Elemental abundance analyses with DAO spectrograms: XXXII. HR 6455 (A3 III), δ Aqr (A3 V), η Lep (F2 V), and 1 Boo (A1 V)

We examine the sharp‐lined stars HR 6455 (A3 III, v sin i = 8.7 km s^–1) and η Lep (F2 V, v sin i = 13.5 km s^–1) as well as δ Aqr (A3 V, v sin i = 81 km s^–1) and 1 Boo (A1 V, v sin i = 59 km s^–1) to increase the number consistently analyzed A and F stars using high dispersion and high S/N (≥200) spectrograms obtained with CCD detectors at the long Coudé camera of the 1.22‐m telescope of the Dominion Astrophysical Observatory. Such studies contribute to understanding systematic abundance differences between normal and non‐magnetic main‐sequence band chemically peculiar A and early F stars. LTE fine analyses of HR 6455, δ Aqr, and 1 Boo using Kurucz's ATLAS suite programs show the same general elemental abundance trends with differences in the metal richness. Light and iron‐peak element abundances are generally solar or overabundant while heavy element and rare earth element abundances are overabundant. HR 6455 is an evolved Am star while δ Aqr and 1 Boo show the phenomenon to different extents. Most derived abundances of η Lep are solar (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Intrinsic colour indices of Be stars obtained from 2MASS photometry

This paper is based on 2MASS photometry (J H K_s magnitudes) of 1172 Be stars. The observed mean intrinsic colours have been derived with aid of two‐colour diagrams for Be stars of luminosity classes Ie‐IIe, IIIe and IVe‐Ve. The obtained results are the first determinations of their intrinsic colours in the astronomical literature. The smoothed infrared colours are compared with those obtained for “normal” B stars. Several two‐colour diagrams and plots of observed and smoothed intrinsic colour versus spectral type of luminosity classes Ie‐IIe, IIIe and IVe‐Ve are presented. Generally the determined infrared intrinsic colours of Be stars (V – J)₀, (V – H)₀, and (V – K_s)_o differ substantially from those of “normal” B stars. It is found that the intrinsic colours of B stars are generally bluer than Be stars of corresponding spectral type and luminosity class. The mean absolute visual magnitude M_v of 528 Be stars for luminosity classes Iae, Ibe‐Iabe, IIe, IIIe and IVe‐Ve is derived from HIPPARCOS parallaxes. The M_v calibration is compared with the existing ones. The Be stars are generally brighter than “normal” B stars of corresponding spectral types. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of rotation on the colours and line indices of stars 5. The ZRMS and the ZRZAMS

The observeduvby and H_α indices of member stars of the Hyades and Praesepe clusters have been analysed in detail for rotation effects. The Alpha Persei, Pleiades and the Centaurus subgroup of the Scorpio—Centaurus association have been reanalysed using the observed indices instead of the extinction-corrected indices used earlier. The observed rotation effects from the analysis of these cluster data are found to be in excellent agreement with the theoretical predictions of Collins & Sonneborn (1977). We have also analysed the α,c and (u − b) values of the member stars of NGC 1976, 2264, 2287, 2422, 4755,1C 2391, IC 2602 and IC 4665 for rotation effects. The results are found to be consistent with the theoretical predictions. The observed slopes of the rotation effects were used to determine the zero rotation main sequence values of the intermediate band photometric indices for selected clusters. We also corrected the observed indices for each star in each cluster using the theoretical predictions of Collins and Sonneborn and derived the ZRMS values for each cluster. The agreement between the two determinations is found to be good. The various ZRMS curves were utilised to derive the ZRZAMS values. A preliminary calibration of the absolute visual magnitudes as a function of α valid for ZRZAMS has also been derived. The ZRMS values of the intermediate band photometric indices for different clusters and the ZRZAMS values are listed as a function of α. on leave from Assumption College, Changanacherry, Kerala.     

A near‐infrared/optical/X‐ray survey in the centre of σ Orionis

Because of the intense brightness of the OB‐type multiple star system σ Ori, the low‐mass stellar and substellar populations close to the centre of the very young σ Orionis cluster is poorly know. I present an IJHK_s survey in the cluster centre, able to detect from the massive early‐type stars down to cluster members below the deuterium burning mass limit. The near‐infrared and optical data have been complemented with X‐ray imaging. Ten objects have been found for the first time to display high‐energy emission. Previously known stars with clear spectroscopic youth indicators and/or X‐ray emission define a clear sequence in the I vs. I – K_s diagram. I have found six new candidate cluster members that follow this sequence. One of them, in the magnitude interval of the brown dwarfs in the cluster, displays X‐ray emission and a very red J – K_s colour, indicative of a disc. Other three low‐mass stars have excesses in the K_s band as well. The frequency of X‐ray emitters in the area is 80±20 %. The spatial density of stars is very high, of up to 1.6±0.1 arcmin^–2. There is no indication of lower abundance of substellar objects in the cluster centre. Finally, I also report two cluster stars with X‐ray emission located at only 8000–11000 AU to σ Ori AB, two sources with peculiar colours and an object with X‐ray emission and near‐infrared magnitudes similar to those of previously‐known substellar objects in the cluster. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kinematics of the galaxy from Cepheids with proper motions from the Gaia DR1 catalogue

A sample of classical Cepheids with known distances and line-of-sight velocities has been supplemented with proper motions from the Gaia DR1 catalogue. Based on the velocities of 260 stars, we have found the components of the peculiar solar velocity vector (U, V, W)_⊙ = (7.90, 11.73, 7.39) ± (0.65, 0.77, 0.62) km s^?1 and the following parameters of the Galactic rotation curve: Ω₀ = 28.84 ± 0.33 km s^?1 kpc^?1, Ω′₀ = ?4.05 ± 0.10 km s^?1 kpc^?2, and Ω″₀ = 0.805 ± 0.067 km s^?1 kpc^?3 for the adopted solar Galactocentric distance R ₀ = 8 kpc; the linear rotation velocity of the local standard of rest is V ₀ = 231 ± 6 km s^?1.     

Galactic rotation curve from the space velocities of selected masers

Based on currently available observations of 28 maser sources in 25 star-forming regions with measured trigonometric parallaxes, proper motions, and radial velocities, we have constructed the rotation curve of the Galaxy. Taking different distances to the Galactic center R ₀, we have estimated the peculiar velocity of the Sun, the angular velocity of Galactic rotation, and its three derivatives. For R ₀ = 8 kpc, we have found the circular velocity of the Sun to be V ₀ = 243 ± 16 km s⁻¹, which corresponds to a revolution period of 202 ± 10 Myr. We have obtained the Oort constants A = 16.9 ± 1.2 km s⁻¹ kpc⁻¹ and B = −13.5 ± 1.4 km s⁻¹ kpc⁻¹. Our simulation of the influence of a spiral density wave has shown that the peculiar velocity of the Sun with respect to the local standard of rest and the component (V _⊙)_LSR depend significantly on the Sun’s phase in the spiral wave.     

Kinematics of the galaxy from OB stars with proper motions from the Gaia DR1 catalogue

We consider two samples of OB stars with different distance scales that we have studied previously. The first and second samples consist of massive spectroscopic binaries with photometric distances and distances determined from interstellar calcium lines, respectively. The OB stars are located at heliocentric distances up to 7 kpc. We have identified them with the Gaia DR1 catalogue. Using the proper motions taken from the Gaia DR1 catalogue is shown to reduce the random errors in the Galactic rotation parameters compared to the previously known results. By analyzing the proper motions and parallaxes of 208 OB stars from the Gaia DR1 catalogue with a relative parallax error of less than 200%, we have found the following kinematic parameters: (U, V)_⊙ = (8.67, 6.63)± (0.88, 0.98) km s^?1, Ω₀ = 27.35 ± 0.77 km s^?1 kpc^?1, Ω′₀ = ?4.13 ± 0.13 km s^?1 kpc^?2, and Ω″₀ = 0.672 ± 0.070 km s^?1 kpc^?3, the Oort constants are A = ?16.53 ± 0.52 km s^?1 kpc^?1 and B = 10.82 ± 0.93 km s^?1 kpc^?1, and the linear circular rotation velocity of the local standard of rest around the Galactic rotation axis is V ₀ = 219 ± 8 km s^?1 for the adopted R ₀ = 8.0 ± 0.2 kpc. Based on the same stars, we have derived the rotation parameters only from their line-of-sight velocities. By comparing the estimated values of Ω′₀, we have found the distance scale factor for the Gaia DR1 catalogue to be close to unity: 0.96. Based on 238 OB stars of the combined sample with photometric distances for the stars of the first sample and distances in the calcium distance scale for the stars of the second sample, line-of-sight velocities, and proper motions from the Gaia DR1 catalogue, we have found the following kinematic parameters: (U, V, W)_⊙ = (8.19, 9.28, 8.79)± (0.74, 0.92, 0.74) km s^?1, Ω₀ = 31.53 ± 0.54 km s^?1 kpc^?1, Ω′₀ = ?4.44 ± 0.12 km s^?1 kpc^?2, and Ω″₀ = 0.706 ± 0.100 km s^?1 kpc^?3; here, A = ?17.77 ± 0.46 km s^?1 kpc^?1, B = 13.76 ± 0.71 km s^?1 kpc^?1, and V ₀ = 252 ± 8 km s^?1.     

Effective temperature vs. line‐depth ratio for ELODIE spectra: Gravity and rotational velocity effects

The dependence on the temperature of photospheric line‐depth ratios (LDRs) in the spectral range 6190–6280 Å is investigated by using a sample of 174 ELODIE Archive stellar spectra of luminosity class from V to III. The rotational broadening effect on LDRs is also studied. We provide useful calibrations of effective temperature versus LDRs for giant and main sequence stars with 3800 ≃ T_eff ≃6000 K and v sin i in the range 0–30 km s^–1. We found that, with the exception of very few line pairs, LDRs, measured at a spectral resolution as high as 42 000, depend on v sin i and that, by neglecting the rotational broadening effect, the T_eff determination can be wrong by ∼100 K in the worst cases. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential rotation in F stars

Differential rotation can be detected in single line profiles of stars rotating more rapidly than about v sin i = 10km s-1 with the Fourier transform technique. This allows to search for differential rotation in large samples to look for correlations between differential rotation and other stellar parameters. I analyze the fraction of differentially rotating stars as a function of color, rotation, and activity in a large sample of F-type stars. Color and rotation exhibit a correlation with differential rotation in the sense that more stars are rotating differentially in the cooler, less rapidly rotating stars. Effects of rotation and color, however, cannot be disentangled in the underlying sample. No trend with activity is found. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Preliminary results on the fundamental parameters of the eclipsing binary V398 Lacertae

The Hipparcos Space Astrometry Mission photometric observations of V398 Lac, led to the discovery of its variability, allowing to classify it as an eclipsing binary with an orbital period of about 5.4 days. This prompted us to acquire highresolution échelle spectra with the aim of performing accurate radial velocity measurements and to determine the main physical parameters of the system's components. We present, for the first time, a double‐lined radial velocity curve and determine the orbital and physical parameters of the two components, that can be classified both as late B‐type stars. In particular, we obtained an orbital inclination i ∼ 85°. With this value of the inclination, we deduced masses M₁ = 3.83±0.35 M_⊙ andM₂ = 3.29±0.32 M_⊙, and radii R₁ = 4.89±0.18 R_⊙ and R₂ = 2.45±0.11 R_⊙ for the more massive and less massive components, respectively. Both components are well inside their own Roche lobes. The mass ratio is M₂/M₁ ∼ 0.86. We derived also the projected rotational velocities as v₁ sin i = 79±2 km s^–1 and v² sin i = 19±2 km s^–1. Our measurements indicate that the rotation of the primary star is essentially pseudo‐synchronized with the orbital velocity at the periastron, while the secondary appears to rotate very slowly and has not yet attained synchronization. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Testing the Distance Scale of the Gaia TGAS Catalogue by the Kinematic Method

We have studied the simultaneous and separate solutions of the basic kinematic equations obtained using the stellar velocities calculated on the basis of data from the Gaia TGAS and RAVE5 catalogues. By comparing the values of Ω'₀ found by separately analyzing only the line-of-sight velocities of stars and only their proper motions, we have determined the distance scale correction factor p to be close to unity, 0.97 ± 0.04. Based on the proper motions of stars from the Gaia TGAS catalogue with relative trigonometric parallax errors less than 10% (they are at a mean distance of 226 pc), we have found the components of the group velocity vector for the sample stars relative to the Sun (U, V,W)_⊙ = (9.28, 20.35, 7.36) ± (0.05, 0.07, 0.05) km s^?1, the angular velocity of Galactic rotation Ω⁰ = 27.24 ± 0.30 km s?1 kpc?1, and its first derivative Ω'₀ = ?3.77 ± 0.06 km s^?1 kpc^?2; here, the circular rotation velocity of the Sun around the Galactic center is V₀ = 218 ± 6 km s^?1 kpc (for the adopted distance R₀ = 8.0 ± 0.2 kpc), while the Oort constants are A = 15.07 ± 0.25 km s^?1 kpc^?1 and B = ?12.17 ± 0.39 km s^?1 kpc^?1, p = 0.98 ± 0.08. The kinematics of Gaia TGAS stars with parallax errors more than 10% has been studied by invoking the distances from a paper by Astraatmadja and Bailer-Jones that were corrected for the Lutz–Kelker bias. We show that the second derivative of the angular velocity of Galactic rotation Ω'₀ = 0.864 ± 0.021 km s^?1 kpc^?3 is well determined from stars at a mean distance of 537 pc. On the whole, we have found that the distances of stars from the Gaia TGAS catalogue calculated using their trigonometric parallaxes do not require any additional correction factor.     

Galactic kinematics from OB3 stars with distances determined from interstellar Ca II lines

Based on data for 102 OB3 stars with known proper motions and radial velocities, we have tested the distances derived by Megier et al. from interstellar Ca II spectral lines. The internal reconciliation of the distance scales using the first derivative of the angular velocity of Galactic rotation Ω′₀ and the external reconciliation with Humphreys’s distance scale for OB associations refined by Mel’nik and Dambis show that the initial distances should be reduced by ≈20%. Given this correction, the heliocentric distances of these stars lie within the range 0.6–2.6 kpc. A kinematic analysis of these stars at a fixed Galactocentric distance of the Sun, R ₀ = 8 kpc, has allowed the following parameters to be determined: (1) the solar peculiar velocity components (u _⊙, v _⊙, ω _⊙) = (8.9, 10.3, 6.8) ± (0.6, 1.0, 0.4) km s⁻¹; (2) the Galactic rotation parameters Ω₀ = −31.5 ± 0.9 km s⁻¹ kpc⁻¹, Ω′₀ = +4.49 ± 0.12 km s⁻¹ kpc⁻², Ω″₀ = −1.05 ± 0.38 km s⁻¹ kpc⁻³ (the corresponding Oort constants are A = 17.9 ± 0.5 km s⁻¹ kpc⁻¹, B = −13.6 ± 1.0 km s⁻¹ kpc⁻¹ and the circular rotation velocity of the solar neighborhood is |V ₀| = 252 ± 14 km s⁻¹); (3) the spiral density wave parameters, namely: the perturbation amplitudes for the radial and azimuthal velocity components, respectively, f _R = −12.5±1.1 km s⁻¹ and f _ϑ = 2.0 ± 1.6 km s⁻¹; the pitch angle for the two-armed spiral pattern i = −5.3° ± 0.3°, with the wavelength of the spiral density wave at the solar distance being λ = 2.3 ± 0.2 kpc; the Sun’s phase in the spiral wave x _⊙ = −91° ± 4°.     

Early-Type Stars

Away from the young disk, several classes of early type stars are found. They include (i) the old, metal-poor blue horizontal branch stars of the halo and the metal-poor tail of the thick disk; (ii) metal-rich young A stars in a rapidly rotating subsystem but with a much higher velocity dispersion than the A stars of the young disk, and (iii) a newly discovered class of metal-poor young main sequence A stars in a subsystem of intermediate galactic rotation (V_rot ≈ 120 km s⁻¹). The existence and kinematics of these various classes of early type stars provide insight into the formation of the metal-poor stellar halo of the Galaxy and into the continuing accretion events suffered by our Galaxy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Polarimetric Investigations of Stellar Associations

The degree of polarization of light from stars in 44 O B associations as a function of interstellar absorption is investigated. It is shown that the character of the dependence of P on A _V for stars in associations and stars not in associations depends on the value of A _V: for A _V 2 ^m .5 it has a linear character and is the same for both groups of stars. For A _V > 2 ^m .5 the dependence of P on A _V for stars in and not in associations departs from linearity and for A _V = 4 ^m .5 it reaches P _ass = 1.8% and P _nonass = 1%, respectively. Such a difference is explained by the additional depolarization in stellar associations. Such strong depolarization in associations may be due to the overall magnetic field of the Galaxy and to physical peculiarities in the association itself.     

New absolute magnitude calibrations for detached binaries

Lutz‐Kelker bias corrected absolute magnitude calibrations for the detached binary systems with main‐sequence components are presented. The absolute magnitudes of the calibrator stars were derived at intrinsic colours of Johnson‐Cousins and 2MASS (Two Micron All Sky Survey) photometric systems. As for the calibrator stars, 44 detached binaries were selected from the Hipparcos catalogue, which have relative observed parallax errors smaller than 15% (σ_π/π ≤ 0.15). The calibration equations which provide the corrected absolute magnitude for optical and near‐infrared pass bands are valid for wide ranges of colours and absolute magnitudes: –0.18 < (B – V)₀ < 0.91, –1.6 < M_V < 5.5 and –0.15 < (J – H)₀ < 0.50, –0.02 < (H – K_s)₀ < 0.13, 0 < M_J < 4, respectively. The distances computed using the luminosity‐colours (LCs) relation with optical (BV) and near‐infrared (JHK_s) observations were compared to the distances found from various other methods. The results show that new absolute magnitude calibrations of this study can be used as a convenient statistical tool to estimate the true distances of detached binaries out of Hipparcos' distance limit. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Photometric and spectroscopic observations of three rapidly rotating late‐type stars: EY Dra,V374 Peg,and GSC 02038‐00293

Here, BV (RI)_C broad band photometry and intermediate resolution spectroscopy in H_α region are presented for two rapidly rotating late‐type stars: EY Dra and V374 Peg. For a third rapid rotator, GSC 02038‐00293, intermediate resolution H_α spectroscopy and low resolution spectroscopy are used for spectral classification and stellar parameter investigation of this poorly known object. The low resolution spectrum of GSC 02038‐00293 clearly indicates that it is a K‐type star. Its intermediate resolution spectrum can be best fitted with a model with T_eff = 4750 K and v sin i = 90 km s^–1, indicating a very rapidly rotating mid‐K star. The H_α line strength is variable, indicating changing chromospheric emission on GSC 02038‐00293. In the case of EY Dra and V374 Peg, the stellar activity in the photosphere is investigated from the photometric observations, and in the chromosphere from the H_α line. The enhanced chromospheric emission in EY Dra correlates well with the location of the photospheric active regions, indicating that these features are spatially collocated. Hints of this behaviour are also seen in V374 Peg, but it cannot be confirmed from the current data. The photospheric activity patterns in EY Dra are stable during one observing run lasting several nights, whereas in V374 Peg large night‐tonight variations are seen. Two large flares, one in the H_α observations and one from the broadband photometry, and twelve smaller ones were detected in V374 Peg during the observations spanning nine nights. The energy of the photometrically detected largest flare is estimated to be 4.25 × 10³¹– 4.3 × 10³² erg, depending on the waveband. Comparing the activity patterns in these two stars, which are just below and above the mass limit of full convection, is crucial for understanding dynamo operation in stars with different internal structures (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A search for the age-dependency of Ap star parameters

Some observational data of the sample of the magnetic chemically peculiar stars (MCP stars) are investigated statistically. For the MCP stars of spectral types later than A2 both the frequency distribution and the R ⋅ sin i-values suggest the existence of a linear relation between stellar diameter and rotation period. The MCP stars of spectral types earlier than B9 show an overpopulation of small R ⋅ sin i which may indicate the existence of a second group with smaller radius in this sample. The equatorially symmetric rotator is used as the magnetic model. With respect to its temporal behaviour the effective magnetic field is separated into dipolar and quadrupolar contribution. Both signs of the axisymmetric quadrupole moment appear with equal frequency. The dipole moment which produces the amplitude of the B_eff(t) curve forms for longer periods two groups which are separated by a distinct gap. Both of the groups exhibit magnetic fields which are the stronger the greater the stellar radius is, contrary to what is expected for frozen-in fields. The dominance of magnetic curves without polarity reversal for longer-period stars is in accordance with predictions of the dynamo theory.     

Kinematics of Hot Subdwarfs from the Gaia DR2 Catalogue

We have studied the kinematic properties of the candidates for hot subdwarfs (HSDs) selected by Geier et al. from theGaiaDR2 catalogue. We have used a total of 12 515 stars with relative trigonometric parallax errors less than 30%. The HSDs are shown to have different kinematics, depending on their positions on the celestial sphere. For example, the sample of low-latitude (|b| < 20°) HSDs rotates around the Galactic center with a linear velocity V0 = 221 ± 5 km s^?1. This suggests that they belong to the Galactic thin disk. At the same time, they lag behind the local standard of rest by ΔV_☉ ~ 16 km s^?1 due to the asymmetric drift. The high-latitude (|b| ≥ 20°) HSDs rotate with a considerably lower velocity, V_☉ = 168 ^± 6 km s^?1. Their lagging behind the local standard of rest is already ΔV_☉ ～ 40 km s^?1. Based on the entire sample of 12 515 HSDs, we have found a positive rotation around the x axis significantly differing from zero with an angular velocity ω₁ = 1.36±0.24 km s^?1 kpc^?1. We have studied the samples of HSDs that are complete within r < 1.5 kpc. Based on them, we have traced the evolution of the parameters of the residual velocity ellipsoid as a function of both latitude |b| and coordinate |z|. The following vertical disk scale heights have been found: h = 180 ± 6 and 290 ± 10 pc from the low- and high-latitude HSDs, respectively. A new estimate of the local stellar density Σ_out = 53 ± 4 M☉ kpc^?2 has been obtained for z_out = 0.56 kpc from the high-latitude HSDs.

     

V792 Her=HD 155638: A totally eclipsing RS CVn binary

Photometry of HD 155638=V792 Her has been analyzed to determine the elements of this totally eclipsing RS CVn binary. The light variation outside eclipse was found to have a period of 27^d.07±0^d.07, which is slightly different from the 27^d.5384±0^d.0045 orbital period. Analysis of the eclipses was achieved by a modification of the Russell-Merrill technique. With the aid of radial velocity measures, absolute elements were obtained for the hot and cool stars, respectively;R _h=2.58R ,R _c=12.28R ,M _h=1.40M ,M _c=1.46M ,i=80^o.61 and velocity semi-amplitudesK _c=48.36 km s^–1±0.79 km s^–1, andK _h=50.50 km s^–1±0.33 km s^–1. The apparent magnitudes areV _h=9 ^m .73 andV _c=8 ^m .48. The distance to HD 155638 was estimated to be 310 parsecs.     

The kinematics of Trapezium-type systems

Summary In this paper the results of the research of the stars proper motions Trapezium components are reported. They are: the galactic coordinates of the solar aprx and the Sun velocity (L _⊙=43±18°,B _⊙=+28±13°,V _⊙=13±4 km s⁻¹), the dispersion of peculiar velocities in the direction of the galactic coordinates for the above mentioned stars (σ _l =±11 km s⁻¹, σ _b =±7 km s⁻¹).The attained accuracy of the proper motions (±0.005″ yr⁻¹) is shown to be insufficient to the study of internal space motions in these systems. At present the work to increase the relative proper motions accuracy for multiple system components and to improve reductions from the relative to absolute proper motions, is being carried out in the Main Astronomical Observatory (Academy of Sciences of the Ukrainian SSR). The new catalogue of the AGK3 stars is composed now in the vicinity of the galactic equator in order to improve reductions from the relative to absolute proper motions. The r.m.s. errors of the proper motions, obtained in the AGK3 system, are ±0.005″ yr⁻¹.