Stellar Intensity Research Articles

Differential Rotation of CoRoT Stars and a Kepler Binary Star from Starspot Transit Mapping

Abstract While direct magnetic field measurements are rare for slowly rotating stars, spots observed during planetary transits provide a potential indicator of magnetic activity on stellar surfaces. Moreover, the rotation of the stellar surface can be probed by monitoring the spots’ position with time in subsequent transits. This study investigates the dynamic interplay of rotational shear and stellar rotation rate in six stars of spectral types F to M, all hosting exoplanets observed by the CoRoT space mission, except for one binary star from Kepler. The analysis, facilitated by the ECLIPSE code, unveils the physical properties of stellar spots, including radius, intensity, temperature, and position. The five CoRoT stars exhibit spot characteristics consistent with those observed in solar type stars. The determination of a spot longitude during different transits allows for the inference of the star’s differential rotation profile, revealing a decreasing trend of rotational shear with the mean stellar rotation period, given by Δ Ω ∝ P ¯ − 0.9 . This implies that, at least for slow rotators (mean rotation period >5 days), as stars age, their differential rotation decreases. Additionally, the six stars analyzed here seem to fall into two categories, according to their spot flux deficit: those with ΔF spot > 0.005 and those with ΔF spot < 0.002.

An Angular Diameter Measurement of β UMa via Stellar Intensity Interferometry with the VERITAS Observatory

We use the Very Energetic Radiation Imaging telescope Array System (VERITAS) imaging air Cherenkov telescope array to obtain the first measured angular diameter of β UMa at visual wavelengths using stellar intensity interferometry (SII) and independently constrain the limb-darkened angular diameter. The age of the Ursa Major moving group has been assessed from the ages of its members, including nuclear member Merak (β UMa), an A1-type subgiant, by comparing effective temperature and luminosity constraints to model stellar evolution tracks. Previous interferometric limb-darkened angular-diameter measurements of β UMa in the near-infrared (Center for High Angular Resolution Astronomy (CHARA) Array, 1.149 ± 0.014 mas) and mid-infrared (Keck Nuller, 1.08 ± 0.07 mas), together with the measured parallax and bolometric flux, have constrained the effective temperature. This paper presents current VERITAS-SII observation and analysis procedures to derive squared visibilities from correlation functions. We fit the resulting squared visibilities to find a limb-darkened angular diameter of 1.07 ± 0.04 (stat) ± 0.05 (sys) mas, using synthetic visibilities from a stellar atmosphere model that provides a good match to the spectrum of β UMa in the optical wave band. The VERITAS-SII limb-darkened angular diameter yields an effective temperature of 9700 ± 200 ± 200 K, consistent with ultraviolet spectrophotometry, and an age of 390 ± 29 ± 32 Myr, using MESA Isochrones and Stellar Tracks. This age is consistent with 408 ± 6 Myr from the CHARA Array angular diameter.

Performance and first measurements of the MAGIC stellar intensity interferometer

ABSTRACT In recent years, a new generation of optical intensity interferometers has emerged, leveraging the existing infrastructure of Imaging Atmospheric Cherenkov Telescopes (IACTs). The MAGIC telescopes host the MAGIC-SII system (Stellar Intensity Interferometer), implemented to investigate the feasibility and potential of this technique on IACTs. After the first successful measurements in 2019, the system was upgraded and now features a real-time, dead-time-free, 4-channel, GPU-based correlator. These hardware modifications allow seamless transitions between MAGIC’s standard very-high-energy gamma-ray observations and optical interferometry measurements within seconds. We establish the feasibility and potential of employing IACTs as competitive optical Intensity Interferometers with minimal hardware adjustments. The measurement of a total of 22 stellar diameters are reported, 9 corresponding to reference stars with previous comparable measurements, and 13 with no prior measurements. A prospective implementation involving telescopes from the forthcoming Cherenkov Telescope Array Observatory’s Northern hemisphere array, such as the first prototype of its Large-Sized Telescopes, LST-1, is technically viable. This integration would significantly enhance the sensitivity of the current system and broaden the UV-plane coverage. This advancement would enable the system to achieve competitive sensitivity with the current generation of long-baseline optical interferometers over blue wavelengths.

Science with the ASTRI Mini-Array: From Experiment to Open Observatory

Although celestial sources emitting in the few tens of GeV up to a few TeV are being investigated by imaging atmospheric Čerenkov telescope arrays such as H.E.S.S., MAGIC, and VERITAS, at higher energies, up to PeV, more suitable instrumentation is required to detect ultra-high-energy photons, such as extensive air shower arrays, as HAWC, LHAASO, Tibet AS-γ. The Italian National Institute for Astrophysics has recently become the leader of an international project, the ASTRI Mini-Array, with the aim of installing and operating an array of nine dual-mirror Čerenkov telescopes at the Observatorio del Teide in Spain starting in 2025. The ASTRI Mini-Array is expected to span a wide range of energies (1–200 TeV), with a large field of view (about 10 degrees) and an angular and energy resolution of ∼3 arcmin and ∼10 %, respectively. The first four years of operations will be dedicated to the exploitation of Core Science, with a small and selected number of pointings with the goal of addressing some of the fundamental questions on the origin of cosmic rays, cosmology, and fundamental physics, the time-domain astrophysics and non γ-ray studies (e.g., stellar intensity interferometry and direct measurements of cosmic rays). Subsequently, four more years will be dedicated to Observatory Science, open to the scientific community through the submission of observational proposals selected on a competitive basis. In this paper, I will review the Core Science topics and provide examples of possible Observatory Science cases, taking into account the synergies with current and upcoming observational facilities.

Self-consistent modeling of metastable helium exoplanet transits

Absorption of stellar X-ray and extreme ultraviolet (EUV) radiation in the upper atmosphere of close-in exoplanets can give rise to hydrodynamic outflows, which may lead to the gradual shedding of their primordial light element envelopes. Excess absorption by neutral helium atoms in the metastable 2 3S state [He I(2 3S)], at ~10 830 Å, has recently emerged as a viable diagnostic of atmospheric escape. Here we present a public add-on module to the 1D photoionization hydrodynamic code ATES, designed to calculate the He I(2 3S) transmission probability for a broad range of planetary parameters. By relaxing the isothermal outflow assumption, the code enables a self-consistent assessment of the He I(2 3S) absorption depth along with the atmospheric mass-loss rate and the outflow temperature profile, which strongly affects the recombination rate of He II into He I(2 3S). We investigate how the transit signal can be expected to depend upon known system parameters, including host spectral type, orbital distance, and planet gravity. At variance with previous studies, which identified K-type stars as favorable hosts, we conclude that late M dwarfs with Neptune-sized planets orbiting at ~0.05–0.1 AU can be expected to yield the strongest transit signal, well in excess of 30% for near-cosmological He-to-H abundances. More generally, we show that the physics that regulates the population and depletion of the metastable state, combined with geometrical effects, can yield somewhat counterintuitive results, such as a nonmonotonic dependence of the transit depth on orbital distance. These are compounded by a strong degeneracy between the stellar EUV flux intensity and the atmospheric He-to-H abundance, both of which are highly uncertain. Compared with spectroscopy data, now available for over 40 systems, our modeling suggests either that a large fraction of the targets have helium-depleted envelopes or that the input stellar EUV spectra are systematically overestimated. The updated code and transmission probability module are available publicly as an online repository.

Wide-field intensity fluctuation imaging.

The temporal intensity fluctuations contain important information about the light source and light-medium interaction and are typically characterized by the intensity autocorrelation function, g2(τ). The measurement of g2(τ) is a central topic in many optical sensing applications, ranging from stellar intensity interferometer in astrophysics, to fluorescence correlation spectroscopy in biomedical sciences and blood flow measurement with dynamic light scattering. Currently, g2(τ) at a single point is readily accessible through high-frequency sampling of the intensity signal. However, two-dimensional wide-field imaging of g2(τ) is still limited by the cameras' frame rate. We propose and demonstrate a 2-pulse within-exposure modulation approach to break through the camera frame rate limit and obtain the quasi g2(τ) map in wide field with cameras of only ordinary frame rates.

Photon counting intensity interferometry in the blue at a 0.5 m telescope

Abstract Intensity interferometry is a re-emerging interferometry tool that alleviates some of the challenges of amplitude interferometry at the cost of reduced sensitivity. We demonstrate the feasibility of intensity interferometry with fast single-photon counting detectors at small telescopes by utilizing a telescope of diameter of merely 0.5 m. The entire measurement set-up, including collimation, optical filtering, and two single-photon detectors, is attached directly to the telescope without the use of optical fibres, facilitated by the large area of our single-photon detectors. For digitization and timing, we utilize a time-to-amplitude-converter. Observing α Lyrae (Vega) for a total exposure time of 32.4 h over the course of six nights, an auto-correlation signal with a contrast of (9.5 ± 2.7) × 10−3 and a coherence time of (0.34 ± 0.12) ps at a signal-to-noise ratio of 2.8 is measured. The result fits well to preceding laboratory tests as well as expectations calculated from the optical and electronic characteristics of our measurement set-up. This measurement, to our knowledge, constitutes the first time that a bunching signal with starlight was measured in the B band with single-photon counting detectors. Simultaneously, this is to date the stellar intensity interferometry measurement utilizing the smallest telescope. Our successful measurement shows that intensity interferometry can be adopted not only at large-scale facilities, but also at readily available and inexpensive smaller telescopes.

Electronics and Detectors for the Stellar Intensity Interferometer of the ASTRI Mini-Array Telescopes.

The ASTRI Mini-Array is an international collaboration led by the Italian National Institute for Astrophysics (INAF) that will operate nine telescopes to perform Cherenkov and optical stellar intensity interferometry (SII) observations. At the focal plane of these telescopes, we are planning to install a stellar intensity interferometry instrument. Here we present the selected design, based on Silicon Photomultiplier (SiPM) detectors matching the telescope point spread function together with dedicated front-end electronics.

A Pipeline for Modeling Rapidly Rotating Stars

Recent stellar intensity interferometry observations of stars at 416 nm complement Michelson interferometry observations in the near-infrared where stellar surface intensity gradients (e.g., limb darkening) are weaker. Intensity gradients due to gravity darkening in rapidly rotating stars are also expected to show higher contrast at 416 nm relative to the near-infrared. We have created a software pipeline to model stellar photospheres of rapidly rotating stars to compare predictions at these wavelength regions. The pipeline can produce model images, visibility predictions, and synthetic spectra. Here we show examples for the Be star β CMi, which has not been interferometrically imaged. We see higher contrast from gravity darkening at 416 nm in model images for rapid rotators, but only for those stars that are not viewed equator-on.

Multidimensional Simulations of Core Convection

The cores of main sequence intermediate- and high-mass stars are convective. Mixing at the radiative–convective boundary, waves excited by the convection, and magnetic fields generated by convective dynamos all influence the main sequence and post-main sequence evolution of these stars. These effects must be understood to accurately model the structure and evolution of intermediate- and high-mass stars. Unfortunately, there are many challenges in simulating core convection due to the wide range of temporal and spatial scales, as well as many important physics effects. In this review, we describe the latest numerical strategies to address these challenges. We then describe the latest state-of-the-art simulations of core convection, summarizing their main findings. These simulations have led to important insights into many of the processes associated with core convection. Two outstanding problems with multidimensional simulations are, 1. it is not always straightforward to extrapolate from simulation parameters to the parameters of real stars; and 2. simulations using different methods sometimes appear to arrive at contradictory results. To address these issues, next generation simulations of core convection must address how their results depend on stellar luminosity, dimensionality, and turbulence intensity. Furthermore, code comparison projects will be essential to establish robust parameterizations that will become the new standard in stellar modeling.

Imaging via Correlation of X-Ray Fluorescence Photons.

We demonstrate that x-ray fluorescence emission, which cannot maintain a stationary interference pattern, can be used to obtain images of structures by recording photon-photon correlations in the manner of the stellar intensity interferometry of Hanbury Brown and Twiss. This is achieved utilizing femtosecond-duration pulses of a hard x-ray free-electron laser to generate the emission in exposures comparable to the coherence time of the fluorescence. Iterative phasing of the photon correlation map generated a model-free real-space image of the structure of the emitters. Since fluorescence can dominate coherent scattering, this may enable imaging uncrystallised macromolecules.

Effect of gravitational wave onto stellar intensity interferometry

Effect of gravitational wave onto stellar intensity interferometry

Python programming code for stellar photometry in astrophysics teaching on a cloud computing service

Nowadays, there is various software used for both education and astronomy research. For photometry, licensed software and high-performance computer operating systems are required, which is a fund limitation for some schools in Thailand. Thus, in this article, we develop and present the Demonstration Photometry Scripts for Astrophysics Teaching (DPSAT version 1.0). The program is designed to work on cloud computing services via internet browsers to avoid hardware and operation requirement pain points. The DPSAT is programming on flexible, low-cost, on-trend language, Python, and Jupyter Notebook online editor. In advance, our new code supports the home-use image or video file format, i.e., jpg, png, or mp4. Thus, it will be more accessible for teachers and students who do not have standard astronomical instruments. The DPSAT measures the stellar light intensity from the time-series still-images or video files from a smartphone or other digital devices. The code can extract video files into sequenced still images, then transform the RGB color space images into greyscale. The light intensity signal of selected pixels is counted with a simple aperture method in time series. It shows the results, for example, the mean signal, standard variation, measured signal as light intensity versus time, and image of light sources. This will be fruitful for low-cost and easily accessible teaching of astrophysics subjects.

First Release of PLATO Consortium Stellar Limb-darkening Coefficients

We release the first grid of stellar limb-darkening coefficients (LDCs) and intensity profiles (IPs) computed by the consortium of the PLAnetary Transits and Oscillations of stars (PLATO), the next medium-class (M3) mission under development by the European Space Agency to be launched in 2026. We have performed spectral synthesis with TurboSpectrum on a grid of MARCS model atmospheres. Finally, we adopted ExoTETHyS to convolve the high-resolution spectra (R = 2 × 105) with the state-of-the-art response functions for all the PLATO cameras, and computed the LDCs that best approximate the convolved IPs. In addition to the PLATO products, we provide new LDCs and IPs for the Kepler mission, based on the same grid of stellar atmospheric models and calculation procedures. The data can be downloaded from the following link: https://doi.org/10.5281/zenodo.7339706.

Investigating the accuracy achievable in reconstructing the angular sizes of stars through stellar intensity interferometry observations

Context. In recent years, stellar intensity interferometry has seen renewed interest from the astronomical community because it can be efficiently applied to Cherenkov telescope arrays. Aims. We have investigated the accuracy that can be achieved in reconstructing stellar sizes by fitting the visibility curve measured on the ground. The large number of expected available astronomical targets, the limited number of nights in a year, and the likely presence of multiple baselines will require careful planning of the observational strategy to maximise the scientific output. Methods. We studied the trend of the error on the estimated angular size, considering the uniform disk model, by varying several parameters related to the observations, such as the total number of measurements, the integration time, the signal-to-noise ratio, and different positions along the baseline. Results. We found that measuring the value of the zero-baseline correlation is essential to obtain the best possible results. Systems that can measure this value directly or for which it is known in advance will have better sensitivity. We also found that to minimise the integration time, it is sufficient to obtain a second measurement at a baseline half-way between 0 and that corresponding to the first zero of the visibility function. This function does not have to be measured at multiple positions. Finally, we obtained some analytical expressions that can be used under specific conditions to determine the accuracy that can be achieved in reconstructing the angular size of a star in advance. This is useful to optimise the observation schedule.

Comparing different approaches for stellar intensity interferometry

ABSTRACTStellar intensity interferometers correlate photons within their coherence time and could overcome the baseline limitations of existing amplitude interferometers. Intensity interferometers do not rely on phase coherence of the optical elements and thus function without high-grade optics and light combining delay lines. However, the coherence time of starlight observed with realistic optical filter bandwidths ($\gt {0.1}\, {\rm nm}$) is usually much smaller than the time resolution of the detection system ($\gt {10}\, {\rm ps}$), resulting in a greatly reduced correlation signal. Reaching high signal-to-noise ratio in a reasonably short measurement time can be achieved in different ways: either by increasing the time resolution, which increases the correlation signal height, or by increasing the photon rate, which decreases statistical uncertainties of the measurement. We present laboratory measurements employing both approaches and directly compare them in terms of signal-to-noise ratio. A high-time-resolution interferometry setup designed for small-to-intermediate-sized optical telescopes and thus lower photon rates (diameters $\lt \,$some metres) is compared to a setup capable of measuring high photon rates, which is planned to be installed at Cherenkov telescopes with dish diameters of $\gt {10}\, {\rm m}$. We use a xenon lamp as a common light source simulating starlight. Both setups measure the expected correlation signal and work at the expected shot-noise limit of statistical uncertainties for measurement times between 10 min and 23 h. We discuss the quantitative differences in the measurement results and give an overview of suitable operation regimes for each of the interferometer concepts.

A Shortcut to Calculate SPAM Limb-darkening Coefficients

Abstract We release a new grid of stellar limb-darkening coefficients (LDCs, using the quadratic, power-2 and claret-4 laws) and intensity profiles for the Kepler, U, B, V and R passbands, based on STAGGER model atmospheres. The data can be downloaded from Zenodo: https://doi.org/10.5281/zenodo.5593162. We compare the newly released LDCs, computed by ExoTETHyS, with previously published values, based on the same atmospheric models using a so-called “SPAM” procedure. The SPAM method relies on synthetic light curves in order to compute the LDCs that best represent the photometry of exoplanetary transits. We confirm that ExoTETHyS achieves the same objective with a much simpler algorithm.

Active alignment of space astronomical telescopes by matching arbitrary multi-field stellar image features.

Space-based optical astronomical telescopes are susceptible to mirror misalignments due to space disturbance in mechanics and temperature. Therefore, it is of great importance to actively align the telescope in orbit to continuously maintain imaging quality. Traditional active alignment methods usually need additional delicate wavefront sensors and complicated operations (such as instrument calibration and pointing adjustment). This paper proposes a novel active alignment approach by matching the geometrical features of several stellar images at arbitrary multiple field positions. Based on nodal aberration theory and Fourier optics, the relationship between stellar image intensity distribution and misalignments of the system can be modeled for an arbitrary field position. On this basis, an objective function is established by matching the geometrical features of the collected multi-field stellar images and modeled multi-field stellar images, and misalignments can then be solved through nonlinear optimization. Detailed simulations and a real experiment are performed to demonstrate the effectiveness and practicality of the proposed approach. This approach eliminates the need for delicate wavefront sensors and pointing adjustment, which greatly facilitates the maintainance of imaging quality.

Radiative Transfer with Opacity Distribution Functions: Application to Narrowband Filters

Abstract Modeling of stellar radiative intensities in various spectral passbands plays an important role in stellar physics. At the same time, direct calculation of the high-resolution spectrum and then integration of it over the given spectral passband is computationally demanding due to the vast number of atomic and molecular lines. This is particularly so when employing three-dimensional (3D) models of stellar atmospheres. To accelerate the calculations, one can employ approximate methods, e.g., the use of opacity distribution functions (ODFs). Generally, ODFs provide a good approximation of traditional spectral synthesis, i.e., computation of intensities through filters with strictly rectangular transmission functions. However, their performance strongly deteriorates when the filter transmission noticeably changes within its passband, which is the case for almost all filters routinely used in stellar physics. In this context, the aims of this paper are (a) to generalize the ODFs method for calculating intensities through filters with arbitrary transmission functions, and (b) to study the performance of the standard and generalized ODFs methods for calculating intensities emergent from 3D models of stellar atmospheres. For this purpose we use the newly developed MPS-ATLAS radiative transfer code to compute intensities emergent from 3D cubes simulated with the radiative magnetohydrodynamics code MURaM. The calculations are performed in the 1.5D regime, i.e., along many parallel rays passing through the simulated cube. We demonstrate that the generalized ODFs method allows accurate and fast syntheses of spectral intensities and their center-to-limb variations.

Stellar intensity interferometry of Vega in photon counting mode

ABSTRACT Stellar intensity interferometry is a technique based on the measurement of the second-order spatial correlation of the light emitted from a star. The physical information provided by these measurements is the angular size and structure of the emitting source. A worldwide effort is presently underway to implement stellar intensity interferometry on telescopes separated by long baselines and on future arrays of Cherenkov telescopes. We describe an experiment of this type, realized at the Asiago Observatory (Italy), in which we performed for the first time measurements of the correlation counting photon coincidences in post-processing by means of a single photon software correlator and exploiting entirely the quantum properties of the light emitted from a star. We successfully detected the temporal correlation of Vega at zero baseline and performed a measurement of the correlation on a projected baseline of ∼2 km. The average discrete degree of coherence at zero baseline for Vega is $\lt g^{(2)} \gt \, = 1.0034 \pm 0.0008$, providing a detection with a signal-to-noise ratio S/N ≳ 4. No correlation is detected over the km baseline. The measurements are consistent with the expected degree of spatial coherence for a source with the 3.3 mas angular diameter of Vega. The experience gained with the Asiago experiment will serve for future implementations of stellar intensity interferometry on long-baseline arrays of Cherenkov telescopes.