Image Quality of the Helioseismic and Magnetic Imager (HMI) Onboard the Solar Dynamics Observatory (SDO)

We describe the imaging quality of the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) as measured during the ground calibration of the instrument. We describe the calibration techniques and report our results for the final configuration of HMI. We present the distortion, modulation transfer function, stray light, image shifts introduced by moving parts of the instrument, best focus, field curvature, and the relative alignment of the two cameras. We investigate the gain and linearity of the cameras, and present the measured flat field.     

Wavelength Dependence of the Helioseismic and Magnetic Imager (HMI) Instrument onboard the Solar Dynamics Observatory (SDO)

The Helioseismic and Magnetic Imager (HMI) instrument will produce Doppler-velocity and vector-magnetic-field maps of the solar surface, whose accuracy is dependent on a thorough knowledge of the transmission profiles of the components of the HMI optical-filter system. Here we present a series of wavelength-dependence calibration tests, performed on the instrument from 2005 onwards, to obtain these profiles. We obtained the transmittances as a function of wavelength for the tunable and non-tunable filter elements, as well as the variation of these transmittances with temperature and the angle of incidence of rays of light. We also established the presence of fringe patterns produced by interferences inside the blocking filter and the front window, as well as a change in transmitted intensity with the tuning position. This thorough characterization of the HMI-filter system confirmed the very high quality of the instrument, and showed that its properties are well within the required specifications to produce superior data with high spatial and temporal resolution.     

On-Orbit Performance of the <Emphasis Type="Italic">Helioseismic and Magnetic Imager</Emphasis> Instrument onboard the <Emphasis Type="Italic">Solar Dynamics Observatory</Emphasis>

The Helioseismic and Magnetic Imager (HMI) instrument is a major component of NASA's Solar Dynamics Observatory (SDO) spacecraft. Since commencement of full regular science operations on 1 May 2010, HMI has operated with remarkable continuity, e.g. during the more than five years of the SDO prime mission that ended 30 September 2015, HMI collected 98.4% of all possible 45-second velocity maps; minimizing gaps in these full-disk Dopplergrams is crucial for helioseismology. HMI velocity, intensity, and magnetic-field measurements are used in numerous investigations, so understanding the quality of the data is important. This article describes the calibration measurements used to track the performance of the HMI instrument, and it details trends in important instrument parameters during the prime mission. Regular calibration sequences provide information used to improve and update the calibration of HMI data. The set-point temperature of the instrument front window and optical bench is adjusted regularly to maintain instrument focus, and changes in the temperature-control scheme have been made to improve stability in the observable quantities. The exposure time has been changed to compensate for a 20% decrease in instrument throughput. Measurements of the performance of the shutter and tuning mechanisms show that they are aging as expected and continue to perform according to specification. Parameters of the tunable optical-filter elements are regularly adjusted to account for drifts in the central wavelength. Frequent measurements of changing CCD-camera characteristics, such as gain and flat field, are used to calibrate the observations. Infrequent expected events such as eclipses, transits, and spacecraft off-points interrupt regular instrument operations and provide the opportunity to perform additional calibration. Onboard instrument anomalies are rare and seem to occur quite uniformly in time. The instrument continues to perform very well.     

Analysis of Supergranule Sizes and Velocities Using Solar Dynamics Observatory (SDO)/Helioseismic Magnetic Imager (HMI) and Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (MDI) Dopplergrams

Co-temporal Doppler images from Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (MDI) and Solar Dynamics Observatory (SDO)/Helioseismic Magnetic Imager (HMI) have been analyzed to extract quantitative information about global properties of the spatial and temporal characteristics of solar supergranulation. Preliminary comparisons show that supergranules appear to be smaller and have stronger horizontal velocity flows within HMI data than was measured with MDI. There appears to be no difference in their evolutionary timescales. Supergranule sizes and velocities were analyzed over a ten-day time period at a 15-minute cadence. While the averages of the time-series retain the aforementioned differences, fluctuations of these parameters first observed in MDI data were seen in both MDI and HMI time-series, exhibiting a strong cross-correlation. This verifies that these fluctuations are not instrumental, but are solar in origin. The observed discrepancies between the averaged values from the two sets of data are a consequence of instrument resolution. The lower spatial resolution of MDI results in larger observed structures with lower velocities than is seen in HMI. While these results offer a further constraint on the physical nature of supergranules, they also provide a level of calibration between the two instruments.     

Transient Artifacts in a Flare Observed by the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory

The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) provides a new tool for the systematic observation of white-light flares, including Doppler and magnetic information as well as continuum. In our initial analysis of the highly impulsive $\mathrm{\gamma}$ -ray flare SOL2010-06-12T00:57 (Martínez Oliveros et al., Solar Phys. 269, 269, 2011), we reported the signature of a strong blueshift in the two footpoint sources. Concerned that this might be an artifact due to aliasing peculiar to the HMI instrument, we undertook a comparative analysis of Global Oscillation Network Group (GONG++) observations of the same flare, using the PArametric Smearing Correction ALgorithm (PASCAL) algorithm to correct for artifacts caused by variations in atmospheric smearing. This analysis confirms the artifactual nature of the apparent blueshift in the HMI observations, finding weak redshifts at the footpoints instead. We describe the use of PASCAL with GONG++ observations as a complement to the SDO observations and discuss constraints imposed by the use of HMI far from its design conditions. With proper precautions, these data provide rich information on flares and transients.     

An investigation of the Eigenvalue Calibration Method (ECM) using GASP for non-imaging and imaging detectors

Polarised light from astronomical targets can yield a wealth of information about their source radiation mechanisms, and about the geometry of the scattered light regions. Optical observations, of both the linear and circular polarisation components, have been impeded due to non-optimised instrumentation. The need for suitable observing conditions and the availability of luminous targets are also limiting factors. The science motivation of any instrument adds constraints to its operation such as high signal-to-noise (SNR) and detector readout speeds. These factors in particular lead to a wide range of sources that have yet to be observed. The Galway Astronomical Stokes Polarimeter (GASP) has been specifically designed to make observations of these sources. GASP uses division of amplitude polarimeter (DOAP) (Compain and Drevillon Appl. Opt. 37, 5938–5944, 1998) to measure the four components of the Stokes vector (I, Q, U and V) simultaneously, which eliminates the constraints placed upon the need for moving parts during observation, and offers a real-time complete measurement of polarisation. Results from the GASP calibration are presented in this work for both a 1D detector system, and a pixel-by-pixel analysis on a 2D detector system. Following Compain et al. (Appl. Opt. 38, 3490–3502 1999) we use the Eigenvalue Calibration Method (ECM) to measure the polarimetric limitations of the instrument for each of the two systems. Consequently, the ECM is able to compensate for systematic errors introduced by the calibration optics, and it also accounts for all optical elements of the polarimeter in the output. Initial laboratory results of the ECM are presented, using APD detectors, where errors of 0.2 % and 0.1° were measured for the degree of linear polarisation (DOLP) and polarisation angle (PA) respectively. Channel-to-channel image registration is an important aspect of 2-D polarimetry. We present our calibration results of the measured Mueller matrix of each sample, used by the ECM, when 2 Andor iXon Ultra 897 detectors were loaned to the project. A set of Zenith flat-field images were recorded during an observing campaign at the Palomar 200 inch telescope in November 2012. From these we show the polarimetric errors from the spatial polarimetry indicating both the stability and absolute accuracy of GASP.     

Initial Calibration of the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO)

The Atmospheric Imaging Assembly (AIA) instrument onboard the Solar Dynamics Observatory (SDO) is an array of four normal-incidence reflecting telescopes that image the Sun in ten EUV and UV wavelength channels. We present the initial photometric calibration of AIA, based on preflight measurements of the response of the telescope components. The estimated accuracy is of order 25%, which is consistent with the results of comparisons with full-disk irradiance measurements and spectral models. We also describe the characterization of the instrument performance, including image resolution, alignment, camera-system gain, flat-fielding, and data compression.     

Polarimetric receiver in the forty gigahertz band: new instrument for the Q-U-I joint Tenerife experiment

This paper describes the analysis, design and characterization of a polarimetric receiver developed for covering the 35 to 47 GHz frequency band in the new instrument aimed at completing the ground-based Q-U-I Joint Tenerife Experiment. This experiment is designed to measure polarization in the Cosmic Microwave Background. The described high frequency instrument is a HEMT-based array composed of 29 pixels. A thorough analysis of the behaviour of the proposed receiver, based on electronic phase switching, is presented for a noise-like linearly polarized input signal, obtaining simultaneously I, Q and U Stokes parameters of the input signal. Wideband subsystems are designed, assembled and characterized for the polarimeter. Their performances are described showing appropriate results within the 35-to-47 GHz frequency band. Functionality tests are performed at room and cryogenic temperatures with adequate results for both temperature conditions, which validate the receiver concept and performance.     

Albedo and size determination of potentially hazardous asteroids: (99942) Apophis

The near-Earth object (99942) Apophis will make an extremely close approach to the Earth in 2029, and currently has approximately a one-in-45,000 chance of impacting our planet in 2036 (JPL Sentry, November 2006). Computation of the orbital evolution of this object is limited by insufficient knowledge of physical properties required to determine the role played by non-gravitational effects. Using polarimetric observations, we have obtained the first reliable determination of the albedo of Apophis, obtaining 0.33±0.08. We also derive an updated estimate of the asteroid's absolute magnitude: H=19.7±0.4. Using this albedo and H, we find that Apophis has a diameter of 270±60 m, slightly smaller than preliminary estimates based upon an assumed albedo. Our observations demonstrate the feasibility of polarimetric observations aimed at obtaining albedos and sizes of small, potentially hazardous asteroids.     

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.     

The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: Overview and Performance

The Helioseismic and Magnetic Imager (HMI) began near-continuous full-disk solar measurements on 1 May 2010 from the Solar Dynamics Observatory (SDO). An automated processing pipeline keeps pace with observations to produce observable quantities, including the photospheric vector magnetic field, from sequences of filtergrams. The basic vector-field frame list cadence is 135 seconds, but to reduce noise the filtergrams are combined to derive data products every 720 seconds. The primary 720 s observables were released in mid-2010, including Stokes polarization parameters measured at six wavelengths, as well as intensity, Doppler velocity, and the line-of-sight magnetic field. More advanced products, including the full vector magnetic field, are now available. Automatically identified HMI Active Region Patches (HARPs) track the location and shape of magnetic regions throughout their lifetime. The vector field is computed using the Very Fast Inversion of the Stokes Vector (VFISV) code optimized for the HMI pipeline; the remaining 180^° azimuth ambiguity is resolved with the Minimum Energy (ME0) code. The Milne–Eddington inversion is performed on all full-disk HMI observations. The disambiguation, until recently run only on HARP regions, is now implemented for the full disk. Vector and scalar quantities in the patches are used to derive active region indices potentially useful for forecasting; the data maps and indices are collected in the SHARP data series, hmi.sharp_720s. Definitive SHARP processing is completed only after the region rotates off the visible disk; quick-look products are produced in near real time. Patches are provided in both CCD and heliographic coordinates. HMI provides continuous coverage of the vector field, but has modest spatial, spectral, and temporal resolution. Coupled with limitations of the analysis and interpretation techniques, effects of the orbital velocity, and instrument performance, the resulting measurements have a certain dynamic range and sensitivity and are subject to systematic errors and uncertainties that are characterized in this report.     

The speckle polarimeter of the 2.5-m telescope: Design and calibration

The speckle polarimeter is a facility instrument of the 2.5-mSAIMSU telescope that combines the features of a speckle interferometer and a polarimeter. The speckle polarimeter is designed for observations in several visible bands in the following modes: speckle interferometry, polarimetry, speckle polarimetry, and polaroastrometry. In this paper we describe the instrument design and the procedures for determining the angular scale of the camera and the position angle of the camera and the polarimeter. Our measurements of the parameters for the binary star HD 9165 are used as an example to demonstrate the technique of speckle interferometry. For bright objects the accuracy of astrometry is limited by the error of the correction for the distortion caused by the atmospheric dispersion compensator. At zenith distances less than 45? the additional relative measurement error of the separation is 0.7%, while the additional error of the position angle is 0.3°. In the absence of a dispersion compensator the accuracy of astrometry is limited by the uncertainty in the scale and position angle of the camera, which are 0.15% and 0.06°, respectively. We have performed polarimetric measurements of unpolarized stars and polarization standards. The instrumental polarization at the Cassegrain focus in the V band does not exceed 0.01%. The instrumental polarization for the Nasmyth focus varies between 2 and 4% within the visible range; we have constructed its model and give a method for its elimination from the measurements. For stars with an intrinsic polarization of less than 0.2% during observations at the Cassegrain focus the error is determined mainly by the photon and readout noises and can reach 5 × 10^?5.     

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.     

Temporal Pointing Variations of the Solar Dynamics Observatory’s HMI and AIA Instruments on Subweekly Time Scales

Achieving subarcsecond co-registration across varying time-lines of multi-wavelength and instrument images is difficult and requires an accurate characterization of the instrument pointing jitter. We investigated the internal pointing errors on daily and yearly time-scales that occur across the Solar Dynamics Observatory’s (SDO) Atmospheric Imaging Assembly (AIA) and Helioseismic Magnetic Imager (HMI). Using cross-correlation techniques on the AIA 1700 Å passband and the HMI line-of-sight magnetograms from three years of observational image pairs at approximately three-day intervals, internal pointing errors were quantified. Pointing variations of ±?0.26″ (jitter-limited) and ±?0.50″ in the solar East–West (x) and North–South (y) directions, respectively, were measured. AIA observations of the Venus transit in June 2012 were used to measure existing coalignment offsets in all passbands. We found that the AIA passband pointing variations are 〈ΔX _CO〉=1.10″±1.41″ and 〈ΔY _CO〉=1.25″±1.24″ when aligned to the HMI nominal image center, referred to here as the CutOut technique. Minimal long-term pointing variations found between limb and correlation derived pointings provide evidence that the image-center positions provided by the instrument teams achieve single-pixel accuracy on time scales shorter than their characterization. However, daily AIA passband pointing variations of ??1.18″ indicate that autonomous subarcsecond co-registration is not fully achieved yet.     

Cipher, A Polarimeter Telescope Concept for Hard X-Ray Astronomy

The polarisation of astrophysical source emission in the energy range from a few tens of keV up to the MeV region is an almost unexplored field of high-energy astrophysics. Till date, polarimetry in astrophysics–in the energy domain from hard X-rays up to soft γ-rays–has not been pursued due to the difficulties involved in obtaining sufficient sensitivity. Indeed for those few instruments that are capable of performing this type of measurement (e.g. the COMPTEL instrument on the Compton Gamma-ray Observatory and the IBIS instrument on INTEGRAL), polarimetry itself plays a secondary role in the mission objectives, as the efficiencies (0.5% and 10% maximum, respectively) and polarimetric Q factors (0.1 and 0.3, respectively) are relatively limited. In order to perform efficient polarimetric measurements for hard X-ray and soft gamma-ray sources, with an instrument of relatively robust and simple design, a CdTe based telescope (CIPHER: Coded Imager and Polarimeter for High Energy Radiation) is under study. This instrument is based on a thick (10 mm) CdTe position-sensitive spectrometer comprising four modules of 32 × 32 individual pixels, each with a surface area of 2 × 2 mm² (about 160 cm² total detection area). The polarimetric performance and design optimisation of the CIPHER detection surface have been studied by use of a Monte Carlo code. This detector, due to its intrinsic geometry, can allow efficient polarimetric measurements to be made between 100 keV and 1 MeV. In order to predict the polarimetric performance and to optimise the design and concept of the CIPHER detection plane, a Monte Carlo code based on GEANT4 library modules was developed to simulate the detector behaviour under a polarised photon flux. The Compton double event efficiency, as well bi-dimensional double event distribution maps and the corresponding polarimetric modulation factor will be presented and discussed. Modulation Q factors better than 0.50 and double event total efficiencies greater than 10% were calculated in the energy range between 100 keV and 1 MeV. Herein we will present and discuss the general problems that affect polarimetric measurements in space, such as the inclination of the source with respect to the telescope optical axis and background radiation. Q factor calculations for several beam inclinations as well as for background together with simulated astronomical sources will be presented and discussed.     

Extreme Ultraviolet Variability Experiment (EVE) Multiple?EUV Grating Spectrographs (MEGS): Radiometric Calibrations and Results

The NASA Solar Dynamics Observatory (SDO), scheduled for launch in early 2010, incorporates a suite of instruments including the Extreme Ultraviolet Variability Experiment (EVE). EVE has multiple instruments including the Multiple Extreme ultraviolet Grating Spectrographs (MEGS) A, B, and P instruments, the Solar Aspect Monitor (SAM), and the Extreme ultraviolet SpectroPhotometer (ESP). The radiometric calibration of EVE, necessary to convert the instrument counts to physical units, was performed at the National Institute of Standards and Technology (NIST) Synchrotron Ultraviolet Radiation Facility (SURF III) located in Gaithersburg, Maryland. This paper presents the results and derived accuracy of this radiometric calibration for the MEGS A, B, P, and SAM instruments, while the calibration of the ESP instrument is addressed by Didkovsky et?al. (Solar Phys., 2010, doi: 10.1007/s11207-009-9485-8 ). In addition, solar measurements that were taken on 14 April 2008, during the NASA 36.240 sounding-rocket flight, are shown for the prototype EVE instruments.     

Physical investigation of the potentially hazardous Asteroid (144898) 2004 VD17

In this paper we present the observational campaign carried out at ESO NTT and VLT in April and May 2006 to investigate the nature and the structure of the near-Earth object (144898) 2004 VD17. In spite of a great quantity of dynamical information, according to which it will have a close approach with the Earth in the next century, the physical properties of this asteroid are largely unknown. We performed visible and near-infrared photometry and spectroscopy, as well as polarimetric observations. Polarimetric and spectroscopic data allowed us to classify 2004 VD17 as an E-type asteroid. A good agreement was also found with the spectrum of the aubrite meteorite Mayo Belwa. On the basis of the polarimetric albedo (pv=0.45) and of photometric data, we estimated a diameter of about 320 m and a rotational period of about 2 h. The analysis of the results obtained by our complete survey have shown that (144898) 2004 VD17 is a peculiar NEO, since it is close to the breakup limits for fast rotator asteroids, as defined by Pravec and Harris [Pravec, P., Harris, A.W., 2000. Icarus 148, 12-20]. These results suggest that a more robust structure must be expected, as a fractured monolith or a rubble pile in a “strength regime” [Holsapple, K.A., 2002. Speed limits of rubble pile asteroids: Even fast rotators can be rubble piles. In: Workshop on Scientific Requirements for Mitigation of Hazardous Comets and Asteroids, Washington, September, 2002].     

Polarimetric mapping of the Moon at a phase angle near the polarization minimum

At small phase angles the light scattered by the Moon reveals a negative polarization branch whose average amplitude is 1%. We present results of polarimetric mappings of the Moon in Pmin at a phase angle near 11°. The observations were carried out with the Kharkov 50-cm telescope at the Maidanak Observatory (Middle Asia) using a polarizing filter. A thorough calibration of the camera array allows for the reliable detection of significant variations of |Pmin| over the lunar surface, from 0.2 to 1.6%, at a wavelength of 0.52 μm. The smallest |Pmin| are characteristic of young bright craters, while the |Pmin| are the highest for the lunar highland and bright mare areas. The horse-shoe shape of the correlation dependence Pmin (albedo) is treated with data of our laboratory measurements of powdered surfaces and computer modeling of light scattering by small particles with the DDA (discrete dipole approximation) technique.     

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.     

Polarimetry of the exoplanet system 51 Pegasi

Two-year BVRI polarimetric monitoring of the exoplanet system 51 Peg has been carried out, indicating that there is no orbital phase-dependent periodic variability in linear polarization with amplitudes greater than 0.04% in the R and I bands. The mean value of one of the Stokes parameters is statistically significant and nonzero, being equal to 0.017 ± 0.004% when averaged over all the bands B, V, R, and I. The nonzero mean polarization can be due to light scattering by a circumstellar torus formed as a result of the mass loss by the hot Jupiter 51 Peg b.