Planck Galactic Cold Clumps at High Galactic Latitude-A Study with CO Lines

There are 41 clumps with absolute Galactic latitude higher than $25\arcdeg$ ($|b|>25\arcdeg$) from the Early Cold Core (ECC; Planck Collaboration et al. (2011b)) catalog, which were observed with the 13.7-m millimeter-wavelength telescope of the Purple Mountain Observatory (PMO). The ECC sources have high signal-to-noise ratios (SNR$>$15). Figure 1 shows the distribution of 41 clumps. The distribution of these 41 HGal clumps is not uniform along latitude or along longitude. As shown in Figure 1, the clumps of belonging to the northern sky are located only in the latitude range $25\arcdeg<b<42\arcdeg$ and those in the southern sky mainly group around $-50\arcdeg<b<-25\arcdeg$. The longitudes of the detected clumps are mostly in the range of $90\arcdeg<l<180\arcdeg$ and $0\arcdeg<l<45\arcdeg$. Almost half, 46.3% (19 out of 41) of these clumps are just below Taurus, Perseus, and California Complex at $b\leq-20\arcdeg$ and $l=155-180\arcdeg$ The names of these clumps are listed in column (1), Galactic coordinates in columns (2)–(3) and equatorial coordinates in columns (4)–(7) of Table 2.

The $3\times 3$ beam sideband separation Superconduction Spectroscopic Array Receiver system was used as the front end (Shan et al., 2012). The half-power beam width is 56$\arcsec$ in the 115 GHz band. The mean beam efficiency is about $50\%$. The pointing accuracy is better than 5$\arcsec$. The Fast Fourier Transform Spectrometers (FFTSs) were used as the backend. Each FFTS with a total bandwidth of 1 GHz provides 16384 channels.

The single point mode observations of ¹²CO, ¹³CO and C¹⁸O J=1-0 towards 41 HGal clumps were conducted from April to May in 2011 and from December 2011 to January 2012. The velocity resolutions are 0.16 km s^-1 for ¹²CO and 0.17 km s^-1 for ¹³CO and C¹⁸O. The ¹²CO emission was observed in the upper sideband (USB) with a system temperature (T_sys) around 210 K, while the ¹³CO and C¹⁸O emissions were observed simultaneously in the lower sideband (LSB) with T_sys around 120 K. The typical root mean square (rms) noise in T${}_{A}^{*}$ was 0.2 K for ¹²CO but 0.1 K for ¹³CO and C¹⁸O. Due to time limitations only 26 of these 41 HGal clumps were further mapped in the on-the-fly (OTF) mode in the three CO transitions. The antenna continuously scanned a region of $22\arcmin\times 22\arcmin$ centered on the PGCCs with a scanning rate of $20\arcsec$ per second. Because of the high rms noise level at the edges of the OTF maps, only the central $14\arcmin\times 14\arcmin$ regions were used for analyses in this work (Zhang et al., 2020). Whether the PGCC was mapped with OTF is shown in column (10) of Table 2. If mapped, it is marked by a ‘Y’, if no, then ‘N’.

To trace the high-density region in these 26 mapped HGal clumps, we chose the center of cores defined in Section 3.1 to detect J=1-0 emissions of N₂H⁺ and C₂H. We required that each candidate should have sufficient column density with an antenna temperature of ¹³CO higher than 1 K. Then, 18 of these HGal clumps with absolute latitude larger than 25°were chosen for further observations. To compare the detection rate between high and lower latitudes, we also observed an unbiased sample of 18 PGCCs with latitudes between 21°and 25°. Finally, 36 clumps in total were observed with N₂H⁺ and C₂H in single-point mode from May to June in 2019. The velocity resolutions are 0.19 km s^-1 for N₂H⁺ and 0.21 km s^-1 for C₂H. The N₂H⁺ emission was observed in the USB with T_sys also around 210 K and C₂H in LSB with T_sys around 210 K. The typical noise is 0.2 K for both N₂H⁺ and C₂H.

The raw data were reduced by CLASS and GREG in the GILDAS package (Guilloteau & Lucas, 2000; Pety, 2005).

To evaluate the definition of cores (see Section 3.1) in the special clump G004.15+35.77, the northwestern edge of LDN 134 (Lynds, 1962), the FIR continuum emission images were taken from the project Galactic Cold Cores (Juvela et al., 2010) which is a Herschel satellite survey (Pilbratt et al., 2010) of the source populations revealed by Planck Cold Cores program. The data were obtained with the Photodetector Array Camera and Spectrometer (Poglitsch et al., 2010, PACS) at 100 and 160 $\mu m$ wavelength and the Spectral and Photometric Imaging REceiver (Griffin et al., 2010, SPIRE) at 250, 350, and 500 $\mu m$ wavelength. The original resolution of the maps, in order of increasing wavelengths, is $7\arcsec$, $12\arcsec$, $18\arcsec$, $25\arcsec$ and $36\arcsec$. PACS 100 $\mu m$ image shows no detection with a rms of 0.00144 $Jy/pixel$ and was therefore excluded from further study. We then performed pixel-by-pixel SED fitting following Yuan et al. (2017) with four infared bands (160, 250, 350, 500 $\mu m$) and obtained the temperature $T_{\text{dust}}$ and column density $N_{\text{H}_{2}}$ maps, which are then cut to the same size as our PMO’s observation ($14^{\prime}\times 14^{\prime}$). The method is described in detail in Appendix A.

Distance is always a puzzle in astronomy. Previous works estimated the distances of HGal molecular clouds to be 100 pc by the velocity dispersion and the scale height of the ensemble of clouds (Blitz et al., 1984; Magnani et al., 1985). Follow-up star counts from POSS confirmed that HGal molecular clouds are indeed nearby objects and the upper limit ranges from 125 to 275 pc (Magnani & de Vries, 1986). Besides, both small $V_{lsr}$ and the lack of a double-sine wave signature in the distribution on the $l-V_{lsr}$ plane demonstrate that HGal molecular gas is too close to the Sun for Galactic rotation to modulate the velocities (Magnani et al., 1996). Therefore, we should not expect the co-rotation of HGal objects with the rotation curve, which means that the traditional method relying on the Milky Way rotation curve to derive distances may not be a good choice.

Recently, the Gaia satellite has provided new photometric measurement towards galactic stars (Gaia Collaboration et al., 2016). Together with 2MASS and Pan-STARRS 1 optical and near-infrared photometry, Gaia DR2 parallaxes can help to infer distances and reddenings of $\sim$ 800 million stars. These stars trace the reddening on a small patch of sky, both along the different lines of sight and different distance intervals, allowing us to build up a map of dust reddening in 3D (Green et al., 2014, 2019). With the help of this 3D map, we could infer reddening as a function of distance in the given direction. We turn to this new method to derive the distances of HGal clumps for three reasons:

1. 1.

   Kinematic distances to nearby clouds are very unreliable due to the local Galactic velocity dispersion.

2. 2.

   HGal clumps are less affected by Galactic rotation so it will be better if the estimation of distances is independent from the rotation of the Milky Way.

3. 3.

   Dust and gas are proved to be well coupled in PGCCs (Wu et al., 2012), so it is reasonable to derive the distance of molecular gas from the dust extinction.

In the Gaia dust reddening algorithm, given Galactic longitude and latitude, different distances of dust are assigned with probabilities and we choose the distance with largest probability in our paper. This method is precise enough unless the distance is larger than 1 kpc where the extinction is too strong (Green et al., 2019). But again, HGal clumps are assumed so close that such imprecise cases are avoided. Along with Galactic latitudes, the vertical distance of the clumps from the Galactic midplane (elevation Z) are also derived,

where Z, d, b are the elevation, distance and latitude, respectively. The distances and elevations of all 41 PGCCs from Gaia dust extinction are listed in columns (8) and (9) of Table 2.

From single-point observations, we find several sources with multi-velocity components in our sample. Eight HGal PGCCs have double-velocity components and one has triple-velocity components. In total, 51 velocity components were obtained in HGal. We consider each velocity component as an individual clump, ie. 51 clumps are finally defined. Mapping observations are applied to 26 PGCCs (time is limited and the sample is unbiased) and due to multi-velocity components, we have 33 mapped clumps. The CO integrated intensity maps of three example clumps are shown in Figure 2 and the figures of total 33 clumps are shown in Appendeix B. ¹²CO is shown as colored background and ¹³CO (left) and C¹⁸O (right) are shown with blue contours from 50% to 90 % of the peak integrated intensity. The morphologies include isolated cores, filamentary structures and also diffuse or full-coverage features.

In this paper, we define all the local enhancements of ¹³CO intensity higher than 70% of the peak intensity as individual dense cores. The reasons why we use 70% rather than 50% are two: one is that in some detections the SNR is limited especially on the edge of the field of view, and 70% level helps to remove those mistaken cores by 50% level; the other is that the ¹³CO contours are usually extensive and not concentrated, showing a flat density profile, and therefore we need a more strict criterion to distinguish intensity peaks. A typical example is the filamentary clump G101.62-28.84a, shown in the two medium panels of Figure 2. A 70% level contour helps to distinguish four cores while 50% level cannot do this.

As shown in Figure 2, we mark these cores with black crosses and names “C1”, “C2”, … The 50% isolines are further fitted with ellipses, providing measurements of the semi-major and semi-minor axes ($a$ and $b$). The ICRS coordinate offsets of each core from the observational center are listed in Columns (2)-(3) of Table 5. The distances of cores are assumed to be the same as those of the host clumps and listed in Column (4) of Table 5. The sizes of the cores are given by $R=\sqrt{ab}D$ ($D$ is the distance). Also, due to the beam smearing effect, we only give upper limits for those cores with sizes smaller than the beam size of our telescope. The sizes of cores are listed in Column (5) of Table 5.

For three clumps G089.03-41.28a, G158.77-33.30b and G159.41-34.36b, no cores are found. For only one clump G004.15+35.77, the 50% isolines significantly overstep the boundary of the 14-arcmin box. We check the column density map (blue background) given by pixel-by-pixel SED Fitting (detailed method in Appendix A), shown in panel (b) of Figure 12. Two dust cores are shown with deep blue color. The black and white contours give the ¹³CO and C¹⁸O integrated intensity respectively and only one CO core appears in the map. A shallow yellow circle gives the location of ammonia dense core (L134-A) with kinetic temperature $T_{k}$ of 10 K and volume density of $10^{4.5}\ \text{cm}^{-3}$ (Myers et al., 1983). L134-A correlates well with the northern dust core with a low dust temperature of 10.3 K and C¹⁸O core correlates well with southern dust core with slightly higher dust temperature of 11.1 K. We define the CO core “C1” traced by C¹⁸O as well as dust column density. We also notice the reason why the northern dust core has lower CO emission. This may be caused by a higher CO depletion due to the low temperature (Goldsmith, 2001). For consistency, we still choose ¹³CO emission to define the core size and neglect the part outside the boundary. This is safe as long as the core is nearly elliptical.

In total, 54 cores are identified among the 33 mapped clumps. Velocity components are denoted as “a, b, c, …”, while the cores are labeled as “C1, C2, C3, …” following Wu et al. (2012).

We extract the 1-arcmin box towards the core center, averaging all the spectra inside the box. Then Gaussian fitting is obtained for the three CO lines. If the profiles arise from blended multi-velocity, multiple Gaussian components are fitted simultaneously. If the profile originates from self-absorption, only one Gaussian component is fitted. The centroid velocity ($V_{lsr}$), main beam brightness temperature ($T_{b}$) and FWHM ($\Delta$V) can be obtained from Gaussian fitting directly. For those cores without C¹⁸O detection, the upper limit of $T_{b}$ is given by the noise of the baseline and the FWHM is given the same value as as that for ¹³CO detection, which will be useful in the calculation of the upper limits to the C¹⁸O column density. Three fitting parameters are listed in Table 3. Cores without C¹⁸O detection have three parameters of C¹⁸O only shown with ’…’. The centroid velocity of the ¹³CO J=1-0 line of each core is adopted as the systemic velocity, because the ¹²CO J=1-0 line is optically thick and the C¹⁸O J=1-0 line has only eight solid detections in our 54 cores.

Sometimes, the line profile cannot be fitted as a single Gaussian function and we call them non-Gaussian. Generally, non-Gaussian profiles in optically thick molecular lines ¹²CO(1-0) fall into two main categories: multi-peak and asymmetry.

The criterion set by Mardones et al. (1997) is applied to check whether blue or red profiles indicating cloud contraction or expansion in certain cases. $\delta V$ = ($V_{\text{thick}}$-$V_{\text{thin}}$)/$\delta$ $V_{\text{thin}}$, where $V_{\text{thick}}$ is the peak velocity of ¹²CO(1-0), $V_{\text{thin}}$ and $\delta V_{\text{thin}}$ are the systemic velocity and the line width of ¹³CO(1-0). If $\delta V<$ -0.25, the line is classified as blue asymmetric; if $\delta V>$ 0.25, then red asymmetric. Among those asymmetric profiles, if the optically thick molecular line-¹²CO has double peaks at the same time, then we have a lineshape termed blue or red profile, depending on the blue or red asymmetric profile defined above. The rest of the multi-peak profiles can be well described as multi-velocity components and can be fitted by composition of two or more Gaussian functions.

In total, four non-Gaussian profiles are found by single-point observations (see Figure 3): G089.0-41.2 (blue profile), G182.5-25.3 (red profile), G210.6-36.7 (red profile) and G159.5-32.8 (red asymmetry). However, single-point observations only provide one spectrum from the center (or maybe some little offset), and thus might not represent the real line profiles from the cores. Therefore, as mentioned before, we extract the molecular lines from the center of the 54 cores and then carefully examine the line profiles respectively. A more detailed discussion will be made in Section 4.2.3

Parameters from the 54 extracted dense cores are further calculated in this section.

The excitation temperatures ($T_{ex}$) and optical depths ($\tau$) can be derived from the solution of the radiation transfer equation:

where $T_{bg}$ is the background temperature (2.73 K). Under the assumptions that ¹²CO J=1-0 is optically thick ($\tau\gg$ 1), and the beam filling factor $f$ is equal to 1, according to Equation (2) of ¹²CO, the excitation temperature can be expressed as

Under the condition of local thermodynamic equilibrium (LTE), ¹²CO and ¹³CO have the same excitation temperature. We can obtain the optical depth of ¹³CO ($\tau_{13}$) by

The $T_{\mathrm{ex}}$ of the 54 cores ranges from 6 K to 13 K with a median value of $\sim$ 10.3 K. The values of T_ex and $\tau_{13}$ are listed in columns (2) and (3) of Table 4. The dust temperature (T_dust) of all the PGCCs ranges from 5.8 to 20 K with a median value between 13 and 14.5 K (Planck Collaboration et al., 2016). The similarity of two temperatures indicates that the gas and dust are well coupled. Besides, the different median temperature (T${}_{\mathrm{dust,median}}>$ T_ex,median) implies that the gas might be heated by the dust (Goldreich & Kwan, 1974; Wu & Evans, 1989).

The column density of ¹³CO (N${}_{{}^{13}\mathrm{CO}}$) and C¹⁸O (N${}_{\mathrm{C}^{18}\mathrm{O}}$) can be derived from (Lang, 1978; Garden et al., 1991)

where $B$, $\mu_{d}$ and $J$ are the rotational constant, permanent dipole moment of the molecule and the rotational quantum number of the lower state in the observed transition.

Adopting the typical abundance ratios, $[{\rm H_{2}}]/[{\rm{}^{13}CO}]=89\times 10^{4}$ (McCutcheon et al., 1980) and $[{\rm H_{2}}]/[{\rm C^{18}O}]=7\times 10^{6}$ (Frerking et al., 1982) for the solar neighborhood, the column density of hydrogen (N${}_{\mathrm{H}_{2}}$) can be calculated by Equation (5). Since the detection rate of C¹⁸O is low, we use ¹³CO to calculate H₂ column densities, as listed in column (4) of Table. 4.

The one-dimensional velocity dispersion of ¹³CO is given by

The thermal ($\sigma_{\text{Th}}$) and non-thermal ($\sigma_{\text{NT}}$) velocity dispersion can be calculated from

where m_H is the mass of atomic hydrogen, $\mu$ is the mean weight of molecule which equals 2.33 (Kauffmann et al., 2008), m${}_{{}^{13}\mathrm{CO}}$ is the mass of the molecule ¹³CO and $k$ is the Boltzmann constant. Then the three-dimensional velocity dispersion $\sigma_{3\mathrm{D}}$ can be calculated from

All the derived parameters are listed in Table 4.

The volume density can be derived through $n_{\mathrm{H}_{2}}$ = $N_{\mathrm{H}_{2}}/2R$ ($N$ is the column density of hydrogen molecules and $R$ is the size of the core) under the assumption of homogeneous spherical material distribution. The LTE mass can be obtained directly from

Assuming that the cores are isothermal spheres and supported solely by random motions, we can calculate the virial mass $M_{\mathrm{vir}}$ as (Williams et al., 1994)

where G is the gravitational constant. The density profile is assumed to be uniform (also corresponding to the isothermal distribution mentioned in Section 4.4.2), and then $\gamma$ should be unity.

In molecular clouds, thermal pressure, turbulence and magnetic field can support the gas against gravity collapse. Taking thermal pressure and turbulence into account, the Jeans mass can be expressed as following (Hennebelle & Chabrier, 2008)

where $a_{\mathrm{J}}$ is a dimensionless parameter of the order unity, $n$ is the volume density of H₂, and the effective kinematic temperature $T_{\mathrm{eff}}$ is adopted as $\frac{\mu m_{H}C_{\mathrm{s,eff}}^{2}}{k_{B}}$. The effective sound speed $C_{\mathrm{s,eff}}$ is expressed by $[(\sigma_{\mathrm{NT}})^{2}+(\sigma_{\mathrm{Th}})^{2}]^{1/2}$ to account for combination of both thermal motion and turbulence.

According to Kauffmann et al. (2013), the virial parameter can be applied to gauge stability against gravitational collapse:

The volume density, LTE mass, Jeans mass, virial mass and virial parameter are listed in column (6) – (10) of Table 5, respectively. Also notice that some cores only have upper limits for sizes, the size-related parameters above are then semi-constrained and presented with upper or lower limits.

We have observed two dense gas tracers N₂H⁺ and C₂H in eighteen clumps with high enough ¹³CO antenna temperature among 26 mapped HGal PGCCs, which are thought to be the sub-sample with embedded dense cores. For comparison purpose, we also searched for N₂H⁺ and C₂H in eighteen clumps at the latitude range between 21°and 25°. Only one HGal PGCC has obvious detections, of both two dense tracers, as shown in the lower right panel of Figure 4. For another eighteen low-latitude clumps, we find six of them having at least one kind of dense-gas tracer. G008.5+21.8 and G158.8-21.6 have both N₂H⁺ and C₂H detection respectively in the upper left and upper right panel of Figure 4 and clumps like G008.6+22.1 have only C₂H detection.

The distribution of HGal clumps is shown in Figure 1. The background colormap is the CO survey of the Planck Collaboration (Planck Collaboration et al., 2014). HGal PGCCs we observed are marked with blue crosses. Rectangles with names were defined after Dame et al. (1987) as well as Wu et al. (2012), marking the known CO molecular clouds or complexes. The blue rectangles mark the published PMO 13.7-m data (Liu et al., 2012; Meng et al., 2013; Zhang et al., 2016, 2020). Two bold rectangles at high latitude mark the regions that have large and unbiased survey with higher resolution or spatial spacing (Heithausen et al., 1993; Yamamoto et al., 2003). However, the survey of Dame et al. (1987) was limited to the Galactic plane, while the surveys by Heithausen et al. (1993) and Yamamoto et al. (2003) are limited to certain regions (see Figure 1). Compared to prior surveys, we have detected CO emission at higher latitude. The average latitude of 41 clumps is 36.87°. The highest elevation is 214 pc for G153.74+35.91 and the average value is 119 pc.

To examine the consistency between PGCCs and HGal clouds with CO detections, we cross-match the HGal PGCCs with molecular clouds that have been found and observed in CO before, including Heithausen et al. (1993); Magnani et al. (1996); Hartmann et al. (1998); Magnani et al. (2000). The cross-matching result is shown in Column (11) of Table 2. Filled yellow circles in Figure 1 show 121 HGal objects summarized by Magnani et al. (1996). As we can see, most clumps are embedded in the known molecular clouds, and tend to group in several famous HGal cloud regions. In the Northern Hemisphere, 2 clumps come from the Ursa Major cloud complex, 2 come from MBM 25, 6 come from the L134 complex. In the southern hemisphere, most of clumps gather at 145°$\leq l\leq$195°, -46°$\leq b\leq$-30°, to the south of the Tarus-Aurgiae complex of dark clouds (Magnani et al., 2000). For instance, MBM 11–12 (L1457-c) contains 7 clumps. There are also 2 clumps associated with MBM 53–55 complex surveyed by Yamamoto et al. (2003), which has a significant extent 85°$\leq l\leq$ 96°and -43°$\leq b\leq$ -32°(Blitz & Lockman, 1988; Magnani et al., 2000). We then zoom in two clump-crowded regions of the L134 complex (6 clumps included) and MBM 11–12 complex (7 clumps included) in the lower left and upper right panel of Figure 1, respectively. Those clumps are mainly distributed at the outskirts of these HGal clouds/complexes.

There are 6 clumps G101.62-28.84, G102.72-25.98, G126.65-71.43, G127.31-70.09, G182.54-25.34 and G203.57-30.08 not associated with known HGal clouds, contributing to 14.6% (6 in 41) of the sample. Those clumps, more diffuse in shape and smaller in size, might escape the search with coarse sampling grid of about 1 degree and beamwidth of $\sim 8^{\prime}$ in the surveys of Hartmann et al. (1998) and Magnani et al. (2000). Besides, HGal PGCCs are generally embedded in translucent molecular clouds, so the MBM clouds selected by optical obscuration may also not include those diffuse clumps. Yet those clumps are cold enough to be detected by Planck.

PGCCs are relatively cold and quiescent on the whole compared to other typical star forming regions (Wu et al., 2012) and the non-thermal motions in these clumps are therefore mainly contributed by turbulence (Zhang et al., 2020). In most of the PGCC cores we observed, non-thermal velocity dispersion is larger than thermal one ($\sigma_{NT}\geq\sigma_{Th}$). In other words, the turbulence is super-sonic (above blue-shaded region in Figure 9) in most of the samples (Wu et al., 2012, Table.2). These cores might be still at an early stage along the time sequence of condensations: confined by outer Hi gas pressure (Heithausen, 1996) or even just in a transient phase (Magnani et al., 1993).

First suggested by Larson (1981), a cascade in an incompressible fluid should be responsible for observed $\sigma\sim R^{0.38}$ relation. Further refinements have changed this simple picture and the power law index differs depending on environment (Shore et al., 2007). The grey dash-dotted line (in Figure 9) from the First Quadrant (IQuad) gives a correlation similar to Larson’s relation (Zhang et al., 2020). For HGal cores (purple points with error bars, also purple filled contours), the relation is also checked as:

with a poor correlation coefficient of $R^{2}=0.36$. We exclude the cores with only upper limits of sizes in this linear regression and mark them as light purple with semi-errorbars. Blue contours represent other PGCC cores (hereafter non-HGal) also observed with 13.7-m PMO telescope (Liu et al., 2012; Meng et al., 2013; Zhang et al., 2016, 2020). These non-HGal cores also obey the Larson’s relation derived from grey dash-dotted line on the whole.

HGal clumps are closer in distance and enable us to observe at smaller scale, and on the other hand we tend to observe a farther clump at larger scale. Such observational differences in size enable us to study the turbulent property at the different scales. The conceptual foundation of turbulence is a monotonic cascade from large injection scales to small scales where it is dissipated (Tennekes & Lumley, 1972; McComb & Watt, 1992). As shown in Figure 9, along the blue dash-dotted line from upper right to lower left, $\sigma_{3D}$ decreases with core size R. However, a large-scale (0.1-3 pc) Larson’s relation cannot be extended to the small-scale (0.01-0.1 pc) continuously, which is dramatically shown by the bimodal distribution with purple and blue filled contours. HGal cores (purple), with the smallest size, have significantly higher $\sigma$ than a continuous cascade from the large scale expected, even if the error bars are taken into account.

Since energy can be injected on many scales ranging from Galactic dynamics to individual stellar processes, the turbulent mechanism in ISM can vary due to local differences. Many of the HGal clouds are reported to be part of large Hi shells or fragments of shells in the local ISM (Gir et al., 1994; Bhatt, 2000) where the shock compression at the cloud boundary plays the dominant role. However, HGal clouds like MBM 3, MBM 16 and MBM 40 are thought to be immersed in strong shear flows from the Hi medium, powering the turbulence inside the clouds (Shore et al., 2003, 2006). We notice that whichever mechanism is operating, HGal cores with extra energy injections will restart a new cascade “path” along the purple dash-dotted line (see Figure 9). We then plot the grey point as MBM 3, showing the typical size $\sim$ 1 pc where turbulent energy is injected by shear flow (Shore et al., 2006).

However, the scatter in the data is large and the light purple points can’t be simply explained by a monotonic turbulent cascade along the new “path”. Instead, once the self-similar turbulence scales down to a typical size $R_{0}$, velocity dispersion $\sigma$ doesn’t obey the decreasing trend but seems to be independent of size. Such a turning-point scale $R_{\text{coh}}$ corresponds to the transition to “coherence” (Goodman et al., 1998), which can be the case of HGal clouds MBM 16 (Magnani et al., 1993). One of the accepted efxplanations for “coherence” is Alfvén wave cutoff (Goodman et al., 1998). If the Alfvén waves support the turbulent cascade, then $R_{\text{coh}}$ may be very close to the scale $R_{\text{cut}}$ below which no Alfvén wave can propagate in the medium. $R_{\text{cut}}$ can be simply calculated from (McKee & Zweibel, 1995):

where $B$, $\rho$, $x_{i}$ and $\gamma$ are magnetic field, density, ionization fraction and drag coefficient, respectively. If we take the typical value of number density $n=5\times 10^{3}$ cm^-3, $B=20\mu G$, $x_{i}=10^{-7}$ and $\gamma=3.5\times 10^{13}$ cm³g^-1s^-1, then $R_{\text{cut}}\simeq 0.05$ pc. As shown with grey-shaded area in Figure 9, the turbulent dissipation is suppressed below 0.05 pc.

The idea that HGal gas is different from that in the Galactic disk has been reported already (Blitz et al., 1984; Magnani et al., 1985) and our follow-up work gives further evidence and makes the idea much clearer. Section 4.2.1 shows a significant gradient of the dense-molecule detection rate along latitude. According to the result of 54 HGal cores, the abundance of CO isotopes bears a large deviation from that of Galactic disk (see Section 4.2.1). And no blue or red profiles are found (see Section 4.2.3). Besides, there are no associated YSO candidates found in the host clumps (see Section 4.4.1). As shown in Section 4.4.2, none of the cores are gravitational bound even with a looser criterion. These results demonstrate that at that high latitude, gas is totally different from that of Galactic disk, although they are part of the local interstellar medium within 200 pc or so. Above all, HGal gas traced by PGCCs is at an extremely early stage and transient phase still confined with pressure, without clear indications of star formation at the current time.