CI and CO in the nearby spiral galaxies IC 342 and Maffei 2

We present J=2-1, J=3-2, J=4-3 12CO and 492 GHz [CI] maps as well as J=2-1 and J=3-2 13CO measurements of the central regions in the nearby Sc galaxies IC 342 and Maffei 2. In both galaxies, the distribution of CO and [CI] is strongly concentrated towards the modest starburst centers. Both galaxies have nearly identical 12CO transitional ratios but the relative intensities of their 13CO and [CI] emission lines differ significantly and require modelling with a multi-component molecular gas. Both have a dense component (n(H2) = 10**4 - 10**5 cm**-3) with kinetic temperatures T(kin) = 10 - 20 K (IC 342) or 20 - 60 K (Maffei 2), and a less dense (IC 342: a few hundred cm**-3 at most; Maffei 2: about 3 x 10**3 cm**-3 and hotter (T(kin) = 100 - 150 K) component. In both galaxies, neutral and ionized atomic carbon amounts are between 1.5 and 2.5 times those of CO, and in both about half to two thirds of the molecular gas mass is associated with a hot PDR phase. Within R = 0.25 kpc, the center of IC 342 contains an (atomic and molecular) gas mass of 1 x 10**7 M(sun) and a peak face-on gas mass density of about 70 M(sun) pc**-2. For Maffei 2 these numbers are less clearly defined, mainly because of its uncertain distance and carbon abundance. We find a gass mass M(gas) > 0.5 x 10**7 M(sun) and a peak face-on gas mass density of about 35 M(sun) pc**-2.Comment: 11 pages; accepted by astronomy and Astrophysic

On mass-constraints implied by the relativistic precession model of twin-peak quasi-periodic oscillations in Circinus X-1

Boutloukos et al. (2006) discovered twin-peak quasi-periodic oscillations (QPOs) in 11 observations of the peculiar Z-source Circinus X-1. Among several other conjunctions the authors briefly discussed the related estimate of the compact object mass following from the geodesic relativistic precession model for kHz QPOs. Neglecting the neutron star rotation they reported the inferred mass M_0 = 2.2 +/- 0.3 M_\sun. We present a more detailed analysis of the estimate which involves the frame-dragging effects associated with rotating spacetimes. For a free mass we find acceptable fits of the model to data for (any) small dimensionless compact object angular momentum j=cJ/GM^2. Moreover, quality of the fit tends to increase very gently with rising j. Good fits are reached when M ~ M_0[1+0.55(j+j^2)]. It is therefore impossible to estimate the mass without the independent knowledge of the angular momentum and vice versa. Considering j up to 0.3 the range of the feasible values of mass extends up to 3M_\sun. We suggest that similar increase of estimated mass due to rotational effects can be relevant for several other sources.Comment: 10 pages, 9 figures (in colour

A new proof of a theorem of Mansour and Sun

We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe's identity.Comment: 3 pages, to appear in European J. Combin., see also http://math.univ-lyon1.fr/~gu