Fractal Dimensions and Scaling Laws in the Interstellar Medium and Galaxy Distributions: a new Field Theory Approach

We develop a field theoretical approach to the cold interstellar medium (ISM) and large structure of the universe. We show that a non-relativistic self- gravitating gas in thermal equilibrium with variable number of atoms or fragments is exactly equivalent to a field theory of a scalar field phi(x) with exponential self-interaction. We analyze this field theory perturbatively and non-perturbatively through the renormalization group(RG).We show scaling behaviour (critical) for a continuous range of the physical parameters as the temperature. We derive in this framework the scaling relation M(R) \sim R^{d_H} for the mass on a region of size R, and Delta v \sim R^\frac12(d_H -1) for the velocity dispersion. For the density-density correlations we find a power-law behaviour for large distances \sim |r_1 - r_2|^{2D - 6}.The fractal dimension D turns to be related with the critical exponent \nu by D = 1/ \nu. Mean field theory yields \nu = 1/2, D = 2. Both the Ising and the mean field values are compatible with the present ISM observational data:1.4\leq D \leq 2. We develop a field theoretical approach to the galaxy distribution considering a gas of self-gravitating masses on the FRW background, in quasi-thermal equi- librium. We show that it exhibits scaling behaviour by RG methods. The galaxy correlations are computed without assuming homogeneity. We find \sim r^{D-3} $. The theory allows to compute the three and higher density correlators without any assumption.We find that the connected N-points density scales as r_1^{N(D-3)}, when$ r_1 >> r_i

Planck 2013 results. XX. Cosmology from Sunyaev-Zeldovich cluster counts

We present constraints on cosmological parameters using number counts as a function of redshift for a sub-sample of 189 galaxy clusters from the Planck SZ (PSZ) catalogue. The PSZ is selected through the signature of the Sunyaev--Zeldovich (SZ) effect, and the sub-sample used here has a signal-to-noise threshold of seven, with each object confirmed as a cluster and all but one with a redshift estimate. We discuss the completeness of the sample and our construction of a likelihood analysis. Using a relation between mass $M$ and SZ signal $Y$ calibrated to X-ray measurements, we derive constraints on the power spectrum amplitude $\sigma_8$ and matter density parameter $\Omega_{\mathrm{m}}$ in a flat $\Lambda$CDM model. We test the robustness of our estimates and find that possible biases in the $Y$--$M$ relation and the halo mass function are larger than the statistical uncertainties from the cluster sample. Assuming the X-ray determined mass to be biased low relative to the true mass by between zero and 30%, motivated by comparison of the observed mass scaling relations to those from a set of numerical simulations, we find that $\sigma_8=0.75\pm 0.03$, $\Omega_{\mathrm{m}}=0.29\pm 0.02$, and $\sigma_8(\Omega_{\mathrm{m}}/0.27)^{0.3} = 0.764 \pm 0.025$. The value of $\sigma_8$ is degenerate with the mass bias; if the latter is fixed to a value of 20% we find $\sigma_8(\Omega_{\mathrm{m}}/0.27)^{0.3}=0.78\pm 0.01$ and a tighter one-dimensional range $\sigma_8=0.77\pm 0.02$. We find that the larger values of $\sigma_8$ and $\Omega_{\mathrm{m}}$ preferred by Planck's measurements of the primary CMB anisotropies can be accommodated by a mass bias of about 40%. Alternatively, consistency with the primary CMB constraints can be achieved by inclusion of processes that suppress power on small scales relative to the $\Lambda$CDM model, such as a component of massive neutrinos (abridged).Comment: 20 pages, accepted for publication by A&

Planck 2015 results: XXV. Diffuse low-frequency Galactic foregrounds

We discuss the Galactic foreground emission between 20 and 100 GHz based on observations by Planck and WMAP. The total intensity in this part of the spectrum is dominated by free-free and spinning dust emission, whereas the polarized intensity is dominated by synchrotron emission. The Commander component-separation tool has been used to separate the various astrophysical processes in total intensity. Comparison with radio recombination line templates verifies the recovery of the free-free emission along the Galactic plane. Comparison of the high-latitude H\u3b1 emission with our free-free map shows residuals that correlate with dust optical depth, consistent with a fraction (\ue2\u2030 30%) of H\u3b1 having been scattered by high-latitude dust. We highlight a number of diffuse spinning dust morphological features at high latitude. There is substantial spatial variation in the spinning dust spectrum, with the emission peak (in I\u3bd) ranging from below 20 GHz to more than 50 GHz. There is a strong tendency for the spinning dust component near many prominent H ii regions to have a higher peak frequency, suggesting that this increase in peak frequency is associated with dust in the photo-dissociation regions around the nebulae. The emissivity of spinning dust in these diffuse regions is of the same order as previous detections in the literature. Over the entire sky, the Commander solution finds more anomalous microwave emission (AME) than the WMAP component maps, at the expense of synchrotron and free-free emission. This can be explained by the difficulty in separating multiple broadband components with a limited number of frequency maps. Future surveys, particularly at 5-20 GHz, will greatly improve the separation by constraining the synchrotron spectrum. We combine Planck and WMAP data to make the highest signal-to-noise ratio maps yet of the intensity of the all-sky polarized synchrotron emission at frequencies above a few GHz. Most of the high-latitude polarized emission is associated with distinct large-scale loops and spurs, and we re-discuss their structure. We argue that nearly all the emission at 40deg > l >-90deg is part of the Loop I structure, and show that the emission extends much further in to the southern Galactic hemisphere than previously recognised, giving Loop I an ovoid rather than circular outline. However, it does not continue as far as the "Fermi bubble/microwave haze", making it less probable that these are part of the same structure. We identify a number of new faint features in the polarized sky, including a dearth of polarized synchrotron emission directly correlated with a narrow, roughly 20deg long filament seen in H\u3b1 at high Galactic latitude. Finally, we look for evidence of polarized AME, however many AME regions are significantly contaminated by polarized synchrotron emission, and we find a 2\u3c3 upper limit of 1.6% in the Perseus region

Planck 2015 results. XIII. Cosmological parameters

We present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005. For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent with the B-mode constraints from an analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We find no evidence for isocurvature perturbations or cosmic defects. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. The Planck results for base LCDM are in agreement with BAO data and with the JLA SNe sample. However the amplitude of the fluctuations is found to be higher than inferred from rich cluster counts and weak gravitational lensing. Apart from these tensions, the base LCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets

Photosynthesis in poor nutrient soils, in compacted soils, and under drought

Plants require the uptake of nutrients (in most cases via roots) and their incorporation into plant organs for growth. In non-woody species, 83% of fresh weight is water, 7% is carbon, 5% is oxygen, with the remaining 5% including hydrogen and such nutrients. In natural ecosystems, availability of nutrients in soils is heterogeneous, and many species often adapt their growth to the amount of nutrients that roots can take up by exploring the available soil volume. In agricultural areas, the lack of some nutrients is frequent. In both cases, plants must also face periods of drought and soil compaction. These environmental stresses are therefore not uncommon in natural ecosystems and crops, and the stressed plants often experience a decrease in photosynthetic CO2 fixation. In this chapter, we review changes observed in photosynthesis in response to nutrient deficiencies, soil compaction, and drought. The current knowledge on photosynthesis in carnivorous plants, as a special case of plant species growing in nutrient poor soils, is also included. Pigment limitations (chlorosis and/or necrosis), stomatal limitations, ultrastructural effects and mesophyll conductance limitations, photochemistry (primary reactions), carboxylation and Calvin-cycle reactions, and carbohydrate metabolism and transport will be discussed. With regard to nutrients, we have focused on the most common nutrition-related stresses in plants, the deficiencies of macro- (nitrogen, phosphorous, and potassium) and micronutrients (iron, manganese, copper, and zinc). Other nutrient deficiencies (or toxicities, both in the cases of essential nutrient excess or heavy metals) are not reviewed here. For other nutrient deficiencies and toxicities, and the role of the above-mentioned, and other nutrients (such as calcium and magnesium) in gas exchange, and as intracellular signal transducers, enzyme activators, and structure and function stabilizers of biological membranes, readers are referred to papers published elsewhere (Marschner H, Mineral nutrition of higher plants. Academic, London, 1995; Cakmak I, Kirkby EA, Physiol Plant 133:692–704, 2008; Morales F, Warren CR, Photosynthetic responses to nutrient deprivation and toxicities. In: Flexas J, Loreto F, Medrano H (eds) Terrestrial photosynthesis in a changing environment: a molecular, physiological and ecological approach. Cambridge University Press, Cambridge, pp 312–330, 2012; Hochmal AK, Schulze S, Trompelt K, Hippler M, Biochim Biophys Acta 1847:993–1003, 2015).This study was supported by the Spanish Ministry of Economy and Competitiveness (MINECO; projects AGL2012-31988, AGL2013-42175-R, AGL2016-75226-R, and AGL2016-79868-R, co-financed with FEDER), the Aragón Government (Group A03), grant LO1204 (Sustainable development of research in the Centre of the Region Haná) from the National Program of Sustainability I, and by the Czech Science Foundation Agency (project 16-07366Y). FM wishes to thank JC Martínez for his help with some periodic bibliographic searches.Peer reviewe