Movement of stars - star trails

A major improvement in Gaia Early Data Release 3 (Gaia EDR3) with respect to Gaia DR2 is the precision to which the motions of stars across the sky, the so-called proper motions, have been measured. The precision has increased by a factor of 2 because of the larger number of observations processed for Gaia EDR3 and the larger time difference between the first and last observation. We illustrate this through visualizing the motions of stars across the sky using the new Gaia EDR3 proper motions. The animation shows in short steps the displacements of 40 000 stars within 100 parsec distance from the Sun 1.6 million years into the future. Each trail represents the displacement of one star.

There is a lot going on in this animation! We explain step by step what one can see. Refer back to the animation in between to see if you can spot the things described below.

• The first frame shows the current position on the sky for 40 000 stars within 100 parsecs (326 light-years) from the Sun. The dots also indicate the brightness of the stars.
• The next few frames show trails starting from the locations of the stars. These trails indicate how the stars change position on the sky over time intervals of 80 000 years into the future. The trails also indicate the present-day brightness of the star they correspond to.
• Next, the starting positions of the stars are removed and one sees only the trails moving across the sky. The trails are followed for 1.6 million years into the future.
• The animation ends with the image shown at the top of the page. It shows the full star trails 400 thousand years into the future. The shorter period was chosen to avoid crowding the image too much with the star trails.

If you look closely at the animation there are several interesting things to note, which are also visible in the two stills from the animation, shown just above.

• There are short and long trails. The length of the trail indicates the displacement of a star on the sky over 80 000 years. Short trails indicate that the star moves slowly across the sky, while long trails indicate a faster motion. The motion of a star across the sky, its proper motion, reflects the motion of the star through space with respect to the solar system (from which we observe the star). The displacement on the sky is dictated by the distance to the star and the speed at which it moves. Stars that are nearby and moving at high speeds will change position across the sky quickly, while stars that move at intrinsically low speeds, or are far away, will change position slowly. This explains why the short trails tend to be faint in appearance (the stars are far away) and the long trails bright (the stars are near).
• If you look at the animation several times you will notice that sometimes a short trail turns into a long one and then turns back into a short trail. This indicates that the star is moving towards us and as it gets closer it will move ever faster across the sky. Once the star has passed us it will move away again and the trail consequently becomes shorter as the distance to the star increases.

Towards the end of the animation you can notice that the stars seem to congregate on the right side of the video, while the left side appears to empty. This is caused by the motion of the sun itself with respect to the average motion of the stars around us. The motion of the sun causes an apparent motion of the stars in the opposite direction. If you imagine yourself moving through a crowd of people (who are standing still), then in front of you the people will appear to move apart as you approach them, while behind you the people will appear to stand ever closer together as you move away from them. This effect also happens due to the motion of the sun with respect to the stars. Hence the sun is moving toward a point on the sky in the upper left quadrant of the video, while it moves away from the lower right quadrant. This is further explored below.

How realistic is this animation?

Good question! From the Gaia EDR3 catalogue we know for all the stars their current positions in space (from the parallax and position on the sky) and their motion in three dimensions (from the proper motion and radial velocity). The animation is based on predicting the positions of the stars in space, with respect to the sun, over time. This prediction is scientifically correct and takes into account the effect of the radial velocity of the star which causes it to move closer or further away (for the experts, the predicted positions are calculated according to the prescriptions given in the Gaia EDR3 documentation). However, there are a number of simplifications that make the animation somewhat unrealistic.

• In the calculations of the future positions of the stars we assume they move uniformly through space, that is along straight lines at constant speeds. In reality the stars and the sun describe curved orbits in the gravitational force field of the Milky Way.  This will cause their relative motions to change slowly over time and this will affect where stars appear in the sky. However, over the 1.6 million years considered here the effect is irrelevant at the scale of the movie and images.
• The animation shows only 40 000 stars within 100 parsec from the Sun. There are in fact many more stars within that distance from the Sun, and here only a random subset of stars is shown, those for which the radial velocity is known in Gaia EDR3 and for which the parallaxes are known to better than 10 percent.
• If we want to visualize the motion across the sky of stars within a 100 pc radius sphere around the sun, we should also account for the fact that some stars will disappear beyond the boundary of the sphere, while other stars will enter the sphere as they approach us from beyond 100 pc. This is not done in the simulation.
• The brightness of the star trails is not adjusted according to the distance to the star, but always (incorrectly) reflects the present-day brightness.

The animation was created by calculating the future star positions in Python and creating the frames with matplotlib. The code to do this, with explanations on how to use it and create the video, can be found on GitHub.

Credit: ESA/Gaia/DPAC
Released under CC BY-SA 3.0 IGO

Acknowledgement: this video was created by Anthony Brown, based on an idea from Stefan Jordan, and with inputs from Tineke Roegiers, Xavier Luri, Eduard Masana, and Timo Prusti. Background colour image created by André Moitinho.