• [astro-ph:0801.0336] Astronomical Image Subtraction by Cross-Convolution F. Yuan & C. W. Akerlof
• [math.TH:0801.0158] Frequency estimation based on the cumulated Lomb-Scargle periodogram C. L\’evy-Leduc, E. Moulines, & F. Roueff
• [astro-ph:0801.0451] A cgi synthetic CMD calculator for the YY Isochrones P. Demarque et. al.
• [astro-ph:0801.0554] Likelihood Analysis of CMB Temperature and Polarization Power Spectra S. Hamimeche & A. Lewis

• [astro-ph:0712.3797] Variable stars across the observational HR diagram L. Eyer & N. Mowlavi
• [astro-ph:0712.3800] Merger history trees of dark matter haloes J. Moreno & R. K. Sheth
• [astro-ph:0712.3833] Redshift periodicity in quasar number counts from Sloan Digital Sky Survey J. G. Hartnett
• [astro-ph:0712.4023] On the Origin of Bimodal Horizontal-Branches in Massive Globular Clusters: The Case of NGC 6388 and NGC 6441 S. Yoon et.al.
• [astro-ph:0712.4140] Bayesian Image Reconstruction Based on Voronoi Diagrams G. F. Cabrera, S.Casassus & N. Hitschfeld
• [stat.TH:0712.4250] Goodness of fit test for weighted histograms N. D. Gagunashvili
• [astro-ph:0712.2539] Nonergodicity and central limit behavior for systems with long-range interactions A. Pluchino & A. Rapisarda

This paper presented an observational study of a globular cluster, named NGC 6397, enhanced and more informative compared to previous observations in a sense that 1) a truncation in the white dwarf cooling sequence occurs at 28 magnitude, 2) the cluster main sequence seems to terminate approximately at the hydrogen-burning limit predicted by two independent stellar evolution models, and 3) luminosity functions (LFs) or mass functions (MFs) are well defined. Nothing statistical, but the idea of defining color magnitude diagrams (CMDs) and LFs described in the paper, will assist developing suitable statistics on CMD and LF fitting problems in addition to the improved measurements (ACS imaging) of stars in NGC 6397.

Instead of adding details of data properties and calibration process including the instrument characteristics, I like to add a few things for statisticians: First, ACS stands for Advance Camera of Surveys and its information can be found at this link. Second, NGC is an abbreviation of New General Catalogue, one of astronomers’ cataloging systems (click for its wiki). Third, CMDs and LFs are results of data processing, described in the paper, but can be considered as scatter plots and kernel density plots (histograms) to be analyzed for inferencing physical parameters. This data processing, or calibration requires multi-level transformations, which cause error propagation. Finally, the chi-square method is incorporated to fit LFs and MFs. Among numerous fitting methods, in astronomy, only the chi-square is ubiquitously used (link to a discussion on the chi-square). Could we develop more robust statistics for fitting astronomical (empirical) functions?

The authors applied MATCH (Dolphin, 2002^[1] -note that the year is corrected) to M13, M15, M92, NGC2419, NGC6229, and Pal14 (well known globular clusters), and BooI, BooII, CvnI, CVnII, Com, Her, LeoIV, LeoT, Segu1, UMaI, UMaII and Wil1 (newly discovered Milky Way satellites) from Sloan Digital Sky Survey (SDSS) to fit Color Magnitude diagrams (CMDs) of these stellar clusters and find the properties of these satellites.

A traditional CMD fitting begins with building synthetic CMDs: Completeness of SDSS Data Release 5, Hess diagram (a bivariate histogram from a CMD), and features in MATCH for CMD synthesis were taken into account. The synthetic CMDs of these well known globular clusters were utilized with the observations from SDSS and compared to previous discoveries to validate their modified MATCH for the SDSS data sets. Afterwards, their method was applied to the newly discovered Milky Way satellites and discussion on their findings of these satellites was presented.

The paper provides plots that enhance the understanding of age, metalicity, and other physical parameter distributions of stellar clusters after they were fit with synthetic CMDs. The paper also describes steps and tricks (to a statistician, the process of simulating stars looks very technical without a mathematical/probabilistic justification) to acquire proper synthetic CMDs that match observations. The paper adopted Padova database of stellar evolutionary tracks and isochrones (there are other databases beyond Padova).

At last, I’d like to add a sentence from their paper, which supports my idea that a priori knowledge in choosing a proper isochrone database is necessary.

In the case of M15, this is due to the blue horizontal branch (BHB) stars that are not properly reproduced by the theoretical isochrones, causing the code to fit them as a younger turn-off.

1. Numerical methods of star formation history measurement and applications to seven dwarf spheroidals,Dolphin (2002), MNRAS, 332, p. 91

This paper emphasize the binary population: CMD fitting with the binary population synthetic model outperformed to the single population model. They used Hurley code (Hurley, Tout, and Pols (2002). Evolution of binary stars and the effect of tides on binary populations, MNRAS, 329(4), p.897-928). They mentioned that two color-color grids can disentangle the age-metallicity degeneracy via binary stellar populations. They fitted their isochrone database to M67 and NGC 1868 with the gT-grid and concluded that the database of binary stellar populations fitted the color magnitude diagrams better.

A notable sentence:

According to the work of Li and Han (2007b, arxiv/astro-ph: 0704.1202), (u-R) and (g-J) are sensitive to stellar age while (r-K) and (z-K) to stellar metallicity,

where the upper cases indicate Johnson UBVRIJHK magnitudes and the lower cases SDSS-ugriz magnitudes.

Researchers, including scientists from CHASC, working on color magnitude diagrams to infer ages, metalicities, temperatures, and other physical quantities of stars and stellar clusters may find this paper useful.

Methodologies for temperature calibration (fairly accurate estimation from V-K and a new calibration from b-y), metallicity calibration, absolute magnitude/distance calibration, interstellar reddening, and stellar ages were presented with reviews on stellar models and their parameters, astrophysical calibration errors, metalicity distribution function, age-metallicity diagram, age-velocity relation, and thin disk vs thick disk. It seems like that the previous methodologies for F and G stars need to be revised.

Despite my incapability of full understanding the theory of star formation history and the uncertainties of calibrations (looks like that all go toward regression problems to me), this paper fully manifests the complexity of the stellar models and their calibration process. From a statistical perspective, the complexity of the stellar models and calibrations comes from many predictors and only a few response variables with uncertainties (even more they are heteroskedastic). Furthermore, the relationship between predictors and response variables is sparsely known, which makes fitting the model to a star or a stellar cluster or inferencing physical information from them difficult. The mapping is considered to be highly structured black box and its required careful investigations.

I’d rather end this very technical preprint by citing a sentence:

The question of interest is therefore how well these relations and their intrinsic scatter can be determined from the observations

[hlee: Instead of determining, modeling seems to reflect the flexibilities and uncertainties.]

Spectroscopic Surveys: Present by Yip. C. overviews recent spectroscopic sky surveys and spectral analysis techniques toward Virtual Observatories (VO). In addition that spectroscopic redshift measures increase like Moore’s law, the surveys tend to go deeper and aim completeness. Mainly elliptical galaxy formation has been studied due to more abundance compared to spirals and the galactic bimodality in color-color or color-magnitude diagrams is the result of the gas-rich mergers by blue mergers forming the red sequence. Principal component analysis has incorporated ratios of emission line-strengths for classifying Type-II AGN and star forming galaxies. Lyα identifies high z quasars and other spectral patterns over z reveal the history of the early universe and the characteristics of quasars. Also, the recent discovery of 10 satellites to the Milky Way is mentioned.

Spectral analyses take two approaches: one is the model based approach taking theoretical templates, known for its flaws but straightforward extractions of physical parameters, and the other is the empirical approach, useful for making discoveries but difficult in the analysis interpretation. Neither of them has substantial advantage to the other. When it comes to fitting, Chi-square minimization has been dominant but new methodologies are under developing. For spectral classification problems, principal component analysis (Karlhunen-Loeve transformation), artificial neural network, and other machine learning techniques have been applied.

In the end, the author reports statistical and astrophysical challenges in massive spectroscopic data of present days: 1. modeling galaxies, 2. parameterizing star formation history, 3. modeling quasars, 4. multi-catalog based calibration (separating systematic and statistics errors), 5. estimating parameters, which would be beneficial to VO, of which objective is the unification of data access.