The outskirts of globular clusters as modified gravity probes

In the context of theories of gravity modified to account for the observed dynamics of galactic systems without the need to invoke the existence of dark matter, a prediction often appears regarding low acceleration systems: wherever $a$ falls below $a_{0}$ one should expect a transition from the classical to the modified gravity regime.This modified gravity regime will be characterised by equilibrium velocities which become independent of distance, and which scale with the fourth root of the total baryonic mass, $V^{4} \propto M$. The two above conditions are the well known flat rotation curves and Tully-Fisher relations of the galactic regime. Recently however, a similar phenomenology has been hinted at, at the outskirts of Galactic globular clusters, precisely in the region where $a<a_{0}$. Radial profiles of the projected velocity dispersion have been observed to stop decreasing along Keplerian expectations, and to level off at constant values beyond the radii where $a<a_{0}$. We have constructed gravitational equilibrium dynamical models for a number of globular clusters for which the above gravitational anomaly has been reported, using a modified Newtonian force law which yields equilibrium velocities equivalent to MOND. We find models can be easily constructed having an inner Newtonian region and an outer modified gravity regime, which reproduce all observational constraints, surface brightness profiles, total masses and line of sight velocity dispersion profiles. Through the use of detailed single stellar population models tuned individually to each of the globular clusters in question, we derive estimates of the total masses for these systems. Interestingly, we find that the asymptotic values of the velocity dispersion profiles are consistent with scaling with the fourth root of the total masses, as expected under modified gravity scenarios.Comment: Accepted in ApJ, 13 pages, 7 figure

What is the redshift of the gamma- ray BL Lac source S4 0954+65?

High signal-to-noise ratio spectroscopic observations of the BL Lac object S4 0954+65 at the alleged redshift z = 0.367 are presented. This source was detected at gamma frequencies by MAGIC (TeV) and FERMI (GeV) telescopes during a remarkable outburst that occurred in February 2015, making the determination of its distance particularly relevant for our understanding of the properties of the Extragalactic Background Light. Contrary to previous reports on the redshift, we found that the optical spectrum is featureless at an equivalent width limit of \sim 0.1 Ang. A critical analysis of the existing observations indicates that the redshift is still unknown. Based on the new data we estimate a lower limit to the redshift at z \geq 0.45.Comment: Minor comment and accepted for publication in Astronomical Journa

Evidence for anisotropic motion of the clouds in broad-line regions of BL Lacertae objects

The masses of central massive black holes in BL Lac objects are estimated from their host galaxy absolute magnitude at R-band by using the empirical relation between absolute magnitude of host galaxy and black hole mass. Only a small fraction of BL Lac objects exhibit weak broad-line emission, and we derive the sizes of the broad-line regions (BLRs) in these BL Lac objects from the widths of their broad emission lines on the assumption of the clouds being virilized in BLRs. It is found that the sizes of the BLRs in these sources are usually 2-3 orders of magnitude larger than that expected by the empirical correlation between BLR size and optical luminosity defined by a sample of Seyfert galaxies and quasars. We discuss a variety of possibilities and suggest it may probably be attributed to anisotropic motion of the BLR clouds in these BL Lac objects. If the BLR geometry of these sources is disk-like, the viewing angles between the axis and the line of sight are in the range of 2-12 degrees, which is consistent with the unification schemes.Comment: 5 pages, accepted for publication in Ap

HST Observations of the Optical Jets of PKS 0521-365, 3C371, and PKS 2201+044

HST observations have led to the discovery of the optical counterpart of the radio jet of PKS 2201+044, and to a detailed analysis of the optical jets of PKS 0521-365 and 3C371. At HST spatial resolution these jets are well resolved, displaying knotty morphologies. When compared with radio maps of appropriate resolution, a clear one-to-one correspondence between optical and radio structures is found, showing that all detected optical structures are indeed related to the radio synchrotron emission. Photometry of the brightest knots shows that the radio-to-optical spectral index and the derived intensity of the equipartition magnetic field are approximately constant along the jet. Thus, present observations suggest that the electron energy distribution does not change significantly all along the jet.Comment: Accepted for publications on the Astrphysical Journal. Contains 14 pages and 5 figure

On the distance of PG 1553+11. A lineless BL Lac object active in the TeV band

Context: The redshift of PG 1553+11, a bright BL Lac object (V~14), is still unknown. It has been recently observed in the TeV band, a fact that offers an upper limit for the redshift z<0.4. Aims: We intend to provide a lower limit for the distance of the object. Methods: We used a chi^2 procedure to constrain the apparent magnitude of the host galaxy in archived HST images. Supposing that the host galaxy is typical of BL Lac objects (M_{R} -22.8), a lower limit to the distance can be obtained from the limit on the apparent magnitude of the host galaxy. Results: Using the 3 sigma limit on the host galaxy magnitude, the redshift is found to be greater or equal to 0.25. Conlusions: The redshift of PG 1553+11 is probably in the range z=0.3-0.4, making this object the most distant extragalactic source so far detected in the TeV energies. We suggest that other bright BL Lac objects of unknown redshift and similar spectroscopic characteristics may be interesting targets for TeV observations.Comment: Accepted for publication in A&A letters, 4 pages, 5 figure

Types of front of pack food labels: Do obese consumers care? Evidence from Northern Ireland

The introduction of an effective Front of Pack food labelling (FoPL) system is at the forefront of the food policy debate. Nutritional information is seen as an effective tool to help fight obesity and its associated co-morbidities, such as cancer and cardiovascular disease, for which unhealthy diet represent a major preventable risk factor. This paper explores the influence of FoPL formats on consumer’s stated choice of weekly food baskets using data from a discrete choice experiment carried out in Northern Ireland in 2011. Two of the three baskets were experimentally designed while the third represented the respondent’s actual current food choice (or status-quo basket). Four nutritional attributes were used: (i) total fat, (ii) saturated fat, (iii) salt, and (iv) sugar. Baskets were portrayed at different price levels to elicit the sensitivity of choice to price and to derive marginal willingness to pay estimates. Results from random utility models with various forms of heterogeneity reject the null of no association between preference classes and healthier food baskets and also the null of no effect of the nutritional information described. We find that the influence of the FoPL format used to convey nutritional information combines with selected socio-demographic covariates to determine membership to preference classes. A sensitivity analysis is used to validate the preferred model and the response sensitivity of selection probabilities to potential policy levers, such as a more realistic appreciation of self-body image and the habit of reading labels