Mira Research Articles

SiO maser polarization and magnetic field in evolved cool stars

Magnetic fields, photospheric and atmospheric dynamics can be involved in triggering the high mass loss observed in evolved cool stars. Previous works have revealed that the magnetic field of these objects extends beyond their surface. The origin of this magnetic field is still debated. The possible mechanisms include a turbulent dynamo, convection, stellar pulsation, and cool spots. Our goal is to estimate the magnetic field strength in the inner circumstellar envelope of six evolved cool stars (five Miras and one red supergiant). Combining this work with previous studies, we tentatively constrain the global magnetic field type and shed light on the mechanisms that cause it. Using the XPOL polarimeter installed at the IRAM-30 m telescope, we observed the $^ SiO $ v = 1, J = 2-1 maser line emission and obtained simultaneous spectroscopic measurements of the four Stokes parameters. Applying a careful calibration method for Stokes $Q$, $U$, and $V$, we derived estimates of the magnetic field strength from the circular and linear polarization fractions considering the saturated and unsaturated maser cases under the Zeeman hypothesis. Magnetic field strengths from several Gauss up to several dozen Gauss are derived. These new and more accurate measurements constrain the field strength in the region of 2-5 stellar radii better than previous studies and appear to exclude a global poloidal magnetic field type. The combination of a toroidal and poloidal field is not excluded, however. A variation in the magnetic field strength over a two-month timescale is observed in one Mira star, which suggests a possible link to the stellar phase, that is, a link with pulsation and photospheric activity.

Imaging the innermost gaseous layers of the Mira star R Car with GRAVITY-VLTI

Context. The mass-loss mechanisms in M-type asymptotic giant branch (AGB) stars are still not well understood; these include, in particular, the formation of dust-driven winds from the innermost gaseous layers around these stars. One way to understand the gas-dust interaction in these regions and its impact on the mass-loss mechanisms is through the analysis of high-resolution observations of the stellar surface and its closest environment. Aims. We aim to characterize the inner circumstellar environment (~3 R*) of the M-type Mira star R Car in the near-infrared at different phases of a pulsation period. Methods. We used GRAVITY interferometric observations in the K band obtained during two different epochs over 2018. Those data were analyzed using parametric models and image reconstruction of both the pseudo-continuum and the CO band heads observed. The reported data are the highest angular resolution observations on the source in the K band. Results. We determined sizes of R Car’s stellar disk of 16.67 ± 0.05 mas (3.03 au) in January 2018 and 14.84 ± 0.06 mas (2.70 au) in February, 2018, respectively. From our physical model, we determined temperatures and size ranges for the innermost CO layer detected around R Car. The derived column density of the CO is in the ~9.18×1018–1×1019 cm−2 range, which is sufficient to permit dust nucleation and the formation of stable dust-driven winds. We find that magnesium composites, Mg2SiO4 and MgSiO3, have temperatures and condensation distances consistent with the ones obtained for the CO layer model and pure-line reconstructed images, which are the dust types most likely to be responsible for wind formation. Our reconstructed images show evidence of asymmetrical and inhomogeneous structures, which might trace a complex and perhaps clumpy structure of the CO molecule distribution. Conclusions. Our work demonstrates that the conditions for dust nucleation and thus for initialising dust-driven winds in M-type AGB stars are met in R Car, and we identify magnesium composites as the most probable candidates. We find structural changes between two observing epochs (which are separated by ~10% of the full pulsation period of the star) and evidence of the effects of asymmetries and clumpiness. This observational evidence is crucial to constraining the role of convection and pulsation in M-type stars.

A Three-dimensional Map of the Milky Way Using 66,000 Mira Variable Stars

We study the three-dimensional structure of the Milky Way using 65,981 Mira variable stars discovered by the Optical Gravitational Lensing Experiment survey. The spatial distribution of the Mira stars is analyzed with a model containing three barred components that include the X-shaped boxy component in the Galactic center (GC) and an axisymmetric disk. We take into account the distance uncertainties by implementing the Bayesian hierarchical inference method. The distance to the GC is R 0 = 7.66 ± 0.01(stat.) ± 0.39(sys.) kpc, while the inclination of the major axis of the bulge to the Sun–GC line of sight is θ = 20.°2 ± 0.°6(stat.) ± 0.°7(sys.). We present, for the first time, a detailed three-dimensional map of the Milky Way composed of young and intermediate-age stellar populations. Our analysis provides independent evidence for both the X-shaped bulge component and the flaring disk (being plausibly warped). We provide the complete data set of properties of Miras that were used for calculations in this work. The table includes mean brightness and amplitudes in nine photometric bands (covering a range of wavelengths from 0.5 to 12 μm), photometric chemical type, estimated extinction, and calculated distance with its uncertainty for each Mira variable. The median distance accuracy to a Mira star is at the level of 6.6%.

Light Curve Analysis of Nine Algol (EA) Eclipsing Binaries Discovered During the Dauban Survey

The Dauban Survey was a project focused on photometric observations in the Milky Way. This project was a collaboration between Francois Kugel and Jerome Caron utilizing the Observatoire de Chante-Perdix Dauban (MPC A77) in France between 2012 September 17 and 2014 July 20. Over this period, a total of 7826 known variable stars and 5521 new, unknown variable stars were detected. In particular, 497 new variables were published in the AAVSO VSX database. These included Mira Ceti, cataclysmic variables, RR Lyrae, cepheids, and nine EA eclipsing systems. It is the nine EA eclipsing binaries that are the focus of this research.

Mira Ceti, Atypical Archetype

Abstract With the aim of unraveling the complexity of the morphokinematics of the circumstellar envelope (CSE) of Mira Ceti, we review, extend, and in some cases revisit Atacama Large Millimeter/submillimeter Array observations of the emission of the SiO(5–4) and CO(3–2) molecular lines. In addition, we present a detailed analysis of the optically thin 13CO(3–2) emission, which provides several important new results. In agreement with observations at infrared and visible wavelengths, we give evidence for the confinement and probably rotation of a dense gas volume within ∼50 au from the star and for a large SiO line width within ∼15 au. We show that the mass-loss process is episodic and takes the form of clumps having a very low SiO/CO abundance ratio compared with similar oxygen-rich long-period variables, probably a result of depletion on dust grains and photodissociation. We evaluate the mass-loss rate associated with the main clumps and compare it with values obtained from single-dish observations. We argue that the SiO emission observed in the southwestern quadrant is not related to the mechanism of generation of the nascent wind but to a mass ejection that occurred 11 years before the observations. We remark that Mira Ceti is not a good archetype in terms of its wind: models aiming at describing the very complex gas-dust chemistry in action in the CSE of oxygen-rich AGB stars may find it difficult to account for its peculiar features and small variations in the parameters deciding when and where mass loss can proceed significantly.

Mid-infrared Period–Luminosity Relations for Miras in the Large Magellanic Cloud

Abstract We present the mid-infrared (mid-IR) period–luminosity relations (PLRs) using over 1000 Mira variables in the Large Magellanic Cloud, for the four Wide-field Infrared Survey Explorer and the four Spitzer bands. These PLRs cover a mid-IR wavelength range from 3.4–22 μm and are presented separately for the oxygen-rich (O-rich) and carbon-rich (C-rich) Miras. These relations can be used to measure distances to individual O-rich and/or C-rich Mira stars with an accuracy of 5% and 12%, respectively. They are the most accurate Mira PLRs in the mid-IR to date.

Terahertz Water Masers. II. Further SOFIA/GREAT Detections Toward Circumstellar Outflows, and a Multitransition Analysis*

Abstract Following up on our discovery of terahertz water masers, reported in 2017, we report two further detections of water maser emission at frequencies above 1 THz. Using the GREAT instrument on SOFIA, we have detected emission in the 1.296411 THz 827 − 734 transition of water toward two additional oxygen-rich evolved stars, omicron Ceti (Mira) and R Crateris, and obtained an upper limit on the 1.296 THz line emission from U Orionis. Toward these three sources, and toward the red supergiant star VY Canis Majorae from which 1.296 THz line emission was reported previously, we have also observed several lower-frequency (sub)millimeter water maser transitions using the APEX 12 m telescope along with the 22 GHz transition using the Effelsberg 100 m telescope. We have used a simple model to analyze the multitransition data thereby obtained. Adopting, as a prior, independent literature estimates of the mass-loss rates in these four sources and in W Hydrae, we infer water abundances in a remarkably narrow range: n(H2O)/n(H2) = 1.4–2.5 × 10−4. For o Cet, VY CMa, and W Hya, the model is successful in predicting the maser line fluxes to within a typical factor ∼1.6–3. For R Crt and U Ori, the model is less successful, with typical line flux predictions lying an order of magnitude above or below the observations; such discrepancies are perhaps unsurprising given the exponential nature of maser amplification.

26 NEW MIRA VARIABLES FROM THE ZTF SURVEY

We have continued our search for hitherto unregistered Mira variables in publicly available sky survey data, using observations from the Zwicky Transient Facility and the information provided in the Zwicky Transient Facility Suspected Variables Catalog, which led to the discovery of 26 new Mira stars. Essential data as well as light curves and phase plots for all stars are presented.

ALMA (finally!) discloses a rotating disk+bipolar wind system at the centre of the wind-prominent pPN OH 231.8+4.2

AbstractWe present interferometric continuum and molecular line emission maps obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) of OH231.8+4.2, a well studied bipolar nebula around an asymptotic giant branch (AGB) star that is key to understand the remarkable changes in nebular morphology and kinematics during the short transition from the AGB to the Planetary Nebula (PN) phase. The excellent angular resolution of our maps (∼20 mas ∼30 AU) allows us to scrutinize the central nebular regions of OH231.8+4.2, which hold the clues to understanding how this iconic object assembled its complex nebular architecture. We report, for the first time in this object and others of its kind (i.e. pre-PNe with massive bipolar outflows), the discovery of a rotating circumbinary disk of radius ∼30 AU traced by NaCl, KCl, and H2O emission lines. The disk lies at the base of a young bipolar wind with signs of rotation as well. A compact spatially resolved dust disk is found perpendicular to the bipolar outflow. We also identify a point-like continuum source, which likely represents the central Mira star enshrouded by a ∼3 R* shell or disk of hot (∼1400 K) freshly formed dust. The point source is slightly off-centre from the disk centroid, enabling us for the first time to place constraints to the orbital separation of the central binary system.

Tomography of cool giant and supergiant star atmospheres

Context. Asymptotic giant branch (AGB) stars are characterized by substantial mass loss, however the mechanism behind it not yet fully understood. The knowledge of the structure and dynamics of AGB-star atmospheres is crucial to better understanding the mass loss. The recently established tomographic method, which relies on the design of spectral masks containing lines that form in given ranges of optical depths in the stellar atmosphere, is an ideal technique for this purpose. Aims. We aim to validate the capability of the tomographic method in probing different geometrical depths in the stellar atmosphere and recovering the relation between optical and geometrical depth scales. Methods. We applied the tomographic method to high-resolution spectro-interferometric VLTI/AMBER observations of the Mira-type AGB star S Ori. The interferometric visibilities were extracted at wavelengths contributing to the tomographic masks and fitted to those computed from a uniform disk model. This allows us to measure the geometrical extent of the atmospheric layer probed by the corresponding mask. We then compared the observed atmospheric extension with others measured from available 1D pulsation CODEX models and 3D radiative-hydrodynamics CO5BOLD simulations. Results. While the average optical depths probed by the tomographic masks in S Ori decrease (with ⟨log τ0⟩ = −0.45, − 1.45, and − 2.45 from the innermost to the central and outermost layers), the angular diameters of these layers increase, from 10.59 ± 0.09 mas through 11.84 ± 0.17 mas, up to 14.08 ± 0.15 mas. A similar behavior is observed when the tomographic method is applied to 1D and 3D dynamical models. Conclusions. This study derives, for the first time, a quantitative relation between optical and geometrical depth scales when applied to the Mira star S Ori, or to 1D and 3D dynamical models. In the context of Mira-type stars, knowledge of the link between the optical and geometrical depths opens the way to deriving the shock-wave propagation velocity, which cannot be directly observed in these stars.

DEATHSTAR: Nearby AGB stars with the Atacama Compact Array

Context. This is the first publication from the DEATHSTAR project. The overall goal of the project is to reduce the uncertainties of the observational estimates of mass-loss rates from evolved stars on the Asymptotic Giant Branch (AGB). Aim. The aim in this first publication is to constrain the sizes of the 12CO emitting region from the circumstellar envelopes around 42 mostly southern AGB stars, of which 21 are M-type and 21 are C-type, using the Atacama Compact Array (ACA) at the Atacama Large Millimeter/submillimeter Array. The symmetry of the outflows is also investigated. Methods. Line emission from 12CO J = 2→1 and 3→2 from all of the sources were mapped using the ACA. In this initial analysis, the emission distribution was fit to a Gaussian distribution in the uv-plane. A detailed radiative transfer analysis will be presented in a future publication. The major and minor axis of the best-fit Gaussian at the line center velocity of the 12CO J = 2→1 emission gives a first indication of the size of the emitting region. Furthermore, the fitting results, such as the Gaussian major and minor axis, center position, and the goodness of fit across both lines, constrain the symmetry of the emission distribution. For a subsample of sources, the measured emission distribution is compared to predictions from previous best-fit radiative transfer modeling results. Results. We find that the CO envelope sizes are, in general, larger for C-type than for M-type AGB stars, which is as expected if the CO/H2 ratio is larger in C-type stars. Furthermore, the measurements show a relation between the measured (Gaussian) 12CO J = 2→1 size and circumstellar density that, while in broad agreement with photodissociation calculations, reveals large scatter and some systematic differences between the different stellar types. For lower mass-loss-rate irregular and semi-regular variables of both M- and C-type AGB stars, the 12CO J = 2→1 size appears to be independent of the ratio of the mass-loss rate to outflow velocity, which is a measure of circumstellar density. For the higher mass-loss-rate Mira stars, the 12CO J = 2→1 size clearly increases with circumstellar density, with larger sizes for the higher CO-abundance C-type stars. The M-type stars appear to be consistently smaller than predicted from photodissociation theory. The majority of the sources have CO envelope sizes that are consistent with a spherically symmetric, smooth outflow, at least on larger scales. For about a third of the sources, indications of strong asymmetries are detected. This is consistent with what was found in previous interferometric investigations of northern sources. Smaller scale asymmetries are found in a larger fraction of sources. Conclusions. These results for CO envelope radii and shapes can be used to constrain detailed radiative transfer modeling of the same stars so as to determine mass-loss rates that are independent of photodissociation models. For a large fraction of the sources, observations at higher spatial resolution will be necessary to deduce the nature and origin of the complex circumstellar dynamics revealed by our ACA observations.

A Qualitative Study on Alcohol and Drug Abuse among Undergraduate (University Students) in The Coastal Region of Kenya

BACKGROUND: Substance use poses a significant threat to the health, social and economic fabric of families, communities and nations. In Kenya, alcohol and drug abuse has been identified as a hindrance to education, development and by extension, to national development. Alcohol and drug abuse has been associated with crime and indiscipline e.g. poor class attendance, poor performance, school dropout and destructive strikes that lead to damage the institution property or even death. Alcohol and drug abusers are also likely to lower their morals and engage in risky sexual activities that can lead to sexually transmitted diseases including HIV infection and AIDS. OBJECTIVES: The aim of this study therefore was to explore on the perceptions and the magnitude of substance abuse among undergraduate (University students) in the two public Universities in the coastal region of Kenya. Also find amicable solutions to curb the menace that can destroy the future of a generation aged between 18–29 years at the peak of their life. METHODOLOGY: This was a qualitative study involving undergraduate (University students), dean of students and counsellors from Pwani University and Technical University of Mombasa. Focus Group Discussions(FGDs) and Key informant interviews were used to collect data. The number of KIIs was guided by data saturation. Thematic analysis was done by identifying, coding, and categorizing patterns or themes found in the data. RESULTS: The problem of alcohol and substance abuse among undergraduate students was a reality. The commonly abused substances were alcohol, miraa (khat), marijuana (cannabis) and cigarettes. Some of the factors predisposing students to abuse drugs were; easy accessibility to drugs, peer pressure, availability of funds, excess freedom, male gender, stress, not being active in religious activities, poor parenting and the African culture that uphold substances such as alcohol as an acceptable social drink. Participants noted that alcohol and drug abuse had led to various negative effects. The major ones affecting the students being poor performance, risky sexual behaviour, and mental disturbances. Participants suggested that Universities ought to intensify awareness campaigns to sensitize students against substance use. CONCLUSION: The commonly abused substances were alcohol, marijuana, miraa (Khat) and tobacco. Alcohol and drug abuse has left a negative impact among undergraduates (university students). The main consequences being; discontinuation of studies, mental disturbances and risky sexual activities. All stakeholders must take action creating awareness among students on the negative effects of substance abuse. Universities should set up programs with an aim to curb substance abuse in the institutions of higher learning. The government should reinforce the set laws and regulations and deal with trafficking of illicit substances into the country. Keywords: Alcohol and drug abuse, substance abuse, undergraduate students, qualitative study, Kenya

Trigonometric parallax of O-rich Mira variable star OZ Gem (IRAS 07308+3037): A confirmation of the difference between the P–L relations of the Large Magellanic Cloud and the Milky Way

Abstract OZ Geminorum (OZ Gem) is a galactic Mira variable in the Milky Way (MW). We measured its annual parallax with VLBI Exploration of Radio Astrometry to be π = 0.806 ± 0.039 mas, corresponding to a distance of D = 1.24 ± 0.06 kpc. Based on multi-epoch infrared observations with the Kagoshima University 1 m telescope, we also derived the mean J-, H-, and K′-band magnitudes of OZ Gem to be 5.75 ± 0.47 mag, 4.00 ± 0.16 mag, and 2.65 ± 0.16 mag, respectively. We derived a pulsation period of OZ Gem as 592 ± 1 d from the K′-band lightcurve. From the period–luminosity (P–L) relation and two-color diagram of the Large Magellanic Cloud (LMC), the property of OZ Gem suggests that OZ Gem is assigned among the carbon-rich Mira variables. However, our optical spectroscopic observational results (with the 1.5 m Kanata telescope) confirmed OZ Gem to be an oxygen-rich Mira star with the detection of multiple titanium oxide transition absorption lines. We suggest that OZ Gem is a low-mass star evolving to an OH/IR star with large mass loss and dust formation. It is predicted that the lower limit to the initial mass of AGB stars for developing the C-rich surface chemistry is larger in the MW than in the LMC because of larger metallicity, and OZ Gem is likely to be the first example to prove this. Our results highlight the necessity of deriving the PL relation of the Milky Way with high accuracy.

Revealing new features of the millimetre emission of the circumbinary envelope of Mira Ceti

ABSTRACT We study the morpho-kinematics of the circumbinary envelope of Mira Ceti between ∼100 and ∼350 au from the stars using ALMA observations of the SiO (ν = 0, J= 5−4) and CO (ν = 0, J = 3−2) emissions with the aim of presenting an accurate and reliable picture of what cannot be ignored when modelling the dynamics at stake. A critical study of the uncertainties attached to imaging is presented. The line emissions are shown to be composed of a few separated fragments. They are described in detail and plausible interpretations of their genesis are discussed. Evidence for a focusing effect of the Mira A wind by Mira B over the past century is presented; it accounts for only a small fraction of the overall observed emission but its accumulation over several orbital periods may have produced an enhancement of CO emission in the orbital plane of Mira B. We identify a south-western outflow and give arguments for the anti-correlation observed between CO and SiO emissions being the result of a recent mass ejection accompanied by a shock wave. We discuss the failure of simple scenarios that have been proposed earlier to explain some of the observed features and comment on the apparent lack of continuity between the present observations and those obtained in the close environment of the stars. Evidence is obtained for the presence of large Doppler velocity components near the line of sight aiming to the star, possibly revealing the presence of important turbulence at ∼5–10 au away from Mira A.

On the origin of high Doppler velocity wings in the spectra of O-rich AGB stars

Millimetre ALMA observations of the nascent winds of several Oxygen rich AGB stars have revealed the high Doppler velocity wings in their spectra. However, the physics underlying their production is unclear. In this paper, we illustrate the argument with four examples of oxygen-rich AGB stars: EP Aqr, R Dor, L2 Pup and Mira Ceti.

High-resolution observations of the symbiotic system R Aqr

We have observed the symbiotic stellar system R Aqr, aiming to describe the gravitational interaction between the white dwarf (WD) and the wind from the Mira star, the key phenomenon driving the sy ...

A Model of the Dust Envelope of the Carbon Mira Star V CrB from Photometry, Infrared Spectroscopy, and Speckle Polarimetry

$$UBVJHKLM$$ photometry for the carbon Mira star V CrB are presented. The infrared observations were carried out in the time interval 1989–2018, while the $$U$$ , $$B$$ , and $$V$$ data were obtained in 2001–2014. The light and color curves are analyzed. The pulsation period of V CrB has been found to be $$355\overset{\textrm{d}}{.}2$$ in the infrared $$JHKLM$$ bands and $$352^{\textrm{d}}$$ for the optical $$BV$$ band. In the $$JHK$$ bands, apart from periodic pulsations, there are distinct sinusoidal variations in the average brightness level with a characteristic period of $${\sim}8300$$ days. Color–magnitude relationships have been revealed for the infrared and optical bands. The phase curves exhibit the wavelength dependence of the brightness variability amplitude. The light curves for various bands and colors are discussed. We have constructed the model of a spherically symmetric circumstellar dust envelope that allows the observed spectral energy distribution at both maximum and minimum light to be reproduced equally well (within the model assumptions) and is consistent with the observations of V CrB by differential speckle polarimetry. The model is characterized by the following parameters: the optical depth is $$\tau_{K}=0.33$$ , the inner and outer radii of the envelope are 8 and 40 000 AU, respectively. The envelope contains spherical carbon dust grains ( $$3/4$$ by mass) and silicon carbide dust grains. Dust grains with a radius of 0.5 $$\mu$$ m account for $$90\%$$ of the envelope mass. The remaining $$10\%$$ of the mass is accounted for by finer dust with a grain radius of 0.1 $$\mu$$ m. Based on the observational data, we have estimated the bolometric flux from V CrB: $$2.6\times 10^{-7}$$ and $$5.1\times 10^{-7}$$ erg cm $${}^{-2}$$ s $${}^{-1}$$ at minimum and maximum light, respectively. The effective temperature of the star is $$T_{\textrm{max}}=3000$$ K at maximum light and $$T_{\textrm{min}}=2400$$ K at minimum light.

CHALLENGES FACING THE PREVENTION OF DRUG AND SUBSTANCE ABUSE IN SECONDARY SCHOOLS: CASE OF MALINDI CENTRAL URBAN SUB-COUNTY, KENYA

This study investigated the prevention of drug and substance abuse among students in secondary schools in Malindi Central urban Sub-County of Kenya. The research problem emanated from the concern that many school children are being wasted due to drug and substance abuse despite efforts put in place to prevent it by various stakeholders such as the government, parents, teachers and religious leaders. This study focused on the objectives of finding out the types and sources of drugs and substances abused by secondary school students in Malindi Central Urban Sub-county, the existing measures against the vice as well as establishing the challenges in the prevention of drug and substance abuse in the study locale. The target population was 8 schools and 112 teachers.The sample size was 4 schools and 60 teachers. Schools were chosen through purposeful sampling depending on their closeness to the urban environment of Malindi Sub-County while teachers were also chosen purposively where longest serving teachers participated in the study. The information was elicited by use of interviews and focused group discussions. Quantitative data was analyzed through simple statistics while qualitative data analysis took the thematic approach. The results showed that drugs abused mainly by students were khat (miraa), bhang, cigarettes and alcohol. Such students obtained drugs and substances of abuse from their peers, community and parents. The study established that existing measures in schools within the study locale against drug and substance abuse were mainly guidance and counseling as well as police arrests. However, the study went further and sought the challenges that have made it difficult to curb drug and substance abuse which are mainly as follows: lack of cooperation from parents, the school community and constant watching of media like television sets (TVs). Article visualizations:

Semiregular Variable Stars

The studies of semiregular variables of stars by different authors are considered, and the main theoretical and observational problems associated with these stars are reviewed. Their evolutionary status and possible connection with long-period variables such as Mira Ceti are discussed. Individual objects belonging to different types of semiregular variables are described in detail. After leaving the main sequence, the stars pass through the region of instability of Cepheids, turning into radially pulsating variables of type \delta Cephei. These stars can be associated with semiregular variables giants and supergiants of spectral classes F-K, which are usually denoted by the symbol SRd. In the process of further evolution of the variables of high luminosity fall in the region of red supergiants, becoming the type variables SRc (or Lc), and the variables lower luminosity turn into a semiregular variables SRab (or wrong Lb) of late spectral classes. Variables of the RV Tau type are a class of low-mass (with masses of the order of one solar) pulsating F-K-supergiants, which may be at the short-term evolutionary stage of transition from the red giant to the protoplanetary nebula, which explains the small number of stars of this type of variability. Shklovsky (1956) was the first to point to stars of this type as the progenitors of planetary nebulae.

Asymmetric shocks in χ Cygni observed with linear spectropolarimetry

Aims. We derive information about the dynamics of the stellar photosphere, including pulsation, from a coherent interpretation of the linear polarisation detected in the spectral lines of the Mira star χ Cyg. Methods. From spectropolarimetric observations of χ Cyg, we performed a careful analysis of the polarisation signals observed in atomic and molecular lines, both in absorption and emission, using radiative transfer in the context of polarisation produced through two mechanisms: intrinsic polarisation and continuum depolarisation. We also explain the observed line doubling phenomenon in terms of an expanding shell in spherical geometry, which allows us to pinpoint the coordinates over the stellar disc with enhanced polarisation. Results. We find that the polarised spectrum of χ Cyg is dominated by intrinsic polarisation and has a negligible continuum depolarisation. The observed polarised signals can only be explained by assuming that this polarisation is locally enhanced by velocity fields. During the pulsation, radial velocities are not homogeneous over the disc. We map these regions of enhanced velocities. Conclusions. We set an algorithm to distinguish the origin of this polarisation in any stellar spectra of linear polarisation and to find a way to increase the signal by coherently adding many lines with an appropriated weight. Applied to the Mira star χ Cyg, we reached the unexpected result that during the pulsation, velocities are radial but not homogeneous over the disc. The reason for these local velocity enhancements are probably related to the interplay between the atmospheric pulsation dynamics and the underlying stellar convection.