Do tides play a role in the determination of the pre-stellar core mass function?

TL;DR

This work assesses whether tidal forces shape the pre-stellar core mass function by developing a tensorial, anisotropic treatment of tides around a central Larson core. Using the tensor virial theorem, it derives axis-evolution equations for a turbulence-induced density perturbation and introduces a fragmentation-based collapse barrier that accounts for the tidal field’s anisotropy. The study identifies weak and strong tidal regimes, finding that anisotropy largely mitigates tidal impact, with only modest barrier increases in the weak regime and potential disruption when rotation is included in the strong regime. Consequently, tides are unlikely to set the IMF’s characteristic mass, and the authors propose an alternative accretion-radius mechanism around Larson cores to explain the observed IMF peak, with implications for varying galactic environments.

Abstract

Recent studies have examined the role of tides in the star formation process. They suggest, notably, that the tides determine the characteristic mass of the stellar initial mass function (IMF) by preventing the collapse of density fluctuations that would become gravitationally unstable in the absence of the tidal field generated by a neighboring central mass. However, most of these studies consider the tidal collapse condition as a 1D process or use a scalar virial condition and thus neglect the anisotropy of the tidal field and its compressive effects. In the present paper, we consider a turbulence-induced density perturbation formed in the envelope of a central core. This perturbation is subject to a tidal field generated by the central core. We study its evolution taking dynamical effects and the anisotropy of the tides into account. Based on the general tensorial virial equations, we determine a new collapse condition that takes these mechanisms into account. We identify two regimes: (i) a weak tidal regime in which the dynamics of the perturbation is only slightly modified by the action of the tides and (ii) a strong tidal regime in which the density threshold for collapse can potentially be increased due to the combined effects of the tides and the rotational support generated by the tidal synchronization of the perturbation with the orbital motion. In the case of a turbulence-induced density perturbation formed in the vicinity of a first Larson core, we show that the density threshold above which the perturbation collapses is increased only for low-mass perturbations (less than 2.7 solar mass) and only by at most a factor of 1.5. We conclude that tides likely do not play a major role in the process of star formation or in the determination of the characteristic mass of the IMF. We propose an alternative explanation for the observed value of the characteristic mass of the IMF.

Figures (6)

• Figure 1: Schema of the physical situation studied in this paper. When it is discussed in Sect. \ref{['Sec_Tides_env']}, the rotation is oriented parallel to $\vec{e}_y$.
• Figure 2: Evolution of two axes of the ellipsoid for different tidal field strengths and perturbation densities. The tidal field strength is characterized by $\mu_{\rm c} = 5$ (top) and $\mu_{\rm c} = 30$ (bottom). On the left, the initial density of the structure is equal to the critical density, $\rho_{\rm HC}$, computed by Hennebelle_AnalyticalTheoryInitial2008. Thus, the axis does not evolve in the absence of an external tidal field (dotted black line). On the right, the density is given as $\rho = 0.9\rho_{\rm HC} + 0.1\rho_c$. Depending on the strength of the tidal field, the three axes may or may not collapse: if the tidal field is not too strong, the $c$ axis collapses after a period of expansion at the beginning of the evolution.
• Figure 3: Collapsing barrier (blue line) for different tidal field strengths based on the evolution of the triaxial ellipsoid. This barrier is compared with the barrier computed by Hennebelle_AnalyticalTheoryInitial2008 without tides (orange line), the critical density for collapse of the $c$ axis (green line) as in Colman_OriginPeakStellar2020, and the global critical density, $\rho_{\rm SV}$, computed from the scalar virial theorem (dashed black line).
• Figure 4: Same as Fig. \ref{['Fig_Corr_barr']} but for a tidally locked perturbation. In addition to the action of the tides on the dynamics of the perturbation, the rotational support is taken into account.
• Figure 5: Collapsing barrier (blue) for perturbations at the point closest to the Larson core, compared with the barrier in the absence of tides (Eq. \ref{['eq_HC_collapse']}; orange). The sum of the two tidal coefficients is shown by the dashed black line. As seen, small perturbations are indeed in the strong tidal regime, which justifies the need to include the rotational support in the calculations.