The flux-nuclear mechanism as the cause of cometary outbursts – a solution to an old problem

ABSTRACT

The paper presents a new flux-nuclear mechanism based on which cometary outbursts can be explained. This mechanism should be considered as a two-step process. In the first stage, it is necessary to consider the sublimation flux that occurs through the porous structure of the cometary nucleus. The second stage is the reaction of the cometary nucleus to the sublimation that is taking place. The consequence of this process is responsible for the migration (redistribution) of porous agglomerates on the surface of the cometary nucleus, the formation of landslides (local avalanches), the formation of dunes, the emission of porous agglomerates into the coma, and the loosening of the surface layer, which is consequently destroyed. These processes are part of the broadly understood cometary activity, i.e. the interaction of sublimating ice with the cometary nucleus. As a result of intense ice sublimation, the loose cometary material is ejected into the coma, which causes an increase in the total scattering cross-section. Then the incident sunlight scatters more effectively, which leads to a rise in the cometary brightness, i.e. its outburst. Based on the flux-nuclear mechanism and calculations performed for a model comet from the Jupiter family, it was determined that the upper limit of the outburst is equal to 4 mag. This means that the obtained value of the outburst amplitude fits the typical range of change in the cometary brightness.

1 INTRODUCTION

Analysing extensive observational material on cometary activity, it can be noticed that some observations clearly show certain deviations from the light curve. Deviations whose amplitude is less than 1 mag are referred to as mini outbursts (glow variations), which may simply be missed due to the sky being polluted with artificial light (Gronkowski, Tralle & Wesołowski 2018; Wesołowski 2019, 2023b). However, deviations whose amplitude is greater than 1 mag are referred to as cometary outbursts (Hughes 1975, 1991; Trigo-Rodríguez et al. 2008; Belton et al. 2013; Gronkowski & Wesołowski 2015, 2016; Miles 2016a, b; Agarwal et al. 2017; Hajra et al. 2017; Saki 2021; Bockelée-Morvan et al. 2022; Belousov & Pavlov 2024; Müller 2024; Gritsevich et al., in press; Gritsevich, Wesołowski & Castro-Tirado A. 2025). This phenomenon is a complex process associated with the destruction of a fragment of the cometary nucleus, accompanied by the emission of dust and gases into the coma. Then, the incident sunlight is scattered more effectively, especially on dust particles, causing the cometary brightness to increase, i.e. an outburst. Moreover, the cometary outburst is a process responsible for topographic changes on the surface of the nucleus, contributing to the modification of the cometary landscape (Colwell & Jakosky 1987; Pajola et al. 2016; El-Maarry et al. 2019; Vincent 2019; Wesołowski 2021; Ciarniello, Fulle & Raponi 2022; Jindal et al. 2022). Additionally, recent research has shown that in the case of comets located in the Oort cloud, repeated outbursts can affect the stability of their orbits (Merkulova et al. 2025).

Despite many years of research on the cometary outburst, which began in 1927 (when Schwassmann and Wachmann discovered a comet later called comet 29P/Schwassmann–Wachmann, hereinafter referred to as 29P/SW), this problem has not been fully explained. Questions still arise regarding the fundamental nature of the mechanisms that initiate cometary outbursts (Wesołowski 2022; Müller 2024). When creating classifications of existing outburst mechanisms, they can be divided into two groups. The first is the outer group, in which the mechanism responsible for the outburst may be collisions with other small bodies of the Solar system or fragments of meteor showers (Sekanina 1972), as well as the influence of the solar wind flux (Sekanina 1992). The second internal group concerns mechanisms associated with the nucleus itself. In this group, the most frequently considered mechanisms are transformation of water ice from amorphous to crystalline form (Prialnik & Bar-Nun 1992), complex chemical reactions, radiogenic transformations, polymerization of chemical compounds (HCN) (Donn & Urey 1956), cryovolcanism (Miles 2016a; Wesołowski 2020), avalanche processes – landslides (Wesołowski, Gronkowski & Tralle 2020a), rotational ejection of larger amounts of material (Wesołowski, Gronkowski & Tralle 2020b), cliff collapse (Pajola et al. 2017), an increase in stress leading to the deepening of existing cracks (Skorov et al. 2016). Analysing the individual mechanisms, it can be seen that the measure of the cometary outburst amplitude is the increase in the total scattering cross-section. However, the value of change in the cometary brightness is determined by three basic parameters. The first is the sublimation flux, which depends on the heliocentric distance and the type of cometary ice. The second parameter is the mass ejected, which was created as a result of the destruction of a fragment of the cometary nucleus, and the third parameter is the fraction of the cometary surface that is active in the phase of quiet sublimation (⁠|$\eta _{1}$|⁠) and during the outburst (⁠|$\eta _{2}$|⁠). Note that these last two parameters are very difficult to estimate because they are assessed visually. Therefore, in the general case, a wide range of their values should be assumed, which should additionally depend on the type of ice responsible for the cometary activity at a given heliocentric distance. In the context of correctly estimating the values of these parameters, direct observations of comets are crucial. As an example, you can consider the following two cases. Observations of comet 1P/Halley during its last approach to the Sun in 1986 showed that the size of the total active surface was 36 km|$^{2}$|⁠, which translates to 10 per cent of the total surface area of the nucleus (Keller et al. 1987). The rest of the surface seemed covered with a so-called crust (Gundlach et al. 2015), making sublimation difficult. However, the Rosetta and EPOXI missions show that almost the entire surface of the studied comets was sublimated. In the case of comet 67P/Churyumov–Gerasimenko (hereinafter referred to as 67P), sublimation of water ice occurred from those parts of the nucleus that were illuminated by the Sun (Gicquel et al. 2016). In the case of shadowed areas, CO|$_{2}$| ice was responsible for the sublimation activity (Keller et al. 2017). The detailed morphology of the presence of bright regions associated with exposed water ice on the surface of comet 67P nucleus was recently reported by Fornasier et al. (2023). Their analysis shows that only a small fraction of the total surface of the nucleus are bright areas, which confirms that the surface of comet 67P is dominated by dark areas. Moreover, thanks to the Rosetta mission, it was possible to observe the full development of comet 67P activity in both phases. The analysis of the most important results supported by numerical modelling regarding the activity of comet 67P in both of these phases can be found in the papers El-Maarry et al. (2015, 2016), Fornasier et al. (2015), Gundlach et al. (2015), Thomas et al. (2015), Filacchione et al. (2016), Vincent et al. (2016), Agarwal et al. (2017), Skorov et al. (2017), Bockelée-Morvan et al. (2019), Fulle et al. (2020), Wesołowski (2023a, 2024), and many other papers.

This paper aims to present a universal new flux-nuclear mechanism, which can explain cometary outbursts occurring at different heliocentric distances. At the same time, it is important to remember the reach of the sublimation of individual cometary ices. When considering this mechanism, it is necessary to determine the interaction between sublimating cometary ice and porous agglomerates. Using this mechanism, the influence of the sublimation flux on the change in the cometary brightness during its outburst was determined. Note that the obtained numerical values correspond to real cases of outbursts of many comets.

2 PHYSICAL MODEL

2.1 Sublimation flux

When considering the flux-nuclear mechanism as the cause of cometary outbursts in the first stage, a model of the nucleus structure should be considered. According to modern models, comets were formed due to the aggregation of fragments of primary matter of various sizes. Such a mechanism is possible because the van der Waals forces are large enough to bind fragments of primary matter that collide at velocities of 1 m s|$^{-1}$| (Weidenschilling 1977; Blum et al. 2017). Based on this mechanism, primary fractal structures were formed (Fulle & Blum 2017). As a result of the ongoing collisions, these particles continued to grow to a limit of the order of centimeters. Such a particle is called a porous agglomerate, and the comet nucleus itself should be treated as a cluster of such agglomerates consisting of ice particles, organic matter, and non-volatile dust material (Fulle et al. 2020; Ciarniello et al. 2022). The model of the agglomerator structure of the cometary nucleus fits into the general concept of comet formation as a result of gravitational collapse towards the centre of gravity (Johansen et al. 2007; Skorov & Blum 2012; Blum et al. 2014).

The sublimation activity of comets is closely related to their location in the Solar system. Under the influence of electromagnetic radiation coming from the Sun, individual ices begin to sublimate in a strictly defined order consistent with their sublimation temperatures. This mechanism preserves the porous structure of the nucleus and explains the complexity of the chemical composition of the coma. As a result of sublimation, the agglomerates that are close to the surface of the nucleus are deprived of the ice that binds their structures, and the sublimation process takes place in two directions. The first direction is sublimation directly into space, which contributes to the ejection, and redistribution of dust–ice particles as well as the formation of avalanches and dunes on the surface of the cometary nucleus (El-Maarry et al. 2015; Thomas et al. 2015; Wesołowski et al. 2020a; Wesołowski 2023b, 2024). The second direction is related to sublimation taking place inside the nucleus, where re-condensation takes place. Therefore, to correctly describe the sublimation activity, it is crucial to determine the temperature on the surface of the nucleus. To do this, one of three approaches should be used. The first is to measure the temperature during direct observation of a given comet (Tosi et al. 2019), the second is to measure photometric parameters for selected dust analogues (e.g. hemispherical albedo), and determine the temperature based on the obtained spectrum (Wesołowski et al. 2024; Wesołowski & Potera 2024a, b, 2025), and the third approach means a numerical solution of the energy balance equation assuming a constant bolometric albedo value. Since the presented flux-nuclear mechanism is supposed to be universal, the temperature on the surface of the cometary nucleus was determined based on the third approach. Then this equation can be written as (equation 1):

where S|$_{\odot }$| is the solar constant (S|$_{\odot }$| = 1361.1|$\pm$|0.5 W/m²), |$A_{\mathrm{B}}$| is the nucleus Bond albedo (A|$_{\mathrm{B}}$| = 1.12 per cent), |$\Theta _{\mathrm{Sun}}$| is the solar zenith angle, d is the heliocentric distance of a comet (d = 1.5 au), |$\epsilon$| is the emissivity (⁠|$\epsilon$| = 0.9 (–)), |$\sigma _{\mathrm{B}}$| is the Stefan Boltzmann constant (⁠|$\sigma _{\mathrm{B}}$| = 5.67 10^-8 W /m² K⁴), T is the temperature, |$H(T)$| is the latent heat of sublimation water ice (H = 2.83 10⁶ J /kg), F|$_{\mathrm{i}}$| is a sublimation flux, |$\lambda _{\mathrm{i}}$| is the heat conductivity inside the nucleus, and |$\nabla$|T is the average gradient of the temperature. The left side of equation (1) describes the power of electromagnetic radiation from the Sun that is absorbed by the cometary nucleus. The first term on the right describes the power radiated from the nucleus, the second term defines the power associated with the sublimation of water ice, and the third term defines the power conducted into the interior of the cometary nucleus. Note that the thermal conductivity of the surface layer of the nucleus and the changes occurring in this layer under the influence of the sublimation flux are poorly understood so far. Therefore, this factor may cause some underestimation of the temperature on the surface of the cometary nucleus. This issue was recently discussed in detail in the papers of Skorov et al. (2023a, b).

To correctly describe the sublimation flux, it is necessary to define the average velocity of gas molecules based on the Maxwell–Boltzmann distribution. The detailed derivation of equation (2) is presented in this paper (Wesołowski 2022):

where k|$_{\mathrm{B}}$| is the Boltzmann constant (k_B = 1.38 10^-23 J /K), T is the temperature, the calculation of which is based on the numerical solution of equation (1), and m|$_{\mathrm{g}}$| is the mass of sublimated cometary gas molecules (m_g = 18 1.66 10^-27 kg). Note that the parameter describing the flux in equation (1) has the index ‘i’, which is equal to i = 1–4 and means that four equations describing the sublimation flux are taken into account. In the first case (i = 1), the porous agglomerates that make up the cometary nucleus are covered with a thin layer of desiccated porous dust. Then the sublimation flux F₁ can be expressed as (Kossacki et al. 2022; Wesołowski 2023a):

In the second case (i = 2), the agglomerates are exposed and sublimation takes place directly from their surface. Then the sublimation flux F|$_{2}$| can be expressed as:

In the third case (i = 3), the sublimation flux was corrected by the anomalous evaporation coefficient (the value of this coefficient is in the range of 0 <|$\beta$|< 1). Then the sublimation flux F|$_{3}$| can be expressed as:

In the fourth case (i  = 4), the classic Hertz–Knudsen formula was used to determine the ice sublimation rate without any corrections.

In the equations (3)–(6), the individual symbols mean: C|$_{\mathrm{\psi }}$| is the parametric function, (C|$_{\mathrm{\psi }}$|  = (1.73 − 5.16|$\psi$| + 3.96|$\psi ^{2}$|⁠), |$\psi$| is the porosity of the agglomerates (⁠|$\psi$| = 0.7), |$\psi _{\mathrm{d}}$| is the porosity of the dust layer (⁠|$\psi _{\mathrm{d}}$| = 0.4 (−)), d is the thickness of layer (d = 1 10^-3 m), r|$_{\mathrm{p}}$| is the radius of pores (r_p = 0.2 10^-3 m), |$p_{\mathrm{sat}}$| is the phase equilibrium pressure was calculated using the classical formula (equation 7):

In the equations (3)–(4) there is an important parameter that determines the sublimation coefficient |$\alpha _{\mathrm{s}}$|(T) which depends on the temperature. Its value can be determined based on two dependencies given by Gundlach, Skorov & Blum (2011) and Kossacki et al. (2022). The distribution of the sublimation coefficient taking into account these two dependencies was presented in the paper Wesołowski (2024). Using four equations (3)–(6) to describe the sublimation flux, means that the energy balance equation must be solved four times. The results of these calculations are shown in Table 1.

In the context of cometary activity, the main challenge is to precisely determine the ice sublimation flux occurring through the porous structure of the comet nucleus and to take into account the complex interaction between the sublimation flux, surface morphology, and thermodynamic conditions inside the comet nucleus. As a result of ice sublimation, its gradual loss occurs, which contributes to the drying and loosening of the active surface layer of the comet nucleus. Such a loose structure, even at a lower sublimation flux, can be destroyed. The effect of this destruction is the disintegration of this structure into individual porous agglomerates. Depending on the dimensions of the agglomerates, they are ejected into a coma. This material increases the total scattering cross-section, and the incident sunlight is scattered more efficiently. As a result, the cometary brightness increases, which means its an outburst.

2.2 Ejection of agglomerates from the surface

When considering the ejection of porous agglomerates from the surface of a cometary nucleus, I assume that all the energy absorbed by the nucleus is used to sublimate the cometary ice. For this purpose, two cases must be considered. The first case concerns loose agglomerates, i.e. those that are not bound to the surroundings. The second case, on the other hand, concerns agglomerates bound to the surroundings. A detailed discussion of these two cases was recently discussed in Wesołowski (2024). From this discussion, it follows that for the first case, i.e. determining the maximum dimensions of particles ejected from the surface of the nucleus, the following relationship is valid:

In equation (8), the individual symbols take the following notation: C|$_{\mathrm{D}}$| is the modified free-molecular drag coefficient for spherical body (C|$_{\mathrm{D}}$| = 2; Grün et al. 1993), |$v_{\mathrm{g,i}}$| is the mean radial velocity of gas molecules, F|$_{\mathrm{i}}$| is the sublimation flux, |$\varrho _{\mathrm{agl}}$| is the density of agglomerates, and R|$_{\mathrm{N}}$| is the radius of the nucleus. In the calculations, it was assumed that the agglomerate density meets the following relationship: 600|$\le \varrho _{\mathrm{agl}} \le$|1200 kg m|$^{-3}$|⁠. Other symbols mean: g|$_{\mathrm{c}}$| is the gravitational acceleration of the cometary nucleus (g|$_{\mathrm{c}}$| = 2.25 10^-4 m/s²; Vincent et al. 2016), and P is the period of its rotation (P = 12 h). It should be noted that the equation (8) is valid only under the assumption that the ejected porous agglomerates are spherical and that the gas release is constant over the surface of the cometary nucleus.

Using the above considerations, Fig. 1 shows the results of calculations of the maximum radii of porous agglomerates that can be lifted into the coma due to quiet sublimation. In these calculations used two extreme fluxes F|$_{1}$| and F|$_{4}$| to determine the range of particle sizes. In the case of larger particles, they can migrate (redistribute) across the surface of the cometary nucleus. The condition for this type of movement is possible when the following relationship is relationship: |$\mu _{\mathrm{s}} \le \Lambda$|⁠, where |$\mu _{\mathrm{s}}$| is the friction coefficient, and |$\Lambda$| is the mobility coefficient (Wesołowski et al. 2019). The largest boulders remain motionless.

In the second case, i.e. with minimum dimensions of particles ejected from the surface of the nucleus, it is important to investigate the breaking of bonds between the agglomerate and its environment. For this purpose, it is necessary to consider the balance of the drag force and the cohesive force, which depends on the number of contact points. To simplify the calculations, an agglomerate with one contact point was considered. From this equilibrium condition, it follows that (Wesołowski 2024):

In equation (9), the individual symbols take the following notation: S|$_{\mathrm{c}}$| is the describes the particle purity used to compute the cohesive forces in lunar regolith. The calculations assumed a wide range of values for the parameter S|$_{\mathrm{c}}$|⁠, which satisfies the following relationship: 0.1|$\le$|S|$_{\mathrm{c}}\le$| 1.0 (Perko, Nelson & Sadeh 2001; Thomas et al. 2015). Proceeding similarly as in the first case, based on equation (9), the minimum value of the radius of a particle that can be ejected from the surface of the nucleus as a result of the occurring sublimation of water ice was calculated. The results of these calculations are presented in Fig. 2. Analysing the obtained results presented in Figs 1–2, it can be noticed that the greatest influence on the maximum dimension of porous agglomerates lifted to the coma is the sublimation flux, the average thermal velocity of gas molecules and their density. Then the maximum size of the porous agglomerate ejected into the coma is equal to r_gr,max|$_{\mathrm{gr,max}}$| = 57.28 10^-2 m. However, the minimum size of the porous agglomerate that can be thrown into the coma depends mainly on the sublimation flux and the average thermal velocity of gas molecules. Then the minimum size of the porous agglomerate is equal to r_gr,min = 6.47 10^-4 m. In the case of smaller particles, their emission in the quiet phase of sublimation is impossible due to the cohesive force which is greater than the drag force coming from the molecules of sublimating ices.

Due to the sublimation from porous agglomerates occurring in the coma and the impact of the solar wind stream, these particles may disintegrate into primary structures, i.e. single monomers with dimensions of the order of 10^-7 m (Bentley et al. 2016; Fulle, Blum & Rotundi 2019) or even smaller. The obtained ranges of dimensions of porous agglomerates were used to determine the limits of integration in the power law (Wesołowski 2024) based on which the average value of the particle in the coma on which the incident sunlight is scattered was calculated (equation 10):

where K is the normalization constant, f(r) is the distribution function [f(r) = r|$^{\mathrm{- q}}$|], r is the radius of the porous agglomerate, and q is the power index of law (q = 3.7; Lin et al. 2017; Wesołowski 2020). Then the average value of the particle on which the incident sunlight is scattering is equal to r|$_{\mathrm{av}}$| = 1.588 10^-7 m.

2.3 Change in cometary brightness

Using the flux-nuclear mechanism and Pogson’s law, the change of cometary brightness during its outburst was determined. This amplitude can be expressed using the following relationship (equation 11):

where f|$(\vartheta)_{1}$| and f|$(\vartheta)_{2}$| are the phase functions coming from comet particles that were ejected into the coma during the quiet sublimation phase and in the outburst phase. The values of these functions were calculated based on the relationship given by Henyey & Greenstein (1941). The remaining symbols denote that |$N_{1}$| and |$N_{2}$| are the number of particles with the total scattering cross-section C|$_{\mathrm{scat}}$| that were carried to the coma in the quiet sublimation phase and the outburst phase, |$N_{\mathrm{ej}}$| determines the number of particles that come from the destruction of a fragment of the cometary nucleus the total scattering cross-section C|$_{\mathrm{ej}}$|⁠. Furthermore |$Q(r_{\mathrm{j}})$| is the scattering coefficient for a given particle [Q(r|$_{\mathrm{ice}}$|⁠) = 2.044(−), Q(r|$_{\mathrm{org}}$|⁠) = 1.511 (−), Q(r|$_{\mathrm{sil}}$|⁠) = 0.544(−)]. The values of these factors were calculated based on the Mie theory. The individual amounts of particles on which incident sunlight scattering can be expressed as:

and

In equations (12)–(14), the individual symbols mean: |$\xi$| is the volume constant (⁠|$\xi$| = 6.75 10¹³ m|$^{3}$|⁠), |$\eta _{1}$| is the fraction of the active surface in the quiet sublimation phase (10 per cent |$\le \eta _{1} \le$| 50 per cent), |$\varrho _{\mathrm{agl}}$| is the density of the porous agglomerate (⁠|$\varrho _{\mathrm{agl}}$| = 875 kg m|$^{-3}$|⁠; Gundlach et al. 2015). Moreover, for the quiet sublimation, it was assumed that the dust–gas mass ratio is |$\kappa _{1}$| = 1, while for the outburst phase, this ratio is assumed to be |$\kappa _{2}$| = 3 (Wesołowski & Potera 2024b). Furthermore M|$_{\mathrm{ej}}$| is the mass ejected (expressed in kg), |$\varrho _{\mathrm{gr,x}}$| is the density of the particles on which the incident sunlight is scattering. Note that this paper considers three types of particles which consist of water ice (⁠|$\varrho _{\mathrm{gr,ice}}$| = 933 kg m|$^{-3}$|⁠), organic matter (⁠|$\varrho _{\mathrm{gr,org}}$| = 1600 kg m|$^{-3}$|⁠), and silicate (⁠|$\varrho _{\mathrm{gr,sil}}$| = 2950 kg m|$^{-3}$|⁠). Therefore, the index x appearing in equations (13)–(14) refers to the density of the agglomerates consisting of these three components.

Note that in equation (11) the cross-section coming from the cometary nucleus has been omitted because, as research has shown, in the case of small comets its contribution to the change in brightness is negligible (Wesołowski et al. 2020a; Wesołowski, Gronkowski & Kossacki K. 2022). In equations (11)–(14) the integration limits were assumed to be the range satisfying the following condition: 10|$^{-7}$| m |$\le$|r|$\le 10^{-2}$| m. This condition was determined based on the considerations presented in Section 2.2 of this paper.

Using the flux-nuclear mechanism, i.e. the interaction between sublimating cometary ice and porous agglomerates, the change in brightness of a model Jupiter family comet was calculated. The considered interaction concerns three main issues. First, determining the upper and lower limits of the radius of the porous agglomerate that can be ejected into the coma, second, determining the average size of the particle on which the incident sunlight is scattered in the coma, and third, determining the scattering coefficient of the incident light on this particle, which consists of three main components: water ice, organic matter, and dust matter.

An additional contribution to the total scattering cross-section may be the emission of fragments of primary matter via jets (Yelle & Soderblom 2004; Wesołowski et al. 2020b). In such a case, the transported fragment of matter at the local narrowing of the jet channel may lead to its complete or partial blockage. This leads to an increase in the pressure of the trapped gas in the cavity and the channel. If the value of the pressure of the trapped gas exceeds the mechanical strength to fracture, then the fragment (upper part) or even the entire cavity is destroyed (Gronkowski & Wesołowski 2015). The result of this destruction is the disintegration of this nucleus fragment into porous agglomerates and their emission into the coma. This leads to a more effective scattering of incident sunlight, i.e. outburst. Additionally, the coma is fed by the sublimation flux of various cometary ices originating from deeper layers of the nucleus, which explains the rich composition of the coma as in the case of comet 67P (Biver et al. 2023).

The presented calculation results should be considered as examples since they concern the outburst of a model comet that took place at the heliocentric distance d = 1.5 au, and the sublimation activity was controlled by water ice. The results of these calculations are presented as a function of the mass ejected, for which the upper limit is equal to M|$_{\mathrm{ej}}$| = 10|$^{8}$| kg. The value of this mass results directly from observations of typical cometary outbursts (Moreno et al. 2011; Schambeau et al. 2019). The results of these calculations are shown in Figs 3–6. To demonstrate the universal nature of the presented flux-nuclear mechanism, many numerical tests were performed to assess the influence of the heliocentric distance on the change in the cometary brightness. Example results of these simulations for the heliocentric distance r|$_{\mathrm{h}}$| = 3.0 au are presented in Fig. 7. In these calculations, one example sublimation stream described by equation (3) was used, and the scattering of incident sunlight occurred on ice, carbonaceous, and dust particles, respectively.

Based on the above model of a cometary outburst, we can estimate the change in the cometary brightness without taking into account the dynamics, i.e. the evolution in time. This approach results from the fact that cometary outbursts are sudden and occur over a short time.

3 OBSERVATIONAL DATA

Analysing the extensive observational material of numerous comet outbursts, it is easy to see that this phenomenon occurs at different heliocentric distances. This means that the outburst activity of comets is driven by the sublimation of different ices, e.g. H|$_{2}$|O ice, CO|$_{2}$| ice, and CO ice. Furthermore, different types of cometary ices could be responsible for an outburst at a given heliocentric distance (Müller 2024). An example of such activity is presented in the Appendix of this paper. Changes in comet brightness cover a wide range, from mini-outbursts, as in the case of comet 67P (Vincent et al. 2016), to mega-outbursts, as in the case of comet 17P/Holmes in 2007 (Montalto et al. 2008; Moreno et al. 2008).

Table 2 shows an example tally of the outburst amplitude values for various comets along with the heliocentric distance at which the outburst occurred.

Modern observations clearly show that in the case of a given comet, numerous changes in brightness can be observed even in short-time intervals. The Rosetta space mission confirmed this result during the summer outbursts of comet 67P (Vincent et al. 2016). An additional example of multiple outbursts is the brightness variations of comet 12P/Pons-Brooks, for which 14 outbursts were observed between July 2023 and April 2024 (Betzler, Popowicz & de Sousa 2023; Kelley et al. 2023; Ryske et al. 2023; Gritsevich et al., in press). After this comet passed its perihelion, the comet experienced two more outbursts (Gritsevich et al. 2025). In the case of comet 12P/Pons-Brooks, the observed brightness variations ranged from 0.36 to 5.50 mag, and their distribution is shown in Fig. 8. Comparing the results obtained in this paper, it can be seen that these results are largely consistent with the actual brightness variations of comets during their outbursts.

4 DISCUSSION

When analysing cometary outbursts there are three important things to emphasize. First, the loosened surface layer can be ejected into a coma anywhere in the cometary orbit, causing outbursts at various heliocentric distances. This result was confirmed by many years of observations of comets during their outbursts. Secondly, this mechanism, on the one hand, contributes to the destruction of a fragment of the nucleus, and on the other hand, it causes the exposure of the original material from which comets were formed. Third, cometary outbursts provide insight into the internal structure of the nucleus, which can be studied.

Based on the obtained calculation results, the following detailed conclusions can be drawn:

• A measure of the change in the cometary brightness is the increase in the total scattering cross-section. The main factor that determines this cross-section is the mass ejected, the porosity of agglomerates, and the sublimation flux of water ice. Additionally, the sublimation flux value influences the size range of agglomerates that are thrown into the coma during quiet sublimation.

• The greatest change in the cometary brightness was achieved when incident sunlight was scattered by ice particles. In the case of the F|$_{1}$| flux, the obtained range of brightness change ranged from 4.00 to 2.36 mag, for the F|$_{2}$| flux this range ranged from 3.86 to 2.23 mag, for the F|$_{3}$| flux this range ranged from 3.79 to 2.16 mag, and in the case of the F|$_{4}$| flux, this range ranged from 3.65 to 2.05 mag. The smallest change in the cometary brightness was obtained in the case of scattering of incident sunlight that occurs on silicate particles. In the case of the F|$_{1}$| flux, the obtained range of brightness change ranged from 2.81 to 1.35 mag, for the F|$_{2}$| flux this range ranged from 2.67 to 1.24 mag, for the F|$_{3}$| flux this range ranged from 2.60 to 1.19 mag, and in the case of the F|$_{4}$| flux, this range ranged from 2.48 to 1.11 mag. The main factor that influences the obtained ranges of changes in the cometary brightness is the active surface in the quiet sublimation phase (⁠|$\eta _{1}$| parameter) and mass ejected.

• In the case of the F|$_{1}$| flux, the difference in the change in comet brightness between individual particles is 0.57 mag for ice particles and organic particles, 0.62 mag for organic particles and silicate particles, and 1.19 mag for ice particles and silicate particles. These differences were calculated for the mass ejected M|$_{\mathrm{ej}}$| = 10|$^{8}$| kg and the parameter |$\eta$| = 10 per cent. In the case of the remaining three fluxes (F|$_{2}$|⁠, F|$_{3}$|⁠, and F|$_{4}$|⁠), these differences are almost the same. The same statement also applies to the parameter |$\eta$| = 50 per cent. The main factor determining these differences is the assumed density of these particles.

• The presence of even a thin layer of porous fine-grained dust on the surface of the comet nucleus determines a lower value of the sublimation flux, which in turn translates into a greater change in the cometary brightness and higher values of both the temperature and the average thermal velocity of the gas molecules.

• Analysing the effect of the heliocentric distance on the amplitude of the change in cometary brightness, it can be seen that with increasing heliocentric distance the amplitude of the outburst also increases. This result is a consequence of the fact that the sublimation activity (sublimation flux) is a decreasing function of the comet’s distance from the Sun. This result is correct assuming that we are considering the same type of ice that is responsible for the sublimation activity.

The flux-nuclear mechanism presented in this paper is an attempt to explain the change in cometary brightness observed during their outbursts. This mechanism concerns outbursts in which sublimation activity contributed to the destruction of the cometary surface layer. The main challenge was to determine the sublimation flux through the porous structure of the cometary nucleus and to take into account the complex interdependence between sublimation activity and the morphology of the cometary surface layers.

5 SUMMARY

The considerations presented in this paper concern a new flux-nuclear mechanism based on which cometary outbursts can be explained. In this mechanism, the key role is played by the relationship between the sublimation flux, which has been described using four relationships, and the physical structure of the cometary nucleus. The equations used to describe the sublimation flux are universal and can be used for any type of cometary ice that is responsible for initiating the outburst. Based on the classical scattering theory, equations describing individual scattering cross-sections were derived. They are related to two phases of cometary activity, such as quiet sublimation and outburst. Additionally, in the outburst phase, the scattering cross-section resulting from the destruction of a fragment of the surface of the cometary nucleus was taken into account. Due to the complex structure of the nucleus, it was assumed that the incident sunlight is scattering on porous agglomerates which in their structure contain primary particles consisting of water ice, organic, and silicate matter. Using the flux-nuclear mechanism and taking into account the above scattering cross-sections, it is possible to determine the efficiency of scattering incident sunlight, i.e. the change in the cometary brightness, that is the amplitude of the outburst.

ACKNOWLEDGEMENTS

I would like to thank the reviewer for his valuable comments that contributed to the improvement of my paper. This paper has been done due to the support the author received from the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge, University of Rzeszów, Poland (RPPK.01.03.00-18-001/10-00).

DATA AVAILABILITY

The data underlying this article will be shared on reasonable request to the corresponding author.

REFERENCES

APPENDIX A: COMETARY OUTBURST POWERED BY SUBLIMATION OF SUPERVOLATILE COMETARY ICES

Based on the cometary outburst mechanism presented in this paper (the flux-nuclear mechanism), the comet brightness change calculations at large heliocentric distances were performed. In these calculations, it was assumed that the outburst of the model comet took place at the heliocentric distance d = 5 au. The sublimation activity was controlled by the sublimation of CO|$_{2}$| ice and CO ice. Other parameters were the same as in the main part of the manuscript. The results of these calculations are shown in Fig. A1.