Referee Report  WITH RESPONSES
Reviewer's Comments:
I cannot recommend this paper for publication in ApJ.


REFEREE POINT 1

I still strongly feel that the basic foundation of their model as
described in Section 2.1 is flawed. Most importantly, I wish to
emphatically state that there is no relation between N(HI) and
W(MgII). Menard and Chelouche (2009) used data from the literature to
derive a relation for the MEDIAN values of the distribution. It was
never meant to be used to derive N(HI) from W(MgII), or vice-versa.

AUTHOR RESPONSE:

We disagree with the referee's statements "I wish to emphatically
state that there is no relation between N(HI) and W(MgII)." and "It
[the relation] was never meant to be used to derive N(HI) from
W(MgII)".  With regards to the first statement, Menard & Chelouche
write in their abstract "we first show the existence of a 8-sigma
*correlation* between the mean hydrogen column density <NHI> and W_0".
As with many astronomical correlations, the data show considerable
scatter (for example, consider the anti-correlation between MgII EW
and the impact qalaxy-quasar parameter (see Chen etal 2010, ApJ, 714,
1521; Nielsen etal arXiv1211.1280).  Yet, even with such highly
scattered data, the anti-correlation is significant at the ~8 sigma
level, and statistical halo occupation models (see Tinker & Chen 2008,
ApJ, 679, 1218) examining the behavior of galaxy halos based upon dark
matter as the underlying physical quantity are developed based upon
this anti-correlation.  In principle, our work is no different than
such works; where Tinker & Chen use the underlying dark matter
distribution, we use the underlying hydrogen distribution.

For the mean N(HI)-W0 relation, *statistically*, at any given MgII
equivalent width, the mean column density can be predicted from their
parametrization of the correlation.  That is a very different
statement than to say "N(HI) is being derived from W0 (or
vice-versa)"- because our treatment is statistical.  As such, the
relationship is a powerful statistical tool that is, in fact,
"reversible" (i.e., there is scatter in W_0 for a given mean N(HI)).
As for the second statement, we note that there is precedent in the
refereed literature for used of this relationship for statistical
based studies and for modeling of absorbers.  In fact, Menard &
Chelouche employ the relation in their own paper to show that,
statistically, the "mean dust-to-gas ratio of MgII absorbers does not
appreciably depend on rest equivalent width".  Additional refereed
works, including those published in ApJ, include:

Chelouche, D., & Bowen, D.V. 2010, ApJ, 722, 1821
Menard, B., & Fukugita, M. 2012, ApJ, 754, 116
Kacprzak, & Churchill, C.W. 2011, ApJ, 743, L34
Bouche, N., Hohensee, W., Vargas, R., etal. 2012, MNRAS, 426, 801

In two of these works, the relationship is used with the identical
spirit in which we employ it- to model galactic gas in relation to W_O
and N(HI).  In the other two works, the relationship is used to derive
the mean Omega_HI in galaxies halos as traced by MgII absorbers.

Again, we emphasize that our modeling is statistical in nature.  To
state that "the basic foundation of their model as described in
Section 2.1 is flawed" by employing the Menard and Chelouche
relationship for our models is tantamount to declaring that the
aforementioned works by other, including the original paper by Menard
and Chelouche, are also fundamentally flawed.  Three of the works are
by the authors who did the original analysis that yielded the relation
(it is presumed that they are fully aware of the limitations, and
conversely, the predictive power of the relationship), and four of the
five papers were deemed worthy of publication *in the Astrophysical
Journal itself*.


REFEREE POINT 2

The spread in the data above log N(HI)=19.5 is not, as the authors
assume, due to saturation. All MgII lines with W>0.3A are saturated,
and so using a different prescription for log N(HI) < 19.5 and >19.5
to account for saturation does not make sense.  The authors use
equation 2 for log N(HI)<19.5, and a random value from a Gaussian
distribution for log N(HI)>19.5.  As you can clearly see from Figure
2, the pink points, even at log W = 0, span 3 orders of magnitude in
N(HI).  Also, for the high N(HI) regime, they only consider W<2 A,
whereas higher W's are observed; their gray region does not sample
W(MgII)>2A where over half the data points for log N(HI)>19.5
lie. More perplexing is the random assignment of W<0.6A absorbers to
values between 0.6A and 2A.

Equivalent widths of saturated lines represent gas velocity
spread. The authors ignore kinematics of the absorbers (middle of
column 1, page 4), when the equivalent width of these lines is
directly a result of their kinematic width.  Modeling this would take
considerable effort, and is not the main objective of this paper, so I
can see why they have not modeled galaxy rotation or winds.

AUTHOR RESPONSE:

We are not sure why the referee claims that all MgII lines with W>0.3A
are saturated.  If we assume a doublet ratio of 1 as saturated and 2 as
optically thin, we find that 0.3 Ang lines with "effective" b
parameters of b=30 km/s (velocity spread in low resolutions spectra)
have N(MgII)=12.95 and DR=1.77 (closer to 2 than to 1), and an
effective b =70 km/s have DR=1.9.  If the effective b parameter is in
this range (which is very typical of halo absorbing gas) then the DR
can vary close to 2 (not saturated).  We are fully aware that these
are small column densities (~12.5-13), but this point about saturation
at 0.3 angstroms is not centrally relevant to the discussion.

There are two points the referee is making here.  (1) why the
different treatment for generating the EW for N(HI)>19 (not 19.5), and
(2) why, for the N(HI)>19 treatment, do we enforce an unweighted
random deviate redistribution the EW when the original Gaussian
weighted deviate yields EW<=0.6A.

With regard to both issues, we feel we have made our points quite
clearly as they are written in the paper, and that the reasoning we
provide is quite balanced and fair.  Consider our text (page 4):

"The effects of line saturation in the context of our model may be
quite complex, depending on the cloud structure of the Mg II absorbing
gas. For instance, it would be possible to have saturated discrete
clouds (producing saturated line ratios) whose integrated absorption
is nevertheless added linearly along the line of sight through the
galaxy because the clouds have sufficiently different velocities. The
much broader 'beam' of studies using background galaxies rather than
quasars is also relevant because small clouds could cover the pc^2 area
of the quasar beam but not the 10^8 pc^2 beam probed by a background
galaxy."

Our text provides a balanced view of the issue of saturation and
velocity; as presented it is quite clear that at no point do we state
that the spread in N(HI) is due to saturation (as claimed by the
referee).  Furthermore, our text goes beyond simple statements that
"saturated EWs represent velocity width".  In fact, that is not an
entirely true statement. There is a great deal of scatter between EW
and velocity width (this is based upon our experience over years of
working with high resolution spectra).  It is the number of components
comprising an absorption profile that directly (and very very tightly)
correlate with EW.  This has been shown, for example, in Churchill,
Vogt, & Charlton (2003, AJ, 125, 98), and Evans (2011, PhD, New Mexico
State, which is based upon 400 HIRES/Keck MgII absorption systems).
Since the column density distribution of MgII is a power law N^-1.65,
most clouds are of lower column density, indicating that saturation of
the individual components is not driving low resolution doublet ratios
toward unity; that occurs as a result of blending of the individual
components.  The tight correlation between number of components and EW
breaks down at a mean EW ~ 1.5A.  At this point, the blending is so
severe that the kinematic information is pretty much lost- the EW
could be anything between 1 and 2A for a fixed number of components
(this can be seen on plots of EW versus number of components in the
aforementioned works).  This empirical behavior is the basis by which
we adopt a different scheme for modeling the EWs of ~2A (corresponding
to a mean logN(HI)>19).  We are accounting for the scatter in EW in
this regime where kinematics information is lost.  Furthermore, the
MgII EW distribution drops exponentially above 2A [such systems are
very rare], so the cut off above 2A is also empirically motivated.
Thus, motivated by our empirical understanding of the behavior of MgII
absorption line, we ensure that we treat the regime where kinematic
information is lost, by accounting for the rapid decline in the EW
distribution (of course, this is all a crude statistical treatment to
emulate the behavior in nature).

As the referee points out, there is significant scatter in the
relation between the mean N(HI) and W0 for W>1A.  However, as
discussed above, the treatment of high EW systems is based upon the
*observed* behavior of EWs in the regime of highly optically thick
neutral hydrogen (on average).  We have modified the manuscript by
removing the statement "The values are chosen to more or less
approximate the scatter in the data used to estimate equation 2."  We
replace it with the statement "This treatment reflects the general
behavior of the Mg II equivalent width distribution and blending of
kinematic components in this equivalent width regime (e.g., Churchill,
Vogt, & Charlton 2003).

**** NOTE FOR RONGMON (to be removed) ******************************
I stated in the above paragraph that we modified the manuscript, if
you agree, please make the changes to the manuscript
********************************************************************

In summary, we agree with the referee that the EW is "a direct result
of kinematic width", but with the understanding that high resolution
observations provides insight into the behavior of EW and the
kinematics in the large EW regime.  In this regime, the majority of
the N(HI) is almost always associated with one dominant component of a
MgII absorption profile, whereas the EW depends upon the spread and
blending of the remaining components.  Thus, for a given N(HI) in the
range N(HI)>19, the EW can have a great deal of scatter, but given the
behavior of MgII kinematics, the EW will be in the range 1ish to 2ish
angstroms. Recall that Rao & Turnshek find a high frequency of DLAs
for W>0.6A, but that not all of these systems are DLAs, many are
sub-DLAs, i.e., N(HI)>19.  Thus, we adopt the statistical Monte Carlo
treatment that when the model line of sight yields N(HI)>19, we are in
this regime and use an empirically guided recipe to yield a physically
reasonable EW.  And, most importantly, we statistically account, in a
reasonable fashion, for the range of scatter and upper and lower
boundaries of EW in the high HI column density regime (based upon
observational insights, not simply due to scatter in the N(HI)-W0
relation).

REFEREE POINT 3

It appears as though the authors grabbed an empirical prescription for
their model from the literature without understanding its
implications. Here is a case where an incorrect model has been used to
derive results that I think actually make sense.  To quote from their
reply to my first report:


"The point of this paper is therefore (i) to resolve the discrepancy
between the conclusions of the two papers K11 and B11, (ii) to clarify
the sometimes non-intuitive behavior of the projections of 3-d spatial
distributions, (iii) to establish whether a consistent picture emerges
from the two approaches to MgII absorption."

I come back to the point I made in my previous report:

"Why not use a W(r) relation for the run of MgII rest equivalent width
with radius? I don't see any motivation for starting with an HI disk
and then inserting an arbitrary N(HI)-W prescription." i.e., they can
begin with their equation 3 and remove all reference to N(HI). They
would still arrive at the same conclusions.

AUTHOR RESPONSE

We disagree with the referee that we are unaware of the implications
of our prescription for the 2D disk model.  Though not discussed in
our manuscript (section 2.2), a column density model is firmly based
upon the physical scenario of a plane parallel slab with a well
defined pressure scale height (though we collapse the scale height
dimension in our parametrization for simplicity) and a decreasing
density with radius in the plane of the disk.  This model is firmly
founded upon models of the Milky way gas disk as constrained by HST
absorption line analysis (see Savage etal 1997, AJ, 113, 2158), 21-cm
HI emission studies of edge on and face on spiral galaxies (Fraternali
etal 2001, ApJ, 562, 47; Heald etal 2007, ApJ, 633, 933; Sancisi etal
2008, A&ARv, 15, 189), and simulations comparing observations (Acreman
etal 2012, MNRAS, 422, 241).  Our formalism also provides a very
reasonable geometric model for accounting for changes in N(HI) as a
function of disk inclination and position angle with respect to the
line of sight.  And we emphasize that this latter attribute is
critical to the scientific goals of our work.  On the other hand, the
only data that can provide insight into how MgII EW behaves in a
galaxy disk is from the HST Key Project (Paper XV. Savage etal ApJS,
129, 563).  They report some 80 sight lines of moderate resolution MgII
EW measurements through the Milky Way disk and halo (actually through
half of these structures).  And, although one could examine the
behavior of EW with galactic latitude (see their Figure 10) and
longitude of the sight line (and translate them into inclination and
position angle of the sight lines), there is one major shortcoming: all
the sight lines are through the solar circle, i.e., at a fixed R along
the disk.  Thus, there are no data sets capable of providing enough
constraints from which to build a full 2D disk model of MgII
absorption.  On the other hand, the observational constraints on HI
disks are abundant AND a highly significant correlation (8~sigma)
between mean N(HI) and MgII EW provides a statistically robust
conversion to MgII EW for a given N(HI).  We gain, emphasize that the
model provides a clear geometric relationship between N(HI) as a
function of disk inclination and line of sight position angle.

Per our responses to Points 1 and 2 above, we maintain that the use of
the mean N(HI)-W0 relation, and our treatment at large EWs is
legitimately applicable for our statistical modeling approach.  The
mean N(HI)-W0 relation provides a statistical relationship between
N(HI) and EW, and the Monte Carlo redistribution at N(HI)>19 emulates
the behavior of the EW distribution at large EW and is consistent with
observations of MgII EW and N(HI) at large HI column densities.

SUMMARY OF RESPONSES

It is our assessment that there are no clear observational constraints
available from which to develop our model based upon MgII equivalent
width.  In our view, to do so would constitute an approach that has no
empirical foundation, far greater uncertainty, and would require
rather ad-hoc assumptions.

We stand behind our approach to the modeling and the statistical
application of the mean N(HI)-W0.  We hope that our responses to the
referees comments and concerns have been affective at clarifying much
of the reasoning that motivated the design of our models and
statistical treatment of the observed quantities.  For us, it has been
very helpful to re-discuss these issues among ourselves and has served
to further focus our thoughts on the design and assumptions underlying
our work.