All About FASR

Results from Level 1 (spectrum-based) analysis. The spectra at right are obtained in the centers of the two large negative-error re-gions in the Level 0 Error map, above. This is the place where the contours were assumed to represent s = 3, but from the spectra there are abrupt drops at fB and 2fB, showing that the relevant harmonic in x-mode (dashed line in left panel, solid line in right panel) is s = 2, not s = 3. Doing a similar analysis of spectra at each pixel gives the results in the figure below.

Assessment of Level 1. (a)Magnetic field strength from the model, evaluated at a height of 500 km. (b) Magnetic field strength de-rived from the radio spectra, after folding through the FASR instrumen-tal response, using the Level 1 method of spectral analysis. Identifi-cation of the s=2 region is better, but still goes awry at boundary between s=3 and s=2 region. Black pixels are where spectra do not fit simple crite-ria for automatic determination of harmonics. (c) Comparison of (b; symbols) with (a; solid line), along the white horizontal line shown in a and b. Gray symbols are those where the relevant harmonic is misidenti-fied, but are easily corrected by mul-tiplying by a factor 1.5 (asterisks).

Results from Level 0 (image-based) analysis. (a) Magnetic field strength from the model, evaluated at the 300,000 K temperature level. (b) Magnetic field strength derived from the ra-dio maps, after folding through the FASR instru-mental response, using the Level 0 method with contours taken at a brightness temperature of 300,000 K. (c) Schematic diagram of percent er-ror in quantitative comparison of (b) with (a). Negative errors are almost entirely due to choice of s = 3 over sunspots, when the correct choice is s = 2 (see Level 1 analysis, below). Positive errors at the edge are due to free-free emission.

Height Uncertainty Unlike B field measurements in the photo-sphere, the corona is inherently 3D, so to be useful one must have some idea of the height. This can be measured directly for active regions seen in profile on the limb, but for regions on the disk it is not known. In the Level 0 method, the relevant height is where the electron tem-perature matches the contour level. The figure at left shows the height variation of the 300,000 K level, which is typically 1000 km, but ranges from 500-5000 km.

Coronal magnetic fields: The figure at right shows an active region with its gyroresonance layers at three frequencies. The radio emission at these frequen-cies arise in “resonance layers” at different magnetic field strengths. The characteristics of gyroresonance emission are exploited to the fullest by FASR, to allow FASR to function as a true coronal magnetograph, measuring the stronger fields (>120 G) everywhere in the corona.

Physics of flares: FASR will provide a unique view of solar flares, with images covering the rele-vant height range to capture particle acceleration in the act. The figure below-left shows a flaring loop as seen by SXT and Nobeyama (17 GHz), corre-sponding to the loops labeled SXR and MW in the schematic view above- left. However, spectro-graphs operating at decimeter frequencies (0.3-3 GHz) suggest that electron beams emanate from a higher region above these loops. FASR will pro-vide the first imaging observations of this accel-eration region, with sufficiently high temporal and spectral resolution to follow the trajectories and pin-point the acceleration site.

Drivers of space weather: FASR will im-age coronal mass ejections (a CME observed with Nancay radioheliograph is shown at right, along with sprectral analysis, from Bastian et al. 2001), shock-associated type II burst emission, and the radio coun-terpart of EIT waves both on the disk and off the limb of the Sun. Quiet Sun: FASR will have the sensitivity to image the chromospheric network, as well as tiny mi-croflares and other dynamic events that take place in both active regions and network structures. Its multi-frequency imaging will yield precise diagnostics of electron temperature, electron density, and con-straints on the longitudinal magnetic field strength. FASR will also provide new diagnostics of fila-ments and prominences, both erupting and quiescent.

The potential magnetic field of the model is shown in panel (a), at right, where the gray-scale shows the longi-tudinal magnetogram at the photosphere, and extrapolated field lines are shown overlaid. In (b), the grayscale shows the model’s cor-onal temperature at a fixed height. Example radio images in total intensity at two fre-quencies are shown in (c) and (d).

Calculating Radio Emission Although the simulated images above utilize only the temperatures and densi-ties of the model, the radio emission depends strongly on the total mag-netic field strength and direction as well. The radio emission was calcu-lated from the model at 100 radio frequencies spaced logarithmically from 1-24 GHz, for both thermal free-free (Bremsstrahlung) emission and gyroreso-nance emission. Gyroresonance emission occurs in the solar corona at typi-cally the first few harmonics, s, of the gyrofrequency, given by: The corresponding opacity is given by (Dulk 1985): where ν = f is the observing frequency, νp is the plasma frequency, β0 is re-lated to the plasma temperature by β0

2 = kT/mec2, B is the magnetic field strength, θ is the angle of the field to the line of sight, and σ = +1 for o-mode and σ = − 1 for x-mode. These modes correspond to the two senses of circu-lar polarization, and the maps were made separately in right hand circular (RCP) and left hand circular (LCP) polarization. In addition to the gyroresonance opacity, the free-free opacity was also calcu-lated according to (e.g. Dulk 1985), where Zi is the charge of ion species i, ni is the density of that species, and Λ is the Coulomb logarithm.

Figure below, from Mok et al. (2003), shows simulated images computed from the tempera-tures and densities extracted from the model: (a-c) EIT 171A, 195A, and SXT 1265 Al filter,

viewed in the x-y plane; (d-f) EIT 286A, 195A, and SXT 1265 Al filter, viewed in the x-z plane. Simulated FASR radio im-ages at two frequencies are shown in the figure at the bottom of this column.

What is FASR? FASR (the Frequency Agile Solar Radiotelescope) is a solar-dedicated in-terferometer array capable of producing high-resolution, high-fidelity, and high-dynamic-range images over an extremely broad range of radio fre-quencies (~0.02-24 GHz). FASR will provide imaging spectroscopy of the full disk of the Sun with up to 0.1 s time resolution. Various aspects of the FASR project appear elsewhere in the literature (Bastian 2003a,b; White et al. 2003; Gary & Keller 2003; Gary 2003). An artist’s conception of the instrument is shown below.

Artist’s conception of FASR, with 100 2-m antennas (white) and 60 6-m antennas (gray) in a three-armed spiral configura-tion as it might appear on the Plains of San Augustine, near the VLA.

Angular Resolution 20/νGHz arcsecFrequency Range ~0.1-24 GHzFrequency Resolution < 3 GHz: 0.1%

> 3 GHz: 1%Time Resolution < 3 GHz: 10 ms

> 3 GHz: 100 msPolarization Stokes I, V, (Q, U)Number of Antennas 2-24 GHz: 100

0.2-3 GHz: 60< 0.3 GHz: 40

Size of Antennas 2-24 GHz: 2 m0.2-3 GHz: 6 m< 0.3 GHz: dipoles

Maximum Antenna Spacing 6 kmAbsolute Positions 1 arcsecAbsolute Flux Calibration < 5%∆T B (snapshot) 1000 K

FASR Instrument Specifications

FASR Science Goals The broad areas of FASR science are:

• The nature and evolution of coronal magnetic fields.

• The physics of flares

• Drivers of space weather

• The quiet Sun

This poster concentrates on the first goal, but others are illustrated briefly below:

Table 1:

Coronal Magnetography Radio Simulation

Model Active Region To investigate FASR’s perfomance in creating coronal magnetograms, we start with a physically plausible model with sufficient complexity that it presents a realistic challenge in both the imaging and spectral domains. The model is from Mok et al. (2003), and consists of a spatial data cube of plasma parameters electron density ne, electron temperature Te, and magnetic field vector B, evaluated on an adaptive grid with number of grid points in (x, y, z) = (126, 86, 126). The physical model is a potential field model ex-trapolated from a vector magnetogram, whose thermal structure was com-puted self-consistently assuming a plasma heating model in which the volu-metric heating rate is directly proportional to the local magnetic field strength. The model does not necessarily reflect the realistic corona, but this application does not require that. We only need a model with similar com-plexity to the actual solar corona. The grayscale figure below shows two density cross-sections from the model, and the color figure shows simula-tions of images as they would appear if obtained by EIT and Yohkoh SXT.

Figure at left, from Mok et al. (2003), shows two cross-sections of electron density in the model described above. The units on the axes are Mm. Note the height variation of the chromosphere (black along the bottom of each panel).

Hz108.22

6 sBcm

eBssffe

B ×===π

2122

02222/5

, )cos1(2sin

!2

2θσθβ

ννπκ −

=

−sp

LRs

ss

c

Λ+

=

∑2/32/1

24

2

22/1

, )(

4

)cos(312

kTm

nZe

c e

iii

B

pLR

π

θσννν

πκ

Analysis Methods The analysis starts with the 100 images, computed from the model at 100 ra-dio frequencies. The images are folded through the FASR response, and a re-alistic level of noise is added. The images are then deconvolved using the standard radio deconvolution technique known as the Maximum Entropy Method (as implemented in the AIPS system in the routine VTESS). The re-sulting set of images forms a spatial/spectral datacube, which can be analyzed in various ways to deduce magnetic fields. The two we use are as follows: • Gyroresonance Level 0: This is an image-based analysis in which the con-

tour at a given temperature level is taken to represent the edge of a gyrore-sonance surface corresponding to the third harmonic of the gyrofrequency.

• Gyroresonance Level 1: This is a simple spectrum-based analysis in which

the abrupt drop in brightness in spectra for a given pixel, in RCP and LCP, are used to determine the relevant harmonic s for that pixel, and the fre-quency of that drop gives the magnetic field strength via equation (1).

Level 0 Bmap at temperature 300,000 K

Level 0 Bmodel at temperature 300,000 K

(a) (b)

(c)

Conclusions • We have simulated FASR radio images of a complex model active region

at 100 frequencies. • The resulting datacube offers a realistic dataset for evaluating different

analysis schemes for realizing one of FASR’s most important science goals—coronal magnetography.

• The results show that even simple, easily automated analysis methods give reasonable quantitative results at the 20% level of accuracy.

• More sophisticated spectrum-based analysis schemes will be studied that are likely to improve the results further.

References Bastian, T. S. 2003a, “Frequency agile solar radiotelescope,” Proc. SPIE, 4853, 98 Bastian, T. S. 2003b, “The frequency agile solar radiotelescope,” Advances in Space Research, in press Dulk, G. A. 1985, “Radio emission from the Sun and stars,” Ann. Rev. Astr. Ap., 23, 169 Gary, D. E. 2003, “The frequency agile solar radiotelescope,” J. Korean Astr. Soc., in press. Gary, D. E. & Keller, C. U. 2003, “Site testing issues for FASR”, Proc. SPIE, 4853, 523 Mok, Y., Lionello, R., Mikic Z. & Linker, J. A. 2003, “Thermal structure of solar active regions in three dimensions,” Ap J, in preparation White, S., Lee, J., Aschwanden, M. A., & Bastian, T. S. 2003, “Imaging capabilities of FASR”, Proc. SPIE, 4853, 531

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Coronal Magnetography Model

Coronal Magnetography Results

Coronal Magnetography with the Frequency Agile Solar Radiotelescope (FASR)

Dale E. Gary & Jeongwoo Lee New Jersey Institute of Technology,

Yung Mok University of California / Irvine