refresp2.txt

Reviewer #1: Comments on revised version
---------------------------

Apologies to the authors for being a few days late.

My comments are interspersed with the authors' responses. Issues from
the first round that I regard as being settled have been deleted
here. The page and line numbers refer to those in the revised version.


- Section 2

General comments on this section:

The authors have chosen largely not to act on my structural comments
on this section. These comments were meant to be helpful, coming more
from a reader's perspective rather than a referee's. I accept their
choice, and consider this settled. Just one point:

"Redshift drift has previously been thought of as a high redshift
measurement..."
That may be true for the authors, but is demonstrably incorrect in the
sweeping generality claimed by the authors. A few examples from the
literature: Phillipps (1982), Darling (2012), Balcerzak & Dabrowski
(2013). Low-redshift measurements of the redshift drift have also been
discussed in the context of ALMA and the SKA.

RESPONSE

We have made sure that that statement does not appear in the text of
the article.

- p 2, right, line 23
"We do not mean to claim dz/dt changes sign when DE begins to dominate. We
clarify this by rephrase: 'When the universe begins to accelerate (speed 
up) under the influence of dark energy in recent times, however, then the 
drift will be positive (see Eq. 2 for the exact condtion for the change of 
sign).' " 

This is only a minor issue, but I disagree that this has been
clarified: "When the universe begins to accelerate ... then the drift
will be positive". To me that still sounds like the two are
coincidental in time. The added parentheses after this sentence does
little to correct this impression.

RESPONSE

We replace the text with 

"At lower redshift, when the expansion rate $\dot{a}$ is lower than
today and thus universe has experience acceleration, the drift will be
positive.", which is more precise.


- p 2, r, line 57
'In the next paragraph we justify it but showing that higher redshift
sources (of the same luminosity) become fainter more rapidly and so if
we are photon noise limited we expect low redshift sources to be
better.  This is not a proof, as the referee says, and we rewrite
"especially if, being closer and thus appearing brighter, they are
more easily observed to high signal-to-noise"'

What I meant was (which did not explain properly) that it is extremely
unlikely that the same type of source would be used at low z as at
high z. QSOs are much more luminous than galaxies, and a QSO at z=2
may appear brighter than an emission line galaxy at z=0.3. That's why
I find this half-sentence somewhat misleading.

RESPONSE

In this paragraph we now specify that the signal-to-noise argument
applies to a fixed class of sources and that to recover the
signal-to-noise at high redshift would require the use of a new class
of sources that are intrinsically more luminous.

- p 3, Fig. 2
Regarding the y-axis label and line figures
We all know that many just scan a paper by looking at the figures. My
suggestions were meant to help make the figure more immediately
accessible to casual readers. But fine.

RESPONSE

Each curve is labeled with what it represents.

- p 3, r, line 49
"This complementarity..."
Does this statement depend on the assumption of a flat universe? If
so, then I think it should be mentioned here.

RESPONSE

We now explicitly state in Sec. 2 (in the paragraph "Figure 1 shows") 
that "The results assume a flat universe..." 

- Part on astrophysical uncertainties
I maintain that this section does not seem to add anything new. Yes,
equation 4 is valuable, but it is not new (it's from Linder 2010). The
rest of this section discusses peculiar accelerations, which have also
been discussed extensively in the literature. Some references to these
studies have presumably been added (although the manuscript I have only
shows two question marks where the references should be) but their
findings are not integrated into the discussion.

However, I confess that I still do not understand the authors' point
about the averaging of peculiar accelerations.
"It is important to realize that estimates of an individual peculiar
acceleration..."
What estimates? Theoretical estimates? Do the authors simply mean to
point out that the peculiar accelerations of individual "objects" (be
they galaxies, absorption systems, or whatever) may be correlated?
Could the authors perhaps provide an example? Apologies for being
thick, but if I don't understand this, chances are that many other
readers won't either.

RESPONSE

We have changed the text to better convey the point we are making.

"Note that when calculating the expected peculiar accelerations of
astronomical sources one must recognize that those sources
preferentially occur in high-density regions, so that improper
assumptions of the linearity of density perturbations or spatial
averaging over the power spectrum will generally underestimate
peculiar accelerations."

- Section 3.1

The additional text at the start of this section improves things, but
contrary to my initial belief, it seems I have not missed anything
fundamental, and hence I maintain that I do not find this section very
illuminating.

"The Hubble drift gives substantially related information to redshift
drift, but comes "for free" with spectroscopic galaxy clustering
surveys"

Measuring BAOs along the line of sight is one of the primary goals of
spectroscopic galaxy clustering surveys. It is not some additional,
incidental thing that comes "for free".

"Differences and pros/cons are discussed in the text and explicitly
shown in Table 1."

Only two of the very many differences are discussed and listed, and a
judgement is made for only one of them (H_0 vs s). This is pretty far
from a discussion of pros and cons.

I mention only two differences, whereas the authors might argue that a
third is mentioned in the last sentence of this section. However, this
hardly counts, as the redshift drift is also unlikely to require a
separate instrument. High-resolution and high-accuracy spectrographs
are being built for large telescopes anyway.

RESPONSE

This section, and table, have received good response and discussion when 
presented in seminars. Analyzing the data to be interpreted in terms of 
Hubble drift comes for free in the sense of requiring no new hardware or 
survey strategy over the redshift surveys already planned. 

- Section 3.2

The authors' response and changes to the text do not address my
comments, except that the Thornton reference is given a better
context. (Note, however, that LSST and SKA are not surveys. They are
telescopes that will carry out surveys.) I maintain that this section
is very superficial and light on content.

RESPONSE

We regard it as useful to bring to the community's notice farther 
future applications such as the use of gravitational wave inspiral signals 
as cosmic clocks. We have also amended the text to read 
"an exciting prospect is that upcoming time domain surveys such as from 
LSST or SKA..." 

- Section 3.3

This section is much improved.

- p 7, r, line 12
time observer baseline --> observer time baseline

RESPONSE

Corrected.

- p 7, r, line 19
"reducing absolute wavelength calibration as a source of uncertainty"

I believe this argument to be a red herring, as I had already
indicated in my previous comments. The difficulty with comparing
spectra of the same source taken at different times is that the
atmospheric conditions are different, the light is not guaranteed to
take the same path through the telescope and instrument, and it will
be detected at a different position on the detector, all while the
physical conditions of the telescope and instrument are different
(although the instrument can be stabilised). Apart from the last item,
all of the others are also true for spectra taken simultaneously of
the two images of a strongly lensed source. All of this means that the
comparison of the spectra has to happen in wavelength (or velocity or
frequency) space, rather than in detector space. Meaning that we have
to worry about wavelength calibration. In the lensed case the
wavelength calibration accuracy must be constant (to within ~1 cm/s)
as a function of position on the detector, while in the "classical"
case it must be constant as a function of both position on the
detector and time. It is not clear at all that it is harder to achieve
the latter than the former.

The reference to the "absolute" wavelength calibration is also
misleading. In both cases we are in principle performing a
differential measurement (lensed case: across detector space;
classical case: across detector space and time). The fact that in
practice one would probably choose to achieve the required
differential wavelength calibration accuracy for the classical case by
using an absolute wavelength calibration method (laser frequency comb)
is irrelevant here. Besides, I'm pretty certain that one would choose
the same wavelength calibration method in the lensed case.

To summarise, I remain unconvinced that the wavelength calibration
requirements for the lensed case are any easier to achieve than for
the classical case.

RESPONSE

The optical systems (from the top of the atmosphere through to the
detector) experienced by two neighboring lines of sight in a single
exposure are more similar than the optical systems experienced by two
neighboring lines of sight taken in separate exposures.  In the former
case the light paths experience the same telescope configuration,
strongly correlated atmosphere, experience the same CCD readout, and
are calibrated with the same images.  The reduced number of degrees of
freedom that can affect wavelength calibration is beneficial.  Common
modes of wavelength calibration uncertainty cancel each other out when
measuring wavelength differences.

We acknowledge that the word "absolute" is not needed and is
misleading, so change the text to read:

"If the lines of sight are within the spectrograph field of view,
multiple images can be observed within a single exposure: sources of
wavelength calibration uncertainty that are correlated in that exposure
for the lines of sight cancel to reduce the contribution of wavelength
calibration as a source of uncertainty in the measurement of
wavelength differences."


- p 7, r, line 25
Instead of a reference only a "?" is shown.

RESPONSE

We have confirmed that the references are visible in the new submission.

- p 7, r, para beginning line 26
I did not really express this in my first report, but I do not really
understand the advantage of "time anchoring". Could the authors
elaborate on this? Here's what I'm guessing: In the lensed case,
although the spectra of the two images are of the same object, they
show the object at different times. Which is relevant since by
definition the object must be variable on the timescale of the
difference of the photon travel time between the two images. If this
difference (apart from the redshift drift) between the *intrinsic*
spectra turns out to be a problem for the extraction of the redshift
drift, then this could conceivably be ameliorated by "time
anchoring". Is this what the authors mean?

If so, then this doesn't seem very relevant to me. After all, the
*observed* spectra will always differ, whether they are taken
simultaneously (but at different positions on the sky) or at different
times, due to transmission, background, and scattered light variations
as a function of position on the sky and time. So the redshift drift
signal will have to be extracted from the data in the presence of
arbitrary additive and multiplicative factors that vary as a function
of position and time. Given this, I find it hard to believe that
variations of the intrinsic source spectrum will matter. (By
"variations" here I of course do not mean intrinsic variations in the
radial velocity of the spectral features of the source.)

RESPONSE

The text was in the wrong place and poorly written.  Here is the new version.

"The spectra from two time-delayed images of the same variable source
observed on the same date is not expected to be the same, complicating
a direct redshift-drift measurement.  By the nature of the strong
lensing time delay, it may be possible to cross-calibrate the spectra
in both space and time.  That is, if the time delay between images A
and B is one year, say, then when observing the system one year later
the spectrum of image B should match that of image A from the previous
year (modulo the redshift drift itself)."

- p 7, r, line 58
"Liske et al. cite 225 metal absorption lines for Q1101-264; we change the
text to use that number and cite Liske et al."

I am totally baffled by the authors' response and by the current text
in the paper. The 225 metal lines of Q1101-264 identified by Liske et
al. are absorption lines in *intervening* absorption systems. This is
entirely obvious from the Liske et al. paper. These lines have
*nothing* to do with the quasar itself and can*not* be used to measure
the quasar's redshift as claimed by the authors. This is completely
wrong. Like I said in my original comment: depending on the redshift
of the quasar and wavelength range of the spectrum a quasar displays
something like ~10 lines that can be used to measure its redshift, and
many of these are broad lines.

RESPONSE

The referee is correct.  The text has been changed to the following:

"The quasar Q1101-264 has embedded within its observed spectrum the
redshifts of individual Lyman-$\alpha$ absorbers and 225 narrow
spectral lines of metal absorbers along the light of sight"

Section 4

- p 8, r, line 28
"To provide context, the redshift measurement as low as..."
The text "with an error" should be inserted between "measurement" and
"as ow as".

RESPONSE

The text now reads

"the redshift measurement with an uncertainty as low as
$\sigma_z=2\times 10^{-8}$"

- p 8, r, line 30
What I presume to be the reference to Darling (2012) is only shown as
a "?".

RESPONSE

Fixed. 

- p 8, r, line 35
'The text did not properly convey our intended meaning. It has been
modified to read:
"differential, rather than absolute wavelength measurements
to get redshift can be more robust."'

I still think that this is not well expressed. I believe that the
authors mean to say that the derivation of an object's redshift from
the separation of a doublet in wavelength space is more robust than
from the position of a single line in wavelength space. However, this
meaning only becomes clear much later. Given the earlier mention of
wavelength calibration, and again in the next paragraph, the use of
the words "differential" and "absolute" could be easily misconstrued
to refer to the wavelength *calibration*, despite the fact that the
authors talk about wavelength *measurements*.
Perhaps it would be clearer to talk of a "differential measurement of
a single-epoch redshift using the wavelength separation of line
doublets"?

RESPONSE

We change the text based on the referee's suggestion.

"the differential measurement of a single-epoch redshift from the
wavelength separation of line doublets can be more accurate than a
measurement based on a single line."

- p 8, r, line 52
References to the laser frequency comb again shown as "??".

RESPONSE

Fixed.

- Section 4.1

- Table 2
"Indeed some of the velocity dispersions are low. As an alternative
extractor of line velocities, we examined the SDSS DR7 catalog made by
the MPA-Garching group. Their catalog contains dispersions as low as
12 km/s."

I note that this is ~10 times larger than the smallest value in Table
2. I further note that the 12 km/s could still be wrong.

"We have asked Daniel Thomas (Portsmouth) specifically on the velocity
numbers and unreported systematic uncertainties but have not heard
back from him. We take the SDSS DR10 database results at face value
but do consider a range of line velocities as broad as Plate 4749
Fiber 757, which is safely non-controversial. As we note shortly, we
now mention the need for higher-resolution spectroscopy for additional
target screening."

This is entirely unacceptable. The authors have essentially accepted
the criticism that the low (< ~15 km/s) velocity dispersion values in
Table 2 are likely to be in error, and they have not addressed my
argument that values < 5 km/s are even unphysical. However, instead
of removing these values, they have essentially added some text that
points out that these values "may be expected" to be wrong. One of the
main results of this paper, as stated in the Section 5 and in the
abstract, namely that a redshift precision of a few * 10^-9 can be
achieved, relies entirely on using velocity dispersions of < ~10 km/s
which are *highly* likely to be erroneous and even unphysical. To my
mind this is unacceptable.

The authors should drop these low velocity dispersions, drop the claim
of a redshift precision of a few * 10^-9, and instead probably focus
on the improvement of the alternative spectroscopic techniques in
comparison to a classical dispersion spectrograph.

"Solar-type stars can have a rotationally-caused dispersion of about 8
km/s. In recognition of the sensitivity of the result to pointing and
unresolved spatial structure that contribute to the lines, we now
mention the benefit from an integral field unit, in part to resolve
different emission regions within the galaxy."

Resolving a galaxy into individual emission line regions would come at
the cost of significantly reducing the line flux and hence the S/N.
This should be mentioned.

RESPONSE

We now select galaxies from the "spZline" 1-d spectral analysis code
described in Bolton et al. (2012). The line velocities appear more
consistent with the observed spectra than those from the Portsmouth
catalog, and the line velocities are significantly higher.  For new
galaxies identified from this catalog they also have higher line fluxes
than those used previously, partially compensating for the reduced
signal-to-noise from the broader lines. 

There is very little reduction in the signal to noise due to light
loss when spatially resolving the line emission.  All the emission
light is used to determine a common velocity change.


- p 9, l, line 55
"It the text it is stated that it is not the NIR, but rather the
[OIII} features shifted into the NIR that are difficult to access."

This is a completely non-sensical statement. Why should [OIII]
features that are redshifted to the NIR be "difficult to access from
ground-based observations [sic]"? Yes, the OH forest in the NIR makes
life harder but we're talking about extremely bright galaxy emission
lines. And in any case, one can always work between the OH lines (for
R > ~3000).

RESPONSE

This statement is removed.

- p 9, r, line 37
"...redshift precision scales with the line width..."
No, the authors are confusing the terms "precision" and "measurement
error". As the line width goes up, the precision decreases (the error
increases). So the precision scales inversely with line
width. Similarly, as the flux goes up, the precision increases (the
error decreases), so it scales with the square root of the flux, not
its inverse.

RESPONSE

The phrasing has been clarified by using the word "uncertainty" rather
than "precision".

- Section 4.2

- p 10, r, line 50 and following
"two-pixel resolution"
"The effective point-spread-function is dominated by the pixel top-hat
function."

These two statements are inconsistent. The term "two-pixel resolution"
implies that the spectrograph's line-spread function is sampled with
two pixels, i.e. it is Nyquist sampled. But the Nyquist frequency is
by definition the frequency at which I must sample a signal so that it
is not affected by the sampling. So the line-spread function cannot
both be "dominated by the pixel top-hat function" *and* be Nyquist
sampled.

RESPONSE

We have kept the same resolution spectrographs while targeting
galaxies with broader features.  The contribution of the pixel to the
ePSF is now irrelevant and removed from the text discussion. 


- p 11, l, line 27 and 33
Confusion between "precision" and "measurement error" again.

RESPONSE

This has been corrected. 

- Section 4.3

- p 11, r, line 33
"The line density is sparse..."
It is true that one does not get one line per pixel. As noted
previously, one can at most get one line per resolution element,
ie. every two pixel. However, calling this line density "sparse" is
ridiculous.

RESPONSE

The sentence is removed.

- p 11, r, line 35
"imager flux calibration"
I strongly suggest to delete the word "imager", and replace it with
"pixel-to-pixel".

RESPONSE

This discussion is removed as this uncertainty is less important for
the broader line-widths of the galaxies now being considered.


"Yes, we now cite HARPS-N, an instrument that uses light scrambling to
measure precision wavelengths."
I could not find any mention of HARPS-N. Also, given that HARPS-N is
based on the original HARPS instrument (which also uses a scrambler)
it would be a bit odd to mention cite HARPS-N in this context, but not
HARPS.

RESPONSE

Some of the references did not appear in the draft you received.
Cosentino et al. 2012 is cited in the third paragraph of Section 3.3.
We have added a reference to HARPS as well.

- Section 5

- p 17, l, line 40
"One surprising result..."
Frankly, this result was not very surprising. Since Dark Energy only
begins to dominate at low redshift, it should not be surprising that
it is best constrained with low-redshift observations.

RESPONSE

We remove the word "surprising".

- p 17, r, line 44
"redshift measurement precision of few x 10^-9"
See my comment above.

- p 17, r, line 48
"Gold targets..."
As the paper currently stands, this sentence is wrong on multiple
levels. First of all, since many of the velocity dispersions in Table
2 are already unphysical, one can hardly expect to find galaxies with
even lower velocity dispersions. Secondly, all of the big upcoming
spectroscopic surveys are also low-resolution surveys and are just as
incapable as the SDSS of discovering extremely narrow emission
lines. At most one can select candidates from these surveys.

RESPONSE

Upcoming surveys can find gold targets, which would be identified as
being gold through subsequent observations with higher resolution
instruments.  This is discussed in the article.

- p 17, r, line 52
"Spatial resolution of the galaxy...
Poor English. Better:
"Spatially resolving a galaxy..."

RESPONSE

Fixed.

- p 18, l, line 18

Again, references show up as "??".
 
RESPONSE

Fixed.