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A&A
Volume 697, May 2025
Article Number L3
Number of page(s) 5
Section Letters to the Editor
DOI https://doi.org/10.1051/0004-6361/202554711
Published online 07 May 2025

© The Authors 2025

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1. Introduction

Classical T Tauri stars (CTTSs) are young (age < 107 yr) low-mass (M ≲ 2.5 M⊙) stars at the stage of gravitation contraction toward the main sequence, and their activity is driven by the magnetospheric accretion of matter from the protoplanetary disk (Bertout et al. 1988; Hartmann et al. 2016). The accretion process is accompanied by the outflow of disk matter in the form of a weakly collimated disk wind and, in some cases, jets. The outflowing matter reduces the mass of the disk and carries away its angular momentum, thereby setting the initial conditions for planet formation (Pascucci et al. 2023). The interaction of the disk wind and jet with the remnants of the protostellar cloud largely determines the morphology of the environment around young stars (Frank et al. 2014).

Jets are extended (up to 3 pc), highly supersonic (V ∼ 300 km s−1), and collimated bipolar gas flows (Bally 2016). They appear as a chain of compact emission nebulae (knots) known as Herbig-Haro (HH) objects and have less dense gas between them. There is a consensus that the large-scale magnetic field of CTTSs and its interaction with the protoplanetary disk are responsible for jet collimation and acceleration (see, e.g., Sheikhnezami & Sepahvand 2024 and references therein). Nevertheless, a number of issues related to the details of jet formation remain poorly known, particularly the size of the disk area from which the jet is launched (Ferreira et al. 2006). In this regard, it is important to search for and explore jets of CTTSs in close binary systems (semimajor axis a ≲ 20 au) since the tidal interaction truncates the radius of the companion’s circumstellar disk to Rout ∼ 0.4 a (Artymowicz & Lubow 1994; Rosotti & Clarke 2018).

In this Letter, we report the discovery of an extended non-trivially shaped jet from the sub-arcsecond young binary DF Tau. The star attracted attention after Joy (1949) discovered emission lines in its spectrum and identified it as an M0 T Tauri type star. Soon afterward, Kholopov & Kurochkin (1951) found that DF Tau is a strongly variable star (Δmpg > 2m). According to Bailer-Jones et al. (2021), the Gaia parallax for DF Tau (DR3 151179966897747840) has a large error, with RUWE ≈ 22 (Gaia Collaboration 2021). Therefore, we use the distance D = 140 pc as the average distance to the D4-North subgroup where DF Tau resides (Krolikowski et al. 2021; Kutra et al. 2025).

Chen et al. (1990) found DF Tau to be a binary system consisting of two CTTSs (White & Ghez 2001) of approximately equal mass and M2.5 spectral type (Hartigan & Kenyon 2003). According to Kutra et al. (2025), the effective temperatures of DF Tau A and B components are 3640 ± 100 K and 3430 ± 80 K, respectively, and both have a global magnetic field of ≈2.5 kG. The orbital period, semimajor axis, and eccentricity of the system are approximately 50 yr, 0 . ″ 1 $ 0{{\overset{\prime\prime}{.}}}1 $, and 0.2, respectively (Allen et al. 2017; Kutra et al. 2025), which corresponds to a minimum distance between the components of less than 12 au.

DF Tau is the source of an outflow observed in forbidden (Hartigan et al. 1995; Nisini et al. 2024) and dipole-allowed (Edwards et al. 1994; Lamzin et al. 2001a) transitions. Hartigan et al. (2004) and Uvarova et al. (2020) concluded that micro jets with a projected length of less than 0 . ″ 2 $ 0{{\overset{\prime\prime}{.}}}2 $ exist on both sides of the binary, “either as a jet and its counter-jet or as separate jets from the primary and secondary”. Considering all the above information, studying large-scale matter outflow in the vicinity of DF Tau is reasonable.

2. Observations

The observations of DF Tau were carried out with the 2.5-m telescope of the Caucasian Mountain Observatory (CMO) of the Sternberg Astronomical Institute of the Lomonosov Moscow State University (SAI MSU) (Shatsky et al. 2020). Spectroscopic data were obtained using the Transient Double-beam Spectrograph (TDS; see Potanin et al. 2020 for a description of the instrument and data reduction procedures). The spectral resolving power of the TDS with the 1″-slit is R = λ/Δλ ≈ 2400 in the red channel (0.56 − 0.74 μm) and ≈1300 in the blue one (0.36 − 0.56 μm). The log of observations is given in Table 1, where rJD = JD − 2 460 000, si refers to the slice numbered i in the right panel of Fig. 1, and PA is the position angle. A slit of 3′ length and 1″ width was used in all cases except the spectrum of DF Tau itself, where it was 3′×10″.

Table 1.

Log of TDS observations.

thumbnail Fig. 1.

Vicinity of DF Tau in the continuum band Halpbc (left panel) and the difference between images in the Halp 656 nm and Halpbc filters (right panel). Red segments indicate the position and orientation of the TDS slits. The close vicinity of DF Tau is highlighted in a 10″ × 10″ subimage located in the upper-left part of the panel. Red dashed lines mark the edges of the 10″-slit used for TDS observation at rJD = 588.6, and southern (s) and western (w) blobs are marked with blue lines. The diagram in the lower-right part of the panel illustrates the nomenclature of nebulae designations used in the text: O – DF Tau; green line – micro jet direction (PA = −59°); A – the first group of bright HH objects; B – counter-jet, C – the second group of bright HH objects; D – the brightest HH object (∼3 × 10−16 erg s−1 Å−1 cm−2 arcsec−2); E – the rim; F – the ring, whose center is marked by a green cross near DF Tau.

Direct 10′×10′ images of the region around DF Tau were obtained with the 4K × 4K CCD camera of the 2.5-m telescope in two filters – Halp 656 nm (λc = 656 nm, W = 7.7 nm), with a total exposure of Δt = 80 min, and nearby continuum Halpbc (λc = 643 nm, W = 12 nm, Δt = 40 min) – on December 3, 2024 (rJD = 648.3), and January 27, 2025 (rJD = 703.3)1. Using the same telescope and the infrared camera ASTRONIRCAM (Nadjip et al. 2017), we also obtained images of the same regions in January–February 2025 in H2 (λc = 2.129 μm, W = 46 nm, Δt = 175 min) and Kcont (λc = 2.270 μm, W = 39 nm, Δt = 108 min) filters. The details of the observations and data reduction are described in Dodin et al. (2019).

3. Results and discussion

A mosaic of two images of DF Tau’s vicinity observed in the Halpbc filter (left panel) and the difference between the Halp and Halpbc filter images of the same region (right panel) are shown in Fig. 1. DF Tau resides in a (relatively) low CO and H2 column density region between the B213 and B18 dark clouds (Onishi et al. 1996). The south-eastern edge of the B213 cloud can be seen in the western part of the Halpbc image. The cometary globule 1 (Goldsmith et al. 2008, Fig. 17 and Table 6) to the south-west of DF Tau can also be seen. A comparison of the images in the left and right panels of Fig. 1 revealed that these areas are mostly reflection nebulae.

The right panel of the figure also allowed us to identify a number of Hα-emitting nebulae in the vicinity of the binary. To understand their nature, we determined the flux-averaged heliocentric radial velocities (RV, Vr) of the nebulae using spectra observed at several characteristic points (see Figs. 1, 2, 3 and Table 1). We compared these velocities with the center-of-mass velocity of DF Tau ( V r cm = + 13 ± 1 $ (V^{\mathrm{cm}}_{\mathrm{r}} = +13 \pm 1 $ km s−1, Allen et al. 2017). The diagram in the bottom-right corner of Fig. 1 (the scheme) illustrates the nomenclature of nebula designations used in this Letter.

thumbnail Fig. 2.

Position-velocity diagrams corresponding to slit positions marked in Fig. 1. The horizontal strip in the left panel is the spectrum of a field star. Letters a and b correspond to different HH objects that fell within the spectrograph slit (s4 in Fig. 1).

3.1. The ring and the filament

The first thing that catches the eye is the ring-shaped nebula surrounding DF Tau (letter F in the scheme of Fig. 1). The radius of the ring is about 110″, which corresponds to a projected distances of ≈1.5 × 104 au. Judging by the TDS spectrum obtained at slit position 3 (see Figs. 1 and 2), the gas in the ring moves with a RV of +24 ± 6 km s−1, indicating that it is moving away from the star at a speed of ∼10 km s−1.

The center of the ring is shifted by ≈10″ to the south-east from the observed position of the binary. The proper motion of DF Tau is practically unknown due to the large errors in the Gaia astrometric solution, so we lack the information needed to interpret this shift.

The Hα-emitting ring could either be an H II region or a shock wave resulting from the interaction of poorly collimated wind of DF Tau’s components with the background gas. The flux ratio ξ of the hydrogen Hα and Hβ lines could help distinguish between these interpretations. Given that the extinction to DF Tau is AV ⪕ 0.6 (Hartigan & Kenyon 2003; Herczeg & Hillenbrand 2014), a value of ξ > 3 would strongly support the shock wave interpretation (Sutherland & Dopita 2017, Fig. 18). Unfortunately, our s3 slice spectrum of the ring is very noisy, and the most we can conclude is that ξ > 2.

We found that the Hα flux from the ring, Fα, is ∼2 × 10−11 erg s−1 cm−2, so the ring’s luminosity is Lα = 4πD2Fα ∼ 5 × 1031 erg s−1. It is clear that components of the binary, with Teff < 3800 K and a bolometric luminosity Lbol < 0.7 L⊙ (Allen et al. 2017), cannot produce enough Lyman continuum photons to sustain a stationary H II region with such a high Hα luminosity. In principle, it is possible that the H II region arose in the past as a result of a short-duration flare(s) of UV radiation, and the observed Hα emission is the result of subsequent recombination.

Extreme flare-like brightenings of DF Tau (ΔB > 4m) were observed twice in the past century (Lamzin et al. 2001b), apparently once per orbital period (P ≈ 50 yr) of the binary. However, the spectra of the year 2000 flare (Li et al. 2001) do not give reason to suspect that powerful Lyman continuum emission occurred during this event, which lasted about a day.

We therefore believe that the ring is not an H II region, but its Hα emission results from the interaction of a poorly collimated gas outflow from DF Tau’s components with the ambient matter. It is possible that the ring is actually a projection of a spherical bubble onto the celestial sphere. In this regard, it is worth noting that several dozen bubbles have been observed in the Taurus star-forming region in CO molecular lines, which are interpreted as “the manifestation of strong stellar winds dispersing the surrounding gas” (Li et al. 2015).

The lines of the [S II] 6716 + 6731 Å doublet are not visible in our spectrum of the ring (s3 in Fig. 3), so we could not estimate the electron number density Ne or the ring’s kinetic energy. Without this information, it is difficult to determine the relationship between the Hα-emitting ring of DF Tau and the “molecular” bubbles found by Li et al. (2015).

thumbnail Fig. 3.

One-dimensional spectra corresponding to the position-velocity diagrams in Fig. 2. The numbers 4a and 4b mark the spectra corresponding to the HH objects a and b in Fig. 2.

We believe that the filament (the rim) running along the north-eastern side of the cometary globule (letter E in the scheme of Fig. 1) has the same origin as the ring; namely, it is the result of the interaction of DF Tau’s wind with the ambient medium. The Hα flux of the rim is three to four times less than that of the ring. Judging by slice 5, the heliocentric RV of the rim is +26 ± 9 km s−1. As can be seen from the s5 spectrum in Fig. 3, the spectrum of the rim is noisy, so it is unclear whether the [N II] 6583 Å line is indeed present. However, we believe that the [S II] 6716 Å line is observed and significantly stronger than the [S II] 6731 Å line, which indicates (Proxauf et al. 2014) that Ne ≲ 30 cm−3 in this part of the rim.

3.2. The jet and HH 1266 flow

Hartigan et al. (2004) found that DF Tau “shows clear jets at PA ≈ 127° and ≈307°”. More precisely, they identified elongated [O I] emission features at a distance of ≈ 0 . ″ 2 $ {\approx}0{{\overset{\prime\prime}{.}}}2 $ from the binary (see also Uvarova et al. 2020).

A portion of our long-slit spectrum of DF Tau, observed on October 5, 2024 (see Table 1), is shown in Fig. 4. Emission features are clearly visible in the [N II] 6583 Å line, which are located on opposite sides of the star at a distance of ≈ 0 . ″ 5 $ {\approx}0{{\overset{\prime\prime}{.}}}5 $ and moving in opposite directions with a RV of ≈100 km s−1. This is likely the micro jet discovered by Hartigan et al. (2004) in the [O I] 6300 and 6363 Å lines. However, we were unable to reliably separate the micro jet’s emission from the telluric oxygen lines in our spectrum, and therefore, we cannot estimate the proper motion of the micro jet, as the line-forming region may differ for the [O I] and [N II] lines (Nisini et al. 2024).

thumbnail Fig. 4.

Long-slit spectra of DF Tau with PA = 128°. The underlying stellar spectrum has been removed. Rest velocities and ±100 km s−1 relative to the stellar velocity are marked for selected forbidden lines with red vertical lines. The color bar shows the flux in pixels ( 0 . ″ 366 × 0 . ″ 366 $ 0{{\overset{\prime\prime}{.}}}366 \times 0{{\overset{\prime\prime}{.}}}366 $) relative to the stellar spectrum, expressed as percentages.

The [S II] 6716 and 6731 Å lines are also present in our spectrum but only in the part of the micro jet approaching us. The RV of the [S II] lines is ≈ − 100 km s−1. The intensity of the red component of the sulfur doublet is noticeably less than that of the blue one, which indicates (Proxauf et al. 2014) that Ne ≲ 300 cm−3 in the line-forming region.

Within the measurement errors, the direction of the micro jet is perpendicular to the node line of DF Tau’s orbit (Allen et al. 2017; Kutra et al. 2025), as expected if the micro jet is directed perpendicular to the orbital plane. The direction of the micro jet is shown by the green line OA in the scheme of Fig. 1. The line with PAj = 301° passes through group A of emission nebulae. The position-velocity diagram and spectrum of the brightest of these nebulae (slice s1) are shown in Figs. 2 and 3, respectively. The RV of this nebulosity is −56 ± 5 km s−1, which means that the nebula is moving away from the binary with Vr ≈ 70 km s−1.

We therefore conclude that this part of the outflow is a jet from DF Tau and that the group A Hα-emitting nebulae are HH objects connected with the jet, as well as other nebulae located to the north-west of point A, as we discuss below. Professor Bo Reipurth agreed with our arguments and includes the HH flow from DF Tau, referred to as HH 1266, in his catalog Reipurth (2000).

The HH 1266 flow has two remarkable features. Firstly, we found that the RV of the elongated nebulosity B (see the scheme in Fig. 1) is +138 ± 6 km s−1 (Figs. 2 and 3), indicating that it moves away from the binary with a RV of ≈125 km s−1, and thus the nebulosity B can be interpreted as a counter-jet with a projected length of 5 . ′ 5 $ 5{{\overset{\prime}{.}}}5 $. Its RV is approximately twice as large as that of the jet. Such velocity asymmetry between jets and counter-jets has been observed in about half of all bipolar jets and is therefore very common (Hirth et al. 1994). More intriguing is the fact that the counter-jet direction (PA ≈ 133°) differs by 12° from PAj − 180°. Moreover, it is clear even upon visual inspection in Fig. 1 that the jet and counter-jet are not aligned in diametrically opposite directions.

This misalignment is possible if the jet and counter-jet are launched by different components of the DF Tau binary. According to Kutra et al. (2025), the inclinations of the circumprimary and circumsecondary disks of DF Tau relative to the orbital plane are 13 ° ±13° and 8 ° ±9°, respectively. The authors conclude that “the disk-orbit obliquity is consistent with zero for both components”, but this does not exclude the possibility of the internal regions of the components disks being tilted relative to each other at an angle of 5 − 10°.

The second interesting feature of the HH 1266 flow is the relative location of the emission nebulae. Fig. 5 shows the north-western part of the jet in an enlarged view. It can be seen that the emission nebulae are not arranged along a single smooth curve. This may be due to the fact that DF Tau’s components were launching jets in different directions or/and jet deflection occurred due to its interaction with a non-homogeneous ambient medium (see, e.g., Raga et al. 2025 and references therein). Information about the proper motion of HH objects is necessary to interpret the observed morphology of the HH 1266 flow. We note that there are no young stellar objects within 0.5° of DF Tau (Luhman 2018).

thumbnail Fig. 5.

Large-scale vicinity of the jet. The letter designations are the same as in the scheme in Fig. 1.

Located ≈ 10 . ′ 5 $ {\approx}10{{\overset{\prime}{.}}}5 $ away from the star, which corresponds to a projected distance of rC ≈ 105 au (Figs. 1, 5 and the s4a, s4b spectra in Figs. 2, 3), our spectra of the two C group nebulae indicate that they are indeed HH objects, and they move with approximately equal RVs of ≈ − 22 ± 4 km s−1. Judging by the flux ratio of the [S II] lines, Ne ∼ 300 cm−3 in both objects. The [N II] 658 nm line is very weak if present at all in the 4b spectrum, but it has nearly the same intensity as the sum of the [S II] doublet lines in the spectrum of the 4a HH object. If we also take into account that the flux ratio of Hα and [O I] 630 nm lines in the s4a spectrum is 1.84 ± 0.35, then we find that the velocity of the shock exciting this HH object is Vsh > 30 km s−1 (Dopita & Sutherland 2017, Fig. 6). Therefore, an order-of-magnitude estimation of the C group age is rC/Vsh ≲ 2 × 104 yr.

The spectrum of the D nebula (s6 in Fig. 3) resembles that of the 4a HH object, but the flux ratio of the [N II] 658 nm line to the [S II] doublet lines is greater than three, implying that the excitation shock velocity is greater than 50 km s−1. Unfortunately, we were unable to separate the [O I] 630 nm line of this HH object from the telluric line to confirm this conclusion. The RV of this HH object is −3 ± 4 km s−1, which is close to that of the background CO molecular gas: +6 ± 2 km s−1 (Li et al. 2015). We therefore believe that the HH object is a terminated shock resulting from the collision of a low-density jet with a much denser ambient cloud (Raga et al. 2020).

In conclusion, we note that we attempted to detect H2 2.12 μm line emission from the HH 1266 flow region (see Sect. 2). However, we obtained only a 1σ upper limit of 7.5 × 10−17 erg s−1 cm−2 arcsec−2.

3.3. The blob

We also found two Hα-emitting nebulae at a distance of d b ≈ 5 . ″ 4 $ d_{\mathrm{b}}\approx 5{{\overset{\prime\prime}{.}}}4 $ from the star located west and south of DF Tau (see the insert in the upper-left corner of the right panel of Fig. 1). The western blob (PA ≈ 65°) is also visible in our 10″-slit spectrum of DF Tau (see Table 1 and Fig. 6). We therefore conclude that at least the western nebulosity is a real structure and not an artifact of image processing. We know the position angle of the slit, the TDS image scale of 0 . ″ 366 $ 0{{\overset{\prime\prime}{.}}}366 $ px−1, the dispersion of 39 km s−1 px−1, and the position of the star relative to the slit center, which we determined under the assumption that RV of the Hα line in the stellar spectrum is zero. From this data, we estimated the RV of the western blob as V r b ∼ − 100 $ V_{\mathrm{r}}^{\mathrm{b}}\sim -100 $ km s−1. Assuming that the tangential velocity of the blob, V t b $ V_{\mathrm{t}}^{\mathrm{b}} $, is approximately equal to its V r b $ V_{\mathrm{r}}^{\mathrm{b}} $, the dynamical time of the blob is t dyn b ∼ d b / V t b ∼ 30 $ t_{\mathrm{dyn}}^{\mathrm{b}}\sim d_{\mathrm{b}}/V_{\mathrm{t}}^{\mathrm{b}}\sim 30 $ yr.

thumbnail Fig. 6.

Wide-slit spectrum of DF Tau near Hα. The slit position is shown in Fig. 1. The white cross marks the stellar position, and the red cross indicates the predicted position of the western blob at zero velocity. It can be seen that the actual position is blueshifted relative to the red cross.

Such t dyn b $ t_{\mathrm{dyn}}^{\mathrm{b}} $ allowed us to assume that the blob (or blobs) could have been produced by the year 2000 flare (Sect. 3.1). The position angle of the western blob is noticeably different from that of the (micro)jet. We note in this regard that the micro jet was discovered from spectra observed before the year 2000, and furthermore, the blueshifted component of the [O I] 6300 Å line, with a velocity of ≈ − 100 km s−1, is present in the spectrum of DF Tau observed on December 6, 1984 (Edwards et al. 1987), long before the year 2000 flare. One can therefore assume that the blob is associated with a weakly collimated ejection resembling something like a bubble in XZ Tau (Krist et al. 1997).

4. Concluding remarks

The Hα images we obtained allowed us to detect a number of unusual emission nebulae in the vicinity of DF Tau. We discovered a ring-shaped nebula around DF Tau, but the binary system is not located at its center. We also identified a jet and a counter-jet emanating from the binary system; however, they are not antiparallel and move with different velocities. Consequently, it remains unclear whether this behavior arises from the peculiarities of collimated flow formation from one or both components of DF Tau. Additionally, it has become apparent that the HH objects of the HH 1266 flow are not arranged along a single smooth curve for some unknown reason.

In this Letter, we have deliberately limited ourselves to a semi-qualitative interpretation of our observations at best. Deeper images and higher-quality spectra in various regions of the HH 1266 flow are needed to reach reliable conclusions. Additionally, information on the proper motion of the discovered nebulae and DF Tau itself is required. One thing is certain: The binary is a source of both collimated and weakly collimated gas outflows with an unusual morphology, and it therefore deserves further study.

Acknowledgments

We thank the staff of the CMO SAI MSU for their assistance with the observations, Drs. A. V. Moiseev and K. A. Postnov for useful discussions, the referee for his helpful comments, and Prof. Bo Reipurth for including the discovered HH-flow in the general catalog of objects of this type and assigning it the number HH 1266. This research has made use of the SIMBAD database (CDS, Strasbourg, France) and Astrophysics Data System (NASA, USA). The work of AVD (data reduction, interpretation) and IASh (spectroscopic observations) was conducted under the financial support from the Russian Science Foundation (grant 23-12-00092). Scientific equipment used in this study was bought partially through the M. V. Lomonosov Moscow State University Program of Development.

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All Tables

Table 1.

Log of TDS observations.

In the text

All Figures

thumbnail Fig. 1.

Vicinity of DF Tau in the continuum band Halpbc (left panel) and the difference between images in the Halp 656 nm and Halpbc filters (right panel). Red segments indicate the position and orientation of the TDS slits. The close vicinity of DF Tau is highlighted in a 10″ × 10″ subimage located in the upper-left part of the panel. Red dashed lines mark the edges of the 10″-slit used for TDS observation at rJD = 588.6, and southern (s) and western (w) blobs are marked with blue lines. The diagram in the lower-right part of the panel illustrates the nomenclature of nebulae designations used in the text: O – DF Tau; green line – micro jet direction (PA = −59°); A – the first group of bright HH objects; B – counter-jet, C – the second group of bright HH objects; D – the brightest HH object (∼3 × 10−16 erg s−1 Å−1 cm−2 arcsec−2); E – the rim; F – the ring, whose center is marked by a green cross near DF Tau.
In the text
thumbnail Fig. 2.

Position-velocity diagrams corresponding to slit positions marked in Fig. 1. The horizontal strip in the left panel is the spectrum of a field star. Letters a and b correspond to different HH objects that fell within the spectrograph slit (s4 in Fig. 1).
In the text
thumbnail Fig. 3.

One-dimensional spectra corresponding to the position-velocity diagrams in Fig. 2. The numbers 4a and 4b mark the spectra corresponding to the HH objects a and b in Fig. 2.
In the text
thumbnail Fig. 4.

Long-slit spectra of DF Tau with PA = 128°. The underlying stellar spectrum has been removed. Rest velocities and ±100 km s−1 relative to the stellar velocity are marked for selected forbidden lines with red vertical lines. The color bar shows the flux in pixels ( 0 . ″ 366 × 0 . ″ 366 $ 0{{\overset{\prime\prime}{.}}}366 \times 0{{\overset{\prime\prime}{.}}}366 $) relative to the stellar spectrum, expressed as percentages.
In the text
thumbnail Fig. 5.

Large-scale vicinity of the jet. The letter designations are the same as in the scheme in Fig. 1.
In the text
thumbnail Fig. 6.

Wide-slit spectrum of DF Tau near Hα. The slit position is shown in Fig. 1. The white cross marks the stellar position, and the red cross indicates the predicted position of the western blob at zero velocity. It can be seen that the actual position is blueshifted relative to the red cross.
In the text

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