TY - JOUR
T1 - The Fragmentation Criteria in Local Vertically Stratified Self-gravitating Disk Simulations
AU - Baehr, Hans
AU - Klahr, Hubert
AU - Kratter, Kaitlin M.
N1 - Publisher Copyright:
© 2017. The American Astronomical Society. All rights reserved..
PY - 2017/10/10
Y1 - 2017/10/10
N2 - Massive circumstellar disks are prone to gravitational instabilities, which trigger the formation of spiral arms that can fragment into bound clumps under the right conditions. Two-dimensional simulations of self-gravitating disks are useful starting points for studying fragmentation because they allow high-resolution simulations of thin disks. However, convergence issues can arise in 2D from various sources. One of these sources is the 2D approximation of self-gravity, which exaggerates the effect of self-gravity on small scales when the potential is not smoothed to account for the assumed vertical extent of the disk. This effect is enhanced by increased resolution, resulting in fragmentation at longer cooling timescales β. If true, it suggests that the 3D simulations of disk fragmentation may not have the same convergence problem and could be used to examine the nature of fragmentation without smoothing self-gravity on scales similar to the disk scale height. To that end, we have carried out local 3D self-gravitating disk simulations with simple β cooling with fixed background irradiation to determine if 3D is necessary to properly describe disk fragmentation. Above a resolution of ∼40 grid cells per scale height, we find that our simulations converge with respect to the cooling timescale. This result converges in agreement with analytic expectations which place a fragmentation boundary at β crit = 3.
AB - Massive circumstellar disks are prone to gravitational instabilities, which trigger the formation of spiral arms that can fragment into bound clumps under the right conditions. Two-dimensional simulations of self-gravitating disks are useful starting points for studying fragmentation because they allow high-resolution simulations of thin disks. However, convergence issues can arise in 2D from various sources. One of these sources is the 2D approximation of self-gravity, which exaggerates the effect of self-gravity on small scales when the potential is not smoothed to account for the assumed vertical extent of the disk. This effect is enhanced by increased resolution, resulting in fragmentation at longer cooling timescales β. If true, it suggests that the 3D simulations of disk fragmentation may not have the same convergence problem and could be used to examine the nature of fragmentation without smoothing self-gravity on scales similar to the disk scale height. To that end, we have carried out local 3D self-gravitating disk simulations with simple β cooling with fixed background irradiation to determine if 3D is necessary to properly describe disk fragmentation. Above a resolution of ∼40 grid cells per scale height, we find that our simulations converge with respect to the cooling timescale. This result converges in agreement with analytic expectations which place a fragmentation boundary at β crit = 3.
KW - hydrodynamics
KW - instabilities
KW - planets and satellites: formation
KW - planets and satellites: gaseous planets
KW - protoplanetary disks
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U2 - 10.3847/1538-4357/aa8a66
DO - 10.3847/1538-4357/aa8a66
M3 - Article
AN - SCOPUS:85032012668
SN - 0004-637X
VL - 848
JO - Astrophysical Journal
JF - Astrophysical Journal
IS - 1
M1 - 40
ER -