Gaussian processes, median statistics, Milky Way rotation curves

We present a sample of 254,882 luminous red giant branch (LRGB) stars selected from the APOGEE and LAMOST surveys. By combining photometric and astrometric information from the Two Micron All Sky Survey and Gaia survey, the precise distances of the sample stars are determined by a supervised machine-learning algorithm: the gradient-boosted decision trees. To test the accuracy of the derived distances, member stars of globular clusters (GCs) and open clusters are used. The tests by cluster member stars show a precision of about 10% with negligible zero-point offsets, for the derived distances of our sample stars. The final sample covers a large volume of the Galactic disk(s) and halo of 0 < R < 30 kpc and ∣Z∣ ≤ 15 kpc. The rotation curve (RC) of the Milky Way across the radius of 5 ≲ R ≲ 25 kpc has been accurately measured with ∼54,000 stars of the thin disk population selected from the LRGB sample. The derived RC shows a weak decline along R with a gradient of −1.83 ± 0.02 (stat.) ± 0.07 (sys.) km s−1 kpc−1, in excellent agreement with the results measured by previous studies. The circular velocity at the solar position, yielded by our RC is 234.04 ± 0.08 (stat.) ± 1.36 (sys.) km s−1, again in great consistency with other independent determinations. From the newly constructed RC, as well as constraints from other data, we have constructed a mass model for our Galaxy, yielding a mass of the dark matter halo of M 200 = (8.05 ± 1.15) × 1011 M ⊙ with a corresponding radius of R 200 = 192.37 ± 9.24 kpc and a local dark matter density of 0.39 ± 0.03 GeV cm−3.

We use mock interferometric HI measurements and a conventional tilted-ring modelling procedure to estimate circular velocity curves of dwarf galaxy discs from the APOSTLE suite of {\Lambda}CDM cosmological hydrodynamical simulations. The modelling yields a large diversity of rotation curves for an individual galaxy at fixed inclination, depending on the line-of-sight orientation. The diversity is driven by non-circular motions in the gas; in particular, by strong bisymmetric fluctuations in the azimuthal velocities that the tilted-ring model is ill-suited to account for and that are difficult to detect in model residuals. Large misestimates of the circular velocity arise when the kinematic major axis coincides with the extrema of the fluctuation pattern, in some cases mimicking the presence of kiloparsec-scale density 'cores', when none are actually present. The thickness of APOSTLE discs compounds this effect: more slowly-rotating extra-planar gas systematically reduces the average line-of-sight speeds. The recovered rotation curves thus tend to underestimate the true circular velocity of APOSTLE galaxies in the inner regions. Non-circular motions provide an appealing explanation for the large apparent cores observed in galaxies such as DDO 47 and DDO 87, where the model residuals suggest that such motions might have affected estimates of the inner circular velocities. Although residuals from tilted ring models in the simulations appear larger than in observed galaxies, our results suggest that non-circular motions should be carefully taken into account when considering the evidence for dark matter cores in individual galaxies.

We present a sample of 1148 ab-type RR Lyrae (RRLab) variables identified from Catalina Surveys Data Release 1, combined with SDSS DR8 and LAMOST DR4 spectral data. We first use a large sample of 860 Galactic halo RRLab stars and derive the circular velocity distributions for the stellar halo. With the precise distances and carefully determined radial velocities (the center-of-mass radial velocities) and by considering the pulsation of the RRLab stars in our sample, we can obtain a reliable and comparable stellar halo circular velocity curve. We follow two different prescriptions for the velocity anisotropy parameter β in the Jeans equation to study the circular velocity curve and mass profile. Additionally, we test two different solar peculiar motions in our calculation. The best result we obtained with the adopted solar peculiar motion 1 of (U, V, W) = (11.1, 12, 7.2) km s−1 is that the enclosed mass of the Milky Way within 50 kpc is (3.75 ± 1.33) × 1011 M ⊙ based on β = 0 and the circular velocity 180 ± 31.92 (km s−1) at 50 kpc. This result is consistent with dynamical model results, and it is also comparable to the results of previous similar works.

We investigate the shape of the rotation curves (RCs) of z ∼ 1 star-forming galaxies (SFGs) and compare them with local SFGs. For this purpose, we have used 344 galaxies from the K-band Multi-Object Spectrograph (KMOS) for Redshift One Spectroscopic Survey (KROSS). This sample covers the redshift range 0.57 ≤ z ≤ 1.04, the effective radii 0.69 ≤ Re [kpc] ≤ 7.76, and the stellar masses 8.7 ≤ log (M* [M⊙]) ≤ 11.32. Using 3DBAROLO, we extract the H α kinematic maps and corresponding RCs. The main advantage of 3DBAROLO is that it incorporates the beam smearing in the 3D observational space, which provide us with the intrinsic rotation velocity even in the low spatial resolution data. We have corrected the RCs for pressure support, which seems to be a more dominant effect than beam smearing in high-z galaxies. Only a combination of the three techniques (3D-kinematic modelling + 3D-beam smearing correction + pressure gradient correction) yields the intrinsic RC of an individual galaxy. Further, we present the co-added and binned RCs constructed out of 256 high-quality objects. We do not see any change in the shape of RCs with respect to the local SFGs. Moreover, we notice a significant evolution in the stellar-disc length (RD) of the galaxies as a function of their circular velocity. Therefore, we conclude that the stellar disc of SFGs evolves over cosmic time (from z ∼ 1) while the total mass stays constant (within ∼20 kpc).

In the conventional approach to decomposing a rotation curve into a set of contributions from mass model components, the measurements of the rotation curve at different radii are taken to be independent. It is clear, however, that radial correlations are present in such data, for instance (but not only) because the orbital speed depends on the mass distribution at all (or, minimally, inner) radii. We adopt a very simple parametric form for a covariance matrix and constrain its parameters using Gaussian process regression. Applied to the rotation curve of the Milky Way, this suggests the presence of correlations between neighbouring rotation curve points with amplitudes of $\lt 10\, \mathrm{km}\, \mathrm{s}^{-1}$ over length scales of 1.5–$2.5\, \mathrm{kpc}$ regardless of the assumed dark halo component. We show that accounting for such covariance can result in a ∼50 per cent lower total mass estimate for the Milky Way than when it is neglected, and that the uncertainty in model parameters increases such that it seems more representative of the uncertainty in the rotation curve measurement. The statistical uncertainty associated with the covariance is comparable to or exceeds the total systematic uncertainty budget. Our findings motivate including more detailed treatment of rotation curve covariance in future analyses.

To gain a better understanding of the Andromeda galaxy M31 and its role in the Local Group, measuring its mass precisely is essential. In this work, we have constructed the rotation curve of M31 out to ∼125 kpc using 13 679 M31 objects obtained from various sources, including the LAMOST data release 9 (LAMOST DR9), the DESI survey, and relevant literature. We divide all objects in our sample into bulge, disc, and halo components. For the sources in the M31 disc, we have measured their circular velocities by a kinematic model with asymmetric drift corrections. For the bulge and halo objects, we calculate their velocity dispersions and use the spherical and projected Jeans equation to obtain the circular velocities. Our findings indicate a nearly isotropic nature for the M31 bulge, while the halo exhibits tangential anisotropy. The results show that the rotation curve remains constant at ∼220 km s−1 up to radius ∼25 kpc and gradually decreases to ∼170 km s−1 further out. Based on the newly determined rotation curve, we have constructed a mass distribution model for M31. Our measurement of the M31 virial mass is $M_{\rm vir} = 1.14^{+0.51}_{-0.35} \times 10^{12} M_\odot$ within rvir = 220 ± 25 kpc.

A family of spherical halo models with flat circular velocity curves is presented. This includes models in which the rotation curve has a finite central value but declines outwards (like the Jaffe model). It includes models in which the rotation curve is rising in the inner parts, but flattens asymptotically (like the Binney model). The family encompasses models with both finite and singular (cuspy) density profiles. The self-consistent distribution function depending on binding energy $E$ and angular momentum $L$ is derived and the kinematical properties of the models discussed. These really describe the properties of the total matter (both luminous and dark). For comparison with observations, it is better to consider tracer populations of stars. These can be used to represent elliptical galaxies or the spheroidal components of spiral galaxies. Accordingly, we study the properties of tracers with power-law or Einasto profiles moving in the doubloon potential. Under the assumption of spherical alignment, we provide a simple way to solve the Jeans equations for the velocity dispersions. This choice of alignment is supported by observations on the stellar halo of the Milky Way. Power-law tracers have prolate spheroidal velocity ellipsoids everywhere. However, this is not the case for Einasto tracers, for which the velocity ellipsoids change from prolate to oblate spheroidal near the pole. Asymptotic forms of the velocity distributions close to the escape speed are also derived, with an eye to application to the high velocity stars in the Milky Way. Power-law tracers have power-law or Maxwellian velocity distributions tails, whereas Einasto tracers have super-exponential cut-offs.

Understanding the Milky Way’s present structure and assembly history constitutes a crucial constraint on galaxy formation and evolution theory. Galactic surveys like the Gaia mission provide high-precision measurements of positions, velocities, and chemical abundances of soon millions of stars in the Milky Way disk. Exploiting these high quality data requires sophisticated modeling tools.&#13;\n&#13;\nThis PhD thesis is dedicated to the development, characterization, and application of RoadMapping, a dynamical modeling machinery aiming to constrain the Galactic gravitational potential and chemo-orbital distribution function (DF) of the stellar disk. RoadMapping proceeds by modeling the observed discrete 6D phase-space positions of stellar mono-abundance populations (MAPs) by an axisymmetric parameterized potential model and an axisymmetric action-based orbit DF in a full-likelihood Bayesian framework. RoadMapping takes into account the survey’s selection function (SF) and measurement uncertainties. RoadMapping builds on previous work by Bovy &amp; Rix (2013), Binney &amp; McMillan (2011), and Binney (2012a).&#13;\n&#13;\nThe first part of this work was published as Trick et al. (2016a) and gives an overview of the RoadMapping machinery. Its characteristics are studied by analyzing a large suite of axisymmetric mock data sets. It is found that RoadMapping constraints on the gravitational potential are robust against minor imperfections in the knowledge of the optimal potential or DF model family, selection effects, or velocity measurement uncertainties, as long as the distance uncertainties of the stars are better than 10%.&#13;\n&#13;\nThe second part is based on Trick et al. (2017) and investigates RoadMapping in the presence of spiral arms by modeling data drawn from an N-body simulation snapshot of a disk-dominated galaxy with strong spiral arms by D'Onghia et al. (2013). This provides a realistic test scenario for RoadMapping to model non-axisymmetric data with axisymmetric models. It is found that RoadMapping always recovers a good average model for the gravitational forces at the location of the stars that entered the analysis.&#13;\n&#13;\nThe third part applies RoadMapping to real data in the Milky Way. It combines measurements by Gaia-TGAS (Lindegren et al. 2016), RAVE (Kunder et al. 2017), and RAVE-on (Casey et al. 2017). Red clump stars are selected and photometric distances are assigned to them following Bovy et al. (2014). A strategy is devised to setup an SF for this sample that can be used in RoadMapping. The sample consists of 16 MAPs in the low-alpha disk. All MAPs provide independent and consistent constraints on the Milky Way’s gravitational potential, measuring the disk scale length and circular velocity at the Sun to high precision, R_s,disk = 3.01 +/- 0.05 kpc and v_circ(R) = 231.4 +/- 0.7 km/s. The total surface mass density at the Sun that is recovered is, with Sigma_tot,1.1kpc = 98 +/- 3 M_sun/pc^2, larger than previous estimates in the literature, which is attributed, however, to the data.&#13;\n&#13;\nOverall, RoadMapping is a well-tested and robust dynamical modeling machinery, whose preliminary and successful application to Gaia data promises new, precise, and reliable constraints on the Galactic gravitational potential in the near future.

In spiral galaxies, we explain their non-Keplerian rotation curves (RCs) by means of a non-luminous component embedding their stellar-gaseous disks. Understanding the detailed properties of this component (labelled Dark Matter, DM) is one of the most pressing issues of Cosmology. We investigate the recent relationship (claimed by Walker et al. 2010, hereafter W+10) between $r$, the galaxy radial coordinate, and $V_h(r)$, the dark halo contribution to the circular velocity at $r$, {\it a}) in the framework of the Universal Rotation Curve (URC) paradigm and directly {\it b}) by means of the kinematics of a large sample of DM dominated spirals. We find a general agreement between the W+10 claim, the distribution of DM emerging from the URC and that inferred in the (low luminosity) objects of our sample. We show that such a phenomenology, linking the spiral's luminosity, radii and circular velocities, implies an evident inconsistency with (naive) predictions in the $\Lambda$ Cold Dark Matter ($\Lambda$CDM) scenario.

A tangential distortion of background source galaxies around foreground lens galaxies in the Hubble Deep Field is detected at the 99.3% confidence level. An important element of our analysis is the use of photometric redshifts to determine distances of lens and source galaxies and rest-frame B-band luminosities of the lens galaxies. The lens galaxy halos obey a Tully-Fisher relation between halo circular velocity and luminosity; the typical lens galaxy, at a redshift z = 0.6, has a circular velocity of 210 +/-40 km/s at M_B = -18.5, if q_0 = 0.5. Control tests, in which lens and source positions and source ellipticities are randomized, confirm the significance level of the detection quoted above. Furthermore, a marginal signal is also detected from an independent, fainter sample of source galaxies without photometric redshifts. Potential systematic effects, such as contamination by aligned satellite galaxies, the distortion of source shapes by the light of the foreground galaxies, PSF anisotropies, and contributions from mass distributed on the scale of galaxy groups are shown to be negligible. A comparison of our result with the local Tully-Fisher relation indicates that intermediate-redshift galaxies are fainter than local spirals by 1.0 +/- 0.6 B mag at a fixed circular velocity. This is consistent with some spectroscopic studies of the rotation curves of intermediate-redshift galaxies. This result suggests that the strong increase in the global luminosity density with redshift is dominated by evolution in the galaxy number density.

Optimization and comparison of models for core temperature prediction of mother rabbits using infrared thermography

view Abstract Citations (77) References (40) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Internal Kinematics of Spiral Galaxies: Gas and Stellar Rotation Curves and Dispersion Profiles Fillmore, J. A. ; Boroson, T. A. ; Dressler, A. Abstract Emission- and absorption-line observations of six moderately inclined spiral galaxies are presented. The mean rotation and velocity dispersion for the gas and the stars have been measured. Two component mass models are fitted to surface brightness measurements are used to fit kinematic models to the velocity data. Models with constant mass-to-light ratios and isotropic velocity dispersions roughly fit the inner regions of spiral galaxies with three caveats: (1) several galaxies show significant kinematic differences between the two sides of the galaxy. While the differences might be caused by nonaxisymmetric potentials, variations in the line-of-sight extinction are a more likely cause; (2) the inner portion (R less than of equal to 1 kpc) of the emission-line (gas) rotation curve falls below the predicted circular velocity. Because the model circular velocities are computed from the observed stellar velocities, variations in the total mass-to-light ratio will not change the model values. It is noted that gas lost from bulge giants (planetary nebulae) will have a significant noncircular velocity component. It is shown that these emitted clouds live a sufficient time to explain the lower-than-circular velocity of the emission-line rotation curves; Some of the bulges are flatter than one would expect from their rotation rate, assuming isotropic random motions, but this additional flattening could be caused by the disk potential. Publication: The Astrophysical Journal Pub Date: March 1986 DOI: 10.1086/163984 Bibcode: 1986ApJ...302..208F Keywords: Galactic Structure; Spiral Galaxies; Stellar Rotation; Absorption Spectra; Emission Spectra; Kinematics; Line Spectra; Mass To Light Ratios; Radial Velocity; Tables (Data); Astrophysics; GALAXIES: INTERNAL MOTIONS; GALAXIES: STRUCTURE full text sources ADS | data products SIMBAD (6) NED (6)

The parameters of an axisymmetric model for the gravitational potential of the Galaxy have been refined. The basic curve of the Galaxy’s rotation in a distance interval of R ~ 0–190 kpc was constructed using the velocities of masers, classical Cepheids, Red Clump stars, Blue Horizontal Branch stars, halo stars, globular clusters, and dwarf satellite galaxies of the Milky Way. The rotation curve was selected in such a way that there would be no dominant burst of circular velocities in the central ( $$R < 2$$ kpc) region of the Galaxy. As a result, we constructed two two-component models of the galactic potential, which include contributions from the disk and the halo of invisible matter, as well as a three-component model with a small-mass bulge added in advance. These models can be useful in studying the long-term orbital evolution of stars and open and globular star clusters in the central ( $$R < 4$$ kpc) region of the Galaxy. The constructed models were tested for self-consistency by comparing their rotation curves with a set of model curves generated with the Illustris TNG50 software package.

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In this work, we seek to overcome these issues through (i) employing variational free energy approximations of GPs operating in tandem with online expectation propagation steps; and (ii) introducing a local splitting step which instantiates a new GP whenever the posterior distribution changes significantly as quantified by the Wasserstein metric over posterior distributions. Over time, then, this yields an ensemble of sparse GPs which may be updated incrementally, and adapts to locality, heterogeneity, and non-stationarity in training data. We provide a 1-dimensional example to illustrate the motivation behind our approach, and compare the performance of our approach to other Gaussian process methods across various data sets, which often achieves competitive, if not superior predictive performance, relative to other locality-based GP regression methods in which hyperparameters are learned in an online manner.

This paper focuses on water demand forecasting for predictive control of Drinking Water Networks (DWN) in the short term by using Gaussian Process (GP). For the predictive control strategy, system states in a finite horizon are generated by a DWN model and demands are regarded as system disturbances. The goal is to provide a demand estimation within a given confidence interval. For the sake of obtaining a desired forecasting performance, the forecasting process is carried out in two parts: the expected part is forecasted by Double-Seasonal Holt-Winters (DSHW) method and the stochastic part is forecasted by GP method. The mean value of water demand is firstly estimated by DSHW while GP provides estimations within a confidence interval. GP is applied with random inputs to propagate uncertainty at each step. Results of the application of the proposed approach to a real case study based on the Barcelona DWN have shown that the general goal has been successfully reached.