Modelling the Break in the Specific Angular Momentum within the Envelope-Disk Transition Zone

Abstract

The observations of protostellar systems show a transition in the radial profile of specific angular momentum (and rotational velocity), evolving from $j\sim{\rm constant}$ ($v_φ\sim r^{-1}$) in the infalling-rotating envelope to $j\propto r^{1/2}$ ($v_φ\sim r^{-1/2}$) in the Keplerian disk. We employ global MHD disk simulations of gravitational collapse starting from a supercritical prestellar core, that forms a disk and envelope structure in a self-consistent manner, in order to determine the physics of the Envelope-Disk Transition Zone (ENDTRANZ). Our numerical results show the transition from the infalling-rotating envelope to Keplerian disk happens through a jump in the $j-r$ profile over a finite radial range, which is characterized by the positive local gravitational torques. The outer edge of the ENDTRANZ is identified where the radial infall speed ($v_r$) begins a sharp decline in magnitude and $j$ begins a transition from $j\sim{\rm constant}$ toward $j\sim r^{1/2}$. Moving radially inward, the centrifugal radius ($r_{\rm CR}$) is defined where $v_φ$ first transitions to Keplerian velocity at the disk's edge. Farther inward of $r_{\rm CR}$, model disk develops a super-Keplerian rotation due to self-gravity. The inner edge of the ENDTRANZ is defined at the centrifugal barrier ($r_{\rm CB}$) where $v_r$ drops to negligible values. Inside $r_{\rm CB}$, a net negative gravitational torque drives mass accretion onto the protostar. On observational grounds, we identify a jump in the observed $j-r$ profile in L1527 IRS for the first time using the ALMA eDisk data. Comparison with the numerical radial behavior from our MHD disk simulations suggests the observed $j-r$ jump can be used as a kinematical tracer for the existence of ENDTRANZ. Our results offer insights into the observable imprint of angular momentum redistribution mechanisms during star-disk formation.

Figures (9)

• Figure 1: Radial profiles of the azimuthally averaged quantities in the equatorial plane obtained from MODEL-2 (from top to bottom): specific angular momentum ($j$), angular velocity ($\Omega$), infall velocity ($v_{r}$), and gas surface density ($\Sigma_{\rm g}$) at different evolutionary times. The evolutionary tracks exhibiting $j \sim r^{1/2}$ represent the evolutionary stages after the disk formation. The respective colored vertical dashed, dash-dotted, and dotted line respectively represent $r_{\rm OTZ}$, $r_{\rm CR}$, and $r_{\rm CB}$, respectively, corresponding to the respective evolutionary times. The colored vertical strips present the EnDTranZ s at the respective timestamps. Each EnDTranZ is bounded by the $r_{\rm OTZ}$ and $r_{\rm CB}$.
• Figure 2: Evolution of the gas surface density ($\Sigma_{\rm g}$, in units of $\log_{10} \, {\rm g \, {cm}^{-2}}$), midplane temperature ($T_{\rm mp}$, in units of $\log_{10} \, {\rm K}$), Toomre-$Q$ parameter, local gravitational torque ($\tau_{\rm grav}$) and local viscous torque ($\tau_{\rm visc}$) in code units (the conversion factor is $=7.79\times 10^{40}\, {\rm dyne\,cm}$), infall speed ($-v_r$ in units of km/s), rotational velocity in units of Keplerian velocity ($v_{\phi}/v_{\rm K}$), and specific angular momentum ($j$ in units of au km/s), shown over a region of $100 \times 100 \, {\rm au}^2$ in the midplane of the disk, showing the large-scale disk structure obtained from MODEL-2 at distinct time instances after the onset of collapse.
• Figure 3: Azimuthally averaged radial profiles of several physical characteristics at two distinct evolutionary times obtained from MODEL-2 (from top to bottom): (a) local gravitational ($\tau_{\rm grav}$) and viscous ($\tau_{\rm visc}$) torque in code units; (b) cumulative (or radially integrated) gravitational ($\mathcal{T}_{\rm grav}$) and viscous ($\mathcal{T}_{\rm visc}$) torque in code units; (c) specific angular momentum ($j$); (d) rotational velocity ($v_{\phi}$) and its mass-weighted value ($v_{{\phi},{\rm m-wt}}$); (e) $Q_{\rm min}$ (defined as the minimum in Toomre-$Q$ across all azimuths at each radius rather than an azimuthally averaged quantity) and mass-weighted Toomre-$Q$ parameter $Q_{\rm {m-wt}}$ along with the azimuthal scatter of Toomre-$Q$ at a given radial distance marked by the blue shaded area; (f) infall speed ($v_r$) are presented. The horizontal black dotted line in the top two panels (a & b) and in the bottom panel (f) present the reference lines for the zero torque and zero infall speed, respectively. The vertical dashed, dash-dotted, and dotted line represent $r_{\rm OTZ}$, $r_{\rm CR}$, and $r_{\rm CB}$, respectively. The pink shaded vertical strip represents the EnDTranZ bounded by $r_{\rm OTZ}$ and $r_{\rm CB}$. The lighter and darker gray shaded regions represent the envelope and the disk interior, respectively.
• Figure 4: Same as in Figure \ref{['fig:torqueanvel_model2']}, but for MODEL-1 (left panel) and MODEL-3 (right panel).
• Figure 5: The azimuthally averaged radial profiles of the gas surface density ($\Sigma_{\rm g}$) and midplane temperature ($T_{\rm mp}$) at a distinct evolutionary time as obtained from MODEL-2. The blue shaded region shows the azimuthal scatter of $T_{\rm mp}$ at a given radius. The vertical dashed, dash-dotted, and dotted line represent $r_{\rm OTZ}$, $r_{\rm CR}$, and $r_{\rm CB}$, respectively. The pink shaded region represents the EnDTranZ. The lighter and darker gray shaded regions represent the envelope and the disk interior, respectively.