Posts with the Tag Gaia:

  • Making Custom Indexes for astrometry.net

    When you have an image or a scan of a photographic plate, you usually only have a vague idea of what position the telescope actually was pointed at. Furnishing the image with (more or less) precise information about what pixel correesponds to what sky position is called astrometric calibration. For a while now, arguably the simplest option to do astrometric calibration has been a package called astrometry.net. The eponymous web page has been experiencing… um… operational problems lately, but thanks to the Debian astronomy team, there is a nice package for it in Debian.

    However, just running apt install astrometry.net will not give you a working setup. Astrometry.net in addition needs an “index”, files that map star patterns (“quads“, in astrometry.net jargon) to positions. Debian comes with two pre-made sets of indexes at the moment (see apt search astrometry-data): those based on the Tycho 2 catalogue, and those based on 2MASS.

    For the index based on Tycho 2, you will find packages astrometry-data-tycho2-10-19, astrometry-data-tycho2-09, astrometry-data-tycho2-08, astrometry-data-tycho2-07[1]. The numbers in there (“scale numbers”) define the size of images the index is good for: 19 means “a major part of the sky”, 10 is “about a degree”, 8 “about half a degree”. Indexes for large images only have a few bright stars and hence are rather compact, which is why 10 though 19 fit into one package, whereas astrometry-data-tycho2-07-littleendian weighs in at 141 MB, and indexes at scale number 0 (suitable for images of a few arcminutes) take dozens of Gigabytes if they are for the whole sky.

    So, when you do astrometric calibration, consider the size of your images first and then decide which scale number is sensible for you. It is usually a good idea to try the neighbouring scale numbers, too.

    You can then feed these to your calibration routine. If you are running DaCHS, you will probably want to use the AnetHeaderProcessor, where you give the names of the indexes in the sp_indices; you also have to say where to find the indexes, as in:

    from gavo import api
    
    class MyObsCalibrator(api.AnetHeaderProcessor):
      indexPath = "/usr/share/astrometry"
      sp_indices = ["index-tycho2-09*.fits",
        "index-tycho2-10*.fits",
        "index-tycho2-11*.fits",]
    

    This would be suitable for images that cover about a degree on the sky.

    Custom Indexes for Targeted Observations

    The Tycho catalogue starts becoming severely incomplete below mV ≈ 11, and since astrometry.net needs a few stars on an image to be able to calibrate it, you cannot use it to calibrate images smaller than a few tens of arcminutes (depending on where you look, of course). If you have smaller images, there are the 2MASS-based indexes; but the bluer your images are, the worse 2MASS as an infrared survey will do, and in addition, having the giant indexes is a big waste of storage and compute resources when you know your images are on a rather small part of the sky.

    In such a situation, you will save a lot of CPU and possibly even improve your astrometry if you create a custom index for your specific data. For instance, assume you have images sized about 10 arcminutes, and the observation programme covers a reasonably small set of objects (as long as it's of order a few hundred, a custom index certainly will be a good deal). You could then make your index based on Gaia positions and photometry like this:

    """
    Create an index for astrometry.net and a few small fields based on Gaia.
    
    Be sure to adapt this for your use case; for instance, if what your are
    calibrating will be from only a part of the sky, pick specific healpixes
    (perhaps on a different level; below, we're using level 5).  Also consider
    changing the target epoch, the photometry, or the magnitude limit.
    
    This script takes the sample positions from a text file; have
    space-separated pairs of ra and dec in targets.txt.
    """
    
    import os
    import subprocess
    
    from astropy.table import Table
    import pyvo
    
    # 0 is for images of about two arcminutes, 10 for about degree, 12 for two
    # degrees, etc.
    SIZE_PRESET = 1
    
    # The typical radius of your images in degrees (this is the size of our cone
    # searches, so cut some slack); this needs to be changed in unison with
    # SIZE_PRESET
    IMAGE_RADIUS = 1/10.
    
    
    def get_target_table():
        """must return an astropy table with columns ra and dec in degrees.
    
        (of course, if you have your data in a proper format with actual metadata,
        you don't need any of the ugly magic).
        """
        targets = Table.read("targets.txt", format="ascii")
        targets["col1"].name, targets["col2"].name = "ra", "dec"
        targets["ra"].meta = {"ucd": "pos.eq.ra;meta.main"}
        targets["dec"].meta = {"ucd": "pos.eq.dec;meta.main"}
        return targets
    
    
    def main():
        tap_service = pyvo.dal.TAPService("http://dc.g-vo.org/tap")
        res = tap_service.run_async(f"""
            SELECT g.ra as RA, g.dec as DEC, phot_g_mean_mag as MAG
            FROM gaia.dr3lite AS g
            JOIN TAP_UPLOAD.t1 as mine
                ON DISTANCE(mine.ra, mine.dec, g.ra, g.dec)<{IMAGE_RADIUS}""",
          uploads={"t1": get_target_table()})
    
        cat_file = "basic-cat.fits"
        res.to_table().write(cat_file, format="fits", overwrite=True)
    
        try:
            subprocess.run(["build-astrometry-index", "-i", cat_file,
                "-o", f"./index-custom-{SIZE_PRESET:02d}.fits",
                "-P", str(SIZE_PRESET), "-S", "MAG"])
        finally:
            os.unlink(cat_file)
    
    
    if __name__=="__main__":
        main()
    

    This writes a single file, index-custom-01.fits (in this case).

    If you read your positions from something else than the simple ASCII file I'm assuming here: Be sure to annotate the columns containing RA and Dec with the proper UCDs as shown here. That makes DaCHS (and perhaps other TAP services, too) create the right hints for the database, speeding up things tremendously.

    You can of course change the ADQL query; it might, for instance, help to replace the G magnitudes with RP or BP ones, or you could use a different catalogue than Gaia. Just make sure the FITS table that is written to basic-cat.fits has exactly the columns RA, DEC, and MAG.

    In DaCHS, I tend to keep scripts like the one above in a subdirectory of the resdir called custom-index, and then in the calibration script I write:

    from gavo import api
    
    RD = api.getRD("myres/q")
    
    class MyObsCalibrator(api.AnetHeaderProcessor):
      indexPath = RD.resdir
      sp_indices = ["custom-index/index-custom-01.fits"]
    

    Custom Indexes for Ancient Observations

    On the other hand, if you have oldish images not going terribly deep, you may want to tailor an index for about the epoch the images were taken at. Many bright stars have a proper motion large enough to matter over a century, and so doing epoch propagation (in this case with the ivo_epoch_prop user defined function, which is not available everywhere) is probably a good idea. The following script computes three full-sky indexes with quads around the desired size; note how you can set the limiting magnitude and the size preset:

    """
    Create a full-sky index for bright stars and astrometry.net based on Gaia.
    
    This only works for rather bright stars because the Gaia service will refuse
    to server more than ~1e7 objects.
    
    Make sure to choose SIZE_PRESET to your use case (19 means 30 deg,
    10 about a degree, two preset steps are about a factor two in scale).
    """
    
    import os
    import subprocess
    
    import pyvo
    
    # see the module docstring
    SIZE_PRESET = 12
    
    # ignore stars fainter than this; you can't go below 14 all-sky with Gaia
    # and the GAVO DC server
    MAX_MAG = 12
    
    # Epoch to transform the stars to
    TARGET_EPOCH = 1910
    
    
    def main():
        tap_service = pyvo.dal.TAPService("http://dc.g-vo.org/tap")
        res = tap_service.run_async(f"""
            SELECT pos[1] as RA, pos[2] as DEC, mag as MAG
            FROM (
                SELECT phot_bp_mean_mag AS mag,
                    ivo_epoch_prop(ra, dec, parallax,
                        pmra, pmdec, radial_velocity, 2016, {TARGET_EPOCH}) as pos
                FROM gaia.dr3lite
              WHERE phot_bp_mean_mag<{MAX_MAG}) AS q""")
    
        cat_file = "current.fits"
        res.to_table().write(cat_file, format="fits", overwrite=True)
    
        try:
            for size_preset in range(SIZE_PRESET-1, SIZE_PRESET+2):
                subprocess.run(["build-astrometry-index", "-i", cat_file,
                    "-o", f"./index-custom-{size_preset:02d}.fits",
                    "-P", str(size_preset), "-S", "MAG"])
        finally:
            os.unlink(cat_file)
    
    
    if __name__=="__main__":
        main()
    

    With this and my custom-index directory, your DaCHS header processor could say:

    from gavo import api
    
    RD = api.getRD("myres/q")
    
    class MyObsCalibrator(api.AnetHeaderProcessor):
      indexPath = RD.resdir
      sp_indices = ["custom-index/index-custom-*.fits"]
    

    Custom Indexes: Full-sky and Deep

    I have covered the cases “deep and spotty” and “shallow and full-sky“. The case “deep and full-sky“ is a bit more involved because it still lies in the realm of big data, which always requires extra tricks. In this case, that would be retrieving the basic catalogue in parts – for instance, by HEALPix – and at the same time splitting the index up between HEALPixes, too. This does not require great magic, but it does require a bit of non-trivial bookkeeping, and hence I will only write about it if someone actually needs it – if that's you, please write in.

    [1]You will also find that each of these exist in a littleendian and bigendian flavours; ignore these, your machine will pick what it needs when you install the packages without tags.
  • Gaia DR3 XP Spectra: All Sampled

    Lots of blue crosses and a few red squares plotted over a sky photograph of a star cluster

    Around this time of the year on the northern hemisphere, you can spot the h and χ Persei double star cluster with the naked eye. One part of it, NGC 884 is shown here with LAMOST DR6 low resolution spectra (red squares) and Gaia DR3 XP spectra (blue crosses) overplotted. Given that LAMOST has already been one of the largest collections of spectra on the planet, you can see that there is really a lot of those XP spectra.

    When Gaia DR3 was released in June, I was somewhat disappointed when I realised what it is that they delivered as the BP/RP (or XP for short) spectra. You see, I had expected to see something rather similar to what I have in DFBS: structurally, arrays of a few dozen spectral points, mapping wavelengths to some sort of measure of the flux.

    What really came were, mainly, “continuous spectra“, that is coefficients of Gauss-Hermite polynomials. You can fetch them from the gaiadr3.xp_continuous_mean_spectrum table at the ARI-Gaia TAP service; the blue part of the spectrum of the star DR3 4295806720 looks like this in there:

    102.93398893929992, -12.336921213781045, -2.668856168170544, -0.12631176306793765, -0.9347021092539146, 0.05636787290132809, [...]

    No common spectral client can plot this. The Gaia DPAC has helpfully provided a Python library called GaiaXPy to turn these into “proper” spectra. Shortly after the data release, my plan has thus been to turn all these spectra into their “sampled” form using GaiaXPy and then re-publish them, both through SSAP for ad-hoc discovery and through TAP for (potentially) global analysis.

    Alas, for objects too faint to make it into DR3's xp_sampled_mean_spectrum table (that's 35 million spectra already turned to wavelength-flux pairs by DPAC), the spectra generated in this way looked fairly awful, with lots of very artificial-looking wiggles (“ringing”, if you will). After a bit of deliberation, I realised that when the errors are given on the Hermite coefficients, once you compute the samples, these errors will be liberally distributed among the output samples. In other words, the error on the samples will be grossly correlated over arbitrary distances; at least I am fairly helpless when trying to separate signal from artefact in these beasts.

    Bummer. Well, fortunately, Rene Andrae from “up the mountain” (i.e., the MPI for Astronomy) has worked out a reasonably elegant way to get more conventional spectra understandable to mere humans. Basically, you compute n distinct “realisations” of the error model given by the table of the continuous spectra and average over them. The more samples you take, the less correlated your spectral points and their errors will be and the less confusing the signal will be. The service docs for gaia/s3 give the math.

    Doing this on more than 200 million spectra is quite an effort, though, and so after some experimentation I decided to settle on 10 realisations per spectrum and have relatively wide bins (10 nm) over just the optical part of the spectrum (400 through 800 nm). The BP and RP bandpaths are a bit wider, and there is probably signal blotted out by the wide bins; I will probably be addressing this for DR4, except if these spectra become the smash hit they deserve to be.

    The result of this procedure is now available through an SSAP service that should show up in the VO Registry by the time the first of you read this; the Aladin image above gives you an impression of the density of results here – and don't forget: the spectra with the blue crosses are all reasonably well flux-calibrated.

    The data is also available on the TAP service http://dc.g-vo.org/tap, which opens up many interesting possibilities. Let me mention two here.

    Comparison with LAMOST

    I was rather nervous whether what I had done resulted in anything that bore even a fleeting resemblance to reality, and so about the first thing I tried was to compare my new data with what LAMOST has.

    That is a nice exercise for TAP and ADQL. Let's first match spectra from the two surveys, which luckily are on the same server, saving us some cross-server uploads. I am selecting a minimum of data, just the position and the two access URLs, and I let DaCHS' MAXREC kick in so I'm just retrieving 20000 of the millions of result records:

    SELECT a.ssa_location, a.accref, b.accref
    FROM
      gdr3spec.ssameta AS a
      JOIN lamost6.ssa_lrs AS b
      ON DISTANCE(a.ssa_location, b.ssa_location)<0.001
    

    (this is using the DISTANCE(.,.)<radius idiom that we will be migrating towards in ADQL 2.1 instead of the dreaded 1=CONTAINS(POINT, CIRCLE) thing everyone has loathed in ADQL 2.0).

    Using the nifty activation actions, you can now tell TOPCAT to open the two spectra next to each other when you click on a row or a point in a sky plot. To reproduce,

    1. Make a sky plot. TOPCAT doesn't yet pick up the POINT in ssa_location, so you have to configure the Lon and Lat fields yourself to ssa_location[0] and ssa_location[1].
    2. Open the activation actions, either from the button bar or from the Views menu.
    3. In there, select Plot Table, make sure it says accref in Table Location and then check Plot Table in the Actions pane. When you now click on a point in the sky plot, you should see a spectrum pop up, except it is plotted with dots, which most people consider inappropriate for spectra. Use the Form tab in the plot window to style it a bit more spectrum-like (I recommend looking into Line and XYError).
    4. But how do you now add the LAMOST plot? I don't think TOPCAT's activation actions let you plot right into the plane plot you just configured. But you can add a second Plot Table action from the Actions menu in the window with the activation actions. As before, configure this new item, except this one needs to plot accref_ (which is what DaCHS has called the access reference for LAMOST to keep the names unique).
    5. As for Gaia, configure to plot to look good as a spectrum. In order to make the two spectra optically comparable, under Axes set the range to 4000 to 8000 Angstrom manually here.

    You can now click on points in your sky plot and, after a second or so, see the corresponding spectra next to each other (if you place the two plot windows that way).

    If you try this, you will (hopefully) see that major features of spectra are nicely reproduced, such as with these, I guess, molecular bands:

    Two line plots next to each other, the right one showing more features.  the left one roughly follows the major wiggles, though.

    As you probably have guessed, the extremely low-resolution Gaia XP spectrum is left, LAMOST's (somewhat higher-resolution) low-resolution spectrum is right:

    This also works with absorption in the blue, as in this example:

    Two line plots next to each other, the right one showing a lot of relatively sharp absoprtion lines, which the left one does not have.  A few major bumps are present in both, and the general shape conincides nicely, expect perhaps at the blue edge.

    In case of doubt, I have to say I'd probably trust Gaia's calibration around 400 nm better than LAMOST's. But that's mere guesswork.

    For fainter objects, you will see remnants of the systematic wiggles from the Hermite polynomials:

    Two line plots next to each other.  Both are relatively noisy, in particular on the blue edge.  The left one also seems to have a rather regular oscillation at the blue edge.

    Anyway, if you keep an eye on the errors, you can probably even work with spectra from the fainter objects:

    Two line plots next to each other.  The left one has fairly strong ringing which is not present in the right one, but it mainly stays within the error bars.  The total flux of this star is at least a factor of 10 less than for the prettier examples above.

    Mass Retrieval of Spectra

    One nice thing about the short spectra is that you can fetch many of them in one go and in very little time. For instance, to retrieve particularly red objects from the Gaia catalogue of Nearby Stars (also on the GAVO server) with spectra, say:

    SELECT
      source_id, ra, dec, parallax, phot_g_mean_mag,
      phot_bp_mean_mag, phot_rp_mean_mag, ruwe, adoptedrv,
      flux, flux_error
    FROM gcns.main
    JOIN gdr3spec.spectra
    USING (source_id)
    WHERE phot_rp_mean_mag<phot_bp_mean_mag-4
    

    [in case you wonder how I quickly got the column names enumerated here: do control-clicks into the Columns pane in TOCPAT's TAP window and then use the Cols button]. For when you do not have Gaia DR3 source_id-s in your source table, there is also gdr3spec.withpos against which you can do more conventional positional crossmatches.

    Within a few seconds, you can retrieve more than 4000 spectra in this way. You can now do whatever analysis you want on these spectra. Or, well, just plot them. The following procedure for that later task uses TOPCAT features only available in the next release, due before mid-October[1].

    First, make a colour-magnitude diagram (CMD) from this table as usual (e.g., BP-RP vs G). Then, open another plane plot and

    1. LayersAdd XYArray Control
    2. Configure the XYArray to plot from the table you just fetched, have nothing in X Values[2] and flux in Y Values.
    3. Under Axes, configure Y Log in order to better show the 4253 spectra at one time.
    4. Throw away or at least uncheck all other layers in the plot.
    5. In order to let TOPCAT highlight the spectrum of the activated source, in the Subsets pane check the Activated subset (that's the bleeding-edge functionality you will not have in older TOPCATs) and give it a sufficiently bright colour.

    With that, you can now click around in your CMD and immediately see that source's spectrum in the context of all the others, like this:

    An animation of someone selecting various points in a CMD and have simulataneous spectra plotted.

    These spectra have also inspired me to design and implement a vector extension for ADQL, which lets you do even more interesting things with these spectra. More on this… soon.

    [1]The Activated subset is only available in TOPCAT versions later than 4.8-7 (released in October 2022).
    [2]These should be the spectral points; DaCHS does not deliver them with this query because I am a coward. I think I will find my courage relatively soon and then fix this. Once that has happened, you can select param$spectral as X values. [Update: Mark Taylor remarks that by writing sequence(41, 400, 10) in bleeding-edge TOPCATs and add(multiply(10,sequence(41)),400) before that, you can add a proper spectral axis until then]
  • The Loneliest Star in the Sky

    sky images and a distribution plot

    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.

  • Histograms and Hidden Open Clusters

    image: reddish pattern

    Colour-coded histograms for distances of stars in the direction of some NGC open clusters -- one cluster per line, so you're looking a a couple of Gigabytes of data here. If you want this a bit more precise: Read the article and generate your own image.

    I have spent a bit of time last week polishing up what will (hopefully) be the definitive source of common ADQL User Defined Functions (UDFs) for IVOA review. What's a UDF, you ask? Well, it is an extension to ADQL where service operators can invent new functionality. If you have been following this blog for a while, you will probably remember the ivo_healpix_index function from our dereddening exercise (and some earlier postings): That was an UDF, too.

    This polishing work reminded me of a UDF I've wanted to blog about for a quite a while, available in DaCHS (and thus on our Heidelberg Data Center) since mid-2018: gavo_histogram. This, I claim, is a powerful tool for analyses over large amounts of data with rather moderate local means.

    For instance, consider this classic paper on the nature of NGC 2451: What if you were to look for more cases like this, i.e., (indulging in a bit of poetic liberty) open clusters hidden “behind” other open clusters?

    Somewhat more technically this would mean figuring out whether there are “interesting” patterns in the distance and proper motion histograms towards known open clusters. Now, retrieving the dozens of millions of stars that, say, Gaia, has in the direction of open clusters to just build histograms – making each row count for a lot less than one bit – simply is wasteful. This kind of counting and summing is much better done server-side.

    On the other hand, SQL's usual histogram maker, GROUP BY, is a bit unwieldy here, because you have lots of clusters, and you will not see anything if you munge all the histograms together. You could, of course, create a bin index from the distance and then group by this bin and the object name, somewhat like ...ROUND(r_est/20) as bin GROUP by name, bin – but that takes quite a bit of mangling before it can conveniently be used, in particular when you take independent distributions over multiple variables (“naive Bayesian”; but then it's the way to go if you want to capture dependencies between the variables).

    So, gavo_histogram to the rescue. Here's what the server-provided documentation has to say (if you use TOPCAT, you will find this in the ”Service” tab in the TAP windows' ”Use Service” tab):

    gavo_histogram(val REAL, lower REAL, upper REAL, nbins INTEGER) -> INTEGER[]
    
    The aggregate function returns a histogram of val with
    nbins+2 elements. Assuming 0-based arrays, result[0] contains
    the number of underflows (i.e., val<lower), result[nbins+1]
    the number of overflows. Elements 1..nbins are the counts in
    nbins bins of width (upper-lower)/nbins. Clients will have to
    convert back to physical units using some external communication,
    there currently is no (meta-) data as to what lower and upper was in
    the TAP response.
    

    This may sound a bit complicated, but the gist really is: type gavo_histogram(r_est, 0, 2000, 20) as hist, and you will get back an array with 20 bins, roughly 0..100, 100..200, and so on, and two extra bins for under- and overflows.

    Let's try this for our open cluster example. The obvious starting point is selecting the candidate clusters; we are only interested in famous clusters, so we take them from the NGC (if that's too boring for you: with TAP uploads you could take the clusters from Simbad, too), which conveniently sits in my data center as openngc.data:

    select name, raj2000, dej2000, maj_ax_deg
    from openngc.data
    where obj_type='OCl'
    

    Then, we need to add the stars in their rough directions. That's a classic crossmatch, and of course these days we use Gaia as the star catalogue:

    select name, source_id
    from openngc.data
    join gaia.dr2light
    on (
      1=contains(
        point(ra,dec),
        circle(raj2000, dej2000, maj_ax_deg)))
    where obj_type='OCl')
    

    This is now a table of cluster names and Gaia source ids of the candidate stars. To add distances, you could fiddle around with Gaia parallaxes, but because there is a 1/x involved deriving distances, the error model is complicated, and it is much easier and safer to adopt Bailer-Jones et al's pre-computed distances and join them in through source_id.

    And that distance estimation, r_est, is exactly what we want to take our histograms over – which means we have to group by name and use gavo_histogram as an aggregate function:

    with ocl as (
      select name, raj2000, dej2000, maj_ax_deg, source_id
      from openngc.data
      join gaia.dr2light
      on (
        1=contains(
          point(ra,dec),
          circle(raj2000, dej2000, maj_ax_deg)))
      where obj_type='OCl')
    
    select
      name,
      gavo_histogram(r_est, 0, 4000, 200) as hist
    from
      gdr2dist.main
      join ocl
      using (source_id)
    where r_est!='NaN'
    group by name
    

    That's it! This query will give you (admittedly somewhat raw, since we're ignoring the confidence intervals) histograms of the distances of stars in the direction of all NGC open clusters. Of course, it will run a while, as many millions of stars are processed, but TAP async mode easily takes care of that.

    Oh, one odd thing is left to discuss (ignore this paragraph if you don't know what I'm talking about): r_est!='NaN'. That's not quite ADQL but happens to do the isnan of normal programming languages at least when the backend is Postgres: It is true if computations failed and there is an actual NaN in the column. This is uncommon in SQL databases, and normal NULLs wouldn't hurt gavo_histogram. In our distance table, some NaNs slipped through, and they would poison our histograms. So, ADQL wizards probably should know that this is what you do for isnan, and that the usual isnan test val!=val doesn't work in SQL (or at least not with Postgres).

    So, fire up your TOPCAT and run this on the TAP server http://dc.g-vo.org/tap.

    You will get a table with 618 (or so) histograms. At this point, TOPCAT can't do a lot with them. So, let's emigrate to pyVO and save this table in a file ocl.vot

    My visualisation proposition would be: Let's substract a “background” from the histograms (I'm using splines to model that background) and then plot them row by row; multi-peaked rows in the resulting image would be suspicious.

    This is exactly what the programme below does, and the image for this article is a cutout of what the code produces. Set GALLERY = True to see how the histograms and background fits look like (hit 'q' to get to the next one).

    In the resulting image, any two yellow dots in one line are at least suspicious; I've spotted a few, but they are so consipicuous that others must have noticed. Or have they? If you'd like to check a few of them out, feel free to let me know – I think I have a few ideas how to pull some VO tricks to see if these things are real – and if they've been spotted before.

    So, here's the yellow spot programme:

    from astropy.table import Table
    import matplotlib.pyplot as plt
    import numpy
    from scipy.interpolate import UnivariateSpline
    
    GALLERY = False
    
    def substract_background(arr):
        x = range(len(arr))
        mean = sum(arr)/len(arr)
        arr = arr/mean
        background = UnivariateSpline(x, arr, s=100)
        cleaned = arr-background(x)
    
        if GALLERY:
            plt.plot(x, arr)
            plt.plot(x, background(x))
            plt.show()
    
        return cleaned
    
    
    def main():
        tab = Table.read("ocl.vot")
        hist = numpy.array([substract_background(r["hist"][1:-1])
          for r in tab])
        plt.matshow(hist, cmap='gist_heat')
        plt.show()
    
    
    if __name__=="__main__":
        main()
    
  • Gaia DR2: A light version and light curves

    screenshot: topcat and matplotlib

    Topcat is doing datalink, and our little python script has plotted a two-color time series of RMC 18 (or so I think).

    If anyone ever writes a history of the VO, the second data release of Gaia on April 25, 2018 will probably mark its coming-of-age – at least if you, like me, consider the Registry the central element of the VO. It was spectacular to view the spike of tens of Registry queries per second right around 12:00 CEST, the moment the various TAP services handing out the data made it public (with great aplomb, of course).

    In GAVO's Data Center we also carry Gaia DR2 data. Our host institute, the Zentrum für Astronomie in Heidelberg, also has a dedicated Gaia server. This gives relieves us from having to be a true mirror of the upstream data release. And since the source catalog has lots and lots of columns that most users will not be using most of the time, we figured a “light” version of the source catalog might fill an interesting ecological niche: Behold gaia.dr2light on the GAVO DC TAP service, containing essentially just the basic astrometric parameters and the diagonal of the covariance matrix.

    That has two advantages: Result sets with SELECT * are a lot less unwieldy (but: just don't do this with Gaia DR2), and, more importantly, a lighter table puts less load on the server. You see, conventional databases read entire rows when processing data, and having just 30% of the columns means we will be 3 times faster on I/O-bound tasks (assuming the same hardware, of course). Hence, and contrary to several other DR2-carrying sites, you can perform full sequential scans before timing out on our TAP service on gaia.dr2light. If, on the other hand, you need to do debugging or full-covariance-matrix error calculations: The full DR2 gaia_source table is available in many places in the VO. Just use the Registry.

    Photometry via TAP

    A piece of Gaia DR2 that's not available in this form anywhere else is the lightcurves; that's per-transit photometry in the G, BP, and RP band for about 0.5 million objects that the reduction system classified as variable. ESAC publishes these through datalink from within their gaia_source table, and what you get back is a VOTable that has the photometry in the three bands interleaved.

    I figured it might be useful if that data were available in a TAP-queriable table with lightcurves in the database. And that's how gaia.dr2epochflux came into being. In there, you have three triples of arrays: the epochs (g_transit_time, bp_obs_time, and rp_obs_time), the fluxes (g_transit_flux, bp_flux, and rp_flux), and their errors (you can probably guess their names). So, to retrieve G lightcurves where available together with a gaia_source query of your liking, you could write something like:

    SELECT g.*, g_transit_time, g_transit_flux
    FROM gaia.dr2light AS g
    LEFT OUTER JOIN gaia.dr2epochflux
    USING (source_id)
    WHERE ...whatever...
    

    – the LEFT OUTER JOIN arranges things such that the g_transit_time and g_transit_flux columns simply are NULL when there are no lightcurves; with a normal (“inner”) join, rows without lightcurves would not be returned in such a query.

    To give you an idea of what you can do with this, suppose you would like to discover new variable blue supergiants in the Gaia data (who knows – you might discover the precursor of the next nearby supernova!). You could start with establishing color cuts and train your favourite machine learning device on light curves of variable blue supergiants. Here's how to get (and, for simplicity, plot) time series of stars classified as blue supergiants by Simbad for which Gaia DR2 lightcurves are available, using pyvo and a little async trick:

    from matplotlib import pyplot as plt
    import pyvo
    
    def main():
      simbad = pyvo.dal.TAPService(
        "http://simbad.u-strasbg.fr:80/simbad/sim-tap")
      gavodc = pyvo.dal.TAPService("http://dc.g-vo.org/tap")
    
      # Get blue supergiants from Simbad
      simjob = simbad.submit_job("""
        select main_id, ra, dec
        from basic
        where otype='BlueSG*'""")
      simjob.run()
    
      # Get lightcurves from Gaia
      try:
        simjob.wait()
        time_series = gavodc.run_sync("""
          SELECT b.*, bp_obs_time, bp_flux, rp_obs_time, rp_flux
          FROM (SELECT
             main_id, source_id, g.ra, g.dec
             FROM
            gaia.dr2light as g
             JOIN TAP_UPLOAD.t1 AS tc
             ON (0.002>DISTANCE(tc.ra, tc.dec, g.ra, g.dec))
          OFFSET 0) AS b
          JOIN gaia.dr2epochflux
          USING (source_id)
          """,
          uploads={"t1": simjob.result_uri})
      finally:
        simjob.delete()
    
      # Now plot one after the other
      for row in time_series.table:
        plt.plot(row["bp_obs_time"], row["bp_flux"])
        plt.plot(row["rp_obs_time"], row["rp_flux"])
        plt.show(block=False)
        raw_input("{}; press return for next...".format(row["main_id"]))
        plt.cla()
    
    if __name__=="__main__":
      main()
    

    If you bother to read the code, you'll notice that we transfer the Simbad result directly to the GAVO data center without first downloading it. That's fairly boring in this case, where the table is small. But if you have a narrow pipe for one reason or another and some 105 rows, passing around async result URLs is a useful trick.

    In this particular case the whole thing returns just four stars, so perhaps that's not a terribly useful target for your learning machine. But this piece of code should get you started to where there's more data.

    You should read the column descriptions and footnotes in the query results (or from the reference URL) – this tells you how to interpret the times and how to make magnitudes from the fluxes if you must. You probably can't hear it any more, but just in case: If you can, process fluxes rather than magnitudes from Gaia, because the errors are painful to interpret in magnitudes when the fluxes are small (try it!).

    Note how the photometry data is stored in arrays in the database, and that VOTables can just transport these. The bad news is that support for manipulating arrays in ADQL is pretty much zero at this point; this means that, when you have trained your ML device, you'll probably have to still download lots and lots of light curves rather than write some elegant ADQL to do the filtering server-side. However, I'd be highly interested to work out how some tastefully chosen user defined functions might enable offloading at least a good deal of that analysis to the database. So – if you know what you'd like to do, by all means let me know. Perhaps there's something I can do for you.

    Incidentally, I'll talk a bit more about ADQL arrays in a blog post coming up in a few weeks (I think). Don't miss it, subscribe to our feed).

    SSAP and Obscore

    If you're fed up with bleeding-edge tech, the light curves are also available through good old SSAP and Obscore. To use that, just get Splat (or another SSA client, preferably with a bit of time series support). Look for a Gaia DR2 time series service (you may have to update the service list before you find it), enter (in keeping with our LBV theme) S Dor as position and hit “Lookup” followed by “Send Query”. Just click on any result to just view the time series – and then apply Splat's rich tool set to it.

    Update (8.5.2018): Clusters

    Here's another quick application – how about looking for variable stars in clusters? This piece of ADQL should get you started:

    SELECT TOP 100
      source_id, ra, dec, parallax, g.pmra, g.pmdec,
      m.name, m.pmra AS c_pmra, m.pmde AS c_pmde,
      m.e_pm AS c_e_pm,
      1/dist AS cluster_parallax
    FROM
      gaia.dr2epochflux
      JOIN gaia.dr2light AS g USING (source_id)
      JOIN mwsc.main AS m
      ON (1=CONTAINS(
        POINT(g.ra, g.dec),
        CIRCLE(m.raj2000, m.dej2000, rcluster)))
    WHERE IN_UNIT(pmdec, 'deg/yr') BETWEEN m.pmde-m.e_pm*3 AND m.pmde+m.e_pm*3
    

    – yes, you'll want to constrain pmra, too, and the distance, and properly deal with error and all. But you get simple lightcurves for free. Just add them in the SELECT clause!

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