Keywords

The error propagation among estimated parameters reflects the correlation among the parameters. We study the capability of machine learning of "learning" the correlation of estimated parameters. We show that machine learning can recover the relation between the uncertainties of different parameters, especially, as predicted by the error propagation formula. Gravitational lensing can be used to probe both astrophysics and cosmology. As a practical application, we show that the machine learning is able to intelligently find the error propagation among the gravitational lens parameters (effective lens mass M_L and Einstein radius θ_E) in accordance with the theoretical formula for the singular isothermal ellipse (SIE) lens model. The relation of errors of lens mass and Einstein radius, (e.g., the ratio of standard deviations ${ \mathcal F }={\sigma }_{\hat{{M}_{L}}}/{\sigma }_{\hat{{\theta }_{E}}}$) predicted by the deep convolution neural network are consistent with the error propagation formula of the SIE lens model. As a proof-of-principle test, a toy model of linear relation with Gaussian noise is presented. We found that the predictions obtained by machine learning indeed indicate the information about the law of error propagation and the distribution of noise. Error propagation plays a crucial role in identifying the physical relation among parameters, rather than a coincidence relation, therefore we anticipate our case study on the error propagation of machine learning predictions could extend to other physical systems on searching the correlation among parameters.

This paper is an initial stage of consideration of the general problem of joint modeling of the vertical structure of a Galactic flat subsystem and the average surface of the disk of the Galaxy, taking into account the natural and measurement dispersions. We approximate the average surface of the Galactic disk in the region covered by the data with a general (polynomial) model and determine its parameters by minimizing the squared deviations of objects along the normal to the model surface. The smoothness of the model, i.e., its order n, is optimized. An outlier elimination algorithm is applied. The developed method allows us to simultaneously identify significant details of the Galactic warping and estimate the offset z_☉ of the Sun relative to the average (in general, non-flat) surface of the Galactic disk and the vertical scale of the object system under consideration for an arbitrary area of the disk covered by data. The method is applied to data on classical Cepheids. Significant local extremes of the average disk surface model were found based on Cepheid data: the minimum in the first Galactic quadrant and the maximum in the second. A well-known warp (lowering of the disk surface) in the third quadrant has been confirmed. The optimal order of the model describing all these warping details was found to be n_o = 4. The local (for a small neighborhood of the Sun, n_o = 0) estimate of ${z}_{\odot }=28.1\pm {\left.6.1\right|}_{{\rm{stat}}.}{\left.\pm 1.3\right|}_{{\rm{cal}}.}$ pc is close to the non-local (taking into account warping, n_o = 4) ${z}_{\odot }=27.1\pm {\left.8.8\right|}_{\mathrm{stat}.}{\left.{}_{-1.2}^{+1.3}\right|}_{\mathrm{cal}.}$ pc (statistical and calibration uncertainties are indicated), which suggests that the proposed modeling method eliminates the influence of warping on the z_☉ estimate. However, the non-local estimate of the vertical standard deviation of Cepheids ${\sigma }_{\rho }=132.0\pm {\left.3.7\right|}_{\mathrm{stat}.}{\left.{}_{-5.9}^{+6.3}\right|}_{\mathrm{cal}.}$ pc differs significantly from the local ${\sigma }_{\rho }={\left.76.5\pm 4.4\right|}_{\mathrm{stat}.}{\left.{}_{-3.4}^{+3.6}\right|}_{\mathrm{cal}.}$ pc, which implies the need to introduce more complex models for the vertical distribution outside the Sun's vicinity.

We combine the kinematics of 159 globular clusters (GCs) provided by the Gaia Early Data Release 3 (EDR3) with other observational data to classify the GCs, and to estimate the mass of the Milky Way (MW). We use the age–metallicity relation, integrals of motion, action space and the GC orbits to identify the GCs as either formed in situ (Bulge and Disk) or ex situ (via accretion). We find that 45.3% have formed in situ, while 38.4% may be related to known merger events: Gaia-Sausage-Enceladus, the Sagittarius dwarf galaxy, the Helmi streams, the Sequoia galaxy and the Kraken galaxy. We also further identify three new sub-structures associated with the Gaia–Sausage–Enceladus. The remaining 16.3% of GCs are unrelated to the known mergers and thought to be from small accretion events. We select 46 GCs which have radii 8.0 < r < 37.3 kpc and obtain the anisotropy parameter $\beta ={0.315}_{-0.049}^{+0.055}$, which is lower than the recent result using the sample of GCs in Gaia Data Release 2, but still in agreement with it by considering the error bar. By using the same sample, we obtain the MW mass inside the outermost GC as $M(\lt 37.3\,\mathrm{kpc})={0.423}_{-0.02}^{+0.02}\times {10}^{12}\,{M}_{\odot }$, and the corresponding ${M}_{200}={1.11}_{-0.18}^{+0.25}\times {10}^{12}{M}_{\odot }$. The estimated mass is consistent with the results in many recent studies. We also find that the estimated β and mass depend on the selected sample of GCs. However, it is difficult to determine whether a GC fully traces the potential of the MW.

Astronomical outliers, such as unusual, rare or unknown types of astronomical objects or phenomena, constantly lead to the discovery of genuinely unforeseen knowledge in astronomy. More unpredictable outliers will be uncovered in principle with the increment of the coverage and quality of upcoming survey data. However, it is a severe challenge to mine rare and unexpected targets from enormous data with human inspection due to a significant workload. Supervised learning is also unsuitable for this purpose because designing proper training sets for unanticipated signals is unworkable. Motivated by these challenges, we adopt unsupervised machine learning approaches to identify outliers in the data of galaxy images to explore the paths for detecting astronomical outliers. For comparison, we construct three methods, which are built upon the k-nearest neighbors (KNN), Convolutional Auto-Encoder (CAE) + KNN, and CAE + KNN + Attention Mechanism (attCAE_KNN) separately. Testing sets are created based on the Galaxy Zoo image data published online to evaluate the performance of the above methods. Results show that attCAE_KNN achieves the best recall (78%), which is 53% higher than the classical KNN method and 22% higher than CAE+KNN. The efficiency of attCAE_KNN (10 minutes) is also superior to KNN (4 h) and equal to CAE+KNN (10 minutes) for accomplishing the same task. Thus, we believe that it is feasible to detect astronomical outliers in the data of galaxy images in an unsupervised manner. Next, we will apply attCAE_KNN to available survey data sets to assess its applicability and reliability.

We propose a new approach to Bayesian prior probability distributions (priors) that can improve orbital solutions for low-phase-coverage orbits, where data cover less than ∼40% of an orbit. In instances of low phase coverage—such as with stellar orbits in the Galactic center or with directly imaged exoplanets—data have low constraining power and thus priors can bias parameter estimates and produce underestimated confidence intervals. Uniform priors, which are commonly assumed in orbit fitting, are notorious for this. We propose a new observable-based prior paradigm that is based on uniformity in observables. We compare performance of this observable-based prior and of commonly assumed uniform priors using Galactic center and directly imaged exoplanet (HR 8799) data. The observable-based prior can reduce biases in model parameters by a factor of two and helps avoid underestimation of confidence intervals for simulations with less than ∼40% phase coverage. Above this threshold, orbital solutions for objects with sufficient phase coverage—such as S0-2, a short-period star at the Galactic center with full phase coverage—are consistent with previously published results. Below this threshold, the observable-based prior limits prior influence in regions of prior dominance and increases data influence. Using the observable-based prior, HR 8799 orbital analyses favor low-eccentricity orbits and provide stronger evidence that the four planets have a consistent inclination of ∼30° to within 1σ. This analysis also allows for the possibility of coplanarity. We present metrics to quantify improvements in orbital estimates with different priors so that observable-based prior frameworks can be tested and implemented for other low-phase-coverage orbits.

Based on Sloan Digital Sky Survey photometric data, Gu developed a new Monte-Carlo-based method for estimating the stellar metallicity distribution functions (MDFs). This method enables a more reliable determination of MDFs compared with the conventional polynomial-based methods. In this work, MDF determined from the method are well fit by a three-Gaussian model, with peaks at [Fe/H] = −0.68, −1.38, and −1.90, associated with the thick disk, the inner halo, and the outer halo, respectively. The vertical metallicity gradient within 1 < Z < 5 kpc is $d\langle [\mathrm{Fe}/{\rm{H}}]\rangle /{dZ}\approx -0.19\,\mathrm{dex}\cdot {\mathrm{kpc}}^{-1}$ around R = 8.25 kpc. But the mean radial gradient is almost negligible. The density profile of the thick disk is fitted with a modified double exponential law decaying to a constant at far distance. The scale height and scale length thus estimated are H ≈ 1.13 kpc and L ≈ 3.63 kpc, which are consistent with the results determined from star-count methods in previous studies. The halos are described with a two-axial power-law ellipsoid, and the axis ratios of both the inner halo and the outer halo, inferred from stellar number density in the R–Z plane, are q_ih ≈ 0.49 and q_oh ≈ 0.61, respectively. It also manifests that the outer halo is more spherical than the inner halo. Moreover, the halo power-law indices estimated are n_ih ≈ 3.4 and n_oh ≈ 3.1, indicating that the stellar number density of the inner halo changes more steeply than that of outer halo.

With the photometric data from the SDSS survey, the spectroscopic data from the SDSS/SEGUE and the LAMOST surveys, and the astrometric data from the Gaia DR2, we have identified 67 highly probable member stars of the GD-1 cold stellar stream spread along almost its entire length (i.e., from 126° to 203° in R.A.). With the accurate spectroscopic (i.e., metallicity and line-of-sight velocity) and astrometric (i.e., proper motions) information, the position–velocity diagrams, i.e., ϕ₁–μ_α, ϕ₁–μ_δ, and ϕ₁–v_gsr, of the GD-1 stream are well mapped. The stream has an average metallicity [Fe/H] = −1.96. The rich information of member stars of the stream now available allow one not only to model its origin, but also to place strong constraints on the mass distribution and the gravitational potential of the Milky Way.

We report trigonometric parallax and proper motion measurements of 6.7 GHz CH₃OH and 22 GHz H₂O masers in eight high-mass star-forming regions (HMSFRs) based on Very Long Baseline Array (VLBA) observations as part of the Bar and Spiral Structure Legacy (BeSSeL) Survey. The distances of these HMSFRs combined with their Galactic coordinates, radial velocities, and proper motions, allow us to assign them to a segment of the Perseus arm with ℓ ≲ 70°. These HMSFRs are clustered in Galactic longitude from ≈30° to ≈50° neighboring a dearth of such sources between longitudes ≈50° to ≈90°.

We present new mass estimates and cumulative mass profiles (CMPs) with Bayesian credible regions for the Milky Way (MW) Galaxy, given the kinematic data of globular clusters (GCs) as provided by (1) the Gaia DR2 collaboration and the HSTPROMO team, and (2) the new catalog in Vasiliev (2019). We use GCs beyond 15 kpc to estimate the CMP of the MW, assuming a total gravitational potential model ${\rm{\Phi }}(r)={{\rm{\Phi }}}_{\circ }{r}^{-\gamma }$, which approximates an NFW-type potential at large distances when γ = 0.5. We compare the resulting CMPs given data sets (1) and (2), and find the results to be nearly identical. The median estimate for the total mass is M₂₀₀ = 0.70 × 10¹² M_⊙ and the 50% Bayesian credible interval is $(0.62,0.81)\times {10}^{12}\,{M}_{\odot }$. However, because the Vasiliev catalog contains more complete data at large r, the MW total mass is slightly more constrained by these data. In this work, we also supply instructions for how to create a CMP for the MW with Bayesian credible regions, given a model for M(<r) and samples drawn from a posterior distribution. With the CMP, we can report median estimates and 50% Bayesian credible regions for the MW mass within any distance (e.g., $M(r=25\,\mathrm{kpc})=0.26\,(0.20,0.36)\times {10}^{12}\,{M}_{\odot }$, $M(r=50\,\mathrm{kpc})\,=0.37\,(0.29,0.51)\times {10}^{12}\,{M}_{\odot }$, $M(r\,=100\,\mathrm{kpc})=0.53\,(0.41,0.74)\times {10}^{12}\,{M}_{\odot }$, etc.), making it easy to compare our results directly to other studies.