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Christian Nitschelm

Publications and source records attributed to Christian Nitschelm.

At least 55 records · Page 3Linked to original sources

The age-chemical abundance structure of the Galactic disc II: $α$-dichotomy and thick disc formation

We extend our previous work on the age-chemical abundance structure of the Galactic outer disc to the inner disc (4 < r < 8 kpc) based on the SDSS/APOGEE survey. Different from the outer disc, the inner disc stars exhibit a clear bimodal distribution in the [Mg/Fe]-[Fe/H] plane. While a number of scenarios have been proposed in the literature, it remains challenging to recover this bimodal distribution with theoretical models. To this end, we present a chemical evolution model embedding a complex multi-phase inner disc formation scenario that matches the observed bimodal [Mg/Fe]-[Fe/H] distribution. In this scenario, the formation of the inner disc is dominated by two main starburst episodes 6 Gyr apart with secular, low-level star formation activity in between. In our model, the first starburst occurs at early cosmic times (t~1 Gyr) and the second one 6 Gyr later at a cosmic time of t~7 Gyr. Both these starburst episodes are associated with gas accretion events in our model, and are quenched rapidly. The first starburst leads to the formation of the high-$α$ sequence, and the second starburst leads to the formation of the metal-poor low-$α$ sequence. The metal-rich low-$α$ stars, instead, form during the secular evolution phase between the two bursts. Our model shows that the $α$-dichotomy originates from the rapid suppression of star formation after the first starburst. The two starburst episodes are likely to be responsible for the formation of the geometric thick disc (z >1 kpc), with the old inner thick disc and the young outer thick disc forming during the first and the second starbursts, respectively.

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The Chemical Compositions of Accreted and {\it in situ} Galactic Globular Clusters According to SDSS/APOGEE

Studies of the kinematics and chemical compositions of Galactic globular clusters (GCs) enable the reconstruction of the history of star formation, chemical evolution, and mass assembly of the Galaxy. Using the latest data release (DR16) of the SDSS/APOGEE survey, we identify 3,090 stars associated with 46 GCs. Using a previously defined kinematic association, we break the sample down into eight separate groups and examine how the kinematics-based classification maps into chemical composition space, considering only $α$ (mostly Si and Mg) elements and Fe. Our results show that: (i) The loci of both in situ and accreted subgroups in chemical space match those of their field counterparts; (ii) GCs from different individual accreted subgroups occupy the same locus in chemical space. This could either mean that they share a similar origin or that they are associated with distinct satellites which underwent similar chemical enrichment histories; (iii) The chemical compositions of the GCs associated with the low orbital energy subgroup defined by Massari and collaborators is broadly consistent with an in situ origin. However, at the low metallicity end, the distinction between accreted and in situ populations is blurred; (iv) Regarding the status of GCs whose origin is ambiguous, we conclude the following: the position in Si-Fe plane suggests an in situ}origin for Liller 1 and a likely accreted origin for NGC 5904 and NGC 6388. The case of NGC 288 is unclear, as its orbital properties suggest an accretion origin, its chemical composition suggests it may have formed in situ.

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Close Binary Companions to APOGEE DR16 Stars: 20,000 Binary-star Systems Across the Color-Magnitude Diagram

Many problems in contemporary astrophysics---from understanding the formation of black holes to untangling the chemical evolution of galaxies---rely on knowledge about binary stars. This, in turn, depends on discovery and characterization of binary companions for large numbers of different kinds of stars in different chemical and dynamical environments. Current stellar spectroscopic surveys observe hundreds of thousands to millions of stars with (typically) few observational epochs, which allows binary discovery but makes orbital characterization challenging. We use a custom Monte Carlo sampler (The Joker) to perform discovery and characterization of binary systems through radial-velocities, in the regime of sparse, noisy, and poorly sampled multi-epoch data. We use it to generate posterior samplings in Keplerian parameters for 232,531 sources released in APOGEE Data Release 16. Our final catalog contains 19,635 high-confidence close-binary (P < few years, a < few AU) systems that show interesting relationships between binary occurrence rate and location in the color-magnitude diagram. We find notable faint companions at high masses (black-hole candidates), at low masses (substellar candidates), and at very close separations (mass-transfer candidates). We also use the posterior samplings in a (toy) hierarchical inference to measure the long-period binary-star eccentricity distribution. We release the full set of posterior samplings for the entire parent sample of 232,531 stars. This set of samplings involves no heuristic "discovery" threshold and therefore can be used for myriad statistical purposes, including hierarchical inferences about binary-star populations and sub-threshold searches.

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The Lazy Giants: APOGEE Abundances Reveal Low Star Formation Efficiencies in the Magellanic Clouds

We report the first APOGEE metallicities and alpha-element abundances measured for 3600 red giant stars spanning a large radial range of both the Large (LMC) and Small Magellanic Clouds (SMC), the largest Milky Way dwarf galaxies. Our sample is an order of magnitude larger than that of previous studies, and extends to much larger radial distances. These are the first results presented that make use of the newly installed Southern APOGEE instrument on the du Pont telescope at Las Campanas Observatory. Our unbiased sample of the LMC spans a large range in metallicity, from [Fe/H]=-0.2 to very metal-poor stars with [Fe/H]=-2.5, the most metal-poor Magellanic Clouds (MCs) stars detected to date. The LMC [alpha/Fe]-[Fe/H] distribution is very flat over a large metallicity range, but rises by ~0.1 dex at -1.0<[Fe/H]<-0.5. We interpret this as a sign of the known recent increase in MC star-formation activity, and are able to reproduce the pattern with a chemical evolution model that includes a recent "starburst". At the metal-poor end, we capture the increase of [alpha/Fe] with decreasing [Fe/H], and constrain the "alpha-knee" to [Fe/H]<-2.2 in both MCs, implying a low star-formation efficiency of ~0.01 Gyr^-1. The MC knees are more metal poor than those of less massive Milky Way (MW) dwarf galaxies such as Fornax, Sculptor, or Sagittarius. One possible interpretation is that the MCs formed in a lower-density environment than the MW, a hypothesis that is consistent with the paradigm that the MCs fell into the MW's gravitational potential only recently.

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Spatial variations in the Milky Way disc metallicity-age relation

Stellar ages are a crucial component to studying the evolution of the Milky Way. Using Gaia DR2 distance estimates, it is now possible to estimate stellar ages for a larger volume of evolved stars through isochrone matching. This work presents [M/H]-age and [$α$/M]-age relations derived for different spatial locations in the Milky Way disc. These relations are derived by hierarchically modelling the star formation history of stars within a given chemical abundance bin. For the first time, we directly observe that significant variation is apparent in the [M/H]-age relation as a function of both Galactocentric radius and distance from the disc mid-plane. The [M/H]-age relations support claims that radial migration has a significant effect in the plane of the disc. Using the [M/H] bin with the youngest mean age at each radial zone in the plane of the disc, the present-day metallicity gradient is measured to be $-0.059 \pm 0.010$ dex kpc$^{-1}$, in agreement with Cepheids and young field stars. We find a vertically flared distribution of young stars in the outer disc, confirming predictions of models and previous observations. The mean age of the [M/H]-[$α$/M] distribution of the solar neighborhood suggests that the high-[M/H] stars are not an evolutionary extension of the low-$α$ sequence. Our observational results are important constraints to Galactic simulations and models of chemical evolution.

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TOI-150: A transiting hot Jupiter in the TESS southern CVZ

We report the detection of a hot Jupiter ($M_{p}=1.75_{-0.17}^{+0.14}\ M_{J}$, $R_{p}=1.38\pm0.04\ R_{J}$) orbiting a middle-aged star ($\log g=4.152^{+0.030}_{-0.043}$) in the Transiting Exoplanet Survey Satellite (TESS) southern continuous viewing zone ($β=-79.59^{\circ}$). We confirm the planetary nature of the candidate TOI-150.01 using radial velocity observations from the APOGEE-2 South spectrograph and the Carnegie Planet Finder Spectrograph, ground-based photometric observations from the robotic Three-hundred MilliMeter Telescope at Las Campanas Observatory, and Gaia distance estimates. Large-scale spectroscopic surveys, such as APOGEE/APOGEE-2, now have sufficient radial velocity precision to directly confirm the signature of giant exoplanets, making such data sets valuable tools in the TESS era. Continual monitoring of TOI-150 by TESS can reveal additional planets and subsequent observations can provide insights into planetary system architectures involving a hot Jupiter around a star about halfway through its main-sequence life.

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The Relationship Between Globular Cluster Mass, Metallicity, and Light Element Abundance Variations

We investigate aluminum abundance variations in the stellar populations of globular clusters using both literature measurements of sodium and aluminum and APOGEE measurements of nitrogen and aluminum abundances. For the latter, we show that the Payne is the most suitable of the five available abundance pipelines for our purposes. Our combined sample of 42 globular clusters spans approximately 2 dex in [Fe/H] and 1.5 dex in $\log{M_{GC}/M_{\odot}}$. We find no fewer than five globular clusters with significant internal variations in nitrogen and/or sodium with little-to-no corresponding variation in aluminum, and that the minimum present-day cluster mass for aluminum enrichment in metal-rich systems is $\log{M_{GC}/M_{\odot}} \approx 4.50 + 2.17(\rm{[Fe/H]}+1.30)$. We demonstrate that the slopes of the [Al/Fe] vs [Na/Fe] and [Al/Fe] vs [N/Fe] relations for stars without field-like abundances are approximately log-linearly dependent on both the metallicity and the stellar mass of the globular clusters. In contrast, the relationship between [Na/Fe] and [N/Fe] shows no evidence of such dependencies. This suggests that there were (at least) two classes of non-supernovae chemical polluters that were common in the early universe, and that their relative contributions within globular clusters somehow scaled with the metallicity and mass of globular clusters. The first of these classes is predominantly responsible for the CNO and NeNa abundance variations, and likewise the second for the MgAl abundance variations. 47 Tuc and M4 are particularly striking examples of this dichotomy. As an auxiliary finding, we argue that abundance variations among Terzan 5 stars are consistent with it being a normal globular cluster.

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A Multi-Year Search For Transits Of Proxima Centauri. II: No Evidence For Transit Events With Periods Between 1-30 Days

Using a global network of small telescopes, we have obtained light curves of Proxima Centauri at 329 observation epochs from 2006 - 2017. The planet Proxima b discovered by Anglada-Escude et al. (2016) with an orbital period of 11.186 d has an a priori transit probability of ~1.5%; if it transits, the predicted transit depth is about 5 millimagnitudes. In Blank et al. (2018), we analyzed 96 of our light curves that overlapped with predicted transit ephemerides from previously published tentative transit detections, and found no evidence in our data that would corroborate claims of transits with a period of 11.186 d. Here we broaden our analysis, using 262 high-quality light curves from our data set to search for any periodic transit-like events over a range of periods from 1 - 30 d. We also inject a series of simulated planet transits and find that our data are sufficiently sensitive to have detected transits of 5 millimagnitude depth, with recoverability ranging from ~100% for an orbital period of 1 d to ~20% for an orbital period of 20 d for the parameter spaces tested. Specifically at the 11.186 d period and 5 millimagnitude transit depth, we rule out transits in our data with high confidence. We are able to rule out virtually all transits of other planets at periods shorter than 5 d and depths greater than 3 millimagnitudes; however, we cannot confidently rule out transits at the period of Proxima b due to incomplete orbital phase coverage and a lack of sensitivity to transits shallower than 4 millimagnitudes.

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Discovery of Resolved Magnetically Split Lines in SDSS/APOGEE Spectra of 157 Ap/Bp Stars

We report on magnetic field measurements of 157 chemically peculiar A/B stars (Ap/Bp) based on resolved, magnetically split absorption lines present in $H$-band spectra provided by the Sloan Digital Sky Survey (SDSS)/Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. These stars represent the extreme magnetic end of a still-growing sample of >900 Ap/Bp stars selected among the APOGEE telluric standard stars as those with Ce III absorption lines and/or literature Ap/Bp classifications. The lines most frequently resolved into their split components for these stars in the $H$-band pertain primarily pertain to Ce III, Cr II, Fe I, Mn II, Si I, and Ca II, in addition to one or more unidentified ions. Using mean magnetic field modulus ( ) estimates for transitions with known Landé factors, we estimate effective Landé factors for 5 Ce III lines and 15 unknown lines and proceed to measure of 157 stars, only 3 of which have previous literature estimates of . This 183% increase in the number of Ap/Bp stars for which has been measured is a result of the large number of stars observed by SDSS/APOGEE, extension of high-resolution Ap/Bp star observations to fainter magnitudes, and the advantages of long wavelengths for resolving magnetically split lines. With =25 kG, the star 2MASS J02563098+4534239 is currently the most magnetic star of the SDSS/APOGEE sample. Effective Landé factors, representative line profiles, and magnetic field moduli are presented. The validity of the results is supported using optical, high-resolution, follow-up spectra for 29 of the stars.

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Chemical Abundances of Main-Sequence, Turnoff, Subgiant and red giant Stars from APOGEE spectra II: Atomic Diffusion in M67 Stars

Chemical abundances for 15 elements (C, N, O, Na, Mg, Al, Si, K, Ca, Ti, V, Cr, Mn, Fe, and Ni) are presented for 83 stellar members of the 4 Gyr old solar-metallicity open cluster M67. The sample contains stars spanning a wide range of evolutionary phases, from G dwarfs to red clump stars. The abundances were derived from near-IR ($λ$1.5 -- 1.7$μ$m) high-resolution spectra ($R$ = 22,500) from the SDSS-IV/APOGEE survey. A 1-D LTE abundance analysis was carried out using the APOGEE synthetic spectral libraries, via chi-square minimization of the synthetic and observed spectra with the qASPCAP code. We found significant abundance differences ($\sim$0.05 -- 0.30 dex) between the M67 member stars as a function of the stellar mass (or position on the HR diagram), where the abundance patterns exhibit a general depletion (in [X/H]) in stars at the main-sequence turnoff. The amount of the depletion is different for different elements. We find that atomic diffusion models provide, in general, good agreement with the abundance trends for most chemical species, supporting recent studies indicating that measurable atomic diffusion operates in M67 stars.

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APOGEE [C/N] Abundances Across the Galaxy: Migration and Infall from Red Giant Ages

We present [C/N]-[Fe/H] abundance trends from the SDSS-IV Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey, Data Release 14 (DR14), for red giant branch stars across the Milky Way Galaxy (MW, 3 kpc $<$ R $<$ 15 kpc). The carbon-to-nitrogen ratio (often expressed as [C/N]) can indicate the mass of a red giant star, from which an age can be inferred. Using masses and ages derived by Martig et al., we demonstrate that we are able to interpret the DR14 [C/N]-[Fe/H] abundance distributions as trends in age-[Fe/H] space. Our results show that an anti-correlation between age and metallicity, which is predicted by simple chemical evolution models, is not present at any Galactic zone. Stars far from the plane ($|$Z$|$ $>$ 1 kpc) exhibit a radial gradient in [C/N] ($\sim$ $-$0.04 dex/kpc). The [C/N] dispersion increases toward the plane ($σ_{[C/N]}$ = 0.13 at $|$Z$|$ $>$ 1 kpc to $σ_{[C/N]}$ = 0.18 dex at $|$Z$|$ $<$ 0.5 kpc). We measure a disk metallicity gradient for the youngest stars (age $<$ 2.5 Gyr) of $-$0.060 dex/kpc from 6 kpc to 12 kpc, which is in agreement with the gradient found using young CoRoGEE stars by Anders et al. Older stars exhibit a flatter gradient ($-$0.016 dex/kpc), which is predicted by simulations in which stars migrate from their birth radii. We also find that radial migration is a plausible explanation for the observed upturn of the [C/N]-[Fe/H] abundance trends in the outer Galaxy, where the metal-rich stars are relatively enhanced in [C/N].

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Chemical Cartography with APOGEE: Multi-element abundance ratios

We map the trends of elemental abundance ratios across the Galactic disk, spanning R = 3-15 kpc and midplane distance |Z|= 0-2 kpc, for 15 elements in a sample of 20,485 stars measured by the SDSS/APOGEE survey (O, Na, Mg, Al, Si, P, S, K, Ca, V, Cr, Mn, Fe, Co, Ni). Adopting Mg rather than Fe as our reference element, and separating stars into two populations based on [Fe/Mg], we find that the median trends of [X/Mg] vs. [Mg/H] in each population are nearly independent of location in the Galaxy. The full multi-element cartography can be summarized by combining these nearly universal median sequences with our measured metallicity distribution functions and the relative proportions of the low-[Fe/Mg] (high-alpha) and high-[Fe/Mg] (low-alpha) populations, which depend strongly on R and |Z|. We interpret the median sequences with a semi-empirical "2-process" model that describes both the ratio of core collapse and Type Ia supernova contributions to each element and the metallicity dependence of the supernova yields. These observationally inferred trends can provide strong tests of supernova nucleosynthesis calculations. Our results lead to a relatively simple picture of abundance ratio variations in the Milky Way, in which the trends at any location can be described as the sum of two components with relative contributions that change systematically and smoothly across the Galaxy. Deviations from this picture and future extensions to other elements can provide further insights into the physics of stellar nucleosynthesis and unusual events in the Galaxy's history.

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The Origin of the 300 km s$^{-1}$ Stream Near Segue 1

We present a search for new members of the 300 km s$^{-1}$ stream (300S) near the dwarf galaxy Segue 1 using wide-field survey data. We identify 11 previously unknown bright stream members in the APOGEE-2 and SEGUE-1 and 2 spectroscopic surveys. Based on the spatial distribution of the high-velocity stars, we confirm for the first time that this kinematic structure is associated with a 24$^{\circ}$-long stream seen in SDSS and Pan-STARRS imaging data. The 300S stars display a metallicity range of $-2.17 < {\rm [Fe/H]} < -1.24$, with an intrinsic dispersion of 0.21$_{-0.09}^{+0.12}$ dex. They also have chemical abundance patterns similar to those of Local Group dwarf galaxies, as well as that of the Milky Way halo. Using the open-source code galpy to model the orbit of the stream, we find that the progenitor of the stream passed perigalacticon about 70 Myr ago, with a closest approach to the Galactic Center of about 4.1 kpc. Using Pan-STARRS DR1 data, we obtain an integrated stream luminosity of $4 \times 10^3$ L$_{\odot}$. We conclude that the progenitor of the stream was a dwarf galaxy that is probably similar to the satellites that were accreted to build the present-day Milky Way halo.

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Spectroscopic identification of INTEGRAL high-energy sources with VLT/ISAAC

The INTEGRAL satellite has been observing the gamma-ray sky for 15 years and has detected over 900 X-ray sources of various nature. However, more than 200 of these sources still lack precise identification. Our goal is to reveal the nature of the high-energy sources detected by INTEGRAL. In particular, we want to improve the census of X-ray binaries. Photometry and spectroscopy were performed in July 2012 on 14 INTEGRAL sources in near-infrared at the Very Large Telescope on the European Southern Observatory-UT3 telescope equipped with the ISAAC spectrograph. We used K$_s$ images reaching to a depth of magnitude 18.5 to look for unique counterparts to high-energy detections to check for both extended sources and photometric variability. The analysis of near-infrared spectral features allows us to constrain the nature of these X-ray sources by comparing them to stellar spectra atlases. We present photometric and/or spectroscopic data for 14 sources (IGR J00465$-$4005, IGR J10447$-$6027, IGR J12489$-$6243, IGR J13020$-$6359, IGR J13186$-$6257, IGR J15293$-$5609, IGR J17200$-$3116, IGR J17404$-$3655, IGR J17586$-$2129, IGR J17597$-$2201, IGR J18457+0244, IGR J18532+0416, IGR J19308$+$0530, and IGR J19378$-$0617). We conclude that 5 of these are active galactic nuclei, 5 are cataclysmic variables, 2 are low- or intermediate-mass X-ray binaries, and 2 are Be high-mass X-ray binaries.

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The Open Cluster Chemical Abundances and Mapping Survey: II. Precision Cluster Abundances for APOGEE using SDSS DR14

The Open Cluster Chemical Abundances and Mapping (OCCAM) survey aims to produce a comprehensive, uniform, infrared-based spectroscopic dataset for hundreds of open clusters, and to constrain key Galactic dynamical and chemical parameters from this sample. This second contribution from the OCCAM survey presents analysis of 259 member stars with [Fe/H] determinations in 19 open clusters, using Sloan Digital Sky Survey Data Release 14 (SDSS/DR14) data from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) and ESA Gaia. This analysis, which includes clusters with R_{GC} ranging from 7 to 13 kpc, measures an [Fe/H] gradient of -0.061 \pm 0.004 dex/kpc. We also confirm evidence of a significant positive gradient in the α-elements ([O/Fe], [Mg/Fe], and [Si/Fe]) and present evidence for a significant negative gradient in iron-peak elements ([Mn/Fe] and [Ni/Fe]).

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The APOGEE-2 Survey of the Orion Star Forming Complex II: Six-dimensional structure

We present an analysis of spectrosopic and astrometric data from APOGEE-2 and Gaia DR2 to identify structures towards the Orion Complex. By applying a hierarchical clustering algorithm to the 6-dimensional stellar data, we identify spatially and/or kinematically distinct groups of young stellar objects with ages ranging from 1 to 12 Myr. We also investigate the star forming history within the Orion Complex, and identify peculiar sub-clusters. With this method we reconstruct the older populations in the regions that are presently largely devoid of molecular gas, such as Orion C (which includes the $σ$ Ori cluster), and Orion D (the population that traces Ori OB1a, OB1b, and Orion X). We report on the distances, kinematics, and ages of the groups within the Complex. The Orion D groups is in the process of expanding. On the other hand, Orion B is still in the process of contraction. In $λ$ Ori the proper motions are consistent with a radial expansion due to an explosion from a supernova; the traceback age from the expansion exceeds the age of the youngest stars formed near the outer edges of the region, and their formation would have been triggered when they were half-way from the cluster center to their current positions. We also present a comparison between the parallax and proper motion solutions obtained by Gaia DR2, and those obtained towards star-forming regions by Very Long Baseline Array.

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Disk-Like Chemistry of the Triangulum-Andromeda Overdensity as Seen by APOGEE

The nature of the Triangulum-Andromeda (TriAnd) system has been debated since the discovery of this distant, low-latitude Milky Way (MW) overdensity more than a decade ago. Explanations for its origin are either as a halo substructure from the disruption of a dwarf galaxy or a distant extension of the Galactic disk. We test these hypotheses using chemical abundances of a dozen TriAnd members from the Sloan Digital Sky Survey's 14th Data Release of Apache Point Observatory Galactic Evolution Experiment (APOGEE) data to compare to APOGEE abundances of stars with similar metallicity from both the Sagittarius (Sgr) dSph, and the outer MW disk. We find that TriAnd stars are chemically distinct from Sgr across a variety of elements, (C+N), Mg, K, Ca, Mn, and Ni, with a separation in [X/Fe] of about 0.1 to 0.4 dex depending on the element. Instead, the TriAnd stars, with a median metallicity of about -0.8, exhibit chemical abundance ratios similar to those of the lowest metallicity ([Fe/H] ~ -0.7) stars in the outer Galactic disk, and are consistent with expectations of extrapolated chemical gradients in the outer disk of the MW. These results suggest that TriAnd is associated with the MW disk, and, therefore, that the disk extends to this overdensity --- i.e., past a Galactocentric radius of 24 kpc --- albeit vertically perturbed about 7 kpc below the nominal disk midplane in this region of the Galaxy.

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The Second APOKASC Catalog: The Empirical Approach

We present a catalog of stellar properties for a large sample of 6676 evolved stars with APOGEE spectroscopic parameters and \textit{Kepler} asteroseismic data analyzed using five independent techniques. Our data includes evolutionary state, surface gravity, mean density, mass, radius, age, and the spectroscopic and asteroseismic measurements used to derive them. We employ a new empirical approach for combining asteroseismic measurements from different methods, calibrating the inferred stellar parameters, and estimating uncertainties. With high statistical significance, we find that asteroseismic parameters inferred from the different pipelines have systematic offsets that are not removed by accounting for differences in their solar reference values. We include theoretically motivated corrections to the large frequency spacing ($Δν$) scaling relation, and we calibrate the zero point of the frequency of maximum power ($ν_{\rm max}$) relation to be consistent with masses and radii for members of star clusters. For most targets, the parameters returned by different pipelines are in much better agreement than would be expected from the pipeline-predicted random errors, but 22\% of them had at least one method not return a result and a much larger measurement dispersion. This supports the usage of multiple analysis techniques for asteroseismic stellar population studies. The measured dispersion in mass estimates for fundamental calibrators is consistent with our error model, which yields median random and systematic mass uncertainties for RGB stars of order 4\%. Median random and systematic mass uncertainties are at the 9\% and 8\% level respectively for RC stars.

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