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).

Datalink

In the results from queries involving gaia.dr2epochflux, we also provide datalinks. These let you retrieve lightcurves that already have mags and that are more easily plotted. Perhaps more importantly, they link back to the full ESAC lightcurves that, in addition, give you a lot more debug information and are required if you want to reliably identify photometry points with the identifiers of the transits that generated them.

Datalink support in clients still is not great, but it’s growing nicely. Your ideas for workflows that should be supported are (again) most welcome – and have a good chance of being adopted. So, try things out, for instance by getting the most recent TOPCAT (as of this writing) and do the following:

  1. Open the VO/TAP dialog from the menu bar and double click the GAVO DC TAP service.
  2. Enter
    SELECT source_id, ra, dec,
    phot_bp_mean_mag, phot_rp_mean_mag, phot_g_mean_mag,
    g_transit_time, g_transit_flux,
    rp_obs_time, rp_flux
    FROM gaia.dr2epochflux 
    JOIN gaia.dr2light
    USING (source_id)
    WHERE parallax>50
    

    into “ADQL” text to retrieve lightcurves for the more nearby variables (in reality, you’d have to be a bit more careful with the distances, but you already knew that).

  3. plot something like phot_bp_mean_mag-phot_rp_mean_mag vs. phot_g_mean_mag (and adapt the plot to fit your viewing habits).
  4. Open the dialog for Views/Activation Actions (from the menu bar or the tool bar – same thing), check “Invoke Service”, choose “View Datalink Table”.
  5. Whenever you click on a a point in your CMD, a window will pop up in which you can choose between the time series in the various bands, and you can pull in the data from ESAC; to load a table, select “Load Table” from the actions near the foot of the datalink table and click “Invoke”.

Yeah. It’s clunky. Help us make it better with your fresh ideas for interfaces (and don’t be cross with us if we have to marry them with what’s technically feasible and readily generalised).

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!