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NASA NTRS2003

The Organic Component of Interstellar Dust

The distribution, chemical structure, and formation of organic matter in the interstellar medium are important to our understanding of the overall evolution of dust. The exchange of dust between the dense and diffuse interstellar medium, and the effects of processing on dust within dense clouds will affect the inventory of material available for incorporation into newly forming star and planetary systems. Observational ground-based studies have confirmed the widespread distribution of the 3.4 pm absorption band attributed to aliphatic hydrocarbons in the diffuse interstellar medium of our own galaxy, and in the dusty spectra of a few nearby galaxies, while space based observations from IS0 probed the signatures of corresponding mid-infrared features. Laboratory experiments which utilize both thermal processes and energetic processing by high energy photons and cosmic rays, produce candidate materials which offer close matches to the observed diffuse interstellar medium and extragalactic hydrocarbon absorption features. Through an analysis of the 4000 to 1000 cm (2.5 to 10 micrometers) region of the spectrum of diffuse interstellar medium (DISM) dust compared with the spectra of thirteen chemical entities produced in the laboratory which serve as analogs to the interstellar material, significant constraints have been placed on the applicability of proposed candidate materials to explain the interstellar features. The results indicate that the organic refractory material in the diffuse interstellar medium is predominantly hydrocarbon in nature, possessing little nitrogen or oxygen, with the carbon distributed between the aromatic and aliphatic forms. Long alkane chains H3C-(CH2),- with n much greater than 4 or 5 are not major constituents of this material. Comparisons to laboratory analogs indicate the DISM organic material resembles plasma processed pure hydrocarbon residues much more so than energetically processed ice residues. This result is consistent with a birthsite for the carrier of the 3.4 micrometers band in the outflow region of evolved carbon stars. Comparisons of dust from our own galaxy with that of distant galaxies suggests that the organic component of interstellar dust is widespread and may be an important universal reservoir of prebiotic organic carbon.

Pendleton, Yvonne↗

NASA NTRS2003

Multi-Temperature Emission and Abundances in the Hot Gaseous Halo

We present the results of XMM-Newton observations of NGC 507, a dominant elliptical galaxy in a small group of galaxies. After carefully considering various systematic effects on abundance measurements, we report 'super-solar' metal abundances (both Fe and a-elements) present in the hot ISM: ZFe = 2-3 times solar with an observational limit of as high as 4 times solar inside the D25 ellipse of NGC 507. This is the highest ZFe reported so far, and fully consistent with those expected by the stellar evolution models where heavy elements are enriched by both type II and Ia supernovae ejecta. No unusual constraint either on the SNe rate or IMF is required. Among various factors affecting the accurate abundance measurement, we find that selecting a proper emission model is most important. As opposed to the X-ray spectral data with limited s/n and poor spatial/spectral resolution obtained in the previous missions, the spatially resolved XMM spectra provide enough statistics to untie the model-Z degeneracy and statistically require at least 3 emission components in each concentric shell (2 thermal components representing a finite range of kT in the hot ISM + 1 hard LMXB component). We show that a simpler model (such as a two-component model) produce a much lower best-fit ZFe. The abundances of a-elements (most accurately determined by Si) is also found to be super-solar and its radio to Fe is close to the solar ratio, suggesting a considerably contribution of heavy elements from Type Ia SNe. We estimate approx. 70% of MFe in the hot ISM originate from Type Ia.

Kim, Dong-Woo↗

NASA NTRS2019

The Lyα Luminosity Function and Cosmic Reionization at z ~ 7.0: A Tale of Two LAGER Fields

We present the largest-ever sample of 79 Lyα emitters (LAEs) at z ~ 7.0 selected in the COSMOS and CDFS fields of the LAGER project (the Lyman Alpha Galaxies in the Epoch of Reionization). Our newly amassed ultradeep narrowband exposure and deeper/wider broadband images have more than doubled the number of LAEs in COSMOS, and we have selected 30 LAEs in the second field CDFS. We detect two large-scale LAE-overdense regions in the COSMOS that are likely protoclusters at the highest redshift to date. We perform injection and recovery simulations to derive the sample incompleteness. We show that significant incompleteness comes from blending with foreground sources, which, however, has not been corrected in LAE luminosity functions (LFs) in the literature. The bright-end bump in the Lyα LF in COSMOS is confirmed with six (two newly selected) luminous LAEs (LLyα > 1043.3 erg s−1). Interestingly, the bump is absent in CDFS, in which only one luminous LAE is detected. Meanwhile, the faint-end LFs from the two fields agree well with each other. The six luminous LAEs in COSMOS coincide with two LAE-overdense regions, while such regions are not seen in CDFS. The bright-end LF bump could be attributed to ionized bubbles in a patchy reionization. It appears associated with cosmic overdensities and thus supports an inside-out reionization topology at z ~ 7.0, i.e., the high-density peaks were ionized earlier compared to the voids. An average neutral hydrogen fraction of xH I ~ 0.2–0.4 is derived at z ~ 7.0 based on the cosmic evolution of the Lyα LF.

cosmology: observations↗

NASA NTRS1978

Survey of some recent stellar-evolution calculations

The stellar-evolution program developed by Sweigart (1973) was used to compute main sequence turnoff, red giant sequences, and horizontal branch sequences for many values of helium abundance and heavy-element abundance. The immediate aim has been to produce a self-consistent set of evolutionary sequences for wide ranges in the composition and mass. The long-term aim involves application to cluster HR diagrams and the integrated properties of galaxies. Turnoff sequences, red giant sequences, and horizontal branch sequences are discussed.

Sweigart, A. V.↗

NASA NTRS2023

Protoplanetary Disk Science with the Orbiting Astronomical Satellite Investigating Stellar Systems (OASIS) Observatory

The Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) is a NASA Astrophysics MIDEX-class mission concept, with the stated goal of Following water from galaxies, through protostellar systems, to Earth’s oceans. This paper details the protoplanetary disk science achievable with OASIS. OASIS’s suite of heterodyne receivers allow for simultaneous, high spectral resolution observations of water emission lines The Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) is a NASA Astrophysics MIDEX-class mission concept, with the stated goal of Following water from galaxies, through protostellar systems, to Earth’s oceans. This paper details the protoplanetary disk science achievable with OASIS. OASIS’s suite of heterodyne receivers allow for simultaneous, high spectral resolution observations of water emission lines HD in 100+ disks, allowing for the most accurate determination of total protoplanetary disk gas mass to date. When combined with the contemporaneous water observations, the HD detection will also allow us to trace the evolution of water vapor across evolutionary stages. These observations will enable OASIS to characterize the time development of the water distribution and the role water plays in the process of planetary system formation.

Kamber R Schwarz↗

NASA NTRS2011

X-Ray Binary Populations in a Cosmological Context, Including NuSTAR Predictions

The new ultradeep 4 Ms Chandra Deep Field South has afforded the deepest view ever of X-ray binary populations. We report on the latest results on both LMXB and HMXB evolution out to redshifts of approximately four, including comparison with the latest theoretical models, using this deepest-ever view of the X-ray universe with Chandra. The upcoming NuSTAR mission will open up X-ray binary populations in the hard X-ray band, similar to the pioneering work of Fabbiano et al. in the Einstein era. We report on plans to study both Local Group and starburst galaxies as well as the implications those observations may have for X-ray binary populations in galaxies contributing to the Cosmic X-ray Background.

Cardiff, Ann Hornschemeier↗

NASA NTRS2012

Radio-to-Gamma-Ray Monitoring of the Narrow-line Seyfert 1 Galaxy PMN J0948+0022 from 2008 to 2011

We present more than three years of observations at different frequencies, from radio to high-energy γ-rays, of the Narrow-Line Seyfert 1 (NLS1) Galaxy PMN J0948+0022 (z = 0.585). This source is the first NLS1 detected at energies above 100 MeV and therefore can be considered the prototype of this emerging new class of γ-ray emitting active galactic nuclei (AGN). The observations performed from 2008 August 1 to 2011 December 31 confirmed that PMN J0948+0022 generates a powerful relativistic jet, which is able to develop an isotropic luminosity at gamma-rays of the order of 1048 erg per second, at the level of powerful quasars. The evolution of the radiation emission of this source in 2009 and 2010 followed the canonical expectations of relativistic jets with correlated multiwavelength variability (gamma-rays followed by radio emission after a few months), but it was difficult to retrieve a similar pattern in the light curves of 2011. The comparison of gamma-ray spectra before and including 2011 data suggested that there was a softening of the highenergy spectral slope. We selected five specific epochs to be studied by modelling the broad-band spectrum, which are characterised by an outburst at gamma-rays or very low/high flux at other wavelengths. The observed variability can largely be explained by changes in the injected power, the bulk Lorentz factor of the jet, or the electron spectrum. The characteristic time scale of doubling/halving flux ranges from a few days to a few months, depending on the frequency and the sampling rate. The shortest doubling time scale at gamma-rays is 2.3 +/- 0.5 days. These small values underline the need of highly sampled multiwavelength campaigns to better understand the physics of these sources.

monitoring↗

NASA NTRS2007

Mini Survey of SDSS [OIII] AGN with Swift: Testing the Hypothesis that L(sub [OIII]) Traces AGN Luminosity

The number of AGN and their luminosity distribution are crucial parameters for our understanding of the AGN phenomenon. Recent work strongly suggests every massive galaxy has a central black hole. However most of these objects either are not radiating or have been very difficult to detect We are now in the era of large surveys, and the luminosity function (LF] of AGN has been estimated in various ways. In the X-ray band. Chandra and XMM surveys have revealed that the LF of hard X-ray selected AGN shows a strong luminosity-dependent evolution with a dramatic break towards low L(sub x) (at all z). This is seen for all types of AGN, but is stronger for the broad-line objects. In sharp contrast, the local LF of optically-selected samples shows no such break and no differences between narrow and broad-line objects. If as been suggested, hard X ray and optical emission line can both can be fair indicators of AGN activity, it is important to first understand how reliable these characteristics are if we hope to understand the apparent discrepancy in the LFs.

Source record↗

NASA NTRS2012

X-Ray Flare Candidates in Short Gamma-Ray Bursts

We present the first systematic study of X-ray flare candidates in short gamma-ray bursts (SGRBs) exploiting the large 6-year Swift database with the aim to constrain the physical nature of such fluctuations. We find that flare candidates appear in different types of SGRB host galaxy environments and show no clear correlation with the X-ray afterglow lifetime; flare candidates are detected both in SGRBs with a bright extended emission in the soft gamma-rays and in SGRBs which do not show such component. We furthermore show that SGRB X-ray flare candidates only partially share the set of observational properties of long GRB (LGRB) flares. In particular, the main parameter driving the duration evolution of X-ray variability episodes in both classes is found to be the elapsed time from the explosion, with very limited dependence on the different progenitors, environments, central engine life-times, prompt variability time-scales and energy budgets. On the contrary, SGRB flare candidates significantly differ from LGRB flares in terms of peak luminosity, isotropic energy, flare-to-prompt luminosity ratio and relative variability flux. However, these differences disappear when the central engine time-scales and energy budget are accounted for, suggesting that (i) flare candidates and prompt pulses in SGRBs likely have a common origin; (ii) similar dissipation and/or emission mechanisms are responsible for the prompt and flare emission in long and short GRBs, with SGRBs being less energetic albeit faster evolving versions of the long class. Finally, we show that in strict analogy to the SGRB prompt emission, flares candidates fall off the lag-luminosity relation defined by LGRBs, thus strengthening the SGRB flare-prompt pulse connection.

Margutti, R.↗

NASA NTRS1980

Galaxy spectral synthesis. II - M32 and the ages of galaxies

The paper presents a population synthesis performed on absolute spectrophotometry for the central 31 in. of M32. The metallicity of M32 is solar with 0.1 dex, implying that major star formation continued in M32 until 5 Gyr ago, or 10 Gyr after the oldest globular clusters formed. The synthesis models predict that the rate of mass return to the interstellar medium in M32 from evolving stars is about 0.0008 solar mass/yr; however, the upper limit for star formation during the past 1 Gyr is about 0.003/yr, showing that the available optical observations do not exclude complete recycling of gas lost during stellar evolution into new generations of stars.

Oconnell, R. W.↗

NASA NTRS1993

A hydrodynamic treatment of the tilted cold dark matter cosmological scenario

A standard hydrodynamic code coupled with a particle-mesh code is used to compute the evolution of a tilted cold dark matter (TCDM) model containing both baryonic matter and dark matter. Six baryonic species are followed, with allowance for both collisional and radiative ionization in every cell. The mean final Zel'dovich-Sunyaev y parameter is estimated to be (5.4 +/- 2.7) x 10 exp -7, below currently attainable observations, with an rms fluctuation of about (6.0 +/- 3.0) x 10 exp -7 on arcmin scales. The rate of galaxy formation peaks at a relatively late epoch (z is about 0.5). In the case of mass function, the smallest objects are stabilized against collapse by thermal energy: the mass-weighted mass spectrum peaks in the vicinity of 10 exp 9.1 solar masses, with a reasonable fit to the Schechter luminosity function if the baryon mass to blue light ratio is about 4. It is shown that a bias factor of 2 required for the model to be consistent with COBE DMR signals is probably a natural outcome in the present multiple component simulations.

Cen, Renyue↗

NASA NTRS1995

Very low mass stars and white dwarfs in NGC 6397

Deep Wide Field/Planetary Camera 2 (WFPC2) images in wide bands centered at 606 and 802 nm were taken with the Hubble Space Telescope (HST) 4.6 min from the center of the galactic globular cluster NGC 6397. The images were used to accurately position approximately 2120 stars detected in the field on a color magnitude diagram down to a limiting magnitude m(sub 814) approximately = m(sub I) approximately = 26 determined reliably and solely by counting statistics. A white dwarf sequence and a rich, narrow cluster main sequence are detected for the first time, the latter stretching from m(sub 814) = 18.5 to m(sub 814) = 24.0 where it becomes indistinguishable from the field population. Two changes of slope of the main sequence at m(sub 814) approximately = 20 and m(sub 814) approximately = 22.5 are evident. The corresponding luminosity function increases slowly from M(sub 814) approximately = 6.5 to 8.5 are expected from ground-based observations but then drops sharply from there dwon to the measurement limit. The corresponding mass function obtained bu using the only presently available mass-luminosity function for the cluster's metallicity rises to a plateau between approximately 0.25 and approximately 0.15 solar mass, but drops toward the expected mass limit of the normal hydrogen burning main sequence at approximately 0.1 solar mass. This result is in clear contrast to that obtained from the ground and implies either a substantial modification of the cluster's initial mass function due to dynamical evolution in its lifetime, or that very low mass stars are not produced in any dynamically significant amount by clusters of this type. The white dwarf sequence is in reasonable agreement with a cooling sequence of models of mass 0.5 solar mass at the canonical distance of NGC 6397 with a scatter that is most likely due to photometric errors, but may also reflect real differences in mass or chemical composition. Contamination from unresolved galaxies, which cannot be reliably identified with our filters, makes it difficult to meaningfully compare the observed white dwarf luminosity function with its theoretical counterpart.

Paresce, Francesco↗

NASA NTRS1997

The Evolving Universe: Structure and Evolution of the Universe Roadmap 2000-2020

The Roadmap for the Structure and Evolution of the Universe (SEU) theme embraces three fundamental, scientific quests: (1) To explain structure in the Universe and forecast our cosmic destiny. (2) To explore the cycles of matter and energy in the evolving Universe. (3) To examine the ultimate limits of gravity and energy in the Universe. These quests are developed into six, focused research campaigns addressing the objectives of one or more quests: Identify dark matter and learn how it shapes galaxies and systems of galaxies; Find out where and when the chemical elements were made; Understand the cycles in which matter, energy, and magnetic field are exchanged between stars and the gas between stars; Discover how gas flows in disks and how cosmic jets are formed; Identify the sources of gamma-ray bursts and high-energy cosmic rays; and Measure how strong gravity operates near black holes and how it affects the early Universe. These campaigns lead to a portfolio of future major missions of strong scientific and popular appeal, strongly endorsed by the scientific community and which has undergone significant initial study. Some of these missions are in a state of readiness that makes ideal candidates for the present Office of Space Science Strategic Plan; others may well feature in the next Strategic Plan. Each provides a golden scientific opportunity to advance our understanding of the Universe. Our highest priority science objectives are addressed by five Observatory Class Missions, unranked by science, but in approximate order of readiness: A high-energy gamma-ray facility that will observe relativistic jets and study the sources of cosmic gamma ray bursts; An ultra-sensitive X-ray telescope, optimized for spectroscopy, to examine the hot gas linked with clusters of galaxies, the disks around black holes, and supernova explosions; A large, radio telescope in deep space to map central regions of distant quasars and perform astrometric investigations; An orbiting gravitational coalescing, massive black holes and test how gravity waves distort spacetime; A pair of Earth-orbiting, optical telescopes that will detect flashes of light produced when ultra high-energy cosmic rays impact the upper atmosphere so as to determine their arrival directions and energies. A new program for supporting pertinent international collaboration is strongly endorsed and maintaining a strong Explorer program is important. The flexibility to exploit exceptional opportunities, such as attaching payloads to space station, should also be acquired. A strong technology development program must be initiated now to enable this mission set.

Source record↗

NASA NTRS2000

Space Infrared Astronomy in the 21st Century

New technology and design approaches have enabled revolutionary improvements in astronomical observations from space. Worldwide plans and dreams include orders of magnitude growth in sensitivity and resolution for all wavelength ranges, and would give the ability to learn our history, from the Big Bang to the conditions for life on Earth. The Next Generation Space Telescope, for example, will be able to see the most distant galaxies as they were being assembled from tiny fragments. It will be 1/4 as massive as the Hubble, with a mirror 3 times as large, cooled to about 30 Kelvin to image infrared radiation. I will discuss plans for NGST and hopes for future large space telescopes, ranging from the Space UV Optical (SUVO) telescope to the Filled Aperture Infrared (FAIR) Telescope, the Space Infrared Interferometric Telescope (SPIRIT), and the Submillimeter Probe of the Evolution of Cosmic Structure (SPECS).

Mather, John C.↗

NASA NTRS2006

Spatial Correlation Function of the Chandra Selected Active Galactic Nuclei

We present the spatial correlation function analysis of non-stellar X-ray point sources in the Chandra Large Area Synoptic X-ray Survey of Lockman Hole Northwest (CLASXS). Our 9 ACIS-I fields cover a contiguous solid angle of 0.4 deg(exp 2) and reach a depth of 3 x 10(exp -15) erg/square cm/s in the 2-8 keV band. We supplement our analysis with data from the Chandra Deep Field North (CDFN). The addition of this field allows better probe of the correlation function at small scales. A total of 233 and 252 sources with spectroscopic information are used in the study of the CLASXS and CDFN fields respectively. We calculate both redshift-space and projected correlation functions in co-moving coordinates, averaged over the redshift range of 0.1 < z < 3.0, for both CLASXS and CDFN fields for a standard cosmology with Omega(sub Lambda) = 0.73,Omega(sub M) = 0.27, and h = 0.71 (H(sub 0) = 100h km/s Mpc(exp -1). The correlation function for the CLASXS field over scales of 3 Mpc< s < 200 Mpc can be modeled as a power-law of the form xi(s) = (S/SO)(exp - gamma), with gamma = 1.6(sup +0.4 sub -0.3) and S(sub o) = 8.0(sup +.14 sub -1.5) Mpc. The redshift-space correlation function for CDFN on scales of 1 Mpc< s < 100 Mpc is found to have a similar correlation length so = 8.55(sup +0.74 sub -0.74) Mpc, but a shallower slope (gamma = 1.3 +/- 0.1). The real-space correlation functions derived from the projected correlation functions, are found to be tau(sub 0 = 8.1(sup +1.2 sub -2.2) Mpc, and gamma = 2.1 +/- 0.5 for the CLASXS field, and tau(sub 0) = 5.8(sup +.1.0 sub -1.5) Mpc, gamma = 1.38(sup +0.12 sub -0.14 for the CDFN field. By comparing the real- and redshift-space correlation functions in the combined CLASXS and CDFN samples, we are able to estimate the redshift distortion parameter Beta = 0.4 +/- 0.2 at an effective redshift z = 0.94. We compare the correlation functions for hard and soft spectra sources in the CLASXS field and find no significant difference between the two groups. We have also found that the correlation between X-ray luminosity and clustering amplitude is weak, which, however, is fully consistent with the expectation using the simplest relations between X-ray luminosity, black hole mass, and dark halo mass. We study the evolution of the AGN clustering by dividing the samples into 4 redshift bins over 0.1 Mpc< z <3.0 Mpc. We find a very mild evolution in the clustering amplitude, which show the same evolution trend found in optically selected quasars in the 2dF survey. We estimate the evolution of the bias, and find that the bias increases rapidly with redshift (b(z = 0.45) = 0.95 +/- 0.15 and b(z = 2.07) = 3.03 +/- 0.83): The typical mass of the dark matter halo derived from the bias estimates show little change with redshift. The average halo mass is found to be log (M(sub halo)/M(sun))approximates 12.1. Subject headings: cosmology: observations - large-scale structure of the universe - x-rays: diffuse background - galaxies: nuclei

Yang, Y.↗

NASA NTRS1989

The intergalactic medium and galaxy formation

Recent observational and theoretical investigations of the intergalactic medium (IGM), defined as the component of the baryon-electron matter which now occupies the space between galaxies and which filled the pregalactic universe, are reviewed. Topics addressed include the Gunn-Peterson constraint on the history of the IGM, the mean mass density of the IGM at high redshift, requirements for ionizing the IGM, the observed quasar contribution, the thermal and ionization history of the IGM (quasar photoionization, stellar sources of the ionizing background, and alternative sources such as protogalactic shock radiation and the decay of exotic particles), and the hydrodynamical evolution of the IGM. Typical results from observations and numerical simulations are presented graphically.

Shapiro, Paul R.↗

NASA NTRS1981

Cloud fluid compression and softening in spiral arms and the formation of giant molecular cloud complexes

With regard to the galactodynamics of the cloudy interstellar medium, the paper considers the response of such a gas to a forcing potential in the tight-winding density wave theory. The cloud fluid is treated in the hydrodynamic limit with an equation of state which softens at high densities. It is shown that in the inner regions of the galaxy, cooling of the cloud fluid in the arms can result in gravitational instability and the formation of large bound complexes of clouds which are identified with the giant molecular clouds (GMCs). Masses, dimensions, distributions, and scale heights of the GMCs are predicted by the theory. It is suggested that the interstellar gas density in the disk is regulated by the gravitational instability mechanism in the arms which siphons material into star formation. Implications for the evolution of individual GMCs and for galactic morphology are discussed.

Cowie, L. L.↗

NASA NTRS1994

Comprehensive stellar population models and the disentanglement of age and metallicity effects

The construction of detailed models for intermediate and old stellar populations is described. Input parameters include metallicity (-2 less than (Fe/H) less than 0.5), single-burst age (between 1.5 and 17 Gyr), and initial mass function (IMF) exponent. Quantities output include broadband magnitudes, spectral energy distributions, surface brightness fluctuation magnitudes, and a suite of 21 absorption feature indices. The models are checked against a wide variety of available observations. Examinations of model output yield the following conclusions. (1) If the percentage change delta age/delta Z approximately equals 3/2 for two populations, they will appear almost identical in most indices. A few indices break this degeneracy by being either more abundance sensitive (Fe4668, Fe5015, Fe5709, and Fe5782) or more age sensitive (G4300, H beta, and presumably higher order Balmer lines) than usual. (2) Present uncertainties in stellar evolution are of the same magnitude as the effects of IMF and Y in the indices studied. (3) Changes in abundance ratios (like (Mg/Fe)) are predicted to be readily apparent in the spectra of old stellar populations. (4) The I-band flux of a stellar population is predicted to be nearly independent of metallicity and only modestly sensitive to age. The I band is therefore recommended for standard candle work or studies of M/L in galaxies. Other conclusions stem from this work. (1) Intercomparison of models and observations of two TiO indices seem to indicate variation of the (V/Ti) ratio among galaxies, but it is not clear how this observation ties into the standard picture of chemical enrichment. (2) Current estimates of (Fe/H) for the most metal-rich globulars that are based on integrated indices are probably slightly too high. (3) Colors of population models from different authors exhibit a substantial range. At solar metallicity and 13 Gyr, this range corresponds to an age error of roughly +/- 7 Gyr. Model colors from different authors applied in a differential sense have smaller uncertainties. (4) In the present models the dominant error for colors is probably the transformation from stellar atmospheric parameters to stellar colors. (5) Stellar B - V is difficult to model, and current spreads among different authors can reach 0.2 mag. (6) If known defects in the stellar flux library are corrected, the population model colors of this work in passbands redder than U would be accurate to roughly 0.03 mag in an absolute sense. These corrections are not made in the tables of model output.

Worthey, Guy↗