Spectroscopic Studies of Solar Corona VIII. Temperature and Non-Thermal Variations in Steady Coronal Structures

With a view to investigate variations in parameters of coronal emission lines over a large range of radial distance from the limb, raster scans were made with sufficiently long exposure times on several days during September – October 2003. An analysis of the data shows that (i) in most of the coronal structures, the FWHM of the Fe xiv 5303 Å line decreases up to 300″±50″, (ii) the FWHM of the Fe x 6374 Å line increases up to about 200″ and then remains unchanged up to about 500″, and (iii) the FWHMs of the Fe xi 7892 Å and Fe xiii 10747 Å lines show an intermediate behaviour with height. The analysis of the data also shows that the ratio of FWHM of 6374 Å to that of 5303 Å increases from 0.93 at the limb to 1.18 at 200″ above the limb. From this and the ratio of intensities of the two lines we infer that the plasma in steady coronal structures at a height of about 200″ has a temperature of about 1.5 MK and a non-thermal velocity around 17 km s^?1. The observations also show that non-homogeneous temperatures and non-thermal velocities largely exist in the lower corona up to about 300″±100″ above the limb. Amplitudes of variations in FWHM of different emission lines with height in the coronal loops are similar to those in the diffuse plasma around the coronal loops.     

Kinematics of the Galaxy from OB Stars with Data from the Gaia DR2 Catalogue

We have selected and analyzed a sample of OB stars with known line-of-sight velocities determined through ground-based observations and with trigonometric parallaxes and propermotions from the Gaia DR2 catalogue. Some of the stars in our sample have distance estimates made from calcium lines. A direct comparison with the trigonometric distance scale has shown that the calcium distance scale should be reduced by 13%. The following parameters of the Galactic rotation curve have been determined from 495 OB stars with relative parallax errors less than 30%: (U, V,W)_⊙ = (8.16, 11.19, 8.55)± (0.48, 0.56, 0.48) km s^?1, Ω₀ = 28.92 ± 0.39 km s^?1 kpc^?1, Ω'₀ = ?4.087 ± 0.083 km s^?1 kpc^?2, and Ω″ ₀ = 0.703 ± 0.067 km s?1 kpc^?3, where the circular velocity of the local standard of rest is V0 = 231 ± 5 km s^?1 (for the adopted R₀ = 8.0 ± 0.15 kpc). The parameters of the Galactic spiral density wave have been found from the series of radial, V_R, residual tangential, ΔV_circ, and vertical, W, velocities of OB stars by applying a periodogram analysis. The amplitudes of the radial, tangential, and vertical velocity perturbations are f_R = 7.1± 0.3 km s^?1, f_θ = 6.5 ± 0.4 km s^?1, and f_W = 4.8± 0.8 km s^?1, respectively; the perturbation wavelengths are λ_R = 3.3 ± 0.1 kpc, λ_θ = 2.3 ± 0.2 kpc, and λ_W = 2.6 ± 0.5 kpc; and the Sun’s radial phase in the spiral density wave is (χ_⊙)_R = ?135? ± 5?, (χ_⊙)θ = ?123? ± 8?, and (χ_⊙)_W = ?132? ± 21? for the adopted four-armed spiral pattern.     

Analysis of the August 7, 1972 white light flare: Light curves and correlation with hard X-rays

Cinematic, photometric observations of the 3B flare of August 7, 1972 are described in detail. The time resolution was 2 s; the spatial resolution was 1–2″. Flare continuum emissivity at 4950 Å and at 5900 Å correlated closely in time with the 60–100 keV non-thermal X-ray burst intensity. The observed peak emissivity was 1.5 × 10¹⁰ erg cm^?2 s^?1 and the total flare energy in the 3900–6900 Å range was ～10³⁰ erg. From the close temporal correspondence and from the small distance (3″) separating the layers where the visible emission and the X-rays arose, it is argued that the hard X-ray source must have had the same silhouette as the white light flare and that the emission patches had cross-sections of 3–5″. There was also a correlation between the location of the most intense visible emissions near sunspots and the intensity and polarization of the 9.4 GHz radio emission. The flare appeared to show at least three distinct particle acceleration phases: one, occurring at a stationary source and associated with proton acceleration gave a very bluish continuum and reached peak intensity at ～ 1522 UT. At 1523 UT, a faint wave spread out at 40 km s^?1 from flare center. The spectrum of the wave was nearly flat in the range 4950–5900 Å. Association of the wave with a slow drift of the microwave emission peak to lower frequencies and with a softening of the X-ray spectrum is interpreted to mean that the particle acceleration process weakened while the region of acceleration expanded. The observations are interpreted with the aid of the flare models of Brown to mean that the same beam of non-thermal electrons that was responsible for the hard X-ray bremsstrahlung also caused the heating of the lower chromosphere that produced the white light flare.     

Interaction Between Two CMEs During 14 – 15 February 2011 and Their Unusual Radio Signature

We report a detailed analysis of an interaction between two coronal mass ejections (CMEs) that were observed on 14?–?15 February 2011 and the corresponding radio enhancement, which was similar to the “CME cannibalism” reported by Gopalswamy et al. (Astrophys. J. 548, L91, 2001). A primary CME, with a mean field-of-view velocity of 669 km?s^?1 in the Solar and Heliospheric Observatory (SOHO)/Large Angle Spectrometric Coronagraph (LASCO), was more than as twice as fast as the slow CME preceding it (326 km?s^?1), which indicates that the two CMEs interacted. A radio-enhancement signature (in the frequency range 1 MHz?–?400 kHz) due to the CME interaction was analyzed and interpreted using the CME data from LASCO and from the Solar Terrestrial Relations Observatory (STEREO) HI-1, radio data from Wind/Radio and Plasma Wave Experiment (WAVES), and employing known electron-density models and kinematic modeling. The following results are obtained: i) The CME interaction occurred around 05:00?–?10:00 UT in a height range 20?–?25 R_⊙. An unusual radio signature is observed during the time of interaction in the Wind/WAVES dynamic radio spectrum. ii) The enhancement duration shows that the interaction segment might be wider than 5 R_⊙. iii) The shock height estimated using density models for the radio enhancement region is 10?–?30 R_⊙. iv) Using kinematic modeling and assuming a completely inelastic collision, the decrease of kinetic energy based on speeds from LASCO data is determined to be 0.77×10²³ J, and 3.67×10²³ J if speeds from STEREO data are considered. vi) The acceleration, momentum, and force are found to be a=?168 m?s^?2, I=6.1×10¹⁸ kg?m?s^?1, and F=1.7×10¹⁵ N, respectively, using STEREO data.     

Interpretation of Solar Magnetic Field Strength Observations

This study based on longitudinal Zeeman effect magnetograms and spectral line scans investigates the dependence of solar surface magnetic fields on the spectral line used and the way the line is sampled to estimate the magnetic flux emerging above the solar atmosphere and penetrating to the corona from magnetograms of the Mt. Wilson 150-foot tower synoptic program (MWO). We have compared the synoptic program λ5250 Å line of Fe?i to the line of Fe?i at λ5233 Å since this latter line has a broad shape with a profile that is nearly linear over a large portion of its wings. The present study uses five pairs of sampling points on the λ5233 Å line. Line profile observations show that the determination of the field strength from the Stokes V parameter or from line bisectors in the circularly polarized line profiles lead to similar dependencies on the spectral sampling of the lines, with the bisector method being the less sensitive. We recommend adoption of the field determined with the line bisector method as the best estimate of the emergent photospheric flux and further recommend the use of a sampling point as close to the line core as is practical. The combination of the line profile measurements and the cross-correlation of fields measured simultaneously with λ5250 Å and λ5233 Å yields a formula for the scale factor δ ^?1 that multiplies the MWO synoptic magnetic fields. By using ρ as the center-to-limb angle (CLA), a fit to this scale factor is δ ^?1=4.15?2.82sin?²(ρ). Previously δ ^?1=4.5?2.5sin?²(ρ) had been used. The new calibration shows that magnetic fields measured by the MDI system on the SOHO spacecraft are equal to 0.619±0.018 times the true value at a center-to-limb position 30°. Berger and Lites (2003, Solar Phys. 213, 213) found this factor to be 0.64±0.013 based on a comparison using the Advanced Stokes Polarimeter.     

Galactic kinematics from data on open star clusters from the MWSC catalogue

Open star clusters from the MWSC (Milky Way Star Clusters) catalogue have been used to determine the Galactic rotation parameters. The circular rotation velocity of the solar neighborhood around the Galactic center has been found from data on more than 2000 clusters of various ages to be V ₀ = 236 ± 6 km s^?1 for the adopted Galactocentric distance of the Sun R ₀ = 8.3 ± 0.2 kpc. The derived angular velocity parameters are Ω ₀ = 28.48 ± 0.36 km s^?1 kpc^?1, Ω’₀ = ?3.50 ± 0.08 km s^?1 kpc_?2, and Ω″₀ = 0.331 ± 0.037 km s^?1 kpc^?3. The influence of the spiral density wave has been detected only in the sample of clusters younger than 50 Myr. For these clusters the amplitudes of the tangential and radial velocity perturbations are f ^θ = 5.6 ± 1.6 km s^?1 and f _R = 7.7 ± 1.4 km s^?1, respectively; the perturbation wavelengths are λ _θ = 2.6 ± 0.5 kpc (i _θ = ^?11? ± 2?) and λ _R = 2.1 ± 0.5 kpc (i _R = ?9? ± 2?) for the adopted four-armed model (m = 4). The Sun’s phase in the spiral density wave is (χ_⊙)_θ = ?62? ± 9? and (χ_⊙)_R = ?85? ± 10? from the residual tangential and radial velocities, respectively.     

Doppler Shifts of the Hα Line and the Ca ii 854.2 nm Line in a Quiet Region of the Sun Observed with the FISS/NST

The characteristics of Doppler shifts in a quiet region of the Sun are compared between the Hα line and the Ca?ii infrared line at 854.2 nm. A small area of 16″×40″ was observed for about half an hour with the Fast Imaging Solar Spectrograph (FISS) of the 1.6 meter New Solar Telescope (NST) at Big Bear Solar Observatory. The observed area contains a network region and an internetwork region, and identified in the network region are fibrils and bright points. We infer Doppler velocity v _m from each line profile at each individual point with the lambdameter method as a function of half wavelength separation Δλ. It is confirmed that the bisector of the spatially averaged Ca?ii line profile has an inverse C-shape with a significant peak redshift of +?1.8 km?s^?1. In contrast, the bisector of the spatially averaged Hα line profile has a C-shape with a small peak blueshift of ??0.5 km?s^?1. In both lines, the bisectors of bright network points are significantly redshifted not only at the line centers, but also at the wings. The Ca?ii Doppler shifts are found to be correlated with the Hα ones with the strongest correlation occurring in the internetwork region. Moreover, we find that here the Doppler shifts in the two lines are essentially in phase. We discuss the physical implications of our results in view of the formation of the Hα line and Ca?ii 854.2 nm line in the quiet region chromosphere.     

Microwave emission above steady and moving sunspots

Two-dimensional maps of radio brightness temperature and polarization, computed assuming thermal emission with free-free and gyroresonance absorption, are compared with observations of active region 2502, performed at Westerbork at λ = 6.16 cm during a period of 3 days in June 1980. The computation is done assuming a homogeneous model in the whole field of view (5′ × 5′) and a force-free extrapolation of the photospheric magnetic field observed at MSFC with a resolution of 2″.34. The mean results are the following:

1. A very good agreement is found above the large leading sunspot of the group, assuming a potential extrapolation of the magnetic field and a constant conductive flux in the transition region ranging from 2 × 10⁶ to 10⁷ erg cm^?2s^?1.
2. A strong radio source, associated with a new-born moving sunspot, cannot be ascribed to thermal emission. It is suggested that this source may be due to synchrotron radiation by mildly relativistic electrons accelerated by resistive instabilities occurring in the evolving magnetic configuration. An order-of-magnitude computation of the expected number of accelerated particles seems to confirm this hypothesis.

     

The High-Resolution Coronal Imager (Hi-C)

The High-Resolution Coronal Imager (Hi-C) was flown on a NASA sounding rocket on 11 July 2012. The goal of the Hi-C mission was to obtain high-resolution (≈?0.3?–?0.4′′), high-cadence (≈?5 seconds) images of a solar active region to investigate the dynamics of solar coronal structures at small spatial scales. The instrument consists of a normal-incidence telescope with the optics coated with multilayers to reflect a narrow wavelength range around 19.3 nm (including the Fe xii 19.5-nm spectral line) and a 4096×4096 camera with a plate scale of 0.1′′?pixel^?1. The target of the Hi-C rocket flight was Active Region 11520. Hi-C obtained 37 full-frame images and 86 partial-frame images during the rocket flight. Analysis of the Hi-C data indicates the corona is structured on scales smaller than currently resolved by existing satellite missions.     

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.     

Kinematics of gas and stars in circumnuclear star-forming regions of early-type spirals

We present high-resolution (R～20,000) spectra in the blue and the far red of circumnuclear star-forming regions (CNSFRs) in three early-type spirals (NGC3351, NGC2903 and NGC3310), which have allowed the study of the kinematics of the stars and the ionized gas in these structures and, for the first time, the derivation of their dynamical masses for the first two. In some cases, these regions, about 100 to 150 pc in size, are composed of several individual star clusters with sizes between 1.5 and 4.9 pc, estimated from Hubble Space Telescope images. The stellar dispersions have been obtained from the Calcium triplet (CaT) lines at λ λ 8494, 8542, 8662 Å, while the gas velocity dispersions have been measured by means of Gaussian fits to the Hβ and [Oiii]λ 5007 Å lines in the high-dispersion spectra. Values of the stellar velocity dispersions are between 30 and 68 km?s^?1. We apply the virial theorem to estimate dynamical masses of the clusters, assuming that systems are gravitationally bounded and spherically symmetric, and using previously measured sizes. The measured values of the stellar velocity dispersions yield dynamical masses of the order of 10⁷ to 10⁸ M_⊙ for the entire CNSFRs. Stellar and gas velocity dispersions are found to differ by about 20 to 30 km?s^?1, with the Hβ emission lines being narrower than both the stellar lines and the [Oiii]λ 5007 Å lines. The douby-ionized oxygen, on the other hand, exhibits velocity dispersions comparable to those of the stars or, in some cases, even larger. We have found indications of the presence of two different kinematical components in the ionized gas of the regions. We have mapped the velocity field in the central kpc of the spiral galaxies NGC3351 and NGC2903. For the first object, the radial velocity curve shows deviations from circular motions for the ionized hydrogen consistent with its infall towards the central regions of the galaxy, at a velocity of about 25 km?s^?1. For NGC3310, we present preliminary results for the velocity dispersions for one of the two observed slit position angles, two CNSFRs and the nucleus.     

A Major Geoeffective CME from NOAA 12371: Initiation,CME–CME Interactions,and Interplanetary Consequences

In this article, we present a multi-wavelength and multi-instrument investigation of a halo coronal mass ejection (CME) from active region NOAA 12371 on 21 June 2015 that led to a major geomagnetic storm of minimum \(\mathrm{Dst} = -204\) nT. The observations from the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory in the hot EUV channel of 94 Å confirm the CME to be associated with a coronal sigmoid that displayed an intense emission (\(T \sim6\) MK) from its core before the onset of the eruption. Multi-wavelength observations of the source active region suggest tether-cutting reconnection to be the primary triggering mechanism of the flux rope eruption. Interestingly, the flux rope eruption exhibited a two-phase evolution during which the “standard” large-scale flare reconnection process originated two composite M-class flares. The eruption of the flux rope is followed by the coronagraphic observation of a fast, halo CME with linear projected speed of 1366 km?s^?1. The dynamic radio spectrum in the decameter-hectometer frequency range reveals multiple continuum-like enhancements in type II radio emission which imply the interaction of the CME with other preceding slow speed CMEs in the corona within \(\approx10\)?–?\(90~\mbox{R} _{\odot}\). The scenario of CME–CME interaction in the corona and interplanetary medium is further confirmed by the height–time plots of the CMEs occurring during 19?–?21 June. In situ measurements of solar wind magnetic field and plasma parameters at 1 AU exhibit two distinct magnetic clouds, separated by a magnetic hole. Synthesis of near-Sun observations, interplanetary radio emissions, and in situ measurements at 1 AU reveal complex processes of CME–CME interactions right from the source active region to the corona and interplanetary medium that have played a crucial role towards the large enhancement of the geoeffectiveness of the halo CME on 21 June 2015.     

Revivals of a coronal arch

The giant post-flare arch of 6 November 1980 revived 11 hr and 25 hr after its formation. Both these revivals were caused by two-ribbon flares with growing systems of loops. The first two brightenings of the arch were homologous events with brightness maxima moving upwards through the corona with rather constant speed; during all three brightenings the arch showed a velocity pattern with two components: a slow one (8–12 km^?1), related to the moving maxima of brightness, and a fast one (～ 35 km s^?1), the source of which is unknown. During the first revival, at an altitude of 100000 km, temperature in the arch peaked ～ 1 hr, brightness ～ 2 hr, and emission measure ～ 3.5 hr after the onset of the brightening. Thus the arch looks like a magnified flare, with the scales both in size and time increased by an order of magnitude. At ～ 100000 km altitude the maximum temperature was ?14 × 10⁶K, max.n _e? 2.5 × 10⁹cm^?3, and max. energy density ? 11.2 erg cm^?3. The volume of the whole arch can be estimated to 1.1 × 10³⁰ cm³, total energy ?1.2 × 10³¹ erg, and total mass ?4.4 × 10¹⁵g. The density decreased with the increasing altitude and remained below 7 × 10⁹ cm^?3 anywhere in the arch. The arch cooled very slowly through radiation whereas conductive cooling was inhibited. Since its onset the revived arch was subject to energy input within the whole extent of the preexisting arch while a thermal disturbance (a new arch?) propagated slowly from below. We suggest that the first heating of the revived arch was due to reconnection of some of the distended flare loops with the magnetic field of the old preexisting arch. The formation of the ‘post’-flare loop system was delayed and started only some 30–40 min later. Since that time a new arch began to be formed above the loops and the velocities we found reflect this formation.     

Alfvén waves in the solar atmosphere

We examine the propagation of Alfvén waves in the solar atmosphere. The principal theoretical virtues of this work are: (i) The full wave equation is solved without recourse to the small-wavelength eikonal approximation (ii) The background solar atmosphere is realistic, consisting of an HSRA/VAL representation of the photosphere and chromosphere, a 200 km thick transition region, a model for the upper transition region below a coronal hole (provided by R. Munro), and the Munro-Jackson model of a polar coronal hole. The principal results are:

1. If the wave source is taken to be near the top of the convection zone, where n _H = 5.2 × 10¹⁶ cm^?3, and if B _⊙ = 10.5 G, then the wave Poynting flux exhibits a series of strong resonant peaks at periods downwards from 1.6 hr. The resonant frequencies are in the ratios of the zeroes of J ₀, but depend on B _⊙, and on the density and scale height at the wave source. The longest period peaks may be the most important, because they are nearest to the supergranular periods and to the observed periods near 1 AU, and because they are the broadest in frequency.
2. The Poynting flux in the resonant peaks can be large enough, i.e. P _⊙ ≈ 10⁴–10⁵ erg cm^?2s^?1, to strongly affect the solar wind.
3. ¦δv¦ and ¦δB¦ also display resonant peaks.
4. In the chromosphere and low corona, ¦δv ≈ 7–25 kms^?1 and ¦δB¦ ≈0.3–1.0 G if P _⊙≈10⁴-10⁵ erg cm^?2s^?1.
5. The dependences of ¦δv¦ and ¦δB¦ on height are reduced by finite wavelength effects, except near the wave source where they are enhanced.
6. Near the base, ¦δB¦ ≈ 350–1200 G if P _⊙ ～- 10⁴–10⁵. This means that nonlinear effects may be important, and that some density and vertical velocity fluctuations may be associated with the Alfvén waves.
7. Below the low corona most wave energy is kinetic, except near the base where it becomes mostly magnetic at the resonances.
8. ?₀ < δv ² > v _A or < δB ² > v _A/4π are not good estimators of the energy flux.
9. The Alfvén wave pressure tensor will be important in the transition region only if the magnetic field diverges rapidly. But the Alfvén wave pressure can be important in the coronal hole.

     

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.     

Photometric and polarimetric studies of three W UMa-type binaries: FZ Ori,V407 Peg and LP UMa

We present analyses of new optical photometric observations of three W UMa-type contact binaries FZ Ori, V407 Peg and LP UMa. Results from the first polarimetric observations of the FZ Ori and V407 Peg are also presented. The periods of FZ Ori, V407 Peg and LP UMa are derived to be 0.399986, 0.636884 and 0.309898 d, respectively. The O?C analyses indicate that the orbital periods of FZ Ori and LP UMa have increased with the rate of 2.28×10^?8 and 1.25×10^?6 d?yr^?1, respectively and which is explained by transfer of mass between the components. In addition to the secularly increasing rate of orbital period, it was found that the period of FZ Ori has varied in sinusoidal way with oscillation period of ～30.1 yr. The period of oscillations are most likely to be explained by the light-time effect due to the presence of a tertiary companion. Small asymmetries have been seen around the primary and secondary maxima of light curves of all three systems, which is probably due to the presence of cool/hot spots on the components. The light curves of all three systems are analysed by using Wilson-Devinney code (WD) and the fundamental parameters of these systems have been derived. The present analyses show that FZ Ori is a W-subtype, and V407 Peg and LP UMa are A-subtype of the W UMa-type contact binary systems. The polarimetric observations in B, V, R and I bands, yield average values of polarization to be 0.26±0.03, 0.22±0.02, 0.22±0.03 and 0.22±0.05 per cent for FZ Ori and 0.21±0.02, 0.29±0.03, 0.31±0.01 and 0.31±0.04 per cent for V407 Peg, respectively.     

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.