EXTRAGALACTIC DISTANCE SCALES: it H 0 FROM HUBBLE (EDWIN) TO HUBBLE (HUBBLE TELESCOPE)

In the first fifty years after Edwin Hubble announced a linear relationship between distances and redshifts of external galaxies, the accepted value of his constant dropped by (or the Universe expanded and aged by) a factor of 5 to 10. More recently, different groups, often using nearly the same data, have passionately defended distance scales that differ by about a factor of two. The sections of this review explore (1) the history of extragalactic distance scales, (2) the relationships between the Hubble constant, H ₀, and other cosmological parameters, (3) types of distance indicators, (4) ways of measuring distances in practice, (5) values of H ₀ reported recently on the basis of these methods, (6) the continuing discrepancies between the 'long' and 'short' distance scales, and (7) prospects for future convergence on a single, global value of H, so that we can all get back to doing other things. The units of the Hubble constant are km s^-1 Mpc^-1 (or reciprocal time), and no one now strongly favors any value outside the range 40–90 km s^-1 Mpc^-1 (time scales of 11–25 Gyr).     

The absolute magnitudes of RR Lyrae stars

A theoretical counterpart to the Barnes-Evans relation between stellar surface brightness and V-R color has been calculated from model atmospheres for parameters appropriate to RR Lyrae stars. Such a relation can be used to derive stellar angular diameters from V,R photometry and, when applied to variable stars and combined with a radial velocity curve, to derive radii, distances, and absolute magnitudes by the method of Barnes et al. (1977, MNRAS,178, 661). This was done for RR Lyr and X Ari using the photometry of Moffett and Barnes (1980, private communication) and radial velocities from the literature. The resulting absolute magnitudes are M_v = ± 0.59 + 0.25 for X Ari and M_v = 0.61 ± 0.35 for RR Lyr. The method is shown to be a very accurate way of determining radii, distances, and absolute magnitudes for RR Lyrae stars which compares very favorably to the variations of the Baade-Wesselink technique currently in use.     

LMC X-4: 13.5 s pulsations and an X-ray flare observed by EXOSAT

EXOSAT observed LMC X-4 on November 17/19, 1983 for one 1.4 day binary period during the high state of the 30.5 day cycle. An eclipse with sharp ingress and slow egress was detected with an eclipse angle of 27.1±1.0 dgr. In the medium energy experiment the source showed a hard power law spectrum. Outside eclipse the source was remarkably constant and only one flare was detected on November 17 at 19 UT lasting for about 1 h. The energy spectrum of the source softens considerably during that time and shows an emission line of cold iron. 13.5 sec pulsations are strongly present during the flare and have also been detected during the quiescent period and during several 1 min flares in another EXOSAT LMC X-4 observation on November 22, 1983. A pulse delay time analysis results in the determination of the pulse period (13.5019±0.0002) s and of the semimajor axis of the orbit of the X-ray star (26.0±0.6) It-sec. These results, together with other available information on LMC X-4, allowed to improve the binary parameters. The mass of the neutron star is found to be 1.34 _±0.44 ^0.48 M_o (95% confidence errors).     

Results of evolutionary computations of primaries of close binaries with different initial composition

The present paper summarizes fundamental evolutionary parameters of primaries of close binaries with initial masses between 9 and 60 M_⊙ and initial composition appropriate for the Galaxy, the LMC and the SMC. The primary timescales and WR binary timescales are compared with corresponding recent single star predictions.     

CCD spectroscopy of the W Serpentis binaries KX And and RX Cas

Initial results are presented from a study of H _γ profiles in the two interacting binaries KX And and RX Cas of W Serpentis type. The used CCD spectra with a resolution of 0.13Å/px were obtained with the 2.2m telescope and the Coudé spectrograph at the German-Spanish Astronomical Center at Calar Alto/Spain. KX And. This star is probably a non-eclipsing member of the W Serpentis type interactive binaries and has a period of P = 38.908 days. Our seven spectra of KX And were obtained at phase 0.54 – 0.75. The P Cyg profiles of the H _γ line during our observations indicate an expanding shell. The asymetry becomes blue-sided at phase 0.67 and increases thereafter. This points toward a strong outflow of matter in the vicinity of the L3 point. RX Cas. According to the model of Andersen et al. (1988) the primary is a mid-B type star with M = 5.8M _⊙ and R = 2.5R _⊙. The star is completely obscured by a geometrically and optically thick disk, which is supplied by mass transfer from the other component. The secondary is a K1 giant with M = 1.8M _⊙ and R = 23.5R _⊙ and fills out his critical Roche lobe. Radiative and geometrical properties of the disk are variable and its structure is probably not homogenous. Five spectra of RX Cas were obtained during the primary eclipse (phase 0.95 – 0.19). The observed double-peak emission is seen only after the eclipse with a separation of ≈ 250 km/s peak-to-peak, while during the eclipse an asymetric line profile can be observed with a red-shifted emission always presented. Also, a central emission at φ = 0.94 should be noticed, probably originating in the vicinity of L1. The observations of both systems indicate that we are dealing with strongly interacting binaries. Further observations are planned for better covering of phase.     

Impact of Distance Determinations on Galactic Structure. I. Young and Intermediate-Age Tracers

Here we discuss impacts of distance determinations on the Galactic disk traced by relatively young objects. The Galactic disk, \(\sim40~\mbox{kpc}\) in diameter, is a cross-road of studies on the methods of measuring distances, interstellar extinction, evolution of galaxies, and other subjects of interest in astronomy. A proper treatment of interstellar extinction is, for example, crucial for estimating distances to stars in the disk outside the small range of the solar neighborhood. We’ll review the current status of relevant studies and discuss some new approaches to the extinction law. When the extinction law is reasonably constrained, distance indicators found in today and future surveys are telling us stellar distribution and more throughout the Galactic disk. Among several useful distance indicators, the focus of this review is Cepheids and open clusters (especially contact binaries in clusters). These tracers are particularly useful for addressing the metallicity gradient of the Galactic disk, an important feature for which comparison between observations and theoretical models can reveal the evolution of the disk.     

Evolution into contact of the low-mass close binary systems

We investigated the effect of mass accretion on the secondary components in close binomy systems (M _total ≤ 2.5 M _⊙ M _2,0 ≤ 0.75 M _⊙) exchanging mass in the case A. The evolution of the low-mass close binary systems (M _total ≤ 2.5 M _⊙) exchanging the mass in the case A depends on the three main factors:

-the initial mass ratio (q ₀ = M _2,0/M _1,0), which determines the rate of mass transfer between components;

-the inital mass of the secondary component (M _2,0) and

-the effectiveness of the heating of the photosphere of the secondary component, by infalling matter.

The second factor allows to divide all systems into two essentially different groups:

1. systems in which the secondary component is a star with a radiative envelope, or with a thin convection zone in the uppermost layers;
2. and systems in which secondary component has a thick convective envelope or is fully convective.

The systems from the first group evolve into contact in a characteristic time scale 10⁵ – 10⁷ years, and reach contact after transfering of 0.03 – 0.3 M _⊙. The mass exchange proceeds only in a thermal time scale. For the systems from the group b the effectiveness of the heating of the stellar surface is the most important. In the case when the entropy of the newly accreted matter is the same as the surface entropy of the secondary, a convective star should shrink upon accretion. Then contact binaries are not formed. In the case when the entropy of the infalling matter is greater then that on the surface, the reaction of the secondary is different. The radius of the secondary component grows rapidly in response to accretion, and the systems reaches contact after the 10³ – 3 10⁶ years, and after transfer of 0.002 – 0.2. M _⊙. The reaction of the secondary is determined by the formation of the temperature inversion layer below the stellar surface. Full references in: Sarna, M.J. and Fedorova, A.V. (1988) “Evolutionary status of W UMa-type Binaries — Evolution into contact”, Astron. Astrophys., in press.     

Parametric study on the flutter sensitivity of a wide-chord hollow fan blade

In recent years, the hollow fan blades have been widely used to meet the demand for light weight and good performance of the aero-engine. However, the relationship between the hollow structure and the aeroelastic stability has not been studied yet in the open literature. In this paper, it has been investigated for an H-shaped hollow fan blade. Before studying the flutter behavior, the methods of parametric modeling and auto-generation of Finite Element Model (FEM) are presented. The influence of the feature parameters on the vibration frequency and mode shape (as the input of flutter calculation) of the first three modes are analyzed by the Orthogonal Experimental Design (OED) method. The results show that the parameters have a more remarkable impact on the first torsional mode and thus it is concerned in the flutter sensitivity analysis. Compared with the solid blade, the minimum aerodynamic damping of the hollow blade decreases, indicating that the hollow structure makes the aeroelastic stability worse. For the parameters describing the hollow section, the rib number N has the greatest influence on the minimum aerodynamic damping, followed by the wall thickness W₅. For the parameters in the height of hollow segment, the aerodynamic damping increases with the increase of parameters M₁ and M₂. This means that reducing the height of the hollow segment is helpful to improve the aeroelastic stability. Compared with the impact of parameters in hollow section, the variation of aerodynamic damping caused by the height of the hollow segment is small.     

Galaxien vom Magellanschen Typ

In the first part of this paper the morphological structure of Magellanic type galaxies (Irr I) is investigated. The galaxies of Magellanic type present a basic pattern consisting of a disk, a bar, stellar arms, rudimentary or well developed, spiral filaments and condensations in the disk. With the help of this pattern a well-defined classification scheme is set up. The subgroup of Irr II-systems consists of normal galaxies which are more or less tidally disturbed. Bursts of star formation have a great influence on structure and colour of irregular galaxies. Using the ESO-B Atlas, 580 galaxies of Magellanic type (out of a sample of 3187 galaxies) were classified; 57 are new SB(s)m systems (prototype Large Magellanic Cloud). The sample shows dominant bar structures at the classification stages d-, dm-, and m. A striking feature is the asymmetric position of bar and disk. This asymmetry is a general characteristic of galaxies of types SBd-SBm IB. The asymmetry can be discribed by a relative displacement parameter \(\tilde \Lambda \) = 0.78 ±0.15, defined as the quotient of small and great distance of the bar center to the optical edge of the disk. The displacement cannot be explained by tidal interaction with neighbouring galaxies. In the second part of the paper the kinematics and dynamics of the Large Magellanic Cloud (LMC) as the nearest and best-known example of a galaxy of Magellanic type is investigated. The main structural features of the LMC are disk, bar, rudimentary and well developed stellar arms as well as spiral filaments (not necessarily connected with density waves); the γ-structure is a broken up ring structure. Embedded into these features are young, asymmetrically located spiral arm filaments. As an explanation for these structures stochastic start formation in an ordered chain reaction is proposed. The pattern of the spiral arm filaments is determined by the rotation curve. The morphological peculiarities of the LMC can also be detected in other galaxies of that type. The mean absolute displacement of the centers of bar and disk, determined from 18 galaxies, is Λ = 800 pc. The displacement between the bar center and the symmetry center of the rotation curve is of the same order. The presently known radial velocities of planetary nebulae, star clusters, Hi and Hii regions and stars belonging to the LMC have been collected in a catalogue as the basis of a discussion of the kinematics and dynamics of the LMC. Contrary to earlier work, we have used, for the first time, the radial velocities of objects of all subgroups together by a proper weighting scheme. Thus the basic kinematics and dynamics of the LMC has been deduced. The radial velocity field shows no central symmetry; it is characterized by large scale (2–3 kpc) disturbances. By comparison with the velocity field of other galaxies three main disturbances are identified: an oval distortion of the velocity field in the bar region, a radial velocity field around 30 Doradus, and disturbances connected with a warp or material above the disk in the southern quadrants. The results of a detailed numerical analysis of these three facts can be summed up as follows:

1. The rotation curve is determined over 10° diameter; it shows differential rotation, an asymmetric behavior in the south and a double structure in its Hi component. The rotation center is displaced by 0°.7 from the bar center. The orientation of the kinematic line of nodes and the systemic velocity vary as functions of the distance from the center. Therefore, it is possible to show definitely that large scale disturbances (warping, z-structure and streaming motions) are existent.
2. By variation of the kinematical parameters (systemic velocity, inclination, orientation of the line of nodes, rotation center) the dispersion of the measured radial velocities was minimized and the basic rotation curve determined. The rotation curves for the north and south side of the LMC are significantly different. The south side is either warped or there is material above the main plane. There seems to be a connection between this structure, the Panmagellanic Gas and the Magellanic Stream. The north side appears to be free of distorsion.
3. The residual velocity field (observed minus model) deduced from a basic rotation curve shows that the displacement between the rotation center and the bar center is not caused by local streaming motions. The rotation center must be the mass center. The bar shows a radial velocity field; in the 30 Doradus region inward and outward motions are found.

The mean velocity dispersion of population I objects is 10.5 km s^-1 of population II objects 16.0 km s^-1. Red and blue globular clusters show different kinematical behavior. By comparison of eight mass models, taking into consideration thickness effects and controlled by surface photometric data, the mass of the LMC is found to be (0.5 ± 0.1) × 10¹⁰ \(\mathfrak{M}_ \odot \) (assuming the inclination 33°, the systemic velocity 46.9 km s^-1, and the distance 56 kpc). Dynamically, the LMC can be described by a dominating disk potential with an additional bar potential as a disturbance. The mass of the bar is 0.6 × 10⁹ \(\mathfrak{M}_ \odot \) . The stable neutral point of such a configuration can be found in the residual velocity field. The absorption feature crossing the bar coincides with the maximum velocity gradient of the computed radial velocity field in the plane of the system.     

The atmospheric composition,extinction and luminosity of the LBV R71

ESO 3.6m Caspec spectra of the LMC luminous blue variable (LBV) taken at minimum have been analysed using NLTE model atmospheres and line formation calculations to derive atmospheric parameters and chemical composition. Using the silicon ionization balance and the hydrogen Balmer lines we deriveT _eff =17250, log g=1.80 and a microturbulent velocity of 15–20 km/s. The analysis yields abundance ratios by number of approximately 0.43 for He/H, 0.03 for C/N and 0.14 for O/N, implying that enrichment of the atmosphere by processed material has taken place. We have re-evaluated the reddening of R71 using IUE low resolution data and published UBVRIJHKL photometry and derive a value for A _V of 0.63. We also construct an extinction curve using archive IUE data for mid-B LMC supergiants and show that the extinction is anomalous; the 2175A bump being almost absent and the far UV rise very pronounced. A comparison of our model flux in theV-band with the observed (dereddened)V magnitude and the D.M. of the LMC (18.45), implies that the bolometric magnitude or R71 is –9.9. This is significantly higher than the value of –9.0 usually adopted for R71 and suggests that this object may not in fact be a subluminous LBV.     

Direct correlations between coronal transients and interplanetary disturbances

Major interplanetary shock waves have often been successfully associated with major solar flares. The interplanetary response to weaker solar events, e.g., eruptive prominences (EP) and slow coronal transients, is far less pronounced. Recently, progress has been made by combining the newly-available data of white-light-coronagraph measurements from the earth-orbiting satellite P78/1 (these data show the development of coronal transients between 2.5 and 10 R _bd, in-situ plasma measurements from the HELIOS solar probes positioned mostly above the Sun's limb at solar distances between 60 and 200 R _bd (showing the reactions of the interplanetary plasma), ground based Hα-coronagraphs (showing in a few cases the evolution of EP's from the Sun's limb up to 1.5 A_bd). In the years 1979 to 1981 about 25 uniquely associated events were identified, 19 of which allow some detailed analysis. The events can be sorted into three main categories:

The ‘flare-type’: 13 events, probably all of them flare-related, transient speeds v _t from 560 to 1460 km s^?1, no evidence for post-acceleration of the transient (indicating impulsive injection), all transients followed by drastic interplanetary shock waves, some of them probably involving magnetic clouds.

The ‘EP-type’: 4 events, none of them flare-related, at least one was observed as an Hα-EP, transient speed from 200 to 410 km s^-1, all post-accelerated (indicating ‘driven’ injection), all followed by shocks with at least one magnetic cloud, one showing presence of He⁺ and O²⁺ behind the shock.

The ‘NCDE-type’: 2 events, one observed as an Hα-EP, the other without known solar source, v _t , = 130 and 470 km s^?1, one post-accelerated, the other one not, considerable density increase in interplanetary plasma (however, in pressure equilibrium with surroundings), one event including shock, the other not. These two events may not belong to the same category.

Our results are not completely consistent with previous work which is mainly based on data from the Skylab era, 1973/74. This could be due to the different phase in the solar cycle. The study is being continued.     

A dissection of 30 Doradus and a discussion of other Magellanic Cloud OB associations

I Present the results of ground-based and Hubble Space Telescope photometry and spectroscopy of the stars in the central region (roughly 7×7 arcmin) of 30 Doradus in the Large Magellanic Cloud (LMC). Using photometric data for over 2400 stars (complete toV18 mag), and spectroscopic observations of over 150 stars in the region, the best estimate of the initial mass function (IMF) yields a slope of =–1.5±0.2 for masses > 12M, where the Salpeter slope is =–1.35. I compare these results to other measurements of the IMF for OB associations in the Magellanic Clouds.     

Type Ia Supernova Cosmology

The primary agent for Type Ia supernova cosmology is the uniformity of their appearance. We present the current status, achievements and uncertainties. The Hubble constant and the expansion history of the universe are key measurements provided by Type Ia supernovae. They were also instrumental in showing time dilation, which is a direct observational signature of expansion. Connections to explosion physics are made in the context of potential improvements of the quality of Type Ia supernovae as distance indicators. The coming years will see large efforts to use Type Ia supernovae to characterise dark energy.     

Random copolymer membrane coated PBO fibers with significantly improved interfacial adhesion for PBO fibers/cyanate ester composites

Poly(p-phenylene-2,6-benzobisoxazole) (PBO) fibers possess excellent dielectric, mechanical properties and heat resistance. However, the surface of PBO fibers is smooth and highly chemical inert, resulting in poor interfacial compatibility to polymer matrix, which severely limits its wider application in high-performance fiber-reinforced resin matrix composites. In this work, random copolymers (P(S-co-BCB-co-MMA)) containing benzocyclobutene in the side-chain were synthesized by reversible addition-fragmentation chain transfer (RAFT) polymerization, which were then utilized to form dense random copolymer membrane on the surface of PBO fibers by thermally cross-linking at 250 °C (PBO@P fibers). Four kinds of synthesized P(S-co-BCB-co-MMA) with different number-average molar mass (M_n) were well controlled and possessed narrow dispersity. When the M_n was 32300, the surface roughness of PBO@P fibers was increased from 11 nm (PBO fibers) to 39 nm. In addition, PBO@P fibers presented the optimal interfacial compatibility with bisphenol A cyanate (BADCy) resins. And the single fiber pull-out strength of PBO@P fibers/BADCy micro-composites was 4.5 MPa, increasing by 45.2% in comparison with that of PBO fibers/BADCy micro-composites (3.1 MPa). Meantime, PBO@P fibers still retained excellent tensile strength (about 5.1 GPa). Overall, this work illustrates a simple and efficient surface functionalization method, which would provide a strong theoretical basis and technical support for controlling the surface structure & chemistry of inert substrates.     

Who is who in Algol-land ?- Part I -

We computed the evolution through case A mass transfer for 8 systems with mass of the primary equal to 3 and 5 M₀, mass ratios 0.7 and 0.9, and different periods. To this we added similar results from Packet (1988) for M_i = 9 M₀, q_i = 0.6, P_i = 1.62 d.During the mass transfer two competing mechanisms in the gainer decide on the evolution of the system: the rejuvenation of this star as the increasing convective core mixes fresh hydrogen into the inner regions, and the acceleration of nuclear burning, responding to the increasing mass.In all the cases the net result is a faster decrease of the central hydrogen content compared to the mass losing star. The secondary fills its own critical Roche lobe and reversed mass transfer starts.From our results and those of Nakamura and Nakamura (1984), we find that reversed mass transfer occurs after core hydrogen burning of the secondary (case A₁B₂) approximately for periods larger than 1 d (M_1i = 3 M₀) to 2 d (M_1i = 13.4 M₀). For smaller periods this happens before the gainer ends its core hydrogen burning (case A₁A₂).     

The Strength and Structure of the Coronal Magnetic Field

I discuss a method for determining the strength and spatial structure of the coronal magnetic field by observations of the Faraday rotation of a radio galaxy which is in conjunction with the Sun. Given a knowledge of the plasma density in the outer corona, and the magnetic field sector structure (both independently available), the strength of the coronal field can be determined, as well as the magnitude of spatial variations on scales of 1000 km to several solar radii. Such knowledge is crucial for testing computational models of the solar corona, which are prominently featured in this meeting. Results are presented from observations with the Very Large Array radio telescope of the radio galaxy 3C228 on August 16, 2003, when the line of sight to the source was at heliocentic distances of 7.1−6.2R _⊙. The observations are consistent with a coronal magnetic field which is proportional to the inverse square of the distance in the range 6 ≤ r ≤ 10R _⊙, and has a value of 39 mG at 6.2R _⊙. The Faraday rotation is uniform across the source, indicating an absence of strong plasma inhomogeneity on spatial scales up to 35,000 km.     

Measuring Black Hole Spin Using X-Ray Reflection Spectroscopy

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on “best practices” that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5×10⁷ M _⊙) and low (M<2×10⁶ M _⊙) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GRO J1655–40 and 4U 1543–475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC 4151, NGC 7314 and MCG–5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.     

Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets

The spins of ten stellar black holes have been measured using the continuum-fitting method. These black holes are located in two distinct classes of X-ray binary systems, one that is persistently X-ray bright and another that is transient. Both the persistent and transient black holes remain for long periods in a state where their spectra are dominated by a thermal accretion disk component. The spin of a black hole of known mass and distance can be measured by fitting this thermal continuum spectrum to the thin-disk model of Novikov and Thorne; the key fit parameter is the radius of the inner edge of the black hole’s accretion disk. Strong observational and theoretical evidence links the inner-disk radius to the radius of the innermost stable circular orbit, which is trivially related to the dimensionless spin parameter a _? of the black hole (|a _?|<1). The ten spins that have so far been measured by this continuum-fitting method range widely from a _?≈0 to a _?>0.95. The robustness of the method is demonstrated by the dozens or hundreds of independent and consistent measurements of spin that have been obtained for several black holes, and through careful consideration of many sources of systematic error. Among the results discussed is a dichotomy between the transient and persistent black holes; the latter have higher spins and larger masses. Also discussed is recently discovered evidence in the transient sources for a correlation between the power of ballistic jets and black hole spin.     

Electrochemical trepanning with an auxiliary electrode

Electrochemical trepanning (ET) is one of the main methods for processing the blisks in aero-engines. However, stray corrosion in ET has a very negative impact on the machining quality of the blades. This paper proposes an innovative ET method with an auxiliary electrode surrounding the inner wall of the cavity above the cathode. Two-dimensional electric-field models are established and simulations are carried out with the auxiliary electrode at different positions and different electric potentials. The electric-field simulations show that adding the auxiliary electrode reverses the directions of the current lines in the processed area, thereby protecting it. The results show that when the distance from the bottom of the auxiliary electrode to the top of the cathode tool is 3 mm and the potential difference between the auxiliary electrode and the anode workpiece is 5 V, the area corroded by stray current is decreased. Experiments are performed under the parameter values determined by the simulations, and they confirm that this method is effective at reducing stray corrosion. Specifically, at a feed rate of 2.5 mm/min, the blade taper angle is decreased from 1.37° to −0.09°, the thickness of the leading and trailing edges is increased from 0.307 mm to 0.704 mm, and the average surface roughness is decreased from S_a =8.239 μm to S_a=7.028 μm.