Spectropolarimetric Observations of Solar Noise Storms at Low Frequencies

A new high-resolution radio spectropolarimeter instrument operating in the frequency range of 15?–?85 MHz has recently been commissioned at the Radio Astronomy Field Station of the Indian Institute of Astrophysics at Gauribidanur, 100 km north of Bangalore, India. We describe the design and construction of this instrument. We present observations of a solar radio noise storm associated with Active Region (AR) 12567 in the frequency range of \({\approx}\,15\,\mbox{--}\,85~\mbox{MHz}\) during 18 and 19 July 2016, observed using this instrument in the meridian-transit mode. This is the first report that we are aware of in which both the burst and continuum properties are derived simultaneously. Spectral indices and degree of polarization of both the continuum radiation and bursts are estimated. It is found that

1. i)
   Type I storm bursts have a spectral index of \({\approx}\,{+}3.5\),
    
2. ii)
   the spectral index of the background continuum is \({\approx}\,{+}2.9\),
    
3. iii)
   the transition frequency between Type I and Type III storms occurs at \({\approx}\,55~\mbox{MHz}\),
    
4. iv)
   Type III bursts have an average spectral index of \({\approx}\,{-}2.7\),
    
5. v)
   the spectral index of the Type III continuum is \({\approx}\,{-}1.6\), and
    
6. vi)
   the degree of circular polarization of all Type I (Type III) bursts is \({\approx}\,90\%\) (\(30\%\)).
    

The results obtained here indicate that the continuum emission is due to bursts occurring in rapid succession. We find that the derived parameters for Type I bursts are consistent with suprathermal electron acceleration theory and those of Type III favor fundamental plasma emission.

     

The luminosity correlation analysis for Fermi blazars

In this paper, multiwavelength chromatic luminosity at radio (\(\log L _{\mathrm{R}}\)), optical (\(\log L_{\mathrm{O}}\)), X-ray (\(\log L _{\mathrm{X}}\)), and \(\gamma \)-rays (\(\log L_{\gamma }\)) for a sample of 442 Fermi blazars with known redshifts are collected from Fan et al. (2016), to study the correlations between the \(\gamma \)-rays and the low-energy bands using a multiple linear regression analysis. In this way, we can see which band is more important for the \(\gamma \)-ray emissions. Mutual correlation analysis is also used to discuss the correlations between the \(\gamma \)-ray and the low energy bands for the whole sample and subclasses. We come to following conclusions:

1. 1.
   The multiple linear correlation indicates that the \(\gamma \)-rays are correlated with the radio, optical and the X-ray emissions for the whole sample and the subclasses of flat spectrum radio quasars (FSRQs) and BL Lac objects (BL Lacs), the correlation between the \(\gamma \)-rays and the radio emissions is the strongest one.
    
2. 2.
   For BL Lacs, the optical emissions are more important than the X-rays for the \(\gamma \)-rays, while the X-ray emissions are more important than optical ones in FSRQs.
    
3. 3.
   The \(\gamma \)-ray emissions in HBL are from an synchrotron self-Compton, while those in FSRQs may be from external Compton and synchrotron self-Compton as well.
    

     

Inverse problem of central configurations and singular curve in the collinear 4-body problem

In this paper, we consider the inverse problem of central configurations of n-body problem. For a given \({q=(q_1, q_2, \ldots, q_n)\in ({\bf R}^d)^n}\), let S(q) be the admissible set of masses denoted \({ S(q)=\{ m=(m_1,m_2, \ldots, m_n)| m_i \in {\bf R}^+, q}\) is a central configuration for m}. For a given \({m\in S(q)}\), let S _m (q) be the permutational admissible set about m = (m ₁, m ₂, . . . , m _n ) denoted

$S_m(q)=\{m^\prime | m^\prime\in S(q),m^\prime \not=m \, {\rm and} \, m^\prime\,{\rm is\, a\, permutation\, of }\, m \}.$

The main discovery in this paper is the existence of a singular curve \({\bar{\Gamma}_{31}}\) on which S _m (q) is a nonempty set for some m in the collinear four-body problem. \({\bar{\Gamma}_{31}}\) is explicitly constructed by a polynomial in two variables. We proved:

1. (1)
   If \({m\in S(q)}\), then either ^# S _m (q) = 0 or ^# S _m (q) = 1.
    
2. (2)
   ^#S _m (q) = 1 only in the following cases:

   1. (i)
      If s = t, then S _m (q) = {(m ₄, m ₃, m ₂, m ₁)}.
       
   2. (ii)
      If \({(s,t)\in \bar{\Gamma}_{31}\setminus \{(\bar{s},\bar{s})\}}\), then either S _m (q) = {(m ₂, m ₄, m ₁, m ₃)} or S _m (q) = {(m ₃, m ₁, m ₄, m ₂)}.
       
    

     

Observations of small-scale solar magnetic fields

Spectrograms, obtained during moments of good seeing with the high spatial resolution afforded by the 80-cm solar image at the Kitt Peak National Observatory, show the following:

1. (1)
   Magnetic fields of several hundred gauss occur in tiny areas easily as small as 500 km in extent in regions of the solar surface sometimes well removed from areas of sunspot activity.     
   
   

Addendum to: Strength of the Solar Coronal Magnetic Field – A Comparison of Independent Estimates Using Contemporaneous Radio and White-Light Observations

This addendum uses an alternate fit for the electron density distribution \(N(r)\) (see Figure 1) and estimates the coronal magnetic field using the new model. We find that the estimates of the magnetic field are in close agreement using both the models.

We have fit the \(N(r)\) distribution obtained from STEREO-A/COR1 and SOHO/LASCO-C2 using a fifth-order polynomial (see Figure 1). The expression can be written as

$$\begin{aligned} N_{\text{cor}}(r) &= 1.43 \times 10^{9} r^{-5} - 1.91 \times 10^{9} r^{-4} + 1.07 \times 10^{9} r^{-3} - 2.87 \times 10^{8} r^{-2} \\ &\quad {} + 3.76 \times 10^{7} r^{-1} - 1.91 \times 10^{6} , \end{aligned}$$

(1)

where \(N_{\text{cor}}(r)\) is in units of cm^?3 and \(r\) is in units of \(\mathrm{R}_{\odot}\). The background coronal electron density is enhanced by a factor of 5.5 at 2.63 \(\mathrm{R}_{\odot}\) during the coronal mass ejection (CME). The estimated coronal magnetic field strength (\(B\)) using radio data indicates that \(B(r) \approx(0.51\text{\,--\,}0.48) \pm 0.02\ \mathrm{G}\) in the range \(r \approx2.65\text{\, --\,}2.82\ \mathrm{R}_{\odot}\). The field strengths for STEREO-A/COR1 and SOHO/LASCO-C2 are ≈?0.32 G at \(r \approx 3.11\ \mathrm{R}_{\odot}\) and ≈?0.12 G at \(r \approx 4.40\ \mathrm{R}_{\odot}\), respectively.

     

Viscoelastic tides: models for use in Celestial Mechanics

In this note, by using Smale’s \(\alpha \)-theorem on the convergence of Newton’s method, the \(\alpha \)-sets of convergence of some starters of solving the elliptic Kepler’s equation are derived. For each starter we compute the exact \(\alpha \)-set in the eccentricity-main anomaly \((e,M)\in [0,1)\times [0,\pi ]\), showing that these sets are larger than those derived by Avendaño et al. (Celest Mech Dyn Astron 119:27–44, 2014). Further, new convergence tests based on the Newton–Kantorowitch theorem are given comparing with the derived from Smale’s \(\alpha \)-test.     

Some properties of velocity fields in the solar photosphere

Photoelectric records of the Doppler effect (DE) and longitudinal Zeeman effect (LZE) were obtained with the Capri magnetograph of the Fraunhofer Institut photoelectric, using the Fei line λ 5250.22. Each record consists of 65 scans repeated along the same line on the sun. The analysis of 16 records covering a total of 485 oscillating regions (period 300 sec) leads to the following results:

1. (1)
   The mean lifetime of the DE-oscillations outside active regions is 20 min and 32 min in the neighborhood of spotgroups. Discarding the weakest sporadic osculations, one obtains 27 min and 43 min respectively. The most frequent lifetime in both cases is 15 min.     
   
   

An analysis of the convergence of Newton iterations for solving elliptic Kepler’s equation

In this note a study of the convergence properties of some starters \( E_0 = E_0(e,M)\) in the eccentricity–mean anomaly variables for solving the elliptic Kepler’s equation (KE) by Newton’s method is presented. By using a Wang Xinghua’s theorem (Xinghua in Math Comput 68(225):169–186, 1999) on best possible error bounds in the solution of nonlinear equations by Newton’s method, we obtain for each starter \( E_0(e,M)\) a set of values \( (e,M) \in [0, 1) \times [0, \pi ]\) that lead to the q-convergence in the sense that Newton’s sequence \( (E_n)_{n \ge 0}\) generated from \( E_0 = E_0(e,M)\) is well defined, converges to the exact solution \(E^* = E^*(e,M)\) of KE and further \( \vert E_n - E^* \vert \le q^{2^n -1}\; \vert E_0 - E^* \vert \) holds for all \( n \ge 0\). This study completes in some sense the results derived by Avendaño et al. (Celest Mech Dyn Astron 119:27–44, 2014) by using Smale’s \(\alpha \)-test with \(q=1/2\). Also since in KE the convergence rate of Newton’s method tends to zero as \( e \rightarrow 0\), we show that the error estimates given in the Wang Xinghua’s theorem for KE can also be used to determine sets of q-convergence with \( q = e^k \; \widetilde{q} \) for all \( e \in [0,1)\) and a fixed \( \widetilde{q} \le 1\). Some remarks on the use of this theorem to derive a priori estimates of the error \( \vert E_n - E^* \vert \) after n Kepler’s iterations are given. Finally, a posteriori bounds of this error that can be used to a dynamical estimation of the error are also obtained.     

Photoelectric photometry of solar granulation in several regions of the continuum

Photospheric brightness fluctuations were recorded photoelectrically across a part of the sun near the center of the disk, and simultaneously for two regions of the continuous spectrum chosen at various wavelengths between λ3500 Å and λ5500 Å. The auto-correlation functions and spatial power spectra were derived for each recording, and the cross-correlation functions, spatial relative phase and coherence spectra were computed for each pair of recordings. The main results are:

1. (1)
   The cross-correlation between any two recordings obtained for various regions of the continuous spectrum, is a function of the wavelength distance Δλ between these regions. The decrease of the cross-correlation with increasing Δλ is due to the fact that separate photometric inhomogeneities radiate in limited spectral ranges.     
   
   

First integrals for the Kepler problem with linear drag

In this work we consider the Kepler problem with linear drag, and prove the existence of a continuous vector-valued first integral, obtained taking the limit as \(t\rightarrow +\infty \) of the Runge–Lenz vector. The norm of this first integral can be interpreted as an asymptotic eccentricity \(e_{\infty }\) with \(0\le e_{\infty } \le 1\). The orbits satisfying \(e_{\infty } <1\) approach the singularity by an elliptic spiral and the corresponding solutions \(x(t)=r(t)e^{i\theta (t)}\) have a norm r(t) that goes to zero like a negative exponential and an argument \(\theta (t)\) that goes to infinity like a positive exponential. In particular, the difference between consecutive times of passage through the pericenter, say \(T_{n+1} -T_n\), goes to zero as \(\frac{1}{n}\).     

On the exactness of estimates for irregularly structured bodies of the general term of Laplace series

The main form of the representation of a gravitational potential V for a celestial body T in outer space is the Laplace series in solid spherical harmonics \((R/r)^{n+1}Y_n(\theta ,\lambda )\) with R being the radius of the enveloping T sphere. The surface harmonic \(Y_n\) satisfies the inequality

$$\begin{aligned} \langle Y_n\rangle < Cn^{-\sigma }. \end{aligned}$$

The angular brackets mark the maximum of a function’s modulus over a unit sphere. For bodies with an irregular structure \(\sigma = 5/2\), and this value cannot be increased generally. However, a class of irregular bodies (smooth bodies with peaked mountains) has been found recently in which \(\sigma = 3\). In this paper, we will prove the exactness of this estimate, showing that a body belonging to the above class does exist and

$$\begin{aligned} 0<\varlimsup n^3\langle Y_n\rangle <\infty \end{aligned}$$

for it.

     

Spectroscopic Variability of Supergiant Star HD14134, B3Ia

Profile variations in the \(\hbox {H}\alpha \) and \(\hbox {H}\beta \) lines in the spectra of the star HD14134 are investigated using observations carried out in 2013–2014 and 2016 with the 2-m telescope at the Shamakhy Astrophysical Observatory. The absorption and emission components of the \(\hbox {H}\alpha \) line are found to disappear on some observational days, and two of the spectrograms exhibit inverse P-Cyg profile of \(\hbox {H}\alpha \). It was revealed that when the \(\hbox {H}\alpha \) line disappeared or an inversion of the P-Cyg-type profile is observed in the spectra, the \(\hbox {H}\beta \) line is displaced to the longer wavelengths, but no synchronous variabilities were observed in other spectral lines (CII \( \lambda \) 6578.05 Å, \( \lambda \) 6582.88 Å  and HeI \( \lambda \) 5875.72 Å) formed in deeper layers of the stellar atmosphere. In addition, the profiles of the \(\hbox {H}\alpha \) and \(\hbox {H}\beta \) lines have been analysed, as well as their relations with possible expansion, contraction and mixed conditions of the atmosphere of HD14134. We suggest that the observational evidence for the non-stationary atmosphere of HD14134 can be associated in part with the non-spherical stellar wind.     

Average Magnetic Field Magnitude Profiles of <Emphasis Type="Italic">Wind</Emphasis> Magnetic Clouds as a Function of Closest Approach to the Clouds’ Axes and Comparison to Model

We examine the average magnetic field magnitude (\(| \boldsymbol{B} | \equiv B\)) within magnetic clouds (MCs) observed by the Wind spacecraft from 1995 to July 2015 to understand the difference between this \(B\) and the ideal \(B\)-profiles expected from using the static, constant-\(\alpha\), force-free, cylindrically symmetric model for MCs of Lepping, Jones, and Burlaga (J. Geophys. Res. 95, 11957, 1990, denoted here as the LJB model). We classify all MCs according to an assigned quality, \(Q_{0}\) (\(= 1, 2, 3\), for excellent, good, and poor). There are a total of 209 MCs and 124 when only \(Q_{0} = 1\), 2 cases are considered. The average normalized field with respect to the closest approach (\(\mathit{CA}\)) is stressed, where we separate cases into four \(\mathit{CA}\) sets centered at 12.5 %, 37.5 %, 62.5 %, and 87.5 % of the average radius; the averaging is done on a percentage-duration basis to treat all cases the same. Normalized \(B\) means that before averaging, the \(B\) for each MC at each point is divided by the LJB model-estimated \(B\) for the MC axis, \(B_{0}\). The actual averages for the 209 and 124 MC sets are compared to the LJB model, after an adjustment for MC expansion (e.g. Lepping et al. in Ann. Geophys. 26, 1919, 2008). This provides four separate difference-relationships, each fitted with a quadratic (Quad) curve of very small \(\sigma\). Interpreting these Quad formulae should provide a comprehensive view of the variation in normalized \(B\) throughout the average MC, where we expect external front and rear compression to be part of its explanation. These formulae are also being considered for modifying the LJB model. This modification will be used in a scheme for forecasting the timing and magnitude of magnetic storms caused by MCs. Extensive testing of the Quad formulae shows that the formulae are quite useful in correcting individual MC \(B\)-profiles, especially for the first \({\approx\,}1/3\) of these MCs. However, the use of this type of \(B\) correction constitutes a (slight) violation of the force-free assumption used in the original LJB MC model.     

Fine-resolution analysis of exoplanetary distributions by wavelets: hints of an overshooting iceline accumulation

We investigate 1D exoplanetary distributions using a novel analysis algorithm based on the continuous wavelet transform. The analysis pipeline includes an estimation of the wavelet transform of the probability density function (p.d.f.) without pre-binning, use of optimized wavelets, a rigorous significance testing of the patterns revealed in the p.d.f., and an optimized minimum-noise reconstruction of the p.d.f. via matching pursuit iterations.In the distribution of orbital periods, \(P\), our analysis revealed a narrow subfamily of exoplanets within the broad family of “warm Jupiters”, or massive giants with \(P\gtrsim 300~\mbox{d}\), which are often deemed to be related with the iceline accumulation in a protoplanetary disk. We detected a p.d.f. pattern that represents an upturn followed by an overshooting peak spanning \(P\sim 300\mbox{--}600~\mbox{d}\), right beyond the “period valley”. It is separated from the other planets by p.d.f. concavities from both sides. It has at least 2-sigma significance.In the distribution of planet radii, \(R\), and using the California Kepler Survey sample properly cleaned, we confirm the hints of a bimodality with two peaks about \(R=1.3R_{\oplus }\) and \(R=2.4R_{ \oplus }\), and the “evaporation valley” between them. However, we obtain just a modest significance for this pattern, 2-sigma only at the best. Besides, our follow-up application of the Hartigan and Hartigan dip test for unimodality returns 3 per cent false alarm probability (merely 2.2-sigma significance), contrary to 0.14 per cent (or 3.2-sigma), as claimed by Fulton et al. (2017).     

A study of the geomagnetic indices asymmetry based on the interplanetary magnetic field polarities

Data of geomagnetic indices (aa, Kp, Ap, and Dst) recorded near 1 AU over the period 1967–2016, have been studied based on the asymmetry between the interplanetary magnetic field (IMF) directions above and below of the heliospheric current sheet (HCS). Our results led to the following conclusions: (i) Throughout the considered period, 31 random years (62%) showed apparent asymmetries between Toward (\(\mathbf{T}\)) and Away (\(\mathbf{A}\)) polarity days and 19 years (38%) exhibited nearly a symmetrical behavior. The days of \(\mathbf{A}\) polarity predominated over the \(\mathbf{T}\) polarity days by 4.3% during the positive magnetic polarity epoch (1991–1999). While the days of \(\mathbf{T}\) polarity exceeded the days of \(\mathbf{A}\) polarity by 5.8% during the negative magnetic polarity epoch (2001–2012). (ii) Considerable yearly North–South (N–S) asymmetries of geomagnetic indices observed throughout the considered period. (iii) The largest toward dominant peaks for \(aa\) and \(Ap\) indices occurred in 1995 near to minimum of solar activity. Moreover, the most substantial away dominant peaks for \(aa\) and \(Ap\) indices occurred in 2003 (during the descending phase of the solar cycle 23) and in 1991 (near the maximum of solar activity cycle) respectively. (iv) The N–S asymmetry of \(Kp\) index indicated a most significant away dominant peak occurred in 2003. (v) Four of the away dominant peaks of Dst index occurred at the maxima of solar activity in the years 1980, 1990, 2000, and 2013. The largest toward dominant peak occurred in 1991 (at the reversal of IMF polarity). (vi) The geomagnetic indices (aa, Ap, and \(Kp\)) all have northern dominance during positive magnetic polarity epoch (1971–1979), while the asymmetries shifts to the southern solar hemisphere during negative magnetic polarity epoch (2001–2012).     

Geomagnetic Effects of Corotating Interaction Regions

We present an analysis of the geoeffectiveness of corotating interaction regions (CIRs), employing the data recorded from 25 January to 5 May 2005 and throughout 2008. These two intervals in the declining phase of Solar Cycle 23 are characterised by a particularly low number of interplanetary coronal mass ejections (ICMEs). We study in detail how four geomagnetic-activity parameters (the Dst, Ap, and AE indices, as well as the Dst time derivative, \(\mathrm{dDst}/\mathrm{d}t\)) are related to three CIR-related solar wind parameters (flow speed, \(V\), magnetic field, \(B\), and the convective electric field based on the southward Geocentric solar magnetospheric (GSM) magnetic field component, \(\mathit{VB}_{s}\)) on a three-hour time resolution. In addition, we quantify statistical relationships between the mentioned geomagnetic indices. It is found that Dst is correlated best to \(V\), with a correlation coefficient of \(\mathrm{cc}\approx0.6\), whereas there is no correlation between \(\mathrm{dDst}/\mathrm{d}t\) and \(V\). The Ap and AE indices attain peaks about half a day before the maximum of \(V\), with correlation coefficients ranging from \(\mathrm{cc}\approx0.6\) to \(\mathrm{cc}\approx0.7\), depending on the sample used. The best correlations of Ap and AE are found with \(\mathit{VB}_{s}\) with a delay of 3 h, being characterised by \(\mathrm{cc}\gtrsim 0.6\). The Dst derivative \(\mathrm{dDst}/\mathrm{d}t\) is also correlated with \(\mathit{VB}_{s}\), but the correlation is significantly weaker \(\mathrm{cc}\approx 0.4\)?–?0.5, with a delay of 0?–?3 h, depending on the employed sample. Such low values of correlation coefficients indicate that there are other significant effects that influence the relationship between the considered parameters. The correlation of all studied geomagnetic parameters with \(B\) are characterised by considerably lower correlation coefficients, ranging from \(\mathrm{cc}=0.3\) in the case of \(\mathrm{dDst}/\mathrm{d}t\) up to \(\mathrm{cc}=0.56\) in the case of Ap. It is also shown that peak values of geomagnetic indices depend on the duration of the CIR-related structures. The Dst is closely correlated with Ap and AE (\(\mathrm{cc}=0.7\)), Dst being delayed for about 3 h. On the other hand, \(\mathrm{dDst}/\mathrm{d}t\) peaks simultaneously with Ap and AE, with correlation coefficients of 0.48 and 0.56, respectively. The highest correlation (\(\mathrm{cc}=0.81\)) is found for the relationship between Ap and AE.     

GONG p-Mode Parameters Through Two Solar Cycles

We investigate the parameters of global solar p-mode oscillations, namely damping width \(\Gamma\), amplitude \(A\), mean squared velocity \(\langle v^{2}\rangle\), energy \(E\), and energy supply rate \(\mathrm{d}E/\mathrm{d}t\), derived from two solar cycles’ worth (1996?–?2018) of Global Oscillation Network Group (GONG) time series for harmonic degrees \(l=0\,\mbox{--}\,150\). We correct for the effect of fill factor, apparent solar radius, and spurious jumps in the mode amplitudes. We find that the amplitude of the activity-related changes of \(\Gamma\) and \(A\) depends on both frequency and harmonic degree of the modes, with the largest variations of \(\Gamma\) for modes with \(2400~\upmu\mbox{Hz}\le\nu\le3300~\upmu\mbox{Hz}\) and \(31\le l \le60\) with a minimum-to-maximum variation of \(26.6\pm0.3\%\) and of \(A\) for modes with \(2400~\upmu\mbox{Hz}\le\nu\le 3300~\upmu\mbox{Hz}\) and \(61\le l \le100\) with a minimum-to-maximum variation of \(27.4\pm0.4\%\). The level of correlation between the solar radio flux \(F_{10.7}\) and mode parameters also depends on mode frequency and harmonic degree. As a function of mode frequency, the mode amplitudes are found to follow an asymmetric Voigt profile with \(\nu_{\text{max}}=3073.59\pm0.18~\upmu\mbox{Hz}\). From the mode parameters, we calculate physical mode quantities and average them over specific mode frequency ranges. In this way, we find that the mean squared velocities \(\langle v^{2}\rangle\) and energies \(E\) of p modes are anticorrelated with the level of activity, varying by \(14.7\pm0.3\%\) and \(18.4\pm0.3\%\), respectively, and that the mode energy supply rates show no significant correlation with activity. With this study we expand previously published results on the temporal variation of solar p-mode parameters. Our results will be helpful to future studies of the excitation and damping of p modes, i.e., the interplay between convection, magnetic field, and resonant acoustic oscillations.     

The Cadmium Zinc Telluride Imager on AstroSat

The Cadmium Zinc Telluride Imager (CZTI) is a high energy, wide-field imaging instrument on AstroSat. CZTI’s namesake Cadmium Zinc Telluride detectors cover an energy range from 20 keV to \(>200\) keV, with 11% energy resolution at 60 keV. The coded aperture mask attains an angular resolution of 17\(^\prime \) over a 4.6\(^\circ \) \(\times \) 4.6\(^\circ \)  (FWHM) field-of-view. CZTI functions as an open detector above 100 keV, continuously sensitive to GRBs and other transients in about 30% of the sky. The pixellated detectors are sensitive to polarization above \(\sim \)100 keV, with exciting possibilities for polarization studies of transients and bright persistent sources. In this paper, we provide details of the complete CZTI instrument, detectors, coded aperture mask, mechanical and electronic configuration, as well as data and products.     

Dynamics of Large-Scale Solar-Wind Streams Obtained by the Double Superposed Epoch Analysis: 3. Deflection of the Velocity Vector

This work is a continuation of our previous articles (Yermolaev et al. in J. Geophys. Res.120, 7094, 2015 and Yermolaev et al. in Solar Phys.292, 193, 2017), which describe the average temporal profiles of interplanetary plasma and field parameters in large-scale solar-wind (SW) streams: corotating interaction regions (CIRs), interplanetary coronal mass ejections (ICMEs, including both magnetic clouds (MCs) and ejecta), and sheaths as well as interplanetary shocks (ISs). Changes in the longitude angle, \(\varphi\), in CIRs from ?2 to \(2^{\circ}\) agree with earlier results (e.g. Gosling and Pizzo, 1999). We have also analyzed the average temporal profiles of the bulk velocity angles in sheaths and ICMEs. We have found that the angle \(\varphi\) in ICMEs changes from 2 to \(-2^{\circ}\), while in sheaths it changes from ?2 to \(2^{\circ}\) (similar to the change in CIRs), i.e. the angle in CIRs and sheaths deflects in the opposite sense to ICMEs. When averaging the latitude angle \(\vartheta\) on all the intervals of the chosen SW types, the angle \(\vartheta\) is almost constant at \({\sim}\,1^{\circ}\). We made for the first time a selection of SW events with increasing and decreasing \(\vartheta\) and found that the average \(\vartheta\) temporal profiles in the selected events have the same “integral-like” shape as for \(\varphi\). The difference in \(\varphi\) and \(\vartheta\) average profiles is explained by the fact that most events have increasing profiles for the angle in the ecliptic plane as a result of solar rotation, while for the angle in the meridional plane, the numbers of events with increasing and decreasing profiles are equal.