Planetary (exoplanetary) systems can lose comets, asteroids, and planets due to their host stars close approaches. Such encounters may occur during stars motion in the Galaxy disk. In this work, we calculate the number of pairwise encounters of the stars inside the open star cluster Hyades and in the selected volume of efild stars in order to estimate the number of interstellar small bodies in the Galaxy. The resulting catalog was compiled with data obtained by the Gaia spacecraft. Gaia data amount is increasing and systematically updating. These factors are fit into the Big Data concept.
Recent researches of seemingly completely diferent phenomena, such as an
increasing number of exoplanets (for example, see [
If the star has a planetary system, thus, it has asteroids, comets, and planets
(ACP). In the paper [
The interstellar ACP may occur when stars approach each other. The first
idea to calculate the influence of close passages of stars on the Oort cloud comets
was proposed by [
Purpose. We aim to estimate the volume of the population of small interstellar bodies in the Galaxy generated by paired stellar encounters of the field stars and encounters within OSCs. Then, we integrate stellar orbits backward up to 500 Myr, and calculate the close approaches of a limited sample of stars, then extrapolate the obtained data to the Galaxy.
Data and Methods. We use the last available release of the Gaia spacecraft
catalog [
In order to statistically estimate the star paired approaches frequency in the
Galaxy disk and find stars that had close encounters up to 1 pc, we used the
most precise available data from Gaia Early Data Release 3 (Gaia EDR3 [
Our task is to choose Gaia EDR3 stars for which is available data allowing us to integrate the orbits in their motion around the Galactic Center. Thus, we load data and filter stars with available positions on the sky (right ascension and declination α, δ ), proper motions (µ α , µ δ ), parallaxes (π ) and radial velocities (Vr).
Data Quality and Quantity. The full astrometric Gaia solution (5
parameters) – α, δ , µ α , µ δ , π – for around 1.468 billion sources, with a limiting magnitude
of about G ∼ 21 (mag hereinafter) and a bright limit of about G ∼ 3 (for more
details, see [
The parallax uncertainties are – 0.02 − 0.03 mas for G < 15 – 0.07 mas at G = 17 – 0.5 mas at G = 20 – 1.3 mas at G = 21
Radial velocities at Gaia EDR3 hence contains Gaia DR2 (Data release 2) median radial velocities for about 7.21 million stars with a mean G magnitude between ∼ 4 and ∼ 13. The overall precision of the radial velocities at the bright end is of the order of ∼ 200 − 300 m/s while at the faint end, the overall precision is ∼ 1.2 km/s.] Data Filtering and Completeness. According to Gaia EDR3 data, we filtered stars with distances closer to 20 pc to the Sun (π ≥ 50 mas). We obtained 2626 stars, including 677 stars with available radial velocity Vr (according to Gaia DR2). We selected stars with Vr relative error less than 20%.
For the Hyades OSC, we match the latest available catalog of the Hyades
stars [
Both field stars and Hyades stars samples are presented in Figures 1,2 in the projection on the Galaxy plane. Black dots represent the stars, color represent levels of equal density (nlevels = 10).
For the field stars, we can estimate the completeness of the data by considering the dependence of the number of stars on the distance to them. The completeness of the sample is suficient until the moment when the number of stars begins to decrease. Thus, as we can see in Figure 3, the completeness of our stars sample is up to ∼19 pc.
Integration Method. We integrated backward on 500 Myr field stars and Hyades stars during its motion in the Galaxy disk using galpy. The main assumption is the representation of the stars as a point.
In galpy, Galaxy is represented with Milky Way potential (MWPotential2014),
described in [
To calculate the minimal distance dmin between each stars pair, we unloaded the galactocentric cartesian coordinates X, Y, Z and applied an algorithm to calculate the euclidian distance between each star pair. Minimal distance is a distance of the minimal approach between pair of stars during their motion in the Galaxy disk on a considered time interval. Then, for each pair we selected dmin and corresponding time tmin. The algorithm avoids repetition, thus, we get a complete statistical picture of the distances between all the stars we have chosen on the considered time interval.
Calculation Results. As a result of backward orbit integration, we listed minimal distances dmin and corresponding times tmin of the stars pairs. Fig. 3. Dependence of the number of field stars (ordinate or vertical axis) of our sample (see Fig. 1) on the distance to them (abscissa or horizontal axis, pc).
Now, we consider such pairs that approach close enough to afect the outer
boundaries of the Oort clouds of each other. Results for field pairs and Hyades
pairs with minimal distance less than 1 pc are shown in Figure 7. Table 2 contains
list of the dmin–tmin and ID according to Gaia EDR3 for the filed and Hyades
stars (see Appendix A). Extremely close pairs (dmin < 0.05) in the Table 2
could be a binary stars, or an encountering pairs with accidentally unaccounted
calculation error.
Afecting of the Input Parameters Errors. The integration output depends
not only on the orbit parameters but also on the Sun distance to the Galaxy
center and its circular velocity R0 and V0. R0 is defined in dozens of publications,
diferent authors received values in the range of 7.4 to 8.7 kpc. In [
To estimate the uncertanties in determination dmin and tmin, we calculated dmin and tmin in extreme error values of the right ascention and declination (α , δ ), proper motions (µ α , µ δ ), and radial velocity (Vr). As a result we obtained + + dmin, tmin and d−min, t−min by integration with input values α ± σ α , δ ± σ δ , µ α ± σµ α , µ δ ± σ µ δ , Vr ± σ Vr . Although it should be noted that Gaia errors of the astrometric parameters have cross-correlations, which we did not take into account here. For the stars in Figure 7 errors described below do not exceed 20%. 3.1
Estimation of the Interstellar Comets Number in the Galaxy Obtained results allow us to estimate the number of events that can produce interstellar small bodies. The list of values for calculations is presented in Table 1. Columns contain time intervals we integrated for searching close pairs, number of stars in the sample, spatial size and volume of the sample, number of pairs for which we calculated the minimal distance, and number of close pairs that can produce the interstellar small bodies. Stars sample at time moment t=0 presented at Fig. 1 for field stars and 2 for the Hyades star cluster.
Now we could estimate the rate of producing the interstellar small bodies by ifeld stars and by open clusters.
From the table, we see that the OSC produces 62 close pairs for 500 Myr, and the field stars produce 64 close pairs for the same period for a considered volume. There are 105 OSCs in the Galaxy, which means that the clusters replenish the ACP population of the Galaxy by 62 × 105 objects in 500 Myr, or 1.24 × 104 ACP in a 1 Myr.
The volume of the Galaxy V is the volume of a cylinder with a height of 2 kpc and a base area S = 2πR , where R is the radius of the Galaxy of 16 kpc. Thus, V = 2 × 2π × 16 = 201 kpc 3. If for the volume calculated by us 5.5 × 10−5 kpc 3 the productivity is 64 close pairs, then for the entire Galaxy it will be 2.35 × 108 in 500 Myr, or 47 × 104 ACP in a 1 Myr.
Next, we calculate the density of the ACP in the Galaxy. The age of the Galaxy is 1.35 × 1010, thus, over the entire period of its existence were produced 0.67 × 1010 interstellar ACP. The ACP density is ρ = 0.67×10 10 = 3.3 × 108 ACP 201 per 1 kpc 3
It should be noted, that close flyby may not cause noticeable disruption of
the Oort cloud (see, for example, [
Besides, note that our estimate does not take into account those stars that left the circumsolar neighborhood and could also approach both other stars and the Sun. Taking such encounters into account will increase the number of paired encounters and the number of free ACP objects, respectively. 4
– Using filters to restrict Big Data of the Gaia EDR3 spacecraft, we composed
samples of the field stars (n = 642) and the Hyades cluster stars (n = 280).
Thus, only a small percentage of Gaia stars can still be used for our research.
To accumulate the growing amount of data, it is possible to use the Russian
Virtual Observatory.
– The integration of the motion of the stars around the Galaxy center in past
epochs was carried out. Using the developed algorithm, we calculated the
minimal distances dmin and corresponding time tmin of the star pairs of our
sample (Fig. 4, 5, 6), and considered pairs that could provide interstellar
small bodies (Fig. 7). Found pairs of stars approaching at a critical distance
that may cause a loss of comets from their Oort clouds.
– We estimated the frequency of the interstellar small bodies production over
the past 500 million years. Assuming that one close encounter delivers at
least one ACP object to interstellar space, we obtained that the density of
interstellar ACP is 3.3 × 108 ACP per 1 kpc 3. Thus, about 10% of stars
in the Galaxy may provide an interstellar ACP. This estimate is consistent
with the observed data on the number of planetary systems in the Galaxy
[
As part of this task, we encountered technical limitations specific to working
with big data. First, the Gaia data contains terabytes of information, so we are
forced to artificially limit the sample of stars under our study (in our case, by
parallaxes, that is, by the distance from the Sun). Second, our computational
capabilities are also limited, which prevents us from performing a pairwise search
on a large amount of Gaia data. However, the Gaia data itself also has a number
of limitations - even with an unlimited power reserve, we would face the
problem of a lack of information in terms of radial velocities (astrometry of stars is
much simpler and more accurate than spectral studies), as well as the limited
observable part of the Galaxy. Nevertheless, even these problems can be partially
solved using modern machine learning methods - the available sample of stars
is enough to use the so-called ”supervised learning” method, which would allow
us to calculate statistics of stellar encounters across the entire disk. It is worth
mentioning that machine learning is widely applied in astronomy, including open
clusters studying (see, for example, the paper on searching for solar siblings [
Table with dmin and tmin pf the close star pairs (see section 3)
dmin, t[min], pc Myr 0.00459 0 0.00500 0 0.00539 0 0.00660 0 0.00708 0 0.00774 0 0.00779 0 0.00847 0 0.00884 0 0.00925 0 0.00939 0 0.00969 0 0.00984 0 0.01760 0 0.01881 0 0.02295 0 0.02763 0 0.03612 0 0.06225 0 0.11509 0 0.19464 -1.0010 0.30701 0 0.30728 0 0.34775 0 0.42527 0 0.42762 0 0.43257 0 0.45622 -0.5005 0.48556 0 0.52180 0 0.58470 0 0.58553 0 0.61610 -0.5005 0.63606 0 0.65386 -0.5005 0.65398 0 0.65537 0 0.69301 0 0.69675 0 0.70644 0 0.74452 0 0.74830 -2.5025
dmin, t[min], pc Myr 0.75198 0 0.80494 0 0.81364 0 0.81697 0 0.83519 0 0.84161 0 0.84248 -0.5005 0.87358 0 0.93959 0 0.94686 -0.5005 0.95268 0 0.95995 0 0.97118 0 0.97479 0 0.98441 0 0.178 0 0.192 -5.6306 0.254 0 0.299 0 0.324 -1.2512 0.344 -0.6256 0.410 0 0.419 0 0.446 -0.6256 0.459 0 0.488 -158.90 0.521 -3.7537 0.541 -389.13 0.543 0 0.559 -0.6256 0.561 0 0.572 0 0.589 -1.2512 0.607 -26.276 0.610 0 0.611 0 0.637 0 0.643 -0.6256 0.646 0 0.654 0 0.656 0 0.665 0