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At least 199 records · Page 11
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DOE OSTI2023

The Evolution of Population III and Extremely Metal-poor Binary Stars

Numerical simulations have now shown that Population III (Pop III) stars can form in binaries and small clusters and that these stars can be in close proximity to each other. If so, they could be subject to binary interactions such as mass exchange that could profoundly alter their evolution, ionizing UV and Lyman–Werner photon emission and explosion yields, with important consequences for early cosmological reionization and chemical enrichment. Here we investigate the evolution of Pop III and extremely metal-poor binary stars with the MESA code. We find that interactions ranging from stable mass transfer to common envelope evolution can occur in these binaries for a wide range of mass ratios and initial separations. Mass transfer can nearly double UV photon yields in some of these binaries with respect to their individual stars by extending the life of the companion star, which in turn can enhance early cosmological reionization but also suppress the formation of later generations of primordial stars. Binary interactions can also have large effects on the nucleosynthetic yields of the stars by promoting or removing them into or out of mass ranges for specific SN types. We provide fits to total photon yields for the binaries in our study for use in cosmological simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Compact binary mergers as the origin of r-process elements in the Galactic halo

Compact binary mergers (of double neutron star and black hole-neutron star systems) are suggested to be the major site of the r-process elements in the Galaxy by recent hydrodynamical and nucleosynthesis studies. It has been pointed out, however, that estimated long lifetimes of compact binaries are in conflict with the presence of r-process-enhanced stars at the metallicity [Fe/H] ∼ −3. To resolve this problem, we examine the role of compact binary mergers in the early Galactic chemical evolution on the assumption that our Galactic halo was formed from merging sub-halos. The chemical evolutions are modeled for sub-halos with their total stellar masses between 10{sup 4}M{sub ⊙} and 2 × 10{sup 8}M{sub ⊙}. The lifetimes of compact binaries are assumed to be 100 Myr (95%) and 1 Myr (5%) according to recent binary population synthesis studies. We find that the r-process abundances (relative to iron; [r/Fe]) start increasing at [Fe/H] ≤ −3 if the star formation rates are smaller for less massive sub-halos. Our models also suggest that the star-to-star scatter of [r/Fe]'s observed in Galactic halo stars can be interpreted as a consequence of greater gas outflow rates for less massive sub-halos. In addition, the sub-solar [r/Fe]'s (observed as [Ba/Fe] ∼ −1.5 for [Fe/H] < −3) are explained by the contribution from the short-lived (∼ 1 Myr) binaries. Our result indicates, therefore, that compact binary mergers can be potentially the origin of the r-process elements throughout the Galactic history.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

WOCS 40007: A DETACHED ECLIPSING BINARY NEAR THE TURNOFF OF THE OPEN CLUSTER NGC 6819

We analyze extensive BVR{sub c}I{sub c} time-series photometry and radial-velocity measurements for WOCS 40007 (Auner 259; KIC 5113053), a double-lined detached eclipsing binary and a member of the open cluster NGC 6819. Utilizing photometric observations from the 1 m telescope at Mount Laguna Observatory and spectra from the WIYN 3.5 m telescope, we measure precise and accurate masses ({approx}1.6% uncertainty) and radii ({approx}0.5%) for the binary components. In addition, we discover a third star orbiting the binary with a period greater than 3000 days using radial velocities and Kepler eclipse timings. Because the stars in the eclipsing binary are near the cluster turnoff, they are evolving rapidly in size and are sensitive to age. With a metallicity of [Fe/H] = +0.09 {+-} 0.03, we find the age of NGC 6819 to be about 2.4 Gyr from color-magnitude diagram (CMD) isochrone fitting and 3.1 {+-} 0.4 Gyr by analyzing the mass-radius (M-R) data for this binary. The M-R age is above previous determinations for this cluster, but consistent within 1{sigma} uncertainties. When the M-R data for the primary star of the additional cluster binary WOCS 23009 is included, the weighted age estimate drops to 2.5 {+-} 0.2 Gyr, with a systematic uncertainty of at least 0.2 Gyr. The age difference between our CMD and M-R findings may be the result of systematic error in the metallicity or helium abundance used in models, or due to slight radius inflation of one or both stars in the WOCS 40007 binary.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Photometric investigation of the totally eclipsing contact binary V12 in the intermediate-age open cluster NGC 7789

NGC 7789 is an intermediate-age open cluster with an age similar to the mean age of contact binary stars. V12 is a bright W UMa-type binary star with an orbital period of 0.3917 days. The first complete light curves of V12 in the V, R, and I bands are presented and analyzed with the Wilson–Devinney (W-D) method. The results show that V12 is an intermediate-contact binary (f=43.0(±2.2)%) with a mass ratio of 3.848, and it is a W-type contact binary where the less massive component is slightly hotter than the more massive one. The asymmetry of the light curves is explained by the presence of a dark spot on the more massive component. The derived orbital inclination (i=83{sub .}{sup ∘}6) indicates that it is a totally eclipsing binary, which suggests that the determined parameters are reliable. The orbital period may show a long-term increase at a rate of P-dot =+2.48(±0.17)×10{sup −6} days yr{sup −1} that reveals a rapid mass transfer from the less massive component to the more massive one. However, more observations are needed to confirm this conclusion. The presence of an intermediate-contact binary in an intermediate-age open cluster may suggest that some contact binaries have a very short pre-contact timescale. The presence of a third body and/or stellar collision may help to shorten the pre-contact evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

On the accuracy of Hipparcos using binary stars as a calibration tool

Stellar binary systems, specifically those that present the most accurate available orbital elements, are a reliable tool to test the accuracy of astrometric observations. We selected all 35 binaries with these characteristics. Our objective is to provide standard uncertainties for the positions and parallaxes measured by Hipparcos relative to this trustworthy set, as well as to check supposed correlations between several parameters (measurement residuals, positions, magnitudes, and parallaxes). In addition, using the high-confidence subset of visual–spectroscopic binaries, we implemented a validation test of the Hipparcos trigonometric parallaxes of binary systems that allowed the evaluation of their reliability. Standard and non-standard statistical analysis techniques were applied in order to achieve well-founded conclusions. In particular, errors-in-variables models such as the total least-squares method were used to validate Hipparcos parallaxes by comparison with those obtained directly from the orbital elements. Previously, we executed Thompson's τ technique in order to detect suspected outliers in the data. Furthermore, several statistical hypothesis tests were carried out to verify if our results were statistically significant. A statistically significant trend indicating larger Hipparcos angular separations with respect to the reference values in 5.2 ± 1.4 mas was found at the 10{sup −8} significance level. Uncertainties in the polar coordinates θ and ρ of 1.°8 and 6.3 mas, respectively, were estimated for the Hipparcos observations of binary systems. We also verified that the parallaxes of binary systems measured in this mission are absolutely compatible with the set of orbital parallaxes obtained from the most accurate orbits at least at the 95% confidence level. This methodology allows us to better estimate the accuracy of Hipparcos observations of binary systems. Indeed, further application to the data collected by Gaia should yield a standard procedure to compare both data sets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

SuperWASP J015100.23-100524.2: A SPOTTED SHALLOW-CONTACT BINARY BELOW THE PERIOD LIMIT

SuperWASP J015100.23-100524.2 (hereafter J015100) is an eclipsing binary with an orbital period of 0.d2145 that is below the short-period limit of contact binary stars. Complete light curves of J015100 in B, V, R, and I bands are presented and are analyzed with the Wilson–Devinney method. It has been discovered that J015100 is a shallow-contact binary (f = 14.6(±2.7)%) with a mass ratio of 3.128. It is a W-type contact binary where the less massive component is about 130 K hotter than the more massive one. The asymmetries of light curves are explained as one dark spot on the more massive component. The detection of J015100 as a contact binary below the period limit suggests that contact binaries below this limit are not rapidly destroyed. This shallow-contact system may be formed from a detached short-period binary similar to DV Psc (Sp. = K4/K5; P = 0.d30855) via orbital shrinkage due to angular momentum loss through magnetic stellar wind.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

MICROLENSING DISCOVERY OF A POPULATION OF VERY TIGHT, VERY LOW MASS BINARY BROWN DWARFS

Although many models have been proposed, the physical mechanisms responsible for the formation of low-mass brown dwarfs (BDs) are poorly understood. The multiplicity properties and minimum mass of the BD mass function provide critical empirical diagnostics of these mechanisms. We present the discovery via gravitational microlensing of two very low mass, very tight binary systems. These binaries have directly and precisely measured total system masses of 0.025 M{sub Sun} and 0.034 M{sub Sun }, and projected separations of 0.31 AU and 0.19 AU, making them the lowest-mass and tightest field BD binaries known. The discovery of a population of such binaries indicates that BD binaries can robustly form at least down to masses of {approx}0.02 M{sub Sun }. Future microlensing surveys will measure a mass-selected sample of BD binary systems, which can then be directly compared to similar samples of stellar binaries.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Very wide binary stars as the primary source of stellar collisions in the galaxy

We present numerical simulations modeling the orbital evolution of very wide binaries, pairs of stars separated by over ∼10{sup 3} AU. Due to perturbations from other passing stars and the Milky Way's tide, the orbits of very wide binary stars occasionally become extremely eccentric, which forces close encounters between the companion stars. We show that this process causes a stellar collision between very wide binary companion stars once every 1000-7500 yr on average in the Milky Way. One of the main uncertainties in this collision rate is the amount of energy dissipated by dynamic tides during close (but not collisional) periastron passages. This dissipation presents a dynamical barrier to stellar collisions and can instead transform very wide binaries into close or contact binaries. However, for any plausible tidal dissipation model, very wide binary stars are an unrealized, and potentially the dominant, source of stellar collisions in our Galaxy. Such collisions should occur throughout the thin disk of the Milky Way. Stellar collisions within very wide binaries should yield a small population of single, Li-depleted, rapidly rotating massive stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Ultra-short period binaries from the Catalina Surveys

We investigate the properties of 367 ultra-short period binary candidates selected from 31,000 sources recently identified from Catalina Surveys data. Based on light curve morphology, along with WISE, Sloan Digital Sky Survey, and GALEX multi-color photometry, we identify two distinct groups of binaries with periods below the 0.22 day contact binary minimum. In contrast to most recent work, we spectroscopically confirm the existence of M dwarf+M dwarf contact binary systems. By measuring the radial velocity variations for five of the shortest-period systems, we find examples of rare cool white dwarf (WD)+M dwarf binaries. Only a few such systems are currently known. Unlike warmer WD systems, their UV flux and optical colors and spectra are dominated by the M-dwarf companion. We contrast our discoveries with previous photometrically selected ultra-short period contact binary candidates and highlight the ongoing need for confirmation using spectra and associated radial velocity measurements. Overall, our analysis increases the number of ultra-short period contact binary candidates by more than an order of magnitude.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Radiation-driven warping of circumbinary disks around eccentric young star binaries

We study a warping instability of a geometrically thin, non-self-gravitating, circumbinary disk around young binary stars on an eccentric orbit. Such a disk is subject to both the tidal torques due to a time-dependent binary potential and the radiative torques due to radiation emitted from each star. The tilt angle between the circumbinary disk plane and the binary orbital plane is assumed to be very small. We find that there is a radius within/beyond which the circumbinary disk is unstable to radiation-driven warping, depending on the disk density and temperature gradient indices. This marginally stable warping radius is very sensitive to viscosity parameters, a fiducial disk radius and the temperature measured there, the stellar luminosity, and the disk surface density at a radius where the disk changes from optically thick to thin for the irradiation from the central stars. On the other hand, it is insensitive to the orbital eccentricity and binary irradiation parameter, which is a function of the binary mass ratio and luminosity of each star. Since the tidal torques can suppress the warping in the inner part of the circumbinary disk, the disk starts to be warped in the outer part. While the circumbinary disks are most likely to be subject to the radiation-driven warping on an AU to kilo-AU scale for binaries with young massive stars more luminous than 10{sup 4} L {sub ☉}, the radiation-driven warping does not work for those around young binaries with the luminosity comparable to the solar luminosity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

STELLAR LOCI II. A MODEL-FREE ESTIMATE OF THE BINARY FRACTION FOR FIELD FGK STARS

We propose a stellar locus outlier (SLOT) method to determine the binary fraction of main-sequence stars statistically. The method is sensitive to neither the period nor mass ratio distributions of binaries and is able to provide model-free estimates of binary fraction for large numbers of stars of different populations in large survey volumes. We have applied the SLOT method to two samples of stars from the Sloan Digital Sky Survey (SDSS) Stripe 82, constructed by combining the recalibrated SDSS photometric data with the spectroscopic information from the SDSS and LAMOST surveys. For the SDSS spectroscopic sample, we find an average binary fraction for field FGK stars of 41% ± 2%. The fractions decrease toward late spectral types and are 44% ± 5%, 43% ± 3%, 35% ± 5%, and 28% ± 6% for stars with g – i colors in the range 0.3-0.6 mag, 0.6-0.9 mag, 0.9-1.2 mag, and 1.2-1.6 mag, respectively. A modest metallicity dependence is also found. The fraction decreases with increasing metallicity. For stars with [Fe/H] between –0.5 and 0.0 dex, –1.0 and –0.5 dex, –1.5 and –1.0 dex, and –2.0 and –1.5 dex, the inferred binary fractions are 37% ± 3%, 39% ± 3%, 50% ± 9%, and 53% ± 20%, respectively. We have further divided the sample into stars from the thin disk, the thick disk, the transition zone between them, and the halo. The results suggest that the Galactic thin and thick disks have comparable binary fractions, whereas the Galactic halo contains a significantly larger fraction of binaries. Applying the method to the LAMOST spectroscopic sample yields consistent results. Finally, other potential applications and future work with the method are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

FORMATION OF BINARY MILLISECOND PULSARS BY ACCRETION-INDUCED COLLAPSE OF WHITE DWARFS UNDER WIND-DRIVEN EVOLUTION

Accretion-induced collapse (AIC) of massive white dwarfs (WDs) has been proposed to be an important channel to form binary millisecond pulsars (MSPs). Recent investigations on thermal timescale mass transfer in WD binaries demonstrate that the resultant MSPs are likely to have relatively wide orbit periods (≳ 10 days). Here we calculate the evolution of WD binaries taking into account the excited wind from the companion star induced by X-ray irradiation of the accreting WD, which may drive rapid mass transfer even when the companion star is less massive than the WD. This scenario can naturally explain the formation of the strong-field neutron star in the low-mass X-ray binary 4U 1822–37. After AIC the mass transfer resumes when the companion star refills its Roche lobe, and the neutron star is recycled owing to mass accretion. A large fraction of the binaries will evolve to become binary MSPs with an He WD companion, with the orbital periods distributed between ≳ 0.1 days and ≲ 30 days, while some of them may follow the cataclysmic variable-like evolution toward very short orbits. If we instead assume that the newborn neutron star appears as an MSP and that part of its rotational energy is used to ablate its companion star, the binaries may also evolve to be the redback-like systems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A NEW CLASS OF NASCENT ECLIPSING BINARIES WITH EXTREME MASS RATIOS

Early B-type main-sequence (MS) stars (M {sub 1} ≈ 5-16 M {sub ☉}) with closely orbiting low-mass stellar companions (q = M {sub 2}/M {sub 1} < 0.25) can evolve to produce Type Ia supernovae, low-mass X-ray binaries, and millisecond pulsars. However, the formation mechanism and intrinsic frequency of such close extreme mass-ratio binaries have been debated, especially considering none have hitherto been detected. Utilizing observations of the Large Magellanic Cloud galaxy conducted by the Optical Gravitational Lensing Experiment, we have discovered a new class of eclipsing binaries in which a luminous B-type MS star irradiates a closely orbiting low-mass pre-MS companion that has not yet fully formed. The primordial pre-MS companions have large radii and discernibly reflect much of the light they intercept from the B-type MS primaries (ΔI {sub refl} ≈ 0.02-0.14 mag). For the 18 definitive MS + pre-MS eclipsing binaries in our sample with good model fits to the observed light-curves, we measure short orbital periods P = 3.0-8.5 days, young ages τ ≈ 0.6-8 Myr, and small secondary masses M {sub 2} ≈ 0.8-2.4 M {sub ☉} (q ≈ 0.07-0.36). The majority of these nascent eclipsing binaries are still associated with stellar nurseries, e.g., the system with the deepest eclipse ΔI {sub 1} = 2.8 mag and youngest age τ = 0.6 ± 0.4 Myr is embedded in the bright H II region 30 Doradus. After correcting for selection effects, we find that (2.0 ± 0.6)% of B-type MS stars have companions with short orbital periods P = 3.0-8.5 days and extreme mass ratios q ≈ 0.06-0.25. This is ≈10 times greater than that observed for solar-type MS primaries. We discuss how these new eclipsing binaries provide invaluable insights, diagnostics, and challenges for the formation and evolution of stars, binaries, and H II regions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

STABLE CONIC-HELICAL ORBITS OF PLANETS AROUND BINARY STARS: ANALYTICAL RESULTS

Studies of planets in binary star systems are especially important because it was estimated that about half of binary stars are capable of supporting habitable terrestrial planets within stable orbital ranges. One-planet binary star systems (OBSS) have a limited analogy to objects studied in atomic/molecular physics: one-electron Rydberg quasimolecules (ORQ). Specifically, ORQ, consisting of two fully stripped ions of the nuclear charges Z and Z′ plus one highly excited electron, are encountered in various plasmas containing more than one kind of ion. Classical analytical studies of ORQ resulted in the discovery of classical stable electronic orbits with the shape of a helix on the surface of a cone. In the present paper we show that despite several important distinctions between OBSS and ORQ, it is possible for OBSS to have stable planetary orbits in the shape of a helix on a conical surface, whose axis of symmetry coincides with the interstellar axis; the stability is not affected by the rotation of the stars. Further, we demonstrate that the eccentricity of the stars’ orbits does not affect the stability of the helical planetary motion if the center of symmetry of the helix is relatively close to the star of the larger mass. We also show that if the center of symmetry of the conic-helical planetary orbit is relatively close to the star of the smaller mass, a sufficiently large eccentricity of stars’ orbits can switch the planetary motion to the unstable mode and the planet would escape the system. We demonstrate that such planets are transitable for the overwhelming majority of inclinations of plane of the stars’ orbits (i.e., the projections of the planet and the adjacent start on the plane of the sky coincide once in a while). This means that conic-helical planetary orbits at binary stars can be detected photometrically. We consider, as an example, Kepler-16 binary stars to provide illustrative numerical data on the possible parameters and the stability of the conic-helical planetary orbits, as well as on the transitability. Then for the general case, we also show that the power of the gravitational radiation due to this planet can be comparable or even exceed the power of the gravitational radiation due to the stars in the binary. This means that in the future, with a progress of gravitational wave detectors, the presence of a planet in a conic-helical orbit could be revealed by the noticeably enhanced gravitational radiation from the binary star system.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

PERIODIC SIGNALS IN BINARY MICROLENSING EVENTS

Gravitational microlensing events are powerful tools for the study of stellar populations. In particular, they can be used to discover and study a variety of binary systems. A large number of binary lenses have already been found through microlensing surveys and a few of these systems show strong evidence of orbital motion on the timescale of the lensing event. We expect that more binary lenses of this kind will be detected in the future. For binaries whose orbital period is comparable to the event duration, the orbital motion can cause the lensing signal to deviate drastically from that of a static binary lens. The most striking property of such light curves is the presence of quasi-periodic features, which are produced as the source traverses the same regions in the rotating lens plane. These repeating features contain information about the orbital period of the lens. If this period can be extracted, then much can be learned about the lensing system even without performing time-consuming, detailed light-curve modeling. However, the relative transverse motion between the source and the lens significantly complicates the problem of period extraction. To resolve this difficulty, we present a modification of the standard Lomb–Scargle periodogram analysis. We test our method for four representative binary lens systems and demonstrate its efficiency in correctly extracting binary orbital periods.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

SDSS J001641-000925: THE FIRST STABLE RED DWARF CONTACT BINARY WITH A CLOSE-IN STELLAR COMPANION

SDSS J001641-000925 is the first red dwarf contact binary star with an orbital period of 0.19856 days that is one of the shortest known periods among M-dwarf binary systems. The orbital period was detected to be decreasing rapidly at a rate of P-dot ∼8 s yr{sup −1}. This indicated that SDSS J001641-000925 was undergoing coalescence via a dynamical mass transfer or loss and thus this red dwarf contact binary is dynamically unstable. To understand the properties of the period change, we monitored the binary system photometrically from 2011 September 2 to 2014 October 1 by using several telescopes in the world and 25 eclipse times were determined. It is discovered that the rapid decrease of the orbital period is not true. This is contrary to the prediction that the system is merging driven by rapid mass transfer or loss. Our preliminary analysis suggests that the observed minus calculated (O–C) diagram shows a cyclic oscillation with an amplitude of 0.00255 days and a period of 5.7 yr. The cyclic variation can be explained by the light travel time effect via the presence of a cool stellar companion with a mass of M {sub 3}sin i' ∼ 0.14 M {sub ☉}. The orbital separation between the third body and the central binary is about 2.8 AU. These results reveal that the rarity of red dwarf contact binaries could not be explained by rapidly dynamical destruction and the presence of the third body helps to form the red dwarf contact binary.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Binary Stars in Upper Scorpius

To address the statistics of binary stars in the 8 Myr old Upper Scorpius (USco) star formation region, we conducted a speckle interferometric survey of 614 association members more massive than 0.4 M{sub ⊙} (spectral types earlier than M3V) based on the list of Luhman et al. (2018). We resolved 187 pairs, 55 of which are new discoveries. Also using the published data and the Gaia DR2, a catalog of 250 physical binaries was produced. We carefully estimated detection limits for each target and studied binary statistics in the separation range from 0.″06 to 20″ (9–2800 au), as well as clustering at larger separations. The frequency of companions with mass ratios q > 0.3 in this separation range is 0.33 ± 0.04 and 0.35 ± 0.04 for early M- and solar-type stars, respectively, larger by 1.62 ± 0.22 and 1.39 ± 0.18 times compared to field stars of similar masses. The excess is produced mostly by pairs closer than 100 au. At separations from 100 to 10{sup 4} au, the separation distribution and companion fraction resemble those of solar-type stars in the field. However, unlike in the field, we see a relative deficit of equal-mass binaries at separations of ∼500 au, compared to smaller and larger separations. The distribution of q depends on the separation, with a preference of larger q and a larger fraction of twins with q > 0.95 at smaller separations. The binary population of USco differs from binaries in the field in several ways and suggests that binary statistics is not universal.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Photometric Study and Absolute Parameter Estimation of Six Totally Eclipsing Contact Binaries

High precision CCD observations of six totally eclipsing contact binaries were presented and analyzed. It is found that only one target is an A-type contact binary (V429 Cam), while the others are W-type contact ones. By analyzing the times of light minima, we discovered that two of them exhibit secular period increase while three manifest long-term period decrease. For V1033 Her, a cyclic variation superimposed on the long-term increase was discovered. By comparing the Gaia distances with those calculated by the absolute parameters of 173 contact binaries, we found that the Gaia distance can be applied to estimate the absolute parameters for most contact binaries. The absolute parameters of our six targets were estimated using their Gaia distances. The evolutionary status of contact binaries was studied, and we found that the A- and W-subtype contact binaries may have different formation channels. The relationship between the spectroscopic and photometric mass ratios for 101 contact binaries was presented. It was discovered that the photometric mass ratios are in good agreement with the spectroscopic ones for almost all of the totally eclipsing systems, which is corresponding to the results derived by Pribulla et al. and Terrell & Wilson.

47 OTHER INSTRUMENTATION↗