## Final Report Summary - EDIT (Evolution of Dust in Turbulent Protoplanetary Disks)

The project is carried out in order to understand how dust particles and in particular aggregate dust particles behave and evolve in turbulent protoplanetary disks (PPD) and how their evolution influences the spectral energy distribution.

Protoplanetary disks (PPDs) are the birthplace of planets like our Earth. In recent years hundreds of planetary systems have been detected, where some planets appear to be in the habitable zone and show best conditions to retain water, a prerequisite for life. So far the formation of planets and planetary systems is not totally understood. It is known that planet formation takes place in PPDs and that dust particles are the basic modules for planet construction. In order to understand the growth of dust particles in to planets, the dynamical behaviour of dust grains in PPRs has to be studied. The dynamical behaviour of dust grains leads to mutual collisions, which result in growth or fragmentation. Due to collisional growth and accretion, particles are likely to be aggregates, i.e. small single grains of core-mantle composition connected together into larger grains in a very open structure. Compared to solid spherical grains of the same mass, aggregates have a much larger geometric cross section, and so they behave differently in a dynamical system because of the influence of gas drag. This is particular true in PPDs where dust growth is expected to be rapid. In this study the dynamical behaviour of aggregate dust particles was studied together with their evolution in PPDs. Furthermore the influence of dust evolution on the spectral energy distribution (SED) was studied.

For the model calculations, T Tauri type disks with typical densities and temperatures are assumed and model calculations to study the aggregates dynamical behaviour are carried out. A first question was if PPDs with dust particles and in particular aggregates dust particles are rather turbulent or laminar. If a disk is turbulent or laminar depends very strongly on the abundance of electrons in the disk, and this electron abundance is dependent on the dust abundance and dust properties. Dr M. Koehler therefore derived the electron abundance in the disk, considering spherical as well as aggregate dust particles. The disk is divided into cells, where each cell has a fixed density and temperature. For each cell the electron abundance is calculated, where Dr M. Koehler considered three different chemical reaction networks and three different ionisation rates.

In order to implement the dust particles in each of these calculations, the first step was to calculate how the dust and gas interact. For this implementation of dust in the chemical network Dr M. Koehler followed the paper by Ilgner and Nelson 2009 and Bai and Goodman 2009. For each type of dust particles, spheres and aggregates, the rate coefficient for the collision of electrons/ions and dust particles collide, for the collision of neutrons and dust particles, for the collision of dust particles and for the desorption process was calculated, which included a detailed derivation of the sticking probability in each case. These processes lead to a charge exchange between dust and gas. Each process is dependent on the dust properties.

Dr M. Koehler then included the rate coefficients in the three different chemical reaction networks. The first network is based on model 4 presented in Ilgner and Nelson 2009. In this case, only H2 and Mg plus their ions, electron and dust particles, with 5 charges, are assumed. This is the most simple network and calculations are very fast. Dr M. Koehler’s results are comparable to the results from Ilgner and Nelson 2009, considering the same ionisation rate as described in their paper. The second network is described as model 7 in lgner and Nelson 2009. This network is based on 174 gaseous species. Dr M. Koehler’s results are again comparable to the results from Ilgner and Nelson 2009, considering the same ionisation rate as described in their paper. The third network is the most complex one. It includes all species and reaction published in the UMIST database (McElroy et al. 2013). As in all other model dust particles with 5 different charges are assumed. Each calculations take a considerable amount of time (about 3-4 weeks).

For each of these chemical reaction networks Dr M. Koehler assumed three different ionisation rates. The first ionisation rate is calculated following Fromang et al. 2002. These calculations include only X-rays and neglect the scattering of X-rays into the disk. The second calculations, following Bai and Goodman 2009, include the scattering of X-rays into the disk and are otherwise similar to the Forming et al. 2002 assumptions. The third calculations are based on the Monte Carlo ionisation code from Bergin and Bethell 2011a, 2011b and Cleeves et al. 2013, who consider not only X-rays but also UV radiation, which is scattered into the disk. Dr M. Koehler calculated the ionisation rates for each model and compare the results. Assuming the scattering process clearly increases the ionisation rate inside the disk.

The ionisation rates for these three model where then implemented into the three chemical reaction networks and the electron abundance was calculated. The electron abundances for each case, that is for each ionisation rate, each chemical reaction network and each dust particles type, were compared. In order to get a first approximation if the disk is turbulent or not, the Reynolds-number and Elsasser numbers were calculated, where for the latter the magnetic field presented in Cleeves et al. 2013 were assumed. In general, it is assumed that disks are rather stable when the Reynolds-number and Elsasser numbers are smaller than around 100, although this limit is rather ambiguous. Dr M. Koehler’s results show, in agreement with Gressel et al. 2014 and Bai 2013, that the main part of the disk is stable. Only at large distances (>300 AU and perhaps in the very upper layers) unstable regions can occur, but this strongly depends on the limit given for the Reynolds-number and Elsasser numbers. In any case, the region of planet formation (<10AU) is clearly stable in the model calculations, which is independent on the chemical reaction model, on the ionisation rate and on the properties of the dust particles.

However, in the scenario of laminar disks, dust settling plays an important role. Dust particles settle from upper regions in the disks, towards the midplance and migrate towards the central star. This process revealed a problem in the PPD evolution, since in this case the disk should lose a lot of dust particles with time, but even older disks show evidence of dust.

With the knowledge that the PPDs are rather stable, Dr M. Koehler carried out model calculations on how aggregates behave in stable disks in comparison to spherical grains. Using the Epstein drag force and the gravitational force, she calculated the settling time for aggregates with different properties, for example different fractal dimensions D and different size and number of constituent grains, and compared these results to the settling time of spheres of the same mass. Her results clearly show, that the settling time of aggregates is longer than for spherical grains. For example, a 1 mm spherical silicate grain at a height of 0.03 AU above the mid plane and 1 AU distance from the star, settles to the mid plane in 300 years, while an aggregate (D=1.8) of the same mass consisting of 0.1 μm size monomers takes around 300 000 years, i.e., about 3 orders of magnitude longer. This simple example clearly illustrates the critical importance of the dust physics in determining the physical structure of PPDs and might help to understand the discrepancies between settling time calculations and observations.

Due to the dust settling, although taking longer than so far assumed, the density of dust particles in the disk decreases, first in the upper layers and then in lower layers. This reduction of dust density was included in the before described calculations of the dynamical state of the disk. The results show that with a decrease in density by a factor of around 100, the disk starts to become turbulent again. This results show that in a later state of the disk evolution, when the settling process of dust grains towards the midplane results in a decrease of dust density in the disk, the disk become turbulent.

In addition to carrying out model calculations to derive the dynamical behaviour of aggregates in the disk, the influence of dust properties, based on evolutionary behaviour, on the spectral energy distribution was studied. It is assumed that the size of dust grains influences the shape of the spectral energy distribution, in particular the slope at longer wavelength. So far, no detailed model calculations were carried out, to prove this assumption. Dr M Koehler carried out model calculations to analyse to what size grains have to grow in order to see a change in the spectral energy distribution. This study was carried out for grains with different material compositions, different grain size distributions and different maximum grain sizes. The spectral energy distribution was calculations for different size distributions, assuming a typical T Tauri-type disk. The maximum grain size, the power-law of the size distribution and the material composition of the grains was varied and the spectral energy distribution was calculated for the different cases. The results show, that when grains are small the slope of the spectral energy distribution at long wavelength is steep, while when grains grow to large grains, the slope is weak. For all grain sizes in between, a change in slope is observed from weak to steep. At what wavelength this change occurs, depends on the size of the largest grain. Observational data were included in the study to see if and at what wavelength the change occurs. This result is of great value for many astrophysical studies, not only to analyse spectral energy distribution of PPDs, but also to denser clouds and cold cores in the interstellar medium.

Protoplanetary disks (PPDs) are the birthplace of planets like our Earth. In recent years hundreds of planetary systems have been detected, where some planets appear to be in the habitable zone and show best conditions to retain water, a prerequisite for life. So far the formation of planets and planetary systems is not totally understood. It is known that planet formation takes place in PPDs and that dust particles are the basic modules for planet construction. In order to understand the growth of dust particles in to planets, the dynamical behaviour of dust grains in PPRs has to be studied. The dynamical behaviour of dust grains leads to mutual collisions, which result in growth or fragmentation. Due to collisional growth and accretion, particles are likely to be aggregates, i.e. small single grains of core-mantle composition connected together into larger grains in a very open structure. Compared to solid spherical grains of the same mass, aggregates have a much larger geometric cross section, and so they behave differently in a dynamical system because of the influence of gas drag. This is particular true in PPDs where dust growth is expected to be rapid. In this study the dynamical behaviour of aggregate dust particles was studied together with their evolution in PPDs. Furthermore the influence of dust evolution on the spectral energy distribution (SED) was studied.

For the model calculations, T Tauri type disks with typical densities and temperatures are assumed and model calculations to study the aggregates dynamical behaviour are carried out. A first question was if PPDs with dust particles and in particular aggregates dust particles are rather turbulent or laminar. If a disk is turbulent or laminar depends very strongly on the abundance of electrons in the disk, and this electron abundance is dependent on the dust abundance and dust properties. Dr M. Koehler therefore derived the electron abundance in the disk, considering spherical as well as aggregate dust particles. The disk is divided into cells, where each cell has a fixed density and temperature. For each cell the electron abundance is calculated, where Dr M. Koehler considered three different chemical reaction networks and three different ionisation rates.

In order to implement the dust particles in each of these calculations, the first step was to calculate how the dust and gas interact. For this implementation of dust in the chemical network Dr M. Koehler followed the paper by Ilgner and Nelson 2009 and Bai and Goodman 2009. For each type of dust particles, spheres and aggregates, the rate coefficient for the collision of electrons/ions and dust particles collide, for the collision of neutrons and dust particles, for the collision of dust particles and for the desorption process was calculated, which included a detailed derivation of the sticking probability in each case. These processes lead to a charge exchange between dust and gas. Each process is dependent on the dust properties.

Dr M. Koehler then included the rate coefficients in the three different chemical reaction networks. The first network is based on model 4 presented in Ilgner and Nelson 2009. In this case, only H2 and Mg plus their ions, electron and dust particles, with 5 charges, are assumed. This is the most simple network and calculations are very fast. Dr M. Koehler’s results are comparable to the results from Ilgner and Nelson 2009, considering the same ionisation rate as described in their paper. The second network is described as model 7 in lgner and Nelson 2009. This network is based on 174 gaseous species. Dr M. Koehler’s results are again comparable to the results from Ilgner and Nelson 2009, considering the same ionisation rate as described in their paper. The third network is the most complex one. It includes all species and reaction published in the UMIST database (McElroy et al. 2013). As in all other model dust particles with 5 different charges are assumed. Each calculations take a considerable amount of time (about 3-4 weeks).

For each of these chemical reaction networks Dr M. Koehler assumed three different ionisation rates. The first ionisation rate is calculated following Fromang et al. 2002. These calculations include only X-rays and neglect the scattering of X-rays into the disk. The second calculations, following Bai and Goodman 2009, include the scattering of X-rays into the disk and are otherwise similar to the Forming et al. 2002 assumptions. The third calculations are based on the Monte Carlo ionisation code from Bergin and Bethell 2011a, 2011b and Cleeves et al. 2013, who consider not only X-rays but also UV radiation, which is scattered into the disk. Dr M. Koehler calculated the ionisation rates for each model and compare the results. Assuming the scattering process clearly increases the ionisation rate inside the disk.

The ionisation rates for these three model where then implemented into the three chemical reaction networks and the electron abundance was calculated. The electron abundances for each case, that is for each ionisation rate, each chemical reaction network and each dust particles type, were compared. In order to get a first approximation if the disk is turbulent or not, the Reynolds-number and Elsasser numbers were calculated, where for the latter the magnetic field presented in Cleeves et al. 2013 were assumed. In general, it is assumed that disks are rather stable when the Reynolds-number and Elsasser numbers are smaller than around 100, although this limit is rather ambiguous. Dr M. Koehler’s results show, in agreement with Gressel et al. 2014 and Bai 2013, that the main part of the disk is stable. Only at large distances (>300 AU and perhaps in the very upper layers) unstable regions can occur, but this strongly depends on the limit given for the Reynolds-number and Elsasser numbers. In any case, the region of planet formation (<10AU) is clearly stable in the model calculations, which is independent on the chemical reaction model, on the ionisation rate and on the properties of the dust particles.

However, in the scenario of laminar disks, dust settling plays an important role. Dust particles settle from upper regions in the disks, towards the midplance and migrate towards the central star. This process revealed a problem in the PPD evolution, since in this case the disk should lose a lot of dust particles with time, but even older disks show evidence of dust.

With the knowledge that the PPDs are rather stable, Dr M. Koehler carried out model calculations on how aggregates behave in stable disks in comparison to spherical grains. Using the Epstein drag force and the gravitational force, she calculated the settling time for aggregates with different properties, for example different fractal dimensions D and different size and number of constituent grains, and compared these results to the settling time of spheres of the same mass. Her results clearly show, that the settling time of aggregates is longer than for spherical grains. For example, a 1 mm spherical silicate grain at a height of 0.03 AU above the mid plane and 1 AU distance from the star, settles to the mid plane in 300 years, while an aggregate (D=1.8) of the same mass consisting of 0.1 μm size monomers takes around 300 000 years, i.e., about 3 orders of magnitude longer. This simple example clearly illustrates the critical importance of the dust physics in determining the physical structure of PPDs and might help to understand the discrepancies between settling time calculations and observations.

Due to the dust settling, although taking longer than so far assumed, the density of dust particles in the disk decreases, first in the upper layers and then in lower layers. This reduction of dust density was included in the before described calculations of the dynamical state of the disk. The results show that with a decrease in density by a factor of around 100, the disk starts to become turbulent again. This results show that in a later state of the disk evolution, when the settling process of dust grains towards the midplane results in a decrease of dust density in the disk, the disk become turbulent.

In addition to carrying out model calculations to derive the dynamical behaviour of aggregates in the disk, the influence of dust properties, based on evolutionary behaviour, on the spectral energy distribution was studied. It is assumed that the size of dust grains influences the shape of the spectral energy distribution, in particular the slope at longer wavelength. So far, no detailed model calculations were carried out, to prove this assumption. Dr M Koehler carried out model calculations to analyse to what size grains have to grow in order to see a change in the spectral energy distribution. This study was carried out for grains with different material compositions, different grain size distributions and different maximum grain sizes. The spectral energy distribution was calculations for different size distributions, assuming a typical T Tauri-type disk. The maximum grain size, the power-law of the size distribution and the material composition of the grains was varied and the spectral energy distribution was calculated for the different cases. The results show, that when grains are small the slope of the spectral energy distribution at long wavelength is steep, while when grains grow to large grains, the slope is weak. For all grain sizes in between, a change in slope is observed from weak to steep. At what wavelength this change occurs, depends on the size of the largest grain. Observational data were included in the study to see if and at what wavelength the change occurs. This result is of great value for many astrophysical studies, not only to analyse spectral energy distribution of PPDs, but also to denser clouds and cold cores in the interstellar medium.