Spectral Line Selection for HMI: A Comparison of Fe I 6173 Å and Ni I 6768 Å

We present a study of two spectral lines, Fe I 6173 Å and Ni I 6768 Å, that were candidates to be used in the Helioseismic and Magnetic Imager (HMI) for observing Doppler velocity and the vector magnetic field. The line profiles were studied using the Mt. Wilson Observatory, the Advanced Stokes Polarimeter and the Kitt Peak-McMath Pierce telescope and one-meter Fourier transform spectrometer atlas. Both Fe I and Ni I profiles have clean continua and no blends that threaten instrument performance. The Fe I line is 2% deeper, 15% narrower, and has a 6% smaller equivalent width than the Ni I line. The potential of each spectral line to recover pre-assigned solar conditions is tested using a least-squares minimization technique to fit Milne-Eddington models to tens of thousands of line profiles that have been sampled at five spectral positions across the line. Overall, the Fe I line has a better performance than the Ni I line for vector-magnetic-field retrieval. Specifically, the Fe I line is able to determine field strength, longitudinal and transverse flux four times more accurately than the Ni I line in active regions. Inclination and azimuthal angles can be recovered to ≈2^° above 600 Mx cm^?2 for Fe I and above 1000 Mx cm^?2 for Ni I. Therefore, the Fe I line better determines the magnetic-field orientation in plage, whereas both lines provide good orientation determination in penumbrae and umbrae. We selected the Fe I spectral line for use in HMI due to its better performance for magnetic diagnostics while not sacrificing velocity information. The one exception to the better performance of the Fe I line arises when high field strengths combine with high velocities to move the spectral line beyond the effective sampling range. The higher g _eff of Fe I means that its useful range of velocity values in regions of strong magnetic field is smaller than Ni I.     

Remarks concerning Ward's ‘the latitudinal motion of sunspots and solar meridional circulations’

Oscillator strengths are calculated for 259 lines of Ti i by taking configuration interaction into account in a somewhat simplified treatment. Radial integrals are obtained by an adaptation of the scaled Thomas-Fermi method. The great majority of selected lines originate from slightly perturbed terms. From a satisfactory comparison of our g \({\text{f}}\) -values with recent experimental data and with solar results in the visible region, we have been able to extend the work for some infrared lines. Very few transition probabilities were known for Ti i in that spectral range. On the basis of our oscillator strengths, a mean value logN _ti = 4.88 ± 0.12 (in the usual scale), is proposed for the solar photospheric abundance, in agreement with the meteoritic value.     

DLA abundances in the CUBES’s spectral window

Absorption systems observed along the line of sights to distant quasars are observed at all redshifts and the full range of the electromagnetic spectrum is needed to recover the variety of transitions of different elements. However, some important elements are found within the Lyman forest and their absorption line profiles need to be analyzed against the presence of possible Ly-α contamination. Considering the cosmological evolution of the number density of hydrogen clouds, the probability to detect uncontaminated metal lines is higher in the UV-Optical region exploited by CUBES. The list of these elements includes some important ones such as D, H₂, O?i, N?i, O?vi, Ar?i, P?ii, C?ii, S?ii and B?ii. The determination of some of them in the Damped Ly-α galaxies and their astronomical interest are briefly discussed.     

Coronal Diagnostics from Narrowband Images Around 30.4 nm

Images taken in the band centered at 30.4 nm are routinely used to map the radiance of the He?ii Ly?α line on the solar disk. That line is one of the strongest, if not the strongest, line in the EUV observed in the solar spectrum, and one of the few lines in that wavelength range providing information on the upper chromosphere or lower transition region. However, when observing the off-limb corona, the contribution from the nearby Si?xi 30.3 nm line can become significant. In this work we aim at estimating the relative contribution of those two lines in the solar corona around the minimum of solar activity. We combine measurements from CDS taken in August 2008 with temperature and density profiles from semiempirical models of the corona to compute the radiances of the two lines, and of other representative coronal lines (e.g. Mg?x 62.5 nm, Si?xii 52.1 nm). Considering both diagnosed quantities from line ratios (temperatures and densities) and line radiances in absolute units, we obtain a good overall match between observations and models. We find that the Si?xi line dominates the He?ii line from just above the limb up to ≈?2?R _⊙ in streamers, while its contribution to narrowband imaging in the 30.4 nm band is expected to become smaller, even negligible in the corona beyond ≈?2?–?3?R _⊙, the precise value being strongly dependent on the coronal temperature profile.     

Analysis of the intensities and profiles of the spectral line Mg xii 8.42 Å in the solar X-ray spectrum

High resolution profiles of the Mg xii 8.42 Å line in the solar X-ray spectrum were recorded from the Intercosmos 7 satellite. The Mg xii line intensity provides a sensitive indicator of the hot plasma content (T ? 3 × 10⁶ K) in coronal condensations and X-ray flare volumes. The ratio of the line intensity to the intensity of the adjacent continuum has been used to compute approximate thermal models of the emitting regions. For all the investigated coronal condensations the temperature distribution of plasma has been found to be a function monotonically decreasing with temperature. But for some X-ray bursts there occurred a distinct excess of the hot plasma of temperature between 6–10 × 10⁶K. FWHM values of the Mg xii line profiles have been used to estimate ion temperature in the emitting regions.     

A Statistical Study on Photospheric Magnetic Nonpotentiality of Active Regions and Its Relationship with Flares During Solar Cycles 22?–?23

A statistical study is carried out on the photospheric magnetic nonpotentiality in solar active regions and its relationship with associated flares. We select 2173 photospheric vector magnetograms from 1106 active regions observed by the Solar Magnetic Field Telescope at Huairou Solar Observing Station, National Astronomical Observatories of China, in the period of 1988??C?2008, which covers most of the 22nd and 23rd solar cycles. We have computed the mean planar magnetic shear angle ( $\overline{\Delta\phi}$ ), mean shear angle of the vector magnetic field ( $\overline{\Delta\psi}$ ), mean absolute vertical current density ( $\overline{|J_{z}|}$ ), mean absolute current helicity density ( $\overline{|h_{\mathrm{c}}|}$ ), absolute twist parameter (|?? _av|), mean free magnetic energy density ( $\overline{\rho_{\mathrm{free}}}$ ), effective distance of the longitudinal magnetic field (d _E), and modified effective distance (d _Em) of each photospheric vector magnetogram. Parameters $\overline{|h_{\mathrm{c}}|}$ , $\overline{\rho_{\mathrm{free}}}$ , and d _Em show higher correlations with the evolution of the solar cycle. The Pearson linear correlation coefficients between these three parameters and the yearly mean sunspot number are all larger than 0.59. Parameters $\overline {\Delta\phi}$ , $\overline{\Delta\psi}$ , $\overline{|J_{z}|}$ , |?? _av|, and d _E show only weak correlations with the solar cycle, though the nonpotentiality and the complexity of active regions are greater in the activity maximum periods than in the minimum periods. All of the eight parameters show positive correlations with the flare productivity of active regions, and the combination of different nonpotentiality parameters may be effective in predicting the flaring probability of active regions.     

Lifetimes of some excited states in the rare earths: La ii,Ce ii,Pr ii,Nd ii,Sm ii,Yb i,Yb ii,and Lu ii

Radiative lifetimes for excited states in La ii, Ce ii, Pr ii, Nd ii, Sm ii, Yb i, Yb ii, and Lu ii have been determined by means of the beam-foil technique or the zero-field level-crossing method. The lifetimes for La, Ce, Pr, Nd, Sm, and Yb are shorter than those computed by summing the transition probabilities of Corliss and Bozman by a factor of up to ~5. The large discrepancies between the abundance of La, Ce, Pr, Nd, and Sm in the solar photosphere and in meteorites are eliminated or greatly reduced if the abundance determinations of the solar photosphere are based upon the gf values of Corliss and Bozman, corrected for by the present lifetimes.     

Normality condition in the ideal resonance problem

The Ideal Resonance Problem, defined by the Hamiltonian $$F = B(y) + 2\mu ^2 A(y)\sin ^2 x,\mu \ll 1,$$ has been solved in Garfinkelet al. (1971). As a perturbed simple pendulum, this solution furnishes a convenient and accurate reference orbit for the study of resonance. In order to preserve the penduloid character of the motion, the solution is subject to thenormality condition, which boundsAB" andB' away from zero indeep and inshallow resonance, respectively. For a first-order solution, the paper derives the normality condition in the form $$pi \leqslant max(|\alpha /\alpha _1 |,|\alpha /\alpha _1 |^{2i} ),i = 1,2.$$ Herep _i are known functions of the constant ‘mean element’y', α is the resonance parameter defined by $$\alpha \equiv - {\rm B}'/|4AB\prime \prime |^{1/2} \mu ,$$ and $$\alpha _1 \equiv \mu ^{ - 1/2}$$ defines the conventionaldemarcation point separating the deep and the shallow resonance regions. The results are applied to the problem of the critical inclination of a satellite of an oblate planet. There the normality condition takes the form $$\Lambda _1 (\lambda ) \leqslant e \leqslant \Lambda _2 (\lambda )if|i - tan^{ - 1} 2| \leqslant \lambda e/2(1 + e)$$ withΛ ₁, andΛ ₂ known functions of λ, defined by $$\begin{gathered} \lambda \equiv |\tfrac{1}{5}(J_2 + J_4 /J_2 )|^{1/4} /q, \hfill \\ q \equiv a(1 - e). \hfill \\ \end{gathered}$$      

Evolution of the \mathcal {L}_1 halo family in the radial solar sail circular restricted three-body problem

We present a detailed investigation of the dramatic changes that occur in the \(\mathcal {L}_1\) halo family when radiation pressure is introduced into the Sun–Earth circular restricted three-body problem (CRTBP). This photo-gravitational CRTBP can be used to model the motion of a solar sail orientated perpendicular to the Sun-line. The problem is then parameterized by the sail lightness number, the ratio of solar radiation pressure acceleration to solar gravitational acceleration. Using boundary-value problem numerical continuation methods and the AUTO software package (Doedel et al. in Int J Bifurc Chaos 1:493–520, 1991) the families can be fully mapped out as the parameter \(\beta \) is increased. Interestingly, the emergence of a branch point in the retrograde satellite family around the Earth at \(\beta \approx 0.0387\) acts to split the halo family into two new families. As radiation pressure is further increased one of these new families subsequently merges with another non-planar family at \(\beta \approx 0.289\) , resulting in a third new family. The linear stability of the families changes rapidly at low values of \(\beta \) , with several small regions of neutral stability appearing and disappearing. By using existing methods within AUTO to continue branch points and period-doubling bifurcations, and deriving a new boundary-value problem formulation to continue the folds and Krein collisions, we track bifurcations and changes in the linear stability of the families in the parameter \(\beta \) and provide a comprehensive overview of the halo family in the presence of radiation pressure. The results demonstrate that even at small values of \(\beta \) there is significant difference to the classical CRTBP, providing opportunity for novel solar sail trajectories. Further, we also find that the branch points between families in the solar sail CRTBP provide a simple means of generating certain families in the classical case.     

Coupling between corotation and Lindblad resonances in the presence of secular precession rates

We investigate the dynamics of two satellites with masses $\mu _s$ and $\mu '_s$ orbiting a massive central planet in a common plane, near a first order mean motion resonance $m+1{:}m$ (m integer). We consider only the resonant terms of first order in eccentricity in the disturbing potential of the satellites, plus the secular terms causing the orbital apsidal precessions. We obtain a two-degrees-of-freedom system, associated with the two critical resonant angles $\phi = (m+1)\lambda ' -m\lambda - \varpi $ and $\phi '= (m+1)\lambda ' -m\lambda - \varpi '$ , where $\lambda $ and $\varpi $ are the mean longitude and longitude of periapsis of $\mu _s$ , respectively, and where the primed quantities apply to $\mu '_s$ . We consider the special case where $\mu _s \rightarrow 0$ (restricted problem). The symmetry between the two angles $\phi $ and $\phi '$ is then broken, leading to two different kinds of resonances, classically referred to as corotation eccentric resonance (CER) and Lindblad eccentric Resonance (LER), respectively. We write the four reduced equations of motion near the CER and LER, that form what we call the CoraLin model. This model depends upon only two dimensionless parameters that control the dynamics of the system: the distance $D$ between the CER and LER, and a forcing parameter $\epsilon _L$ that includes both the mass and the orbital eccentricity of the disturbing satellite. Three regimes are found: for $D=0$ the system is integrable, for $D$ of order unity, it exhibits prominent chaotic regions, while for $D$ large compared to 2, the behavior of the system is regular and can be qualitatively described using simple adiabatic invariant arguments. We apply this model to three recently discovered small Saturnian satellites dynamically linked to Mimas through first order mean motion resonances: Aegaeon, Methone and Anthe. Poincaré surfaces of section reveal the dynamical structure of each orbit, and their proximity to chaotic regions. This work may be useful to explore various scenarii of resonant capture for those satellites.     

On the Formation Height of the SDO/HMI Fe 6173 ? Doppler Signal

The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) is designed to study oscillations and the magnetic field in the solar photosphere. It observes the full solar disk in the Fe?i absorption line at 6173 Å. We use the output of a high-resolution, 3D, time-dependent, radiation-hydrodynamic simulation based on the CO ⁵ BOLD code to calculate profiles F(??,x,y,t) for the Fe?i 6173 Å line. The emerging profiles F(??,x,y,t) are multiplied by a representative set of HMI filter-transmission profiles R _i (??, 1??i??6) and filtergrams I _i (x,y,t; 1??i??6) are constructed for six wavelengths. Doppler velocities V _HMI(x,y,t) are determined from these filtergrams using a simplified version of the HMI pipeline. The Doppler velocities are correlated with the original velocities in the simulated atmosphere. The cross-correlation peaks near 100 km, suggesting that the HMI Doppler velocity signal is formed rather low in the solar atmosphere. The same analysis is performed for the SOHO/MDI Ni?i line at 6768 Å. The MDI Doppler signal is formed slightly higher at around 125 km. Taking into account the limited spatial resolution of the instruments, the apparent formation height of both the HMI and MDI Doppler signal increases by 40 to 50 km. We also study how uncertainties in the HMI filter-transmission profiles affect the calculated velocities.     

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.     

Velocities and Linewidths in the Network and Cell Interiors of a Polar Coronal Hole Compared with the Quiet Sun

The relative Doppler velocities and linewidths in a polar coronal hole and the nearby quiet-Sun region have been obtained from the Solar and Heliospheric Observatory (SOHO)/Coronal Diagnostic Spectrometer (CDS) observations using emission lines originating at different heights in the solar atmosphere from the lower transition region (TR) to the low solar corona. The observed region is separated into the network and the cell interior, and the behavior of the above parameters were examined in the different regions. It has been found that the histograms of Doppler velocity and width are generally broader in the cell interior than in the network. The histograms of Doppler velocities of the network and cell interior do not show significant differences in most cases. However, in the case of the quiet Sun, the Doppler velocities of the cell interior are more blueshifted than those of the network for the lowermost line He?ii 304 Å, and an opposite behavior is seen for the uppermost line Mg?ix 368 Å. The linewidth histograms show that the network–cell difference is more prominent in the coronal hole. The network has a significantly larger linewidth than the cell interior for the lowermost TR line He?ii 304 Å for the quiet Sun. For the coronal hole, this is true for the three lower TR lines: He?ii 304 Å, O?iii 599 Å, and O?v 630 Å. We also obtained the correlations between the relative Doppler velocity and the width. A mild positive correlation is found for the lowermost transition-region line He?ii 304 Å, which decreases even more or become insignificant for the intermediate lines. For the low coronal line Mg?ix 368 Å, the correlation becomes strongly negative. This might be caused by standing waves or waves propagating from the lower to the upper solar atmosphere. The results may have implications for the generation of the fast solar wind and coronal heating.     

An evaluation of the possibility of studying flare plasma turbulence using the satellites of Hei line forbidden components

Using the Baranger-Mozer method, we explore the possibility of diagnosing the flare plasma of forbidden Hei lines, that permits the determination of the plasma oscillation frequency and noise level. Examination of the Hei lines observed in solar flare has led us to conclude that:

1. the appearance of satellites of forbidden components in the flares spectrum, due to turbulent electric fields, is the most probable for Hei 3819.606 Å lines;
2. the Baranger-Mozer method is more sensitive to the high-frequency component of turbulent fields than to the low-frequency ones;
3. the upper limit of the turbulent oscillation level in flares is evaluated.

In the spectrum of the solar flare of 26 September, 1963 we detected satellites of the forbidden component of the 3820 Å line and used its relative intensity to derive the level of low-frequency oscillations (～1.5 kVcm^-1).     

Optical spectral decomposition of NGC 4051

Considering the host galaxy contribution, a spectral decomposition method is used to reanalyzed the archive data of optical spectra for a narrow line Seyfert 1 galaxy, NGC 4051. The light curves of the continuum f _λ (5100 Å), and Hβ, He ii, Fe ii emission lines are given. We find strong flux correlations between line emissions of Hβ, He ii, Fe ii and the continuum f _λ (5100 Å). These low-ionization lines (Hβ, Fe ii, He ii) have “inverse” intrinsic Baldwin effects. Using the methods of the cross-correlation function and the Monte Carlo simulation, we find the time delays, with respect to the continuum, are $3.45^{+12.0}_{-0.5}~\mbox{days}$ with the probability of 34 % for the intermediate component of Hβ, $6.45^{+13.0}_{-1.0}~\mbox{days}$ with the probability of 65 % for the intermediate component of He ii. From these intermediate components of Hβ and He ii, the calculated central black hole masses are $0.86^{+4.35}_{-0.33}\times 10^{6}$ and $0.82^{+3.12}_{-0.45}\times 10^{6}~M_{\odot }$ . We also find that the time delays for Fe ii are $9.7^{+3.0}_{-5.0}~\mbox{days}$ with the probability of 36 %, $8.45^{+1.0}_{-2.0}~\mbox{days}$ with the probability of 18 % for the total epochs and “subset 1” data, respectively. It seems that the Fe ii emission region is outside of the Hβ emission region.     

Asymmetries in stokes profiles of magnetic lines: A linear analysis in terms of velocity gradients

A linear analysis of the asymmetries in Stokes profiles of magnetic lines is performed. The asymmetries in the linear and circular polarization profiles are characterized by suitable quantities, \(\delta \tilde Q\) and \(\delta \tilde V\) , strictly related to observed profiles. The response functions of \(\delta \tilde Q\) and \(\delta \tilde V\) to velocity fields are introduced and computed for various configurations of the magnetic field vector in a Milne-Eddington atmosphere. Some conclusions are drawn as to the importance of the asymmetries in Stokes profiles for recovering the velocity gradients from observations.     

The potassium abundance in the solar photosphere

High precision center-limb spectrograms of the K i resonance doublet line at λ 7699 Å were used to study the line formation and to determine the abundance of potassium in the solar atmosphere. The LTE assumption is not valid for these lines. Synthetic profiles computed in NLTE reproduce very well the observed center-limb line behaviour and yield log? _K = 5.14±0.10 for the solar abundance of potassium (on the scale of log? _H = 12 for Hydrogen).     

Physical properties of X-ray gas in galaxy cluster CL0024+17

We analyzed the X-ray data obtained by the Chandra telescope for the galaxy cluster CL0024+17 (z = 0.39). The mean temperature of the cluster is estimated (kT = 4.35 _?0.44 ^+0.51 keV) and the surface brightness profile is derived. We generated the mass and density profiles for dark matter and gas using numerical simulations and the Navarro-Frenk-White dark matter density profile (Navarro et al., 1995) for a spherically symmetric cluster in which gas is in hydrostatic equilibrium with the cluster field. The total mass of the cluster is estimated to be M ₂₀₀ = 3.51 _?0.47 ^+0.38 × 10 _Sun ¹⁴ within a radius of R ₂₀₀ = 1.24 _?0.17 ^+0.12 Mpc of the cluster center. The contribution of dark matter to the total mass of the cluster is estimated as ${{M_{200_{DM} } } \mathord{\left/ {\vphantom {{M_{200_{DM} } } {M_{tot} }}} \right. \kern-0em} {M_{tot} }} = 0.89$ .     

Sun–Earth L_{1} and L_{2} to Moon transfers exploiting natural dynamics

This paper examines the design of transfers from the Sun–Earth libration orbits, at the \(L_{1}\) and \(L_{2}\) points, towards the Moon using natural dynamics in order to assess the feasibility of future disposal or lifetime extension operations. With an eye to the probably small quantity of propellant left when its operational life has ended, the spacecraft leaves the libration point orbit on an unstable invariant manifold to bring itself closer to the Earth and Moon. The total trajectory is modeled in the coupled circular restricted three-body problem, and some preliminary study of the use of solar radiation pressure is also provided. The concept of survivability and event maps is introduced to obtain suitable conditions that can be targeted such that the spacecraft impacts, or is weakly captured by, the Moon. Weak capture at the Moon is studied by method of these maps. Some results for planar Lyapunov orbits at \(L_{1}\) and \(L_{2}\) are given, as well as some results for the operational orbit of SOHO.     

Variability of Fe ii in Two NLS1s, PG 1700+815 and NGC 4051

We analyze the spectral variability for two narrow line Seyfert 1 galaxies, PG 1700+518 and NGC 4051 using the spectral decomposition method. We focus on their optical Fe ii variability to investigate the origin of Fe ii in AGNs. For PG 1700+518, we find that the Fe ii size is about 200 light-days, which is consistent with the Hβ size derived from the empirical R–L relation. For NGC 4051, the [O iii] 5007 Å flux is strongly correlated with continuum flux, suggesting that we should recalibrate the spectral flux on a scale defined by [O iii] flux. The corrected light curves of Fe ii, Hβ, He ii, f _λ (5100 Å) are given here. A detailed analysis will be given in the near future.