The global mass function of M15

Data obtained with the NICMOS instrument on board the Hubble Space Telescope (HST) have been used to determine the H-band luminosity function (LF) and mass function (MF) of three stellar fields in the globular cluster M15, located ~7' from the cluster centre. The data confirm that the cluster MF has a characteristic mass of ~0.3 Msolar, as obtained by Paresce & De Marchi (2000) for a stellar field at 4.6' from the centre. By combining the present data with those published by other authors for various radial distances (near the centre, at 20" and at 4.6'), we have studied the radial variation of the LF due to the effects of mass segregation and derived the global mass function (GMF) using the Michie-King approach. The model that simultaneously best fits the LF at various locations, the surface brightness profile and the velocity dispersion profile suggests that the GMF should resemble a segmented power-law with the following indices: x ~ 0.8 for stars more massive than 0.8 Msolar, x ~ 0.9 for 0.3 - 0.8 Msolar and x ~ -2.2 at smaller masses (Salpeter's IMF would have x=1.35). The best fitting model also suggests that the cluster mass is ~5.4 10^5 Msolar and that the mass-to-light ratio is on average M/L_V ~ 2.1, with M/L_V ~ 3.7 in the core. A large amount of mass (~ 44 %) is found in the cluster core in the form of stellar heavy remnants, which may be sufficient to explain the mass segregation in M15 without invoking the presence of an intermediate-mass black hole.Comment: 12 pages, 10 figures, accepted for publication in A&

NGC2298: a globular cluster on its way to disruption

We have studied the stellar main sequence (MS) of the globular cluster NGC2298 using deep HST/ACS observations in the F606W and F814W bands covering an area of 3.4' x 3.4' around the cluster centre or about twice the cluster's half-mass radius. The colour-magnitude diagram that we derive in this way reveals a narrow and well defined MS extending down to the 10 sigma detection limit at m_606~26.5, m_814~25, corresponding to stars of ~0.2 Msolar. The luminosity function (LF) obtained with these data, once corrected for the limited effects of photometric incompleteness, reveals a remarkable deficiency of low-mass stars as well as a radial gradient, in that the LF becomes progressively steeper with radius. Using the mass-luminosity relation appropriate for the metallicity of NGC2298, we derive the cluster's global mass function (GMF) by using a multi-mass Michie-King model. Over the range 0.8 - 0.2 Msolar, the number of stars per unit mass decreases following a power-law distribution of the type dN/dm \propto m^(0.5), where, for comparison, typical halo clusters have dN/dm \propto m^(-1.5). If the IMF of NGC2298 was similar to that of other metal poor halo clusters, like e.g. NGC6397, the present GMF that we obtain implies that this object must have lost of order 85% of its original mass, at a rate much higher than that suggested by current models based on the available cluster orbit. The latter may, therefore, need revision.Comment: 9 pages, 6 figures, accepted for publication in Astronomy and Astrophysic

Why haven't loose globular clusters collapsed yet?

We report on the discovery of a surprising observed correlation between the slope of the low-mass stellar global mass function (GMF) of globular clusters (GCs) and their central concentration parameter c=log(r_t/r_c), i.e. the logarithmic ratio of tidal and core radii. This result is based on the analysis of a sample of twenty Galactic GCs with solid GMF measurements from deep HST or VLT data. All the high-concentration clusters in the sample have a steep GMF, most likely reflecting their initial mass function. Conversely, low-concentration clusters tend to have a flatter GMF implying that they have lost many stars via evaporation or tidal stripping. No GCs are found with a flat GMF and high central concentration. This finding appears counter-intuitive, since the same two-body relaxation mechanism that causes stars to evaporate and the cluster to eventually dissolve should also lead to higher central density and possibly core-collapse. Therefore, more concentrated clusters should have lost proportionately more stars and have a shallower GMF than low concentration clusters, contrary to what is observed. It is possible that severely depleted GCs have also undergone core collapse and have already recovered a normal radial density profile. It is, however, more likely that GCs with a flat GMF have a much denser and smaller core than suggested by their surface brightness profile and may well be undergoing collapse at present. In either case, we may have so far seriously underestimated the number of post core-collapse clusters and many may be lurking in the Milky Way.Comment: Four pages, one figure, accepted for publication in ApJ Letter

Absorptive capacity and relationship learning mechanisms as complementary drivers of green innovation performance

This paper aims to explore in depth how internal and external knowledge-based drivers actually affect the firms\u2019 green innovation performance. Subsequently, this study analyzes the relationships between absorptive capacity (internal knowledge-based driver), relationship learning (external knowledge-based driver) and green innovation performance. This study relies on a sample of 112 firms belonging to the Spanish automotive components manufacturing sector (ACMS) and uses partial least squares path modeling to test the hypotheses proposed. The empirical results show that both absorptive capacity and relationship learning exert a significant positive effect on the dependent variable and that relationship learning moderates the link between absorptive capacity and green innovation performance. This paper presents some limitations with respect to the particular sector (i.e. the ACMS) and geographical context (Spain). For this reason, researchers must be thoughtful while generalizing these results to distinct scenarios. Managers should devote more time and resources to reinforce their absorptive capacity as an important strategic tool to generate new knowledge and hence foster green innovation performance in manufacturing industries. The paper shows the importance of encouraging decision-makers to cultivate and rely on relationship learning mechanisms with their main stakeholders and to acquire the necessary information and knowledge that might be valuable in the maturity of green innovations. This study proposes that relationship learning plays a moderating role in the relationship between absorptive capacity and green innovation performance

Why is the mass function of NGC 6218 flat?

We have used the FORS-1 camera on the VLT to study the main sequence (MS) of the globular cluster NGC 6218 in the V and R bands. The observations cover an area of 3.4 x 3.4 around the cluster centre and probe the stellar population out to the cluster's half-mass radius (r_h ~ 2.2). The colour-magnitude diagram (CMD) that we derive in this way reveals a narrow and well defined MS extending down to the 5 sigma detection limit at V~25, or about 6 magnitudes below the turn-off, corresponding to stars of ~ 0.25 Msolar. The luminosity function (LF) obtained with these data shows a marked radial gradient, in that the ratio of lower- and higher-mass stars increases monotonically with radius. The mass function (MF) measured at the half-mass radius, and as such representative of the clusters global properties, is surprisingly flat. Over the range 0.4 - 0.8 Msolar, the number of stars per unit mass follows a power-law distribution of the type dN/dm \propto m^{0}, where, for comparison, Salpeter's IMF would be dN/dm \propto m^{-2.35}. We expect that such a flat MF does not represent the cluster's IMF but is the result of severe tidal stripping of the stars from the cluster due to its interaction with the Galaxy's gravitational field. Our results cannot be reconciled with the predictions of recent theoretical models that imply a relatively insignificant loss of stars from NGC 6218 as measured by its expected very long time to disruption. They are more consistent with the orbital parameters based on the Hipparcos reference system that imply a much higher degree of interaction of this cluster with the Galaxy than assumed by those models. Our results indicate that, if the orbit of a cluster is known, the slope of its MF could be useful in discriminating between the various models of the Galactic potential.Comment: 11 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

The Mass Function of Main Sequence Stars in NGC6397 from Near IR and Optical High Resolution HST Observations

We have investigated the properties of the stellar mass function in the globular cluster NGC6397 using a large set of HST observations that include WFPC2 images in V and I, obtained at ~4' and 10' radial distances, and a series of deep images in the J and H bands obtained with the NIC2 and NIC3 cameras of NICMOS pointed to regions located ~4.5' and ~3.2' from the center. These observations span the region from ~1 to ~3 times the cluster's half-light radius. All luminosity functions, derived from color magniutde diagrams, increase with decreasing luminosity up to a peak at M_I~8.5 or M_H~7 and then precipitously drop well before photometric incompleteness becomes significant. Within the observational uncertainties, at M_I~12 or M_H~10.5 (~0.09 Msun) the luminosity functions are compatible with zero. By applying the best available mass- luminosity relation appropriate to the metallicity of NGC6397 to both the optical and IR data, we obtain a mass function that shows a break in slope at \~0.3 Msun. No single exponent power-law distribution is compatible with these data, regardless of the value of the exponent. We find that a dynamical model of the cluster can simultaneously reproduce all the luminosity functions observed throughout the cluster only if the IMF rises as m**-1.6 in the range 0.8-0.3 Msun and then drops as m**0.2 below ~0.3 Msun. Adopting a more physical log-normal distribution for the IMF, all these data taken together imply a best fit distribution with characteristic mass m_c~0.3 and sigma~1.8.Comment: 18 pages, 6 figures (ps). Accepted for publication in Ap

On the Globular Cluster IMF below 1 Solar Mass

(Abridged) Accurate luminosity functions (LF) for a dozen globular clusters have now been measured at or just beyond their half-light radius using HST. They span almost the entire cluster main sequence below ~ 0.75 Msolar. All these clusters exhibit LF that rise continuously from an absolute I magnitude M_I ~ 6 to a peak at M_I ~ 8.5-9 and then drop with increasing M_I. Transformation of the LF into mass functions (MF) by means of the most recent mass luminosity relations that are consistent with all presently available data on the physical properties of low mass, low metallicity stars shows that all the LF observed so far can be obtained from MF having the shape of a log-normal distribution with characteristic mass m_c=0.33 +/- 0.03 Msolar and standard deviation sigma = 1.81 +/- 0.19. After correction for the effects of mass segregation, the variation of the ratio of the number of higher to lower mass stars with cluster mass or any simple orbital parameter or the expected time to disruption recently computed for these clusters shows no statistically significant trend over a range of this last parameter of more than a factor of 100. We conclude that the global MF of these clusters have not been measurably modified by evaporation and tidal interactions with the Galaxy and, thus, should reflect the initial distribution of stellar masses. Since the log-normal function that we find is also very similar to the one obtained independently for much younger clusters and to the form expected theoretically, the implication seems to be unavoidable that it represents the true stellar IMF for this type of stars in this mass range.Comment: Accepted for publication in The Astrophysical Journal. Contains 28 pages with 6 figure

Organic Livestock Production- A Bibliometric Review

Due to the increasing interest in organic farming, an overview of this research area is provided through a bibliometric analysis conducted between April and May 2019. A total of 320 documents were published up until 2018 on organic livestock farming, with an annual growth rate of 9.33% and a clear increase since 2005; 268 documents have been published in 111 journals. Germany is the country with the largest number of published papers (56 documents). Authors\u2019 top keywords (excluding keywords used for running the search) included: animal welfare (29 times), animal health (22 times), cattle (15 times), grazing (10 times), and sheep (10 times). This could indicate that more research has been done on cattle because of the importance of this species in Germany. Moreover, the prevalence of the terms \u2018animal welfare\u2019 and \u2018animal health\u2019 may indicate that the research on organic livestock production has been focused on these two areas. The bibliometric analysis indicates that: i) countries focused the organic livestock production research on their main production, and ii) more research in species other than cattle and sheep is needed