ofDf is written as
P∼ Eroll r03
ρ ρ0
!−3/Df(1−3/Df)
. (2.36)
2.5 Summary 67 boundary. As compression proceeds, the fractal dimension inside the radius of the initial BCCA cluster becomes three, while the fractal dimension on a smaller scale keeps being two. This means that the initial set up, which is that the fractal dimension on a large scale is three and that on a small scale is two, reproduce the structure of a dust aggregate well in static compression as a consequence. This also supports the compressive strength being determined by BCCA structure on a small scale.
• The static compression in the high-density region (φ&0.1) has been investigated in the silicate case in previous studies (Seizinger et al., 2012). We performed the numerical simulations in the silicate case and confirmed that our results are consistent with those of previous studies in the high density region.
The compressive strength formula allowed us to study how static compression affects the porosity evolution of dust aggregates in protoplanetary disks. In applications to dust compression in protoplanetary disks, we use the compressive strength formula to obtain φ with a given P. Moreover, the obtained compressive strength would be applicable to SPH simulations of dust collisions. This application of the static compression process is important future work. In this work, we did not study shear or tensile strengths, but they are also worth investigating in future work.
Planetesimal formation via flu ff y aggregates
A part of this chapter has been published as Kataoka, A., Tanaka, H., Okuzumi, S.,&Wada, K. 2013b, A&A, 557, L4 (Kataoka et al., 2013b).
Several barriers have been proposed in planetesimal formation theory: bouncing, frmentation, and radial drift problems. Understanding the structure evolution of dust ag-gregates is a key in planetesimal formation. Dust grains become fluffy by coagulation in protoplanetary disks. However, once they are fluffy, they are not sufficiently compressed by collisional compression to form compact planetesimals. We aim to reveal the pathway of dust structure evolution from dust grains to compact planetesimals. Using the compressive strength formula, we analytically investigate how fluffy dust aggregates are compressed by static compression due to ram pressure of the disk gas and self gravity of the aggregates in protoplanetary disks. We reveal the pathway of the porosity evolution from dust grains via fluffy aggregates to form planetesimals, circumventing the barriers in planetesimal for-mation. The aggregates are compressed by the disk gas to a density of 10−3g/cm3in coag-ulation, which is more compact than is the case with collisional compression. Then, they are compressed more by self-gravity to 10−1g/cm3when the radius is 10 km. Although the gas compression decelerates the growth, the aggregates grow rapidly enough to avoid the radial drift barrier when the orbital radius is.6 AU in a typical disk. We propose a fluffy dust growth scenario from grains to planetesimals. It enables icy planetesimal formation in a wide range beyond the snowline in protoplanetary disks. This result proposes a concrete initial condition of planetesimals for the later stages of the planet formation.
70 Planetesimal formation via fluffy aggregates
3.1 Introduction
Planetesimals, the seeds of planets, are believed to form by coagulation of dust grains in pro-toplanetary disks. How micron-sized dust grains grow to kilometer-sized planetesimals has been an unsolved problem in the complete planet formation theory; the intermediate-sized bodies are believed to be poorly sticky (Zsom et al., 2010), easily disrupted by collisions (Blum & Wurm, 2008), or liable to fall quickly onto the central star (Adachi et al., 1976;
Weidenschilling, 1977).
Several possibilities have been proposed to overcome these barriers (Garaud et al., 2013;
Johansen et al., 2007; Lambrechts & Johansen, 2012; Pinilla et al., 2012; Ros & Johansen, 2013; Windmark et al., 2012a). However, there has not yet been any coherent scenario explaining planetesimal formation from dust grains that avoids all of the barriers.
The internal structure evolution is a key to understanding how dust coagulation forms planetesimals. Figure 3.1(a) and (b) show the schematic diagram of the structure evolution previously considered. Dust grains become porous aggregates composed of sub-micron monomer particles by coagulation in protoplanetary disks, as illustrated in Fig.3.1(a) (Blum
& Wurm, 2000; Kempf et al., 1999; Krause & Blum, 2004; Meakin, 1991; Paszun & Do-minik, 2006; Smirnov, 1990). When the dust aggregates become massive, they are gradually compacted or disrupted in dust-dust collisions because of the increase in the impact energy, as illustrated in Fig.3.1(b)(Dominik & Tielens, 1997; Okuzumi et al., 2012; Paszun & Do-minik, 2008, 2009; Suyama et al., 2008, 2012; Wada et al., 2007, 2008, 2009).
Growth via fluffy aggregates has been proposed to be one possible scenario to over-come the barriers in Okuzumi et al. (2012). They have shown that fluffy aggregates rapidly coagulate to avoid the radial drift problem. On the other hand, although the aggregates are compressed by dust-dust collisions, their internal density remainsρ∼10−5g/cm3(Okuzumi et al., 2012; Suyama et al., 2008). This is not consistent with the fact that planetesimals are believed to haveρ∼0.1g/cm3as well as comets, the remnants of planetesimals (A’Hearn, 2011). Therefore other mechanisms to compress the fluffy aggregates are required.
In this paper, we introduce the static compression of aggregates due to ram pressure of the disk gas and self-gravity in protoplanetary disks, as illustrated in Fig.3.1(c) and (d). We use the compressive strength of porous aggregates numerically derived by Kataoka et al.
(2013a) to obtain the porosity (equivalent to the internal density) of dust aggregates. We show how much the dust aggregates are compressed by the disk gas and by self-gravitational compression in their growth. Moreover, we investigate whether the growth is rapid enough to avoid the radial drift barrier by comparing the dust growth and radial drift timescale.
(a) Hit-and-stick
(b) Collisional compression
(c) Gas compression
(d) Self-gravitational compression
gas flow
gravitational force
Fig. 3.1 Schematic drawing to illustrate dust growth via fluffy aggregates. (a) The dust aggregate hits another aggregate to be stick. This reduces dust density and occurs in a very early stage of dust growth. (b) When the collisional speed is high enough to disrupt the dust aggregates, they are compressed. (c) Dust aggregates have a velocity difference against gas, and they feel the ram pressure by the gas. The ram pressure statically compresses the dust aggregates. (d) When the dust aggregates become so massive that they do not support their structure, they are compressed by their own self-gravity.
72 Planetesimal formation via fluffy aggregates