Comparison of Line-of-Sight Magnetograms Taken by the Solar Dynamics Observatory/Helioseismic and Magnetic Imager and Solar and Heliospheric Observatory/Michelson Doppler Imager

We compare line-of-sight magnetograms from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) and the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO). The line-of-sight magnetic signal inferred from the calibrated MDI data is greater than that derived from the HMI data by a factor of 1.40. This factor varies somewhat with center-to-limb distance. An upper bound to the random noise for the 1′′ resolution HMI 720-second magnetograms is 6.3 Mx?cm^?2, and 10.2 Mx?cm^?2 for the 45-second magnetograms. Virtually no p-mode leakage is seen in the HMI magnetograms, but it is significant in the MDI magnetograms. 12-hour and 24-hour periodicities are detected in strong fields in the HMI magnetograms. The newly calibrated MDI full-disk magnetograms have been corrected for the zero-point offset and underestimation of the flux density. The noise is 26.4 Mx?cm^?2 for the MDI one-minute full-disk magnetograms and 16.2 Mx?cm^?2 for the five-minute full-disk magnetograms observed with four-arcsecond resolution. The variation of the noise over the Sun’s disk found in MDI magnetograms is likely due to the different optical distortions in the left- and right-circular analyzers, which allows the granulation and p-mode to leak in as noise. Saturation sometimes seen in sunspot umbrae in MDI magnetograms is caused by the low intensity and the limitation of the onboard computation. The noise in the HMI and MDI line-of-sight magnetic-field synoptic charts appears to be fairly uniform over the entire map. The noise is 2.3 Mx?cm^?2 for HMI charts and 5.0 Mx?cm^?2 for MDI charts. No evident periodicity is found in the HMI synoptic charts.     

An empirical method to correct the saturation seen in the SOHO/MDI magnetograms

The magnetic field of the umbrae is sometimes found to be saturated in the magnetograms taken by the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO).It is suggested that the combination of the low intensity of sunspot umbrae and the limitation of the 15-bit onboard numerical data acquisition leads to this saturation.In this paper,we propose to use the MDI's intensity data to correct this saturation.This method is based on the well-established relationship between the continuum intensity and the magnetic field (the so-called I-B relationship).A comparison between the corrected magnetic field and the data taken by the Stokes-Polarimeter of the Solar Optical Telescope (SOT/SP) onboard Hinode shows a reasonable agreement,suggesting that this correction is effective.     

Numerical Simulation of a Solar Active Region. I: Bastille Day Flare

We present three-dimensional unsteady modeling and numerical simulations of a coronal active region, carried out within the compressible single-fluid MHD approximation. We focus on AR 9077 on 14 July 2000, and the triggering of the X5.7 GOES X-ray class “Bastille Day” flare. We simulate only the lower corona, although we include a virtual photosphere and chromosphere below. The boundary conditions at the base of this layer are set using temperature maps from line intensities and line-of-sight magnetograms (SOHO/MDI). From the latter, we generate vector magnetograms using the force-free approximation; these vector magnetograms are then used to produce the boundary condition on the velocity field using a minimum energy principle (Longcope, Astrophys. J. 612, 1181, 2004). The reconnection process is modeled through a dynamical hyper-resistivity which is activated when the current exceeds a critical value (Klimas et al., J. Geophys. Res. 109, 2218, 2004). Comparing the time series of X-ray fluxes recorded by GOES with modeled time series of various mean physical variables such as current density, Poynting energy flux, or radiative loss inside the active region, we can demonstrate that the model properly captures the evolution of an active region over a day and, in particular, is able to explain the initiation of the flare at the observed time.     

Accurate Intensity – Velocity Phase Difference in the Potassium Resonance Line Obtained with VAMOS

We present new results about the phase difference between the intensity and velocity fluctuations of the solar photosphere obtained with the Velocity And Magnetic Observations of the Sun (VAMOS) instrument, which uses the magneto-optical filter (MOF) technique. Before this observing run, we applied the calibration method described in Magrì, Oliviero, and Severino (Solar Phys. 232, 159, 2005) to reduce the instrumental cross-talk which was present in previous VAMOS data. The quality of this calibration, which can be easily applied to any MOF-based instrument, has been confirmed by comparing with the MOF transmission-profile measurements obtained with a diode laser system. Finally, we discuss the new VAMOS phase-difference value in relation to data obtained by other authors in the same potassium spectral line and in other lines that can be used to study nonadiabatic effects of solar global oscillations.     

Comparison of Ground-Based and Space-Based Longitudinal Magnetograms

We compare photospheric line-of-sight magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) instrument with observations from the 150-foot Solar Tower at Mt. Wilson Observatory (MWO), the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO), and the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO). We find very good agreement between VSM and the other data sources for both disk-averaged flux densities and pixel-by-pixel measurements. We show that the VSM mean flux density time series is of consistently high signal-to-noise ratio with no significant zero offsets. We discuss in detail some of the factors ?C spatial resolution, flux dependence, and position on the solar disk ?C affecting the determination of scaling between VSM and SOHO/MDI or SDO/HMI magnetograms. The VSM flux densities agree well with spatially smoothed data from MDI and HMI, although the scaling factors show a clear dependence on flux density. The factor to convert VSM to HMI increases with increasing flux density (from ??1 to ??1.5). The nonlinearity is smaller for the VSM vs. SOHO/MDI scaling factor (from ??1 to ??1.2).     

A Study of AR 9144; A Fast-Growing EFR

This paper is a study of NOAA region 9144, an emerging flux region (EFR) which grew rapidly beginning 25 August 2000. This region was visible in SOHO data at 0 UT on 25 August 2000 as a small, isolated spot. It was recognizable as an active region with multiple spots by 06:00 UT on the 25th and was a fully developed AR by 24^h UT on the 26th of August. Data are presented from the Michelson Doppler Imager (MDI) experiment on the Solar and Heliospheric Observatory satellite (SOHO), from Big Bear Solar Observatory (BBSO) and from the San Fernando Observatory (SFO). The MDI data are Dopplergrams, magnetograms, and continuum images. The BBSO data are high-resolution Hα filtergrams. The SFO data are Dopplergrams, magnetograms and continuum images from the Video SpectraSpectroHeliograph (VSSHG). MDI Doppler images show that during the rapid growth of this EFR during the day of 26 August, the most obvious feature in area and lifetime is a red-shifted area in the trailing part of the region. SFO Doppler images show a more complex pattern, but still dominated by red shifts in the trailing part of the region near the end of the day of 26 August.     

Sources of Solar Total Irradiance Variations

The daily images and magnetograms acquired by MDI are a rich source of information about the contributions of different types of solar regions to variations in the total solar irradiance (TSI). These data have been used to determine the temporal variation of the MDI irradiance, the mean intensity of the solar disk in the continuum at 676.8 nm. The short-term (days to weeks) variations of the MDI irradiance and TSI are in excellent agreement with rms differences of 0.011%. This indicates that MDI irradiance is an excellent proxy for short-term variations of TSI from the competing irradiance contributions of regions causing irradiance increases, such as plages and bright network, and regions causing irradiance decreases, such as sunspots. However, the long-term or solar cycle variation of the MDI proxy and TSI differ over the 11-year period studied. The results indicate that the primary sources of the long-term (several months or more) variations in TSI are regions with magnetic fields between about 80 and 600 G. The results also suggest that the difference in the long-term variations of the MDI proxy and TSI is due to a component of TSI associated with sectors of the solar spectrum where the contrast in intensity between plages and the quiet Sun is enhanced (e.g., the UV) compared to the MDI proxy. This is evidence that the long-term variation of TSI is due primarily to solar cycle variations of the irradiance from these portions of solar spectrum, a finding consistent with modeling calculations indicating that approximately 60% of the change in TSI between solar minimum and maximum is produced by the UV part of the spectrum shortward of 400 nm (Solanki and Krivova, Space Sci. Rev. 125, 53, 2006).     

Solar Polar Fields During Cycles 21 – 23: Correlation with Meridional Flows

We have examined polar magnetic fields for the last three solar cycles, viz. Cycles 21, 22, and 23 using NSO/Kitt Peak synoptic magnetograms. In addition, we have used SOHO/MDI magnetograms to derive the polar fields during Cycle 23. Both Kitt Peak and MDI data at high latitudes (78° – 90°) in both solar hemispheres show a significant drop in the absolute value of polar fields from the late declining phase of the Solar Cycle 22 to the maximum of the Solar Cycle 23. We find that long-term changes in the absolute value of the polar field, in Cycle 23, are well correlated with changes in meridional-flow speeds that have been reported recently. We discuss the implication of this in influencing the extremely prolonged minimum experienced at the start of the current Cycle 24 and in forecasting the behavior of future solar cycles.     

Inferring Small-Scale Flatfields from Solar Rotation

We present a method to infer small-scale flatfields for imaging solar instruments using only regular-observation intensity images with a fixed field of view. The method is related to the flatfielding method developed by Kuhn, Lin, and Loranz (Publ. Astron. Soc. Pac. 103, 1097 – 1108, 1991), but does not require image offsets. Instead, it takes advantage of the fact that the solar image is changing in the CCD reference frame due to solar rotation. We apply the method to data sets of MDI filtergrams and compare the results to flat fields derived with other methods. Finally, we discuss the planned implementation of this method in the data processing for Helioseismic and Magnetic Imager on the Solar Dynamics Observatory.     

Global Forces in Eruptive Solar Flares: The Lorentz Force Acting on the Solar Atmosphere and the Solar Interior

We compute the change in the Lorentz force integrated over the outer solar atmosphere implied by observed changes in vector magnetograms that occur during large, eruptive solar flares. This force perturbation should be balanced by an equal and opposite force perturbation acting on the solar photosphere and solar interior. The resulting expression for the estimated force change in the solar interior generalizes the earlier expression presented by Hudson, Fisher, and Welsch (Astron. Soc. Pac. CS-383, 221, 2008), providing horizontal as well as vertical force components, and provides a more accurate result for the vertical component of the perturbed force. We show that magnetic eruptions should result in the magnetic field at the photosphere becoming more horizontal, and hence should result in a downward (toward the solar interior) force change acting on the photosphere and solar interior, as recently argued from an analysis of magnetogram data by Wang and Liu (Astrophys. J. Lett. 716, L195, 2010). We suggest the existence of an observational relationship between the force change computed from changes in the vector magnetograms, the outward momentum carried by the ejecta from the flare, and the properties of the helioseismic disturbance driven by the downward force change. We use the impulse driven by the Lorentz-force change in the outer solar atmosphere to derive an upper limit to the mass of erupting plasma that can escape from the Sun. Finally, we compare the expected Lorentz-force change at the photosphere with simple estimates from flare-driven gasdynamic disturbances and from an estimate of the perturbed pressure from radiative backwarming of the photosphere in flaring conditions.     

Study of Differences Between Sunspot and White Light Facular Area Data Determined from SDO/HMI and SOHO/MDI Observations

Sunspot and white light facular areas are important data for solar activity and are used, for example, in the study of the evolution of sunspots and their effect on solar irradiance. Solar Dynamic Observatory??s Helioseismic and Magnetic Imager (SDO/HMI) solar images have much higher resolution (??0.5????pixel^?1) than Solar and Heliospheric Observatory??s Michelson Doppler Imager (SOHO/MDI) solar images (??2????pixel^?1). This difference in image resolution has a significant impact on the sunspot and white light facular areas measured in the two datasets. We compare the area of sunspots and white light faculae derived from SDO/HMI and SOHO/MDI observations. This comparison helps the calibration of the SOHO sunspot and facular area to those in SDO observations. We also find a 0.22 degree difference between the North direction in SDO/HMI and SOHO/MDI images.     

An Improved Approach to Non-Force-Free Coronal Magnetic Field Extrapolation

We develop an approach to deriving the three-dimensional non-force-free coronal magnetic field from vector magnetograms. Based on the principle of minimum dissipation rate, a general non-force-free magnetic field is expressed as the superposition of one potential field and two constant-α (linear) force-free fields. Each is extrapolated from its bottom boundary data, providing the normal component only. The constant-α parameters are distinct and determined by minimizing the deviations between the numerically computed and measured transverse magnetic field at the bottom boundary. The boundary conditions required are at least two layers of vector magnetograms, one at the photospheric level and the other at the chromospheric level, presumably. We apply our approach to a few analytic test cases, especially to two nonlinear force-free cases examined by Schrijver et al. (Solar Phys. 235, 161, 2006). We find that for one case with small α parameters, the quantitative measures of the quality of our result are better than the median values of those from a set of nonlinear force-free methods. The reconstructed magnetic-field configuration is valid up to a vertical height of the transverse scale. For the other cases, the results remain valid to a lower vertical height owing to the limitations of the linear force-free-field solver. Because our method is based on the fast-Fourier-transform algorithm, it is much faster and easy to implement. We discuss the potential usefulness of our method and its limitations.     

A Note on Saturation Seen in the MDI/SOHO Magnetograms

A type of saturation is sometimes seen in sunspot umbrae in MDI/SOHO magnetograms. In this paper, we present the underlying cause of such saturation. By using a set of MDI circular polarization filtergrams taken during an MDI line profile campaign observation, we derive the MDI magnetograms using two different approaches: the on-board data processing and the ground data processing, respectively. The algorithms for processing the data are the same, but the former is limited by a 15-bit lookup table. Saturation is clearly seen in the magnetogram from the on-board processing simulation, which is comparable to an observed MDI magnetogram taken one and a half hours before the campaign data. We analyze the saturated pixels and examine the on-board numerical calculation method. We conclude that very low intensity in sunspot umbrae leads to a very low depth of the spectral line that becomes problematic when limited to the 15-bit on-board numerical treatment. This 15-bit on-board treatment of the values is the reason for the saturation seen in sunspot umbrae in the MDI magnetogram. Although it is possible for a different type of saturation to occur when the combination of a strong magnetic field and high velocity moves the spectral line out of the effective sampling range, this saturation is not observed.     

Multiscale Analysis of Active Region Evolution

Flows in the photosphere of solar active regions are turbulent in nature. Because magnetic fields are frozen into the plasma on the solar surface, magnetograms can be used to investigate the processes responsible for structuring active regions. Here, a continuous wavelet technique is developed, analyzed, and used to investigate the multiscale structure of an evolving active region using magnetograms obtained by the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO). The multiscale structure was measured using a 2D continuous wavelet technique to extract the energy spectrum of the region over the time scale of 13 days. Preliminary evidence of an inverse cascade in active region NOAA 10488 is presented as well as a potential relationship between energy scaling and flare productivity.     

Comments on “Effects of Strong Regular Refraction in the Solar Radio Pulse Structure in Spike Events” by Afanasiev and Altyntsev and “Mathematical Modeling of the Formation of Type IIId Solar Decameter Radio Bursts with Echo Components” by Afanasiev

Presented are some comments on the papers by Afanasiev and Altyntsev (Solar Phys. 234, 151, 2006) and by Afanasiev (Solar Phys. 238, 87, 2006) devoted to the study of the influence of solar corona inhomogeneities on the form of radio bursts. It is pointed out that in these papers incorrect use is made of methods used previously in investigations into radio wave propagation through a randomly inhomogeneous ionosphere.     

Correction of Offset in MDI/SOHO Magnetograms

Shutter noise induces a small random shift of the zero point in full-disk magnetograms obtained by the Michelson Doppler Imager (MDI) instrument aboard SOHO. In this paper, we develop a method to remove this offset by fitting the distribution of the magnetic field strength with a Gaussian function (Ulrich et al., 2002). We also discover a systematic error in the five-minute magnetograms that are the sum of five individual magnetograms computed on-board; this error can be removed together with the offset. The mean solar magnetic field and synoptic frames derived from corrected magnetograms show significant improvement. Standard synoptic charts benefit from reduced noise and elimination of systematic errors in the individual magnetograms. This indicates that this correction is effective and necessary.     

Velocity Characteristics of Rotating Sunspots

A statistical study is carried out to investigate the detailed relationship between rotating sunspots and the emergence of magnetic flux tubes. This paper presents the velocity characteristics of 132 sunspots in 95 solar active regions. The rotational characteristics of the sunspots are calculated from successive SOHO/MDI magnetograms by applying the Differential Affine Velocity Estimator (DAVE) technique (Schuck, 2006, Astrophys. J. 646, 1358). Among 82 sunspots in active regions exhibiting strong flux emergence, 63 showed rotation with rotational angular velocity larger than 0.4° h⁻¹. Among 50 sunspots in active regions without well-defined flux emergence, 14 showed rotation, and the rotation velocities tend to be slower, compared to those in emerging regions. In addition, we investigated 11 rotating sunspot groups in which both polarities show evidence for co-temporary rotation. In seven of these cases the two polarities co-rotate, while the other four are found to be counter-rotating. Plausible reasons for the observed characteristics of the rotating sunspots are discussed.     

On Short-Term Periodicity of the Solar Radius Measurements

The aim of the present study is to investigate the short-term periodicity in the solar radius measurements and to compare with the short periods in sunspot numbers, sunspot areas and flare index data. The spectral analysis of data sets covering a time interval from 26 February 2000 to 26 October 2007 during Solar Cycle 23 were made by using the Date Compensated Discrete Fourier Transform (DCDFT). The power spectrum of solar radius data corrected for the seeing effect gives an evident peak at 25.7 days with the amplitude of 0.034 arcsec, which is slightly different from the peaks of 26.2 and 26.7 days produced by sunspot numbers and sunspot areas data, respectively. Besides, the main peak of 25.7 days detected in the power spectrum of solar radius data is in agreement with the period of 25.5 days, suggested to be the fundamental period of the Sun by Bai and Sturrock (in Nature 350, 141, 1991).     

The Correlation between the Magnetic and Velocity Fields on the Full Solar Disk

A possible correlation between the magnetic and velocity fields has been analyzed based on the SOHO/MDI magnetograms and Dopplergrams. It is found that the observed large-scale weak magnetic field (weaker than 50 G (gauss)) is correlated with the velocity statistically. The curves of u⋅b with latitude, where u and b are the velocity and magnetic fields in a rectangular region (±15^○ in longitude, ±45^○ in latitude) on the Sun, show the same patterns in the years 2000, 2004, and 2007. The patterns indicate that u and b are positively correlated near the equator but are anti-correlated at the middle latitudes. For a strong magnetic field between 50 G and 3000 G, the curves of u⋅b with latitude show the same tendencies at the middle latitudes. Near the equator, however, the slope of the curve is positive in 2000 and is negative in 2004 and 2007. In addition, we give an estimation for the amplitude of the cross helicity h _χ (h_c=[`(u·b)]h_{\chi}=\overline{\mathbf{u}\cdot\mathbf{b}}) inferred from the MDI data, which is of the order of 10³ G m s⁻¹ near the center of the solar disk.     

Direct Propagation of Photospheric Acoustic <Emphasis Type="Italic">p</Emphasis> Modes into Nonmagnetic Solar Atmosphere

Solar p modes are one of the dominant types of coherent signals in Doppler velocity in the solar photosphere, with periods showing a power peak at five minutes. The propagation (or leakage) of these p-mode signals into the higher solar atmosphere is one of the key drivers of oscillatory motions in the higher solar chromosphere and corona. This paper examines numerically the direct propagation of acoustic waves driven harmonically at the photosphere, into the nonmagnetic solar atmosphere. Erdélyi et al. (Astron. Astrophys. 467, 1299, 2007) investigated the acoustic response to a single point-source driver. In the follow-up work here we generalise this previous study to more structured, coherent, photospheric drivers mimicking solar global oscillations. When our atmosphere is driven with a pair of point drivers separated in space, reflection at the transition region causes cavity oscillations in the lower chromosphere, and amplification and cavity resonance of waves at the transition region generate strong surface oscillations. When driven with a widely horizontally coherent velocity signal, cavity modes are caused in the chromosphere, surface waves occur at the transition region, and fine structures are generated extending from a dynamic transition region into the lower corona, even in the absence of a magnetic field.