Outer Disk Regions Research Articles

Magnetic fields in protoplanetary discs: from MHD simulations to ALMA observations

Abstract Magnetic fields significantly influence the evolution of protoplanetary discs and the formation of planets, following the predictions of numerous magnetohydrodynamic (MHD) simulations. However, these predictions are yet observationally unconstrained. To validate the predictions on the influence of magnetic fields on protoplanetary discs, we apply 3D radiative transfer simulations of the polarized emission of aligned aspherical dust grains that directly link 3D global non-ideal MHD simulations to Atacama Large Millimeter/submillimeter Array (ALMA) observations. Our simulations show that it is feasible to observe the predicted toroidal large-scale magnetic field structures, not only in the ideal observations but also with high-angular resolution ALMA observations. Our results show further that high-angular resolution observations by ALMA are able to identify vortices embedded in outer magnetized disc regions.

Critical luminosity of Super-Dddington accretion disks

Slim disk is a kind of optically thick, advection dominated accretion flow, in which the disk height can be comparable with the disk radius. The Slim disk has been widely used to explain the observation phenomena of various Super Eddington accretion disks. Outflows are always present in the numerical simulations of Super Eddington accretion disks, which implies that only a small fraction of gas in the disk is finally swallowed by the black hole. In the study of the Slim disk, we adopt an explicit vertical gravitational force in the thermal equilibrium solutions. The results of our calculation show that there is a maximum for the gravitational force of a black hole in the vertical direction of the accretion disk, and there exists a maximally possible accretion rate for each radius in the outer region of the slim disk. The existence of a maximally possible accretion rate in the case of Super-Eddington accretion implies that only the inner region of these flows can possibly take the form of Slim disk, and strong outflows from the outer region are required to reduce the accretion rate in order for Slim disks to be realized. This result is in agreement with the numerical simulation result. Finally, we fit the curve of the disk luminosity L disk/ L Edd with the dimensionless accretion rate m ˙ , and derive an analytic relation between the total luminosity and the mass accretion rate.

The radial dependence of pebble accretion rates: A source of diversity in planetary systems

Context. The classical "planetesimal" accretion scenario for the formation of planets has recently evolved with the idea that "pebbles", centimeter- to meter-sized icy grains migrating in protoplanetary disks, can control planetesimal and/or planetary growth. Aims. We investigate how pebble accretion depends on disk properties and affects the formation of planetary systems Methods. We construct analytical models of pebble accretion onto planetary embryos that consistently account for the mass and orbital evolution of the pebble flow and reflect disk structure. Results. We derive simple formulas for pebble accretion rates in the so-called "settling" regime for planetary embryos with more than 100 km in size. For relatively smaller embryos or in outer disk regions, the accretion mode is 3D, meaning that the thickness of the pebble flow must be taken into account, and resulting in an accretion rate that is independent of the embryo mass. For larger embryos or in inner regions, the accretion is in a 2D mode, i.e., the pebble disk may be considered to be infinitely thin. We show that the radial dependence of the pebble accretion rata is different (even the sign of the power-law exponent changes) for different disk conditions such as the disk heating source (viscous heating or stellar irradiation), the drag law (Stokes or Epstein, and weak or strong coupling), and in the 2D or 3D accretion modes. We also discuss the effect of the sublimation/destruction of icy pebbles inside the snow line. Conclusions. Pebble accretion easily produces a large diversity of planetary systems. In other words, to correctly infer the results of planet formation through pebble accretion, detailed prescriptions of disk evolution and pebble growth, sublimation/destruction and migration are required.

THE OPTICAL VARIABILITY OF SDSS QUASARS FROM MULTI-EPOCH SPECTROSCOPY. II. COLOR VARIATION

ABSTRACT We investigated the optical/ultraviolet (UV) color variations for a sample of 2169 quasars based on multi-epoch spectroscopy in the Sloan Digital Sky Survey data releases seven (DR7) and nine (DR9). To correct the systematic difference between DR7 and DR9 due to the different instrumental setup, we produced a correction spectrum by using a sample of F-stars observed in both DR7 and DR9. The correction spectrum was then applied to quasars when comparing the spectra of DR7 with DR9. In each object, the color variation was explored by comparing the spectral index of the continuum power-law fit on the brightest spectrum with the faintest one, and also by the shape of their difference spectrum. In 1876 quasars with consistent color variations from two methods, we found that most sources (1755, ∼94%) show the bluer-when-brighter (BWB) trend, and the redder-when-brighter (RWB) trend is detected in only 121 objects (∼6%). The common BWB trend is supported by the composite spectrum constructed from bright spectra, which is bluer than that from faint spectra, and also by the blue composite difference spectrum. The correction spectrum is proven to be highly reliable by comparing the composite spectrum from corrected DR9 and original DR7 spectra. Assuming that the optical/UV variability is triggered by fluctuations, the RWB trend can likely be explained if the fluctuations occur first in the outer disk region, and the inner disk region has not yet fully responded when the fluctuations are being propagated inward. In contrast, the common BWB trend implies that the fluctuations likely more often happen first in the inner disk region.

On the water delivery to terrestrial embryos by ice pebble accretion

Standard accretion disk models suggest that the snow line in the solar nebula migrated interior to the Earth's orbit in a late stage of nebula evolution. In this late stage, a significant amount of ice could have been delivered to 1 AU from outer regions in the form of mm to dm-sized pebbles. This raises the question why the present Earth is so depleted of water (with the ocean mass being as small as 0.023% of the Earth mass). Here we quantify the amount of icy pebbles accreted by terrestrial embryos after the migration of the snow line assuming that no mechanism halts the pebble flow in outer disk regions. We use a simplified version of the coagulation equation to calculate the formation and radial inward drift of icy pebbles in a protoplanetary disk. The pebble accretion cross section of an embryo is calculated using analytic expressions presented by recent studies. We find that the final mass and water content of terrestrial embryos strongly depends on the radial extent of the gas disk, the strength of disk turbulence, and the time at which the snow lines arrives at 1 AU. The disk's radial extent sets the lifetime of the pebble flow, while turbulence determines the density of pebbles at the midplane where the embryos reside. We find that the final water content of the embryos falls below 0.023 wt% only if the disk is compact (< 100 AU), turbulence is strong at 1 AU, and the snow line arrives at 1 AU later than 2-4 Myr after disk formation. If the solar nebula extended to 300 AU, initially rocky embryos would have evolved into icy planets of 1-10 Earth masses unless the snow-line migration was slow. If the proto-Earth contained water of ~ 1 wt% as might be suggested by the density deficit of the Earth's outer core, the formation of the proto-Earth was possible with weaker turbulence and with earlier (> 0.5-2 Myr) snow-line migration.

Properties of the outer regions of spiral disks: abundances, colors and ages

AbstractWe summarize the results obtained from our suite of chemical evolution models for spiral disks, computed for different total masses and star formation efficiencies. Once the gas, stars and star formation radial distributions are reproduced, we analyze the Oxygen abundances radial profiles for gas and stars, in addition to stellar averaged ages and global metallicity. We examine scenarios for the potential origin of the apparent flattening of abundance gradients in the outskirts of disk galaxies, in particular the role of molecular gas formation prescriptions.

The atomic gas in outer disks in semi-analytic models of galaxy formation

AbstractWe use semi-analytic models of galaxy formation L-Galaxies based on ΛCDM cosmology to study the HI gas component in galaxy outskirts. We adopt the radially-resolved version of the models by Fu et al. (2013), which includes both atomic and molecular gas component in interstellar medium. This model has been recently updated by Luo et al. (2016) to include cold gas stripping in the outer disk regions of the satellite galaxies by ram pressure. In our models, we can perfectly reproduce the HI size-mass relation, which is discovered by Broeils &amp; Rhee (1997) and confirmed by many subsequent observations. In our model, the reason for such tight correlation between HI size and mass is atomic-molecular phase conversion in high gas surface density regions while HI ionization in low gas surface density region, which leads to very narrow distribution of HI mean surface density. The models also reproduce the universal exponential HI radial profiles in galaxy outskirts found by Bluedisk (Wang et al. 2013), which arises from cold gas accretion onto the galaxy disks in exponentially profiles.

Voracious vortexes in cataclysmic variables

We present multi-epoch, time-resolved optical spectroscopic observations of the dwarf nova HT Cas, which were obtained during 1986, 1992, 1995, and 2005 with the aim of studying the properties of emission structures in the system. We determined that the accretion disc radius, measured from the double-peaked emission-line profiles, is consistently large and lies within the range of 0.45–0.52a, where a is the binary separation. This is close to the tidal truncation radius rmax = 0.52a. However, this result is not consistent with previous radius measurements. An extensive set of Doppler maps reveals a very complex emission structure of the accretion disc. Apart from a ring of disc emission, the tomograms display at least three areas of enhanced emission: the hot spot from the area of interaction between the gas stream and the disc, which is superposed on the elongated spiral structure, and the extended bright region on the leading side of the disc, which is opposite to the location of the hotspot. The position of the hotspot in all the emission lines is consistent with the trajectory of the gas stream. However, the peaks of emission are located in the range of distances 0.22–0.30a, which are much closer to the white dwarf than the disc edge. This suggests that the outer disc regions have a very low density, allowing the gas stream to flow almost freely before it starts to be seen as an emission source. We have found that the extended emission region on the leading side of the disc is always observed at the very edge of the large disc. Observations of other cataclysmic variables, which show a similar emission structure in their tomograms, confirm this conclusion. We propose that the leading side bright region is caused by irradiation of tidally thickened sectors of the outer disc, by the white dwarf and/or hot inner disc regions.

Vertical convection in turbulent accretion disk and light curves of X-ray Nova A0620-00

We describe phenomenon of X-ray Novae in a model of non-stationary accretion α-disk with account for irradiation and vertical convection in outer disk region. We extended the commonly used disk vertical structure model by adding viscous turbulent energy generation in mixing length theory. This model was used to simulate both optical and X-ray light curves of the 1975 outburst of X-ray Nova A0620-00.

Accretion timescales and style of asteroidal differentiation in an 26Al-poor protoplanetary disk

The decay of radioactive 26Al to 26Mg (half-life of 730,000years) is postulated to have been the main energy source promoting asteroidal melting and differentiation in the nascent solar system. High-resolution chronological information provided by the 26Al–26Mg decay system is, therefore, intrinsically linked to the thermal evolution of early-formed planetesimals. In this paper, we explore the timing and style of asteroidal differentiation by combining high-precision Mg isotope measurements of meteorites with thermal evolution models for planetesimals. In detail, we report Mg isotope data for a suite of olivine-rich [Al/Mg∼0] achondritic meteorites, as well as a few chondrites. Main Group, pyroxene and the Zinder pallasites as well as the lodranite all record deficits in the mass-independent component of μ26Mg (μ26Mg∗) relative to chondrites and Earth. This isotope signal is expected for the retarded ingrowth of radiogenic 26Mg∗ in olivine-rich residues produced through partial silicate melting during 26Al decay and consistent with their marginally heavy Mg isotope composition relative to ordinary chondrites, which may reflect the early extraction of isotopically light partial melts from the source rock. We propose that their parent planetesimals started forming within ∼250,000years of solar system formation from a hot (>∼500K) inner protoplanetary disk region characterized by a reduced initial (26Al/27Al)0 abundance (∼1–2×10−5) relative to the (26Al/27Al)0 value in CAIs of 5.25×10−5. This effectively reduced the total heat production and allowed for the preservation of solid residues produced through progressive silicate melting with depth within the planetesimals. These ‘non-carbonaceous’ planetesimals acquired their mass throughout an extended period (>3Myr) of continuous accretion, thereby generating onion-shell structures of incompletely differentiated zones, consisting of olivine-rich residues, overlaid by metachondrites and undifferentiated chondritic crusts. In contrast, individual olivine crystals from Eagle Station pallasites record variable μ26Mg∗ excesses, suggesting that these crystals captured the 26Mg∗ evolution of a magmatic reservoir controlled by fractional crystallization processes during the lifespan of 26Al. Similar to previous suggestions based on isotopic evidence, we suggest that Eagle Station pallasites formed from precursor material similar in composition to carbonaceous chondrites from a cool outer protoplanetary disk region characterized by (26Al/27Al)0⩾2.7×10−5. Protracted planetesimal accretion timescales at large orbital distances, with onset of accretion 0.3–1Myr post-CAIs, may have resulted in significant radiative heat loss and thus efficient early interior cooling of slowly accreting ‘carbonaceous’ planetesimals.

A CONCENTRATION OF CENTIMETER-SIZED GRAINS IN THE OPHIUCHUS IRS 48 DUST TRAP

Azimuthally asymmetric dust distributions observed with ALMA in transition disks have been interpreted as dust traps. We present VLA Ka band (34 GHz or 0.9 cm) and ALMA Cycle 2 Band 9 (680 GHz or 0.45 mm) observations at 0.2" resolution of the Oph IRS 48 disk, which suggest that larger particles could be more azimuthally concentrated than smaller dust grains, assuming an axisymmetric temperature field or optically thin 680 GHz emission. Fitting an intensity model to both data demonstrates that the azimuthal extent of the millimeter emission is 2.3 $\pm0.9$ times as wide as the centimeter emission, marginally consistent with the particle trapping mechanism under the above assumptions. The 34 GHz continuum image also reveals evidence for ionized gas emission from the star. Both the morphology and the spectral index variations are consistent with an increase of large particles in the center of the trap, but uncertainties remain due to the continuum optical depth at 680 GHz. Particle trapping has been proposed in planet formation models to allow dust particles to grow beyond millimeter sizes in the outer regions of protoplanetary disks. The new observations in the Oph IRS 48 disk provide support for the dust trapping mechanism for centimeter-sized grains, although additional data is required for definitive confirmation.

Identification of new transitional disk candidates in Lupus withHerschel

New data from the Herschel Space Observatory are broadening our understanding of the physics and evolution of the outer regions of protoplanetary disks in star forming regions. In particular they prove to be useful to identify transitional disk candidates. The goals of this work are to complement the detections of disks and the identification of transitional disk candidates in the Lupus clouds with data from the Herschel Gould Belt Survey. We extracted photometry at 70, 100, 160, 250, 350 and 500 $\mu$m of all spectroscopically confirmed Class II members previously identified in the Lupus regions and analyzed their updated spectral energy distributions. We have detected 34 young disks in Lupus in at least one Herschel band, from an initial sample of 123 known members in the observed fields. Using the criteria defined in Ribas et al. (2013) we have identified five transitional disk candidates in the region. Three of them are new to the literature. Their PACS-70 $\mu$m fluxes are systematically higher than those of normal T Tauri stars in the same associations, as already found in T Cha and in the transitional disks in the Chamaeleon molecular cloud. Herschel efficiently complements mid-infrared surveys for identifying transitional disk candidates and confirms that these objects seem to have substantially different outer disks than the T Tauri stars in the same molecular clouds.

SU UMa stars: Rebrightenings after superoutburst

Abstract SU UMa stars after their long superoutbursts often show single or multiple rebrightenings. We show how this phenomenon can be understood as repeated reflections of transition waves which mediate changes between the hot and the cool state of the accretion disk and travel back and forth in the outer disk region, leaving an inner part permanently hot. This points to a temporarily increased viscosity, possibly related to the formation of large-scale and longer persisting magnetic fields by the dynamo operation during the long superoutburst. The “mini-rebrightenings” in the early post-outburst light curve of V585 Lyr discovered by Kato and Osaki (2013, PASJ, 65, 97) in Kepler observations seem to be understandable as a small limit cycle of low-luminosity changes originating from a “wiggle” feature in the thermal equilibrium curve of the cool, optically thick disk.

Photodesorption of H2O, HDO, and D2O ice and its impact on fractionation

The HDO/H2O ratio in interstellar gas is often used to draw conclusions on the origin of water in star-forming regions and on Earth. In cold cores and in the outer regions of protoplanetary disks, gas-phase water comes from photodesorption of water ice. We present fitting formulae for implementation in astrochemical models using photodesorption efficiencies for all water ice isotopologues obtained using classical molecular dynamics simulations. We investigate if the gas-phase HDO/H2O ratio reflects that present in the ice or whether fractionation can occur during photodesorption. Probabilities for the top four monolayers are presented for photodesorption of X (X=H,D) atoms, OX radicals, and X2O and HDO molecules following photodissociation of H2O, D2O, and HDO in H2O amorphous ice at temperatures from 10-100 K. Isotope effects are found for all products: (1) H atom photodesorption probabilities from H2O ice are larger than those for D atom photodesorption from D2O ice by a factor of 1.1; the ratio of H and D photodesorbed upon HDO photodissociation is a factor of 2. This process will enrich the ice in deuterium atoms over time; (2) the OD/OH photodesorption ratio upon D2O and H2O photodissociation is on average a factor of 2, but the ratio upon HDO photodissociation is almost constant at unity for all temperatures; (3) D atoms are more effective in kicking out neighbouring water molecules than H atoms. However, the ratio of the photodesorbed HDO and H2O molecules is equal to the HDO/H2O ratio in the ice, therefore, there is no isotope fractionation upon HDO and H2O photodesorption. Nevertheless, the enrichment of the ice in D atoms due to photodesorption can over time lead to an enhanced HDO/H2O ratio in the ice, and, when photodesorbed, also in the gas. The extent to which the ortho/para ratio of H2O can be modified by the photodesorption process is also discussed. (Abridged)

Gaps, rings, and non-axisymmetric structures in protoplanetary disks

Recent observations by the Atacama Large Millimeter/submillimeter Array (ALMA) of disks around young stars revealed distinct asymmetries in the dust continuum emission. In this work we want to study axisymmetric and non-axisymmetric structures, evocated by the magneto-rotational instability in the outer regions of protoplanetary disks. We combine the results of state-of-the-art numerical simulations with post-processing radiative transfer (RT) to generate synthetic maps and predictions for ALMA. We performed non-ideal global 3D MHD stratified simulations of the dead-zone outer edge using the FARGO MHD code PLUTO. The stellar and disk parameters are taken from a parameterized disk model applied for fitting high-angular resolution multi-wavelength observations of circumstellar disks. The 2D temperature and density profiles are calculated consistently from a given surface density profile and Monte-Carlo radiative transfer. The 2D Ohmic resistivity profile is calculated using a dust chemistry model. The magnetic field is a vertical net flux field. The resulting dust reemission provides the basis for the simulation of observations with ALMA. The fiducial model develops a large gap followed by a jump in surface density located at the dead-zone outer edge. The jump in density and pressure is strong enough to stop the radial drift of particles. In addition, we observe the generation of vortices by the Rossby wave instability (RWI) at the jumps location close to 60 AU. The vortices are steadily generated and destroyed at a cycle of 40 local orbits. The RT results and simulated ALMA observations predict the feasibility to observe such large scale structures appearing in magnetized disks without having a planet.

PROTOSTELLAR JETS ENCLOSED BY LOW-VELOCITY OUTFLOWS

A protostellar jet and outflow are calculated for \sim 270 yr following the protostar formation using a three dimensional magnetohydrodynamics simulation, in which both the protostar and its parent cloud are spatially resolved. A high-velocity (\sim100km/s) jet with good collimation is driven near the disk's inner edge, while a low-velocity (<10km/s) outflow with a wide opening angle appears in the outer-disk region. The high-velocity jet propagates into the low-velocity outflow, forming a nested velocity structure in which a narrow high-velocity flow is enclosed by a wide low-velocity flow. The low-velocity outflow is in a nearly steady state, while the high-velocity jet appears intermittently. The time-variability of the jet is related to the episodic accretion from the disk onto the protostar, which is caused by gravitational instability and magnetic effects such as magnetic braking and magnetorotational instability. Although the high-velocity jet has a large kinetic energy, the mass and momentum of the jet are much smaller than those of the low-velocity outflow. A large fraction of the infalling gas is ejected by the low-velocity outflow. Thus, the low-velocity outflow actually has a more significant effect than the high-velocity jet in the very early phase of the star formation.

LONG-TERM EVOLUTION OF PLANET-INDUCED VORTICES IN PROTOPLANETARY DISKS

Recent observations of large-scale asymmetric features in protoplanetary disks suggest that large-scale vortices exist in such disks. Massive planets are known to be able to produce deep gaps in protoplanetary disks. The gap edges could become hydrodynamically unstable to the Rossby wave/vortex instability and form large-scale vortices. In this study we examine the long term evolution of these vortices by carrying out high-resolution two dimensional hydrodynamic simulations that last more than $10^4$ orbits (measured at the planet's orbit). We find that the disk viscosity has a strong influence on both the emergence and lifetime of vortices. In the outer disk region where asymmetric features are observed, our simulation results suggest that the disk viscous $\alpha$ needs to be low $\sim 10^{-5 }$ - $10^{-4}$ to sustain vortices to thousands and up to $10^{4}$ orbits in certain cases. The chance of finding a vortex feature in a disk then decreases with smaller planet orbital radius. For $\alpha \sim 10^{-3}$ or larger, even planets with masses of 5 Jupiter-masses will have difficulty either producing or sustaining vortices. We have also studied the effects of different disk temperatures and planet masses. We discuss the implications of our findings on current and future protoplanetary disk observations.

CO map and steep Kennicutt-Schmidt relation in the extended UV disk of M 63

Results from the UV satellite GALEX revealed large extensions of disks in some nearby spiral galaxies, extending out to 3 to 4 times the isophotal radius, r25. M63 is a remarkable example of a spiral galaxy with one of the most extended UV disks, so it offers the opportunity to search for the molecular gas and characterize the star formation in outer disk regions as revealed by the UV emission. We obtained deep CO(1-0) and CO(2-1) observations on the IRAM 30 m telescope along the major axis of the M63 disk from the center out to the galactocentric radius rgal = 1.6 r25 and over a bright UV region at rgal = 1.36 r25. CO(1-0) is detected all along the M63 major axis out to r25, and CO(2-1) is confined to rgal = 0.68 r25, which may betray lower excitation temperatures in the outer disk. CO(1-0) is also detected in the external bright UV region of M63. The radial profiles of the CO emission and of the Halpha, 24 micron, NUV and FUV star formation tracers and HI taken from the literature show a severe drop with the galactocentric radius, such that beyond r25 they are all absent with the exception of a faint UV emission and HI. The CO emission detection in the external UV region, where the UV flux is higher than the UV flux observed beyond r25, highlights a tight correlation between the CO and UV fluxes, namely the amount of molecular gas and the intensity of star formation. This external UV region is dominated by the atomic gas, suggesting that HI is more likely the precursor of H2 rather than the product of UV photodissociation. A broken power law needs to be invoked to describe the Kennicutt-Schmidt (K-S) relation of M63 from the center of the galaxy out to rgal = 1.36 r25. While all along the major axis out to r25 the K-S relation is almost linear, in the external UV region the SFR regime is highly nonlinear and characterized by a steep K-S relation and very low star formation efficiency.

ROTATIONAL INSTABILITY IN THE OUTER REGION OF PROTOPLANETARY DISKS

We analytically calculate the marginally stable surface density profile for rotational instability of protoplanetary disks. The derived profile can be utilized for considering the region in a rotating disk where radial pressure gradient force is comparable to the gravitational force, such as an inner edge, steep gaps or bumps and an outer region of the disk. In this paper we especially focus on the rotational instability in the outer region of disks. We find an protoplanetary disk with a surface density profile of similarity solution becomes rotationally unstable at a certain radius, depending on its temperature profile and a mass of the central star. If the temperature is relatively low and the mass of the central star is high, disks have rotationally stable similarity profiles. Otherwise, deviation from the similarity profiles of surface density could be observable, using facilities with high sensitivity, such as ALMA.

DISK-LOSS AND DISK-RENEWAL PHASES IN CLASSICAL Be STARS. II. CONTRASTING WITH STABLE AND VARIABLE DISKS

Recent observational and theoretical studies of classical Be stars have established the utility of polarization color diagrams (PCD) in helping to constrain the time-dependent mass decretion rates of these systems. We expand on our pilot observational study of this phenomenon, and report the detailed analysis of a long-term (1989-2004) spectropolarimetric survey of 9 additional classical Be stars, including systems exhibiting evidence of partial disk-loss/disk-growth episodes as well as systems exhibiting long-term stable disks. After carefully characterizing and removing the interstellar polarization along the line of sight to each of these targets, we analyze their intrinsic polarization behavior. We find that many steady-state Be disks pause at the top of the PCD, as predicted by theory. We also observe sharp declines in the Balmer jump polarization for later spectral type, near edge-on steady-state disks, again as recently predicted by theory, likely caused when the base density of the disk is very high, and the outer region of the edge-on disk starts to self absorb a significant number of Balmer jump photons. The intrinsic $V$-band polarization and polarization position angle of $\gamma$ Cas exhibits variations that seem to phase with the orbital period of a known one-armed density structure in this disk, similar to the theoretical predictions of Halonen & Jones. We also observe stochastic jumps in the intrinsic polarization across the Balmer jump of several known Be+sdO systems, and speculate that the thermal inflation of part of the outer region of these disks could be responsible for producing this observational phenomenon. Finally, we estimate the base densities of this sample of stars to be between $\approx 8\times 10^{-11}$ to $\approx 4 \times 10^{-12}\,\rm g cm^{-3}$ during quasi steady state periods given there maximum observed polarization.