Definition at line 21 of file Disk.h.
Definition at line 24 of file Disk.cc.
Definition at line 33 of file Disk.cc.
References disker, IamWorkerProcess(), and KidIdentifier.
Referenced by Rock::SwapDir::allowOptionReconfigure(), and optionObjectSizeParse().
Implemented in Rock::SwapDir, Fs::Ufs::UFSSwapDir, and TestSwapDir.
Definition at line 164 of file Disk.cc.
References Store::Storage::currentSize(), debugs, EBIT_TEST, ENTRY_SPECIAL, flags, StoreEntry::flags, HERE(), index, max_objsize, maxSize(), objectSizeIsAcceptable(), and Store::Disk::Flags::read_only.
Referenced by Fs::Ufs::UFSSwapDir::canStore(), and storeDirSelectSwapDirLeastLoad().
Reimplemented in Rock::SwapDir, and Fs::Ufs::UFSSwapDir.
Definition at line 40 of file Disk.cc.
Implemented in Fs::Ufs::UFSSwapDir, Transients, TestStore, MemStore, Rock::SwapDir, Store::Controller, Store::Disks, and TestSwapDir.
Referenced by Store::Disks::currentCount(), getStats(), and Store::Storage::~Storage().
Referenced by canStore(), Store::Disks::currentSize(), diskFull(), getStats(), storeDirSelectSwapDirLeastLoad(), and Store::Storage::~Storage().
Definition at line 139 of file Disk.cc.
Referenced by Store::Disks::dereference(), and maxSize().
References dumpOptions(), finalizeSwapoutFailure(), finalizeSwapoutSuccess(), getOptionTree(), hasReadableEntry(), parseOptions(), and reconfiguring.
References Store::Storage::currentSize(), DBG_IMPORTANT, debugs, index, max_size, and maxSize().
Referenced by disconnect(), and Fs::Ufs::UFSSwapDir::dump().
Implemented in Transients, MemStore, Fs::Ufs::UFSSwapDir, Rock::SwapDir, Store::Disks, Store::Controller, and TestSwapDir.
Referenced by Store::Disks::evictCached(), and Store::Storage::~Storage().
Referenced by Store::Disks::evictIfFound(), and Store::Storage::~Storage().
Implemented in Fs::Ufs::UFSSwapDir, Rock::SwapDir, and TestSwapDir.
Referenced by disconnect(), and storeSwapOutFileClosed().
Definition at line 258 of file Disk.cc.
References optionObjectSizeDump(), optionObjectSizeParse(), optionReadOnlyDump(), optionReadOnlyParse(), and ConfigOptionVector::options.
Referenced by disconnect(), dumpOptions(), Fs::Ufs::UFSSwapDir::getOptionTree(), Rock::SwapDir::getOptionTree(), and parseOptions().
References StoreInfoStats::Part::capacity, StoreInfoStats::Part::count, Store::Storage::currentCount(), Store::Storage::currentSize(), doReportStat(), maxSize(), StoreInfoStats::Part::size, and StoreInfoStats::swap.
Referenced by Store::Disks::getStats(), and maxSize().
Implemented in Rock::SwapDir, Transients, TestStore, MemStore, Fs::Ufs::UFSSwapDir, Store::Controller, TestSwapDir, and Store::Disks.
Referenced by Store::Disks::init(), and Store::Storage::~Storage().
Definition at line 86 of file Disk.cc.
Referenced by Store::Disks::maintain(), and maxSize().
References Config, max_objsize, SquidConfig::maxObjectSize, maxSize(), min(), and SquidConfig::Store.
Referenced by maxSize(), objectSizeIsAcceptable(), storeDirSelectSwapDirLeastLoad(), Rock::SwapDir::validateOptions(), and Fs::Ufs::UFSStoreState::write().
References DBG_PARSE_NOTE, debugs, max_objsize, maxSize(), and path.
References dereference(), getStats(), maintain(), max_size, maxObjectSize(), minObjectSize(), minSize(), objectSizeIsAcceptable(), reference(), smpAware(), stat(), and Ping::stats.
Referenced by canStore(), Rock::SwapDir::create(), Rock::SwapDir::currentSize(), diskFull(), Fs::Ufs::UFSSwapDir::dump(), getStats(), Rock::SwapDir::ioCompletedNotification(), Fs::Ufs::UFSSwapDir::maintain(), maxObjectSize(), Store::Disks::maxSize(), minSize(), Rock::SwapDir::slotLimitActual(), Fs::Ufs::UFSSwapDir::statfs(), Rock::SwapDir::statfs(), storeDirSelectSwapDirLeastLoad(), and Rock::SwapDir::validateOptions().
References Config, min_objsize, SquidConfig::minObjectSize, and SquidConfig::Store.
Referenced by maxSize(), and objectSizeIsAcceptable().
References Config, SquidConfig::lowWaterMark, maxSize(), and SquidConfig::Swap.
Referenced by Fs::Ufs::UFSSwapDir::maintain(), maxSize(), and Store::Disks::minSize().
References assert, maxObjectSize(), and minObjectSize().
Referenced by canStore(), and maxSize().
Definition at line 382 of file Disk.cc.
References max_objsize, min_objsize, PRId64, and storeAppendPrintf().
Referenced by getOptionTree(), and sizeInBlocks().
Definition at line 347 of file Disk.cc.
References allowOptionReconfigure(), DBG_IMPORTANT, debugs, max_objsize, min_objsize, NULL, path, self_destruct(), size, and strtoll().
Definition at line 340 of file Disk.cc.
References flags, Store::Disk::Flags::read_only, and storeAppendPrintf().
Definition at line 318 of file Disk.cc.
References DBG_PARSE_NOTE, debugs, flags, Store::Disk::Flags::read_only, and xatoi().
References DBG_IMPORTANT, debugs, flags, getOptionTree(), ConfigParser::NextToken(), NULL, ConfigOption::parse(), path, Store::Disk::Flags::read_only, and self_destruct().
Referenced by disconnect(), Rock::SwapDir::parse(), and Rock::SwapDir::reconfigure().
Definition at line 136 of file Disk.cc.
Referenced by maxSize(), and Store::Disks::reference().
References fs, optionObjectSizeDump(), optionObjectSizeParse(), optionReadOnlyDump(), and optionReadOnlyParse().
References RemovalPolicy::_type, doReportStat(), fs, index, path, repl, statfs(), RemovalPolicy::Stats, storeAppendPrintf(), and type().
Referenced by Rock::SwapDir::create(), Fs::Ufs::UFSSwapDir::createDirectory(), Fs::Ufs::UFSSwapDir::doubleCheck(), maxSize(), Fs::Ufs::UFSSwapDir::openTmpSwapLog(), Fs::Ufs::UFSSwapDir::pathIsDirectory(), Store::Disks::stat(), and Fs::Ufs::UFSSwapDir::writeCleanStart().
Definition at line 83 of file Disk.cc.
Referenced by dump_cachedir(), parse_cachedir(), and stat().
Referenced by active(), and configDoConfigure().
Referenced by canStore(), optionReadOnlyDump(), optionReadOnlyParse(), parseOptions(), Fs::Ufs::UFSSwapDir::statfs(), Rock::SwapDir::statfs(), and storeDirSelectSwapDirLeastLoad().
Referenced by Fs::Ufs::UFSSwapDir::addDiskRestore(), Disk(), Fs::Ufs::UFSSwapDir::evictCached(), Fs::Ufs::UFSSwapDir::finalizeSwapoutSuccess(), sizeInBlocks(), and stat().
Referenced by Fs::Ufs::UFSSwapDir::addDiskRestore(), Rock::SwapDir::anchorEntry(), canStore(), Fs::Ufs::UFSSwapDir::closeLog(), Fs::Ufs::UFSSwapDir::closeTmpSwapLog(), Rock::SwapDir::createStoreIO(), Rock::SwapDir::createUpdateIO(), Rock::SwapDir::disconnect(), diskFull(), Rock::SwapDir::evictCached(), Rock::Rebuild::failure(), Rock::Rebuild::freeBadEntry(), Rock::Rebuild::freeSlot(), Rock::SwapDir::ioCompletedNotification(), Rock::Rebuild::loadingSteps(), Rock::Rebuild::loadOneSlot(), Fs::Ufs::UFSSwapDir::logFile(), Rock::SwapDir::noteFreeMapSlice(), Fs::Ufs::UFSSwapDir::openLog(), Rock::SwapDir::openStoreIO(), Fs::Ufs::UFSSwapDir::openTmpSwapLog(), Rock::SwapDir::parse(), Fs::Ufs::UFSSwapDir::replacementAdd(), Fs::Ufs::UFSSwapDir::replacementRemove(), Rock::Rebuild::start(), stat(), storeDirWriteCleanLogs(), Rock::Rebuild::swanSong(), Fs::Ufs::UFSStoreState::UFSStoreState(), Rock::SwapDir::updateAnchored(), and Rock::Rebuild::validationSteps().
Referenced by canStore(), maxObjectSize(), optionObjectSizeDump(), and optionObjectSizeParse().
Referenced by diskFull(), maxSize(), and Rock::SwapDir::parseSize().
Referenced by minObjectSize(), optionObjectSizeDump(), and optionObjectSizeParse().
Referenced by Rock::SwapDir::create(), Fs::Ufs::UFSSwapDir::createSwapSubDirs(), Fs::Ufs::UFSSwapDir::DirClean(), dump_cachedir(), Rock::SwapDir::freeSlotsPath(), Fs::Ufs::UFSSwapDir::fullPath(), Rock::SwapDir::inodeMapPath(), Fs::Ufs::UFSSwapDir::logFile(), Fs::Ufs::UFSSwapDir::maintain(), maxObjectSize(), optionObjectSizeParse(), Rock::SwapDir::parse(), parse_cachedir(), parseOptions(), Rock::SwapDir::parseRateOption(), Rock::SwapDir::parseSize(), Rock::SwapDir::parseSizeOption(), Rock::SwapDir::parseTimeOption(), stat(), Fs::Ufs::UFSSwapDir::statfs(), Fs::Ufs::UFSSwapDir::swapSubDir(), Rock::SwapDir::validateOptions(), Fs::Ufs::UFSSwapDir::verifyCacheDirs(), and ~Disk().
Referenced by Fs::Ufs::UFSSwapDir::dereference(), Rock::SwapDir::dereference(), Rock::SwapDir::ignoreReferences(), Fs::Ufs::UFSSwapDir::maintain(), Rock::SwapDir::parse(), Fs::Ufs::UFSSwapDir::reference(), Rock::SwapDir::reference(), Fs::Ufs::UFSSwapDir::replacementAdd(), Fs::Ufs::UFSSwapDir::replacementRemove(), stat(), Rock::SwapDir::trackReferences(), and Fs::Ufs::UFSSwapDir::writeCleanStart().
Definition at line 94 of file Disk.h.


text:
\section{Introduction} \label{sec:intro}
Understanding the connection between disks around young stars and the planets formed within these environments requires knowledge about a wide range of physical processes, as well as how these processes vary between different stellar systems. One of the key disk properties is the non-thermal, non-Keplerian turbulent motion, which theoretically influences a range of processes ranging from the growth of grains from micron-sizes up to planets \citep[e.g.][]{orm07,bir10} and the orbital evolution of fully-formed planets \citep[e.g.][]{nel04,paa11,fun14} to the chemical \citep{sem11,fur14,xu17} and angular momentum \citep[e.g.][]{lyn74} evolution of the disk.

Efforts to broadly characterize the turbulence among a large sample of young stellar objects have relied on indirect techniques. Assuming that a planet-forming disk evolves through viscous processes, in which angular momentum is transported outwards while mass is transported inwards, leads to a predicted connection between accretion rate, disk mass, disk radius, and time \citep{har98} that can be used to constrain turbulence. In the context of an $\alpha$-disk model of viscosity \citep{sha73}, in which the viscosity ($\nu$) is equal to the product of $\alpha$, the local sound speed ($c_s$), and the gas pressure scale height ($H$), a number of studies have examined various predictions of viscous evolution using samples of $\sim$30-50 sources \citep{ste98,mul17,lod17,raf17,ans18,naj18} and have found a wide range of $\alpha$ values (10$^{-4}$ - 0.1). \citet{mul12} rely on the connection between turbulence and the settling of dust grains \citep[e.g.][]{you07}, and use the average spectral energy distributions of Herbig stars, T-Tauri stars, and brown dwarfs to find that $\alpha\sim10^{-4}$ best reproduces the average emission profile. High resolution continuum imaging of dust structures also provides constraints on non-thermal motion through the sharpness and morphology of both dark gaps and bright rings \citep[e.g.][]{pin16,hua18,dul18}.

Gas motion provides a more direct measure of the turbulence, but observational constraints are limited to small samples. \citet{hug11} studied the disks around HD 163296 and TW Hya, while \citet{gui12} studied the disk around DM Tau. In the ALMA era, TW Hya and HD 163296 have been revisited \citep{fla15,tea16,fla17,fla18,tea18a}, finding upper limits on the turbulence of $\lesssim$5-10\%\ of the local sound speed for gas at distances of $\sim$30 au and larger from the central star. Near-infrared observations, more sensitive to gas within a few au of the central star, have found evidence of non-thermal broadening components comparable to the local sound speed among samples of similar sizes \citep{car04,naj09,dop11,ile14}.

Here we build on our previous efforts to measure turbulence directly from ALMA observations of molecular gas emission lines to include the disks around DM Tau, MWC 480, and V4046 Sgr. While still representing a modest sample, these sources were chosen to cover a range of accretion rates, X-ray luminosities, and far-ultraviolet (FUV) luminosities. This parameter space is particularly relevant for the magneto-rotational instability \citep{bal98}. The MRI relies on the coupling between gas and magnetic field to destabilize a rotating disk to generate the correlated turbulent fluctuations that can transport angular momentum and drive accretion through the disk. The outcome of the MRI, especially the level of turbulence, is sensitive to the level of disk ionization \citep[e.g.][]{sim18}. Therefore, observationally establishing a relation between turbulence and other disk parameters offers important physical insight into the microphysical processes governing disk evolution.

In section 2 we present the ALMA observations of these three systems, and in section~\ref{models} we discuss our framework for modeling the CO emission. We present our finding of weak turbulence around MWC 480 and V4046 Sgr, and non-zero turbulence around DM Tau in section~\ref{sec_results}, while in section~\ref{discussion} we examine the evidence that weak turbulence may be common among planet-forming disks, as well as the physical conditions that influence the difference in the measured level of turbulence between DM Tau and the other systems.

\section{Observations}
ALMA band 6 observations of the disks around DM Tau, MWC 480, and V4046 Sgr were taken as part of project 2016.1.00724.S. These observations were split into short and long baseline components in order to capture the full spatial extent of the CO emission (out to $\sim$6$\arcsec$) at high spatial resolution ($\sim$0$\farcs$3). Observations were taken between December 2016 and July 2017, with baselines ranging from 15 m to 2.6 km (Table~\ref{observing_table}).

The spectral windows were split between a continuum window centered at 232 GHz, and three windows centered on CO(2-1), $^{13}$CO(2-1), and C$^{18}$O(2-1) respectively. This paper focuses on CO(2-1), while future work will consider the isotopologues. For the spectral lines, the correlator was configured for 960 channels, each 61.035 kHz wide ($\sim$80 m s$^{-1}$).  The standard ALMA reduction scripts were used to produce calibrated visibilities. For each set of observations, two rounds of phase self-calibration and one round of amplitude self-calibration was performed, based on the high S/N continuum data with the exception of the short-baseline DM Tau observations where the amplitude self-calibration was excluded. The spectra were binned down by a factor of 2 (0.16 km s$^{-1}$).

Uncertainties in the flux calibration will result in small variations in the flux between the two sets of observations. To remove this effect, we compare the continuum visibilities with baselines $<$200 k$\lambda$ among the two observational epochs. We find that the long baseline observations are 1.06, 1.04, and 0.93 times brighter than the short baselines observations for DM Tau, MWC 480, and V4046 Sgr respectively; the size of the amplitude differences is consistent with that expected from the uncertainty in the ALMA calibration \citep{but12}. These scale factors are applied to the model images before fitting to the long baseline data.

The positional offset of the disk between the two epochs can vary based on e.g. errors in the proper motion correction or errors in the astrometric accuracy of ALMA. We estimate the positional offset between the short and long baselines observations by fitting an elliptical Gaussian to the continuum observations, and apply a phase offset to each epoch to correct the disk center to the phase center. For MWC 480 the positional offsets are 73 mas, -86 mas in RA and Dec for the short baseline data, and 56 mas, -3 mas for the long baseline data. For the DM Tau disk, the offsets in RA and Dec are 230 mas, 3.6 mas for the short baseline data and 230 mas, -2.2 mas for the long baseline data. No significant offset between the short and long-baseline data was found for V4046 Sgr, although for both data sets the center of the disk was offset by 270 mas in RA and 17 mas in Dec from the phase center, which is included in the models. The observed locations of the disks are consistent with the stellar positions now available in the GAIA DR2 database \citep{gaia18}. The amplitude differences between the short and long baselines are unaffected by these positional offsets.

Cleaned images were generated by combining the short and long baseline visibilities. Using natural weighting results in $\sim$0$\farcs$3-0$\farcs$5 beam with an rms of 2-4 mJy/beam per 0.16 km s$^{-1}$ wide channel.

\begin{deluxetable*}{ccccccc}[h]
\tabletypesize{\scriptsize}
\tablewidth{0pt}
\tablecaption{Observing Summary\label{observing_table}}
\tablehead{\colhead{Star} & \colhead{Date} & \colhead{Time on source} & \colhead{Baselines} & \colhead{PWV} & \colhead{Calibrators} & \colhead{Phase Center}}
\startdata
DM Tau & 2016-12-27 & 10 min & 15-459 m & 1.5 mm & J0510+1800 (bandpass, phase), J0423-0120 (flux) & 04:33:48.732781 +18:10:09.67744 \\
DM Tau & 2017-07-05 & 32 min & 21-2647 m & 0.61 mm & J0510+1800 (bandpass, phase), J0423-0120 (flux) & 04:33:48.733234 +18:10:09.66785\\
MWC 480 & 2016-12-27 & 12 min & 15-459 m & 1.65 mm & J0510+1800 (bandpass,flux), J0438+3004 (phase) & 04:58:46.271217 +29:50:36.52973\\
MWC 480 & 2016-10-27 & 39 min & 18-1124 m & 0.77 mm & J0510+1800 (bandpass,flux), J0438+3004 (phase) & 04:58:46.271713 +29:50:36.53469\\
V4046 Sgr & 2017-04-08 & 8 min & 15-390 m & 1.18 mm & Titan (flux), J1924-2914 (bandpass), J1826-2924 (phase) & 18:14:10.468875 -32:47:35.43708 \\
V4046 Sgr & 2017-05-03 & 27 min & 15-1110 m & 0.38 mm & J1924-2914 (flux,bandpass), J1826-2924 (phase) & 18:14:10.468886 -32:47:35.44081\\
\enddata
\end{deluxetable*}

\section{Models\label{models}}
The modeling code used to derive the turbulence has been described previously in \citet{fla15}, \citet{fla17}, and \citet{fla18}, and is based on earlier work by \citet{ros13} and \citet{dar03}. We summarize the relevant equations below, including the key free parameters and the assumptions made for each source.

The surface density is assumed to follow a power law, with an exponential tail, as expected for a viscously evolving disk \citep{lyn74,har98}.
\begin{equation}
\Sigma_{\rm gas}(r) = \frac{M_{\rm gas}(2-\gamma)}{2\pi R^2_c}\left(\frac{r}{R_c}\right)^{-\gamma}\exp\left[-\left(\frac{r}{R_c}\right)^{2-\gamma}\right],
\end{equation}
where $M_{\rm gas}$, $R_c$ and $\gamma$ are the gas mass (in M$_{\odot}$), critical radius (in au) and power law index respectively. The disk extends from $R_{\rm in}$ to 1000 au.

The temperature structure is defined as a power law with radius, with a vertical gradient connecting the cold midplane with the warm atmosphere.
\begin{eqnarray}
T_{\rm mid} & = & T_{\rm mid0}\left(\frac{r}{150\ \rm au}\right)^{q}\\
T_{\rm atm} & = & T_{\rm atm0}\left(\frac{r}{150\ \rm au}\right)^{q}\\
T_{\rm gas}(r,z) & = & \left\{
\begin{array}{ll}
T_{\rm atm} + (T_{\rm mid}-T_{\rm atm})(\cos\frac{\pi z}{2Z_q})^{2} & \mbox{if $z < Z_q$} \\
T_{\rm atm} & \mbox{if $z \ge Z_q$}
\end{array}
\right.\\
Z_q & = & Z_{q0} (r/150\ {\rm au})^{1.3}
\end{eqnarray}
The parameter $Z_q$ is the height above the midplane at which the gas temperature reaches its maximum value. Once the temperature structure and surface density profile have been specified, the hydrostatic equilibrium calculation is performed at each radius to derive the gas volume density at each height above the midplane. The velocity field is assumed to be Keplerian, with corrections for the height above the midplane and the pressure support of the gas, as in \citet{ros13}.

The line profile is a Gaussian whose width is set by the thermal and non-thermal motions. We associate the non-thermal term with turbulence ($\delta v_{\rm turb}$) although we consider other sources of non-Keplerian, non-thermal motion in section~\ref{sec:zonal}. We focus on cases in which the non-thermal term is proportional to the local isothermal sound speed:
\begin{equation}
\Delta V = \sqrt{\left(2k_BT(r,z)/m_{CO}\right)(1+\delta v_{\rm turb}^2)}.
\end{equation}
This parameterization is physically motivated by numerical simulations that predict that the turbulence scales with the local sound speed \citep[e.g.][]{shi14,sim15,flo17}.

One important component in fitting the CO observations is the midplane temperature. As demonstrated in \citet{fla18}, an overestimate of the midplane temperature can lead to an underestimate of the turbulence. The data themselves do not provide strong constraints on the midplane temperature; C$^{18}$O(2-1) has a strong degeneracy between $T_{\rm mid}$ and the CO abundance, while CO(2-1), unlike other systems \citep[e.g.][]{ros13,pin18a,dul19}, does not have enough sight lines at low optical depth that reach to the midplane.

For DM Tau, the value of $T_{\rm mid0}$ is chosen such that CO freeze-out at the midplane ($T_{\rm mid}$=19 K) occurs at 70 au, as predicted by the chemical models of \citet{loo15}. To preserve the location of CO freeze-out while the temperature structure, through the parameter $q$, is varied during the model fitting, the exact value of the $T_{\rm mid0}$ parameter is defined based on the value of $q$ (i.e. $T_{\rm mid0}$=19(70/150)$^{-q}$). For MWC 480, we use the temperature structure derived by \citet{pie07} based on observations of $^{13}$CO, which corresponds to $T_{\rm mid0}$=18.8 K. For the disk around V4046 Sgr, we use a midplane normalization based on a D'Alessio model fitting of the SED, which results in $T_{\rm mid0}$=12 K (C. Qi. private communication). In addition to these fiducial values, we also consider lower $T_{\rm mid0}$ values to examine the effect of a different assumed value of the midplane temperature on the turbulence estimates.

In our initial attempts at fitting the CO emission, we found that the models were unable to simultaneously reproduce the emission at radii $\lesssim$200 au and $\gtrsim$200 au. This likely reflects complexities in the CO freeze-out/desorption process that are not included in our initial model prescription; we implicitly assume that thermal desorption and photo-dissociation set the CO molecular layer, while recent chemical models have shown that non-thermal desorption effects are important around IM Lup \citep{obe15} and TW Hya \citep{tea17}. Similarly, extended cold CO emission has been observed around AS 209 \citep{hua16}, and TW Hya \citep{sch16}. To account for non-thermal desorption of CO, we re-introduce CO to the disk in the region between $N_{H_2}=1.3$ and 4.8 $\times$10$^{21}$ cm$^{-2}$ when $T_{\rm gas}<$20 K, as described in Appendix~\ref{CO_photo_desorption}.

In our fiducial models we allow $T_{\rm atm0}$, $q$, $R_c$, $i$, $\delta v_{\rm turb}$, and $R_{\rm in}$ to vary, along with the systemic velocity of the disk ($v_{\rm sys}$). Table~\ref{fixed_params} lists the fixed parameters for each source. All distances are based on GAIA DR2 parallax measurements \citep{gaia18,lin18}. The position angle of the disk is determined based on initial fitting of the system (PA=154.8$^{\circ}$, 147.8$^{\circ}$, 75.65$^{\circ}$ for DM Tau, MWC 480, and V4046 Sgr respectively), and was kept fixed due to its independence from the other model parameters, while $\gamma$ is always fixed at 1. For the disk around V4046 Sgr, we use the sum of the masses of the two stars to set the Keplerian motion of the disk. The sign on the inclination is adjusted so as to minimize asymmetric residuals (Appendix~\ref{inclination_sign}). Using GAIA DR2 distances \citet{sim19} derive stellar masses for MWC 480 and DM Tau of 2.11$\pm$0.01 M$_{\odot}$ and 0.55$\pm$0.02 M$_{\odot}$ respectively. Utilizing these updated masses will most strongly affect the derived inclination \citep[e.g.][]{cze16} while their affect on turbulence is likely to be small, especially for DM Tau, and will be investigated in more detail in future work.

The posterior distributions for each parameter are estimated using the MCMC routine EMCEE \citep{for13}, based on the Affine-Invariant algorithm originally proposed in \citet{goo10}. The uncertainties in the data are estimated based on the calculated dispersion among baselines of similar distances in line-free channels. Typical MCMC chains consist of 80 walkers and 800 steps, with convergence on the final solution occurring within 300 steps. The first 500 steps are removed as burn-in, after which the median of the posterior distributions varies by $<$1\%. We use linear spacing in all parameters except $R_c$, where we fit $\log(R_c)$. We assume uniform priors that simply restrict parameters to physically realistic values (e.g. $\delta v_{\rm turb}>$0, $T_{\rm atm0}>$0, $R_{\rm in}>0$).

 \begin{deluxetable*}{cccccccc}
\tabletypesize{\scriptsize}
\tablecaption{Fixed Model Parameters\label{fixed_params}}
\tablehead{\colhead{Star} & \colhead{Stellar Mass (M$_{\odot}$)} & \colhead{M$_{\rm gas}$ (M$_{\odot}$)} & \colhead{X$_{\rm CO}$} & \colhead{Distance (pc)} & \colhead{PA} & \colhead{$Z_{q0}$ (au)} & \colhead{$\gamma$}}
\startdata
DM Tau & 0.54 (1) & 0.04 (2,3) & 2$\times$10$^{-5}$ (3) & 144.5 $\pm$ 1.1 (4) & 154.8$^{\circ}$ & 70 & 1\\
MWC 480 & 1.85 (5) & 0.046 (6) & 10$^{-4}$ & 161.1 $\pm$ 2.0 (4) & 147.8$^{\circ}$ & 50 & 1\\
V4046 Sgr & 1.75 (7) & 0.09 (8) & 3$\times$10$^{-6}$ (7) & 72.26 $\pm$ 0.34 (4) & 75.7$^{\circ}$ & 35 & 1\\
\enddata
\tablenotetext{}{References: (1) \citet{sim00}, (2) \citet{and11}, (3) \citet{mcc16}, (4) \citet{lin18,bai18}, (5) \citet{pie07}, (6) This work (7) \citet{ros12},  (8) \citet{ros13b}}
\end{deluxetable*}

\section{Results\label{sec_results}}
\subsection{Non-zero turbulence around DM Tau}
Unlike in the disks around HD 163296 and TW Hya, we find that a non-zero turbulence provides the best fit to the disk around DM Tau, with a 99.7\% confidence interval on the turbulent motion of 0.279$^{+0.005}_{-0.004}$c$_s$ (Table~\ref{results}), corresponding to velocities of 60-80 m s$^{-1}$. Model spectra, and residuals generated from the difference between model and data visibilities, are shown in Figure~\ref{dmtau_results}. Full posterior distributions, along with the progression of the walkers through the chains, are shown in appendix~\ref{pdfs}. The non-zero turbulence model spectrum is well matched to the data, and outside of a persistent unresolved (diameter $<$ 40 au) positive residual at the center, indicating that the model underestimates the data, the channel maps do not show strong residuals. As discussed below, similar central residuals are seen around MWC 480 and V4046 Sgr and may be due to deviations from our simple prescriptions for density and temperature, or a sign of changing CO abundance with radius.

The MCMC modeling indicates that a non-zero turbulence exists at a highly significant level. To verify this conclusion, we perform an additional MCMC run with the turbulence fixed at zero. This results in a model that systematically underestimates the flux of the disk (Figure~\ref{dmtau_results}). Comparing the median models from both trials using the Akaike Information Criterion \citep{aka74} the difference is confirmed, with the zero turbulence model being worse than the non-zero turbulence model at a level that is much greater than 10$\sigma$. We also can confirm the non-zero turbulence by fitting to the un-binned spectra while allowing turbulence to vary. Again we find non-zero turbulence (0.252$^{+0.003}_{-0.004}$c$_s$) confirming our fit to the binned spectrum.

\begin{figure*}
\includegraphics[scale=.4]{imspec_dmtau.eps}
\includegraphics[scale=.28]{resid_dmtau_co21_han.png}
\caption{(Left:) Spectra of the DM Tau CO(2-1) emission (black line) and the model defined by the median of the PDFs (red-dashed line). The blue dotted line indicates a model fit in which turbulence has been fixed at zero, while the rest of the parameters are allowed to vary. The zero-turbulence fit is significantly worse than the non-zero turbulence fit.
(Right:) Channel maps of the data (top row), model with non-zero turbulence (middle row), and the imaged residuals (bottom row). For the data and model frames the black contours mark the 5$\sigma$ (=22mJy/beam$\sim$17\%\ of the peak flux) boundary. In the residual frames, positive (black) contours and negative (red dashed) contours are included at multiples of 5$\sigma$. The bottom left panel includes a 100 au scale bar and the synthesized beam. Here we only show the model with non-zero turbulence, which is able to reproduce nearly all of the CO emission from around DM Tau. \label{dmtau_results}}
\end{figure*}

We find an uncertainty on the turbulence at the $\sim$2\%\ level, but this does not include the systematic uncertainty on the amplitude calibration, which may affect the derived temperature structure, and in turn the turbulent broadening. The 4-7\%\ variation in amplitude measured between the short and long baseline observations of the three systems under study here is consistent with some uncertainty in the flux calibration of these data. To test the robustness of our result in the face of the amplitude calibration uncertainty, we run additional trials in which the model is systematically scaled by $\pm$20\%, simulating a true disk flux that is 20\%\ fainter/brighter than is actually observed. Again we find significant turbulence, with $\delta v_{\rm turb}$=0.300$\pm$0.005c$_s$ for a faint disk and $\delta v_{\rm turb}$=0.257$^{+0.004}_{-0.005}$c$_s$ for a bright disk. These results differ in the gas temperature with $T_{\rm atm0}$=21.26$^{+0.09}_{-0.08}$ K for the faint disk and $T_{\rm atm0}$=28.08$^{+0.15}_{-0.12}$ K for the bright disk, which in turn affects the exact value of the sound speed. This anti-correlation between T$_{\rm atm0}$ and $\delta v_{\rm turb}$ is also seen in the fiducial model posterior distribution (Figure~\ref{dmtau_pdfs}). The range in $\delta v_{\rm turb}$ values between the systematic uncertainty models is larger than in the fiducial model since the amplitude calibration uncertainty allows for a larger range in $T_{\rm atm0}$. The anti-correlation between $\delta v_{\rm turb}$ and $T_{\rm atm0}$ does indicate that uncertainty in the gas temperature structure influence our turbulence constraints.

As discussed earlier, the assumed midplane temperature also influences the final turbulence result. We run an additional MCMC ensemble in which $T_{\rm mid0}$ has been reduced to 11 K, as suggested by observations of N$_2$H$^+$ \citep{qi19}, and lower than employed in the chemical models of \citet{loo15}. Again we find non-zero turbulence, at a level of $\delta v_{\rm turb}$=0.328$\pm$0.004c$_s$. The anti-correlation between midplane temperature and turbulence arises because both influence the strength of the emission at the edges of the emitting regions within a given channel map \citep{fla18}. These regions have low optical depth and probe the gas temperature closer to the midplane; increasing the midplane temperature will increase the intensity of the emission from these edges. At the same time, increasing turbulence will increase the amount of emission that ``bleeds over" from nearby channels, leading to an increase in the optical depth and emission that arises from higher and warmer layers. As a result, a given intensity along the edges of the emission within a specific channel can be achieved with either a cold midplane and strong turbulence, or weaker turbulence and a warmer midplane. When combined with the results from the amplitude calibration trials, the low $T_{\rm mid0}$ trial indicates that systematic uncertainties dominate over statistical uncertainties in our measurement of turbulence. Based on the sample of trials run here, we find $\delta v_{\rm turb}=0.25-0.33$c$_s$, significantly larger than zero, but with a larger uncertainty than indicated by any individual trial.

\begin{figure*}
\center
\includegraphics[scale=.5]{turb_struct_dmtau.png}
\caption{(Left) Turbulence levels as a function of radius in the disk around DM Tau, as derived from CS (\citet{gui12}, wide grey band) and CO (this work, narrow hatched band). For the \citet{gui12} results we show the 3$\sigma$ range, including the uncertainty on both the derived turbulence and the gas temperature (when deriving turbulence as a function of the sound speed), while in the results from this work we include systematic uncertainties. Our results are consistent with the previous measurements, albeit with smaller uncertainties. (Right) Molecular emitting regions for CO (this work) and CS \citep{gui12}. Both molecules are probing similar regions, at one to three pressure scale heights (H) above the midplane. \label{turb_struct_dmtau}}
\end{figure*}

Previous analysis of CS(3-2) and CS(5-4) \citep{gui12} found significant turbulence around DM Tau, at a level of 120 m s$^{-1}$, with CS being used instead of CO because of its larger molecular weight and hence smaller thermal broadening. When including the uncertainty on the turbulence velocity and the temperature structure, this translates to a 3$\sigma$ range of (0.12-0.69)c$_s$, consistent with our measured range of (0.25-0.33)c$_s$ when accounting for systematic uncertainties (Figure~\ref{turb_struct_dmtau}). The higher signal-to-noise and higher spatial resolution ALMA data provide a tighter constraint on the turbulence around DM Tau.

Interpreting these results in the context of theoretical models requires knowledge of the emitting region of the molecular emission. Figure~\ref{turb_struct_dmtau} shows the emitting region of CO derived from our models as well as that of CS from \citet{gui12}; the emission from both molecules arises from between two and three pressure scale heights above the midplane. The emitting regions are at low column densities, where far ultraviolet photons are expected to ionize the disk, making it more susceptible to MRI \citep{per11}. At $\delta v_{\rm turb}=0.25-0.33$c$_s$, the turbulence is at the low end for model predictions from MRI \citep{sim15,sim18}, consistent with gravito-turbulence \citep{for12,shi14,shi16}, and at the high end for the vertical shear instability \citep{ric16,flo17}. Distinguishing between these different models for the source of the turbulence may require a measure of the vertical structure of the turbulence \citep{sim15}, more detailed knowledge of the physical conditions within the outer disk \citep{lyr19,sim18}, or complementary observations of other disk properties that are influenced by the turbulence \citep[e.g. dust settling][]{flo17}

\begin{deluxetable*}{ccccccccc}[h]
\tabletypesize{\scriptsize}
\tablewidth{0pt}
\tablecaption{CO(2-1) Model results\label{results}}
\tablehead{\colhead{Model} & \colhead{q} & \colhead{$\log (R_c (\rm au))$} & \colhead{$\delta v_{\rm turb}$ (c$_s$)} & \colhead{$T_{\rm atm0}$ (K)} & \colhead{$T_{\rm mid0}$ (K)} & \colhead{inclination ($^{\circ}$)}  & \colhead{$R_{\rm in}$ (au)} & \colhead{$v_{\rm sys}$ (km s$^{-1}$)}}
\startdata
\cutinhead{DM Tau}
Fiducal & -0.371$^{+0.003}_{-0.002}$ & 2.444$_{-0.003}^{+0.004}$ & 0.279$^{+0.005}_{-0.004}$  & 24.68$^{+0.11}_{-0.09}$ & 14.3\tablenotemark{a} & 36.0$^{+0.12}_{-0.09}$ & $<$9 & 6.017$\pm0.001$\\
sys=1.2 & -0.344$\pm0.003$ & 2.452$^{+0.003}_{-0.004}$ & 0.257$^{+0.004}_{-0.005}$  & 28.08$^{+0.15}_{-0.12}$ & 14.6\tablenotemark{a} & 36.21$^{+0.12}_{-0.13}$ & $<$9 & 6.018$^{+0.001}_{-0.002}$\\
sys=0.8 & -0.403$^{+0.003}_{-0.002}$ & 2.44$\pm0.01$ & 0.300$\pm0.005$  & 21.26$^{+0.09}_{-0.08}$ & 14.0\tablenotemark{a} & 35.81$^{+0.12}_{-0.13}$ & $<$9 & 6.016$\pm0.001$\\
highres & -0.352$^{+0.001}_{-0.002}$ & 2.440$\pm0.002$ & 0.252$^{+0.003}_{-0.004}$  & 24.92$^{+0.08}_{-0.07}$ & 14.5\tablenotemark{a} & 35.99$^{+0.09}_{-0.08}$ & $<$9 & 6.045$\pm0.001$\\
$\delta v_{\rm turb}$=0 & -0.352$^{+0.004}_{-0.002}$ & 2.456$^{+0.004}_{-0.003}$ & 0\tablenotemark{b} & 27.54$\pm0.09$ & 14.5\tablenotemark{a} & 37.73$^{+0.16}_{-0.11}$ & $<$9 & 6.013$^{+0.002}_{-0.001}$\\
low $T_{\rm mid0}$ & -0.310$^{+0.002}_{-0.003}$ & 2.469$^{+0.004}_{-0.005}$ & 0.328$\pm$0.004 & 25.57$^{+0.09}_{-0.07}$ & 11.0\tablenotemark{c} & 35.86$\pm0.11$ & $<$9 & 6.019$\pm0.001$\\
\cutinhead{MWC 480}
Fiducial & -0.467$\pm0.002$ & 2.161$^{+0.004}_{-0.001}$ & $<$0.12 & 60.3$^{+0.3}_{-0.2}$ & 18.8\tablenotemark{b} & -40.34$^{+0.05}_{-0.06}$ & $<$9 & 5.102$\pm0.001$\\
highres & -0.457$\pm0.002$ & 2.172$^{+0.002}_{-0.001}$ & $<$0.08  & 62.1$\pm0.2$ & 18.8\tablenotemark{b} & -40.37$^{+0.05}_{-0.04}$ & $<$9 & 5.137$\pm0.001$ \\
$\delta v_{\rm turb}$=0 & -0.463$\pm0.002$ & 2.168$^{+0.002}_{-0.003}$ & 0\tablenotemark{b} & 62.3$\pm0.1$ & 18.8\tablenotemark{b} & -40.49$^{+0.06}_{-0.05}$ & $<$9 & 5.102$\pm0.001$ \\
low $T_{\rm mid0}$ & -0.413$^{+0.001}_{-0.003}$ & 2.208$^{+0.004}_{-0.003}$ & $<$0.18 & 70.02$^{+0.36}_{-0.05}$ & 14\tablenotemark{b} & -40.06$\pm0.05$ & $<$9 & 5.141$\pm0.001$ \\
\cutinhead{V4046 Sgr}
Fiducial & -0.565$\pm0.003$ & 1.939$^{+0.004}_{-0.003}$ & $<$0.15 & 27.84$^{+0.13}_{-0.09}$ & 12\tablenotemark{b} & 34.69$^{+0.03}_{-0.04}$ & $<$7 & 2.857$\pm0.001$\\
highres & -0.564$^{+0.003}_{-0.001}$ & 1.939$^{+0.001}_{-0.003}$ & $<$0.12  & 28.26$^{+0.10}_{-0.05}$ & 12\tablenotemark{b} & 34.68$^{+0.02}_{-0.03}$ & $<$7 & 2.8957$^{+0.0005}_{-0.0006}$\\
$\delta v_{\rm turb}$=0 & -0.579$\pm0.002$ & 1.956$^{+0.004}_{-0.003}$ & 0\tablenotemark{b} & 28.80$^{+0.04}_{-0.07}$ & 12\tablenotemark{b} & 34.76$^{+0.04}_{-0.03}$ & $<$7 & 2.857$^{+0.001}_{-0.001}$\\
low $T_{\rm mid0}$ & -0.565$^{+0.002}_{-0.004}$ & 2.078$^{+0.012}_{-0.002}$ & $<$0.18 & 29.27$^{+0.17}_{-0.06}$ & 8\tablenotemark{b} & 34.59$^{+0.05}_{-0.03}$ & $<$6.5 & 2.857$\pm0.001$ \\
\enddata
\tablenotetext{}{{\it sys=1.2}: A trial simulating if the data were systematically 20\%\ brighter than measured, {\it sys=0.8}: A trial simulating if the data were systematically 20\%\ fainter than measured, {\it highres}: A trial fitting to the data at full spectral resolution, rather than the binned spectra used in the fiducial model, {\it v$_{turb}$=0}: A trial in which turbulence is fixed at zero, {\it low $T_{mid0}$}: A trial in which the midplane gas temperature is lower than the fiducial model.}
\tablenotetext{a}{$T_{\rm mid0}=19(70/150)^{-q}$. This forces the midplane temperature to 19 K at 70 au, matching the location of the CO condensation front in the chemical modeling of \citet{loo15}}
\tablenotetext{b}{Held fixed during the fitting process.}
\tablenotetext{c}{$T_{\rm mid0}=14(70/150)^{-q}$. }
\end{deluxetable*}

\subsubsection{Anisotropic vs Isotropic motion\label{sec:zonal}}
Within our models we assume that the non-thermal non-Keplerian component of the motion is isotropic turbulence, but other forms of non-Keplerian motion may exist in protoplanetary disks. Deviations are predicted to be induced by planets \citep{per18,bae18} and recent observational studies have found evidence for deviations from Keplerian motion due to the gravitational influence of unseen planets \citep{pin18,tea18b,tea18c,pin19}. Zonal flows, radial density variations associated with magnetic field concentrations, as well as the vertical shear instability (VSI), arising in part from the change in Keplerian velocity with vertical distance from the midplane, produce corrugated variations in the gas motions on velocity scales that are comparable to the non-thermal non-Keplerian motion observed around DM Tau \citep[e.g.][]{sim14,flo17}. If deviations from Keplerian motion are spread through a large region of the outer disk, and are of a sufficiently high velocity at a sufficiently small spatial scale, they may mimic the appearance of isotropic turbulence.

To test the sensitivity of our data to structured motion, we employ a toy model in which we add a velocity component in the orbital direction that varies as a function of radius:
\begin{equation}
dv_{\phi} = dv\sin\left(\frac{2\pi R}{dR}\right)
\end{equation}
Here $dv$ represents the maximum deviation from Keplerian motion, while $dR$ is the spatial scale of the perturbation. This perturbation is added to a model with parameters ($T_{\rm atm0}$, $R_c$, etc.) based on the DM Tau fiducial model. Visibilities are generated from the model images, and are used to create a cleaned image, using the same procedure as for the data.

In Figure~\ref{zonal_vsi} we show the central velocity channel of three models: (1) large spatial scale and high velocity ($dR$=150 au, $dv$=1.5 km s$^{-1}$), (2) small spatial scale and high velocity ($dR$=70 au, $dv$=1.5 km s$^{-1}$), and (3) large spatial scale and small velocity ($dR$=150 au, $dv$=0.3 km s$^{-1}\sim$c$_s$). Anisotropic motion is easily distinguishable from isotropic turbulence in the large size scale and large velocity model due to the corrugated emission structure but becomes more difficult to detect as the size and velocity scales become smaller. When the distance between the minimum and maximum velocity deviation ($dR$/2) becomes smaller than the beam size ($\sim$40 au for DM Tau) the features are no longer spatially resolved, and blend together into a general broadening of the emission. For small velocity scales the azimuthal perturbations to the image are small enough that they are not resolvable as distinct features. Leveraging the full three-dimensional data cube, rather than a single channel as shown in Fig~\ref{zonal_vsi}, provides greater sensitivity to smaller fluctuations \citep{tea18b,tea18c}, although is still limited by the spatial resolution of the data.

\begin{figure*}
\center
\includegraphics[scale=.33]{chmap_zonal_dr150_dv1p5.png}
\includegraphics[scale=.33]{chmap_zonal_dr70_dv1p5.png}
\includegraphics[scale=.33]{chmap_zonal_dr150_dv0p3.png}
\caption{Simulated images of the central velocity channel for a radial variation in azimuthal velocity. For features with large velocities and large size scales ($dR$=150 au, $dv$ = 1.5 km s$^{-1}$, left panel), the anisotropic motion displays a corrugated pattern in the images. When the size scale of the features is small ($dR$ = 70 au, center panel) the features are unresolved and appear as a general broadening of the image. When the velocity scale of the features is small ($dv$=0.3 km s$^{-1}\sim$c$_s$, right panel) corrugated features can be difficult to detect even though they are spatially resolved. This indicates that it is difficult for us to distinguish isotropic turbulence from anisotropic motion below the sound speed and at size scales below the resolution of the observations. \label{zonal_vsi}}
\end{figure*}

Theoretical models of structured non-Keplerian motion suggest that the radial and velocity scales of typical features are small enough to make them difficult to distinguish from purely isotropic motion in our data. The size scale of these features generally scale with the pressure scale height (H) and for DM Tau our model fits indicate a pressure scale height that reaches 70 au at 500 au from the central star. With a beam size of $\sim$ 40 au, features as large as (5-10)H would be easily resolved. Global non-ideal MHD simulations find that when the net poloidal field is relatively strong (thus driving high accretion rates), the disk tends to form zonal flows of scales\footnote{The cited papers typically discuss the size scale of individual features, e.g. the radial size of a region with higher than Keplerian motion, which corresponds to $dR/2$ in the context of our toy model. In comparing with our sensitivity tests, we quote size scales that are consistent with our definition of $dR$, and hence are typically twice as large as the values mentioned in the cited papers.} of $\sim$2H \citep{bet17,sur18}, while in shearing box simulations, zonal flows are found at a broader range of disk magnetizations, on scales of 4H or beyond and is dependent on the box size \citep{bai14,sim14} and the magnetization of the disk \citep{rio19}. Vertical shear instabilities produce corrugated variations in the gas motion with velocities of 10-20\%\ of the local sound speed and size scales of $\sim$2H \citep{flo17}. At these scales, zonal flows and VSI are difficult to distinguish from isotropic motion in our data, although other factors, such as the efficient lifting of dust grains by VSI \citep{flo17} may break this degeneracy. Planet induced motions are unlikely to be mis-interpreted as turbulence because of the highly localized nature of the perturbation \citep{per18}. In modeling the CO emission from around DM Tau we assume that a single turbulence value, relative to the local sound speed, applies uniformly throughout the disk. The residuals do not show a strong deviation from this assumption, outside of the unresolved emission at the center of the disk. This suggests that instabilities that generate features over a wide radial range within the disk, such as is possible under certain physical conditions with zonal flows and vertical shear instabilities, as well as MRI assuming the surface layers are sufficiently ionized, are consistent with our results around DM Tau.

\subsection{Weak Turbulence around MWC 480 and V4046 Sgr}
For both the disk around MWC 480 and the disk around V4046 Sgr we do not detect significant nonthermal motion of the gas. Figures~\ref{mwc480_results} and ~\ref{v4046_results} show the data as compared to the model defined by the median of the posterior distributions (posterior distributions are shown in Appendix~\ref{pdfs}). For both MWC 480 and V4046 Sgr, the MCMC routine returns a posterior that nominally indicates a detection of turbulence. We run additional trials with turbulence fixed at zero and find that the zero turbulence fit is nearly indistinguishable, in both the spectra and the channel maps, from the non-zero turbulence result, although as discussed below there are still residuals between the best fit models and the data. For this reason we conservatively interpret the results for MWC 480 and V4046 Sgr as upper limits rather than detections.

For MWC 480, we are able to constrain turbulence to $<$0.12c$_s$. Fitting to the un-binned data pushes the limit down to $<$0.08 c$_s$, corresponding to velocities below 20-40 m s$^{-1}$ beyond 100 au. For V4046 Sgr a fit to the binned spectrum constrains turbulence to $<$0.15c$_s$, while a fit to the un-binned spectrum pushes the upper limit down to $<$0.12c$_s$, corresponding to velocities below 30-55 m s$^{-1}$ beyond 100 au. As with DM Tau, we consider models with colder midplane temperatures ($T_{\rm mid0}$ = 14 K for MWC 480, and 8 K for V4046 Sgr) and in both cases the upper limits rise to $<$0.18 c$_s$, but are still consistent with a non-detection of turbulence. This suggests that systematic effects (e.g., the assumed midplane temperature) are significant compared to statistical uncertainties when constraining the turbulence level in these systems.

\begin{figure*}
\includegraphics[scale=.4]{imspec_mwc480.eps}
\includegraphics[scale=.27]{resid_mwc480_co21_han.png}
\caption{(Left:) Spectra of the MWC480 CO(2-1) emission (black line) and the model defined by the median of the PDFs when turbulence is allowed to vary (red dashed line) as well as when turbulence is fixed at zero (blue dotted line).
(Right:) Channel maps of the data (top row), model (middle row), and residuals (bottom row). The contour in the data and model frames is at 5$\sigma$ (=29mJy/beam$\sim$10\%\ of the peak flux), while the contours in the residual frame are at multiples of 5$\sigma$.  \label{mwc480_results}}
\end{figure*}

In the case of both MWC 480 and V4046 Sgr, the imaged residuals show structure (Figure~\ref{mwc480_results}, \ref{v4046_results}), although at a level that is less than 10\%\ of the peak flux. Both systems show an unresolved positive residual at the center of the disk, with a diameter $<$50 au and $<$20 au for MWC 480 and V4046 Sgr respectively, which may be a result of a deviation from simple prescriptions for the temperature and surface density radial profiles, a change in CO abundance with radius \citep[e.g.][]{sch18}, or a change in the velocity profile due to a warp \citep[e.g.][]{wal17} or rapid inward radial flow \citep[e.g.][]{ros14}. Around V4046 Sgr negative residuals extend out to $\sim$200 au, corresponding to the radius beyond which our simple photo-desorption treatment sets the CO abundance. This suggests that a more detailed treatment of photodesorption would bring the model in closer agreement with the data. None of these residuals are indicative of an underestimate of the turbulence level. In the channel maps turbulence acts to broaden emission rather than to change the radial profile \citep{sim15}. Also, the similarity between the model derived when turbulence was fixed at zero versus the model derived when turbulence was allowed to vary supports our interpretation of the model results as an upper limit. We can rule out turbulence levels comparable to that around DM Tau, but cannot completely rule out modest turbulent motions within these systems.

\begin{figure*}
\includegraphics[scale=.4]{imspec_v4046_new.eps}
\includegraphics[scale=.27]{resid_v4046_co21_han.png}
\caption{(Left:) Spectra of the V4046 CO(2-1) emission (black line) and the model defined by the median of the PDFs when turbulence is allowed to vary (red dashed line) as well as when turbulence is fixed at zero (blue dotted line).
(Right:) Channel maps of the data (top row), model (middle row), and residuals (bottom row). The contour in the data and model frames is at 5$\sigma$ (=24mJy/beam$\sim$7\%\ of the peak flux), while the contours in the residual frame are at multiples of 5$\sigma$.  \label{v4046_results}}
\end{figure*}

\section{Discussion\label{discussion}}
\subsection{Is weak turbulence common among planet-forming disks?}
Based on an analysis of CO(2-1) ALMA observations of the disks around DM Tau, MWC 480, and V4046 Sgr we find significant non-zero turbulence around DM Tau, but only upper limits for the disks around MWC 480 and V4046 Sgr, similar to what has been found in the disks around HD 163296 \citep{fla15,fla17} and TW Hya \citep{fla18,tea18a}.

Molecular line emission provides a direct measure of gas motions, but it is not the only tracer of turbulence in the outer disk. Strong turbulence will loft dust grains away from the disk midplane \citep{you07,tun10}, making dust settling an indirect tracer of turbulence, in particular the turbulence at the midplane of the disk. Using the influence of dust settling on the SED, \citet{bon16} find $\alpha\sim(0.1-6.3)\times10^{-3}$ around HD 163296, while \citet{mul12} use the average SEDs of T Tauri stars, Herbig stars, and brown dwarfs and find $\alpha$=10$^{-4}$ is a better fit to the data than $\alpha$=10$^{-2}$, for regions of the disk within $\sim$100 au of the central star. In combining scattered light observations and the SED, \citet{van17} find $\alpha\sim2\times10^{-4}$ around TW Hya. \citet{qi19} find that, in SED fitting and comparison with the N$_2$H$^+$ emission morphology, the disk around V4046 Sgr exhibits more dust settling, and hence has weaker turbulence, than the disk around DM Tau, consistent with our results.

High resolution images of gaps in planet-forming disks have opened up additional probes of turbulence through the effect of turbulence on the appearance of dust and gas gaps. The well defined dust gaps around HL Tau are a sign of substantial dust settling, as expected for $\alpha\sim10^{-4}$ \citep{pin16}. Using hydrodynamic simulations of gas and dust gap formation via gravitational interactions with massive planets, \citet{liu18} find that $\alpha$ increases with radius from $<$10$^{-4}$ to 8$\times10^{-3}$ in the disk around HD 163296, while \citet{oha19} find that the polarization pattern is also consistent with a rise in $\alpha$, although at a factor of ten higher level ($\alpha\lesssim1.5\times10^{-3}$ at 50 au rising to 0.015-0.3 at 90 au). In high resolution ALMA images the disks around AS 209, DoAr 25, Elias 20, and RU Lup \citep{hua18} and HD 169142 \citep{per19} exhibit `double gap' features consistent with clearing by a single planet in a low viscosity disk \citep[$\alpha<10^{-4}$][]{don17}. Overall, while observations are limited to the brightest systems, they suggest that large turbulence is not a frequent occurrence around protoplanetary disks at least in the mid-plane.

In the context of the $\alpha$-disk model, turbulent velocities from molecular line observations can be converted to $\alpha$ via $\alpha\sim$($\delta$v$_{\rm turb}$/c$_s$)$^2$, but caution is needed when comparing to $\alpha$ values derived in different observational studies, as well as $\alpha$ values from numerical simulations. Direct conversion from turbulent velocities to $\alpha$ values results in $\alpha$=0.078$\pm$0.002 for the disk around DM Tau, $\alpha<0.006$ for disk around MWC 480 and $\alpha<$0.01 for the disk around V4046 Sgr. These $\alpha$ values only apply to the localized region where the CO emission arises, which is well above the midplane (e.g. Figure~\ref{turb_struct_dmtau}). Observations of millimeter dust continuum emission will be more sensitive to the turbulence at smaller radii than the gas, since dust emission is often more compact than gas emission \citep[e.g.][]{kas18}, and at the midplane, in part because large grains quickly settle to the midplane and because the scale height of the dust is most sensitive to the turbulence near the midplane \citep{cie07}. If the turbulence varies with vertical height, as is expected for MRI driven turbulence, the local $\alpha$ value will change with height as well. For example, in an MRI simulation at 100 au from \citet{sim15} with an initial gas to magnetic pressure ratio at the midplane of $\beta_0$=10$^5$ and an FUV penetration depth of $\Sigma_{\rm FUV}$=0.01 g cm$^{-2}$ the turbulent velocity varies with height by a factor of $\sim$10 (0.7c$_s$ at 3 pressure scale heights vs. 0.04c$_s$ at the midplane), resulting in a factor of $\sim$100 difference between the local $\alpha$ values ($\alpha$=0.49 at 3 pressure scale heights vs. 0.002 at the midplane). These local $\alpha$ values are distinct still from the density-weighted average of the stress tensor ($\alpha$=0.0026), which is related to the accretion flow through the disk and is weighted more strongly toward the high density midplane. Measurements of the turbulence near the midplane through optically thin molecular line tracers or dust observations, in addition to confirmation that the measured non-thermal motion around DM Tau is due to turbulence and not unresolved structured motion, are needed to fully characterize the $\alpha$-viscosity in these systems.

\begin{deluxetable*}{cccccccc}
\tabletypesize{\scriptsize}
\tablewidth{0pt}
\tablecaption{System properties\label{properties}}
\tablehead{\colhead{Star} & \colhead{$\delta v_{\rm turb}$} & \colhead{M$_{*}$ } & \colhead{M$_{\rm disk}$ } & \colhead{Age} & \colhead{$\dot{M}_{\rm acc}$ } & \colhead{L$_{\rm X-ray}$ } & \colhead{L$_{\rm FUV}$ } \\
\colhead{} & \colhead{} & \colhead{M$_{\odot}$} & \colhead{M$_{\odot}$} & \colhead{Myr} & \colhead{M$_{\odot}$ yr$^{-1}$} & \colhead{L$_{\odot}$} & \colhead{L$_{\odot}$}}
\startdata
HD 163296 & $<$0.05c$_s$ (1) & 2.3 & 0.09 (2)  & 5 & 5$\times$10$^{-7}$ (3) & 10$^{-4}$  (4, 5) & 3.21-5.58 (6)\\
TW Hya & $<$0.08c$_s$ (7) & 0.6 & 0.05 (8) & 10-12 & 2$\times$10$^{-9}$ (9, 10, 11) & 6.8$\times$10$^{-4}$ (12, 13, 14, 15) & 7$\times$10$^{-3}$ (16)\\
MWC 480 & $<$0.08c$_s$ (17) & 1.85 (18) & 0.046 (17) & 7-8 & 5.3$\times$10$^{-7}$ (19, 3, 20) & 2.6$\times$10$^{-6}$ (21) & $\ldots$\\
V4046 Sgr & $<$0.12c$_s$ (17) & 0.9,0.9 & 0.09 (22) & 12-23 (23, 24, 25) & 1.3$\times$10$^{-8}$ (26) & 3.1$\times$10$^{-4}$ (27, 28) & 10$^{-2}$ (16)\\
DM Tau & 0.25-0.33c$_s$ (17) & 0.54 (29) & 0.04 (30,31) & 1-5 & 2.9$\times$10$^{-9}$  (16, 32) & 7.8$\times$10$^{-5}$ (33) & 3$\times$10$^{-3}$ (34, 16)\\
\hline
Typical Disk Ranges& $\ldots$ & $\ldots$ & 3$\times$10$^{-4}$ - 0.03 (35) & 1-10 & 5$\times$10$^{-11}$ - 10$^{-7}$ (36) & 2$\times10^{-6}$ - 0.02 (37) & 2$\times10^{-3}$ - 0.2 (16)\\
\enddata
\tablenotetext{}{References: (1) \citet{fla17} (2) \citet{ise07}, (3) \citet{men13}, (4) \citet{gun09}, (5) \citet{scw05}, (6) \citet{mee12}, (7) \citet{fla18}, (8) \citet{ber13}, (9) \citet{ale02}, (10) \citet{her04}, (11) \citet{ing13}, (12) \citet{bri10}, (13) \citet{dup12}, (14) \citet{kas99}, (15) \citet{kas02}, (16) \citet{fra14}, (17) This work, (18) \citet{pie07} (19) \citet{cos14}, (20) \citet{don11}, (21) \citet{hen10}, (22) \citet{ros13b}, (23) \citet{mam14} (24) \citet{tor06}, (25) \citet{bin14}, (26) \citet{cur11}, (27) \citet{esp13}, (28) \citet{sac12}, (29) \citet{sim00}, (30) \citet{and11}, (31) \citet{mcc16}, (32) \citet{ing11}, (33) Cleeves, private communication, (34) \citet{yan12}, (35) \citet{and13}, (36) \citet{man16}, (37) \citet{fei05}  }
\end{deluxetable*}

\subsection{Physical conditions for turbulence}
Physical conditions within the disk can set the turbulence level and may explain the lack of turbulence among many of the studied sources. In the context of MRI, \cite{sim18} explore the turbulence levels among models with different ionization conditions and magnetic field strengths. They find that the presence of FUV emission drives strong turbulence (0.2c$_s$ - 0.7c$_s$), while the removal of this ionization component, especially when combined with weak magnetic fields, can lead to weak turbulence (0.02c$_s$ - 0.09c$_s$). Among the sources with constraints on turbulence from molecular line emission, DM Tau exhibits the weakest FUV flux (Table~\ref{properties}) despite having the only turbulent disk. X-ray emission can also ionize gas, but again DM Tau does not posses the strongest X-ray emission among our sample. This suggests that FUV and X-ray emission strength alone does not set the turbulence level.

Observations constrain the FUV and X-ray emission near the stellar surface, while the relevant parameter for MRI models is the FUV  and X-ray field as seen by material in the outer disk. High energy radiation can be severely attenuated before reaching the outer disk if intervening material, such as a wind launched by the inner disk, acts as an obscuring screen. TW Hya \citep{pas11}, MWC 480 \citep{fer18}, V4046 Sgr \citep{sac12}, and HD 163296 \citep{kla13} show evidence of a disk wind based on optical/infrared forbidden lines (TW Hya, V4046 Sgr), infrared emission (MWC 480), and extended CO emission (HD 163296). In contrast, the optical forbidden line emission from DM Tau can be explained entirely with a gas disk in Keplerian motion \citep{sim16}. Whether or not a wind is the defining factor between a turbulent and non-turbulent disk depends on the density of the wind, with vertical column densities of 0.01 g cm$^{-2}$ sufficient to absorb a majority of the FUV radiation \citep{per11}.

Regardless of the ionizing source, the ionization level of the outer disk can be constrained based on observations of ionized molecular species. The presence of e.g. DCO$^+$, HCO$^+$, N$_2$H$^+$ in the outer disk of HD 163296 \citep{fla17}, TW Hya \citep{qi13}, DM Tau \citep{dut97,obe11,tea15}, MWC 480 \citep{obe10,hua17} and V4046 Sgr \citep{obe11b,hua17} suggests that some ionizing radiation reaches the outer disk. \citet{obe11} measure an ionization fraction of $\sim$4$\times10^{-10}$ in the CO layer around DM Tau, comparable to the ionization fraction in the models from \citet{sim18} that assumed no FUV photons but still included X-rays and cosmic-rays. A subset of these models displayed vigorous turbulence in the upper disk layers.

\citet{cle17} found that the H$^{13}$CO$^+$ abundance around IM Lup varied in response to an X-ray flare, indicating that the ionization level may change on short timescales. In the presence of variable ionization, MRI will respond with varying turbulence levels on its growth/decay timescale. Since the MRI relies on the differential rotation of gas, its growth/decay timescale is, at its fastest, the dynamical timescale of the gas. Molecular line observations with ALMA probe regions of the disk beyond $\sim$30 au, corresponding to dynamical timescales of hundreds to thousands of year. In their chemical modeling, \citet{cle17} find that the HCO$^+$ abundance would be enhanced for 10-20 days at 100 au following an X-ray flare, much shorter than the time needed for MRI to respond to changes in the ionization, resulting in little variation in turbulence with time. Longer timescale fluctuations in e.g. the wind mass loss rate may still lead to oscillations in the turbulence level over the course of the disk lifetime.

For reasonable values of the magnetic field strength, as informed by theoretical models \citep[e.g.][]{bai11,bai16,sim18}, stronger fields generally result in stronger turbulence, and possibly higher accretion rates. The predicted correlation between turbulence and accretion rate seems to be contradicted in our sample, with DM Tau showing the strongest turbulence at yet the weakest accretion rate. This may be due to the fact that the measured accretion rate is the instantaneous accretion rate onto the star, and does not reflect the accretion rate in the outer disk where the turbulence is measured, or that the turbulence signature does not reflect MRI-generated turbulence but instead reflects other sources of non-thermal motion (e.g., unresolved spatial variations in azimuthal velocity).

Age may also play a factor in the strength of the turbulence by driving the evolution of the physical conditions that set the turbulence level. DM Tau is one of the youngest targets within our sample; as a member of the Taurus star forming region its age likely lies between 1 Myr \citep{luh10} and 5 Myr \citep{sim00,gui14}. Larger turbulence at younger ages is consistent with the findings of \citet{naj18} of large $\alpha$ values among class I objects. But ages of individual objects are difficult to constrain; DM Tau and MWC 480 are both part of the Taurus region, and would be expected to have similar ages, yet MWC 480 is typically assumed to be older than DM Tau \citep{sim00}. Accounting for internal magnetic fields can push stellar ages to systematically higher values \citep{sim19}. Similarly, the lack of turbulence around the class I object HL Tau \citep{pin16} suggests that not all objects of the same age have the same turbulence properties.

In the absence of MRI, other processes may drive turbulence under the right conditions. \citet{for12} find that gravitational instabilities can drive large scale accretion, with the driving source transitioning from large scale spiral arms to gravito-turbulence as the disk mass decreases. The measured disk masses (Table~\ref{properties}) are 4-8\%\ of the stellar mass, resulting in minimum Toomre Q values of 5-15, inconsistent with the presence of gravito-turbulence. \citet{pow19} derive larger disk masses for HD 163296 and TW Hya based on the structure of the dust emission, but they find that even these large masses do not push these disks into the gravitationally unstable regime. The weak levels of turbulence may also open up the possibility of hydrodynamic instabilities, which can produce $\alpha\sim10^{-4}-10^{-3}$, playing a larger role  \citep[e.g. Vertical Shear Instability, Convective Overstability, and Zombie Vortex Instability as reviewed by ][]{lyr19}. The Vertical Shear Instability (VSI) develops due to the change in orbital velocity with vertical height within a disk that has sufficiently rapid cooling \citep{sim14,flo17}, conditions that are likely in the outer disk \citep{lin15}. VSI can operate in a magnetized disk \citep{cui19}, and produces highly anisotropic motion, dominated by vertical motion reaching 10-20\%\ of the local sound speed \citep{flo17}. Such motions can be ruled out for some of the sample HD 163296, TW Hya, MWC 480). Relying on the ability of turbulence to spread dust in the radial direction, \citet{dul18} use the resolved widths of narrow dust rings around AS 209, Elias 24, HD 163296, GW Lup, and HD 143006 to rule out $\alpha\ll$5$\times10^{-4}$ for grain sizes $\gg$0.1 cm, suggesting that some modest level of turbulence may exist in these systems.

\section{Conclusion}
Using new ALMA observations of CO(2-1) emission, we detect turbulence around DM Tau at a level of $\delta v_{\rm turb}=$0.279$^{+0.005}_{-0.004}$c$_s$, although this range extends from 0.25c$_s$ to 0.33c$_s$ when accounting for systematic effects (e.g., assumptions about the midplane temperature). Around MWC 480 and V4046 Sgr we find no strong evidence for non-zero turbulence, restricting the turbulence levels to $<$0.08c$_s$ and $<$0.12c$_s$ respectively. The finding of larger turbulence around DM Tau than around V4046 Sgr is consistent with the enhanced dust settling in the disk around V4046 Sgr relative to the disk around DM Tau \citep{qi19}.

The upper limits on turbulence in the disks around MWC 480 and V4046 Sgr put them at a turbulence level similar to that around HD 163296 \citep{bon16,fla17,liu18,dul18} and TW Hya \citep{van17,fla18,tea18a}. While this is still a modest sample, the results are consistent with studies of high resolution images of continuum emission, sensitive to disk properties closer to the midplane and smaller radii than the CO emission, which found modest turbulence among additional planet-forming systems \citep[$\alpha\sim10^{-4}$,][]{pin16,hua18,per19}, suggesting that weak turbulence may be a common feature among planet-forming disks. At the same time the robust detection of turbulence around DM Tau provides an important anchor point in comparison with models of instabilities within planet-forming disks.

Amongst this small sample we can begin to look for clues as to the explanation for these results. In the context of MRI, the strength of the ionizing radiation reaching the outer disk and the magnetic field are two defining factors \citep[e.g.][]{sim18}. While the FUV and X-ray flux emitted by DM Tau is not large relative to MWC 480, V4046 Sgr, HD 163296, or TW Hya, DM Tau is the only source among this sample that does not show evidence for an inner disk wind that could potentially block the ionizing radiation from reaching the outer disk. The presence of ionized molecular species in all of these systems indicate that some modest level of ionization exists in the outer disk, although the exact ionization level has only been quantified in the case of the disk around DM Tau. Instead the magnetic field strength may be the defining factor in setting the strength of the turbulence. Magnetic field strengths remain largely unconstrained, with observational upper limits \citep[e.g.][]{vle19} still lying above the levels examined by theoretical models. Age also may play a role, given that DM Tau is the youngest source among our sample, although further measurements are needed to determine if this trend holds up.

\acknowledgments
The work of KMF was performed in part at the Aspen Center for Physics, which is supported by the National Science Foundation grant PHY-1607611. A.M.H. is supported by a Cottrell Scholar Award from the Research Corporation for Science Advancement. This paper makes use of the following ALMA data: ADS/JAO.ALMA\#2016.1.00724.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under grant agreement No 716155 (SACCRED).

\vspace{5mm}
\facilities{ALMA}

\software{astropy \citep{astropy}, EMCEE \citep{for13}, MIRIAD}

redpajama_set_name: RedPajamaArXiv


text:
FORAGE SEED
Portulaca Oleracea seeds
Posted February 16, 2018 March 16, 2018 eicegyexport
Name: Portulaca Oleracea seeds / verdolaga
Botanical name: Portulaca Oleracea
What is Portulaca Oleracea / verdolaga?
Portulaca Oleracea is a yearly succulent plant.
It belongs to the genus of Portulacaceae.
It is also called as purslane, verdolaga, little hogweed, and red root.
Its height is about 40 cm.
What is the description of purslane?
The plant of purslane includes a red, soft and prone stems.
Its leaves gathered on the joints and ends of the stem.
It has yellow flowers with width of 6 mm and five regular parts. The flowers bloom when the rain falls. The flowers open individually for a while in the morning sun.
The seeds of purslane are found in a small pod. This pods open after the full maturity of seeds.
Purslane contains secondary fibrous roots enabling it to bear dryness and poor soils.
What are the culinary uses of Portulaca Oleracea / verdolaga?
Due to the distinctive flavor of verdolaga, it is added in making many delicious foods such as soups, salads, stews, meat, and bread.
Its rich content of the nutritional components made it unique in the world of vegetable so that its cultivation spread all over the world.
What are the traditional medical uses of Purslane?
The plant of purslane was a very common alternative remedy in the traditional medicine in China and India.
In China, they used Purslane to treat bites of insect or snake, boils, sores, stings of bee, bacillary dysentery, postpartum bleeding ,hemorrhoids, diarrhea , and intestinal bleeding.
What are the nutritional components of Purslane?
Purslane includes several acids of omega-3 fatty such as alpha-linolenic acid.
It contains 0.01 mg/g of eicosapentaenoic acid (EPA).
It also has a rich content of vitamins including vitamin A, vitamin B, vitamin C, vitamin E, and carotenoids.
Also there are many dietary minerals in Purslane including magnesium, potassium, calcium, and iron.
Many studies has revealed that:
– 100 gram of fresh leaves of purslane includes 300- 400 mg of alpha-linolenic acid.
– And 250 ml of cooked leaves of purslane includes calcium by 90 mg, potassium by 561 mg, and vitamin A by more than 2000 IUs.
What is the history of Portulaca Oleracea?
Ancient Egyptians have known and used Purslane since old ages.
Ancient Greeks have used Purslane and mentioned it in their manuscripts of 600 BC.
Ancient Romans have used Purslane for the treatment of sore eyes, inflammation, dermatitis, headache, dysentery, abdominal pain, and intestinal worms.
What are the healthy benefits of Purslane?
1. Purslane can protect the health of heart. Due to its rich content of omega-3 fatty acids, Pursalne can improve cardiovascular system, protect from cardiovascular diseases, regulate the cholesterol balance in bloodstream, prevent atherosclerosis, and keep the body safe of heart attacks or strokes.
2. Purslane helps to low down the blood pressure due to its content of potassium which made it works a as vasodilator. So it can calm the blood vessels and decrease pressure on the heart.
3. Purslane helps to lose weight. Whereas it is rich in nutritional components and dietary fiber, it contains a low percent of calories. Therefore, a meal of purslane gives the body a sense of satiety without increasing the calories, which helps in reducing weight.
4. Purslane works to enhance the development of children. Many studies have declared that its rich content of omega-3s can prevent some developmental disorders, such as ADHD, autism, and other problems.
5. Purslane can fight against cancer due to its antioxidants elements of vitamin C and vitamin A which can protect from certain types of cancers as lung and oral cancers. Purslane also contains anti-mutagenic compounds of betalain pigment which can protect healthy cells from mutations and limit the growth of cancer cells.
How to plant Purslane?
At first, prepare the ground.
Sow the seeds on the surface of the soil.
Make it appear to light to grow simply.
Irrigate the seeds.
In case you used cuttings of purslane, you have to put them on the ground and irrigate the stem. Then it will lay its roots in soil during few days
More related articles:
Celery seeds
⟵Parsley seeds
Spinach seed⟶
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Stuck with an out-of-date and mundane pool? Maybe your existing swimming pool was set up over 30 years earlier, or is that you are the new owners of a previous pool owner's lack of design. We can work with you to come up with a design concept that will enhance and transform your present swimming pool.
We offer swimming pool remodellings to help you upgrade the out-of-date and ordinary. We are renowned for their capability to innovatively integrate the latest advances in water filtration, heating, resurfacing and lighting technology with quality restoration techniques and design principles.
Our objective is to ensure that our clients get their vision, whether you want to re-surface, re-shape or re-design your pool area, we will come up with a flawless improvement that will perfectly flow with the existing style of your home and landscape.
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Modern resurfacing strategies can be utilized over any existing pool surface, including pebbles, initial fibreglass, vinyl, concrete, tiled or painted swimming pool surface areas. Depending on your budget and the look you wish to attain, we can utilize different strategies to resurface. There is a definite cost advantage in resurfacing your swimming pool.
Fibreglass is popular. It is really smooth, and resistant to stain, but is also really quick to apply. The new Aquaguard ® innovations produce an extremely professional pool resurfacing surface.
Quartzon swimming pools look magnificent– Quartzon contains distinct a reflective aggregate which creates a stunning shimmer to your swimming pool. It is made so it is definitely consistent, and provides a smooth, yet firm surface which is kind to on feet and swimwear.
Aristone is a natural looking, white cement base with fantastic flecks of coloured stone that include shimmer and vibrancy to any pool interior. It is smoother than pebbles and significantly more budget-friendly than tiles, you can select various colours including crisp blues, fresh aquas and extremely brilliant whites.
In essence we build a "new" pool surface over your existing swimming pool. Resurfacing repairs any leaks, rust or osmosis by using a shell over the existing degrade swimming pool surface. It also coats damaged and mouldy swimming pool surface areas and invigorates your existing swimming pools.
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Resurfacing gives the supreme smoothness in your pool. The surface is non-abrasive and there are no sharp edges or rough surfaces compared to concrete or old pebble swimming pools that are abrasive and can damage your skin. It also offers the pool its colourful surface area.
When we re-surface your swimming pool, you can have the swimming pool colour you always wanted, however you can also insert patterns and designs into the surface area coat to match the elegant designs you see in upmarket swimming pools. You are not restricted to a single colour throughout.
The new surface is non-porous,this means that it's extremely resistant to stains, algae and discolouration. And it's also simpler to clean too, the smoother surface permits fast, uncomplicated cleansing.
We are equipped with the skills that will change your existing swimming pool or spa into a brand-new and improved state. We offer a totally free quotation, no obligation service so that you can discuss with all of us of your pool and spa|health spa remodelling, refinishing or restorative ideas and aspirations.
With professional recommendations, we promise a transformation you will like with our swimming pool designs and guidance, your old swimming pool will be unrecognisable and as good as brand-new!
A pool remodelling is the perfect method to re-vamp the appearance of your yard, and you can accomplish excellent outcomes with our renovations services. It can be as simple as giving your swimming pool or spa a remodeling with a brand-new swimming pool surface or pool paint job.
We can service your swimming pool, so for strong suggestions on how to enhance the feel and look of your pool, call us for refreshing concepts and a complimentary quote, we assure to give you a lot of alternatives in a service that will fit all of your swimming pool and spa remodeling needs.
Recently, pool tiling has ended up being the sought-after alternative, with an explosion of high quality, low expense immersible tiles which offer remarkable choice for the homeowner.
Gone are the days where a tiled pool was expensive, today, there's a brilliant series of swimming pool tiling choices which are all designed to survive the extreme sun and consistent immersion.
We can refurbish your swimming pool to look absolutely new, with modern swimming pool tiles made from mosaics, glass and hardened ceramics. We can use ornamental natural stone and travertine around the swimming pool surrounds, and develop impressive murals on the pool flooring and walls which add thousands of dollars in value.
Pool tiling has changed, however we haven't. We have the skills to transform your swimming pool or spa into a jubilant addition to your lifestyle, rupturing with style and colour, and much, much safer than the rough edges of the past. Gone are the days of slips and damaged swimming pool tiles.
Luxapool provides two distinct formulas to guarantee the best outcome is enabled and in order to establish the most ideal product for you we have provided the LuxaPool brochure. Here you are able to visualize the variety of colours you are able to pick from!
You will find that the current trends in colours are optional and this develops a perfect opportunity to modernise your pool or spa. Our group are also able to assist, we rely on our comprehensive experience to provide ideas and assist you in picking the best swimming pool products for your refurbished swimming pool or spa.


We're back with the last installment of our Seattle City Council primary election series. Here's a quick look at who's running in Districts 6 and 7.
Missed part one and two? Read them here and here.
Neighborhood activist, professional planner and designer, and 2013 mayoral candidate who also launched a campaign to save the viaduct and turn it into a High Line-style aerial park; after seismic studies concluded that the proposal would be unsafe, it was scaled back to an initiative—that was ultimately unsuccessful--to build an aerial park that would include a preserved section of the viaduct.
Current Navy intelligence officer and TV news analyst whose platform includes hiring more police officers, implementing "good government" strategies, and better growth management. Jamali, who lives in Queen Anne, also opposes supervised drug consumption sites.
A Queen Anne resident and former Garfield High School student who is currently suing the Seattle Police Department for allegedly mishandling a police report she filed about an assault she experienced on Capitol Hill. She's promoting the use of shipping containers as a solution to homelessness.
Editor's Note: This article has been updated since publication.


Lisa Chauvet is a Research Fellow at the Institut de recherche pour le développement (IRD). She is based in Paris in the research centre DIAL. Her research primarily focuses on foreign aid, international financing and the economics of civil war. She has published in Economic Policy, Journal of Development Studies, Review of Development Economics and other academic journals. She received her PhD in Economics from the University of Clermont-Ferrand in 2003.


text:
Q: What's the difference between individual account SSH keys and team SSH keys in Bitbucket settings Our team has two entities on Bitbucket, the Freelensia.com "individual" account and the Freelensors "team".

Each of them has an "SSH keys" section, for example the individual account SSH keys are below:

For the Freelensors team, we currently have no SSH keys.
We understand that the individual SSH keys enable that particular user to push codes to bitbucket. Meaning that whenever Bitbucket sees this key coming in, it will automatically associate it with the individual and validate his permissions.
But how do SSH keys for teams work? Especially when we have multiple groups within a team with different access rights. Does Bitbucket automatically assume that whoever is using a key inside team SSH keys is an administrator?
We looked up The Teams page of Bitbucket but there is no mention how SSH keys work. https://confluence.atlassian.com/bitbucket/teams-321853005.html

A: The ssh key is not used only for authorizing access to that account, but also to uniquely identify the connecting user, which is a reason why it can not have the key assigned to multiple users.
But the keys do not need to be used only for publishing code, but might be used also for reading the code by some services (CI/CD) if the code is in private repository.
In that case, it is useful to have some keys with read-only access given to the team that can access all the projects under the team

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text:
You are here: Home › NCAA Football › Florida State University
Archive | Florida State University
Florida State University Announces Unconquered Campaign
By Football Stadium Digest Editors on September 4, 2018 in Florida State University, NCAA Football
Florida State University has announced the Unconquered Campaign, a $100 million fundraising effort for a new football operations building and other athletics initiatives. (more…)
The Back Porch to Debut at Doak Campbell Stadium
By Football Stadium Digest Editors on August 1, 2018 in Florida State University, NCAA Football
Florida State is adding the Back Porch to Doak Campbell Stadium, an addition that should offer a new aspect of the fan experience in 2018. (more…)
FSU Unveils Doak Campbell Stadium Videoboards
By Football Stadium Digest Editors on March 25, 2016 in Florida State University
Fans should be dazzled this fall by the new Doak Campbell Stadium videoboards videoboards, as Florida State University unveiled plans for 9,368 square feet of LED video displays, set to be running for the Sept. 10 season opener. (more…)
FSU Begins Champions Club Addition
By Zach Spedden on January 6, 2016 in Florida State University, NCAA Football
Work has begun on the Champions Club addition to Doak Campbell Stadium, a state-of-the art space that will provide new premium and private seating options, improved concourses, and upgraded video and game day production features. (more…)


Phycology Section, Patrick Center for Environmental Research, Academy of Natural Sciences of Drexel University. Eunotia suecica (NADED 33160). https://diatom.ansp.org/taxaservice/ShowTaxon1.ashx?naded_id=33160. Accessed 20 Apr 2019. This web service reports all information about a given algae taxon available at the time of retrieval.


This years marks the 100th anniversary of the Chimacum Grange, a non-profit volunteer organization that has served our rural community for a century by offering opportunities for education, entertainment and connection. A handful of committed "Grange Revivalists" have been working hard this last year to give this beloved community resource the tools and financial resources she needs to prosper in the next century.
We are celebrating with a Pancake Feed on September 16th, Farm Tour Weekend, and we would love your support! The Pancake Breakfast will feature a delicious menu of locally grown and produced foods, live music by Wild Bill and the Buffalo Gals, and a raffle for local food boxes. We hope to sell between 200-300 advance tickets.
We are asking local businesses and organizations to participate by becoming sponsors with "$100 for 100 Years" sponsorships. Your $100 sponsorship will be recognized in the event promotions and marketing being done by the Grange (website, posters, announcements, Facebook). WSU Farm Tour and Thunderbull Productions will also be marketing this event. All funds will go to support Grange operations.
We will be designing posters soon, so don't delay. If you can help us out, email us your logo and you can pay online below. Tell us if you would rather we mail you an invoice so you can pay by check.
We believe the Grange can continue to play an important role in our rural community and we hope you'll join us — with a sponsorship and by attending the breakfast! We are so appreciative of your support. Tickets for this event go on sale to the public on August 8th. Tell us if you would like us to set aside any tickets for you before then ($12 adults, $7 kids 10 and under). We expect this to sell out.


Duty Awaits: YJ06YRZ, one of three vehicles painted in TrawsCymru livery some time ago for the T5 service that has only just appeared.
Each of these points probably deserve a post of their own, and I intend to do just that. How long it will take me to complete all that is another question.
I am part way through the January 2015 issue of 'Modern Railways'. On page 14, there is a piece hailing the success of Community Rail Partnerships. Over six years (2006/07 to 2012/13) they report an overall patronage growth across the regional passenger sector of the UK rail network of 23%. Within that though, the use of lines supported by Community Rail Partnerships grew by 45%. Further growth on many of the lines is apparently now being hampered by the national shortage of DMU stock.
It is a shame then that one of Wales' Community Rail Partnerships, the one covering the Pembrokeshire branches (including, if I recall correctly, the line from Swansea to Carmarthen) appears to have become defunct. It was called 'All Points West', but I noticed some time ago that their website URL now pointed to something totally irrelevant. Arriva Trains Wales' website still mentions 'All Points West' but they have since removed the hyperlink when they learned that the 'All Points West' site was gone. They obviously had no money for web hosting, and I don't think they exist any more at all. They were, if I recall correctly, either part of or supported by SWWITCH, the South West Wales Integrated Transport Consortium. SWWITCH itself now appears to have gone the way of the dodo. There now doesn't seem to be any single co-ordinated body promoting the rail network in the bottom left-hand corner of Wales, just a handful of independent, mostly informal, groups.
In terms of promotion, as I remarked in one of my 'Trains For Fishguard' videos, it is a shame that the lines do not have a marketing name. Another of Wales' Community Rail Partnerships is a great example of the opposite end of the scale: 'The Heart Of Wales Line'. That has to be one of the best marketing names out there, but south-west Wales has nothing.
The best idea I've come up so far is to resurrect 'All Points West' as 'LLAnBranches CRP', the Landsker Line And Branches Community Rail Partnership. A bit of a mouthful, but the main route from Llanelli through to Clarbeston Road could be simply the 'Landsker Line' as it roughly follows the boundary between the areas where Welsh is spoken more (north of the line) or less (south of the line).
Perhaps trying to bring about the 'LLAnBranches CRP' is something to add to my already stupidly long to-do list for 2015. I'm REALLY slow, so I might need 100 of me to get all my work done. In other words, it is unlikely I will get round to doing anything about it. Still, at least I've managed a blog post to start the new year, and it wasn't even the rant about the new TrawsCymru T5 service I'd expected to post, so that is still to come. I hope 2015 will be a happy year for you, me and the rest of life on earth.