TGAS Limitations

Submitted by Kevin Jardine on 16 October, 2016 - 18:02

The Tycho-Gaia Astrometric Solution (TGAS) star parallax catalog, released as part of Gaia DR1 on September 14, 2016, was created by combining star position data from the Tycho-2 catalog (produced in the late 1990s) with observations from the first few months of Gaia observations. Because of the short scanning period and the dependence on older observations, it has a number of limitations.

The most obvious of these limitations is the accuracy of the data.

An important paper published in 2015, Bailer-Jones, Coryn AL. "Estimating distances from parallaxes." Publications of the Astronomical Society of the Pacific 127.956 (2015): 994 (read in arXiv), concludes that converting parallax measurements with errors to distances is not straightforward unless the estimated error/parallax ratio is < 0.2. If the error/parallax ratio is higher, not only are the results less reliable, but the formula depends upon a model of the distribution of the stars in the Milky Way. In other words, to place these higher error stars on a map, you essentially already have to have a map!

Is the lack of bright stars near the Sun real or a TGAS limitation? (View in Tycho Galaxy)

Half the TGAS stars have a parallax error of 0.32 mas according to the Gaia DR1 documentation. Plugging this error into Bailer-Jones's formula shows that most of the TGAS results can only be reliably placed on a map for distances less than 625 parsecs (about 2000 light years). The green disk in the image above shows this distance superimposed on an artist's model of the Milky Way. As you can see, 625 parsecs only covers the solar neighbourhood and does not even reach any of the galaxy's major spiral arms.

There are more limitations than this. According to the DR1 release notes:

  • Many bright stars at G≲7 are missing from Gaia DR1;
  • Sources close to bright objects are sometimes missing;
  • High proper motion stars (μ>3.5 arcsec yr-1) are missing;
  • Extremely blue and red sources are missing;

The net effect is that no naked eye stars and few stars close to the Sun are included in TGAS (and therefore appear on Tycho Galaxy). This might explain the odd dearth of bright stars near the Sun in the Tycho Galaxy map of the solar neighbourhood.

There is even more bad news. In addition to the 0.32 mas parallax measurement error for most of the TGAS stars, the Gaia DR1 release notes warn that the Gaia data may have a systematic error and that this error might be as high as 0.3 mas. If we add this to the 0.32 mas measurement error, Bailer-Jones's formula gives us a usable distance of 323 parsecs. This is not even as far as the Orion nebula and not that much further than the Hipparcos results from the 1990s.

I have ignored the possible systematic error in producing Tycho Galaxy but it does place a question mark over much of the map.

Another limitation is caused by Gaia's incomplete sky scans during the DR1 period. As the Gaia data that went into TGAS was gathered only over the first few months of the mission, some of the sky was not completely scanned. Gaia scientist Ronald Drimmel tweated the incompleteness maps:

So am I disappointed with all this? Not really. The scans will be completed and the naked eye and high proper motion stars will be added to a future release. Moreover, the science goal of the Gaia mission is to produce parallaxes with an error of 0.0067 mas for the brighter stars. This is smaller than the size of a euro coin on the moon as seen from the Earth, and is fifty times more accurate than achieved for the TGAS release.

The Gaia scientists say that with more observation and calibration, the mission is still on track to achieve this high accuracy over the next few years. Plugging this reduced error into Bailer-Jones's formula gives us a usable distance that is larger than the entire galaxy. Clearly, the real limitation is the brightness of the stars as seen from Gaia. For those stars not embedded in thick dust clouds, the effective range of Gaia will include about a billion stars distributed through most of the Milky Way on this side of the galactic nucleus.

That is a big map.

The Stars, Like Dust

Submitted by Kevin Jardine on 14 October, 2016 - 13:15

The stars, like dust, encircle me
In living mists of light;
And all of space I seem to see
In one vast burst of sight.

Isaac Asimov

September 14, 2016 was the day when everything changed in astronomy with the release of parallax estimates for more than 2 million stars. My last few blog posts have covered the momentous release of the Tycho-Gaia Astrometric Solution (TGAS) as part of Gaia DR1.

Today I have put up the Tycho Explorer, a zoomable, pannable, clickable interface to the Tycho-2 catalog, both as it appears in the sky (Tycho Sky) and as it appears as a face-on map of the galactic plane (Tycho Galaxy).

Tycho Sky includes 2.5 million stars from the Tycho-2 catalog with provided B and V magnitudes (which is almost all of them), and Tycho Galaxy includes more than a million of these stars with reasonably low parallax errors (measured error/parallax ratio < 0.2) stretching out to a distance of about 700 parsecs (2300 light years). At the highest zoom level you can click on each star to get more information and use links to see the star in Tycho Sky and Tycho Galaxy. Search boxes enable you to zoom into a star in the maps by entering an identifier.

Much more information about both the sky and face-on Tycho viewers can be found by clicking the Help links at the upper right of the viewers. The Tycho Explorer is still very much in beta. The infrared background to Tycho Sky has a number of artifacts and limitations, and not all the functions work yet on mobile devices. TGAS itself does not include any naked eye stars or many stars close to the Sun. I'll mention the limitations in more detail in my next blog post.

The Tycho Explorer will continue to improve and the next Gaia data release at the end of 2017 will have more and more accurate data.

Despite the limitations, the results are already amazing. We are on the verge of the greatest mapping project in human history - one that dwarfs that of the New World. The Milky Way is appearing in all its glory before our eyes.

You can download a 4K wallpaper image of some of Tycho Galaxy here (warning, 10 Mb file).

Update: I think I have fixed the issues for mobile and the Tycho Explorer should now work for Android and iOS devices. The interface is not very convenient for small screens (I recommend a large monitor - it looks spectacular on my 4K Philips monitor). If there is demand I might work on a tailored interface for phones.

The code is now in GitHub: https://github.com/kevinjardine/galaxymap. Contributions are welcome.

TGAS high temperature / luminosity map

Submitted by Kevin Jardine on 16 September, 2016 - 17:07

I've now created the first real face-on map/poster from the Tycho Gaia Astrometric Solution (TGAS) data set that was part of Gaia DR1. The download links for the full resolution version are at the end of this blog post.

TGAS contains parallax data for about 2 million stars, which is most of the Tycho-2 catalog.

Of this data, about half has an error/parallax ratio < 0.2, which is very good. (Keep in mind that this is the precision of the specific measurements. The Gaia DR1 documents warn that in addition the data has a systematic error which is unknown but could be as high as 0.3 milliarcseconds. If the systematic error is really 0.3 milliarcseconds, this would throw off much of the map, especially the regions beyond 300 parsecs. I'm ignoring that for now. In any case, I'll redo all my Gaia maps after DR2 comes out towards the end of 2017. For now, TGAS is the best we have.)

The data with error/parallax ratio < 0.2 goes out to about 700 parsecs or so. The map has a radius of 800 parsecs, which includes pretty well all of the Gould Belt. So this map really shows pretty well all of what most astronomers would consider the solar neighbourhood.

This first map shows only a tiny fraction of the data set: stars with a colour index < 0.1 (meaning that they are very high temperature) or an absolute magnitude < -2 (meaning that they are very luminous). These are the spectacular galactic beacons that might be used as way points in some distant future. There are 50269 of these stars in TGAS with an error/parallax ratio < 0.2.

As this is a map and not just a data dump, I have provided a background to provide some context. The most important background is the face-on dust cloud map provided by this wonderful paper:

Lallement, R., Vergely, J. L., Valette, B., Puspitarini, L., Eyer, L., & Casagrande, L. (2014). 3D maps of the local ISM from inversion of individual color excess measurements. Astronomy & Astrophysics, 561, A91.

which is essential reading for any Milky Way cartographer. This is shown in green.

I have also provided a few of the larger HII regions from the Sharpless, Gum and RCW catalogs. These are shown as red circles.

Finally, I used TGAS itself to create a blue background - this is a weighted density map . Basically what this does is cut the Milky Way into cylinders that go above and below the galactic plane and have a radius of 10 parsecs. I then take the weighted mean of all the stars with a colour index < 0.1 within each cylinder (weighted by the star's estimated temperature) and use the resulting mean with a centre of each parsec to create a luminosity value. Finally I smooth the result using a gaussian blur with a radius of 20 parsecs.

This all sounds complex but takes very little time to do with Python's wonderful scipy/numpy packages.

In a nutshell, the blue background shows where the hot stars are concentrated. These are typically young stars that have not drifted yet from their places of origin.

You can download the full 8192x8192 pixel map poster here (warning, files sizes are a bit over 30 Mb):

This is just a start - eventually you can expect to see a searchable, zoomable, pannable, clickable face-on map of a million TGAS stars on this site but that will take a little more time to pull together.

First Gaia face-on map

Submitted by Kevin Jardine on 14 September, 2016 - 17:38

This is not a "real" finished map, but it was interesting to select the stars in the Gaia DR1 TGAS release with a error/parallax ratio of less than 0.2 and project a density value onto a face-on map as seen from above the Milky Way.

You can view a higher resolution version by clicking here.

This map has HII regions taken from the Sharpless, Gum and RCW catalogs and dust clouds taken from a recent 2014 paper, 3D maps of the local ISM from inversion of individual color excess measurements from Lallement, Vergeley, Valette, Puspitarini, et.al.

Here is the density map by itself:

The dust clouds in the face on map have obvious finger-like projections caused by a lack of data, but it is interesting that even the TGAS density map has these projections. I'm not sure if this is an artifact in the Tycho-2 catalog or in the way Gaia collected its first round of data.

There may be real practical limits for collecting data at visual frequencies in some directions (such as much of the first quadrant) caused by thick dust clouds. Perhaps we will not have fully complete maps until an infrared equivalent to the Gaia mission, which can see through those clouds.

Not surprisingly, the highest star density is in the Local Bubble surrounding the Sun as well as the Heiles cavity in the third and fourth quadrant as they are both relatively easy to observe.

Still, it looks like there are a reasonably large number of accurate measurements even as far away as the Barnard Loop and Orion nebula, so I am going to be working on much more detailed maps soon.

It turns out that the error/parallax < 0.2 condition is true for a million stars (half the TGAS stars) so there are plenty of reasonably accurate measurements to work with.

(For anyone wondering how I created the density map, it shows the mean number of stars in cylinders with a radius of 5 pc in the galactic plane and includes all TGAS stars from the top to the bottom of that section of the galaxy.)

Mind the Errors

Submitted by Kevin Jardine on 14 September, 2016 - 00:07

The first data release of the Gaia star mapping mission is coming out tomorrow. The release is creating a lot of understandable excitement but be careful! The Gaia scientists have already announced the parallax errors and for many of the first release stars they are similar to the previous Hipparcos mission, not the revolutionary accuracy expected by the end of the Gaia mission.

The limited accuracy in this first release is not because of a malfunction in the Gaia machinery but because the data is derived by combining the very first Gaia observations with the star positions and motions given in the older Tycho-2 catalog. This combination, the Tycho Gaia Astrometric Solution (TGAS), is in one way a bit of a data hack, but it does dramatically increase the number of stars with Hipparcos level accuracy from 100 thousand in the original Hipparcos catalog to about 2 million. This delivers a much more detailed map for the near solar neighbourhood (out to about 100-200 parsecs or 330-660 light years).

It is worth spending a bit of time looking at parallax error and how it determines the size of accurate star maps.

One reason that professional astronomers almost exclusively use parsecs when discussing distances within the Milky Way is that it is easy to convert parallax into parsecs. The formula could not be simpler. If we know that the parallax for a star is p arcseconds, then the distance d to the star in parsecs is given by the formula:

d = 1/p

However, even an incredibly accurate device like Gaia cannot measure parallax with complete accuracy and so both the Hipparcos and Gaia catalogs provide a standard error value measured in milliarcsecond standard deviations.

If you remember your stats classes, you will know that the odds of a correct value appearing within one standard deviation if the errors are normally distributed are 68%, within 2 standard deviations, 95%, and within 3 standard deviations 99.7%.

The Hipparcos median parallax error was about 1 milliarcsecond, so if you wanted to produce a map where the star positions were fairly accurate, you would likely go for two standard deviations, which in the Hipparcos case would be 2 milliarcseconds.

This accuracy standard puts strong limitations on the size of the map. A star with a distance of 100 parsecs has a parallax of 10 milliarcseconds. Using two Hipparcos standard deviations, this means that there is a 95% chance that a star with a measured parallax of 10 milliarcseconds falls within a real parallax of 10±2 milliarcseconds. This corresponds to a distance between 1000/(10+2) = 83 parsecs and 1000/(10-2) = 125 parsecs.

What this calculation shows is that if we use the Hipparcos data out to about 100 parsecs then we are 95% sure that the distances are accurate to about 25%.

Some Hipparcos stars have better than a 1 millisecond error, so if we filter to a list smaller than the 100 thousand stars, we can do better than 25% accuracy and even extend the map (with a loss of detail) to about 200 parsecs or so. If we go beyond about 200 parsecs, however, the parallax errors imply that the odds are remote that distance estimates are accurate for all but a tiny number of stars. So a detailed and reasonably accurate map using Hipparcos is restricted to a region between 100-200 parsecs from the Sun.

Although the overall accuracy of tomorrow's release will be similar to Hipparcos, the much larger number of stars (2 million) means that we can likely extend the map a little further using low error stars and still have significant detail. My hope is that we can even get some details as far away as the Orion nebula (400 parsecs). We'll know soon. My plan is to produce a face-on map as far out as the error values will allow.

Gaia will continue to produce regular data releases. Gaia DR2 will arrive by the end of 2017. So far the signs are still good that Gaia will ultimately meet its objectives and produce parallax data with far higher accuracy, allowing us to map the Milky Way out for thousands of parsecs. I can hardly wait!

(The parallax error map at the top of this blog post was made available by ESA before the Gaia release.)

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