Trade-Offs Between Size and Degree in Polynomial Calculus

Building on [Clegg et al. \u2796], [Impagliazzo et al. \u2799] established that if an unsatisfiable k-CNF formula over n variables has a refutation of size S in the polynomial calculus resolution proof system, then this formula also has a refutation of degree k + O(?(n log S)). The proof of this works by converting a small-size refutation into a small-degree one, but at the expense of increasing the proof size exponentially. This raises the question of whether it is possible to achieve both small size and small degree in the same refutation, or whether the exponential blow-up is inherent. Using and extending ideas from [Thapen \u2716], who studied the analogous question for the resolution proof system, we prove that a strong size-degree trade-off is necessary

Automating Resolution is NP-Hard

We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatizable unless P = NP. Indeed, we show it is NP-hard to distinguish between formulas that have Resolution refutations of polynomial length and those that do not have subexponential length refutations. This also implies that Resolution is not automatizable in subexponential time or quasi-polynomial time unless NP is included in SUBEXP or QP, respectively

CO ro-vibrational lines in HD100546: A search for disc asymmetries and the role of fluorescence

We have studied the emission of CO ro-vibrational lines in the disc around the Herbig Be star HD100546 with the final goal of using these lines as a diagnostic to understand inner disc structure in the context of planet formation. High-resolution IR spectra of CO ro-vibrational emission at eight different position angles were taken with CRIRES at the VLT. From these spectra flux tables, CO ro-vibrational line profiles, and population diagrams were produced. We have investigated variations in the line profile shapes and line strengths as a function of slit position angle. We used the thermochemical disc modelling code ProDiMo based on the chemistry, radiation field, and temperature structure of a previously published model for HD100546. Comparing observations and the model, we investigated the possibility of disc asymmetries, the excitation mechanism (UV fluorescence), the geometry, and physical conditions of the inner disc. The observed CO ro-vibrational lines are largely emitted from the inner rim of the outer disc at 10-13 AU. The line shapes are similar for all v levels and line fluxes from all vibrational levels vary only within one order of magnitude. All line profile asymmetries and variations can be explained with a symmetric disc model to which a slit correction and pointing offset is applied. Because the angular size of the CO emitting region (10-13 AU) and the slit width are comparable the line profiles are very sensitive to the placing of the slit. The model reproduces the line shapes and the fluxes of the v=1-0 lines as well as the spatial extent of the CO ro-vibrational emission. It does not reproduce the observed band ratios of 0.5-0.2 with higher vibrational bands. We find that lower gas volume densities at the surface of the inner rim of the outer disc can make the fluorescence pumping more effcient and reproduce the observed band ratios.Comment: 20 pages, 21 figure

Transmission spectroscopy of the inflated exo-Saturn HAT-P-19b

We observed the Saturn-mass and Jupiter-sized exoplanet HAT-P-19b to refine its transit parameters and ephemeris as well as to shed first light on its transmission spectrum. We monitored the host star over one year to quantify its flux variability and to correct the transmission spectrum for a slope caused by starspots. A transit of HAT-P-19b was observed spectroscopically with OSIRIS at the Gran Telescopio Canarias in January 2012. The spectra of the target and the comparison star covered the wavelength range from 5600 to 7600 AA. One high-precision differential light curve was created by integrating the entire spectral flux. This white-light curve was used to derive absolute transit parameters. Furthermore, a set of light curves over wavelength was formed by a flux integration in 41 wavelength channels of 50 AA width. We analyzed these spectral light curves for chromatic variations of transit depth. The transit fit of the combined white-light curve yields a refined value of the planet-to-star radius ratio of 0.1390 pm 0.0012 and an inclination of 88.89 pm 0.32 degrees. After a re-analysis of published data, we refine the orbital period to 4.0087844 pm 0.0000015 days. We obtain a flat transmission spectrum without significant additional absorption at any wavelength or any slope. However, our accuracy is not sufficient to significantly rule out the presence of a pressure-broadened sodium feature. Our photometric monitoring campaign allowed for an estimate of the stellar rotation period of 35.5 pm 2.5 days and an improved age estimate of 5.5^+1.8_-1.3 Gyr by gyrochronology.Comment: 14 pages, 9 figures, Accepted for publication in A&

Do galaxies that leak ionizing photons have extreme outflows?

To reionize the early universe, high-energy photons must escape the galaxies that produce them. It has been suggested that stellar feedback drives galactic outflows out of star-forming regions, creating low density channels through which ionizing photons escape into the inter-galactic medium. We compare the galactic outflow properties of confirmed Lyman continuum (LyC) leaking galaxies to a control sample of nearby star-forming galaxies to explore whether the outflows from leakers are extreme as compared to the control sample. We use data from the Cosmic Origins Spectrograph on the Hubble Space Telescope to measure the equivalent widths and velocities of Si II and Si III absorption lines, tracing neutral and ionized galactic outflows. We find that the Si II and Si III equivalent widths of the LyC leakers reside on the low-end of the trend established by the control sample. The leakers' velocities are not statistically different than the control sample, but their absorption line profiles have a different asymmetry: their central velocities are closer to their maximum velocities. The outflow kinematics and equivalent widths are consistent with the scaling relations between outflow properties and host galaxy properties -- most notably metallicity -- defined by the control sample. Additionally, we use the Ly\alpha\ profiles to show that the Si II equivalent width scales with the Ly\alpha\ peak velocity separation. We determine that the low equivalent widths of the leakers are likely driven by low metallicities and low H I column densities, consistent with a density-bounded ionization region, although we cannot rule out significant variations in covering fraction. While we do not find that the LyC leakers have extreme outflow velocities, the low maximum-to-central velocity ratios demonstrate the importance of the acceleration and density profiles for LyC and Ly\alpha\ escape. [abridged]Comment: 17 pages, 8 Figures. Accepted for publication in Astronomy & Astrophysic

Probing the initial conditions of high-mass star formation -- IV. Gas dynamics and NH2_2D chemistry in high-mass precluster and protocluster clumps

The initial stage of star formation is a complex area study because of its high density and low temperature. Under such conditions, many molecules become depleted from the gas phase by freezing out onto dust grains. However, the deuterated species could remain gaseous and are thus ideal tracers. We investigate the gas dynamics and NH$_2$D chemistry in eight massive pre/protocluster clumps. We present NH$_2$D 1$_{11}$-1$_{01}$ (at 85.926 GHz), NH$_3$ (1, 1) and (2, 2) observations in the eight clumps using the PdBI and the VLA, respectively. We find that the distribution between deuterium fractionation and kinetic temperature shows a number density peak at around $T_{\rm kin}=16.1$ K, and the NH$_2$D cores are mainly located at a temperature range of 13.0 to 22.0 K. We detect seven instances of extremely high deuterium fractionation of $1.0 \leqslant D_{\rm frac} \leqslant 1.41$. We find that the NH$_2$D emission does not appear to coincide exactly with either dust continuum or NH$_3$ peak positions, but often surrounds the star-formation active regions. This suggests that the NH$_{2}$D has been destroyed by the central young stellar object (YSO) due to its heating. The detected NH$_2$D lines are very narrow with a median width of $\rm 0.98\pm0.02 km/s$. The extracted NH$_2$D cores are gravitationally bound ($\alpha_{\rm vir} < 1$), are likely prestellar or starless, and can potentially form intermediate-mass or high-mass stars. Using NH$_3$ (1, 1) as a dynamical tracer, we find very complicated dynamical movement, which can be explained by a combined process with outflow, rotation, convergent flow, collision, large velocity gradient, and rotating toroids. High deuterium fractionation strongly depends on the temperature condition. NH$_2$D is a poor evolutionary indicator of high-mass star formation in evolved stages, but a useful tracer in the starless and prestellar cores.Comment: 27 pages, 25 figures, 6 tables, accepted for publication in A&

A new astrophysical solution to the Too Big To Fail problem - Insights from the MoRIA simulations

We test whether advanced galaxy models and analysis techniques of simulations can alleviate the Too Big To Fail problem (TBTF) for late-type galaxies, which states that isolated dwarf galaxy kinematics imply that dwarfs live in lower-mass halos than is expected in a {\Lambda}CDM universe. Furthermore, we want to explain this apparent tension between theory and observations. To do this, we use the MoRIA suite of dwarf galaxy simulations to investigate whether observational effects are involved in TBTF for late-type field dwarf galaxies. To this end, we create synthetic radio data cubes of the simulated MoRIA galaxies and analyse their HI kinematics as if they were real, observed galaxies. We find that for low-mass galaxies, the circular velocity profile inferred from the HI kinematics often underestimates the true circular velocity profile, as derived directly from the enclosed mass. Fitting the HI kinematics of MoRIA dwarfs with a theoretical halo profile results in a systematic underestimate of the mass of their host halos. We attribute this effect to the fact that the interstellar medium of a low-mass late-type dwarf is continuously stirred by supernova explosions into a vertically puffed-up, turbulent state to the extent that the rotation velocity of the gas is simply no longer a good tracer of the underlying gravitational force field. If this holds true for real dwarf galaxies as well, it implies that they inhabit more massive dark matter halos than would be inferred from their kinematics, solving TBTF for late-type field dwarf galaxies.Comment: 21 pages, 21 figures. Accepted for publication in A&A. Corrected certain values in Table

A necklace of dense cores in the high-mass star forming region G35.20-0.74N: ALMA observations

The present study aims at characterizing the massive star forming region G35.20N, which is found associated with at least one massive outflow and contains multiple dense cores, one of them recently found associated with a Keplerian rotating disk. We used ALMA to observe the G35.20N region in the continuum and line emission at 350 GHz. The observed frequency range covers tracers of dense gas (e.g. H13CO+, C17O), molecular outflows (e.g. SiO), and hot cores (e.g. CH3CN, CH3OH). The ALMA 870 um continuum emission map reveals an elongated dust structure (0.15 pc long and 0.013 pc wide) perpendicular to the large-scale molecular outflow detected in the region, and fragmented into a number of cores with masses 1-10 Msun and sizes 1600 AU. The cores appear regularly spaced with a separation of 0.023 pc. The emission of dense gas tracers such as H13CO+ or C17O is extended and coincident with the dust elongated structure. The three strongest dust cores show emission of complex organic molecules characteristic of hot cores, with temperatures around 200 K, and relative abundances 0.2-2x10^(-8) for CH3CN and 0.6-5x10^(-6) for CH3OH. The two cores with highest mass (cores A and B) show coherent velocity fields, with gradients almost aligned with the dust elongated structure. Those velocity gradients are consistent with Keplerian disks rotating about central masses of 4-18 Msun. Perpendicular to the velocity gradients we have identified a large-scale precessing jet/outflow associated with core B, and hints of an east-west jet/outflow associated with core A. The elongated dust structure in G35.20N is fragmented into a number of dense cores that may form massive stars. Based on the velocity field of the dense gas, the orientation of the magnetic field, and the regularly spaced fragmentation, we interpret this elongated structure as the densest part of a 1D filament fragmenting and forming massive stars.Comment: 24 pages, 26 figures, accepted for publication in Astronomy and Astrophysics (abstract modified to fit arXiv restrictions

A multi-wavelength observation and investigation of six infrared dark clouds

Context. Infrared dark clouds (IRDCs) are ubiquitous in the Milky Way, yet they play a crucial role in breeding newly-formed stars. Aims. With the aim of further understanding the dynamics, chemistry, and evolution of IRDCs, we carried out multi-wavelength observations on a small sample. Methods. We performed new observations with the IRAM 30 m and CSO 10.4 m telescopes, with tracers ${\rm HCO^+}$, HCN, ${\rm N_2H^+}$, ${\rm C^{18}O}$, DCO$^+$, SiO, and DCN toward six IRDCs G031.97+00.07, G033.69-00.01, G034.43+00.24, G035.39-00.33, G038.95-00.47, and G053.11+00.05. Results. We investigated 44 cores including 37 cores reported in previous work and seven newly-identified cores. Toward the dense cores, we detected 6 DCO$^+$, and 5 DCN lines. Using pixel-by-pixel spectral energy distribution (SED) fits of the $\textit{Herschel}$ 70 to 500 $\mu$m, we obtained dust temperature and column density distributions of the IRDCs. We found that ${\rm N_2H^+}$ emission has a strong correlation with the dust temperature and column density distributions, while ${\rm C^{18}O}$ showed the weakest correlation. It is suggested that ${\rm N_2H^+}$ is indeed a good tracer in very dense conditions, but ${\rm C^{18}O}$ is an unreliable one, as it has a relatively low critical density and is vulnerable to freezing-out onto the surface of cold dust grains. The dynamics within IRDCs are active, with infall, outflow, and collapse; the spectra are abundant especially in deuterium species. Conclusions. We observe many blueshifted and redshifted profiles, respectively, with ${\rm HCO^+}$ and ${\rm C^{18}O}$ toward the same core. This case can be well explained by model "envelope expansion with core collapse (EECC)".Comment: 24 pages, 11 figures, 4 tables. To be published in A&A. The resolutions of the pictures are cut dow

Structure and Fragmentation of a high line-mass filament: Nessie

An increasing number of hundred-parsec scale, high line-mass filaments have been detected in the Galaxy. Their evolutionary path, including fragmentation towards star formation, is virtually unknown. We characterize the fragmentation within the Nessie filament, covering size-scales between $\sim$ 0.1-100 pc. We also connect the small-scale fragments to the star-forming potential of the cloud. We combine near-infrared data from the VVV survey with mid-infrared GLIMPSE data to derive a high-resolution dust extinction map and apply a wavelet decomposition technique on it to analyze the fragmentation characteristics of the cloud, which are compared with predictions from fragmentation models. We compare the detected objects to those identified in $\sim$ 10 times coarser resolution from ATLASGAL data. We present a high-resolution extinction map of Nessie. We estimate the mean line-mass of Nessie to be $\sim$ 627 M$_\odot$/pc and the distance to be $\sim$ 3.5 kpc. We find that Nessie shows fragmentation at multiple size scales. The nearest-neighbour separations of the fragments at all scales are within a factor of 2 of the Jeans' length at that scale. However, the relationship between the mean densities of the fragments and their separations is significantly shallower than expected for Jeans' fragmentation. The relationship is similar to the one predicted for a filament that exhibits a Larson-like scaling between size-scale and velocity dispersion; such a scaling may result from turbulent support. Based on the number of YSOs in Nessie, we estimate that the star formation rate is $\sim$ 371 M$_\odot$/Myr; similar values result if using the number of dense cores, or the amount of dense gas, as the proxy of star formation. The star formation efficiency is 0.017. These numbers indicate that Nessie's star-forming content is comparable to the Solar neighborhood giant molecular clouds like Orion A