Posts with the Tag Astrometry:

• Computing Residuals of an Astrometric Calibration

  2022-11-29 Markus Demleitner

  

  The kind of plot you can make following the recipe given here: Left, a comparison of the photometry, right, a positional residuals, not taking into account the SIP plate solution, when comparing the HDAP plate B3261a against Gaia DR3. Note that the cut-off a 4 arcsec is because of the match radius when obtaining the calibrator stars.

  I recently had to assess the quality of the astrometric calibration of a photographic plate. What I am going to show you in this post will of course work just as well for CCD frames, and if these have a sufficiently large field of view, this may be an issue for them as well. However, the sort of data that needs this assessment most typically are scans of plates, as these tend to have a “wobble”, systematic offsets in the scan direction resulting from imperfections in the mechanics.

  Prerequisites: An astronomical frame with a calibration in ICRS (or some frame not very far from it), called my-image.fits in the following, SExtractor (in Debian and derivatives: apt install source-extractor – long live Debian Astro; since it's called source-extractor in Debian, that's what I'll use here, too), and of course TOPCAT.

  Step 1: Extract Sources. Source extraction is of course a high science, and if you know better than me, by all means do it the way you think is appropriate. Meanwhile, the following might very well work for you sufficiently well.

  Create a working directory and enter it. Then, to create a file telling source-extractor what columns you would like to see, write the following to a file default.param:

  ALPHA_SKY
  DELTA_SKY
  X_IMAGE
  Y_IMAGE
  MAG_ISO
  FLUX_AUTO
  ELONGATION
  

  Next, give a few parameters to source-extractor; depending on the sort of image you have, you may want to play around with DETECT_MINAREA (how many pixels need to show a signal to register as a source) and DETECT_THRESH (how many sigmas a pixel has to be above the background to register as a candidate for belonging to a source). Meanwhile, write the following into a file default.control:

  CATALOG_TYPE     FITS_1.0
  CATALOG_NAME     img.axy
  PARAMETERS_NAME  default.param
  FILTER           N
  DETECT_MINAREA   30
  DETECT_THRESH    4
  SEEING_FWHM      1.2
  

  – but if the following call gives you a few hundred sources, that ought to work for the present purpose.

  Then run:

  source-extractor -c default.control my-image.fits
  

  This will give you a catalogue of extracted objects in the file img.axy.

  Step 2: Fix source-extractor's output. Load that img.axy into TOPCAT. Regrettably, source-extractor does not add any useful metadata to the columns of its output table. To add the absolute bare minimum, in TOPCAT go to Views → Column Info. In that window, check UCD in the Display menu, and then put pos.eq.ra and pos.eq.dec into the UCD fields of the ALPHA_SKY and DELTA_SKY columns, respectively; double click to change fields in TOPCAT.

  To see if you have done the annotation right, in TOPCAT's main window, click Graphics → Sky Plot. If the objects show up, you have just provided enough annotation to let TOPCAT figure out the position for each row.

  Step 3: Get calibrators. We will now try to add counterparts for Gaia DR3 to the extracted sources. To do that, click VO → Table Access Protocol, and in the window popping up double click the entry for the GAVO DC TAP.

  In the Find box, type dr3lite to look for this site's version of the Gaia DR3 source catalogue. Click on gaia.dr3lite to select that table, and then select the Columns pane. This should show some of the Gaia DR3 columns.

  Now Examples → Upload Join will generate a query that will cross-match your extracted sources with the Gaia sources. You should edit it a bit, only selecting the columns you will actually need, removing the TOP 1000 (at least on large images with more than 1000 sources), and reducing the match radius a bit when the calibration is not actually completely off and your epoch is sufficiently close to J2000.

  Hint: you can control-click in the Columns pane and then use the Cols button to insert all the column names in one go[1]. For me, the resulting query would be:

  SELECT
     source_id, ra, dec, phot_bp_mean_mag,
     tc.*
     FROM gaia.dr3lite AS db
     JOIN TAP_UPLOAD.t1 AS tc
     ON 1=CONTAINS(POINT('ICRS', db.ra, db.dec),
                   CIRCLE('ICRS', tc.ALPHA_SKY, tc.DELTA_SKY, 4./3600.))
  

  This should result in about as many matches as your extraction had – a few more is ok, because you will have some spurious matches, a few less is ok, too, as there are always some outliers and artefacts, but you should clearly not pull a magnitude more or less objects here than you put in; fiddle with the match radius as necessary.

  See if there is a rough correlation between the Gaia calibrators and your extracted sources by plotting phot_bp_mean_mag against MAG_ISO. Absent more information, MAG_ISO, source-extractor's guess for the magnitude of the extracted object, will be just some crazy number, but it should have some discernable correlation with the actual magnitude. Do not expect too much here, in particular with old plates, for which good photometry is a science of their own.

  In my example, this looked like this:

  

  The green points certainly are spurious matches; this observation did not reach beyond 14th magnitude or so, and there are many weak stars on the sky, so a few of them will show up in just about any cross match. See the opening picture for an example with a better correlation.

  Step 4: Do the correlation plot. Do Graphics → Plane Plot and then plot ra-alpha_sky or dec-delta_sky against X_IMAGE or Y_IMAGE. You could get something like this:

  

  This rather certainly reflects some optical distortion; source-extractor regrettably does not take into account SIP corrections yet, so it is likely that a large part of this would be taken care of by the polynomials of the plate solution (the github issue I am linking to tells you how to be sure).

  But it can also look like this:

  

  This certainly is not the result of a lens or anything optical at all. It's the scanner's gears that you are looking at here. With an amplitude of perhaps three arcseconds this is rather excessive here; but something like this you will rather likely see even on good scanners – though it may essentially be invisible, as of the Heidelberg scanner we used for HDAP:

  

  [1]	I'm using the BP magnitude in the query below as most historical plates tend to be “blue sensitive“ (in some sense). Hence, BP magnitudes should be a bit closer to what source-extractor has extracted.

• The Loneliest Star in the Sky

  2021-01-20 Markus Demleitner

  

  The loneliest star in the sky on the left, and on the right a somewhat more lonelier one (it's explained in the text). The inset shows the distribution of the 500 loneliest stars on the whole sky in Galactic coordinates.

  In early December, the object catalogue of Gaia's data release 3 was published (“eDR3“), and I've been busy in various ways on this data off and on since then – see, for instance, the The Case of the disappearing bits on this blog.

  One of the things I have missed when advising people on projects with previous Gaia data releases is a table that, for every object, gives the nearest neighbour. And so for this release I've created it and christened it, perhaps just a bit over-grandiosely, “Gaia eDR3 Autocorrelation”. Technically, it is just a long (1811709771 rows, to be precise) list of pairs of Gaia eDR3 source ids, the ids of their nearest neighbour, and a spherical distance between.

  This kind of data is useful for many applications, mostly when looking for objects that are close together or (more often) things that fail for such close pairs for a wide variety of reasons. I have taken some pains to not only have close neighbours, though, because sometimes you may want specifically objects far away from others.

  As in the case of this article's featured image: The loneliest star in the sky (as seen by Gaia, that is) is eDR3 6049144983226879232, which is 4.3 arcminutes from its neighbour, 6049144021153793024, which in turn is the second-loneliest star in the sky. They are, perhaps a bit surprisingly, in Ophiuchus (and thus fairly close to the Milky Way plane), and (probably) only about 150 parsec from Earth. Doesn't sound too lonely, hm? Turns out: these stars are lonely because dust clouds blot out all their neighbours.

  Rank three is in another dust cloud, this time in Taurus, and so it continues in low Galactic latitude to rank 8 (4402975278134691456) at Galactic latitude 36.79 degrees; visualising the thing, it turns out it's again in a dark cloud. What about rank 23 at 83.92 Galactic (3954600105683842048)? That's probably bona-fide, or at least it doesn't look very dusty in the either DSS or PanSTARRS. Coryn (see below) estimates it's about 1100 parsec away. More than 1 kpc above the galactic disk: that's more what I had expected for lonely stars.

  Looking at the whole distribution of the 500 loneliest stars (inset above), things return a bit more to what I had expected: Most of them are around the galactic poles, where the stellar density is low.

  So: How did I find these objects? Here's the ADQL query I've used:

  SELECT TOP 500
    ra, dec, source_id, phot_g_mean_mag, ruwe,
    r_med_photogeo,
    partner_id, dist,
    COORD2(gavo_transform('ICRS', 'GALACTIC',
      point(ra, dec))) AS glat
  FROM
    gedr3dist.litewithdist
    NATURAL JOIN gedr3auto.main
  ORDER BY dist DESC
  

  – run this on the TAP server at http://dc.g-vo.org/tap (don't be shy, it's a cheap query).

  Most of this should be familiar to you if you've worked through the first pages of ADQL course. There's two ADQL things I'd like to advertise while I have your attention:

  1. NATURAL JOIN is like a JOIN USING, except that the database auto-selects what column(s) to join on by matching the columns that have the same name. This is a convenient way to join tables designed to be joined (as they are here). And it probably won't work at all if the tables haven't been designed for that.
  2. The messy stuff with GALACTIC in it. Coordinate transformations had a bad start in ADQL; the original designers hoped they could hide much of this; and it's rarely a good idea in science tools to hide complexity essentially everyone has to deal with. To get back on track in this field, DaCHS servers since about version 1.4 have been offering a user defined function gavo_transfrom that can transform (within reason) between a number of popular reference frames. You will find more on it in the server's capabilities (in TOPCAT: the “service” tab). What is happening in the query is: I'm making a Point out of the RA and Dec given in the catalogue, tell the transform function it's in ICRS and ask it to make Galactic coordinates from it, and then take the second element of the result: the latitude.

  And what about the gedr3dist.litewithdist table? That doesn't look a lot like the gaiaedr3.gaiasource we're supposed to query for eDR3?

  Well, as for DR2, I'm again only carrying a “lite” version of the Gaia catalogue in GAVO's Heidelberg data center, stripped down to the columns you absolutely cannot live without even for the most gung-ho science; it's called gaia.edr3lite.

  But then my impression is that almost everyone wants distances and then hacks something to make Gaia's parallax work for them. That's a bad idea as the SNR goes down to levels very common in the Gaia result catalogue (see 2020arXiv201205220B if you don't take my word for it). Hence, I'm offering a pre-joined view (a virtual table, if you will) with the carefully estimated distances from Coryn Bailer-Jones, and that's this gedr3dist.litewithdist. Whenever you're doing something with eDR3 and distances, this is where I'd point you first.

  Oh, and I should be mentioning that, of course, I figured out what is in dust clouds and what is not with TOPCAT and Aladin as in our tutorial TOPCAT and Aladin working together (which needs a bit of an update, but you'll figure it out).

  There's a lot more fun to be had with this (depending on what you find fun in). What about finding the 10 arcsec-pairs with the least different luminosities (which might actually be useful for testing some optics)? Try this:

  SELECT TOP 300
    a.source_id, partner_id, dist,
    a.phot_g_mean_mag AS source_mag,
    b.phot_g_mean_mag AS partner_mag,
    abs(a.phot_g_mean_mag-b.phot_g_mean_mag) AS magdiff
  FROM gedr3auto.main
    NATURAL JOIN gaia.edr3lite AS a
    JOIN gaia.edr3lite AS b
      ON (partner_id=b.source_id)
  WHERE
    dist BETWEEN 9.999/3600 AND 10.001/3600
    AND a.phot_g_mean_mag IS NOT NULL
    AND b.phot_g_mean_mag IS NOT NULL
  ORDER BY magdiff ASC
  

  – this one takes a bit longer, as there's many 10 arcsec-pairs in eDR3; the query above looks at 84690 of them. Of course, this only returns really faint pairs, and given the errors stars that weak have they're probably not all that equal-luminosity as that. But fixing all that is left as an exercise to the reader. Given there's the RP and BP magnitude columns, what about looking for the most colourful pair with a given separation?

  Acknowledgement: I couldn't have coolly mumbled about Ophiuchus or Taurus without the SCS service ivo://cds.vizier/vi/42 (”Identification of a Constellation From Position, Roman 1982”).

  Update [2021-02-05]: I discovered an extra twist to this story: Voyager 1 is currently flying towards Ophiuchus (or so Wikipedia claims). With an industrial size package of artistic licence you could say: It's coming to keep the loneliest star company. But of course: by the time Voyager will be 150 pc from earth, eDR3 6049144983226879232 will quite certainly have left Ophiuchus (and Voyager will be in a completely different part of our sky, that wouldn't look familar to us at all) – so, I'm afraid apart from a nice conincidence in this very moment (galactically speaking), this whole thing won't be Hollywood material.

• See Who's Kinking the Sky

  2017-03-14 Markus Demleitner

  A new arrival in the GAVO Data Center is UCAC5, another example of a slew of new catalogs combining pre-existing astrometry with Gaia DR1, just like the HSOY catalog we've featured here a couple of weeks back.

  That's a nice opportunity to show how to use ADQL's JOIN operator for something else than the well-known CONTAINS-type crossmatch. Since both UCAC5 and HSOY reference Gaia DR1, both have, for each object, a notion which element of the Gaia source catalog they correspond to. For HSOY, that's the gaia_id column, in UCAC5, it's just source_id. Hence, to compare results from both efforts, all you have to do is to join on source_id=gaia_id (you can save yourself the explicit table references here because the column names are unique to each table.

  So, if you want to compare proper motions, all you need to do is to point your favourite TAP client's interface to http://dc.g-vo.org/tap and run:

  SELECT
      in_unit(avg(uc.pmra-hsoy.pmra), 'mas/yr') AS pmradiff,
      in_unit(avg(uc.pmde-hsoy.pmde), 'mas/yr') AS pmdediff,
      count(*) as n,
      ivo_healpix_index (6, raj2000, dej2000) AS hpx
      FROM hsoy.main AS hsoy
      JOIN ucac5.main as uc
      ON (uc.source_id=hsoy.gaia_id)
      WHERE comp IS NULL    -- hsoy junk filter
      AND clone IS NULL     -- again, hsoy junk filter
      GROUP BY hpx
  

  (see Taylor et al's All of the Sky if you're unsure what do make of the healpix/GROUP BY magic).

  Of course, the fact that both tables are in the same service helps, but with a bit of upload magic you could do about the same analysis across TAP services.

  Just so there's a colourful image in this post, too, here's what this query shows for the differences in proper motion in RA:

  (equatorial coordinates, and the aux axis is a bit cropped here; try for yourself to see how things look for PM in declination or when plotted in galactic coordinates).

  What does this image mean? Well, it means that probably both UCAC5 and HSOY would still putt kinks into the sky if you wait long enough.

  In the brightest and darkest points, if you waited 250 years, the coordinate system induced by each catalog on the sky would be off by 1 arcsec with respect to the other (on a sphere, that means there's kinks somewhere). It may seem amazing that there's agreement to at least this level between the two catalogs – mind you, 1 arcsec is still more than 100 times smaller than you could see by eye; you'd have to go back to the Mesolithic age to have the slightest chance of spotting the disagreement without serious optical aids. But when Gaia DR2 will come around (hopefully around April 2018), our sky will be more stable even than that.

  Of course, both UCAC5 and HSOY are, indirectly, standing on the shoulders of the same giant, namely Hipparcos and Tycho, so the agreement may be less surprising, and we strongly suspect that a similar image will look a whole lot less pleasant when Gaia has straightened out the sky, in particular towards weaker stars.

  But still: do you want to bet if UCAC5 or HSOY will turn out to be closer to a non-kinking sky? Let us know. Qualifications („For bright stars...”) are allowed.

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