Photophoretic Strength on Chondrules. 1. Modeling

Abstract

Photophoresis is a physical process that transports particles in optical thin parts of protoplanetary disks, especially at the inner edge and at the optically surface. To model the transport and resulting effects in detail, it is necessary to quantify the strength of photophoresis for different particle classes as a fundamental input. Here, we explore photophoresis for a set of chondrules. The composition and surface morphology of these chondrules was measured by X-ray tomography. Based on the three-dimensional models, heat transfer through illuminated chondrules was calculated. The resulting surface temperature map was then used to calculate the photophoretic strength. We found that irregularities in particle shape and variations in composition induce variations in the photophoretic force. These depend on the orientation of a particle with respect to the light source. The variations of the absolute value of the photophoretic force on average over all chondrules is 4.17%. The deviation between the direction of the photophoretic force and illumination is 3.0 • ± 1.5 • . The average photophoretic force can be well approximated and calculated analytically assuming a homogeneous sphere with a volume equivalent mean radius and an effective thermal conductivity. We found an analytic expression for the effective thermal conductivity. The expression depends on the two main phases of a chondrule, and decreases with the amount of fine-grained devitrified, plagioclase-normative mesostasis up to factor of three. For the chondrule sample studied (Bjurböle chondrite), we found a dependence of the photophoretic force on chondrule size.

Photophoresis on particles hotter/colder than the ambient gas in the free molecular flow

“…Below, we describe a homogeneous solid particle by a sphere of radius r 0 . Non-spherical particles can be quantified in the same way (Loesche 2015;Loesche et al 2013) by using the radius of a volume-equivalent sphere, yielding an average force exerted on the particle. Also inhomogeneous particles can be described by the same means as homogeneous spheres (Loesche 2015;Loesche et al 2013).…”

“…20 was solved. We do this by employing COMSOL for a parameter sweep of 63 · 10 6 parameter combinations to obtain the necessary temperature distributions on the particle surface (details can be found in Loesche & Wurm (2012); Loesche et al (2013); Loesche (2015)). The parameters range in the intervals given in Tab.…”

The motion of chondrules and other particles in a protoplanetary disc with temperature fluctuations

“…Photophoretic forces also act on differentially irradiated particles in a gas (Loesche & Husmann 2016;Rohatschek 1995;Beresnev et al 1993). The photophoretic force for bare and dust-mantled chondrules has been calculated by Loesche & Wurm (2012), Loesche et al (2013) and Loesche et al (2014) with the latter two works focused on chondrule motion, covering the case of the chondrule temperature being different from the gas temperature. Here though, after a short equilibration period, the particles and the gas will have nearly the same temperature (T d T g ).…”

“…If particles are initially in a random state of rotation this has influence on the photophoretic strength, as rotation impedes the establishment of the strongest possible temperature gradients across the particle. This has been studied in Loesche et al (2013Loesche et al ( , 2014. However, random rotations damp on timescales of the gas grain friction time, while photophoresis itself only excites rotations around the direction of radiation, which do not exchange the front and back side (van Eymeren & Wurm 2012).…”

Dust photophoretic transport around a T Tauri star: Implications for comets composition

“…The presence of crystals in comets is not the only issue for which photophoresis is supposed to play a role, Teiser and Dodson-Robinson (2013) have proposed that photophoresis could accelerate the giant planets formation and Wurm et al (2013) have investigated the involvement of this effect in the formation of Mercury-like planets and in the metal depletion in chondrites. Detailed theoretical and experimental studies on chondrules photophoretic properties have been also conducted (Wurm et al, 2010;Loesche et al, 2013). Concerning the photophoretic transport itself we have essentially adopted the approach described in Krauss et al (2007) and Moudens et al (2011), as recalled in Sec.…”