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High-precision observational astrophysics: solar and stellar spectroscopy, stellar surface structure, radial velocities and wavelength shifts, methods in searches for exoplanets, intensity interferometry, quantum optics, and other.

Highest-precision stellar spectroscopy

Spectroscopy reveals the structure of stellar surfaces and enables to determine their physical properties.  ‘Ab-initio’ hydrodynamic simulations provide realistic descriptions for the convective photospheres of various stars.  Such simulations enable synthetic spectra to be computed for various positions across stellar disks. These are confronted with observations across stellar surfaces, where the spatial resolution is enabled by transiting exoplanets.

Modeled granulation
Stellar surfaces in 3-dimensional hydrodynamic models of stellar surface convection. Left: T=6456 K (approximate stellar type F5V); Right (on same horizontal scale): T=3964 K (~K8V). CO5BOLD models by H.-G.Ludwig, Heidelberg.
Synthetic full stellar spectra
Synthetic spectra computed from 3-D hydrodynamic models: Left: T=3964 K (approximate spectral type K8V) . Right: T=6726 K (~F3V). (Dravins et al., A&A 649, A16, 2021)
Synthetic stellar spectra at different center-to-limb positions
Synthetic spectra from 3-D atmospheres for a T=4982 K model (~K2 V), at different center-to-limb positions. In such cooler stars, there is a significant limb darkening. (Dravins et al., A&A 649, A16, 2021)
Exoplanet transit across stellar disk
Stellar surfaces can be spatially resolved using exoplanet transits. Differences during the transit reveal temporarily hidden stellar surface segments. Changing flux is measured by photometry, spectral changes by spectroscopy.  (Dravins et al., A&A 605, A90, 2017)
Reconstructed line profiles across a stellar disk
Reconstructed Fe line profiles across the disk of HD209458 (G0V). Solid blue: near disk center, dashed brown: closer to limb. Spatially resolved lines are not rotationally broadened and are narrower and deeper than the disk average. Wavelength shifts during transit illustrate stellar rotation and the prograde orbital motion of the exoplanet.  Planet size and positions on the stellar disk are to scale. (Dravins et al., A&A 605, A91, 2017)
Spectral line shapes in different stars
Spectral line shapes across different stars.  Line profiles and their bisectors at stellar disk centers (µ=1; left) and close to the stellar limb (µ=0.09; right) from hydrodynamic 3-D models for ‘F3V’ (T=6726 K), ‘F7V’ (6233 K) and ‘G1V’ (5865 K).  More vigorous convection in hotter stars produces greater convective blueshifts.  (Dravins et al., A&A 649, A16, 2021)


Spectral microvariability and low-mass exoplanets

Finding small exoplanets comparable to the Earth in orbit around the Sun remains an outstanding challenge.  Plausible detections might be through the radial-velocity wobble induced by the planet onto the star.  Instrumental performances are about to be met but a limitation is set by stellar variability which overwhelms the tiny signal induced by a small planet.  To understand how to segregate wavelength shifts caused by a planet from those caused by atmospheric motions, microvariability is studied in numerical time-dependent hydrodynamic simulations and in time series of the observed spectrum of the Sun seen-as-a-star.

Temporal variability in stellar spectral lines
Temporal variability: Spatially averaged but temporally resolved profiles in ‘K8V’ and ‘G2V’ models. Three different line strengths from 20 simulation snapshots, with profiles from four stellar disk quadrants.  The cooler 'K8'-star has a much quieter photosphere.  (Dravins et al., A&A 649, A17, 2021)


Radial velocities without spectroscopy

Wavelength shifts are commonly interpreted as caused through the Doppler effect by motion in the radial direction.  However, they involve also effects such as convective-, gravitational-, or pressure-shifts.  For nearby stars, their radial motion can also be determined through astrometry, without any spectroscopic measurements.  The required accuracy is now available from the astrometric space missions of Hipparcos and Gaia. 

A popular overview of the method is in an article by Ken Croswell: 


Issues in defining the concept of "radial velocity"
Mechanisms causing wavelength shifts include motion of the object; the emission of an electromagnetic signal; its propagation through space; motion of the observer; and the reception of the signal.  (Lindegren & Dravins, A&A 401, 1185, 2003)
Gravitational redshifts in different stellar types
Expected gravitational redshifts throughout the HR-diagram change by three orders of magnitude (here white dwarfs become the giants!).  (Dravins, IAU Symp. 210, E4, 2003)
Hyades proper motions measured from Hipparcos
Proper motions in the Hyades, with symbol size indicating stellar brightness.  Stars in a moving cluster share the same average velocity vector. Parallaxes give the distance, while proper-motion vectors show the fractional change with time of the cluster's angular size.  The latter corresponds to the time derivative of distance, yielding the radial velocity.  (Dravins et al., ESA SP-402, 733, 1997)


Intensity interferometry

Direct imaging of stellar surfaces needs angular resolution in the tens of microarcseconds.  The required kilometer-sized optical interferometers are becoming feasible by intensity interferometry, a quantum-optical method that is immune to both atmospheric turbulence and telescopic imperfections.  This exploits the way instantaneous intensity fluctuations correlate between light measured in separate telescopes.  Telescopes monitor the intensity of starlight with a very high time resolution and the noise budget relates to electronic timescales of nanoseconds and corresponding light-travel distances of many centimeters (speed of light =30 cm/ns) rather than fractions of an optical wavelength. The method can be used on air Cherenkov telescopes erected to study gamma-ray sources from optical flashes in the atmosphere.  In particular, CTA - the Cherenkov Telescope Array, with its numerous telescopes planned across its southern site in Chile, will be particularly suitable for stellar surface imaging.

Array of telescopes used in interferometry
By connecting telescopes electronically, rather than optically, effects of atmospheric turbulence can be circumvented and microarcsecond resolution may be achieved.  Spatially separated telescopes observe the same source, and the measured time-variable intensities — I1(t), I2(t), I3(t), etc. are electronically cross-correlated between different pairs of telescopes.  telescopes enable N*(N-1)/2 different baselines. Electronic signals can be copied, combined or stored for later analysis.  (Dravins, WSPC Handbook of Astronomical Instrumentation, vol.3:2, 31, 2021)
Diffraction patterns and images in intensity interferometry
Intensity interferometry retrieves Fourier-plane information about the source.  Such ‘diffraction patterns’ are shown in the left column, corresponding to ‘normal’ images on the right.  The familiar Airy diffraction pattern (top left) can be recognized as originating from a circular aperture.  A measured pattern from an artificial asymmetric binary star (bottom left) is built up from intensity interferometry measurements over 180 baselines between pairs of laboratory telescopes.  The reconstructed image is shown on the bottom right, where the gray circle indicates the diffraction-limited spatial resolution realized by this array of optical telescopes connected only through electronic software, with no optical links​​​​​.  (Dravins et al., Nature Comm. 6, 6852, 2015)
Simulated image of an exoplanet transiting a star
The true meaning of microarcsecond resolution: A simulated image of a hypothetical Jupiter-size exoplanet (with a Saturn-type ring and four moons) transiting across the disk of the relatively close star Sirius (6 milliarcsecond diameter), assumed to have an active chromosphere, illustrates the significance of a 40 microarcsecond optical resolution. That is the resolution expected with the Cherenkov Telescope Array used as an optical intensity interferometer. (Dravins, Proc. SPIE 9907, 99070M, 2016)
Artist's vision of Cherenkov Telescope Array southern site
Artist’s vision of the almost 100 telescopes planned at the Cherenkov Telescope Array site in Chile.  ( )


Other astronomical quantum optics

Intensity interferometry has, so far, been the only astronomical application of quantum optics.  However, in principle, a stream of photons carries much additional information besides its classical properties of intensity, spectrum, and polarization.  Extremely large telescopes will provide particularly large photon fluxes and may permit the study of also quantities such as the statistics of photon arrival times.

Differences in photon arrival statistics
Statistics of photon arrival times carry information on how the light originated and how it has been modified along its path of propagation. Top: Bunched photons (Bose-Einstein distribution in thermal equilibrium; ‘quantum-random’).  Center: Antibunched photons (like fermions obeying Fermi-Dirac statistics).  Bottom: High-order coherent light with a uniform photon probability distribution (like an ideal laser).  (Dravins, High Time Resolution Astrophysics, p.95, 2008)



Highest-precision stellar spectroscopy

D.Dravins, H.-G.Ludwig, B.Freytag: Spatially resolved spectroscopy across stellar surfaces. V. Observational prospects: Toward Earth-like exoplanet detectionAstron.Astrophys. 649, A17 (2021), 

D.Dravins, H.-G.Ludwig, B.Freytag: Spatially resolved spectroscopy across stellar surfaces. IV. F, G, & K-stars: Synthetic 3D spectra at hyper-high resolutionAstron.Astrophys. 649, A16 (2021),

D.Dravins, M.Gustavsson, H.-G.Ludwig: Spatially Resolved Spectroscopy across Stellar Surfaces. III. Photospheric Fe I Lines across HD189733A (K1 V), Astron.Astrophys. 616, A144 (2018), 

D.Dravins, H.-G.Ludwig, E.Dahlén, H.Pazira: Spatially resolved spectroscopy across stellar surfaces. II. High-resolution spectra across HD209458 (G0 V)Astron.Astrophys. 605, A91 (2017), 

D.Dravins, H.-G.Ludwig, E.Dahlén, H.Pazira: Spatially resolved spectroscopy across stellar surfaces. I. Using exoplanet transits to analyze 3-D stellar atmospheres, Astron.Astrophys. 605, A90 (2017),

D.Dravins: High-fidelity spectroscopy at the highest resolutionsAstron.Nachr. 331, 535 (2010), 

D.Dravins: 'Ultimate' Information Content in Solar and Stellar Spectra: Photospheric line asymmetries and wavelength shiftsAstron.Astrophys. 492, 199 (2008),

Radial velocities without spectroscopy

L.Lindegren, D.Dravins: Astrometric radial velocities for nearby starsAstron.Astrophys. 652, A45 (2021),

L.Lindegren, D.Dravins: The fundamental definition of ‘radial velocity’Astron.Astrophys. 401, 1185 (2003),

S.Madsen, D.Dravins, L.Lindegren: Astrometric Radial Velocities III. Hipparcos measurements of nearby star clusters and associationsAstron.Astrophys. 381, 446 (2002),

L.Lindegren, S.Madsen, D.Dravins: Astrometric Radial Velocities II. Maximum-likelihood estimation of radial velocities in moving clustersAstron.Astrophys. 356, 1119 (2000),

D.Dravins, L.Lindegren, S.Madsen: Astrometric Radial Velocities I. Non-spectroscopic methods for measuring stellar radial velocityAstron.Astrophys. 348, 1040 (1999), 


Intensity interferometry and quantum optics

D.Dravins: Intensity interferometry, chapter in: The WSPC Handbook of Astronomical Instrumentation, vol.3, Part 2, pp.31-43 (2021),

D.Dravins: Intensity interferometry: Optical imaging with kilometer baselines, Proc. SPIE 9907, 99070M (2016), 

D.Dravins, T.Lagadec, P.D.Nuñez: Long-baseline optical intensity interferometry – Laboratory demonstration of diffraction-limited imaging, Astron.Astrophys, 580, A99 (2015),

D.Dravins, T.Lagadec, P.D.Nuñez: Optical aperture synthesis with electronically connected telescopes, Nature Communications, 6, 6852 (2015), 

D.Dravins, S.LeBohec, H.Jensen, P.D.Nuñez, for the CTA Consortium: Optical Intensity Interferometry with the Cherenkov Telescope Array, Astroparticle Physics 43, 331 (2013),

D.Dravins, S.LeBohec, H.Jensen, P.D.Nuñez: Stellar Intensity Interferometry: Prospects for sub-milliarcsecond optical imaging, New Astronomy Reviews 56, 143 (2012),

D.Dravins: Photonic Astronomy and Quantum Optics, In D.Phelan, O.Ryan & A.Shearer, eds.: High Time Resolution Astrophysics, Astrophysics and Space Science Library vol. 35195, Springer (2008),

D.Dravins, C.Barbieri, V.Da Deppo, D.Faria, S.Fornasier, R.A.E.Fosbury, L.Lindegren, G.Naletto, R.Nilsson, T.Occhipinti, F.Tamburini, H.Uthas, L.Zampieri: QuantEYE: Quantum Optics Instrumentation for Astronomy (Designing a quantum-optical instrument for extremely large telescopes), ESO ELT Instrument Concept Study; 280 pp. (2005),…


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