Colors Of Stars Research Articles

Star coloring under some graph operations

A star coloring of a graph [Formula: see text] is a proper coloring of [Formula: see text] such that no path of length [Formula: see text] in [Formula: see text] is bicolored. In this paper, the star chromatic number of join of graphs is computed. Some sharp bounds for the star chromatic number of corona, lexicographic, deleted lexicographic and hierarchical product of graphs together with a conjecture on the star chromatic number of lexicographic product of graphs are also presented.

From χ- to χp-bounded classes

χ-bounded classes are studied here in the context of star colorings and, more generally, χp-colorings. This fits to a general scheme of sparsity and leads to natural extensions of the notion of bounded expansion class. In this paper we solve two conjectures related to star coloring (i.e. χ2) boundedness. One of the conjectures is disproved and in fact we determine which weakening holds true. χp-boundedness leads to more stability and we give structural characterizations of (strong and weak) χp-bounded classes. We also generalize a result of Wood relating the chromatic number of a graph to the star chromatic number of its 1-subdivision. As an application of our characterizations, among other things, we show that for every odd integer g>3 even hole-free graphs G contain at most φ(g,ω(G))|G| holes of length g.

A New Method for Aerosol Measurement Using Wide-field Photometry

Abstract We present a new method to measure the vertical aerosol optical depth (VAOD) during clear nights using a wide-field imager—a CCD camera with a photographic lens on an equatorial mount. A series of 30 s exposures taken at different altitudes above the horizon can be used to measure the VAOD with a precision better than 0.008 optical depths within a few minutes. Such a measurement does not produce any light and is thus suitable for use at sites where other astronomical instruments are located. The precision of the VAOD measurement depends on the laboratory calibration of spectral properties of the system and of the response of the camera electronics to varying illumination levels, as well as careful considerations of the details of stellar photometry and modeling of the dependence of the measured stellar flux, the star color, and the position within the field of view. The results obtained with robotic setups at the future sites of the Cerenkov Telescope Array show good internal consistency and agreement with simultaneous measurements from a Sun/Moon photometer located at the same sites.

Color stability of three provisional dental materials submerged in two pigmenting agents

Objective: To determine the color stability of three provisional dental materials when immersed in two pigment agents. Materials and methods : it is an experimental, analytical, prospective and longitudinal study. A total of 270 discs 15 mm in diameter and 1 mm thick were made with 3 temporary dental materials: bisacrylic resin (Luxatemp Star) color A1, acrylic resin (Alike) color 59 and PMMA self-curing (Vitalloy) color 59 being submerged 30 of each sample in purple corn, coffee and distilled water (control). Color readings are used initially, at 7 and 28 days using the VITA® EasyShade® V spectrophotometer with the CIELab system. Results: The acrylic resin presented greater color stability compared to the bisacrylic resin and PMMA self-curing (p <0.01). The coffee presented the greatest color change (p <0.001). After 28 days of storage, there was a color change in all the materials analyzed. Conclusion: Acrylic resin has the highest color stability. The coffee caused the greatest color change and the immersion's time was decisive for the color stability.

On star 5-colorings of sparse graphs

A stark-coloring of a graph G is a proper (vertex) k-coloring of G such that the vertices on a path of length three receive at least three colors. Given a graph G, its star chromatic number, denoted χs(G), is the minimum integer k for which G admits a star k-coloring. Studying star coloring of sparse graphs is an active area of research, especially in terms of the maximum average degree of a graph; the maximum average degree, denoted mad(G), of a graph G is max2|E(H)||V(H)|:H⊂G. It is known that for a graph G, if mad(G)<83, then χs(G)≤6 (Kündgen and Timmons, 2010), and if mad(G)<187 and its girth is at least 6, then χs(G)≤5 (Bu et al., 2009). We improve both results by showing that for a graph G, if mad(G)≤83, then χs(G)≤5. As an immediate corollary, we obtain that a planar graph with girth at least 8 has a star 5-coloring, improving the best known girth condition for a planar graph to have a star 5-coloring (Kündgen and Timmons, 2010; Timmons, 2008).

Star chromatic number of some graphs

A proper vertex coloring of a graph [Formula: see text] is called a star coloring if every two color classes induce a forest whose each component is a star, which means there is no bicolored [Formula: see text] in [Formula: see text]. In this paper, we show that the Cartesian product of any two cycles, except [Formula: see text] and [Formula: see text], has a [Formula: see text]-star coloring.

Star edge coloring of graphs with Mad(G)&lt; 14/5

A star edge coloring of a graph $G$ is a proper edge coloring such that there is no bicolored path or cycle of length four. The minimum number of colors needed for a graph $G$ to admit a star edge coloring is called the star chromatic index and it is denoted by $\chi_s^{'}(G)$. In this paper, we consider graphs of maximum degree $\Delta \geq 4$ and show that if the maximum average degree of a graph is less than $\frac{14}{5}$ then $\chi_s^{'}(G) \leq 2\Delta + 1$.

The formation of isolated ultradiffuse galaxies in romulus25

ABSTRACT We use the romulus25 cosmological simulation volume to identify the largest-ever simulated sample of field ultradiffuse galaxies (UDGs). At z = 0, we find that isolated UDGs have average star formation rates (SFRs), colours, and virial masses for their stellar masses and environment. UDGs have moderately elevated H i masses, being 70 per cent (300 per cent) more H i rich than typical isolated dwarf galaxies at luminosities brighter (fainter) than MB = −14. However, UDGs are consistent with the general isolated dwarf galaxy population and make up ∼20 per cent of all field galaxies with 107 &amp;lt; M⋆/M⊙ &amp;lt; 109. The H i masses, effective radii, and overall appearances of our UDGs are consistent with existing observations of field UDGs, but we predict that many isolated UDGs have been missed by current surveys. Despite their isolation at z = 0, the UDGs in our sample are the products of major mergers. Mergers are no more common in UDG than non-UDG progenitors, but mergers that create UDGs tend to happen earlier – almost never occurring after z = 1, produce a temporary boost in spin, and cause star formation to be redistributed to the outskirts of galaxies, resulting in lower central SFRs. The centres of the galaxies fade as their central stellar populations age, but their global SFRs are maintained through bursts of star formation at larger radii, producing steeper negative g −r colour gradients. This formation channel is unique relative to other proposals for UDG formation in isolated galaxies, demonstrating that UDGs can potentially be formed through multiple mechanisms.

Development and Evaluation of a System for showing Star Attribute Information with Sounds on a Virtual Planetarium

Currently, there are many contents related to celestial bodies in the world. However, their systems introduce constellations mainly. Most of them don’t introduce information about each star. Existing systems read aloud names of stars and constellations and show their color and brightness only visually. Therefore, in this research, we developed a system that can quickly present information of the color and brightness of stars by associating them with pitches and volumes of sounds. In the evaluation experiment, we compared experimental group using this system with control group using the voice reading system. We verified the speed and accuracy of grasping the information of stars in each system.

Runaway blue main-sequence stars at high Galactic latitudes

Context. The ESA Gaia mission is a remarkable tool for stellar population analysis through its accurate Hertzsprung–Russell diagram. Its precise astrometry has propelled detailed kinematic studies of the Milky Way and the identification of high-velocity outliers. Aims. Motivated by the historical identification of runaway main-sequence (MS) stars of an early spectral type at high Galactic latitudes, we test the capability of Gaia at identifying new such stars. Methods. We selected ≈2300 sources with Gaia magnitudes of GBP − GRP ≤ 0.05, which are compatible with the colors of low-extinction MS stars that are earlier than a mid-A spectral type, and obtained low-resolution optical spectroscopy for 48 such stars. By performing detailed photometric and spectroscopic analyses, we derived their atmospheric and physical parameters (effective temperature, surface gravity, radial velocity, interstellar reddening, spectrophotometric distance, mass, radius, luminosity, and age). The comparison between spectrophotometric and parallax-based distances enabled us to disentangle the MS candidates from older blue horizontal branch (BHB) candidates. Results. We identify 12 runaway MS candidates, with masses between 2 and 6 M⊙. Their trajectories were traced back to the Galactic disk in order to identify their most recent Galactic plane crossings and the corresponding flight times. All 12 candidates are ejected from the Galactic disk within 2 to 16.5 kpc from the Galactic center and possess flight times that are shorter than their evolutionary ages, which is compatible with a runaway hypothesis. Three MS candidates have ejection velocities exceeding 450 km s−1, thus, they appear to challenge the canonical ejection scenarios for late B-type stars. The fastest star of our sample also has a non-negligible Galactic escape probability if its MS nature can be confirmed. We identify 27 BHB candidates, and the two hottest stars in our sample are rare low-mass stars of late O- and early B-types, evolving towards the white dwarf cooling sequence. Conclusions. The combination of Gaia parallaxes and proper motions can lead to the efficient selection of runaway blue MS candidates up to 10 kpc away from the Sun. High resolution spectra are needed to confirm the MS status, via precise measurements of projected rotational velocities and chemical compositions.

Refining the mass estimate for the intermediate-mass black hole candidate in NGC 3319

Abstract Recent X-ray observations by Jiang et al. have identified an active galactic nucleus (AGN) in the bulgeless spiral galaxy NGC 3319, located just $14.3\pm 1.1$ Mpc away, and suggest the presence of an intermediate-mass black hole (IMBH; $10^2\leq M_\bullet/\textrm{M}_{\odot}\leq 10^5$ ) if the Eddington ratios are as high as 3 to $3\times10^{-3}$ . In an effort to refine the black hole mass for this (currently) rare class of object, we have explored multiple black hole mass scaling relations, such as those involving the (not previously used) velocity dispersion, logarithmic spiral arm pitch angle, total galaxy stellar mass, nuclear star cluster mass, rotational velocity, and colour of NGC 3319, to obtain 10 mass estimates, of differing accuracy. We have calculated a mass of $3.14_{-2.20}^{+7.02}\times10^4\,\textrm{M}_\odot$ , with a confidence of 84% that it is $\leq $ $10^5\,\textrm{M}_\odot$ , based on the combined probability density function from seven of these individual estimates. Our conservative approach excluded two black hole mass estimates (via the nuclear star cluster mass and the fundamental plane of black hole activity—which only applies to black holes with low accretion rates) that were upper limits of ${\sim}10^5\,{\textrm M}_{\odot}$ , and it did not use the $M_\bullet$ – $L_{\textrm 2-10\,\textrm{keV}}$ relation’s prediction of $\sim$ $10^5\,{\textrm M}_{\odot}$ . This target provides an exceptional opportunity to study an IMBH in AGN mode and advance our demographic knowledge of black holes. Furthermore, we introduce our novel method of meta-analysis as a beneficial technique for identifying new IMBH candidates by quantifying the probability that a galaxy possesses an IMBH.

On Star Coloring of Several Corona Graphs

Let G be a simple graph with vertex set V(G) and edge set E(G). A vertex coloring of G is called a star coloring of G if any of the paths of 4 order are bicolored. The minimum number of colors required for a star coloring of G is denoted by χs (G). The corona product of simple graphs G of order m and H of order n is graph G ∘ H with vertex set V(G ∘ H) = {vi |i = 1,2,⋯m}∪{vij |i = 1,2,⋯m, j = 1,2,⋯n}, in which vi is adjacent to every vertex of Hi if and only if, vi ∈ V(G), vij ∈ V(Hi ). According to the existing graph dyeing literature, it has become a very important technical means to study the graph dyeing problem by using the graph structure operation. Therefore, it is of great significance to study the star coloring of graphs for studying the acyclic coloring and distance coloring of graphs, the study has strong application background and great theoretical value for computing graphs. In this paper, we find the upper bound of χs (G ∘ H) and the exact values of χs (G ∘ H) of the corona product G ∘ H of two graphs G and H as: χs (G ∘ H) ≤ χs (G) + χs (H); χs (Pm ∘ H) = χs (H) + 2; χs (K 1,m ∘ H) = χs (H) + 2; χs (Cn ∘ H) = χs (H) + 2, where n ≠ 5.

Star chromatic number of Harary graphs

A proper vertex coloring of a graph [Formula: see text] is called a star coloring if every path on four vertices in [Formula: see text] is not 2-colored. The star chromatic number is the minimum number of colors required to star color [Formula: see text] and it is denoted by [Formula: see text]. In this paper, the star coloring of Harary graphs [Formula: see text], where [Formula: see text] is even and [Formula: see text] is odd, is discussed.

Proper motion measurements for stars up to 100 kpc with Subaru HSC and SDSS Stripe 82

ABSTRACT We present proper motion measurements for more than 0.55 million main-sequence stars, by comparing astrometric positions of matched stars between the multiband imaging data sets from the Hyper Suprime-Cam (HSC) Survey and the Sloan Digital Sky Survey (SDSS) Stripe 82. In doing this, we use 3 million galaxies to recalibrate the astrometry and set up a common reference frame between the two catalogues. The exquisite depth and the nearly 12 yr of time baseline between HSC and SDSS enable high-precision measurements of statistical proper motions for stars down to i ≃ 24. A validation of our method is demonstrated by the agreement with the Gaia proper motions, to the precision better than 0.1 mas yr−1. To retain the precision, we make a correction of the subtle effects due to the differential chromatic refraction in the SDSS images based on the comparison with the Gaia proper motions against colour of stars, which is validated using the SDSS spectroscopic quasars. Combining with the photometric distance estimates for individual stars based on the precise HSC photometry, we show a significant detection of the net proper motions for stars in each bin of distance out to 100 kpc. The two-component tangential velocities after subtracting the apparent motions due to our own motion display rich phase-space structures including a clear signature of the Sagittarius stream in the halo region of distance range [10, 35] kpc. We also measure the tangential velocity dispersion in the distance range 5–20 kpc and find that the data are consistent with a constant isotropic dispersion of 80 ± 10 km s−1. More distant stars appear to have random motions with respect to the Galactic Centre on average.

Precise calibration of the dependence of surface brightness–colour relations on colour and class for late-type stars (Corrigendum)

Precise calibration of the dependence of surface brightness–colour relations on colour and class for late-type stars (<i>Corrigendum</i>)

On star coloring of modular product of graphs

A star coloring of a graph $G$ is a proper vertex coloring in which every path on four vertices in $G$ is not bicolored. The star chromatic number $\chi_{s}\left(G\right)$ of $G$ is the least number of colors needed to star color $G$. In this paper, we find the exact values of the star chromatic number of modular product of complete graph with complete graph $K_m \diamond K_n$, path with complete graph $P_m \diamond K_n$ and star graph with complete graph $K_{1,m}\diamond K_n$. \par All graphs in this paper are finite, simple, connected and undirected graph and we follow \cite{bm, cla, f} for terminology and notation that are not defined here. We denote the vertex set and the edge set of $G$ by $V(G)$ and $E(G)$, respectively. Branko Gr\"{u}nbaum introduced the concept of star chromatic number in 1973. A star coloring \cite{alberton, fertin, bg} of a graph $G$ is a proper vertex coloring in which every path on four vertices uses at least three distinct colors. The star chromatic number $\chi_{s}\left(G\right)$ of $G$ is the least number of colors needed to star color $G$. \par During the years star coloring of graphs has been studied extensively by several authors, for instance see \cite{alberton, col, fertin}.

Precise calibration of the dependence of surface brightness–colour relations on colour and class for late-type stars

Context. Surface brightness–colour relations (SBCRs) are used to derive the stellar angular diameters from photometric observations. They have various astrophysical applications, such as the distance determination of eclipsing binaries or the determination of exoplanet parameters. However, strong discrepancies between the SBCRs still exist in the literature, in particular for early and late-type stars. Aims. We aim to calibrate new SBCRs as a function of the spectral type and the luminosity class of the stars. Our goal is also to apply homogeneous criteria to the selection of the reference stars and in view of compiling an exhaustive and up-to-date list of interferometric late-type targets. Methods. We implemented criteria to select measurements in the JMMC Measured Diameters Catalog. We then applied additional criteria on the photometric measurements used to build the SBCRs, together with stellar characteristics diagnostics. Results. We built SBCRs for F5/K7–II/III, F5/K7–IV/V, M–II/III and M–V stars, with respective rms of σFV = 0.0022 mag, σFV = 0.0044 mag, σFV = 0.0046 mag, and σFV = 0.0038 mag. This results in a precision on the angular diameter of 1.0%, 2.0%, 2.1%, and 1.7%, respectively. These relations cover a large V − K colour range of magnitude, from 1 to 7.5. Our work demonstrates that SBCRs are significantly dependent on the spectral type and the luminosity class of the star. Through a new set of interferometric measurements, we demonstrate the critical importance of the selection criteria proposed for the calibration of SBCR. Finally, using the Gaia photometry for our samples, we obtained (G − K) SBCRs with a precision on the angular diameter between 1.1% and 2.4%. Conclusions. By adopting a refined and homogeneous methodology, we show that the spectral type and the class of the star should be considered when applying an SBCR. This is particularly important in the context of PLATO.

ON STAR COLORING OF DEGREE SPLITTING OF COMB PRODUCT GRAPHS

A star coloring of a graph G is a proper vertex coloring in which every path on four vertices in G is not bicolored. The star chromatic number χs (G) of G is the least number of colors needed to star color G. Let G = (V,E) be a graph with V = S1 [ S2 [ S3 [ . . . [ St [ T where each Si is a set of all vertices of the same degree with at least two elements and T =V (G) − St i=1 Si. The degree splitting graph DS (G) is obtained by adding vertices w1,w2, . . .wt and joining wi to each vertex of Si for 1 i t. The comb product between two graphs G and H, denoted by G ⊲ H, is a graph obtained by taking one copy of G and |V (G)| copies of H and grafting the ith copy of H at the vertex o to the ith vertex of G. In this paper, we give the exact value of star chromatic number of degree splitting of comb product of complete graph with complete graph, complete graph with path, complete graph with cycle, complete graph with star graph, cycle with complete graph, path with complete graph and cycle with path graph.

Multiwavelength Absolute Magnitudes and Colors of Red Clump Stars in the Gaia Era

Abstract This study presents the multiwavelength investigation of the absolute magnitudes and colors of the red clump (RC) stars selected from APOGEE and GALAH DR2 combined catalog which is complemented with Gaia DR2 astrometric data and multiwavelength photometric data of GALEX GR6/7, SDSS DR7, Gaia DR2, 2MASS, and WISE sky surveys. The analyses are centered on the different distance estimation methods using Gaia trigonometric parallaxes, (1/ϖ) and Bayes statistics, and chemically defined Galactic disk populations on [α/Fe] × [Fe/H] plane. This investigation questions the long-studied problem of the population effects on RC luminosity. Using two different distance estimation approaches, (i) chemical thin and chemical thick disk RC stars are shown to have different absolute magnitudes, while colors remain the same in all photometric bands. Absolute magnitudes vary between −0.12 and +0.13 mag for the 1/ϖ with the change of the Galactic population. This variation in absolute magnitudes is found to be larger for the other method, (ii) the Besançon population synthesis model of Galaxy for 2MASS photometry, in which the absolute magnitude difference between chemical populations were found between −0.35 and −0.40 mag from thin disk to thick disk. When results compared with each other, differences of absolute magnitudes are about three times larger in the model than in the observations. We confirm that the RC absolute magnitudes depend on α-element abundances of Galactic populations.

Magnetic field structure of the Galactic plane from differential analysis of interstellar polarization

Abstract A new method for measuring the global magnetic field structure of the Galactic plane is presented. We have determined the near-infrared polarization of field stars around 52 Cepheids found in recent surveys toward the Galactic plane. The Cepheids are located at the galactic longitudes $-10^{\circ} \le l \le +10.^{\!\!\!\circ }5$ and latitudes $-0.^{\!\!\!\circ }22\le b \le +0.^{\!\!\!\circ }45$, and their distances are mainly in the range of 10 to 15 kpc from the Sun. Simple classification of the sightlines is made with the polarization behavior vs. $H-K_{\mathrm{S}}$ color of field stars, and typical examples of three types are presented. Then, division of the field stars in each line of sight into (a) foreground, (b) bulge, and (c) background is made with the Gaia DR2 catalog, the peak of the $H-K_{\mathrm{S}}$ color histogram, and $H-K_{\mathrm{S}}$ colors consistent with the distance of the Cepheid in the center, respectively. Differential analysis between them enables us to examine the magnetic field structure more definitely than just relying on the $H-K_{\mathrm{S}}$ color difference. In one line of sight, the magnetic field is nearly parallel to the Galactic plane and well aligned all the way from the Sun to the Cepheid position on the other side of the Galactic center. Contrary to our preconceived ideas, however, sightlines having such well-aligned magnetic fields in the Galactic plane are rather small in number. At least 36 Cepheid fields indicate random magnetic field components are significant. Two Cepheid fields indicate that the magnetic field orientation changes more than $45^{\circ }$ in the line of sight. The polarization increase per color change $\Delta P/\Delta (H-K_{\mathrm{S}})$ varies from region to region, reflecting the change in the ratio of the magnetic field strength and the turbulence strength.