Subject: Thoughts on astrometry

From: Dave Monet

Submitted: Thu, 27 Feb 2003 11:43:00 -0700

Message number: 87 (previous: 86, next: 88 up: Index)

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In advance of explicit instructions from Michael, let me set out a few
of my thoughts about the relationship between astrometry and LSST.  I
sincerely hope that all, and especially those who have signed up for
the astrometry group, will make suggestions and comments.  It is far
less work for me to be the scribe than the leader.

1) Astrometry as an observatory resource:

    Astrometry will catch several Requirements of which the most important
    is to supply astrometric reference objects for any and all combinations
    of cadence, filter, and observing circumstances.  As I am learning the
    hard way from Pan-STARRS, this task is not as simple as it seems.  For
    those with more time than common sense, I have attached a couple of
    notes that I wrote for the Pan-STARRS folks, but they are relevant
    to LSST.  "refract.3" discusses the importance of Differential Color
    Refraction, and "refract.11" uses the SDSS EDR to study the apparent
    magnitudes and colors for stars.

2) Astrometric discoveries:

    There will be some objects whose astrometric attributes will be
    so unique that they will be the subject of further studies on the
    basis of astrometry alone.  Objects within 5pc or with motions
    greater than 1 arcsec per year or with wiggles larger than 1
    arcsec (for the sake of argument, +/- a lot, etc.) are important
    additions to our inventory of known objects.

3) Astrometry as one of many measured parameters:

    For the vast majority of objects, astrometry will be used to
    complement photometry, position, etc., to aid in our understanding
    of an object, and particularly with this object as
    a member of a group or class.  This is the area wherein there
    is significant overlap with the Stellar Populations folks, and
    astrometry and photometry will be the combined in the analysis
    of these objects.

4) Astrometry for the sake of astrometry:

    LSST will be measuring astrometric parameters for many more objects
    than are in its input catalog.  Some mechanism is needed to collect
    these, compile catalogs, and distribute them to the community.
    I have nominated USNO in general, and me in particular, to help
    facilitate this.  Whereas there is minimal scientific content
    in the catalog itself, it will enable comparisons of objects
    viewed with other telescopes and at other wavelengths.  Dull, yes,
    but it needs to be done well.

Having defined astrometric deliverables (in management speak), the
next step understand what we need from the observatory.  Let me ignore
(for the moment) specifics of the telescope and detectors, and move
on to the cadence and filter discussion requested by Michael.

a) The mandatory minimum requirements to satisfy Item 1 can be met
    with existing or projected catalog products.  We have Hipparcos,
    Tycho-2, UCAC, USNO-B, and 2MASS with all-sky coverage, and it
    is clear that we can supply reference objects at the 100mas level
    easily and at 30mas if LSST can observe relatively bright (R=15
    or so) stars.

b) Geometry is independent of wavelength, so most astrometric measurements
    can be made in whatever filter seems most appropriate.  Hence, let
    me summarize the typical needs.

      i) Two observations in the same color per lunation, at least
         for the first year, so that we can identify objects with large
         proper motions and/or large parallaxes as quickly as possible.

     ii) Observations must be taken near the meridian or at a range of
         hour angles so that we can fit and remove DCR from the data.

    iii) Observations in each survey color at least once per month
         so that we can search for unseen companions, astrometric
         binaries, or other sources of wiggles with enough temporal
         resolution so that we don't miss many, and at enough colors so
         that we can begin to identify the components of a blended image.

     iv) For many interesting objects, we will detect them in only one
         filter.  Hence, we cannot rely on a single filter to carry the
         astrometric burden.

      v) We should be able to characterize the astrometric performance
         of LSST under specific cases of cadence, filter, and circumstances
         of observation.  These can be used to plan observations and/or
         develop an error tree.  I am most worried about looking for
         solar system objects using wide filters and observations far
         from the meridian.  Astrometry can assist in the sense of Item 1
         above, but the data may not be useful for Items 2 through 4.

c) At specific times and for specific reasons, special astrometric surveys
    or configurations may be needed.  I am thinking of ensuring a rigid
    tie to the system of bright astrometric standards and perhaps other
    tasks that might involve a special filter or cadence.  Given the
    efficiency of LSST, the scheduling of different programs during
    bright time, etc., I think that such requests will be a very low
    impact on the observatory.

Having sat through a large number of LSST meetings, I don't see any of
the above as being drivers unique to astrometry.  I still view astrometry
as mostly a parasitic activity that can extract useful information from
most of the observations that are taken for other reasons.

Finally, I don't mind spamming lsst-general every once in a while, but I
would like to have a list of those folks who either signed up for the
astrometry group or are interested in getting the soon-to-be-more-often
exchanges as we have to deliver stuff to the Project.  Can those folks
send me a note so that I can make my list?  At some point, Michael may
wish to make an lsst-astrometry exploder but we can get started without it.

Blast away!  My Nomex suit has only a few holes.
-Dave Monet is dgm@nofs.navy.mil

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While worrying many issues such as an escaped hamster at home, I have made
a bit of headway looking at differential color refraction (DCR).  Again,
this is a topic that can go on forever, and even short discussions seem to
reach this limit.  Also, we already know the qualitative answers: narrow
filters have less of a problem, and you ought to observe on the meridian.
Well, real surveys cannot work like this, and as long as astrometry does
not pay the bill, we need to work with what data we get.

Assuming that my simulator is reasonably correct (nobody has asked for
a copy so this assumes that I can debug my own code), then the following
conclusions can be drawn with minimal effort.  In the following, GSnnn
refers to this entry in the Gunn-Stryker atlas, and KCtype refers to the
generic galaxy models presented by Kinney and Calzetti in 1996.  In all
of these simple cases, I have computed DCR at 60 degrees zenith distance
as being the difference of the flux-weighted mean of the target object
with respect to the reference object.  Geometry gets involved if you want to
evaluate a specific hour angle and declination since the refraction
always points to the zenith.  The calculation assumes (P/P0)=0.6 which
is valid for a 14,000 foot site and 0C.

1) How bad is bad?

   Consider various stellar spectral types with respect to a G5V
   reference star.  For OPEN (==no) filter, I get

   Spectrum      GSnnn      DCR (mas)
   ---------------------------------
     O5            1          513
     B0V           4          459
     A0V          14          296
     F0V          30          142
     G0V          36           86
     K0V          48           20
     M0V          61         -162
     M8V          70         -326

   I think that this suggests that stellar astrometry is pretty compromised
   under the extreme (i.e., normal) PHA observing scenarios.  This also
   gives an estimate of the lower limit for an astrometric mis-match
   leading to a triggered event in the difference image.

2) Well, maybe it really isn't that bad?

   If folks are willing to use filters, then the situation gets much better.

   Spectrum   GSnnn    DCR     DCR     DCR     DCR     DCR     DCR     DCR
                        g'      r'      i'      z'    g'+r'   r'+i'  g'+r'+i'
   --------------------------------------------------------------------------
      O5        1      136      24      12       5     241      58     314
      B0V       4      125      22      11       4     219      54     284
      A0V      14       90      18       8       1     159      40     203
      F0V      30       49       9       5       0      80      21      99
      G0V      36       25       3      17       0      35      32      75
      K0V      48        9       0       3      -1      11       3      13
      M0V      61      -54     -14      -7      -4    -104     -32    -121
      M8V      70     -105     -41     -30     -10    -171    -116    -265

   So we get the expected result that blue photons cause the most damage,
   and that almost any combination between r' and z' has the DCR less
   than 50mas, which is something like what I expect the seeing-limited
   random component of the astrometry to be.

3) Are the PHA folks toast?

   Not really.  Their targets have B-Vs similar to stars in the range
   of G0 to K0, and (non-coincidentally) if you use something like a
   G5 reference star, then their errors are under control.

   Spectrum   GSnnn    DCR     DCR     DCR     DCR     DCR     DCR     DCR
                        g'      r'      i'    g'+r'   r'+i'  g'+r'+i'  open
   --------------------------------------------------------------------------
      G2V      46       12       1      17      18      30      58      58
      G8V      54      -16      -3      13     -21      17       8     -18
      K0V      48        9       0       3      11       3      13      20

   My guess is that most of these predictions fall within the noise of the
   model and that asteroid spectra are probably not overly good matches to
   stars with similar B-V values.

4) What about galaxies?

   The KC96 atlas lists 12 generic spectra.  To the extent that these
   describe reality (i.e., I don't do galaxies so I need help), then
   these DCRs describe what we might see.

   KC Label         DCR     DCR     DCR     DCR
                     g'      r'      i'      z'
   --------------------------------------------
   bulge            -36      -9      -4      -4
   elliptical       -31      -8      -7      -7
   s0               -30      -8      -6      -5
   sa               -10      -8      -5      -3
   sb               -13      -9      -6      -6
   sc                57     -14      -7      -4
   starburst1        40      -6       1      -4
   starburst2        35     -13       0     -11
   starburst3        36      -7      -2      -9
   starburst4        38      -9      -5      -6
   starburst5        33     -15      -3      -8
   starburst6        34     -10      -4      -8

Very Preliminary Conclusions:

a) It is clear that Astrometry must provide the users with a catalog of
   stars with near-solor colors to use as reference stars.  I haven't
   done the numbers, but my feeling is that there should be enough of
   them to enable the routine astrometric solutions.  Note that Astrometry
   needs to measure the positions of all the stars, but it is the color-
   selected list that should be given to the Pipeline.

   In other words, photometry is just as important as astrometry when it
   comes to selecting reference objects.

b) By extension, Astrometry needs to provide different color-selected
   catalogs for targets of different colors if there is a desire to
   save observations made at large zenith distances.  For example, if
   you are looking for L- and T-dwarfs, do not use hot white dwarfs for
   reference stars.

c) If g' is part of the bandpass, or if there is no filter, then Astrometry
   may not be able to save measures at large zenith distances.  As the
   French would say, "C'est la damn vie!"

d) I thought that the galaxies would be worse than they appear to be.
   Perhaps I can find a more perverse set of spectral energy distributions.

-Dave

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Yet another boring note on astrometric aspects of Pan-STARRS.  The current
topic is the color of stars as a function of apparent brightness.  Since
I do not trust USNO-B photometry at this level, I used the SDSS Early
Data Release for this study.  Yes, I have access to the DR1 data, but I
didn't feel like having 500 co-authors on this note.

Jeff Pier was kind enough to extract the "stars" from the EDR.  I took
this sample, broke it into bins of 0.5 magnitudes in r', and then sorted the
g'-r' and r'-i' colors in each bin to find the colors for the typical stars.
The results for each bin are shown on 2 lines.  The first gives the color
at the various percentiles for the SDSS colors g'-r' and r'-i'.  The
second line converts the g'-r' color into B-V.

Mean       N    10%   25%   50%   75%   90%   10%   25%   50%   75%   90% LogN
 g'            |----------- g'-r' --------|  |----------- r'-i' --------|
(second line)  |-----------  B-V  --------|
-------------------------------------------------------------------------------
14.25   11068  0.34  0.42  0.52  0.68  0.87  0.08  0.13  0.18  0.25  0.33 4.04
 B-V           0.54  0.62  0.71  0.87  1.05
14.75   19228  0.36  0.44  0.54  0.71  0.95  0.11  0.15  0.19  0.26  0.37 4.28
 B-V           0.56  0.64  0.73  0.90  1.12
15.25   27559  0.37  0.45  0.56  0.74  1.08  0.12  0.16  0.20  0.28  0.42 4.44
 B-V           0.57  0.65  0.75  0.92  1.25
15.75   35637  0.38  0.45  0.58  0.79  1.19  0.13  0.16  0.21  0.30  0.49 4.55
 B-V           0.58  0.65  0.77  0.97  1.35
16.25   44732  0.38  0.46  0.60  0.89  1.29  0.13  0.17  0.23  0.33  0.57 4.65
 B-V           0.58  0.66  0.79  1.07  1.45
16.75   55457  0.38  0.47  0.63  0.99  1.35  0.14  0.17  0.24  0.37  0.65 4.74
 B-V           0.58  0.67  0.82  1.16  1.50
17.25   66912  0.38  0.48  0.67  1.11  1.39  0.14  0.18  0.26  0.43  0.75 4.83
 B-V           0.58  0.68  0.86  1.28  1.54
17.75   79932  0.37  0.50  0.72  1.23  1.42  0.14  0.19  0.28  0.51  0.87 4.90
 B-V           0.57  0.70  0.90  1.39  1.57
18.25   94887  0.36  0.50  0.79  1.32  1.44  0.14  0.19  0.31  0.60  0.98 4.98
 B-V           0.56  0.70  0.97  1.48  1.59
18.75  114430  0.35  0.50  0.88  1.36  1.45  0.13  0.20  0.34  0.69  1.07 5.06
 B-V           0.55  0.70  1.06  1.51  1.60
19.25  136515  0.34  0.51  0.98  1.38  1.47  0.13  0.20  0.38  0.78  1.15 5.14
 B-V           0.54  0.70  1.15  1.53  1.62
19.75  163224  0.34  0.52  1.11  1.40  1.49  0.13  0.21  0.45  0.89  1.22 5.21
 B-V           0.54  0.71  1.28  1.55  1.64
20.25  193705  0.34  0.53  1.19  1.41  1.51  0.13  0.22  0.50  0.97  1.28 5.29
 B-V           0.54  0.72  1.35  1.56  1.66
20.75  229424  0.34  0.56  1.23  1.43  1.54  0.12  0.24  0.55  1.03  1.32 5.36
 B-V           0.54  0.75  1.39  1.58  1.69
21.25  271190  0.36  0.62  1.22  1.44  1.59  0.12  0.26  0.57  1.07  1.36 5.43
 B-V           0.56  0.81  1.38  1.59  1.73
21.75  334146  0.37  0.65  1.17  1.46  1.70  0.08  0.26  0.56  1.06  1.37 5.52
 B-V           0.57  0.84  1.33  1.61  1.84
22.25  433322  0.36  0.68  1.13  1.49  1.81 -0.09  0.20  0.52  0.98  1.35 5.64
 B-V           0.56  0.87  1.30  1.64  1.94
22.75  479320  0.28  0.66  1.09  1.52  1.93 -0.45  0.04  0.54  0.98  1.35 5.68
 B-V           0.49  0.85  1.26  1.67  2.06

A few of the conclusions that can be drawn from this table are as follows.

1) The median color gets redder as you go fainter.  At g'=14.25 the B-V
   of 0.71 corresponds to late G whereas at g'=22.75 the B-V of 1.26
   corresponds to late K.

2) The spread between the 25% and 75% percentile is just about one
   full spectral class.

3) If DCR is a problem, then you (meaning me) need to be very careful
   about choosing a reference frame.  Using a few of the nearest faint
   stars may be systematically different than using a grid of brighter
   stars that sparser but have higher SNRs for each image.  Yet again,
   we see the importance of the magnitude and color in doing the
   astrometric solution.

4) The slope of LogN as a function of g' is about 0.162 +/- 0.002
   just in case it helps predict source counts.  Of course, most of
   the objects at r'=23 are galaxies but the SDSS folks haven't
   told me how their classifier behaves at such faint magnitudes.

Before everybody jumps on me, here are some of the caveats.

   The EDR region is at high galactic latitude so reddening is
   only a minor correction.

   The EDR is a pretty small region, so there may be residual pieces
   of Galactic structure confusing the issue.  Should DR1 ever go public,
   this analysis can be repeated.

   For those who are totally lost, Allen's Astrophysical Quantities
   section 15.3.1 gives B-V as a function of spectral type.  Here
   are a few entries.
      A0V   -0.02
      F0V    0.30
      GOV    0.58
      K0V    0.81
      M0V    1.40
      M5V    1.64
   The conversion from Fukugita et al. (AJ v111, p1748, 1996) is
   (g'-r') = 1.05*(B-V) - 0.23

   Yes, the SDSS color system is wandering around, but only by a
   few hundredths of a magnitude.  Again, the crude nature of these
   results is not affected by this week's version of the SDSS
   magnitude system.

-Dave

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