The ESA mission Comet Interceptor will target an Oort or interstellar comet during its first approach to the Sun. Meanwhile, the Vera Rubin LSST Survey will observe hundreds of active comets per month beyond 4 au from the Sun, where water vapour pressure is expected to be too low to eject dust. We discuss observations of dust tails at heliocentric distances larger than 4 au in order to retrieve the physical parameters driving cometary activity beyond Jupiter by means of a probabilistic tail model, which is consistent with the activity model defining the gas coma parameters due to the sublimation of carbon monoxide, molecular oxygen, methane, ethane, and carbon dioxide since the activity onset at 85 au from the Sun. We find that: (i) All the observed dust tails are consistent with the adopted activity model; (ii) The tail fits depend on three free parameters only, all correlated to the nucleus size; (iii) Tail fits are always improved by anisotropic dust ejection, suggesting activity of Oort nuclei dominated by seasons; (iv) Inbound seasons suggest cometary activity before the ejection of protocomets into the Oort cloud, as predicted by the activity model; (v) Oort nuclei larger than 1 km may be characterized by a fallout up to ∼100 m thick deposited during ∼60 yr inbound; (vi) On the other side, Oort nuclei smaller than 1 km may appear more pristine than Jupiter Family Comets when observed at 1 au from the Sun.

Pressure P of CO2 gas inside the pebbles versus the depth s. Continuous straight line: tensile strength, S, bonding a dust homogeneous aggregate of size s (Skorov & Blum 2012). Continuous curved line: P at T_s = 160 K and ∇T = 39 K cm^-1 crosses S at s_m = 9 μm and s_M = 12 mm, where s_m and s_M are the minimum and maximum sizes of the ejected dust. Dot and dashed line: P at T_s = 139 K and ∇T = 17 K cm^-1 crosses S at s_m = 60 μm and s_M = 2 cm. Dashed line: P at T_s = 123 K and ∇T = 7 K cm^-1 crosses S at s_m = 0.4 mm and s_M = 25 mm. Dotted line: the curve P at T_s = 111 K and ∇T = 2 K cm^-1 is tangent to the line S at s_m = s_M = 1 cm

Images of the dust tails summarized in Table 3. Each image covers a field of view of 25".2 × 25".2. Black arrow: antisolar direction. White arrow: Trailing orbit direction

Afρ of comet C/2017K2 versus the heliocentric distance r_h measured within a sky-projected coma radius ρ₀ = 5×10⁴ km. Diamonds: observations of the CARA network. Squares: observations at Loiano Observatory. Dashed line: best fit of Loiano’s data constrained by the dust tail model (Table 5).

Isophotes of the observed (grey isophotes) and of the model (black isophotes) dust tail of comet C/2017K2 at r_h = 6.35 au. The North direction is up, and the East direction to the left. The brightness step between isophotes is a factor two. The tail model assumes isotropic dust ejection from the nucleus, provides d = 0.175 and is larger than observations on the western side.

Isophotes of the observed (grey isophotes) and of the model (black isophotes) dust tail of comet C/2017K2 at r_h = 6.35 au. Black arrow: antisolar direction. Grey arrow: trailing orbit direction. The tail model assumes no dust ejection from nucleus latitudes <-60 deg, with a lower d = 0.165.

Isophotes of the observed (grey isophotes) and of the model (black isophotes) dust tail of comet C/2019O3 at r_h = 8.86 au. The North direction is up, and the East direction to the left. The brightness step between isophotes is a factor three. The tail model assumes isotropic dust ejection from the nucleus, provides d = 0.108 and is larger than observations on the eastern side.

Isophotes of the observed (grey isophotes) and of the model (black isophotes) dust tail of comet C/2019O3 at r_h = 8.86 au. Black arrow: antisolar direction. Grey arrow: trailing orbit direction. The tail model assumes no dust ejection from nucleus latitudes <-60 deg, with a lower d = 0.081.

Isophotes of the observed (grey isophotes) and of the model (black isophotes) dust tail of comet C/2020F2 at r_h = 9.17 au. The North direction is up, and the East direction to the left. The brightness step between isophotes is a factor three. The tail model assumes isotropic dust ejection, provides d = 0.148 and is larger than observations on the northern and southern sides.

Isophotes of the observed (grey isophotes) and of the model (black isophotes) dust tail of comet C/2020F2 at r_h = 9.17 au. Black arrow: antisolar direction. Grey arrow: trailing orbit direction. The tail model assumes no dust ejection from nucleus latitudes <-60 and >+60 deg, with a lower d = 0.122

Isophotes of the observed (grey isophotes) and of the model (black isophotes) dust tail of comet C/2020H6 at r_h = 4.84 au. The North direction is up, and the East direction to the left. The brightness step between isophotes is a factor three. The tail model assumes isotropic dust ejection from the nucleus, provides d = 0.143 and is larger than observations on the eastern side.

Isophotes of the observed (grey isophotes) and of the model (black isophotes) dust tail of comet C/2020H6 at r_h = 4.84 au. Black arrow: antisolar direction. Grey arrow: trailing orbit direction. The tail model assumes no dust ejection from nucleus latitudes <-60 deg, with a lower d = 0.115.

Isophotes of the observed (grey isophotes) and of the model (black isophotes) dust tail of comet C/2020R2 at r_h = 4.83 au. The North direction is up, and the East direction to the left. The brightness step between isophotes is a factor three. The tail model assumes isotropic dust ejection from the nucleus, provides d = 0.073 and is larger than observations on the southern side.

Isophotes of the observed (grey isophotes) and of the model (black isophotes) dust tail of comet C/2020R2 at r_h = 4.83 au. Black arrow: antisolar direction. Grey arrow: trailing orbit direction. The tail model assumes no dust ejection from nucleus latitudes <-40 deg, with a lower d = 0.057.