Formation of Galactic Center Magnetic Loops

A survey for the molecular clouds in the Galaxy with NANTEN mm telescope has discovered molecular loops in the Galactic center region. The loops show monotonic gradients of the line of sight velocity along the loops and the large velocity dispersions towards their foot points. It is suggested that these loops are explained in terms of the buoyant rise of magnetic loops due to the Parker instability. We have carried out global three-dimensional magneto-hydrodynamic simulations of the gas disk in the Galactic center. The gravitational potential is approximated by the axisymmetric potential proposed by Miyamoto & Nagai (1975). At the initial state, we assume a warm (~ 10^4 K) gas torus threaded by azimuthal magnetic fields. Self-gravity and radiative cooling of the gas are ignored. We found that buoyantly rising magnetic loops are formed above the differentially rotating, magnetically turbulent disk. By analyzing the results of global MHD simulations, we have identified individual loops, about 180 in the upper half of the disk, and studied their statistical properties such as their length, width, height, and velocity distributions along the loops. Typical length and height of a loop are 1kpc and 200pc, respectively. The line of sight velocity changes linearly along a loop and shows large dispersions around the foot-points. Numerical results indicate that loops emerge preferentially from the region where magnetic pressure is large. We argue that these properties are consistent with those of the molecular loops discovered by NANTEN.Comment: 16pages, 10figures. Accepted for publication in PASJ. Replace to higher resolution versio

Discovery of Molecular Loop 3 in the Galactic Center: Evidence for a Positive-Velocity Magnetically Floated Loop towards L=355∘−359∘L=355^\circ-359^\circ

We have discovered a molecular dome-like feature towards $355^{\circ} \leq l \leq 359^{\circ}$ and $0^{\circ} \leq b \leq 2^{\circ}$. The large velocity dispersions of 50--100 km s$^{-1}$ of this feature are much larger than those in the Galactic disk and indicate that the feature is located in the Galactic center, probably within $\sim1$ kpc of Sgr A$^{*}$. The distribution has a projected length of $\sim600$ pc and height of $\sim300$ pc from the Galactic disk and shows a large-scale monotonic velocity gradient of $\sim130$ km s $^{-1}$ per $\sim600$ pc. The feature is also associated with HI gas having a more continuous spatial and velocity distribution than that of $^{12}$CO. We interpret the feature as a magnetically floated loop similar to loops 1 and 2 and name it "loop 3". Loop 3 is similar to loops 1 and 2 in its height and length but is different from loops 1 and 2 in that the inner part of loop 3 is filled with molecular emission. We have identified two foot points at the both ends of loop 3. HI, $^{12}$CO and $^{13}$CO datasets were used to estimate the total mass and kinetic energy of loop 3 to be \sim3.0 \times 10^{6} \Mo and $\sim1.7 \times 10^{52}$ ergs. The huge size, velocity dispersions and energy are consistent with the magnetic origin the Parker instability as in case of loops 1 and 2 but is difficult to be explained by multiple stellar explosions. We argue that loop 3 is in an earlier evolutionary phase than loops 1 and 2 based on the inner-filled morphology and the relative weakness of the foot points. This discovery indicates that the western part of the nuclear gas disk of $\sim1$ kpc radius is dominated by the three well-developed magnetically floated loops and suggests that the dynamics of the nuclear gas disk is strongly affected by the magnetic instabilities.Comment: 30 pages, 10 figures. High resolution figures are available at http://www.a.phys.nagoya-u.ac.jp/~motosuji/fujishita09_figs

A Detailed Observational Study of Molecular Loops 1 and 2 in the Galactic Center

Fukui et al. (2006) discovered two huge molecular loops in the Galactic center located in (l, b) ~ (355 deg-359 deg, 0 deg-2 deg) in a large velocity range of -180-40 km s^-1. Following the discovery, we present detailed observational properties of the two loops based on NANTEN 12CO(J=1-0) and 13CO(J=1-0) datasets at 10 pc resolution including a complete set of velocity channel distributions and comparisons with HI and dust emissions as well as with the other broad molecular features. We find new features on smaller scales in the loops including helical distributions in the loop tops and vertical spurs. The loops have counterparts of the HI gas indicating that the loops include atomic gas. The IRAS far infrared emission is also associated with the loops and was used to derive an X-factor of 0.7(+/-0.1){\times}10^20 cm^-2 (K km s^-1)^-1 to convert the 12CO intensity into the total molecular hydrogen column density. From the 12CO, 13CO, H I and dust datasets we estimated the total mass of loops 1 and 2 to be ~1.4 {\times} 106 Msun and ~1.9 {\times} 10^6 Msun, respectively, where the H I mass corresponds to ~10-20% of the total mass and the total kinetic energy of the two loops to be ~10^52 ergs. An analysis of the kinematics of the loops yields that the loops are rotating at ~47 km s-1 and expanding at ~141 km s^-1 at a radius of 670 pc from the center. Fukui et al. (2006) presented a model that the loops are created by the magnetic flotation due to the Parker instability with an estimated magnetic field strength of ~150 {\mu}G. We present comparisons with the recent numerical simulations of the magnetized nuclear disk by Machida et al. (2009) and Takahashi et al. (2009) and show that the theoretical results are in good agreements with the observations. The helical distributions also suggest that some magnetic instability plays a role similarly to the solar helical features.Comment: 40 pages, 22 figures, submitted to publication in PAS

Similarity between the Molecular Loops in the Galactic Center and the Solar Chromospheric Arch Filaments

We carried out two-dimensional magnetohydrodynamic simulations of the Galactic gas disk to show that the dense loop-like structures discovered by the Galactic center molecular cloud survey by NANTEN 4 m telescope can be formed by the buoyant rise of magnetic loops due to the Parker instability. At the initial state, we assumed a gravitationally stratified disk consisting of the cool layer ($T \sim 10^3$ K), warm layer ($T \sim 10^4$ K), and hot layer ($T \sim 10^5$ K). Simulation box is a local part of the disk containing the equatorial plane. The gravitational field is approximated by that of a point mass at the galactic center. The self-gravity, and the effects of the galactic rotation are ignored. Numerical results indicate that the length of the magnetic loops emerging from the disk is determined by the scale height of the hot layer ($\sim$ 100 pc at 1 kpc from the Galactic center). The loop length, velocity gradient along the loops and large velocity dispersions at their foot points are consistent with the NANTEN observations. We also show that the loops become top-heavy when the curvature of the loop is sufficiently small, so that the rising loop accumulates the overlying gas faster than sliding it down along the loop. This mechanism is similar to that of the formation of solar chromospheric arch filaments. The molecular loops emerge from the low temperature layer just like the dark filaments observed in the H$\alpha$ image of the emerging flux region of the sun.Comment: 23 pages, 13 figures. Accepted for publication in PAS

High Excitation Molecular Gas in the Galactic Center Loops; 12CO(J =2-1 and J =3-2) Observations

We have carried out 12CO(J =2-1) and 12CO(J =3-2) observations at spatial resolutions of 1.0-3.8 pc toward the entirety of loops 1 and 2 and part of loop 3 in the Galactic center with NANTEN2 and ASTE. These new results revealed detailed distributions of the molecular gas and the line intensity ratio of the two transitions, R3-2/2-1. In the three loops, R3-2/2-1 is in a range from 0.1 to 2.5 with a peak at ~ 0.7 while that in the disk molecular gas is in a range from 0.1 to 1.2 with a peak at 0.4. This supports that the loops are more highly excited than the disk molecular gas. An LVG analysis of three transitions, 12CO J =3-2 and 2-1 and 13CO J =2-1, toward six positions in loops 1 and 2 shows density and temperature are in a range 102.2 - 104.7 cm-3 and 15-100 K or higher, respectively. Three regions extended by 50-100 pc in the loops tend to have higher excitation conditions as characterized by R3-2/2-1 greater than 1.2. The highest ratio of 2.5 is found in the most developed foot points between loops 1 and 2. This is interpreted that the foot points indicate strongly shocked conditions as inferred from their large linewidths of 50-100 km s-1, confirming the suggestion by Torii et al. (2010b). The other two regions outside the foot points suggest that the molecular gas is heated up by some additional heating mechanisms possibly including magnetic reconnection. A detailed analysis of four foot points have shown a U shape, an L shape or a mirrored-L shape in the b-v distribution. It is shown that a simple kinematical model which incorporates global rotation and expansion of the loops is able to explain these characteristic shapes.Comment: 59 pages, accepted to PAS

Temperature and Density in the Foot Points of the Molecular Loops in the Galactic Center; Analysis of Multi-J Transitions of 12CO(J=1-0, 3-2, 4-3, 7-6), 13CO(J=1-0) and C18O(J=1-0)

Fukui et al. (2006) discovered two molecular loops in the Galactic center and argued that the foot points of the molecular loops, two bright spots at both loops ends, represent the gas accumulated by the falling motion along the loops, subsequent to magnetic flotation by the Parker instability. We have carried out sensitive CO observations of the foot points toward l=356 deg at a few pc resolution in the six rotational transitions of CO; 12CO(J=1-0, 3-2, 4-3, 7-6), 13CO(J=1-0) and C18O(J=1-0). The high resolution image of 12CO (J=3-2) has revealed the detailed distribution of the high excitation gas including U shapes, the outer boundary of which shows sharp intensity jumps accompanying strong velocity gradients. An analysis of the multi-J CO transitions shows that the temperature is in a range from 30-100 K and density is around 10^3-10^4 cm^-3, confirming that the foot points have high temperature and density although there is no prominent radiative heating source such as high mass stars in or around the loops. We argue that the high temperature is likely due to the shock heating under C-shock condition caused by the magnetic flotation. We made a comparison of the gas distribution with theoretical numerical simulations and note that the U shape is consistent with numerical simulations. We also find that the region of highest temperature of ~100 K or higher inside the U shape corresponds to the spur having an upward flow, additionally heated up either by magnetic reconnection or bouncing in the interaction with the narrow neck at the bottom of the U shape. We note these new findings further reinforce the magnetic floatation interpretation.Comment: 40 pages, 23 figures, accepted by PASJ on Vol.62 No.

The Advertising–price Relationship: Theory and Evidence

Abstract The relationship between advertising and price is important because the welfare effect of advertising depends upon the price effect of advertising. We attempt to provide a better understanding of the theoretical relationship between advertising and price. We establish theoretical conditions sufficient for advertising to raise prices. This will occur, for example, when firms play a supermodular game – a structure that considers the type of advertising (i.e., persuasive, image creating, or informative) and the effect that advertising has on a firm’s demand and costs. We also compare results from two simple duopoly models, one with horizontal and the other with vertical differentiation, and find that only the model with horizontal differentiation is supermodular for the forms of advertising that are thought to raise price (e.g., persuasive advertising). In consideration of these theoretical issues, we then develop an empirical model to determine whether advertising raises prices in the US brewing and cigarette industries.Advertising, Price, Supermodularity, Brewing Industry, Cigarette Industry, L13, L66, M37,

Unusual hepatocellular carcinoma with macroscopic biliary tumor thrombus accompanied by rim calcification and no arterial-phase enhancement

We encountered a case of hepatocellular carcinoma (HCC) with macroscopic biliary tumor thrombus, which was a rare manifestation of HCC that simultaneously showed rim calcification and no arterial-phase enhancement. A 67-year-old woman was admitted with back pain. Enhanced computed tomography revealed a hypodense hepatic tumor surrounded by rim calcification, and a dilated left hepatic duct containing dense material indicating tumor thrombi. Magnetic resonance imaging showed fat deposition in the main part of the tumor. Malignancy was strongly suspected because of the tumor thrombus and elevated PIVKA-II, left hepatic lobectomy was performed. Subsequent pathological examination revealed a moderately differentiated HCC invading into the left hepatic duct. It is well known that HCCs can show variety of imaging features. In this case, however, triple atypical features were observed simultaneously; those were macroscopic biliary tumor thrombus, no arterial-phase enhancement and rim calcification. We discussed how these unusual radiological images could be seen through comparing with pathological features