Eccentricity samples: implications on the potential and the velocity distribution

Planar and vertical epicycle frequencies and local angular velocity are related to the derivatives up to the second order of the local potential and can be used to test the shape of the potential from stellar disc samples. These samples show a more complex velocity distribution than halo stars and should provide a more realistic test. We assume an axisymmetric potential allowing a mixture of independent ellipsoidal velocity distributions, of separable or Staeckel form in cylindrical or spherical coordinates. We prove that values of local constants are not consistent with a potential separable in addition in cylindrical coordinates and with a spherically symmetric potential. The simplest potential that fits the local constants is used to show that the harmonical and non-harmonical terms of the potential are equally important. The same analysis is used to estimate the local constants. Two families of nested subsamples selected for decreasing planar and vertical eccentricities are used to borne out the relation between the mean squared planar and vertical eccentricities and the velocity dispersions of the subsamples. According to the first-order epicycle model, the radial and vertical velocity components provide accurate information on the planar and vertical epicycle frequencies. However, it is impossible to account for the asymmetric drift which introduces a systematic bias in estimation of the third constant. Under a more general model, when the asymmetric drift is taken into account, the rotation velocity dispersions together with their asymmetric drift provide the correct fit for the local angular velocity. The consistency of the results shows that this new method based on the distribution of eccentricities is worth using for kinematic stellar samples.Peer ReviewedPostprint (author's final draft

Orbital eccentricities as indicators of stellar populations. II. Vertical velocity distribution from the Gaia DR2 catalogue

Context. In previous work, we showed how the planar and vertical eccentricities of disc stars, e and e' , could be used as indicators of the stars’ kinematic populations. For a local stellar sample drawn from the Gaia DR2 catalogue, these populations were represented geometrically in the eccentricity diagram, e'² vs e² , approximately separated by straight lines. Aims. In the current work, we propose a new relationship between the star’s perpendicular velocity and its vertical eccentricity, allowing for a reevaluation of the critical vertical eccentricity and maximum height, z_max, specific to each population component. Methods. We approximated the local potential function to be consistent with the actual shape of the curve that relates the maximum vertical speed of a star and its maximum height. The curve corresponds to a non-linear restoring vertical force, where the stiffness decreases with an increase in the maximum height. The constants involved in this fitting, together with the population velocity dispersions, determine the specific region for each population in the eccentricity diagram. Results. The new classification determines 88% of the sample is made up of thin disc stars and 9% of thick disc stars, whereby 3% of the stars have been relabelled, by providing thinner thin and thick discs. Nested thin disc subsamples allow us to estimate Strömberg’s asymmetric drift equation, leading to a heliocentric velocity of the circular orbit of V_c ˜ -12.9 km s -1 , an absolute rotation velocity of T_c ˜ 227 km s -1 , and a rotation component of the Galactocentric velocity of the Sun at T_¿ ˜ 240 km s -1 . Conclusions. The thin disc stars of our local sample are characterised based on values 0 = e = 0.32, 0 = e' = 0.09, and z_max = 0.7 kpc. Disc stars satisfy 0 = e = 0.44, 0 = e' = 0.18, z_max = 1.5 kpc. The maximum vertical peculiar velocity for disc stars is found to be w_0 = 115 km s -1 . The assumed potential provides a stellar density of the disc vanishing at z_0 = 1.8 kpc. The approximate behaviour in the local disc is that a small decrease in the stiffness is associated with a relative decrease in the limiting velocity, which produces a thinner disc and a loss of stars in the local cylinder, both in a similar proportion to the limiting velocity.Peer ReviewedPostprint (author's final draft

Orbital eccentricities as indicators of stellar populations: a kinematical analysis of the local disc from GAIA DR2 catalogue

Aims. Based on a local sample from Gaia DR2 catalogue composed of 74 339 stars, we are able to derive more accurate kinematic statistics defining the local stellar populations and classify the stars in terms of their planar and vertical orbital eccentricities. Methods. Firstly, we carried out a kinematical characterisation of stellar populations from a tested mixture model that fits the trivariate velocity cumulants up to the fourth order, maximises the entropy of the mixture probability, and minimises the ¿2 error. We then proposed several approaches to classifying the stars according to the population they are most likely to belong to. None of these approaches provided a definitive solution due to the overlapping of the partial distributions. Finally, by using the epicycle approximation, we transformed the three-dimensional velocity probability space into a two-dimensional diagram. In one direction, the information of the two planar velocity components is picked up by the planar eccentricity. In the other direction, the vertical eccentricity does the same with the vertical velocity component. However, in the vertical direction, the epicycle approximation is not valid and it is replaced by a biquadratic approximation. Results. In the eccentricity diagram, the region of maximum probability for a population is approximately delimited by straight line. We characterise three local kinematic populations: thin disc, thick disc (composed of two subpopulations: canonical thick disc and metal-weak thick disc), and kinematical halo (metal-rich thick-disc plus chemical halo). The Gaia DR2 sample allows us to estimate small mean radial differential motion of 5 ± 2 km s-1 between the thin and thick discs, and of 9 ± 3 km s-1 between both thick-disc subpopulations, as well as between the disc and the kinematical halo. All disc populations and subpopulations have significant vertex deviations. Conclusions. The classification of the stars from the eccentricity diagram resolves the problem of overlapping velocity distributions by producing a segregation that is more net, along with a more precise kinematical characterisation of populations.Peer ReviewedPostprint (author's final draft

ADVERSE EFFECTS OF WET DISTILLERS GRAINS WITH SOLUBLES (WDGS) IN THE DIET OF DAIRY COWS

Corn wet distillers grains with solubles (WDGS) included up to 25% in the diet of 16 Simmental dairy cows, 27 to 72 months old, during three weeks, negatively affected rumen function monitored by non-invasive parameters, such as fecal consistency, and also influenced milk quality by reducing milk fat content. Dry distillers' grains with solubles (DDGS) are currently the most attractive by-product of the bioethanol industry due to the possibility of application in the diet of various animal species, whereas WDGS is often more locally available and financially affordable; however, there is little data in the literature indicating potential negative consequences of its use. Therefore, this report aims to point out, based on a practical example, the possible problems of its application in the diet of dairy cows as the most metabolically sensitive category, as well as to demonstrate steps to prevent and/or mitigate eventual errors

Eccentricity samples: implications on the potential and the velocity distribution

Planar and vertical epicycle frequencies and local angular velocity are related to the derivatives up to the second order of the local potential and can be used to test the shape of the potential from stellar disc samples. These samples show a more complex velocity distribution than halo stars and should provide a more realistic test. We assume an axisymmetric potential allowing a mixture of independent ellipsoidal velocity distributions, of separable or Staeckel form in cylindrical or spherical coordinates. We prove that values of local constants are not consistent with a potential separable in addition in cylindrical coordinates and with a spherically symmetric potential. The simplest potential that fits the local constants is used to show that the harmonical and non-harmonical terms of the potential are equally important. The same analysis is used to estimate the local constants. Two families of nested subsamples selected for decreasing planar and vertical eccentricities are used to borne out the relation between the mean squared planar and vertical eccentricities and the velocity dispersions of the subsamples. According to the first-order epicycle model, the radial and vertical velocity components provide accurate information on the planar and vertical epicycle frequencies. However, it is impossible to account for the asymmetric drift which introduces a systematic bias in estimation of the third constant. Under a more general model, when the asymmetric drift is taken into account, the rotation velocity dispersions together with their asymmetric drift provide the correct fit for the local angular velocity. The consistency of the results shows that this new method based on the distribution of eccentricities is worth using for kinematic stellar samples.Peer Reviewe

Prognostic importance of steroid receptor status for disease free and overall survival after surgical resection of isolated liver metastasis in breast cancer patients

PURPOSE: Breast cancer (BC) is the most common malignancy among women, while isolated operable liver metastases (LMs) from BC are very rare and occur in only 1-5% of the patients. Besides, positive steroid receptor (SR) status for oestrogen and/or progesterone is known as a factor which improves disease free survival (DFS) and overall survival (OS). The primary aim of this study was to examine the impact of SR status on DFS and OS after liver metastasectomy in female patients with primary BC. METHODS: We analyzed 32 medical records of female patients diagnosed and treated for primary BC with LMS as the first and only site of disease progression, at the Institute of Oncology and Radiology of Serbia (IORS), during 2006- 2009. All of them underwent primary BC surgery as well as LMs resection. RESULTS: Patients with metachronous BC and LMs and positive SR status in both BC and LM (BC+/LM+) had a median time from BC to LM occurrence (TTLM) of 36 months, compared to BC+/LM- and BC-/LM- subgroups, whose medians for TTLM were 30.5 and 14.5 months, respectively (p<0.01). For all patients, positive SR status showed high correlation with longer DFS and OS after LM resection (medians according survival analysis for DFS/OS in subgroups BC-/LM-, BC+/LM- and BC+-LM+ were 10/19, 25/45, 50/not reached months respectively; p<0.01 for DFS/ OS). Cox regression analysis confirmed that the subgroup of patients with BC-/LM- had 10.8 and 18.8 higher risk of events for DFS (disease relapse or death) and event for OS (death only), respectively, compared to BC+/LM+ subgroup of patients. CONCLUSION: Positive SR status in BC and LM has a high impact not only on time from BC to LM occurrence, but also on longer DFS and OS after LM resection