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At least 397 records · Page 22

Understanding the Phase of Responsivity and Noise Sources in Frequency-Domain Multiplexed Readout of Transition Edge Sensor Bolometers

Abstract Cosmic microwave background (CMB) experiments have deployed focal planes with $$\mathcal {O}(10^{4})$$ O ( 10 4 ) transition edge sensor (TES) bolometers cooled to sub-Kelvin temperatures by multiplexing the readout of many TES channels onto a single pair of wires. Digital Frequency-domain Multiplexing (DfMux) is a multiplexing technique used in many CMB polarization experiments, such as the Simons Array, SPT-3 G, and EBEX. The DfMux system studied here uses LC filters with resonant frequencies ranging from 1.5 to 4.5 MHz connected to an array of TESs. Each detector has an amplitude-modulated carrier tone at the resonant frequency of its accompanying LC resonator. The signal is recovered via quadrature demodulation where the in-phase (I) component of the demodulated current is in phase with the complex admittance of the circuit and the quadrature (Q) component is orthogonal to I. Observed excess current noise in the Q component is consistent with fluctuations in the resonant frequency. This noise has been shown to be non-orthogonal to the phase of the detector’s responsivity. We present a detailed analysis of the phase of responsivity of the TES and noise sources in our DfMux readout system. Further, we investigate how modifications to the TES operating resistance and bias frequency can affect the phase of noise relative to the phase of the detector responsivity, using data from Simons Array to evaluate our predictions. We find that both the phase of responsivity and phase of noise are functions of the two tuning parameters, which can be purposefully selected to maximize signal-to-noise (SNR) ratio.

47 OTHER INSTRUMENTATION↗

On Anomaly Detection for Transactive Energy Systems with Competitive Market

Two anomaly-detection criteria are proposed for transactive energy systems with competitive markets. Participants of transactive energy systems seek an optimal power allocation through hybrid economic-control methods to facilitate the integration of various types of distributed energy resources to power distribution systems. In transactive energy systems, every participant is assumed to be a rational entity, and consumers have diminishing marginal utility and suppliers have increasing marginal cost. With the first proposed anomaly-detection criterion, the monotonicity of marginal cost and marginal utility are examined. The impact of line flow constraints is also taken into consideration. Then, the second anomaly-detection criterion is proposed for TESs with marginal cost and marginal utility which change faster than a certain rate. The second criterion is more accurate than the first one for TES with marginal cost and marginal utility which change faster than a certain rate, but it requires the knowledge of that rate. Neither criteria requires more data than those necessary to find the optimal power allocation and the market-clear price in a transactive energy system. Therefore, the proposed criteria do not disclose any more data than necessary. As the monotonicity of marginal cost and marginal utility in a TES with competitive markets results in convex objective functions in an optimization problem and strongly convex ones when marginal cost and marginal utility changes faster than a certain rate, the two detection criteria are also applicable to anomaly detection of general convex optimization problems. Simulations are carried out to show the efficacy of the proposed criteria to detect anomalies caused by cyberattacks.

Wang, Peng↗

Constraining the oblateness of transiting planets with photometry and spectroscopy

ABSTRACT Rapid planetary rotation can cause the equilibrium shape of a planet to be oblate. While planetary oblateness has mostly been probed by examining the subtle ingress and egress features in photometric transit light curves, we investigate the effect of oblateness on the spectroscopic Rossiter–McLaughlin (RM) signals. We found that a giant planet, with planet-to-star radius ratio of 0.15 and Saturn-like oblateness of 0.098, can cause spectroscopic signatures with amplitudes up to 1.1 m s−1 which is detectable by high-precision spectrographs such as ESPRESSO. We also found that the spectroscopic oblateness signals are particularly amplified for transits across rapidly rotating stars and for planets with spin-orbit misalignment thereby making them more prominent than the photometric signals at some transit orientations. We compared the detectability of oblateness in photometry and spectroscopy and found that photometric light curves are more sensitive to detecting oblateness than the spectroscopic RM signals mostly because they can be sampled with higher cadence to better probe the oblateness ingress and egress anomaly. However, joint analyses of the light curve and RM signal of a transiting planet provides more accurate and precise estimate of the planet’s oblateness. Therefore, ESPRESSO alongside ongoing and upcoming photometric instruments such as TESS, CHEOPS, PLATO, and JWST will be extremely useful in measuring planet oblateness.

Akinsanmi, B.↗

Discovery of multiple p-mode pulsation frequencies in the roAp star, HD 86181

ABSTRACT We report the frequency analysis of a known roAp star, HD 86181 (TIC 469246567), with new inferences from Transiting Exoplanet Survey Satellite (TESS) data. We derive the rotation frequency to be νrot = 0.48753 ± 0.00001 d−1. The pulsation frequency spectrum is rich, consisting of two doublets and one quintuplet, which we interpret to be oblique pulsation multiplets from consecutive, high-overtone dipole, quadrupole, and dipole modes. The central frequency of the quintuplet is 232.7701 d−1 (2.694 mHz). The phases of the sidelobes, the pulsation phase modulation, and a spherical harmonic decomposition all show that the quadrupole mode is distorted. Following the oblique pulsator model, we calculate the rotation inclination, i, and magnetic obliquity, β, of this star, which provide detailed information about the pulsation geometry. The i and β derived from the best fit of the pulsation amplitude and phase modulation to a theoretical model, including the magnetic field effect, slightly differ from those calculated for a pure quadrupole, indicating the contributions from ℓ = 4, 6, 8,... are small. Non-adiabatic models with different envelope convection conditions and physics configurations were considered for this star. It is shown that models with envelope convection almost fully suppressed can explain the excitation at the observed pulsation frequencies.

Shi, Fangfei (ORCID:0000000323998216)↗

Progenitor and close-in circumstellar medium of type II supernova 2020fqv from high-cadence photometry and ultra-rapid UV spectroscopy

ABSTRACT We present observations of SN 2020fqv, a Virgo-cluster type II core-collapse supernova (CCSN) with a high temporal resolution light curve from the Transiting Exoplanet Survey Satellite (TESS) covering the time of explosion; ultraviolet (UV) spectroscopy from the Hubble Space Telescope (HST) starting 3.3 d post-explosion; ground-based spectroscopic observations starting 1.1 d post-explosion; along with extensive photometric observations. Massive stars have complicated mass-loss histories leading up to their death as CCSNe, creating circumstellar medium (CSM) with which the SNe interact. Observations during the first few days post-explosion can provide important information about the mass-loss rate during the late stages of stellar evolution. Model fits to the quasi-bolometric light curve of SN 2020fqv reveal 0.23 M⊙ of CSM confined within 1450 R⊙ (1014 cm) from its progenitor star. Early spectra (<4 d post-explosion), both from HST and ground-based observatories, show emission features from high-ionization metal species from the outer, optically thin part of this CSM. We find that the CSM is consistent with an eruption caused by the injection of ∼5 × 1046 erg into the stellar envelope ∼300 d pre-explosion, potentially from a nuclear burning instability at the onset of oxygen burning. Light-curve fitting, nebular spectroscopy, and pre-explosion HST imaging consistently point to a red supergiant (RSG) progenitor with $M_{\rm ZAMS}\approx 13.5\!-\!15 \, \mathrm{M}_{\odot }$, typical for SN II progenitor stars. This finding demonstrates that a typical RSG, like the progenitor of SN 2020fqv, has a complicated mass-loss history immediately before core collapse.

Tinyanont, Samaporn (ORCID:0000000214814676)↗

ASAS J071404+7004.3 – a close, bright nova-like cataclysmic variable with gusty winds

ABSTRACT Despite being bright (V ≃ 11.8) and nearby (d = 212 pc) ASAS J071404+7004.3 has only recently been identified as a nova-like cataclysmic variable. We present time-resolved optical spectroscopy obtained at the Isaac Newton and the Hiltner and McGraw-Hill Telescopes, together with Swift X-ray and ultraviolet observations. We combined these with TESS photometry and find a period of 3.28 h and a mass transfer rate of $4\!-\!9\times 10^{-9}\, {\mathrm{M_{\odot }\, yr}^{-1}}$. Historical photometry shows at least one low state establishing the system as a VY Scl star. Our high-cadence spectroscopy also revealed rapidly changing winds emanating from the accretion disc. We have modelled these using the Monte Carlo python code and shown that all the emission lines could emanate from the wind – which would explain the lack of double-peaked lines in such systems. In passing, we discuss the effect of variability on the position of cataclysmic variables in the Gaia Hertzsprung–Russell diagram.

Inight, K. (ORCID:0000000222002416)↗

Reanalysis of c-type RR Lyrae variable BE Dor, period modulations and possible mechanism

ABSTRACT We reanalysed the c-type RR Lyrae star BE Dor (MACHO 5.4644.8, OGLE-LMC-RRLYR-06002) that had been discovered to show cyclic period changes. The photometric data of several sky surveys (DASCH, MACHO, OGLE, ASAS-SN, and TESS) were used for analyses. The O − C diagram and pulsation period obtained from Fourier analysis show significant period modulations in BE Dor. However, different from the previous viewpoint, the changes are quasi-periodic and abrupt. Therefore, the light-traveltime effect caused by the companion motion cannot explain the changes. Noting a same subtype star KIC 9453114 with similar phenomena has a high macroturbulent velocity, and the degree of O − C changes seem to be positively correlated with these velocities, we consider that the mechanism leading to period modulation should be caused by the interaction between turbulent convection and magnetic field activity in the ionization zone, i.e. the viewpoint of Stothers. It may not explain the general Blazhko effect but should explain such period modulations in BE Dor and those other c-type RR Lyrae stars. We hope our discoveries and viewpoints can provide some information and inspiration for relevant research.

Li, L-J↗

TYC 2990-127-1: An Algol-type SB2 binary system of subgiant and red giant with a probable ongoing mass-transfer

ABSTRACT We present a study of the spectroscopic binary TYC 2990-127-1 from the LAMOST survey. We use full-spectrum fitting to derive radial velocities and spectral parameters. The high mass ratio indicates that the system underwent mass transfer in the past. We compute the orbital solution and find that it is a very close sub-giant/red giant pair on circular orbit, slightly inclined to the sky-plane. Fitting of the TESS photometrical data confirms this and suggests an inclination of i ∼ 39.8°. The light curve and spectrum around Hα show signs of irregular variability, which supports ongoing mass transfer. The binary evolution simulations suggest that the binary may experience non-conservative mass transfer with accretion efficiency 0.3, and the binary will enter into common envelope (CE) phase in the subsequent evolution. The remnant product after the ejection of CE may be a detached double helium white dwarf (He WD) or a merger.

79 ASTRONOMY AND ASTROPHYSICS↗

The ‘Giraffe’: discovery of a stripped red giant in an interacting binary with an ∼2 M ⊙ lower giant

We report the discovery of a stripped giant + lower giant Algol-type binary, 2M04123153+6738486 (2M0412), identified during a search for non-interacting compact object – star binaries. 2M0412 is an evolved ( T eff, giant ≃ 4000 K), luminous ( L giant ≃ 150 L ⊙ ) red giant in a circular P = 81.2 d binary. 2M0412 is a known variable star previously classified as a semiregular variable. The cross-correlation functions of follow-up Keck/HIRES and LBT/Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) spectra show an radial velocity variable second component with implied mass ratio q = M giant / M comp ≃ 0.20 ± 0.01. The All-Sky Automated Survey for SuperNovae (ASAS-SN), Asteroid Terrestrial-impact Last Alert System (ATLAS), Transiting Exoplanet Survey Telescope ( TESS ), and Zwicky Transient Facility (ZTF) light curves show that the giant is a Roche lobe filling ellipsoidal variable with an inclination of 49.4 ± 0.3°, and a giant mass of M giant = 0.38 ± 0.01 M ⊙ for a distance of ≃ 3.7 kpc. The mass of the giant indicates that its envelope has been partially stripped. The giant companion on the lower red giant branch has a mass of M comp = 1.91 ± 0.03 M ⊙ with T eff, comp ≃ 5000 K, L comp ≃ 60 L ⊙ , and R comp ≃ 11 R ⊙ . The lower giant contributes ${\sim }35{{\ \rm per\ cent}}$ of the flux in the V band. We also identify an orbital phase dependent, broad $\rm H\,\alpha$ emission line which could indicate ongoing accretion from the stripped red giant on to the companion.

(stars:) binaries: spectroscopic↗

Trumpler 16-26: a new centrifugal magnetosphere star discovered via SDSS/APOGEE H -band spectroscopy

ABSTRACT We report the discovery of a new example of the rare class of highly magnetized, rapidly rotating, helium enhanced, early B stars that produce anomalously wide hydrogen emission due to a centrifugal magnetosphere (CM). The star is Trumpler 16-26, a B1.5 V member of the Trumpler 16 open cluster. A CM was initially suspected based on hydrogen Brackett series emission observed in SDSS/APOGEE H-band spectra. Similar to the other stars of this type, the emission was highly variable and at all times remarkable due to the extreme velocity separations of the double peaks (up to 1300 km s−1.) Another clue lay in the TESS light curve, which shows two irregular eclipses per cycle when phased with the likely 0.971 8115-d rotation period, similar to the behaviour of the well-known CM host star σ Ori E. To confirm a strong magnetic field and rotation-phase-locked variability, we initiated a follow-up campaign consisting of optical spectropolarimetry and spectroscopy. The associated data revealed a longitudinal magnetic field varying between −3.1 and +1.6 kG with the period found from photometry. The optical spectra confirmed rapid rotation (v sin i = 195 km s−1), surface helium enhancement, and wide, variable hydrogen emission. Tr16-26 is thus confirmed as the 20th known, the fourth most rapidly rotating, and the faintest CM host star yet discovered. With a projected dipole magnetic field strength of Bd > 11 kG, Tr16-26 is also among the most magnetic CM stars.

79 ASTRONOMY AND ASTROPHYSICS↗

Fundamental effective temperature measurements for eclipsing binary stars – IV. Selection of new benchmark stars and first results for HD 22064

I describe the selection and initial characterization of 20 eclipsing binary stars that are suitable for calibration and testing of stellar models and data analysis algorithms used by the PLATO mission and spectroscopic surveys. The binary stars selected are F-/G-type dwarf stars with M-type dwarf companions that contribute less than 2 per cent of the flux at optical wavelengths. The light curves typically show well-defined total eclipses with very little variability between the eclipses. I have used near-infrared spectra obtained by the APOGEE survey to measure the spectroscopic orbit for both stars in HD 22064. Combined with an analysis of the TESS light curve, I derive the following masses and radii: M 1 = 1.35 ± 0.03M ⊙ , M 2 = 0.58 ± 0.01M ⊙ , R 1 = 1.554 ± 0.014R ⊙ , R 2 = 0.595 ± 0.008R ⊙ . Using R 1 and the parallax from Gaia EDR3, I find that the primary star’s angular diameter is θ = 0.1035 ± 0.0009 mas. The apparent bolometric flux of the primary star is ${\mathcal {F}}_{{\oplus },0} = (7.51\pm 0.09)\times 10^{-9}$ erg cm -2 s -1 . Hence, this F2V star has an effective temperature $T_{\rm eff,1} = 6763{\rm \, K} \pm 39{\rm \, K}$. HD 22064 is an ideal benchmark star that can be used for ‘end-to-end’ tests of the stellar parameters measured by large-scale spectroscopic surveys or stellar parameters derived from asteroseismology with PLATO. The techniques described here for HD 22064 can be applied to the other eclipsing binaries in the sample in order to create an all-sky network of such benchmark stars.

79 ASTRONOMY AND ASTROPHYSICS↗

TOI-908: a planet at the edge of the Neptune desert transiting a G-type star

ABSTRACT We present the discovery of an exoplanet transiting TOI-908 (TIC-350153977) using data from TESS sectors 1, 12, 13, 27, 28, and 39. TOI-908 is a T = 10.7 mag G-dwarf (Teff = 5626 ± 61 K) solar-like star with a mass of 0.950 ± 0.010 M⊙ and a radius of 1.028 ± 0.030 R⊙. The planet, TOI-908 b, is a 3.18 ± 0.16 R⊕ planet in a 3.18 d orbit. Radial velocity measurements from HARPS reveal TOI-908 b has a mass of approximately 16.1 ± 4.1 M⊕, resulting in a bulk planetary density of $2.7^{+0.2}_{-0.4}$ g cm−3. TOI-908 b lies in a sparsely populated region of parameter space known as the Neptune desert. The planet likely began its life as a sub-Saturn planet before it experienced significant photoevaporation due to X-rays and extreme ultraviolet radiation from its host star, and is likely to continue evaporating, losing a significant fraction of its residual envelope mass.

Hawthorn, Faith (ORCID:000000028675182X)↗

TOI-2374 b and TOI-3071 b: two metal-rich sub-Saturns well within the Neptunian desert

ABSTRACT We report the discovery of two transiting planets detected by the Transiting Exoplanet Survey Satellite (TESS), TOI-2374 b and TOI-3071 b, orbiting a K5V and an F8V star, respectively, with periods of 4.31 and 1.27 d, respectively. We confirm and characterize these two planets with a variety of ground-based and follow-up observations, including photometry, precise radial velocity monitoring and high-resolution imaging. The planetary and orbital parameters were derived from a joint analysis of the radial velocities and photometric data. We found that the two planets have masses of (57 ± 4) M⊕ or (0.18 ± 0.01) MJ, and (68 ± 4) M⊕ or (0.21 ± 0.01) MJ, respectively, and they have radii of (6.8 ± 0.3) R⊕ or (0.61 ± 0.03) RJ and (7.2 ± 0.5) R⊕ or (0.64 ± 0.05) RJ, respectively. These parameters correspond to sub-Saturns within the Neptunian desert, both planets being hot and highly irradiated, with Teq ≈ 745 K and Teq ≈ 1812 K, respectively, assuming a Bond albedo of 0.5. TOI-3071 b has the hottest equilibrium temperature of all known planets with masses between 10 and 300 M⊕ and radii less than 1.5 RJ. By applying gas giant evolution models we found that both planets, especially TOI-3071 b, are very metal-rich. This challenges standard formation models which generally predict lower heavy-element masses for planets with similar characteristics. We studied the evolution of the planets’ atmospheres under photoevaporation and concluded that both are stable against evaporation due to their large masses and likely high metallicities in their gaseous envelopes.

Hacker, Alejandro (ORCID:0009000994520181)↗

TOI–757 b: an eccentric transiting mini–Neptune on a 17.5–d orbit

ABSTRACT We report the spectroscopic confirmation and fundamental properties of TOI$-$757 b, a mini$-$Neptune on a 17.5$-$d orbit transiting a bright star ($V\, =\, 9.7$ mag) discovered by the TESS mission. We acquired high$-$precision radial velocity measurements with the HARPS, ESPRESSO, and PFS spectrographs to confirm the planet detection and determine its mass. We also acquired space$-$borne transit photometry with the CHEOPS space telescope to place stronger constraints on the planet radius, supported with ground$-$based LCOGT photometry. WASP and KELT photometry were used to help constrain the stellar rotation period. We also determined the fundamental parameters of the host star. We find that TOI$-$757 b has a radius of $R_{\mathrm{p}} = 2.5 \pm 0.1 R_{\oplus }$ and a mass of $M_{\mathrm{p}} = 10.5^{+2.2}_{-2.1} M_{\oplus }$, implying a bulk density of $\rho _{\text{p}} = 3.6 \pm 0.8$ g cm$^{-3}$. Our internal composition modelling was unable to constrain the composition of TOI$-$757 b, highlighting the importance of atmospheric observations for the system. We also find the planet to be highly eccentric with e = 0.39$^{+0.08}_{-0.07}$, making it one of the very few highly eccentric planets among precisely characterized mini$-$Neptunes. Based on comparisons to other similar eccentric systems, we find a likely scenario for TOI$-$757 b’s formation to be high eccentricity migration due to a distant outer companion. We additionally propose the possibility of a more intrinsic explanation for the high eccentricity due to star$-$star interactions during the earlier epoch of the Galactic disc formation, given the low metallicity and older age of TOI$-$757.

Alqasim, A. (ORCID:0000000151025505)↗

The luminous, slow-rising orphan afterglow AT2019pim as a candidate moderately relativistic outflow

ABSTRACT Classical gamma-ray bursts (GRBs) have two distinct emission episodes: prompt emission from ultrarelativistic ejecta and afterglow from shocked circumstellar material. While both components are extremely luminous in known GRBs, a variety of scenarios predict the existence of luminous afterglow emission with little or no associated high-energy prompt emission. We present AT 2019pim, the first spectroscopically confirmed afterglow with no observed high-energy emission to be identified. Serendipitously discovered during follow-up observations of a gravitational-wave trigger and located in a contemporaneous TESS sector, it is hallmarked by a fast-rising ($t \approx 2$ h), luminous ($M_{\rm UV,peak} \approx -24.4$ mag) optical transient with accompanying luminous X-ray and radio emission. No gamma-ray emission consistent with the time and location of the transient was detected by Fermi-GBM or by Konus, placing constraining limits on an accompanying GRB. We investigate several independent observational aspects of the afterglow in the context of constraints on relativistic motion and find all of them are consistent with an initial Lorentz factor of $\Gamma _0 \approx$ 10–30 for the on-axis material, significantly lower than in any well-observed GRB and consistent with the theoretically predicted ‘dirty fireball’ scenario in which the high-energy prompt emission is stifled by pair production. However, we cannot rule out a structured jet model in which only the line-of-sight material was ejected at low-$\Gamma$, off-axis from a classical high-$\Gamma$ jet core, and an on-axis GRB with below-average gamma-ray efficiency also remains a possibility. This event represents a milestone in orphan afterglow searches, demonstrating that luminous optical afterglows lacking detected GRB counterparts can be identified and spectroscopically confirmed in real time.

Perley, Daniel A. (ORCID:0000000184721996)↗

Beamline Spectroscopy of Integrated Circuits With Hard X-Ray Transition Edge Sensors at the Advanced Photon Source

At Argonne National Laboratory, we are developing hard X-ray (2 to 20 keV) Transition Edge Sensor (TES) arrays for beamline science. The significantly improved energy resolution provided by superconducting detectors compared to semiconductor-based energy-dispersive detectors, but with better collection efficiency than wavelength-dispersive instruments, will enable greatly improved X-ray emission and absorption spectroscopic measurements. Additionally, a prototype instrument with 24 microwave-frequency multiplexed pixels is now in testing at the Advanced Photon Source (APS) 1-BM beamline. Initial measurements show an energy resolution ten times better (150 eV compared to < 15 eV) than the silicon-drift detectors currently available to APS beamline users, and in particular demonstrate the ability to resolve closely-spaced emission lines in samples containing multiple transition metal elements, such as integrated circuits. Comparing fluorescence spectra of integrated circuits measured with our TESs at the beamline to those measured with silicon detectors, we find emission lines and elements largely hidden (e.g. Hf alongside Cu) from a semiconductor-based detector but well resolved by a TES. This directly shows the strengths of TES-based instruments in fluorescence mapping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Hyperspectral X-ray Imaging: Progress Towards Chemical Analysis in the SEM

The Hyperspectral X-ray Imaging (HXI) project will enable non-destructive chemical-state determination of nano-scale samples in the electron microscope for nuclear safeguards applications. To efficiently measure chemical state through electron-excited X-ray emission requires a combination of wide spectral bandwidth, high resolution, and high count rate capability. We are building a next-generation X-ray detector based on an array of transition edge sensors (TESs) to make these measurements possible and routine in the scanning electron microscope (SEM). Leveraging the large pixel densities afforded by microwave multiplexing readout and continuous, uninterrupted operation of a cryogen-free dilution refrigerator, this instrument will have efficiency to allow chemical species identification of nano-scale samples in hours instead of days to weeks. We describe prototype pixel designs for this HXI instrument, comprising three pixel types that will make up the hybrid TES array. Engineering design of the integrated HXI cryostat and SEM system is in progress, with full detector commissioning expected in Spring 2021 followed closely by full-scale integration with the SEM. Furthermore, we also report on the commissioning of a complementary TES-based X-ray emission spectroscopy platform for bulk samples to build a spectral library for HXI sample identification.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Transactive Energy System Deployment Over Insecure Communication Links

Here, in this paper, the privacy and security issues associated with the transactive energy system (TES) deployment over insecure communication links are addressed. In particular, it is ensured that 1) individual agents’ bidding information is kept private throughout hierarchical market-based interactions; and 2) any extraneous data injection attack can be quickly and easily detected. An implementation framework is proposed to enable the cryptography-based enhancement of privacy and security for the deployment of any general hierarchical systems including TESs. Under the proposed framework, a unified cryptography-based approach is developed to achieve both privacy and security simultaneously. Specifically, privacy preservation is realized by an enhanced Paillier encryption scheme, where a block design is proposed to significantly improve computational efficiency. Attack detection is further achieved by an enhanced Paillier digital signature scheme, where a stamp-concatenation mechanism is proposed to enable detection of data replace and reorder attacks. Simulation results verify the effectiveness of the proposed cyber-resilient design for transactive energy systems. Note to Practitioners—This paper is motivated by addressing the issues of cyber resiliency for practically deploying transactive energy system (TES) but it is also applicable to the problem of enhancing the privacy and security for any general hierarchical control systems. TES is an emerging control approach that engages energy suppliers and customers through market operations and uses the price to optimally allocate energy resources. While it has been shown to be promising for power system applications, the underlying market-based interactions raise significant concerns of privacy (data leakage) and security (data tampering). However, existing TES works only focus on the coordination mechanism instead of privacy and security issues. This paper proposes a new cryptography-based TES design for practical deployment. Specifically, to protect privacy, individual supply and demand amounts to be exchanged are all encrypted in a particular way such that the original amounts cannot be inferred from the encrypted amounts, while the desired computation for setting the market clearing price can be carried out over the encrypted amounts, thus generating an encrypted result which, when decrypted, matches that of the same computation over the original amounts. To achieve security, for each exchanged data, its sender generates a particular digital signature which is exchanged together with the data. This enables the receiver to automatically detect the integrity by checking whether a mathematical relationship holds for the pair of data and signature. In our future research, we will investigate more challenging scenarios where some suppliers and customers themselves could be corrupted and purposely submit distorted amounts.

97 MATHEMATICS AND COMPUTING↗