Line-of-Sight Observables Algorithms for the <Emphasis Type="Italic">Helioseismic and Magnetic Imager</Emphasis> (HMI) Instrument Tested with <Emphasis Type="Italic">Interferometric Bidimensional Spectrometer</Emphasis> (IBIS) Observations

The Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory produces line-of-sight (LOS) observables (Doppler velocity, magnetic-field strength, Fe i line width, line depth, and continuum intensity) as well as vector magnetic-field maps at the solar surface. The accuracy of LOS observables is dependent on the algorithm used to translate a sequence of HMI filtergrams into the corresponding observables. Using one hour of high-cadence imaging spectropolarimetric observations of a sunspot in the Fe i line at 6173 Å through the Interferometric Bidimensional Spectrometer installed at the Dunn Solar Telescope, and the Milne–Eddington inversion of the corresponding Stokes vectors, we test the accuracy of the observables algorithm currently implemented in the HMI data-analysis pipeline: the MDI-like algorithm. In an attempt to improve the accuracy of HMI observables, we also compare this algorithm to others that may be implemented in the future: a least-squares fit with a Gaussian profile, a least-squares fit with a Voigt profile, and the use of second Fourier coefficients in the MDI-like algorithm.     

Spatial Size and Plasma Variables of RHESSI Flares

We have analysed 64 flares observed with GOES and RHESSI in the 3.1?–?24.8 keV band (0.5?–?4 Å). Flares were randomly chosen to represent different GOES classes, between B1 and M6. RHESSI was used to image the flaring region on the surface of the Sun. We derived the spatial area of the flare on the surface of the Sun from the imaging observations, scaled it dimensionally to volume, and used the spectroscopically derived emission measure to obtain several flare parameters. We experimented with several imaging methods and selected the use of 50% maximum image photon flux contours to define the flare area (F _50%). Most of the flares showed a single spherical loop-top source. The volume measurement for V, temperature T, and electron density N produced power indices that showed no correlation within the boundaries of error. Larger flares by loop-top source volume are thus neither hotter nor denser. The background-subtracted GOES flux?–?RHESSI Total Emission Measure (TEM _RHESSI) and TEM _GOES?–?TEM _RHESSI dependencies were in agreement with the instrument characteristics and earlier studies. Nonthermal flux was noticed to increase with thermal energy and TEM, which can be said to agree with the “Big Flare Syndrome,” with nonthermal photon flux being considered as one flare manifestation.     

Behaviour of physical parameters in extended gravity with hyperbolic function

In this paper, we have constructed the cosmological model of the universe in f(R, T) theory of gravity in a Bianchi type \(\mathrm{VI}_h\) universe for the functional f(R, T) in the form \(f(R,T)=\mu R+\mu T\), where R and T are respectively Ricci scalar and trace of energy momentum tensor and \(\mu \) is a constant. We have made use of the hyperbolic scale factor to find the physical parameters and metric potentials defined in the space-time. The physical parameters are constrained from different representative values to build up a realistic cosmological model aligned with the observational behaviour. The state finder diagnostic pair is found to be in the acceptable range. The energy conditions of the model are also studied.     

Imaging Spectropolarimeter for the Multi-Application Solar Telescope at Udaipur Solar Observatory: Characterization of Polarimeter and Preliminary Observations

The Multi-Application Solar Telescope (MAST) is a 50 cm off-axis Gregorian telescope that has recently become operational at the Udaipur Solar Observatory (USO). An imaging spectropolarimeter is being developed as one of the back-end instruments of MAST to gain a better understanding of the evolution and dynamics of solar magnetic and velocity fields. This system consists of a narrow-band filter and a polarimeter. The polarimeter includes a linear polarizer and two sets of liquid crystal variable retarders (LCVRs). The instrument is intended for simultaneous observations in the spectral lines 6173 Å and 8542 Å, which are formed in the photosphere and chromosphere, respectively. In this article, we present results from the characterization of the LCVRs for the spectral lines of interest and the response matrix of the polarimeter. We also present preliminary observations of an active region obtained using the spectropolarimeter. For verification purposes, we compare the Stokes observations of the active region obtained from the Helioseismic Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) with that of MAST observations in the spectral line 6173 Å. We find good agreement between the two observations, considering the fact that MAST observations are limited by seeing.     

Evolutionary studies of the young star clusters: NGC 1960, NGC 2453 and NGC 2384

We report the analysis of the young star clusters NGC 1960, NGC 2453 and NGC 2384 observed in the J (1.12 μm), H (1.65 μm) and K′ (2.2 μm) bands. Estimates of reddening, distance and age as E(B?V)=0.25, d=1380 pc and t=31.6 to 125 Myr for NGC 1960, E(B?V)=0.47, d=3311 pc and t=40 to 200 Myr for NGC 2453 and E(B?V)=0.25, d=3162 pc and t=55 to 125 Myr for NGC 2384 have been obtained. Also, we have extended the color–magnitude diagrams of these clusters to the fainter end and thus extended the luminosity functions to fainter magnitudes. The evolution of the main sequence and luminosity functions of these clusters have been compared with themselves as well as Lyngå 2 and NGC 1582.     

Site Characterization Using Solar Hα Images

A Multi-Application Solar Telescope (MAST) is proposed to be installed at the lake site (Lake Fatehsagar) of Udaipur Solar Observatory (USO) in India. The lake site Observatory of USO is located on a small island in the middle of the lake. To determine the optimum size of the MAST (for use with an adaptive optics system), it was decided to quantify the seeing conditions prevailing at the lake site during the different months of the year. For this purpose, we have used short-exposure (3 ms) high-resolution Hα (6563 Å) images (spatial scale of ～0.55 arc sec per pixel) of the Sun taken in burst mode with the 15-cm refractor Spar telescope located at the lake site of USO. Spectral ratio technique as reported by von der Lühe (1984, J. Opt. Soc. Am. A1, 510) has been used to estimate the Fried’s parameter (r ₀) at this site, which gives the quantitative measure of astronomical seeing. This study has been carried out daily on an hourly basis during 4:30?–?10:30 UT over the months January?–?June of the years 2005 and 2006 to understand the diurnal and seasonal variations in r ₀ at this site. It is noteworthy that the lake was almost dry during the observing period in 2005, while it overflowed during our observations in 2006 because of abundant monsoon rains. The seeing in the presence of water shows improvement in r ₀ by about 1.0 cm with respect to the previous year’s dry condition and mean r ₀ varies between 4.0 and 4.5 cm as evident from the data obtained between January and June, 2006.     

The matter in the Big-Bang model is dust and not any arbitrary perfect fluid!

We consider a spherically symmetric general relativistic perfect fluid in its comoving frame. It is found that, by integrating the local energy momentum conservation equation, a general form of g ₀₀ can be obtained. During this study, we get a cue that an adiabatically evolving uniform density isolated sphere having ρ(r,t)=ρ ₀(t), should comprise “dust” having p ₀(t)=0; as recently suggested by Durgapal and Fuloria (J. Mod. Phys. 1:143, 2010) In fact, we offer here an independent proof to this effect. But much more importantly, we find that for the homogeneous and isotropic Friedmann-Robertson-Walker (FRW) metric having p(r,t)=p ₀(t) and ρ(r,t)=ρ ₀(t), \(g_{00} = e^{-2p_{0}/(p_{0} +\rho_{0})}\). But in general relativity (GR), one can choose an arbitrary t→t _?=f(t) without any loss of generality, and thus set g ₀₀(t _?)=1. And since pressure is a scalar, this implies that p ₀(t _?)=p ₀(t)=0 in the Big-Bang model based on the FRW metric. This result gets confirmed by the fact the homogeneous dust metric having p(r,t)=p ₀(t)=0 and ρ(r,t)=ρ ₀(t) and the FRW metric are exactly identical. In other words, both the cases correspond to the same Einstein tensor \(G^{a}_{b}\) because they intrinsically have the same energy momentum tensor \(T^{a}_{b}=\operatorname {diag}[\rho_{0}(t), 0,0, 0]\).     

Simultaneous seeing measurement through the Subaru Telescope in the visible and near-infrared bands for the wavelength dependence evaluation

Stellar images have been obtained under natural seeing at visible and near-infrared wavelengths simultaneously through the Subaru Telescope at Mauna Kea. The image quality is evaluated by the full-width at the half-maximum (FWHM) of the stellar images. The observed ratio of FWHM in the V-band to the K-band is 1.54 ± 0.17 on average. The ratio shows tendency to decrease toward bad seeing as expected from the outer scale influence, though the number of the samples is still limited. The ratio is important for simulations to evaluate the performance of a ground-layer adaptive optics system at near-infrared wavelengths based on optical seeing statistics. The observed optical seeing is also compared with outside seeing to estimate the dome seeing of the Subaru Telescope.     

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)}.
       
    

     

Contractivity-preserving explicit multistep Hermite–Obrechkoff series differential equation solvers

New optimal, contractivity-preserving (CP), explicit, d-derivative, k-step Hermite–Obrechkoff series methods of order p up to \(p=20\), denoted by CP HO(d, k, p), with nonnegative coefficients are constructed. These methods are used to solve nonstiff first-order initial value problems \(y'=f(t,y)\), \(y(t_0)=y_0\). The upper bound \(p_u\) of order p of HO(d, k, p) can reach, approximately, as high as 2.4 times the number of derivatives d. The stability regions of HO(d, k, p) have generally a good shape and grow with decreasing \(p-d\). We, first, note that three selected CP HO methods: 4-derivative 7-step HO of order 13, denoted by HO(4, 7, 13), 5-derivative 6-step HO of order 13, denoted by HO(5, 6, 13), and 9-derivative 2-step HO of order 13, denoted by CMDAHO(13) compare favorably with Adams–Cowell of order 13, denoted by AC(13), in solving standard N-body problems over an interval of 1000 periods on the basis of the relative error of energy as a function of the CPU time. Next, the three HO methods compare positively with AC(13) in solving standard N-body problems on the basis of the growth of relative positional error and relative energy error over 10, 000 periods of integration. Finally, these three methods compare also well with P-stable methods of Cash and Franco et al. on some quasi periodic, second-order linear and nonlinear problems. The coefficients of selected HO methods are listed in the appendix.     

ASTRONIRCAM—the infrared camera-spectrograph for the 2.5-m telescope of SAI Caucasian observatory

ASTRONIRCAM is a cryogenic-cooled slit camera-spectrograph for the spectral range 1–2.5 μm installed at the Nasmyth focus of the 2.5-meter telescope of the Caucasian observatory of the Sternberg Astronomical Institute of Lomonosov Moscow State University. The instrument is equipped with a HAWAII-2RG 2048×2048 HgCdTe array. Grisms are used as dispersive elements. In the photometric mode ASTRONIRCAM allows for extended astronomical object imaging in a 4.′6 × 4.′6 field of view with a 0.269 arcsec/pixel scale in standard photometric bands J, H, K, and K _s as well as in the narrow-band filters centered on the lines CH₄, [Fe II], H₂ v=1-0 S(1), Br _γ , and CO. In the spectroscopic mode, ASTRONIRCAM takes spectra of extended or point-like sources with a spectral resolution of R = λ/Δλ ≤ 1200. The general design, optical system, detector electronics and readout, amplification and digitization schemes are considered. The GAIN conversion factor measurement results are described as well as its dependence on the accumulated signal (nonlinearity).The full transmission of the atmosphere-to-detector train ranges from 40 to 50% in the wide-band photometry mode. The ASTRONIRCAMsensitivity at the 2.5-m telescope is characterized by the limiting J = 20, K = 19 stellar magnitudes measured with a 10% precision and 15 minute integration for 1″ atmospheric seeing conditions. References to the first results based on ASTRONIRCAM observations are given.     

Imaging Spectroscopy of a White-Light Solar Flare

We report observations of a white-light solar flare (SOL2010-06-12T00:57, M2.0) observed by the Helioseismic Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) and the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The HMI data give us the first space-based high-resolution imaging spectroscopy of a white-light flare, including continuum, Doppler, and magnetic signatures for the photospheric Fe i line at 6173.34 Å and its neighboring continuum. In the impulsive phase of the flare, a bright white-light kernel appears in each of the two magnetic footpoints. When the flare occurred, the spectral coverage of the HMI filtergrams (six equidistant samples spanning ±172 mÅ around nominal line center) encompassed the line core and the blue continuum sufficiently far from the core to eliminate significant Doppler crosstalk in the latter, which is otherwise a possibility for the extreme conditions in a white-light flare. RHESSI obtained complete hard X-ray and γ-ray spectra (this was the first γ-ray flare of Cycle 24). The Fe i line appears to be shifted to the blue during the flare but does not go into emission; the contrast is nearly constant across the line profile. We did not detect a seismic wave from this event. The HMI data suggest stepwise changes of the line-of-sight magnetic field in the white-light footpoints.     

On a family of well behaved perfect fluid balls as astrophysical objects in general relativity

A family of well behaved perfect fluid balls has been derived starting with the metric potential g ₄₄=B(1+Cr ²) ⁿ for all positive integral values of n. For n≥4, the members of this family are seen to satisfy the various physical conditions e.g. c ² ρ≥p≥0,dp/dr<0,dρ/dr<0, along with the velocity of sound \((\sqrt{dp/c^{2}d\rho} )< 1\) and the adiabatic index ((p+c ² ρ)/p)(dp/(c ² dρ))>1. Also the pressure, energy density, velocity of sound and ratio of pressure and energy density are of monotonically decreasing towards the pressure free interface (r=a). The fluid balls join smoothly with the Schwarzschild exterior model at r=a. The well behaved perfect fluid balls so obtained are utilised to construct the superdense star models with their surface density 2×10¹⁴  gm/cm³. We have found that the maximum mass of the fluid balls corresponding to various values of n are decreasing with the increasing values of n. Over all maximum mass for the whole family turns out to be 4.1848M _Θ and the corresponding radius as 19.4144 km while the red shift at the centre and red shift at surface as Z ₀=1.6459 and Z _a =0.6538 respectively this all happens for n=4. It is interesting to note that for higher values of n viz n≥170, the physical data start merging with that of Kuchowicz superdense star models and hence the family of fluid models tends to the Kuchowicz fluid models as n→∞. Consequently the maximum mass of the family of solution can not be less than 1.6096 M _Θ which is the maximum mass occupied by the Kuchowicz superdense ball. Hence each member of the family for n≥4 provides the astrophysical objects like White dwarfs, Quark star, typical neutron star.     

Ion acceleration and Alfvén wave generation at the Earth’s bow shock

The processes of ion acceleration and Alfvén wave generation by accelerated particles at the Earth’s bow shock are studied within a quasi-linear approach. Steady-state ion and wave spectra are shown to be established in a time of 0.3–4 h, depending on the background level of Alfvénic turbulence in the solar wind. The Alfvén waves produced by accelerated ions are confined within the frequency range 10^?2–1 Hz and their spectral peak with a wave amplitude βB ～ B comparable to the interplanetary magnetic field strength B corresponds to the frequency v = (2–3) × 10^?2 Hz. The high-frequency part of the wave spectrum (v > 0.2 Hz) undergoes damping by thermal ions. The calculated spectra of the accelerated ions and the Alfvén waves generated by them reproduce the main features observed in experiments.     

An Early Diagnostics of the Geoeffectiveness of Solar Eruptions from Photospheric Magnetic Flux Observations: The Transition from SOHO to SDO

In our previous articles (Chertok et al. in Solar Phys. 282, 175, 2013; Chertok et al. in Solar Phys. 290, 627, 2015), we presented a preliminary tool for the early diagnostics of the geoeffectiveness of solar eruptions based on the estimate of the total unsigned line-of-sight photospheric magnetic flux in accompanying extreme ultraviolet (EUV) arcades and dimmings. This tool was based on the analysis of eruptions observed during 1996?–?2005 with the Extreme-ultraviolet Imaging Telescope (EIT) and the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO). Empirical relationships were obtained to estimate the probable importance of upcoming space weather disturbances caused by an eruption, which just occurred, without data on the associated coronal mass ejections. In particular, it was possible to estimate the intensity of a non-recurrent geomagnetic storm (GMS) and Forbush decrease (FD), as well as their onset and peak times. After 2010?–?2011, data on solar eruptions are obtained with the Atmospheric Imaging Assembly (AIA) and the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). We use relatively short intervals of overlapping EIT–AIA and MDI–HMI detailed observations, and additionally, a number of large eruptions over the next five years with the 12-hour cadence EIT images to adapt the SOHO diagnostic tool to SDO data. We show that the adopted brightness thresholds select practically the same areas of arcades and dimmings from the EIT 195 Å and AIA 193 Å image, with a cross-calibration factor of 3.6?–?5.8 (5.0?–?8.2) for the AIA exposure time of 2.0 s (2.9 s). We also find that for the same photospheric areas, the MDI line-of-sight magnetic flux systematically exceeds the HMI flux by a factor of 1.4. Based on these results, the empirical diagnostic relationships obtained from SOHO data are adjusted to SDO instruments. Examples of a post-diagnostics based on SDO data are presented. As before, the tool is applicable to non-recurrent GMSs and FDs caused by nearly central eruptions from active regions, provided that the southern component of the interplanetary magnetic field near the Earth is predominantly negative, which is not predicted by this tool.     

Multi-product splitting and Runge-Kutta-Nyström integrators

The splitting of e^h(A+B) into a single product of e ^{h A} and e ^hB results in symplectic integrators when A and B are classical Lie operators. However, at high orders, a single product splitting, with exponentially growing number of operators, is very difficult to derive. This work shows that, if the splitting is generalized to a sum of products, then a simple choice of the basis product reduces the problem to that of extrapolation, with analytically known coefficients and only quadratically growing number of operators. When a multi-product splitting is applied to classical Hamiltonian systems, the resulting algorithm is no longer symplectic but is of the Runge-Kutta-Nyström (RKN) type. Multi-product splitting, in conjunction with a special force-reduction process, explains why at orders p = 4 and 6, RKN integrators only need p ? 1 force evaluations.     

Review of Image Quality Measures for Solar Imaging

Observations of the solar photosphere from the ground encounter significant problems caused by Earth’s turbulent atmosphere. Before image reconstruction techniques can be applied, the frames obtained in the most favorable atmospheric conditions (the so-called lucky frames) have to be carefully selected. However, estimating the quality of images containing complex photospheric structures is not a trivial task, and the standard routines applied in nighttime lucky imaging observations are not applicable. In this paper we evaluate 36 methods dedicated to the assessment of image quality, which were presented in the literature over the past 40 years. We compare their effectiveness on simulated solar observations of both active regions and granulation patches, using reference data obtained by the Solar Optical Telescope on the Hinode satellite. To create images that are affected by a known degree of atmospheric degradation, we employed the random wave vector method, which faithfully models all the seeing characteristics. The results provide useful information about the method performances, depending on the average seeing conditions expressed by the ratio of the telescope’s aperture to the Fried parameter, \(D/r_{0}\). The comparison identifies three methods for consideration by observers: Helmli and Scherer’s mean, the median filter gradient similarity, and the discrete cosine transform energy ratio. While the first method requires less computational effort and can be used effectively in virtually any atmospheric conditions, the second method shows its superiority at good seeing (\(D/r_{0}<4\)). The third method should mainly be considered for the post-processing of strongly blurred images.     

Transient Magnetic and Doppler Features Related to the White-Light Flares in NOAA 10486

Rapidly moving transient features have been detected in magnetic and Doppler images of super-active region NOAA 10486 during the X17/4B flare of 28 October 2003 and the X10/2B flare of 29 October 2003. Both these flares were extremely energetic white-light events. The transient features appeared during impulsive phases of the flares and moved with speeds ranging from 30 to 50 km?s^?1. These features were located near the previously reported compact acoustic (Donea and Lindsey, Astrophys. J. 630, 1168, 2005) and seismic sources (Zharkova and Zharkov, Astrophys. J. 664, 573, 2007). We examine the origin of these features and their relationship with various aspects of the flares, viz., hard X-ray emission sources and flare kernels observed at different layers: i) photosphere (white-light continuum), ii) chromosphere (Hα 6563 Å), iii) temperature minimum region (UV 1600 Å), and iv) transition region (UV 284 Å).     

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.     

Existence of wormhole solutions and energy conditions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

This paper is devoted to investigate the spherically symmetric wormhole models in f(R, T) gravity, where T and R are trace of stress energy tensor and the Ricci scalar, respectively. In this context, we discuss three distinct cases of fluid distributions viz, anisotropic, barotropic and isotropic matter contents. After considering the exponential f(R, T) model, the behavior of energy conditions are analyzed that will help us to explore the general conditions for wormhole geometries in this gravity. It is inferred that the usual matter in the throat could obey the energy conditions but the gravitational field emerging from higher order terms of modified gravity favor the existence of the non-standard geometries of wormholes. The stability as well as the existence of wormholes are also analyzed in this theory.