A Note on Computation of Relative Magnetic-Helicity Flux Across the Photosphere

A number of investigations of the rate of relative magnetic-helicity transport across the photosphere [ ${{{\rm d} H}/{{\rm d}t}}|_{S}$ ] have reported differences in the estimates computed from two different formulations of the relative-helicity flux-density proxy G _A and G _θ . There have been suggestions that G _θ is a more robust helicity-flux density proxy and that the differences in the estimates of ${{{\rm d} H}/{{\rm d}t}}|_{S}$ are caused by biases in G _A, noise, and/or the boundary conditions. In this note, we prove that the differences are caused by the inconsistent choice of boundary conditions in the explicit or implicit Green’s function [ $\mathcal{G}(\mathbf {x},\mathbf{x}')$ ] used for computing G _A and G _θ when comparing the helicity-flux estimates based on G _A and G _θ . When the boundary conditions in $\mathcal{G}$ are chosen consistently, the two helicity-flux density proxies, [G _A and G _θ ] produce essentially identical results for the rate of helicity transport across the photosphere. They also yield essentially identical results for the rate of helicity transport of the shearing and advection terms separately. Using MHD simulation, HMI observational data, and Monte Carlo simulations of noise we show that this result is robust. Neither the shape of the active region, nor the shape of the boundary, nor data noise causes any difference in the rate of helicity transport computed via G _A and G _θ .     

The work of the diode array: He 10 830 observations of spicules and subflares

At a spatial resolution of 1″ and with spectral passbands of 0.25–0.47 Å, the chromospheric fine structure was studied with an array of 512 silicon photodiodes. The high quantum efficiency of the diodes in the near infrared allowed low noise spectroheliograms to be constructed from observations in the lines of H i, Ca ii, and He i. Magnetograms of the underlying photosphere were obtained simultaneously. Tachograms in the He 10830 Å line revealed 1″ points and elongated features that are interpreted as spicules seen against the disk. Active regions and filaments at 10830 are compared with Hα and Ca ii (8542 Å) features. Filament contrast increases with the proximity of bright plage. Twelve subflares were studied and in eight cases, 3–5″ kernels of He I emission appeared over small, growing pores or over 5″ patches of magnetic field emerging through the photosphere. All the subflares showed 10830 emission, contrary to established belief that the 10830 line goes into emission only in the largest flares. All the subflares included at least one emission kernel over regions where the photospheric magnetic field, as seen with a resolution of 1–2″, broke down into a mosaic of both polarities with 3–5″ diam. elements.     

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.     

Nova Monocerotis 2002 (V838 Mon) at early outburst stages

We obtained U BV R photometric and spectroscopic observations during the outburst of V838 Mon. Before its outburst, the B brightness of the star had been stable ( $\tilde15.^m 85$ ) for 45 years. This was a blue star with the color index $(B - V)_0 = - 0\mathop .\limits^m 03 \pm 0\mathop .\limits^m 1$ and may have been a cataclysmic variable. In the middle of March 2002, the outburst amplitude reached $8\mathop .\limits^m 1$ in B. The star has the counterpart V 1006/7 in M 31 in luminosity at maximum and in spectrum. The unusual spectrum at the premaximum stage originated in the expanding photosphere of a cool K-type giant. The expansion velocity of the photosphere was 150 km s^?1; the maximum velocity in the expanding stellar envelope reached 500 km s^?1. The absorption components of neutral metal lines were enhanced by a factor of 3 or 4 compared to a normal K-type star. No overabundance of s-process elements was found. One day before the brightness peak, an intense Hα emission line with broad wings, FWZI=3100 km s^?1, and numerous lines of ionized metals appeared in V838 Mon, which is characteristic of normal classical novae. We show light, color, and spectral variations of the object.     

Direct Measurement Results of the Time Lag of LOS-Velocity Oscillations Between Two Heights in Solar Faculae and Sunspots

We present an investigation of line-of-sight (LOS) velocity oscillations in solar faculae and sunspots. To study the phase relations between chromospheric and photospheric oscillations of the LOS velocity, we measured the time lag of the chromospheric signal relative to the photospheric one for several faculae and sunspots in a set of spectral line pairs. The measured time lags are different for different objects. The mean measured delay between the oscillations in the five-minute band in faculae is 50?s for the Si?i 10?827?Å?–?He?i 10?830?Å pair; for the pair Fe?i 6569?Å?–?Hα 6563?Å the mean delay is 20?s; for the pair Fe?i 4551?Å?–?Ba?ii 4554?Å the mean delay is 7?s; for the pair Si?i 8536?Å?–?Ca?ii 8542?Å the mean delay is 20?s. For the oscillations in the three-minute band in sunspot umbrae the mean delay is 55?s for the Si?i 10?827?Å?–?He?i 10?830?Å pair; for the Fe?i 6569?Å?–?Hα 6563?Å pair it was not possible to determine the delay; for the Fe?i 4551?Å?–?Ba?ii 4554?Å pair the mean delay is 6?s; for the Si?i 8536?Å?–?Ca?ii 8542?Å pair the mean delay is 21?s. Measured delays correspond to the wave propagation speed, which significantly exceeds the generally adopted speed of sound in the photosphere. This raises the question of the origin of these oscillations. The possibility that we deal with slow MHD waves is not ruled out.     

Modeling the Subsurface Structure of Sunspots

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this article, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out a helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by Gizon et al. (2009a, 2009b). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.     

Preprocessing the Photospheric Vector Magnetograms for an NLFFF Extrapolation Using a Potential-Field Model and an Optimization Method

Numerical reconstruction/extrapolation of the coronal nonlinear force-free magnetic field (NLFFF) usually takes the photospheric vector magnetogram as input at the bottom boundary. The magnetic field observed at the photosphere, however, contains a force that is in conflict with the fundamental assumption of the force-free model. It also contains measurement noise, which hinders the practical computation. Wiegelmann, Inhester, and Sakurai (Solar Phys. 233, 215, 2006) have proposed to preprocess the raw magnetogram to remove the force and noise to provide better input for NLFFF modeling. In this paper we develop a new code of magnetogram preprocessing that is consistent with our extrapolation method CESE–MHD–NLFFF (Jiang, Feng, and Xiang in Astrophys. J. 755, 62, 2012; Jiang and Feng in Astrophys. J. 749, 135, 2012a). Based on the magnetic-splitting rule that a magnetic field can be split into a potential-field part and a non-potential part, we split the magnetogram and dealt with the two parts separately. The preprocessing of the magnetogram’s potential part is based on a numerical potential-field model, and the non-potential part is preprocessed using the similar optimization method of Wiegelmann, Inhester, and Sakurai (2006). The code was applied to the SDO/HMI data, and results show that the method can remove the force and noise efficiently and improve the extrapolation quality.     

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.     

Connection Between Chromospheric Events and Photospheric Dynamics

We analyzed chromospheric events and their connection to oscillation phenomena and photospheric dynamics. The observations were done with the New Solar Telescope of Big Bear Solar Observatory using a broad-band imager at the wavelength of a TiO band and FISS spectrograph scanning Ca?ii and Hα spectral lines. The event in Ca?ii showed strong plasma flows and propagating waves in the chromosphere. The movement of the footpoints of flux tubes in the photosphere indicated flux tube entanglement and magnetic reconnection as a possible cause of the observed brightening and waves propagating in the chromosphere. An upward propagating train of waves was observed at the site of the downflow event in Hα. There was no clear relationship between photospheric waves and the Ca?ii and Hα events. Our observations indicate that chromospheric waves that were previously thought to originate from the photosphere may be generated by some events in the chromosphere as well.     

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.     

A statistical analysis of NaI D1 profile fluctuations at the center of the solar disk

Three radial-velocity fluctuation arrays V(Δλ, Y) and line-formation fluctuation arrays L(Δλ, Y),where Δλ is wavelength displacement from the center of Nai D₁ and Y is displacement on the Sun's surface along the spectrograph slit, were obtained from Sacramento Peak Observatory spectrograms. The variations of these line profile fluctuations are qualitatively described. The RMS_υ's, coherences, and power spectra shapes for V(Δλ, Y) fluctuations are examined at different Δλ with the corresponding effective heights of formation calculated with Mein weighting functions. Results include: (a) possible anticorrelation between continuum fluctuations and those near line center; (b) RMS _υ ^(cr) 's, which are root-mean-square values of the radial velocity corrected for instrumental and atmospheric blurring, are large (1.5 to 4.0 km s^?1) primarily due to large corrections for atmospheric blurring; (c) RMS _υ ^(cr) minima at effective heights of formation above 350 km suggest penetration of granulation velocities into the upper photosphere; (d) very rough determinations of RMS _υ ^(cr) 's, which are additionally corrected for line-of-sight averaging, range from around 5 km s^?1 in the low chromosphere to a sharp minimum ≤ 0.5 km s^?1 located in the upper photosphere; (e) power spectra shapes reflect decreasing average fluctuation scales above the temperature minimum (possibly high-frequency oscillations) and in the low and middle photosphere (possibly penetration of granulation); and (f) RMS _υ ^(cr) 's and average fluctuation scales suggest changes in the resolvable velocity field occurring near the temperature minimum.     

O VI in the local interstellar medium

We report preliminary results of a search for O VI absorption in the spectra of ～100 hot DA white dwarfs observed by the FUSE satellite. We have carried out a detailed analysis of the radial velocities of interstellar and (where present) stellar absorption lines for the entire sample of stars. In many cases, the velocity differences between the interstellar and photospheric components are below the resolution of the FUSE spectrographs. However, in a significant number of cases the interstellar and photospheric contributions can be separated. In the majority of stars where we find O VI absorption lines, the material is clearly associated with the stellar photosphere and not the interstellar medium. There are a small number of lines-of-sight where the gas is interstellar in nature but the stars are located beyond the boundaries of the local cavity.     

High precision predictions for near-Earth asteroids: the strange case of (3908) Nyx

In November 2004 radar delay measurements of near-Earth asteroid (3908) Nyx obtained at the Arecibo radio telescope turned out to be \(7.5\sigma \) away from the orbital prediction. We prove that this discrepancy was caused by a poor astrometric treatment and an incomplete dynamical model, which did not account for nongravitational perturbations. To improve the astrometric treatment, we remove known star catalog biases, apply suitable weights to the observations, and use an aggressive outlier rejection scheme. The main issue related to the dynamical model is having not accounted for the Yarkovsky effect. Including the Yarkovsky perturbation in the model makes the orbital prediction and the radar measurements statistically consistent by both reducing the offset and increasing the prediction uncertainty to a more realistic level. This analysis shows the sensitivity of high precision predictions to the astrometric treatment and the Yarkovsky effect. By using the full observational dataset we obtain a \(5\sigma \) detection of the Yarkovsky effect acting on Nyx corresponding to an orbital drift \(da/dt = (142 \pm 29)\)  m/year. In turn, we derive constraints on thermal inertia and bulk density. In particular, we find that the bulk density of Nyx is around 1 g/cm \(^3\) , possibly less. To make sure that our results are not corrupted by an asteroid impact or a close approach with a perturbing asteroid not included in our dynamical model, we show that the astrometry provides no convincing evidence of an impulsive variation of Nyx’s velocity while crossing the main belt region.     

High order normal form stability estimates for co-orbital motion

We present estimates of the size of the analytic domain of stability for co-orbital motions obtained by a high order normal form in the framework of the elliptic restricted three body problem. As a demonstration example, we consider the motion of a Trojan body in an extrasolar planetary system with a giant planet of mass parameter $\mu =0.005$ μ = 0.005 and eccentricity $e^{\prime }=0.1$ e ′ = 0.1 . The analysis contains three basic steps: (i) derivation of an accurate expansion of the Hamiltonian, (ii) computation of the normal form up to an optimal order (in the Nekhoroshev sense), and (iii) computation of the optimal size of the remainder at various values of the action integrals (proper elements) of motion. We explain our choice of variables as well as the method used to expand the Hamiltonian so as to ensure a precise model. We then compute the normal form up to the normalisation order $r=50$ r = 50 by use of a computer-algebraic program. We finally estimate the size $||R||$ | | R | | of the remainder as a function of the normalization order, and compute the optimal normalization order at which the remainder becomes minimum. It is found that the optimal value $\log (||R_{opt}||)$ log ( | | R o p t | | ) can serve in order to construct a stability map for the domain of co-orbital motion using only series. This is compared to the stability map found by a purely numerical approach based on chaotic indicators.     

Spectrophotometric studies of star HD 157978

Examination of the stellar spectrum of this star reveals that it has a composite spectrum. It could be classified as (A7V+G5V). It contains three forbidden [Feii] lines which are of the essential features of η Carinae stars. The spectrum also contains H, Hei, Feii, Mni, Tiii, and other different lines. The K-line seems to be sharp double line while other lines appear single ones which suggest early component may be double. This also seems to be true according to radial velocity measurements.     

An analytical proof on certain determinants connected with the collinear central configurations in the n-body problem

In this paper we give a short analytical proof of the inequalities proved by Albouy–Moeckel through computer algebra, in the cases $n=5$ and $n=6$ . These inequalities guarantee that, in the $n$ -body problem, the family of mass vectors making a given collinear configuration a central configuration is 2-dimensional. The induction techniques here may be used to prove the inequalities for general $n$ with more subtle estimation but currently the inequalities still remains unproved for $n\ge 7$ .     

Triple approaches in the plane isosceles equal-mass three-body problem

We analyze flyby-type triple approaches in the plane isosceles equal-mass three-body problem and in its vicinity. At the initial time, the central body lies on a straight line between the other two bodies. Triple approaches are described by two parameters: virial coefficient k and parameter $\mu = \dot r/\sqrt {\dot r^2 + \dot R^2 }$ , where $\dot r$ is the relative velocity of the extreme bodies and $\dot R$ is the velocity of the central body relative to the center of mass of the extreme bodies. The evolution of the triple system is traceable until the first turn or escape of the central body. The ejection length increases with closeness of the triple approach (parameter k). The longest ejections and escapes occur when the extreme bodies move apart with a low velocity at the time of triple approach. We determined the domain of escapes; it corresponds to close triple approaches (k>0.8) and to μ in the range ?0.2<μ<0.7. For small deviations from the isosceles problem, the evolution does not differ qualitatively from the isosceles case. The domain of escapes decreases with increasing deviations. In general, the ejection length increases for wide approaches and decreases for close approaches.     

Evolution of the Sun’s Polar Fields and the Poleward Transport of Remnant Magnetic Flux

Observations of the solar photosphere show spatially compact large-amplitude Doppler velocity events with short lifetimes. In data from the Imaging Magnetograph eXperiment (IMaX) on the first flight of the Sunrise balloon in 2009, events with velocities in excess of 4\(\sigma \) from the mean can be identified in both intergranular downflow lanes and granular upflows. We show that the statistics of such events are consistent with the random superposition of strong convective flows and p-mode coherence patches. Such coincident superposition complicates the identification of acoustic wave sources in the solar photosphere, and may be important in the interpretation of spectral line profiles formed in solar photosphere.

     

On the “blue sky catastrophe” termination in the restricted four-body problem

The restricted three-body problem (R3BP) possesses the property that some classes of doubly asymptotic (i.e., homoclinic or heteroclinic) orbits are limit members of families of periodic orbits, this phenomenon has been known as the “blue sky catastrophe” termination principle. A similar case occurs in the restricted four body problem for the collinear equilibrium point $L_{2}$ L 2 . In the restricted four body problem with primaries in a triangle relative equilibrium, we show that the same phenomenon observed in the R3BP occurs. We prove that there exists a critical value of the mass parameter $\mu _{b}$ μ b such that for $\mu =\mu _{b}$ μ = μ b a Hamiltonian Hopf bifurcation takes place. Moreover we show that for $\mu >\mu _{b}$ μ > μ b the stable and unstable manifolds of $L_{2}$ L 2 intersect transversally and the spectrum corresponds to a complex saddle. This proves that Henrard’s theorem applies at least for $\mu $ μ close to $\mu _{b}$ μ b . In particular there exists a family of periodic orbits having the homoclinic orbit as a limit.     

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.