp) from the simulation with the uniform distribution cut at epsilon_x = 30 deg, as the last three columns in the table now.  We also added new Fig. 22, and we comment on the points briefly in the text about in the middle of Section 4.
We hope that these additions will dispel uncertainties raised by the reviewer.  Specifically, we show that there is no population of „non-eclipsing binaries which aren't being discovered“ (at least for close binary systems we study; even systems with high obliquities have a good probability to be detected as fairly long seasons of eclipses occur twice per their heliocentric orbit periods), but that the selection effect of the observing method biases the distribution and it has to be accounted for as we do in the simulations with the numerical model.

R1: A second issue is whether the observers in deciding to observe these 18 binaries at their next apparition purposefully chose their observation epochs to improve the chances of a second mutual event detection, having some constraints on the initial pole distribution from the first detection. In reading the text it seems like this effect may be accounted for, but the authors do not specifically address this possible biasing of the statistics, and they should.

A: No, we have not estimated or constrained a probability of occurrence of mutual events in the second, return apparition for any of the 45 binaries we discovered before running our observations in the second apparition.  The re-observations were completely „blind“ to their orbit poles.  In the 2nd paragraph in Section 3, we added two sentences on it.

R1: The p_mut probability distribution plays a fundamental role in the paper, but is hardly discussed. I would like to see a bit more discussion of its derivation and to see a number of plots of this distribution as a function of i_c and epsilon. It is a rather non-standard curve, and I think it is appropriate for the authors to clearly describe and present it. 

A: Following the reviewer’s suggestion, and as we wrote above, we added 
the discussion of the p_me function below Eq. 2, and added new Fig. 1 with the plots of the p_me as a function of the cosine of epsilon for three values of sin i_c.  

R1: I find the dynamics discussion to be somewhat confusing and rambling. The authors first lay out a number of hypotheses and then go through them but never clearly or concisely summarize the results. It would probably be better if the authors state their hypotheses, summarize their findings and then provide some details on what was simulated and why. This should work well as their main conclusion seems to be that the orbit planes of binary asteroids do not preferentially accumulate at extreme values of obliquity. 

A: We think that the structure of Section 5 (Intrepretation and discussion) matches the logical flow suggested by the referee.  At the beginning we lay the hypotheses/possibilities for a cause of the observational finding (orbital poles preferentially toward the ecliptic poles).  Out of the three mentioned ones, we say the possibility 3 (short-term dynamical instability of systems with pole orientation near the ecliptic plane) does not hold and we prove it in following parts of the section.

We formulate the model and explain the result intuitively, using qualitative arguments.  Then we proceed with a proof based on a dynamical model and show three different examples of short-term binary-pole evolution. This is important, because we demonstrate that for binaries whose heliocentric orbits have high inclinations with respect to the ecliptic plane, the binary pole evolution may have large oscillations, but it shows no instability.  We are finally left with the possibilities 1 and 2, between which the current data cannot discriminate.

We have improved the style of this section to describe it more clearly now.

R1: Are the asymptotic YORP obliquities always to 0 or 180? I recall seeing some other possibilities (perhaps of lower probability) discussed in the literature.

A: Yes, for most cases -and reasonable surface thermal conductivity values— the asymptotic YORP obliquities are to 0 or 180 (see Capek and Vokrouhlicky 2004, also cited in the text).  This is also evidenced by the observed distribution of pole orientations of single asteroids smaller than ~30 km (see Hanus et al. 2011 cited in the text).

R1: Page 9, paragraph starting with "As given in the ." The authors lay out some specific dynamical evolution possibilities but do not provide any description or citation for this. As it stands, it is difficult to follow the point that is being made. 

A: We included reference to Eq. (17) in Colombo (1966) from which the
stated conclusions follow.

R1: Page 19, first paragraph of Section 6. Impacts are also able to change asteroid rotation poles and spin rates, but do not have such systematic obliquities. Since the discussion is purely on MBAs, mutual impacts must also be discussed here as they are a main driver for the evolution of MBA poles and rotation rates. 

A: We don’t think that mutual impacts are a main driver for the evolution of MBA poles and rotation rates.  Actually, there is evidence for that the opposite is true for asteroids smaller than ~10 km (sizes relevant for the parent bodies of our binary systems and those of their primary components) for which the YORP timescales become shorter than the collisional timescales.  This is evidenced by the pole and rotation-rate distribution of small main-belt asteroids in this size range (e.g., Pravec et al. 2008, Icarus 197, 497; Hanus et al. 2011 quoted in the manuscript).  See also the theoretical work by Marzari et al. 2011, Icarus 214, 622.

R1: Pages 21 and 22, The quantities defined by Equations 9 and 10 are not adequately described, its not entirely clear what they signify. 

A: Definitions of the quantities are explicitly given/recalled in the text now.

R1: Page 24, a discussion of the long-term dynamics of a binary system without reference or discussion of BYORP (which can apparently destroy binaries relatively rapidly) or the newly hypothesized binary relative equilibrium states proposed by Jacobson (in a recent ApJ Letter) is incomplete. Just pointing to collisional lifetime and possible YORP effects is not sufficient given our current understanding of these systems. In addition, some discussion of these effects should also be incorporated into the simulation discussions. 

A: Yes, we modified now the last paragraph of Sec. 5.2 (conclusions) according to referee‘s comment.  Nevertheless, we think that the current understanding of long-term evolution of binary asteroids is fairly incomplete even in gross terms; while there were considerable advancements in the BYORP theory recently, their conclusions are sometimes conflicting and we believe that more work and results, both theoretical and observational, will appear in the near future.  We thus deliberately leave speculations/discussion about the long-term evolution of binaries open.  Our aim in section 5 of the paper was to prove their short-term dynamical stability for any pole orientation.

R1: Page 32, Table 1: The computed value of i_c in the p_mut formula should be given in the table, as this is a crucial number for your computations. The asked-for plots of the p_mut distribution could be tied to certain of these specific asteroids as well. 
Page 34, Table 3: As discussed above, it is important to pass on more information regarding these detection statistics beyond that listed here for them to be meaningful. Specifically, what is the range of obliquities for which the detections dominate, how do the total number of detections increase for the anisotropic distributions, how many eclipsing binaries are included in the statistics for the uniform distribution, etc.

A: We added the values of sin i_c and the solar phase as columns 2 and 3 to Table 3 and a note below the table, commenting on the correlation between the two parameters and the computed values of n_1stapp from the simulation with the assumed isotropic distribution.  We also added there another three columns with values of n_1stapp, n_2ndapp and the probability (n_2ndapp/n_1stapp) from the simulation with the uniform distribution cut at epsilon_x = 30 deg, to illustrate the increase of the total number of initial detections for the anisotropic distribution that the reviewer asked for.  Re. the other comments by the reviewer, see our first block of answers above.

R2: One way to shorten the paper would be to remove the discussion of each object in section 5 that duplicates information also appearing in the tables.  I also suggest removing Figures 2, 4, and 6 (discussed
briefly below) since Figs. 1, 3, 5, 7, and the text provide sufficient coverage of this material.  Section 6 is also too long.  

A: We shortened the main text of the paper by 2 and half pages and removed two of the figures, according to the reviewer’s suggestions (see our comments to other points by the reviewers for specific changes made).

R2: The lead author has done an outstanding job of writing even though English is not his first language.  However, there are still _many_ instances where the text is awkward. The paper's native English-speaking co-authors should have stepped forward to fix  little glitches like this, so I'd like to appeal to one of them to tidy things  up while the paper is in revision.  It would improve the paper and it shouldn't take 
more than a couple of hours.

A: One our native English-speaking co-author (AWH) has checked the manuscript and he found the English OK, with just a few cases of usage (or lack thereof) of articles.  We hope that these matters could be patched up by a copy editor.  AWH didn’t find any cases where meaning would be ambiguous or compromised.

R2: The paper's overall structure seems somewhat out of logical order.  It would make more sense
if material appeared in the following order:
1. Intro
2. Observations
3. Pole estimation for individual objects
4. Probability (or put this into a second appendix)
5. Simulations
6. Interpretation and Discussion
7. Appendix: numerical model for short-term dynamical evolution
I won't insist on this change, but I think it would improve the paper.

A: We re-arranged the paper a bit: The original section 5 (Pole estimates) was shortened substantially and it was made to be Section 3.1 now.  Figures were re-ordered accordingly.  We keep the „Probability“ section as Section 2, for the reasons given in the answers to Reviewer 1 above.

R2: I also suggest a slight change to the title of the paper to "Small, Inner Main-Belt Binary Asteroid Population. 2.  Anisotropic Distribution of Orbit Poles."  The reason is that many binary systems are being found among _larger_ main-belt objects not discussed in this paper, so it's important to distinguish the ones in this paper from the others.

A: We agree that the title should specify what class of binaries are studied in the paper.  We changed it to „Binary Asteroid Population. 2. Anisotropic distribution of orbit poles of small, inner main-belt binaries.“  We prefer to specify it in the latter part of the title rather than in its beginning, as we consider this to be paper 2 of the series „Binary Asteroid Population“.

R2: Below are more detailed comments.  They're all minor and I offer them in the hope of improving the manuscript.  (Thus, I hope the authors won't take them personally.)

A: Definitely not, they all are constructive comments and we certainly don’t take them personally.  We appreciated the reviewer’s effort in pointing out the issues that allowed us to improve the paper.

R2: Abstract
--------
The possible detections of three triple systems in the small main-belt population is noteworthy and deserves to be in the abstract.
It would also be worth pointing out in the abstract and/or introduction that the paper presents NEW observations of these binary systems.  I was surprised that the paper didn't state that explicitly.  

A: We have changed the beginning of the 2nd paragraph of the Introduction section to indicate that we present new observations.  Re. pointing out in the abstract that we have got possible detections of three ternary systems: As their possible detection is not related to the main point of the paper, we think that mentioning the three possible ternaries in the abstract would be somewhat undue.

R2: Introduction
------------
This would be a good place to mention the total number of small, inner main-belt binaries currently known in order to place the 18 objects reported here in context. Instead, the paper buries that information on page 8.  

A: We mention this figure in the Introduction section as well now.

R2: 1st sentence, 2nd paragraph: I suggest citing one of this group's previous papers rather than stating "two years ago."  

A: We cite there two our previous papers now.

R2: Probability of photometric detection of a binary
------------------------------------------------
The principal conclusions of this section are well-known and straightforward so I don't think we need all this discussion here--instead, I suggest retaining just a sentence or two but otherwise moving this section into another appendix.

A: We agree that the principal conclusions of the section are straightforward, but we don’t think that they are well-known, see our comments in the first block of answers to Reviewer 1 above.  Though presenting it in appendix might perhaps be sufficient, we consider it worth presenting it in the main text for the advantage of interested readers.  To our knowledge, the theory of the photometric binary detection, even though it is rather straightforward, was not comprehensively presented in a similar way in a previous paper.

R2: Observations
------------
p. 8, 2nd paragraph: this paragraph spends a lot of effort defining terms that appear in Table 1.  That sort of information belongs in the table caption, not in the main text.

A: We moved the definition of the terms that appear in Table 1 to the note below the table.

R2: p. 8, 4th paragraph: It's not clear how the epochs of mutual events are defined: Do they correspond to the middle of a mutual event or something else?  Please clarify.

A: We write it explicitely there in the mentioned paragraph now: We give the epochs of the first observing session with positive event detection.  

R2: Simulations
-----------
Instead of showing seven figures for this section, how about just four, 
say, every other one starting with the first?  That would still convey the key points and save space in a paper that's already rather long.

A: We agree that the figures with the simulations for the assumed uniform distributions in sin B_p and cos epsilon cut at B_x and 90-epsilon_x equal to 30 deg and 65 deg didn’t bring much new information and we removed them.  The retained five figures are sufficient to convey the key points.  (We keep the figure for B_x and 90-epsilon_x = 53 deg there –it was figure no. 4 in the submitted version and the reviewer suggested to remove it as well- as the resulted probabilities mentioned in Section 4 increase rapidly for 90-epsilon_x from 45 to 60 deg, so presenting the one plot for the value near the middle of the interval seems good.)

R2: p. 9, 2nd paragraph: the last sentence mentions that some effects might not be negligible and cites a previous paper for discussion.  Fine, but it would be helpful to also list the effects _briefly_ here without going into detail so the reader knows what they are.

A: Following this reviewer’s comment, we revisited the issue and checked an influence of the assumptions on our results a bit more now.  We have found only one assumption potentially slightly critical, the one on the bulk density.  We comment on it in detail there in the paragraph now.

R2: Estimated Pole Positions
------------------------
This section is repetitious, long, and should be shortened.  However, the
figures (#8 - 27) are all important so please retain them.  Since much of 
this text repeats information in the tables, it doesn't need to appear
in both places.

A minor suggestion: the last sentence on p. 12 applies to each object, so 
it's not necessary to state it each time.  Just say it once and that it
applies to each asteroid. Furthermore, this would be good to
state in one of figure captions.  

A: We agree with the reviewer that the section was repetitious and too long.  We shortened the text of the section substantially, made it to be Section 3.1 now (see comments above), and present some of the information that was originally given in the text in Table 1 now.  These and other changes and additions (see below) to Table 1 resulted in that the table is rather rich now.  We believe that presenting the estimates and comments in the structured way in the table is superior to having them written in the text as we had it before.

R2: Interpretation and Discussion
-----------------------------
It took multiple readings of this section before I understood its purpose, and as a result, it would be helpful if the authors shortened it. If I bogged down while reading it, so will other readers.

A: We made an effort to improve this Section, see also our replies to related comments by Referee 1.

p. 21, 3rd paragraph: "The thick curve on the right" should be "The thick curve on the left"

A: Fixed.  Thanks.

R2: Tables
------
Table 1: Please list uncertainties for key properties in the table rather than referring readers to a website.  The most important ones are the rotational and orbital periods, but as someone who also observes binary asteroids, I find uncertainties for D2/D1 and a/D1 very useful.
Table 1: Where do the the primary diameter numbers come from?  This is something that should be stated in the table's caption.

A: We added there estimated uncertainties for P_1, P_orb, P_2 and D_2/D_1 and we also describe how the primary diameters were estimated on the lines 1-3 of the note below the table.

R2: Table 2: Why are only two mutual events listed for each object?  The figures show many more.  

A: We list only the first detected mutual event in the discovery as well as the second, return apparition as they were the critical event detections for the survey and their geometric conditions were the critical ones for the survey simulations: The first event detection in the discovery apparition revealed the surveyed asteroid as being a binary and the first event detection in the return apparition revealed that the binary is in an events geometry in the second apparition as well.  The follow-up observations of the mutual events after the first event detections in both apparitions were run to establish the binary nature and to get data needed for estimating the system’s parameters, but whatever amount of the follow-up observations we took or whatever evolution of the events geometry we saw there, it didn’t affect the principal statistics established by the first event detections in the two apparitions.  Considering also that it would be a very long table if we presented there all the observed event epochs, we decided to list just the key event detections.

R2: Figures
-------
In Figs. 1 - 7 the text and legends at the top left corner are small and hard to read. They may be even smaller in the published version, so please enlarge them.

A: The text and legends in the figure enlarged now.

R2: There's a lot of repetition in the figure captions.  To save space, I suggest  stating everything only in the first figure caption and then using subsequent similar captions to refer back to the first one.  For example, it's not necessary to state in *every* caption that the cross marks the pole of the orbit.

A: We shortened many figure captions, eliminating a lot of the repetitions.

R2: Figs. 8, 10, 12,14, 16, 18, 20, 22, 24, 26: Do the shaded uncertainty regions correspond to 1-sigma or something else?  The caption to Fig. 8 should state this explicitly rather than burying this information in the text.

In the captions to the same figures listed immediately above, what do the "offsets in date" mean?  Does this refer to the epoch at the middle of each mutual event? Something else?  It's not clear.

In those same figures, the labels along the abscissa and ordinate are small and difficult to read, so please enlarge them.

Figs. 12 and 16: The text in the captions that attempts to explain the two shades of gray in the figures isn't clear.  Specifically, "the solid curve inside the area bounds" is vague.  I suggest mentioning the two shades of gray explicitly and saying more clearly what they show.  Also, why assume that the tertiary has the same diameter as the primary?

Fig. 14: It would be helpful to change the caption to "The north (left) and south (right) pole" (i.e., add left and right for clarity).

A: We made appropriate changes in the figures and their captions reflecting the reviewer’s suggestions, which were mostly justified.  Re. „Also, why assume that the tertiary has the same diameter as the primary?“, we point out in the text that the diameter of the tertiary was not constrained and that we run our models for a few values of D_3 in the range from 0 to D_1, to check a sensitivity of the model results on the size of the third body.  In Figs. 6 and 10, we plot the resulted (shrinked) orbit pole area for the largest tested size of the tertiary, i.e., for D_3 = D_1, to demonstrate the effect of the third body, and we comment on it in the figure captions. 

R2: Figs. 28-30: I have several comments on these figures, all with the hope of improving their clarity:

1. The labels on the ordinates and abscissas are very small and hard 
to read, so please enlarge them.

2. I suggest adding the asteroid's name to the top of the figure 
(as was done with all the figures showing lightcurves and fits).

3. The dashed lines are faint and hard to see.  Please make them bold.
The labels "C2" and "C3" are also hard to see and they aren't defined in the figure captions.

4. Why show computations spanning 250 000 years?  Figures 29 and 30 are very crowded.  It looks like the main point could be made by showing much shorter intervals, so how about showing only 100 000 years instead?

A: Thanks for the good comments and suggestions, we have modified the figures accordingly.