Sukalpa Kundu and Jayanta Dutta Harish Chandra ResearchInstitute , Chhatnag Rd , Jhusi , Prayagraj, Uttar PradeshABSTRACT: Recent numerical simulations have shown that the unstable disk within the central regime of the primordial gas cloud fragments form multiple protostars on several scales. Their evolution depends on the mass accretion phenomenon, interaction with the surrounding medium, and radiative feedback, respectively. In this work, we use a fast semi-analytical framework in order to model multiple protostars within a rotating cloud, where the mass accretion is estimated via a Bondi-Hoyle flow and the feedback process is approximated through radiation pressure. We observe that while some of the evolving protostars possibly grow massive (≈1−24M⊙) via accretion and mergers, a fraction of them(≈20%) are likely to be ejected from the parent cloud with a mass corresponding to M∗≲0.8M⊙. These low mass. protostars may be considered as the potential candidates to enter the zero-age-main-sequence (ZAMS)phase and possibly survive till the present epoch.
The phase space diagrams, i.e., the r2 vr plot, where r2 and vr signify the distance and relative radial velocity between the protostars, imply the development of an ordered and bounded state over time. The top panel shows that the first binary pair forms between the protostars p4 and p6, denoted by the p4-p6 pair at r2 10 AU around an epoch t 5 kyr. We observe that the evolution of this p4-p6 pair appears to be terminated at an epoch t 9.6 kyr. This is because the protostar p6 is likely to be merged with protostar p4, which is going to form another binary system with the protostar p1, at a later epoch of time (bottom panel). The second one, i.e., the p1-p4 pair, which tends to build at a distance r2 25 AU around the epoch t 40 kyr, continues to evolve till the end of this simulation. The imprints of the binary formation can also be visualised on the dynamics of the protostars shown in the p5 p1 100 p4 M[M] r[AU] M<0.8M 103 p3 p2
id: e401d4de45866f192b79582771a82ddc - page: 8
Mass and radial distance of the six protostars that are left over (out of the ten at the beginning of our simulation) as a consequence of the merger events, are plotted at the end of our simulation. The scatter diagram shows that three protostars are likely to move away (denoted by red marker) from the potential well of the cloud. It is to be noted that the ejected protostars accommodate two low-mass protostars (Mp2 0.35M and Mp5 0.72M) and another protostar with a slightly higher mass (Mp9 1.44M), respectively. These low-mass protostars may possibly go through the ZAMS phase and hence remain as the probable candidates to survive for a longer period of time. The others (denoted by green markers) seem to remain inside the cloud as high-mass protostars.
id: dc7966a88df6407c1ad9e0a5aef37b7f - page: 8
3 in the previous section 3.2. There we see that the protostar p6 has a similar trajectory with protostar p4 during the period 103 104 yr, indicating the formation of the first binary system. In the same plot, we see that as time progresses, the trajectory of the protostars p4 becomes close to that of the protostar p1 during the epoch 2 104 yr 105 yr. This indicates the development of the second pair between p1 and p4. Additionally, we find wide oscillations in the accretion rate (102 107Myr1) for these protostars (shown in the middle panel of Fig. 3). This is a result of rapid changes in their velocities that are caused by strong interactions.
id: 4bf2cf823d680751b80475ca9a763a91 - page: 8
3.5. Possible ejection of the protostars Following the merging phenomenon, our final snapshot contains nearly six protostars of different masses that are distributed throughout the cloud. The evolution of the mass function of these protostars has already been discussed in the previous section. Here we describe the possible implications of our findings. The scatter diagram in Fig. 6 denotes that three protostars contain an effective radial velocity that exceeds
id: d54bf15d947eba9cf971f70d061d35ac - page: 8