© The Authors 2024

1 Introduction

For many years, we have searched for stars that approach the Sun and therefore can perturb orbits of long-period comets (LPCs); for more details, readers can refer to Dybczyński & Kankiewicz (1999); Dybczyński (2006), for example. In Wysoczańska et al. (2020b), we introduced a publicly available Stellar Potential Perturbers Database (StePPeD)¹ containing data on potential stellar perturbers of LPC motion. This database had several revisions and is currently based on Gaia Early Data Release 3 (EDR3; Gaia Collaboration 2021; Dybczyński et al. 2022). Similar results, also based on Gaia EDR3, have also been published by Bobylev & Bajkova (2022) and Bailer-Jones (2022). Recently, Raymond et al. (2024) published an analysis on how an extremely close stellar passage can change the motion of Solar System bodies.

Wysoczańska et al. (2020a) announced for the first time that the star HD 7977 could be an important perturber for some observed LPCs based on Gaia Data Release 2 (DR2 Gaia Collaboration 2018). During the StePPeD database update to version 3.2, Dybczyński et al. (2022) found that according to Gaia EDR3 (Gaia Collaboration 2021) this star (designated as P0230 in StePPeD) nominally passed 2.47 Myr ago as close to the Sun as 0.014 pc (~3000 au). This result means that HD 7977 might have been an important perturber of the motion of most (if not all) LPCs and should be taken into account in all long-term dynamical investigations of the past motion of the Solar System bodies. Some examples of such strong interactions have recently been presented by Dybczyński & Królikowska (2022).

This paper is organised as follows. In the next section, we summarise our current knowledge about the star HD 7977 on the basis of all available results from the Gaia mission. This includes astrometry, distance estimates, and radial velocity measurements. Section 3 describes all the data sources we used in our calculations. It contains both a discussion of historical data and a presentation of our own astrometry. The influence of the HD 7977 data uncertainties on the results presented is discussed in Sect. 4. We also note the existence of several other potential stellar perturbers in Sect. 5. The potential effect of the passage of star HD 7977 very close to the Sun on the motion of LPCs is described in Sect. 6. Some estimates of such an influence on other Solar System bodies are presented in Sect. 7. Our conclusions and prospects for future studies can be found in Sect. 8. This paper is accompanied by three Appendices, which contain a detailed inspection of various current Gaia results for HD 7977.

2 What is known today about HD 7977 on the basis of the Gaia mission results

This section, together with the Appendices A, B, and C, provides a thorough inspection of the various Gaia DR3 data for HD 7977, focussing on a quality assessment of the data and the possibility that the star is an unresolved binary. We find several independent indications that hint at the possibility that HD 7977 is an unresolved binary, namely a poor astrometric fit (Sect. 2.1), scatter in radial velocity measurements (Sect. 2.3) and spectral peculiarities (Appendix C).

None of these separated hints are sufficiently convincing, but the fact that the three hints come from three independent data sets adds weight to the unresolved binary hypothesis. The final confirmation or rejection of this hypothesis requires the publication of Gaia DR4. We recall that the fact that the star is not listed as a non-single star in Gaia DR3 is in no way proof that the object is a single star. The ~800 000 binary systems published in Gaia DR3 (Gaia Collaboration 2023a) are a small subset, heavily impacted by filtering and therefore heavily biased, of all binaries that Gaia has detected and that are currently being processed for publication in Gaia DR4.

2.1 Astrometry

The Gaia astrometry reported in the Gaia catalogue(s) has tiny formal uncertainties, but several caveats apply. First, it is important to realise that the various Gaia data releases are not independent: the astrometry reported in Gaia DR2 (Gaia Collaboration 2018) is based on observations collected during the first 22 months of the mission, whereas the astrometry reported in Gaia DR3 (Gaia Collaboration 2023b) is based on observations collected during the first 34 months of the mission (of which the first 22 months obviously overlap with Gaia DR2). In general, therefore, Gaia DR2 can be considered to be superseded by Gaia DR3 since it is based not only on an extended set of observations but also on improved data reductions (for example, matching of observations to sources) and calibrations (Lindegren et al. 2021b).

The astrometry reported in the main Gaia DR3 source table reflects the formal parameters and formal uncertainties resulting from fitting a single-star motion model to the individual observations. The single-star assumption is clearly strong and can lead to major astrometric model errors that are not included in the formal uncertainties reported in the catalogue if the object is an unresolved binary.

Each astrometric fit is therefore accompanied by a goodness-of-fit parameter, the renormalised unit-weight error (ruwe²), which quantifies how well the individual observation residuals of the single-star fit conform to white noise. In other words, large values of ruwe indicate a poor astrometric fit caused, for instance, by binarity. Although a canonical threshold for acceptable astrometry was ruwe<1.4 for Gaia DR2, the value of Gaia DR3 that denotes the limit above which sources have significant astrometric deviations inconsistent with single source astrome-try is 1.25 (Penoyre et al. 2020). HD7977 has ruwe = 2.01, well above this threshold, suggesting that the object is an astromet-ric binary. Other studies, for example Green et al. (2023), also suggest that HD 7977 could be a member of multiple systems. Although this star does not appear in the final set of binary candidates (formal score is equal to 0), changes in brightness in the TESS data might fit to an ellipsoidal orbital period of 4.73 days. These remarks cannot be underestimated and should be taken into account in further research.

The scrupulous discussion of the Gaia astrometric data and their quality is placed in Appendix A. In conclusion, formal astrometric uncertainties do not tell the full story. Most importantly, they do not include model errors, possibly up to the level of a fraction of a milliarcsecond or more, which would be present if the object were an astrometric binary, as suggested by various quality measures. Moreover, the formal uncertainties are underestimated by up to a factor of 2 or more. One possible interpretation of the proper motion evolution seen between the three Gaia data releases is that it is explained by the additional months of data that have been added in the astrometric fit of each release, together with the aforementioned model error. In other words: neither the DR1, nor the DR2, nor the DR3 proper motion of HD 7977 are reliable and the astrometric model error is (likely) orders of magnitude larger than the formal uncertainties reported in DR3.

2.2 Distance

The Gaia DR3 parallax equals 13.212 ± 0.032 mas (with a formal signal-to-noise ratio of 410). As discussed before, the formal uncertainty is very likely underestimated by a factor of 2 or more, even apart from possible model errors should the source be an astrometric binary. Despite this error underestimation, the relative parallax error is smaller than 1%. This, in turn, justifies the use of the inverse of the measured parallax as an essentially unbiased distance estimate (Luri et al. 2018). This yields a distance estimate of 75.690 ± 0.185 pc. The associated absolute magnitude in the G band equals $$\begin{array}{l}{M}_{\text{G}}=8.891319-0.005-5.0\cdot \left({\log }_{10}(75.690)-1.0\right)\\ =4.49\pm 0.01\text{\hspace{0.17em}mag}\end{array}$$

using an extinction value of ag_gspphot = 0.005 mag (see below).

The Gaia parallaxes are known to suffer from a small systematic bias that depends on magnitude, colour, and sky position (Lindegren et al. 2021a). For HD 7977, the recommended bias correction – to be subtracted from the measured parallax – equals –0.024 mas so that the ‘debiased’ distance estimate becomes 75.551 ± 0.185 pc. The bias correction itself has an RMS scatter of ~0.015 mas. Since the bias estimate, its uncertainty, and the formal parallax uncertainty are all of the same order of magnitude, it is not trivial to conclude whether applying the correction makes sense or not, and hence we do not apply it. Several other distance estimates can be found in the literature; see the Appendix B.

2.3 Radial velocity

The radial velocity of HD 7977 reported in Gaia DR3 equals 26.76 ± 0.21 km s^–1. Similarly to the case of astrometry (Sect. 2.1), the formal uncertainties of the radial velocities are also not perfectly estimated. Figure 8 in Katz et al. (2023) suggests that the uncertainty is underestimated by a factor ~ 1.5–1.75 (HD 7977 has grνs_mag = 8.229 mag). Two elements impact the absolute value of the radial velocity, and hence the trace-back time of the encounter: the radial-velocity zero point and the stellar gravitational redshift. Equation (5) in Katz et al. (2023) suggests that the zero-point offset of the Gaia DR3 radial velocities is negligible at 8th magnitude. The stellar gravitational redshift for this source is estimated to be graνredshift_flame = 0.5624 ± 0.012 km s^–1 (for details, see Sect. 3.3.1 in Fouesneau et al. 2023). A detailed discussion on the Gaia spectral data for HD 7977 can be found in Appendix C.

3 How we completed the data for our calculations

Despite the possible unrecognised multiple nature of HD 7977, while waiting for more detailed data, we now have to base our calculations on data on the bright component that has been recorded in stellar catalogues for over a hundred years. According to our search, the star in question was mentioned for the first time in the catalogue published by Oeltzen (1852) as star number 1383. Later, it was included by Argelander in the Bonner Durchmusterung (Argelander 1903) and designated as BD+61 250. Since then, this star has been included in almost all catalogues of reference stars covering this part of the northern sky, since it is relatively bright (~9 mag). The position of BD+61 250 has been for example absolutely determined by Krueger during the Astronomische Gesellschaft observing campaign in 18691880 in Helsigfors and Gotha for the declination zone from the +55 to +65 zone (Krueger 1890). In the Henry Draper Catalogue (Cannon & Pickering 1918) it is named HD 7977 and we use this name throughout the rest of the text. More information can be found in the SIMBAD database³ (Wenger et al. 2000).

To calculate the past motion of this star through the Gaiaxy and obtain the parameters of its close passage near the Sun, we need its current position, proper motion, parallax, and radial velocity. These data allow us to calculate the six-dimensional starting point for the backward numerical integration of its motion.

3.1 Gaia position and parallax

As the source of the astrometric position and the parallax value for HD 7977, we took the most recent data provided by the Gaia mission, namely the Gaia EDR3 catalogue (Gaia Collaboration 2021), which was later incorporated into the complete Gaia DR3 release (Gaia Collaboration 2023b). Both position and parallax are consistent between Gaia DR2 and DR3 releases, as shown in Table 1. Only in the case of declination do some small discrepancies exist. The situation with the proper motion of HD 7977 is much more complicated.

3.2 Proper motion problem

When searching for stars closely passing near the Sun, it is obvious that we are interested mainly in stars with the smallest observed proper motion. Because of the well-known statistical property: “large proper motion means small distance” stars with an infinitesimal proper motion were excluded from many observational projects dedicated for parallax or radial velocity measurements, as noted in Dybczyński & Kwiatkowski (2003). HD 7977 is such a kind of star, with a very small proper motion and, therefore, difficult to measure.

Several historical and contemporary determinations of HD 7977 proper motion components are collected in Table 2. To our knowledge, the first reliable value of its proper motion can be found in the AGK3 catalogue (Heckmann 1975). It was obtained by a comparison of the astrometric position obtained in 1928.9 for AGK2 catalogue (Astronomische Gesellschaft 1951) and observations made in 1956.73. Unfortunately, the authors did not present an uncertainty of this proper motion value. As a resort, we use mean proper motion errors in AGK3 as estimated by Schwan (1985) that are relatively large. It may be unexpected that, based on the same historical position obtained in 1928.9, the authors of the SAO catalogue (Whipple 1966) obtained a completely different proper motion of HD 7977. Bucciarelli et al. (1992) published an updated version of the AGK3 catalogue, again with the different proper motion of this star; see Table 2.

An independent line of proper motion measurements for HD 7977 is based on the absolute position determination carried out at the Vatican Observatory in the course of the Carte du Ciel project (Hagen 1914). The star in question was recorded on two photographic plates in 1903. An attempt to determine proper motions based on these old photographic observations has been made by Urban et al. (1996) who re-reduced original Vatican plates using the published plate measurements. These positions were used to produce the ACRS catalogue (Corbin et al. 1991). Based on the first edition of the Tycho catalogue (ESA 1997) and several old catalogue positions, Urban et al. (1998) calculated new proper motions for HD 7977 which is included in the ACT catalogue. Another group of catalogues we examined consists of PPM (Roeser & Bastian 1988) and PPMXL (Roeser et al. 2010). Probably the most reliable catalogue values before the Gaia era can be found in the Tycho-2 catalogue (Høg et al. 2000).

It was a big surprise when proper motions well below 1 mas yr^–1 has been presented in the Gaia DR2 (Gaia Collaboration 2018). In Gaia EDR3 (Gaia Collaboration 2021) even a much smaller value for the proper motion in the Right Ascension is presented. See Sect. 2 for a possible explanation and interpretation of Gaia DR2 and EDR3 proper motion inconsistency for HD 7977.

3.3 Our own astrometry

Due to the great spread of published HD 7977’s proper motion components, caused by different combinations of positions, large possible errors of historical measurements, and different precession/nutation standards and time bases, we decided here to perform our own astrometric position estimations. For this purpose, we used the following data sources: two photographic plate measurements from the Vatican Observatory survey (Hagen 1914) obtained in 1903, two scans of photographic plates from the Palomar Observatory Sky Survey I obtained in 1954 (Pennington et al. 1993), one scan of photographic plate from the Palomar Quick V survey obtained in 1983 (Lasker et al. 1990), and three scans of photographic plates from the Palomar Observatory Sky Survey II obtained in 1989 – 1993 (Reid et al. 1991). Data analysis was performed using our own astrometric software with the Gaia DR3 catalogue as reference. To reduce the impact of the large time difference between the Gaia catalogue and the observation epoch, the reference stars were selected in an iterative process. Only stars fitting within 0.1 arcsec in the third-order astrometric plate solution were kept and used in the final solution. The internal statistical uncertainties of the positions obtained were estimated using the bootstrap sampling procedure (Efron 1982). These measurements are presented in Table 3 together with a collection of catalogue positions of HD 7977 we were able to find, all transformed to ICRS.

Listed catalogue positions are often not independent but are based on a different combination of observations. If a mean epoch and a proper motion were included in a catalogue, we propagated the star’s position to this epoch using the given proper motion. A rigorous transformation to the ICRS system has also been performed.

It should be stressed that in almost all cases of historical catalogues, as uncertainty, we use the formal precision of the published position (typically 0^s.01 and 0″.1). To our knowledge, this underestimates the corresponding probable errors by a factor of three to five or more. For example, in the “Catalog von 14680 Sternen” (Krueger 1890) the author gives an estimate of the probable error of the single observation equal to 0^s.101 and 0″.51 for Right Ascension and Declination, respectively. But these values are presented in this catalogue with a precision of 0^s.01 and 0″.1, respectively.

3.4 Our attempt to estimate HD 7977 proper motion

Using data from Table 3, we attempted to determine the proper motion of this star. We assumed a linear trend in both coordinates, as no information on HD 7977 duplicity can be found in any source. Moreover, in some catalogues, the authors comment that, after some checks, the possibility of its double nature has been rejected.

The results of our estimation are presented in Fig. 1. Some of the positions have been excluded from our straight-line fitting. We exclude the data obtained by Krueger (1890) as an obvious outlier. We also exclude SAO, PPM, and PPMX positions since these catalogues are compilations of different data, as is the case for the ACT catalogue. We also exclude Gaia DR1 and DR2 positions by assuming that the DR3 data are the most accurate and taking into account a small time interval between them. The excluded data are presented in black in Fig. 1.

When fitting the straight line, we forced it to pass through the Gaia position assuming that even in future data releases the position would change infinitesimally on the scale of Fig. 1. It should be stressed again that the error bars of all positions before 1940 are underestimated and should be multiplied by 3 or 5. On the other hand, in the case of such a small proper motion, all historical observations are of great value.

From the linear fit presented in Fig. 1 we obtained the following HD 7977 proper motion components µ_α ⋅ cos(δ) = –1.23 mas yr^–1 and µ_δ = −3.19 mas yr^–1. We do not attempt to estimate their uncertainties due to the mentioned fact that the probable errors of the historical positions are unknown. The value obtained seems almost consistent with the proper motions of Tycho-2 and PPMX.

It is worth mentioning that such a small proper motion might be very difficult to measure. For example, the Vatican Observatory plates from 1903 were measured manually with a formal precision of 0″.3. Even if we ignore any (quite probable) random errors and try to estimate proper motion comparing the Vatican observations with the Gaia data, we obtain the formal uncertainty of 0″.3/120 yr = 2.5 mas yr^–1, which is comparable to a proper motion value of HD 7977. If we account for random observational errors in historical data, we may conclude that a very small proper motion of this star presented in Gaia DR3 can be consistent with all previous observations. As a result, we have to accept the possibility of a very close passage of HD 7977 near the Sun.

Fig. 1 HD 7977 position changes over last two centuries. Data are from Table 3, in red we show these which were taken into account in proper motion estimation. No weighing has been applied but straight lines are forced to pass through the Gaia DR3 position. The estimated proper motion components are –2.62 mas yr–1 and –3.19 mas yr–1 in Declination and Right Ascension respectively.

3.5 Radial velocity

The first measurement of HD 7977 radial velocity was published as a part of Gaia DR2 catalogue (Gaia Collaboration 2018). As a result, the past motion of this star could be analysed, and its moderately close pass near the Sun was first announced by Bailer-Jones et al. (2018). Using the same data, Wysoczańska et al. (2020a) presented the possible interaction of this star with the comet C/2002 A3 LINEAR. The second radial velocity measurement for HD 7977 was published by Errmann et al. (2020) owing to a dedicated campaign for stars that closely passed the Sun. Using this later value combined with astrometry from Gaia EDR3, Dybczyński et al. (2022) announced an extremely close nominal passage of HD 7977 near the Sun 2.5 Myr ago at a distance of 0.014 pc (3000 au).

The next value was included in the third Gaia data release (Gaia Collaboration 2023b) and was used by Bobylev & Bajkova (2022) and Bailer-Jones (2022) to estimate the parameters of this star’s close passage near the Sun. The comparison of all these velocity measurements is presented in Table 4.

We checked most of the contemporary stellar databases looking for other determinations of radial velocity and other stellar parameters of the investigated star. According to available data, there are no planets orbiting HD 7977 and no stellar companion has been found so far⁴. In light of the discussion of the quality of Gaia radial velocity measurements presented in Sect. 2, we decided to use the value published by Errmann et al. (2020) in our calculations.

Fig. 2 HD 7977 and its 25 000 clones at the closest encounter with the Sun. The red dot represents the Sun position while the green one corresponds to the star’s nominal position at the closest approach.

4 The influence of the data uncertainties on the HD 7977 close passage parameters

Taking the astrometry from Gaia DR3 and the radial velocity from Errmann et al. (2020), we obtained the nominal distance between HD 7977 and the Sun to be equal 0.011 pc (~2300 au) during its passage 2.47 Myr ago. This is an even slightly closer passage than that obtained by Dybczyński et al. (2022) based on Gaia EDR3. The difference is the result of the modified list of other acting stars, which comes from partially new radial velocities in Gaia DR3.

To estimate the uncertainty of these parameters resulting from the uncertainty of the HD 7977 data, we cloned this star 25 000 times using the covariance matrix from Gaia DR3. Next, we numerically integrated all clones into the past and calculated the parameters of their closest encounter with the Sun. The result of this simulation is shown in Fig. 2. The details of such a calculation including the discussion on the Gaiactic gravitational potential models can be found in Dybczyński et al. (2022).

The formal statistics of the minimal distance results for 25 000 star clones resulted in d_min = 0.012:0.031:0.060 pc, which is presented here in the form of the 10th percentile, the median and the 90th percentile. Analogous statistics for the moment of the closest approach read: t_min = 2.44:2.47:2.50 Myr ago and for the relative velocity of the encounter: v_rel = 30.3:30.6:31.0 km s^–1.

The cloud of star clones presented in Fig. 2 surrounds the Sun, so the formal statistics of the minimal distance are less informative. Instead, we calculated the distance between the Sun and the centroid of this cloud to be equal to 0.011 pc. We can also state that 90% of the clones lie no further than 0.058 pc from this centroid. The main concern with this stellar passage is that it was very close to the Sun but its precise trajectory cannot be reliably calculated because of the still large astrometry uncertainties.

5 Other important stellar perturbers – StePPeD database update

Based on our current knowledge, the nominal passage of HD 7977 near the Sun is the closest one, but we have recognised tens of other potential stellar perturbers of LPCs motion. In July 2022 Gaia DR3 was released (Gaia Collaboration 2023b). No new astrometry for single stars has appeared, but many corrected and new radial velocities have become available. The catalogue contains the radial velocities for about 33 million stars, which is 5 times more than in Gaia EDR3. Moreover, for the first time in the Gaia catalogue there appeared a special part with the new astrometric results for more than 800 000 unresolved binaries with their observations treated with a new, dedicated model (Halbwachs et al. 2023).

With all these new data at hand, we decided to update the StePPeD database from version 3.2 described in Dybczyński et al. (2022) to a new one, namely release 3.3, which was made publicly available in June 2023. According to our own cometary calculations experience and following a similar approach of Bobylev & Bajkova (2022) and Bailer-Jones (2022) we decided to limit the list of potential perturbers to stars that had passed or will pass the Sun closer than 1 pc. There are 59 such stars in our new list. All parameters of known close encounters with the Sun have been recalculated using the corrected radial velocities. Additionally, we searched for new stars using new radial velocities. We have found 26 new perturbers with a miss distance smaller than 1 pc.

We also decided to check all stars suspected to be unresolved binaries and included in the Gaia DR3 Part 3, non-single stars. We found that for two stars from our list, namely P0180 and P0533, we should use the astrometry from tables describing nonsingle-star astrometric models for sources having a nonlinear proper motion which is compatible with an acceleration solution, acceleration model with 9 parameters (for P0180) and with 7 parameters (for P0533). These new data improved our results, for example, the closest approach for P0533 decreased from 0.51±0.12 pc down to 0.23±0.05 pc. But the most important new result was the discovery of a new massive perturber encoded in the StePPed database as P3509.

5.1 The special case of P3509

During our careful inspection of all results presented in Gaia DR3 for unresolved nonsingle stars, we found that star Gaia DR3 3598849446322133248, also known as HD 102928 or HIP 57791, is a binary system that nominally approached the Sun 3.94 Myr ago at a distance of only 0.40 pc. In the StePPeD database, it is named P3509 and we use this in the following text.

The uncertainties in astrometry and radial velocity of P3509 are significantly higher than for HD 7977 and result in a much more spread clones swarm, as shown in Fig. 3. However, it clearly shows that the minimal distance between P3509 and the Sun can be arbitrarily small. What makes this potential perturber very important is its mass. According to Chulkov & Malkov (2022) the total mass of this system equals 3.5 M_⊙. All details on this particular system approach to the Sun, as well as on all other potential stellar perturber encounters, can be found in the StePPeD dabase. Basic data on stars that appear as perturbers in the examples presented in Sect. 6.3 are also quoted in Table 5 for the convenience of the reader.

Fig. 3 P3509 and its 25 000 clones at the closest encounter with the Sun. The red dot represents the Sun position while the green one corresponds to the star’s nominal position at the closest approach. The blue circle marks the traditional extent of the Oort cometary cloud.

5.2 Multiple stars problem

To our knowledge, up to 2022 there was no information in the literature about a recognised binary or multiple system that passed or will pass the Sun closer than 1pc. The only exception is α Centauri triple system which will approach the closest proximity of 1 pc in the future (0.03 Myr from now) but we have to wait for more precise data on this system to calculate precisely the parameters of this event. In Dybczyński et al. (2022) we presented a list of double-star perturbers, but only two of them (P5000 and P5001) remain on our current shortlist. We should also note that there probably exist companions for P0109 (HD 168769, HIP 90112) and P0506 from our current list, but no reliable data for secondaries are available, so we treated these perturbers as single stars.

In the course of preparing the next update of the StePPeD database, we used all new radial velocities from Gaia DR3 and analysed all putative binary systems included in El-Badry et al. (2021). We found a large group of candidates for the close Solar System passage. Most of them have a very high uncertainty of the closest approach distance and its time, and until more precise data from Gaia are released (either in DR4 or DR5) these systems will remain only potentially interesting cases. Taking into account that a large percentage of stars are members of multiple systems (Offner et al. 2023; Merle 2023), this line of research seems to be important.

6 Possible effect of HD 7977 and other stars on LPCs past motion

The potentially extremely close passage of HD 7977 near the Sun raises an obvious question about its influence on the motion of all bodies in the Solar System. In the next sections, we discuss this subject in detail.

We start here with the influence of this stellar passage on the past motion of the long-period comets, since they are naturally the most sensitive bodies to external perturbations acting on their very elongated orbits. It is worth to note that stars can act on LPCs in two different ways:

• A star can pass very near a comet, especially when it is near its aphelion, tens of thousands au from the Sun. LPCs are Solar System bodies that reach the largest heliocentric distances;

• A star can pass very near the Sun, thus perturbing solar motion in the Gaiaxy and, therefore, changing the orbits of all bodies of the Solar System at different scales. The most sensitive are again LPCs.

In the following sections, we present a simple statistical picture of the stellar perturbations acting on LPCs and several particular examples of the past evolution of cometary orbit under simultaneous Gaiactic and stellar perturbations. In both aspects, we focus on indicating the action of the star HD 7977.

6.1 The sample of investigated LPCs

To study the influence of HD 7977 and other stars on comets discovered to date, we selected a subset of the original orbital solutions of 312 long-period comets from the CODE catalogue⁵ (Krόlikowska & Dybczyński 2020, 2023). This source contains an almost complete sample of comets with original semimajor axes greater than 10 000 au, and discovered in the period 19012021 January.

To minimise the impact of nongravitational effects (NG) on the motion of the comets discussed, we selected comets with perihelion distances exceeding 3.5 au for further studies of their evolution in the past. In most cases of well-observed comets with a large number of positional observations, we use the solutions dedicated to the studies of the past dynamics and based only on the preperihelion observations. This method has recently been discussed by Krόlikowska & Dones (2023). As a consequence of this approach, we also exclude from our sample all comets discovered after their perihelion passage.

Finally, we conducted statistical investigations on 125 comets. In this sample, we have only comets with orbits of very good accuracy, classes 1a+, 1a, and 1b in the classification of Krόlikowska & Dybczyński (2013). It is worth noting that finally in this sample there are only 9 comets discovered before 1980, and as many as 86 discovered after 2000.

6.2 The statistical picture of the HD 7977 influence on comets

The overall influence of stars on the past evolution of Oort Cloud comets is important. To our knowledge, the dominant star is HD 7977, but the influence of other stars cannot be ignored. We demonstrate this in Fig. 4 using a sample of 125 comets with the observed osculating perihelion distance greater than 3.5 au (see the previous section for an explanation). Typically, the stellar perturbations do not change the comet’s semimajor axis much, but the overall distribution of the previous semima-jor axes reveals some differences, as shown in the upper part of Fig. 4. The uncertainties of comet orbits are taken into account in this figure by using an additional 5000 orbit clones; for more details on how we construct such distributions, see, for example, Krόlikowska & Dybczyński (2017). The width of the bin for 1/a was assumed 0.000005 au^–1, so it could be compared with Fig. 12 in Krόlikowska (2020).

The grey filled histogram of 1/a_previous represents the evolution taking into account only perturbations related to the Galaxy. The position of the maximum distribution in this case is between 40 and 45 in units of 10⁻⁶ au⁻¹. The black-lined histogram indicates the result of calculations that include all stars from the latest StePPeD database release except for HD7977, and is almost the same as the grey histogram. However, after including HD 7977, we obtain a different distribution with the maximum of 1/a_previous shifted towards less tight orbits, to the value between 35 and 40 in units of 10⁻⁶ au⁻¹ (dashed-red histogram).

The next two panels presented in Fig. 4 show how notable stars change the distribution of previous perihelion distances in the range between 0 and 2500 au (middle panel) and in the range of 1 to 100 au (lowest panel). From the first bin in the middle panel, one can calculate that only 36.3% of the comets in our sample had a previous perihelion distance below 100 au when perturbations from all stars are included in past dynamical evolution. Moreover, our calculations indicate the dominant role of the star HD 7977 here, which is illustrated by similar numbers (percent) of comets in the first bin for calculations without stellar perturbers (filled grey histogram, 75.5% of all orbits) and including perturbations from stars except HD 7977 (black-lined histogram, 74.3%). In other words, HD7977 is solely responsible for about 40% of previous perihelion distances greater than 100 au, in many cases even significantly greater, while perturbations by Galaxy tides are responsible only for about 20%. Detailed statistical research on this sample of comets will be the subject of a separate publication. Some examples of the dominant role of HD 7977 in previous calculations of the perihelion distance are given in the next section.

Fig. 4 Statistics for 125 LPCs with the osculating perihelion distance greater than 3.5 au described in Sect. 6.1. Upper panel: the distribution of previous 1 /a, where the filled grey histogram represents calculations with Galactic tide perturbations (stellar perturbations are ignored), the black-lined histogram represents results including perturbations from all stars except HD 7977, and the red dashed histogram describes the case with perturbations from the Galactic tide and all stars. The light-grey vertical band shows the area traditionally called the Oort spike. The middle and lower panels show the distribution of the previous perihelion distance; the lower panel gives details about the first bin (1–100 au) of the middle panel.

6.3 Selected examples of a strong interaction of HD7977 with comets

As we have already mentioned, HD 7977 (P0230) has passed close to the Sun 2.47 Myr ago. Other stars with potentially strong influence are P0506 with the closest approach 1.08 Myr ago to a distance of 0.2 pc and P0417 with a close encounter at 1.47 Myr ago at 0.5 pc. The perturbations from these two mentioned stars are visible in the figures presented below, but generally, they are weaker than the influence of HD 7977. However, there are comets where the influence of other stellar perturbers is stronger than HD 7977, which comes from the geometry and time coincidence of the star and comet orbital motion; see, for example, the past dynamics of C/2015XY1.

Below we show different stellar action examples on selected comets in order from their longer to shorter original semimajor axes, that is, from their orbital periods longer to shorter. All presented cases are typical and representative.

The first three comets have previous orbital periods of almost 8 Myr (C/2010 S1), ~6Myr (C/2015 XY1) and ~4 Myr (C/2012 LP26), respectively. The fourth case of C/2010 U3 represents a special group of comets that have a previous orbital period shorter than 2.47 Myr, so they cannot meet HD 7977 during their last revolution. In most of such cases, the previous perihelion distance is within the planetary zone. We cannot calculate the path of a comet through it due to uncertainties in the planetary position, so there is no reliable possibility to study the influence of HD 7977 on such comets further in the past. However, the C/2010 U3 shows that the previous perihelion distance can be large.

Fig. 5 Past dynamical evolution of C/2010 S1 nominal orbit (‘pa’ solution, see the CODE Catalogue). Changes in the perihelion distance (green), inclination (fuchsia), and the argument of perihelion (red) are shown; angular elements are expressed with respect to the Galactic disc frame. The thick lines show the result of the full dynamical model, while the thin lines show the evolution of elements in the absence of any stellar perturbations. The panel on the left – all stars included, the panel on the right - all stars included, except HD 7977 (P0230 in the plot). In both panels, noticeable changes in the perihelion distance are marked with arrows accompanied by the name of the corresponding stellar perturber (see Table 5).

6.3.1 C/2010 S1 (LINEAR)

The dynamical evolution of C/2010 S1 shows a rather complicated case of multiple potential stellar perturbations acting on this comet orbit. Figure 5 shows the past evolution of C/2010 S1 using purely gravitational orbit (GR) based on preperihelion data (pa in the CODE catalogue, the highest quality class of 1a+). This comet passed its previous perihelion 7.65 Myr ago. Taking into account only Galactic perturbation, we find that the previous perihelion distance, q_prev, was 3.45–3.72−4.02 au (the 10th percentile, the median and the 90th percentile, where only uncertainties of a comet’s orbit are taken into account). Including perturbations of all stars and going back in time, we notice that HD 7977 was responsible for a large change in this comet’s osculating perihelion distance, from almost 2000 au to less than 10 au. This means that, according to our calculations, this comet was nominally moving on orbit with a heliocentric perihelion distance of 1691-1704-1716 au (same three percentiles) before being perturbed by this star.

During our backward numerical integration, we also noticed small perturbations from stars P0506 and P0417. These names come from the StePPeD database and, for the convenience of the reader, in Table 5 we present their conventional names and nominal parameters of their close passages near the Sun.

The right panel of Fig. 5 shows the orbital evolution of C/2010 S1 when we exclude HD 7977 from the dynamical model.

Then, we can notice much smaller stellar perturbations and a rather strong action of a massive perturber P3509. We note that this star does not act noticeably when HD 7977 is in action (see the left part of Fig. 5).

6.3.2 C/2015 XY1 (Lemmon)

The dynamical evolution of C/2015 XY1 displays a very interesting case of a strong double stellar action in the past, namely by P0230 (HD 7977) and P0506; see Fig. 6. This comet passed the current perihelion in April 2018 and was observed for 4 yr at heliocentric distances between 9.52−7.93 (perihelion)–9.62 au. Taking into account only the Galactic perturbation, we find that the previous perihelion distance, q_prev, was 16.47−17.36−18.34 au where the uncertainties of the comet’s orbit are taken into account. We use here and in the following text the same three-percentile notation as before. When including perturbations of all stars, we observe that they lead to a notable larger q_prev in the range of 311.7−354.5−436.2 au. Furthermore, they slightly reduced the previous 1/a to values between 27.06−27.33–28.03 in units of 10⁻⁶ au⁻¹ which changes the orbital period to almost 7.5 Myr.

The case of C/2015 XY1 represents a group of comets that suffered a strong perturbation about 1.08 Myr ago from P0506 as depicted in Fig. 6. This has to be taken into account when we follow their dynamics further into the past. But the reader should be warned that the stellar data for the star P0506, while quite precise, might change in the future since the star Gaia DR3 5571232122386729856 might appear to be a second component of a double system with P0506. Its astrometry has large uncertainties, and we do not know its radial velocity or its mass, so we ignore this secondary in our current model and wait for the next Gaia data release.

6.3.3 C/2012 LP26 (Palomar)

In contrary to the previous examples, the past dynamic evolution of C/2012 LP26 shows that only HD 7977 plays a significant role as the stellar perturber. The evolution we show here starts from the original GR orbit based on 6.4 yr data arc in a range of heliocentric distances: 10.01−6.536 (perihelion) – 9.86 au (solution ‘aa’ in the CODE Catalogue).

During the backward numerical integration, we again notice small perturbations from P0506 and P0417, but generally, without action from HD 7977 the past dynamical evolution of the C/2012 LP26 is almost identical to the case when we exclude all stars, see the right plot in Fig. 7. In this case, we obtain the previous perihelion spread according to the comet orbit uncertainty as 15.1–15.6–16.3 au. But if we take into account the nominal influence of HD 7977, we obtain q_prev as large as 588–619–647 au. The semimajor axis and the orbital period remain almost unchanged here.

Fig. 6 Past dynamical evolution of the C/2015 XY1 nominal orbit (‘ba’ solution, see the CODE Catalogue). Colour-coded curves are described in the previous panels. Left panel - all stars included, right panel - only HD 7977 excluded. Several stellar perturbations are marked.

Fig. 7 Past dynamical evolution of the C/2012 LP26 nominal orbit (‘aa’ solution, see the CODE catalogue). Colour-coded curves are described in the previous panels. Left panel - all stars included; right panel – only HD 7977 excluded.

6.3.4 C/2010 U3 (Boattini)

This is one of the very long observed Oort spike comets so far, the pre-discovery data going back to November 2005, and currently, the positional data cover about 18 yr. The comet passed its perihelion at the end of February 2019 at a distance of 8.45 au from the Sun and is still observable (as of December 2023). Despite the large perihelion distance, some signs of NG acceleration in the motion of this comet are seen (Królikowska & Dones 2023). We used here a very precise orbit obtained using preperihelion data in the range of heliocentric distances from 25.7 au to 11.9 au (the solution ‘sg’ in the CODE catalogue).

C/2010 U3 represents the case in which the comet was at the previous perihelion distance (2.2 Myr ago) after HD 7977’s close encounter with the Sun (2.47 Myr ago), see Fig. 8. Including the comet orbit uncertainties, we obtained q_prev equal to 13.92–14.28–14.67 au. According to our calculations, during the last orbital revolution, this comet suffered only a moderate orbit change due to the action of P0506.

To speculate about the deeper past, we need a fairly fundamental assumption of the neglect of planetary perturbations during this comet’s previous perihelion passage. With this assumption, we can see that when C/2010 U3 motion is followed to the one before the last perihelion, it might have been significantly perturbed by HD 7977 (the almost vertical green line going up the image in the moment of 2.47 Myr). According to our calculations, the perihelion distance could change from almost 200 au down to below 15 au as it is shown in Fig. 8.

7 Possible HD 7977 influence on other Solar System bodies

The HD 7977 flyby could also have impacted the dynamics of other objects in the outer Solar System than Oort cloud comets. It is worth clarifying here. When investigating the influence of HD 7977 on comets in Sect. 6, we followed their motion from the current position backwards to calculate the changes in their orbits 2.5 Myr ago. In this section, to show the level of perturbations caused by a very close stellar passage on other Solar System bodies’ motion, we follow them in an opposite direction, starting a calculation before the star approach and from an assumed initial orbital state.

To investigate the possible gravitational effect on planets and Transneptunian objects (TNOs), we performed a series of simple numerical simulations using the REBOUND (Rein & Liu 2012) N-body simulator including either the giant planets or TNOs.

The relative uncertainty of the flyby distance is larger than the distance itself, so the star could pass by the system arbitrarily close. Because the effect of the flyby increases as the distance decreases, we decided to focus on flybys closer than the nominal distance.

Fig. 8 Past dynamical evolution of the C/2010 U3 nominal orbit (‘sg’ solution, see CODE catalogue). Changes in a perihelion distance (green), an inclination (fuchsia), and an argument of perihelion (red) are shown; angular elements are expressed in a Galactic frame. The thick lines going back in time to the previous perihelion show the result of the full dynamical model while thin lines in this period – the evolution of elements in the absence of any stellar perturbations, that is, only the galactic perturbations are taken into account. See text for the interpretation of the plot before 2.2 Myr ago.

7.1 Action on planets

The star flyby close to the Sun could have a prominent impact on the orbits of giant planets and, therefore, could affect the stability of the entire Solar System. We used the relative change of the semimajor axis of Neptune to estimate the impact of stellar flyby on planets. It was shown by Brown & Rein (2022) that the relative changes of the Neptune semimajor axis $\frac{\text{Δ}a}{a}>0.001$ have a significant probability of affecting stability and $\frac{\text{Δ}a}{a}>0.01$ almost always destabilises the Solar System. We can use this criterion to estimate the closest possible distance of the flyby, where the stability of planets is not affected.

In our simulations, we numerically integrated the orbits of the Sun, HD 7977, and the four giant planets. We used the nominal trajectory of the passing star but reduced the minimal distance. We used the present-day orbits of planets, but to accommodate for the uncertainty, we repeated the simulation 500 times, shifting the flyby moment by 1/500 of the Neptune orbital period to cover the entire possible range of orbital positions of this planet. The starting planetary positions were taken from the latest JPL planetary ephemeris DE441 (Park et al. 2021). Each simulation starts 25 000 yr before the flyby (the moment when HD 7977 passes the perihelion of hyperbolic orbit around the Sun) and ends one million years after the flyby. This allows us to estimate not only the direct impact on the dynamics but also the indirect changes of the orbits due to gravitational interactions between planets perturbed by the passing star. Then, at each step of integration, we compare the orbits of the planets with the orbits resulting from the simulation without the stellar perturbation. The greatest difference in the semimajor axis during the whole simulation we take as the estimate of flyby impact.

In Fig. 9, we show the percentage of flyby simulations in which the relative change of the Neptune semimajor axis reaches the limits of $\frac{\text{Δ}a}{a}<0.001$ and $\frac{\text{Δ}a}{a}<0.01$ at different distance close flybys. The simulation percentage can be used to estimate the probability of orbital elements changing by a certain order of magnitude. For very close flybys, in most cases, the 0.001 limit is exceeded, but there is still a significant number of simulations in which the change of Neptune’s orbit is small enough to maintain the stability of the Solar System.

A recent paper by Kaib & Raymond (2024) discusses a possible influence of the HD 7977 flyby on historical changes of the Earth climate. There appeared also a preprint by Mikryukov & Shevchenko (2024) where the authors simulate the results of a passage of a planetary or substellar object through the internal part of our planetary system.

Fig. 9 Possible effect of a very close flyby of HD 7977 on Neptune’s semimajor axis. The colour bars show the percentage of simulations where the maximum relative difference in a semimajor axis of that planet with and without the flyby is lower than 0.01 or 0.001, respectively.

7.2 Action on transneptunian objects

The transneptunian bodies can be divided simply into two subgroups: Kuiper belt objects (KBOs) and Scattered disc objects (SDOs). The objects in the first group are dynamically cold and have low eccentricities and inclinations. The semimajor axis is bounded by the orbit of Neptune (≈30au) and the distance of the mean-motion resonance 1:2 with Neptune (≈ 44au). At larger distances, the number of objects with low eccentricity and inclination decreases significantly. The second group (SDOs) is dynamically hot, with higher eccentricities and inclinations. This group is not bounded by 1:2 resonance with Neptune, and some objects have a semimajor axis of hundreds of au. The effect of the flyby is stronger on objects more distant from the Sun, so we focus on the object from the second group.

Instead of simulating the effect of a passing star on the currently observed population of SDOs, we decided to use a more uniform distribution of orbital elements. This allows us to check if a close flyby similar to HD 7977 could possibly alter the distribution of studied objects and reshape this arbitrarily constructed population to be closer to the current one (ex. by increasing the eccentricities in the scattered disc and removing the dynamically cold objects from the outer TNO region). In our simulations, we randomly generated a population of objects with a semimajor axis greater than 50 au, an eccentricity less than 0.5, and an inclination smaller than 45 degrees. Then we performed the numerical simulation of the flyby and investigated the orbital elements after the flyby of HD 7977-like star, that is, the star with the same mass and velocity as HD 7977, but we checked different flyby geometries. The change in TNO orbit during flyby comes from two effects. The first is the direct change of the TNO velocity due to the gravitation of the passing star. The second is an indirect effect caused by the change in the velocity of the Sun as a result of the flyby. For the Sun, the total velocity added by the flyby is directed towards the perihelion of the hyperbolic orbit of the passing star and depends on the distance of that perihelion. Similarly, the change in velocity of the TNO depends on the minimum distance between the object and the star. Because our simulated population is a disc of objects with low inclination to the ecliptic plane, we can estimate the direct effect of flyby on TNOs by the distance between the Sun and the Star when a passing star crosses the ecliptic plane. This distance is equal to or greater than the perihelion distance and depends on the geometry of the flyby.

In Fig. 10, we show the effect of a passing star on possible low-to-medium eccentricity objects (initial e < 0.25) between 50 and 100 au. The plot shows the percentage of simulated TNOs that were moved by the flyby outside of their initial zone (orbital elements after the flyby are not in the initial range 50 < a < 100 au and e < 0.25). Each point represents a single simulation, each having a different flyby geometry. Extremely close flybys with perihelion at 100 au can disrupt 20% to 45% objects, and the maximum value of the effect depends on the distance between the Sun and the flying star measured at the moment when the star crosses the ecliptic plane. For the 200 au flyby, the number of disrupted objects drops to 5–15%. For flybys farther away with a perihelion distance greater than 300 au, the percentage of disturbed objects is less than 2%. As shown in the previous paragraph, such close encounters (<300 au) can possibly affect the stability of the planetary system, so it is unlikely that the flyby could explain the low abundance of dynamically cold objects at greater heliocentric distances. If we consider theoretically more distant objects, they can be moved outside their initial zone by a more distant flyby (results for the 500 au distant flyby shown in Fig. 11).

This simple simulation shows that the overall effect on distant TNOs of even a very close flyby is rather small. Using the fact that this effect increases with a semimajor axis, we can extrapolate this result to smaller heliocentric distances and claim that the possible change in orbital elements of closer KBOs is even smaller. However, this simple simulation cannot rule out possible indirect orbital effects arising from the change of orbit of major planets due to flyby, as is described by Raymond et al. (2024).

Our simulations of a close star passage effect on TNOs shows that the possibility of a very close flyby should not be disregarded using the argument that it must have affected the stability of the Solar System or disrupted the TNOs distribution. However, based on these simple dynamical tests, we cannot set the strict minimum flyby distance for HD 7977 or any other star.

Fig. 10 Effect of different flybys on distant TNOs. The plot shows the percentage of simulated objects with an initial semimajor axis between 50 and 100 au and eccentricity <0.25, that have orbital parameters outside this range after a flyby. Each point represents the single simulation of a stellar flyby with a perihelion distance of the Star q equal to 100 or 200 au and different flyby geometry.

Fig. 11 Effect of flybys with perihelion distance 500 au on hypothetical very distant TNOs. The plot shows the percentage of simulated objects with an initial semimajor axis in a given range and eccentricity <0.25, that have orbital parameters outside the initial range after a flyby. Each point represents a single simulation and different colour represents a different population of TNOs.

8 Conclusions and prospects

The main purpose of this paper is to announce that the arbitrarily small proper motion of HD 7977 is not in contradiction with the current data, therefore this star very close passage near the Sun cannot be excluded. We also indicate for the first time another potential massive perturber, namely HD 102928. We discuss in detail the quality of all current Gaia results for HD 7977 that lead to this finding. We also tried to check the validity of its current proper motion estimates, the most important parameters from the point of view of the proximity details.

In conclusion, considering that these estimates cannot be ruled out, we obtained the closest distance of HD 7977 ≤ 0.012 pc with probability 10% or ≤0.060 pc with probability 90%, which happened 2.47 Myr ago. We show the influence of such a close passage of one solar mass star on the orbits of long-period comets. We also show with a series of simple simulations what the effect of such a passage on other bodies of the Solar System may be. No matter which star made a very close passage near the Sun a few million years ago, this event would constitute some kind of dynamical horizon for all studies of the past dynamics of selected Solar System small bodies, for example, LPCs.

As it concerns LPCs it should be stressed that the longstanding problem of discriminating between dynamically old and new comets now seems to be much more complicated. Past dynamics of almost all LPCs strongly depend on stellar perturbations, but these cannot be currently calculated precisely due to still large stellar data uncertainties and an incomplete list of stars to be taken into account.

The main conclusion regarding the HD 7977 close passage event is that it currently cannot be ruled out, but also cannot be described in detail. We simply have to wait for more precise data from the Gaia mission, but a dedicated study of the historical positions of this star would also be of great value. In addition, accurate data for HD 102928 are very necessary.

Our research also pointed out that there exists another line of study, so far almost absent in the literature, namely the search for resolved binary or multiple systems that have passed or will pass near the Sun. Such events may appear to be more important because of the larger total mass of such a perturber. But all candidates we can find suffer from large uncertainties of their astrometry and/or radial velocity and/or mass estimates. This makes the percentage of multiples in the StePPeD database of potential perturbers much too low.

Acknowledgements

We would like to express our thanks to the anonymous referee for so many so detailed and so helpful suggestions and comments. These allowed us to greatly improve this paper. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. The calculations that led to this work were partially supported by the project “GAVIP-GC: processing resources for Gaia data analysis” funded by the European Space Agency (4000120180/17/NL/CBi). P.B. acknowledges funding through the Spanish Government retraining plan ‘María Zambrano 2021–2023’ at the University of Alicante (ZAMBRANO22-04). E.P.-G.: This work has been partially supported by Horizon 2020 grant no. 871149 ‘EPN-2024-RI’. K.L. acknowledges funding by the Italian Space Agency (ASI) within the Hera agreement (ASI-UNIBO, no. 2022-8-HH.0).

Appendix A Detailed remarks on the HD 7977 astrometric data in Gaia

In a comparison sample with 25 397 objects which have a similar scanning geometry and history (ecliptic latitude within 5 degrees) and a similar brightness as HD 7977 (G-band magnitude within 1 magnitude), only 13% have a larger ruwe value (Fig. A.1). An independent suggestion for binarity is given by ipd_gof_harmonic_amplitude = 0.07 for HD 7977, which is greater than the value of 97% of the stars in the comparison sample mentioned above. This harmonic amplitude quantifies the variation of the goodness of the epoch image parameter determination (ipd) fits as a function of the position angle of the scan direction. A nonzero value indicates the presence of a nonisotropic spatial structure of the source, such as caused by a binary that is marginally resolved by Gala on selected transits.

Fig. A.1 Gaia DR3 astrometric properties of a comparison sample of 25 397 stars for HD 7977: ipd_gof_harmonic_amplitude versus ruwe. The sources have comparable scanning geometry and history (ecliptic latitude within 5 degrees) and similar brightness as HD 7977 (G-band magnitude within 1 magnitude). HD 7977 is indicated with a cross-hair. It falls clearly in the domain with poor astrometric fits (ruwe > 1.25) and extended source structure (elevated value of ipd_gof_harmonic_amplitude), compatible with duplicity.

Only 1% of the stars in the comparison sample have a larger ruwe and a larger ipd_gof_harmonic_amplitude value than HD 7977, providing further evidence that the deviating values are not caused by noise but by duplicity. It should be emphasised that further astrometric data of the object do not indicate anything suspicious that could otherwise explain the high ruwe and/or ipd_gof_harmonic_amplitude values. For example, the 54 epoch observations are well spread over the 34 months of mission data, resulting in 28 visibility periods (“independent observation clusters”) and only 1% of the 474 detector transits have been excluded from the astrometric fit.

The astrometric excess noise є, in addition to ruwe, provides further quantification of the level of disagreement of the astrometric epoch data with the best-fit single-star motion model. For HD 7977, є = 0.28 mas. This value was added in quadrature to the observational epoch uncertainties in order to statistically match the residuals in the astrometric solution. In summary, the real error of the astrometry of this particular source exceeds the formal uncertainties reported. Moreover, Gaia astrometry, in particular of bright stars, is generally known to suffer from underestimated uncertainties. Brandt (2021), for instance, reports the need for inflation of astrometric uncertainty by a factor 1.37 for stars brighter than ~ 12 mag and other studies have found even larger statistical inflation factors, up to a factor ~2 or more (for example El-Badry et al. 2021; Maíz Apellániz 2022, and references therein).

Two further remarks can be made on the Gaia astrometric uncertainties:

• The five astrometric parameters do not only come with five associated formal errors but with a full, 5 × 5 co-variance matrix reflecting the fact that the parameters result from one fit. For example, for the two proper motion components, the reported correlation coefficient ρ = −0.36 such that a positive random error in the right ascension proper motion component would be accompanied by a negative random error in the declination proper motion component.

• Cantat-Gaudin & Brandt (2021) provide convincing evidence that the Gaia DR3 reference frame suffers from a magnitude-dependent spin. These authors also provide a global fit as a function of magnitude and an associated correction formula. For HD 7977 (ra = 20.131652206655247 deg, dec = 61.882521645503466 deg, G = 8.891319 mag), this correction suggests that the proper motions of Gaia in this direction in the sky should be corrected by adding 0.031 and 0.025 mas yr⁻¹ in right ascension and declination, respectively (despite acknowledging that colour-dependent systematics of up to ~0.010 mas yr⁻¹ can remain present). These corrections are of the same order of magnitude as the formal proper motion uncertainties (0.024 and 0.034 mas yr⁻¹).

Appendix B Other HD 7977 distance estimations found in the literature

Several other distance estimates are available. However, since the formal parallax error is so small, these are highly correlated with the inverse-parallax estimate reported above:

• Bailer-Jones et al. (2021) present Bayesian distance estimates for stars in Gaia DR3. The first, dubbed geometric distance, uses the measured parallax with a direction-dependent prior to the distance and results in 75.546 ± 0.195 pc. The second, dubbed photo-geometric distance, uses the colour and apparent magnitude in addition and results in 75.560 ± 0.163 pc. In both cases, the distance estimate is dominated by the high signal-to-noise measured parallax and only marginally influenced by the prior.

• Gaia DR3 itself contains a Bayesian distance estimate, dubbed distance_gspphot, returned by the General Stellar Parameterizer from Photometry (GSP-Phot; Andrae et al. 2023), which is part of the astrophysical parameter inference system (Apsis; Creevey et al. 2023). GSP-Phot simultaneously fits the low-resolution BP/RP spectrum, the measured parallax and the apparent G magnitude and returns a distance estimate of 75.791 − 0.401 + 2.846 pc and an absolute magnitude M_G = mg_gspphot = 4.47 mag (with an uncertainty interval [4.35, 4.49] mag) using ag_gspphot = 0.005 mag. Again, most of the weight in this distance estimate comes from the high-precision parallax measurement.

• Anders et al. (2022) also present Bayesian distance estimates for stars in Gaia DR3 after adding photometric constraints from the Pan-STARRS1, SkyMapper, 2MASS, and All-WISE catalogues. The associated StarHorse code returns a distance estimate of 75.437 ± 0.402 pc and an absolute magnitude M_G = 4.31 ± 0.10 mag using A_G = 0.20 ± 0.10 mag.

  Again, the prior in this distance estimate has negligible influence because of the small formal uncertainty on the measured parallax. The addition of the (infrared) photometry has shifted ~0.2 mag between absolute magnitude and G-band extinction between the StarHorse and the GSP-Phot estimates, indicative of some ill-defined properties of the source possibly linked to unrecognised duplicity.

It is important to recall that all the above distance estimates implicitly assume that the source is a single one.

Fig. C.1 Gaia DR3 RVS properties of a comparison sample of 35,629 stars for HD 7977: rv_renormalised_gof versus rv_amplitude_robust, colour-coded with rv_chisq_pvalue. The sources have comparable spectral types (dwarfs with a template effective temperature within 500 K) and similar brightness as HD 7977 (GRVS-band magnitude within 1 magnitude). HD 7977 is indicated with a cross-hair. It falls clearly in the domain where the radial velocity time series is not constant (rv_chisq_pvalue < 1E-2) and also the normalised goodness of fit is excessively large (compared to unity).

Appendix C Detailed remarks on the HD 7977 Gaia spectral data

Gaia DR3 provides a measurement of the peak-to-peak amplitude of the time series of radial velocity after filtering out “probable outliers” (see Section 3.7 in Katz et al. 2023). This scatter equals rv_amplitude_robust = 2.04 km s⁻¹ with an associated rv_time_duration = 911 days (3.4 years). The long-term scatter being an order of magnitude larger than the formal uncertainty on the mean radial velocity is a suggestive indication of radial-velocity variability. To quantify this further, the renormalised goodness of fit, rv_renormalised_gof, is a quantity computed using the source under inspection and all other sources having similar rv_template_teff and grvs_mag such that the scatter of the epoch radial velocities of the source can be meaningfully compared to the typical epoch uncertainty for the appropriate grvs_mag and rv_template_teffranges. For HD 7977, we find rv_renormalised_gof = 3.59, which is clearly anomalous (for constant stars, rv_renormalised_gof follows a normal distribution with a standard deviation equal to one). In a comparison sample with 35,629 objects which have comparable spectral types (dwarfs with a template effective temperature within 500 K) and similar brightness as HD 7977 (G_RVS-band magnitude within 1 magnitude), only 20% have a larger rv_renornalised_gof value (Fig. C.1).

To find (potential) radial-velocity variable stars, the following selection is suggested in Section 11 in Katz et al. (2023): rv_chisq_pvalue < 1E-2 and rv_renormalised_gof > 4 and rv_nb_transits ≥ 10. For HD 7977, two of these three conditions are met with margin (rv_chisq_pvalue = 2E-6 < 1E-2 and rv_nb_transits = 18 ≥ 10) with only the renormalised goodness of fit rv_renormalised_gof = 3.59 staying slightly below the formal limit of 4. In conclusion, the (unpublished) radial velocity time series contains hints for the presence of variability, most likely caused by duplicity, but further quantification and definitive conclusions require the publication of Gaia DR4.

The Gaia low-resolution blue and red photometer spectra (BP and RP) and medium-resolution radial velocity spectrometer (RVS) spectra provide significant additional information on the astrophysical characteristics of the sources. There are several (inconsistent) effective temperature estimates for HD 7977:

• teff_gspphot = 5816 K with an uncertainty interval [5807, 5894] K based on the BP/RP spectra, compatible with a G1V/G2V spectral type (compared to a G1V spectral type inferred from the GSP-Phot absolute magnitude);

• teff_gspspec = 5956 K with an uncertainty interval [5924, 6048] K based on the RVS spectrum, compatible with a G0V spectral type;

• 6149 K with an uncertainty interval [5938, 6280] K derived by Anders et al. (2022) with the StarHorse code that uses Gaia DR3 data and additional photometric constraints, compatible with an F8V spectral type (compared to a G0V spectral type inferred from the StarHorse absolute magnitude).

For reference, the nominal spectral type in SIMBAD is G3 (without luminosity class).

For HD 7977, the BP/RP provides hints on possible unresolved binarity through the discrete source classification (DSC, Delchambre et al. 2023) and the multiple star classification (MSC, Creevey et al. 2023). The DSC probability of being a binary star, derived from an ExtraTrees classifier that uses the BP/RP spectrum (Ulla et al. 2022, Section 11.3.2), equals classprob_dsc_specmod_binarystar = 0.19, with the complementary probability classprob_dsc_specmod_star = 0.81 . Obviously, the binary star probability is below 50%, and, in addition, the DSC results for binaries should be used with caution (Ulla et al. 2022, Section 11.4.4). Nonetheless, the finite value of classprob_dsc_specmod_binarystar does hint at a spectral peculiarity consistent with unresolved duplicity.

The MSC assumes that the BP/RP spectrum is a composite spectrum of an unresolved (coeval) binary with shared metallicity, extinction, and distance (Ulla et al. 2022, Section 11.3.5). It returns these common parameters as well as the effective temperature and surface gravity for both components: T_eff,1 = 6099 K with an uncertainty interval [6084,6112] K and Teff,2 = 5198 K with an uncertainty interval [5134,5279] K, with an estimated extinction of the G band of 0.17 ± 0.04 mag and an estimated distance of 97 ± 1 pc. This distance estimate deviates significantly from the (single-star) distance estimates of ~75 pc (see above) and also the extinction differs significantly from the GSP-Phot value, ag_gspphot = 0.005 mag (uncertainty interval [0. 0005 , 0. 0472] mag), but agrees with the StarHorse estimate of A_G = 0.20 ± 0.10 mag. All in all, the Gaia spectra do not provide unique constraints on the astrophysical nature of the source and leave the possibility of an unresolved binary open.

References

All Tables

All Figures

	Fig. 1 HD 7977 position changes over last two centuries. Data are from Table 3, in red we show these which were taken into account in proper motion estimation. No weighing has been applied but straight lines are forced to pass through the Gaia DR3 position. The estimated proper motion components are –2.62 mas yr–1 and –3.19 mas yr–1 in Declination and Right Ascension respectively.
In the text

	Fig. 2 HD 7977 and its 25 000 clones at the closest encounter with the Sun. The red dot represents the Sun position while the green one corresponds to the star’s nominal position at the closest approach.
In the text

	Fig. 3 P3509 and its 25 000 clones at the closest encounter with the Sun. The red dot represents the Sun position while the green one corresponds to the star’s nominal position at the closest approach. The blue circle marks the traditional extent of the Oort cometary cloud.
In the text

Fig. 4 Statistics for 125 LPCs with the osculating perihelion distance greater than 3.5 au described in Sect. 6.1. Upper panel: the distribution of previous 1 /a, where the filled grey histogram represents calculations with Galactic tide perturbations (stellar perturbations are ignored), the black-lined histogram represents results including perturbations from all stars except HD 7977, and the red dashed histogram describes the case with perturbations from the Galactic tide and all stars. The light-grey vertical band shows the area traditionally called the Oort spike. The middle and lower panels show the distribution of the previous perihelion distance; the lower panel gives details about the first bin (1–100 au) of the middle panel.

In the text

Fig. 5 Past dynamical evolution of C/2010 S1 nominal orbit (‘pa’ solution, see the CODE Catalogue). Changes in the perihelion distance (green), inclination (fuchsia), and the argument of perihelion (red) are shown; angular elements are expressed with respect to the Galactic disc frame. The thick lines show the result of the full dynamical model, while the thin lines show the evolution of elements in the absence of any stellar perturbations. The panel on the left – all stars included, the panel on the right - all stars included, except HD 7977 (P0230 in the plot). In both panels, noticeable changes in the perihelion distance are marked with arrows accompanied by the name of the corresponding stellar perturber (see Table 5).

In the text

	Fig. 6 Past dynamical evolution of the C/2015 XY1 nominal orbit (‘ba’ solution, see the CODE Catalogue). Colour-coded curves are described in the previous panels. Left panel - all stars included, right panel - only HD 7977 excluded. Several stellar perturbations are marked.
In the text

	Fig. 7 Past dynamical evolution of the C/2012 LP26 nominal orbit (‘aa’ solution, see the CODE catalogue). Colour-coded curves are described in the previous panels. Left panel - all stars included; right panel – only HD 7977 excluded.
In the text

Fig. 8 Past dynamical evolution of the C/2010 U3 nominal orbit (‘sg’ solution, see CODE catalogue). Changes in a perihelion distance (green), an inclination (fuchsia), and an argument of perihelion (red) are shown; angular elements are expressed in a Galactic frame. The thick lines going back in time to the previous perihelion show the result of the full dynamical model while thin lines in this period – the evolution of elements in the absence of any stellar perturbations, that is, only the galactic perturbations are taken into account. See text for the interpretation of the plot before 2.2 Myr ago.

In the text

	Fig. 9 Possible effect of a very close flyby of HD 7977 on Neptune’s semimajor axis. The colour bars show the percentage of simulations where the maximum relative difference in a semimajor axis of that planet with and without the flyby is lower than 0.01 or 0.001, respectively.
In the text

	Fig. 10 Effect of different flybys on distant TNOs. The plot shows the percentage of simulated objects with an initial semimajor axis between 50 and 100 au and eccentricity <0.25, that have orbital parameters outside this range after a flyby. Each point represents the single simulation of a stellar flyby with a perihelion distance of the Star q equal to 100 or 200 au and different flyby geometry.
In the text

	Fig. 11 Effect of flybys with perihelion distance 500 au on hypothetical very distant TNOs. The plot shows the percentage of simulated objects with an initial semimajor axis in a given range and eccentricity <0.25, that have orbital parameters outside the initial range after a flyby. Each point represents a single simulation and different colour represents a different population of TNOs.
In the text

Fig. A.1 Gaia DR3 astrometric properties of a comparison sample of 25 397 stars for HD 7977: ipd_gof_harmonic_amplitude versus ruwe. The sources have comparable scanning geometry and history (ecliptic latitude within 5 degrees) and similar brightness as HD 7977 (G-band magnitude within 1 magnitude). HD 7977 is indicated with a cross-hair. It falls clearly in the domain with poor astrometric fits (ruwe > 1.25) and extended source structure (elevated value of ipd_gof_harmonic_amplitude), compatible with duplicity.

In the text

Fig. C.1 Gaia DR3 RVS properties of a comparison sample of 35,629 stars for HD 7977: rv_renormalised_gof versus rv_amplitude_robust, colour-coded with rv_chisq_pvalue. The sources have comparable spectral types (dwarfs with a template effective temperature within 500 K) and similar brightness as HD 7977 (GRVS-band magnitude within 1 magnitude). HD 7977 is indicated with a cross-hair. It falls clearly in the domain where the radial velocity time series is not constant (rv_chisq_pvalue < 1E-2) and also the normalised goodness of fit is excessively large (compared to unity).

In the text