Notch signaling augments the canonical Wnt pathway to specify the size of the otic placode

The inner ear derives from a patch of ectoderm defined by expression of the transcription factor Pax2. We recently showed that this Pax2^+ ectoderm gives rise not only to the otic placode but also to the surrounding cranial epidermis, and that Wnt signaling mediates this placode-epidermis fate decision. We now present evidence for reciprocal interactions between the Wnt and Notch signaling pathways during inner ear induction. Activation of Notch1 in Pax2+ ectoderm expands the placodal epithelium at the expense of cranial epidermis, whereas loss of Notch1 leads to a reduction in the size of the otic placode. We show that Wnt signaling positively regulates Notch pathway genes such as Jag1, Notch1 and Hes1, and we have used transgenic Wnt reporter mice to show that Notch signaling can modulate the canonical Wnt pathway. Gain- and loss-of-function mutations in the Notch and Wnt pathways reveal that some aspects of otic placode development - such as Pax8 expression and the morphological thickening of the placode - can be regulated independently by either Notch or Wnt signals. Our results suggest that Wnt signaling specifies the size of the otic placode in two ways, by directly upregulating a subset of otic genes, and by positively regulating components of the Notch signaling pathway, which then act to augment Wnt signaling

Irregular conformal blocks, with an application to the fifth and fourth Painlev\'e equations

We develop the theory of irregular conformal blocks of the Virasoro algebra. In previous studies, expansions of irregular conformal blocks at regular singular points were obtained as degeneration limits of regular conformal blocks; however, such expansions at irregular singular points were not clearly understood. This is because precise definitions of irregular vertex operators had not been provided previously. In this paper, we present precise definitions of irregular vertex operators of two types and we prove that one of our vertex operators exists uniquely. Then, we define irregular conformal blocks with at most two irregular singular points as expectation values of given irregular vertex operators. Our definitions provide an understanding of expansions of irregular conformal blocks and enable us to obtain expansions at irregular singular points. As an application, we propose conjectural formulas of series expansions of the tau functions of the fifth and fourth Painlev\'e equations, using expansions of irregular conformal blocks at an irregular singular point.Comment: 26 page

Sub-parsec-scale Accleration of the Radio Jet in the Powerful Radio Galaxy NGC 6251

In order to investigate the genesis of powerful radio jet, we have mapped the central 10 pc region of the nearby radio galaxy NGC 6251 with a 0.2 pc resolution using Very Long Baseline Interferometer (VLBI) at two radio frequencies, 5 GHz and 15 GHz, we have found the sub-parsec-scale counterjet for the first time in this radio galaxy. This discovery allows us to investigate the jet acceleration based on the relativistic beaming model.Comment: 7 pages with 7 figures. To appear in PASJ, 52, No. 5, Oct. 25, 200

An Origin of the Huge Far-Infrared Luminosity of Starburst Mergers

Recently Taniguchi and Ohyama found that the higher $^{12}$CO to $^{13}$CO integrated intensity ratios at a transition $J$=1--0, $R = I(^{12}$CO)$/I(^{13}$CO) $\gtrsim 20$, in a sample of starburst merging galaxies such as Arp 220 are mainly attributed to the depression of $^{13}$CO emission with respect to $^{12}$CO. Investigating the same sample of galaxies analyzed by Taniguchi & Ohyama, we find that there is a tight, almost linear correlation between the dust mass and $^{13}$CO luminosity. This implies that dust grains are also depressed in the high-$R$ starburst mergers, leading to the higher dust temperature ($T_{\rm d}$) in them because of the relative increase in the radiation density. Nevertheless, the average dust mass ($M_{\rm d}$) of the high-$R$ starburst mergers is higher significantly than that of non-high $R$ galaxies. This is naturally understood because the galaxy mergers could accumulate a lot of dust grains from their progenitor galaxies together with supply of dust grains formed newly in the star forming regions. Since $L$(FIR) $\propto M_{\rm d} T_{\rm d}^5$ given the dust emissivity law, $S_\nu \propto \lambda^{-1}$, the increases in both $M_{\rm d}$ and $T_{\rm d}$ explain well why the starburst mergers are so bright in the FIR. We discuss that the superwind activity plays an important role in destroying dust grains as well as dense gas clouds in the central region of mergers.Comment: 10 pages (aaspp4.sty), 3 postscript figures (embedded). Accepted for publication in Astrophysical Journal Letter

What Controls the Star Formation in Luminous Starburst Mergers ?

In order to understand what controls the star formation process in luminous starburst mergers (e.g., NGC 6240, Arp 220, and so on), we investigate observational properties of two samples of high-luminosity starburst galaxies mapped in CO($J$=1--0) independently using both the Owens Valley Radio Observatory (Scoville et al. 1991) and the IRAM interferometer (Downes & Solomon 1998). We find that the surface density of far-infrared luminosity, $\Sigma$(FIR), is proportional linearly to the H$_2$ surface mass density, $\Sigma$(H$_2$), for the two samples; $\Sigma$(FIR) $\propto \Sigma$(H$_2$)$^{1.01\pm0.06}$ with a correlation coefficient of 0.96. It is often considered that $\Sigma$(FIR) provides a good measure of the star formation rate per unit area, $\Sigma$(SFR). It is also known that molecular gas is dominated in circumnuclear regions in the luminous starburst mergers; i.e., $\Sigma$(gas) $\simeq \Sigma$(H$_2$). Therefore, the above relationship suggests a star formation law; $\Sigma$(SFR) $\propto \Sigma$(gas). We suggest that this star formation law favors the gravitational instability scenario rather than the cloud-cloud collision one.Comment: 14 pages, 2 figures. The Astrophysical Journal (Letters), in pres

Detection of Polarized Broad Emission in the Seyfert 2 Galaxy Mrk 573

We report the discovery of the scattered emission from a hidden broad-line region (BLR) in a Seyfert 2 galaxy, Mrk 573, based on our recent spectropolarimetric observation performed at the Subaru Telescope. This object has been regarded as a type 2 AGN without a hidden BLR by the previous observations. However, our high quality spectrum of the polarized flux of Mrk 573 shows prominent broad (~3000 km/s) H_alpha emission, broad weak H_beta emission, and subtle Fe II multiplet emission. Our new detection of these indications for the presence of the hidden BLR in the nucleus of Mrk 573 is thought to be owing to the high signal-to-noise ratio of our data, but the possibility of a time variation of the scattered BLR emission is also mentioned. Some diagnostic quantities such as the IRAS color, the radio power, and the line ratio of the emission from the narrow-line region of Mrk 573 are consistent with the distributions of such quantities of type 2 AGNs with a hidden BLR. Mrk 573 is thought to be an object whose level of the AGN activity is the weakest among the type 2 AGNs with a hidden BLR. In terms of the systematic differences between the type 2 AGNs with and without a hidden BLR, we briefly comment on an interesting Seyfert 2 galaxy, Mrk 266SW, which may possess a hidden BLR but has been treated as a type 2 AGNs without a hidden BLR.Comment: 9 pages including 6 figures, to appear in The Astronomical Journa