We present an analysis of the potential follow-up polarimetry microlensing observation to study the stellar atmospheres of the distant stars. First, we produce synthetic microlensing events using the Galactic model, stellar population, and interstellar dust toward the Galactic Bulge. We simulate the polarization microlensing light curves and pass them through the instrument specifications of FOcal Reducer and low dispersion Spectrograph (FORS2) polarimeter at Very Large Telescope (VLT), and then analyze them. We find that the accuracy of the VLT telescope lets us constrain the atmosphere of cool RGB stars. Assuming detection of about $3000$ microlensing events per year by the OGLE telescope, we expect to detect almost $20,~10,~8, $ and $5$ of polarization microlensig events for the four different criteria of being three consecutive polarimetry data points above the baseline with $1σ$, $2σ$, $3σ$, and $4σ$, respectively in the polarimetry light curves. We generalize the covariance matrix formulation and present the combination of polarimetry and photometry information that leads us to measure the scattering optical depth of the atmosphere and the inner radius of the stellar envelope of red giant stars. These two parameters could determine the dust opacity of the atmosphere of cool RGB source stars and the radius where dust can be formed.
It is well known that the polarization signal in microlensing events of hot stars is larger than that of main-sequence stars. Most hot stars rapidly rotate around their stellar axes. The stellar rotation makes ellipticity and gravity-darkening effects which break the spherical symmetry of the source shape and the circular symmetry of the source surface brightness respectively. Hence, it causes a net polarization signal for the source star. This polarization signal should be considered in polarimetry microlensing of fast rotating stars. For moderate rotating stars, lensing can magnify or even c…
We study the benefits of polarimetry observations of microlensing events to detect and characterize circumstellar disks around the microlensed stars located at the Galactic bulge. These disks which are unresolvable from their host stars make a net polarization effect due to their projected elliptical shapes. Gravitational microlensing can magnify these signals and make them be resolved. The main aim of this work is to determine what extra information about these disks can be extracted from polarimetry observations of microlensing events in addition to those given by photometry ones. Hot disks …
In this work, we investigate if gravitational microlensing can magnify the polarization signal of a stellar spot and make it be observable. A stellar spot on a source star of microlensing makes polarization signal through two channels of Zeeman effect and breaking circular symmetry of the source surface brightness due to its temperature contrast. We first explore the characteristics of perturbations in polarimetric microlensing during caustic-crossing of a binary lensing as follows: (a) The cooler spots over the Galactic bulge sources have the smaller contributions in the total flux, although …
We present a time series of synoptic images of the linearly-polarized v=1, J=1-0 SiO maser emission toward the Mira variable, TX Cam. These data comprise 43 individual epochs at an approximate biweekly sampling over an optical pulsation phase range of 0.68 to 1.82. The images have an angular resolution of ~500 microarcsec and were obtained using the Very Long Baseline Array (VLBA), operating in the 43 GHz band in spectral-line, polarization mode. We have previously published the total intensity time series for this pulsation phase range; this paper serves to present the linearly-polarized imag…
We investigate the diagnostic potential of the spectral lines at 850 nm for understanding the magnetism of the lower atmosphere. For that purpose, we use a newly developed 3D simulation of a chromospheric jet to check the sensitivity of the spectral lines to this phenomenon as well as our ability to infer the atmospheric information through spectropolarimetric inversions of noisy synthetic data. We start comparing the benefits of inverting the entire spectrum at 850 nm versus only the Ca II 8542 A spectral line. We found a better match of the input atmosphere for the former case, mainly at low…
One of the important microlensing applications to stellar atmospheres is the study of spots on stellar surface provided by the high resolution of caustic-crossing binary-lens events. In this paper, we investigate the characteristics of spot-induced perturbations in microlensing light curves and explain the physical background of the characteristics. We explore the variation of the spot-induced perturbations depending on various parameters characterizing the spot and investigate how well these parameters can be retrieved from observations in high-cadence future lensing surveys. From this, we fi…
This is a review of a decade-long effort to develop novel tools for exploring magnetism in cold astrophysical media and to establish a new field of molecular spectropolarimetry since Berdyugina et al. (2000). It is most directly applicable to the Sun, cool stars, substellar objects, planets and other minor bodies as well as interstellar and circumstellar matter. It is close to being a mature field with developed theoretical tools poised to uncover new insights into the magnetic structures in cooler environments. Here I attempt a broad description of the literature and present some recent excit…
(Abridged) Context. Stellar limb darkening, I(μ = cosθ), is an important constraint for microlensing, eclipsing binary, planetary transit, and interferometric observations, but is generally treated as a parameterized curve, such as a linear-plus-square-root law. Many analyses assume limb-darkening coefficients computed from model stellar atmospheres. However, previous studies, using I(μ) from plane- parallel models, have found that fits to the flux-normalized curves pass through a fixed point, a common μ location on the stellar disk, for all values of T eff, log g and wavelength. Aims. We stud…
Within the last 10 years, long-baseline optical interferometry (LBOI) has benefited significantly from increased sensitivity, spatial resolution, and spectral resolution, e.g., measuring the diameters and asymmetries of single stars, imaging/fitting the orbits of multiple stars, modeling Be star disks, and modeling AGN nuclei. Similarly, polarimetry has also yielded excellent astrophysical results, e.g., characterizing the atmospheres and shells of red giants/supergiants, modeling the envelopes of AGB stars, studying the morphology of Be stars, and monitoring the short- and long- term behavior…
We re-consider the polarization of the star light that may arise during microlensing events due to the high gradient of magnification across the atmosphere of the source star, by exploring the full range of microlensing and stellar physical parameters. Since it is already known that only cool evolved giant stars give rise to the highest polarization signals, we follow the model by Simmons et al. (2002) to compute the polarization as due to the photon scattering on dust grains in the stellar wind. Motivated by the possibility to perform a polarization measurement during an ongoing microlensing …
Gravitational microlensing, in case of relevant finite source size effects, provides an unique tool for the study of stellar atmospheres through the enhancement of a characteristic polarization signal. Here, we consider a set of highly magnified events and show that for different types of source stars (as hot, late type main sequence and cool giants) showing that the polarization strength may be of $\simeq 0.04$ percent for late type stars and up to a few percent for cool giants.
Limb darkening is a fundamental ingredient for interpreting observations of planetary transits, eclipsing binaries, optical/infrared interferometry and microlensing events. However, this modeling traditionally represents limb darkening by a simple law having one or two coefficients that have been derived from plane-parallel model stellar atmospheres, which has been done by many researchers. More recently, researchers have gone beyond plane-parallel models and considered other geometries. We previously studied the limb-darkening coefficients from spherically symmetric and plane-parallel model s…
Aims: We present a detailed analysis of OGLE 2004-BLG-482, a relatively high-magnification single-lens microlensing event which exhibits clear extended-source effects. These events are relatively rare, but they potentially contain unique information on the stellar atmosphere properties of their source star, as shown in this study. Methods: Our dense photometric coverage of the overall light curve and a proper microlensing modelling allow us to derive measurements of the OGLE 2004-BLG-482 source star's linear limb-darkening coefficients in three bands, including standard Johnson-Cousins I and R…
Context. Limb darkening is an important tool for understanding stellar atmospheres, but most observations measuring limb darkening assume various parameterizations that yield no significant information about the structure of stellar atmospheres. Aims. We use a specific limb-darkening relation to study how the best-fit coefficients relate to fundamental stellar parameters from spherically symmetric model stellar atmospheres. Methods. Using a grid of spherically symmetric Atlas model atmospheres, we compute limb-darkening coefficients, and develop a novel method to predict fundamental stellar pa…
The light received by source stars in microlensing events may be significantly polarized if both an efficient photon scattering mechanism is active in the source stellar atmosphere and a differential magnification is therein induced by the lensing system. The best candidate events for observing polarization are highly magnified events with source stars belonging to the class of cool, giant stars {in which the stellar light is polarized by photon scattering on dust grains contained in their envelopes. The presence in the stellar atmosphere of an internal cavity devoid of dust produces polarizat…
We obtained linear polarization photometry ($J$-band) and low-resolution spectroscopy ($ZJ$-bands) of Trappist-1, which is a planetary system formed by an M8-type low-mass star and seven temperate, Earth-sized planets. The photopolarimetric monitoring campaign covered 6.5 h of continuous observations including one full transit of planet Trappist-1d and partial transits of Trappist-1b and e. The spectrophotometric data and the photometric light curve obtained over epochs with no planetary transits indicate that the low-mass star has very low level of linear polarization compatible with a null v…
In this publication we continue the work started in Quintero Noda et al. (2017) examining this time a numerical simulation of a magnetic flux tube concentration. Our goal is to study if the physical phenomena that take place in it, in particular, the magnetic pumping, leaves a specific imprint on the examined spectral lines. We find that the profiles from the interior of the flux tube are periodically dopplershifted following an oscillation pattern that is also reflected in the amplitude of the circular polarization signals. In addition, we analyse the properties of the Stokes profiles at the …
Model stellar atmospheres are fundamental tools for understanding stellar observations from interferometry, microlensing, eclipsing binaries and planetary transits. However, the calculations also include assumptions, such as the geometry of the model. We use intensity profiles computed for both plane-parallel and spherically symmetric model atmospheres to determine fitting coefficients in the BVRIHK, CoRot and Kepler wavebands for limb darkening using several different fitting laws, for gravity-darkening and for interferometric angular diameter corrections. Comparing predicted variables for ea…
The gravitational microlensing as a unique astrophysical tool can be used for studying the atmosphere of stars thousands of parsec far from us. This capability results from the bending of light rays in the gravitational field of a lens which can magnify the light of a background source star during the lensing. Moreover, one of properties of this light bending is that the circular symmetry of the source is broken by producing distorted images at either side of the lens position. This property makes the possibility of the observation of the polarization and the light centroid shift of images. As…
We used the Tycho-Gaia Astrometric Solution catalogue, part of the Gaia Data Release 1, to search for candidate astrometric microlensing events expected to occur within the remaining lifetime of the Gaia satellite. Our search yielded one promising candidate. We predict that the nearby DQ type white dwarf LAWD 37 (WD 1142-645) will lens a background star and will reach closest approach on November 11th 2019 ($\pm$ 4 days) with impact parameter $380\pm10$ mas. This will produce an apparent maximum deviation of the source position of $2.8\pm0.1$ mas. In the most propitious circumstance, Gaia will…
The physical mechanism through which the outgoing material of massive red supergiants is accelerated above the escape velocity is unclear. Thanks to the transparency of its circumstellar envelope, the nearby red supergiant Betelgeuse gives the opportunity to probe the innermost layers of the envelope of a typical red supergiant down to the photosphere, i.e. where the acceleration of the wind is expected to occur. We took advantage of the SPHERE/ZIMPOL adaptive optics imaging polarimeter to resolve the visible photosphere and close envelope of Betelgeuse. We detect an asymmetric gaseous envelop…
In this article we review the astrophysical application of gravitational microlensing. After introducing the history of gravitational lensing, we present the key equations and concept of microlensing. The most frequent microlensing events are single-lens events and historically it has been used for searching dark matter in the form of compact astrophysical halo objects in the Galactic halo. We discuss about the degeneracy problem in the parameters of lens and perturbation effects that can partially break the degeneracy between the lens parameters. The rest of paper is about the astrophysical a…
Circular polarisation measurements of white dwarfs of various ages and spectral types are useful to understand the origin and evolution of the magnetic field in degenerate stars. In the latest stages of white dwarf evolution, when stars are so cool that spectral lines are no longer formed in the normal H- or He-dominated atmospheres, magnetic fields can be probed only by means of circular polarimetry of the continuum. The study of the fields of featureless DC white dwarfs may reveal whether Ohmic decay acts on magnetic white dwarfs, or if magnetic fields continue to be generated even several b…
Recently published episodic spectral (Levesque and Massey, 2020) and high angular resolution (Montarges et al, 2020) observations of Betelgeuse suggest that the deep minimum of 2019-2020 was caused by an enhanced dust abundance in the stellar atmosphere. Detailed monitoring of such events may prove useful for constructing consistent physical models of mass loss by evolved stars. For such observations it is fundamentally important to employ methods resolving an inhomogeneous stellar atmosphere. We present the differential speckle polarimetric observations of Betelgeuse at 2.5-m telescope of Cau…
Of the two solar lines, K I $D_1$ and $D_2$, almost all attention so far has been devoted to the $D_1$ line, as $D_2$ is severely affected by an O$_2$ atmospheric band. This, however, makes the latter appealing for balloon and space observations from above (most of) the Earth's atmosphere. We estimate the residual effect of the O$_2$ band on the K I $D_2$ line at altitudes typical for stratospheric balloons. Our aim is to study the feasibility of observing the 770 nm window. Specifically, this paper serves as a preparation for the third flight of the Sunrise balloon-borne observatory. The resu…
Since there are several ways planets can survive the giant phase of the host star, we examine the habitability and detection of planets orbiting white dwarfs. As a white dwarf cools from 6000 K to 4000 K, a planet orbiting at 0.01 AU would remain in the Continuous Habitable Zone (CHZ) for ~8 Gyr. We show that photosynthetic processes can be sustained on such planets. The DNA-weighted UV radiation dose for an Earth-like planet in the CHZ is less than the maxima encountered on Earth, hence non-magnetic white dwarfs are compatible with the persistence of complex life. Polarisation due to a terres…
One of the necessary parameters needed for the interpretation of the light curves of transiting exoplanets or eclipsing binaries, as well as interferometric measurements of a star or microlensing events is how the intensity and polarization of a light change from the center to the limb. Scattering and absorption processes in stellar atmosphere affect both the center-to limb variation of intensity (CLVI) and polarization (CLVP). In this paper, we present a study of the CLVI and CLVP in continuum spectra considering different contributions of scattering and absorption opacity for different spect…
We present a novel method for measuring the masses of evolved stars from their limb-darkening observations parameterized as a linear-plus-square-root function with two coefficients. The coefficients of the law are related to integrated moments of the intensity and carry information about the extension of the stellar atmosphere, which is correlated to the ratio of the stellar radius to mass, R/M. Here, we show why the limb-darkening law is related to the R/M, and apply this result to limb-darkening observations of the microlensing event EROS-BLG-2000-5.
Chromospheric observations of sunspot umbrae offer an exceptional view of magneto-acoustic shock phenomena and the impact they have on the surrounding magnetically-dominated plasma. We employ simultaneous slit-based spectro-polarimetry and spectral imaging observations of the chromospheric He I 10830Å and Ca II 8542Å lines to examine fluctuations in the umbral magnetic field caused by the steepening of magneto-acoustic waves into umbral flashes. Following the application of modern inversion routines, we find evidence to support the scenario that umbral shock events cause expansion of the embed…
The nature of the several microlensing events observed by the MACHO team towards the Large Magellanic Cloud (LMC) is still a subject of debate. Low-mass substellar objects and stars with masses larger than ~M_{sun} have been ruled out as major components of a Massive Astrophysical Compact Halo Object (MACHO) Galactic halo, while stars of half a solar mass seem to be viable candidates. Main sequence stars have been already discarded, and there are tight restrictions on the role played by white dwarfs with hydrogen-dominated atmospheres. In this paper we evaluate the contribution to the dark mat…
Limb darkening is an important stellar phenomenon and must be accounted for in the study of stellar spectra, eclipsing binaries, transiting planetary systems, and microlensing events. The power-2 limb-darkening law provides a good match to the specific intensities predicted by stellar atmosphere models: it is better than other two-parameter laws and is only surpassed by the four-parameter law. Predictions of the limb-darkening coefficients for the power-2 law are not widely available. We therefore compute them, using stellar atmosphere models generated by the ATLAS (plane-parallel) code. Limb-…
We report first multicolor polarimetric measurements (UBV bands) for the hot Jupiters HD189733b and confirm our previously reported detection of polarization in the B band (Berdyugina et al. 2008). The wavelength dependence of polarization indicates the dominance of Rayleigh scattering with a peak in the blue B and U bands of ~10^-4+/-10^-5 and at least a factor of two lower signal in the V band. The Rayleigh-like wavelength dependence, detected also in the transmitted light during transits, implies a rapid decrease of the polarization signal toward longer wavelengths. Therefore, the nondetect…
Theory surrounding the origin of the dust-laden winds from evolved stars remains mired in controversy. Characterizing the formation loci and the dust distribution within approximately the first stellar radius above the surface is crucial for understanding the physics that underlie the mass-loss phenomenon. By exploiting interferometric polarimetry, we derive the fundamental parameters that govern the dust structure at the wind base of a red supergiant. We present near-infrared aperture-masking observations of Betelgeuse in polarimetric mode obtained with the NACO/SAMPol instrument. We used bot…
The stellar mass-luminosity relation is poorly constrained by observations for high mass stars. We describe our program to find eclipsing massive binaries in the Magellanic Clouds using photometry of regions rich in massive stars, and our spectroscopic follow-up to obtain radial velocities and orbits. Our photometric campaign identified 48 early-type periodic variables, of which only 15 (31%) were found as part of the microlensing surveys. Spectroscopy is now complete for 17 of these systems, and in this paper we present analysis of the first two, LMC 172231 and ST2-28, simple detached systems…
