Improved time-delay lens modelling and H 0 inference with transient sources
Abstract
ABSTRACT Strongly lensed explosive transients such as supernovae, gamma-ray bursts, fast radio bursts, and gravitational waves are very promising tools to determine the Hubble constant (H0) in the near future in addition to strongly lensed quasars. In this work, we show that the transient nature of the point source provides an advantage over quasars: The lensed host galaxy can be observed before or after the transient’s appearance. Therefore, the lens model can be derived from images free of contamination from bright point sources. We quantify this advantage by comparing the precision of a lens model obtained from the same lenses with and without point sources. Based on Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations with the same sets of lensing parameters, we simulate realistic mock data sets of 48 quasar lensing systems (i.e. adding AGN in the galaxy centre) and 48 galaxy–galaxy lensing systems (assuming the transient source is not visible but the time delay and image positions have been or will be measured). We then model the images and compare the inferences of the lens model parameters and H0. We find that the precision of the lens models (in terms of the deflector mass slope) ismore »
- Authors:
-
[1];
[2];
[5];
- Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan, Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547, USA
- School of Science, Wuhan University of Technology, Wuhan 430070, China
- Kavli Institute for Particle Astrophysics and Cosmology and Department of Physics, Stanford University, Stanford, CA 94305, USA
- Department of Astronomy & Astrophysics, University of Chicago, Chicago, IL 606374, USA
- Department of Physics and Astronomy, University of California, Los Angeles, CA 90095-1547, USA
- School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1784394
- Resource Type:
- Published Article
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Additional Journal Information:
- Journal Name: Monthly Notices of the Royal Astronomical Society Journal Volume: 504 Journal Issue: 4; Journal ID: ISSN 0035-8711
- Publisher:
- Oxford University Press
- Country of Publication:
- United Kingdom
- Language:
- English
Citation Formats
Ding, Xuheng, Liao, Kai, Birrer, Simon, Shajib, Anowar J., Treu, Tommaso, and Yang, Lilan. Improved time-delay lens modelling and H 0 inference with transient sources. United Kingdom: N. p., 2021.
Web. doi:10.1093/mnras/stab1240.
Ding, Xuheng, Liao, Kai, Birrer, Simon, Shajib, Anowar J., Treu, Tommaso, & Yang, Lilan. Improved time-delay lens modelling and H 0 inference with transient sources. United Kingdom. https://doi.org/10.1093/mnras/stab1240
Ding, Xuheng, Liao, Kai, Birrer, Simon, Shajib, Anowar J., Treu, Tommaso, and Yang, Lilan. Tue .
"Improved time-delay lens modelling and H 0 inference with transient sources". United Kingdom. https://doi.org/10.1093/mnras/stab1240.
@article{osti_1784394,
title = {Improved time-delay lens modelling and H 0 inference with transient sources},
author = {Ding, Xuheng and Liao, Kai and Birrer, Simon and Shajib, Anowar J. and Treu, Tommaso and Yang, Lilan},
abstractNote = {ABSTRACT Strongly lensed explosive transients such as supernovae, gamma-ray bursts, fast radio bursts, and gravitational waves are very promising tools to determine the Hubble constant (H0) in the near future in addition to strongly lensed quasars. In this work, we show that the transient nature of the point source provides an advantage over quasars: The lensed host galaxy can be observed before or after the transient’s appearance. Therefore, the lens model can be derived from images free of contamination from bright point sources. We quantify this advantage by comparing the precision of a lens model obtained from the same lenses with and without point sources. Based on Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations with the same sets of lensing parameters, we simulate realistic mock data sets of 48 quasar lensing systems (i.e. adding AGN in the galaxy centre) and 48 galaxy–galaxy lensing systems (assuming the transient source is not visible but the time delay and image positions have been or will be measured). We then model the images and compare the inferences of the lens model parameters and H0. We find that the precision of the lens models (in terms of the deflector mass slope) is better by a factor of 4.1 for the sample without lensed point sources, resulting in an increase of H0 precision by a factor of 2.9. The opportunity to observe the lens systems without the transient point sources provides an additional advantage for time-delay cosmography over lensed quasars. It facilitates the determination of higher signal-to-noise stellar kinematics of the main deflector, and thus its mass density profile, which, in turn plays a key role in breaking the mass-sheet degeneracy and constraining H0.},
doi = {10.1093/mnras/stab1240},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 4,
volume = 504,
place = {United Kingdom},
year = {Tue May 04 00:00:00 EDT 2021},
month = {Tue May 04 00:00:00 EDT 2021}
}
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Works referenced in this record:
Strong gravitational lensing of gravitational waves from double compact binaries—perspectives for the Einstein Telescope
journal, October 2014
- Biesiada, Marek; Ding, Xuheng; Piórkowska, Aleksandra
- Journal of Cosmology and Astroparticle Physics, Vol. 2014, Issue 10
Gravitational lens Modeling with Basis sets
journal, November 2015
- Birrer, Simon; Amara, Adam; Refregier, Alexandre
- The Astrophysical Journal, Vol. 813, Issue 2
Strong Lensing by Galaxies
journal, August 2010
- Treu, Tommaso
- Annual Review of Astronomy and Astrophysics, Vol. 48, Issue 1
Multiply imaged time-varying sources behind galaxy clusters: Comparing fast radio bursts to QSOs, SNe, and GRBs
journal, January 2019
- Wagner, Jenny; Liesenborgs, Jori; Eichler, David
- Astronomy & Astrophysics, Vol. 621
High-redshift supernova rates measured with the gravitational telescope A 1689
journal, October 2016
- Petrushevska, T.; Amanullah, R.; Goobar, A.
- Astronomy & Astrophysics, Vol. 594
Precision cosmology from future lensed gravitational wave and electromagnetic signals
journal, October 2017
- Liao, Kai; Fan, Xi-Long; Ding, Xuheng
- Nature Communications, Vol. 8, Issue 1
A Universal Density Profile from Hierarchical Clustering
journal, December 1997
- Navarro, Julio F.; Frenk, Carlos S.; White, Simon D. M.
- The Astrophysical Journal, Vol. 490, Issue 2
Calibration of the Tip of the Red Giant Branch
journal, March 2020
- Freedman, Wendy L.; Madore, Barry F.; Hoyt, Taylor
- The Astrophysical Journal, Vol. 891, Issue 1
Two Accurate Time-Delay Distances from Strong Lensing: Implications for Cosmology
journal, March 2013
- Suyu, S. H.; Auger, M. W.; Hilbert, S.
- The Astrophysical Journal, Vol. 766, Issue 2
Gravitationally lensed quasars and supernovae in future wide-field optical imaging surveys: Lensed quasars and supernovae
journal, April 2010
- Oguri, Masamune; Marshall, Philip J.
- Monthly Notices of the Royal Astronomical Society
H0LiCOW VIII. A weak-lensing measurement of the external convergence in the field of the lensed quasar HE 0435−1223
journal, April 2018
- Tihhonova, O.; Courbin, F.; Harvey, D.
- Monthly Notices of the Royal Astronomical Society, Vol. 477, Issue 4
TDCOSMO: III. Dark matter substructure meets dark energy. The effects of (sub)halos on strong-lensing measurements of H 0
journal, October 2020
- Gilman, D.; Birrer, S.; Treu, T.
- Astronomy & Astrophysics, Vol. 642
lenstronomy: Multi-purpose gravitational lens modelling software package
journal, December 2018
- Birrer, Simon; Amara, Adam
- Physics of the Dark Universe, Vol. 22
TDCOSMO: IV. Hierarchical time-delay cosmography – joint inference of the Hubble constant and galaxy density profiles
journal, November 2020
- Birrer, S.; Shajib, A. J.; Galan, A.
- Astronomy & Astrophysics, Vol. 643
Analytic Time Delays and H 0 Estimates for Gravitational Lenses
journal, November 2000
- Witt, Hans J.; Mao, Shude; Keeton, Charles R.
- The Astrophysical Journal, Vol. 544, Issue 1
Prediction of Supernova Rates in Known Galaxy–Galaxy Strong-lens Systems
journal, September 2018
- Shu, Yiping; Bolton, Adam S.; Mao, Shude
- The Astrophysical Journal, Vol. 864, Issue 1
Strongly lensed gravitational waves from intrinsically faint double compact binaries—prediction for the Einstein Telescope
journal, December 2015
- Ding, Xuheng; Biesiada, Marek; Zhu, Zong-Hong
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 12
H0LiCOW – III. Quantifying the effect of mass along the line of sight to the gravitational lens HE 0435−1223 through weighted galaxy counts★
journal, February 2017
- Rusu, Cristian E.; Fassnacht, Christopher D.; Sluse, Dominique
- Monthly Notices of the Royal Astronomical Society, Vol. 467, Issue 4
H0LiCOW – I. H0 Lenses in COSMOGRAIL's Wellspring: program overview
journal, February 2017
- Suyu, S. H.; Bonvin, V.; Courbin, F.
- Monthly Notices of the Royal Astronomical Society, Vol. 468, Issue 3
The mass-sheet degeneracy and time-delay cosmography: analysis of the strong lens RXJ1131-1231
journal, August 2016
- Birrer, Simon; Amara, Adam; Refregier, Alexandre
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 08
COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses: XVI. Time delays for the quadruply imaged quasar DES J0408−5354 with high-cadence photometric monitoring⋆
journal, January 2018
- Courbin, F.; Bonvin, V.; Buckley-Geer, E.
- Astronomy & Astrophysics, Vol. 609
Massive Dark Matter Halos and Evolution of Early‐Type Galaxies to z ≈ 1
journal, August 2004
- Treu, Tommaso; Koopmans, Leon V. E.
- The Astrophysical Journal, Vol. 611, Issue 2
The Wave Nature of Continuous Gravitational Waves from Microlensing
journal, April 2019
- Liao, Kai; Biesiada, Marek; Fan, Xi-Long
- The Astrophysical Journal, Vol. 875, Issue 2
emcee : The MCMC Hammer
journal, March 2013
- Foreman-Mackey, Daniel; Hogg, David W.; Lang, Dustin
- Publications of the Astronomical Society of the Pacific, Vol. 125, Issue 925
SHARP – III. First use of adaptive-optics imaging to constrain cosmology with gravitational lens time delays
journal, August 2016
- Chen, Geoff C. -F.; Suyu, Sherry H.; Wong, Kenneth C.
- Monthly Notices of the Royal Astronomical Society, Vol. 462, Issue 4
20 years of Hubble Space Telescope optical modeling using Tiny Tim
conference, September 2011
- Krist, John E.; Hook, Richard N.; Stoehr, Felix
- SPIE Optical Engineering + Applications, SPIE Proceedings
On the Possibility of Determining Hubble's Parameter and the Masses of Galaxies from the Gravitational Lens Effect
journal, September 1964
- Refsdal, S.
- Monthly Notices of the Royal Astronomical Society, Vol. 128, Issue 4
Gravitational lensing of gravitational waves: a statistical perspective
journal, February 2018
- Li, Shun-Sheng; Mao, Shude; Zhao, Yuetong
- Monthly Notices of the Royal Astronomical Society, Vol. 476, Issue 2
Lensing Degeneracies Revisited
journal, October 2000
- Saha, Prasenjit
- The Astronomical Journal, Vol. 120, Issue 4
A SHARP view of H0LiCOW: H0 from three time-delay gravitational lens systems with adaptive optics imaging
journal, September 2019
- Chen, Geoff C-F; Fassnacht, Christopher D.; Suyu, Sherry H.
- Monthly Notices of the Royal Astronomical Society, Vol. 490, Issue 2
Seeing Double: Strong Gravitational Lensing of High-Redshift Supernovae
journal, August 2001
- Holz, Daniel E.
- The Astrophysical Journal, Vol. 556, Issue 2
Gravitational Lensing Model Degeneracies: Is Steepness All‐Important?
journal, December 2006
- Saha, Prasenjit; Williams, Liliya L. R.
- The Astrophysical Journal, Vol. 653, Issue 2
Consistent Calibration of the Tip of the Red Giant Branch in the Large Magellanic Cloud on the Hubble Space Telescope Photometric System and a Redetermination of the Hubble Constant
journal, November 2019
- Yuan, Wenlong; Riess, Adam G.; Macri, Lucas M.
- The Astrophysical Journal, Vol. 886, Issue 1
Lensing degeneracies and mass substructure: Lensing degeneracies and mass substructure
journal, August 2012
- Liesenborgs, J.; De Rijcke, S.
- Monthly Notices of the Royal Astronomical Society, Vol. 425, Issue 3
The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch
journal, August 2019
- Freedman, Wendy L.; Madore, Barry F.; Hatt, Dylan
- The Astrophysical Journal, Vol. 882, Issue 1
Degeneracies and scaling relations in general power-law models for gravitational lenses
journal, June 2002
- Wucknitz, O.
- Monthly Notices of the Royal Astronomical Society, Vol. 332, Issue 4
Cosmological Applications of Gravitational Lensing
journal, January 1992
- Blandford, R.
- Annual Review of Astronomy and Astrophysics, Vol. 30, Issue 1
Time delay cosmography
journal, July 2016
- Treu, Tommaso; Marshall, Philip J.
- The Astronomy and Astrophysics Review, Vol. 24, Issue 1
Precise Time Delays from Strongly Gravitationally Lensed Type Ia Supernovae with Chromatically Microlensed Images
journal, March 2018
- Goldstein, Daniel A.; Nugent, Peter E.; Kasen, Daniel N.
- The Astrophysical Journal, Vol. 855, Issue 1
Generalised model-independent characterisation of strong gravitational lenses: IV. Formalism-intrinsic degeneracies
journal, December 2018
- Wagner, Jenny
- Astronomy & Astrophysics, Vol. 620
Fourth Test of General Relativity
journal, December 1964
- Shapiro, Irwin I.
- Physical Review Letters, Vol. 13, Issue 26
On model-dependent bounds on H(0) from gravitational images Application of Q0957 + 561A,B
journal, February 1985
- Falco, E. E.; Gorenstein, M. V.; Shapiro, I. I.
- The Astrophysical Journal, Vol. 289
H0LiCOW VII: cosmic evolution of the correlation between black hole mass and host galaxy luminosity
journal, August 2017
- Ding, Xuheng; Treu, Tommaso; Suyu, Sherry H.
- Monthly Notices of the Royal Astronomical Society, Vol. 472, Issue 1
Gravitational Lenses
book, January 1992
- Schneider, Peter; Ehlers, Jürgen; Falco, Emilio E.
- Astronomy and Astrophysics Library
The Structure and Dynamics of Massive Early-Type Galaxies: on Homology, Isothermality, and Isotropy Inside one Effective Radius
journal, September 2009
- Koopmans, L. V. E.; Bolton, A.; Treu, T.
- The Astrophysical Journal, Vol. 703, Issue 1
Source-position transformation: an approximate invariance in strong gravitational lensing
journal, April 2014
- Schneider, Peter; Sluse, Dominique
- Astronomy & Astrophysics, Vol. 564
Microlensing makes lensed quasar time delays significantly time variable
journal, September 2017
- Tie, S. S.; Kochanek, C. S.
- Monthly Notices of the Royal Astronomical Society, Vol. 473, Issue 1
The Hubble Constant from the Gravitational Lens B1608+6561
journal, December 2003
- Koopmans, L. V. E.; Treu, T.; Fassnacht, C. D.
- The Astrophysical Journal, Vol. 599, Issue 1
Prospects for Strongly Lensed Supernovae Behind Hubble Frontier Fields Galaxy Clusters with the James Webb Space Telescope
journal, December 2018
- Petrushevska, T.; Okamura, T.; Kawamata, R.
- Astronomy Reports, Vol. 62, Issue 12
The Internal Structure and Formation of Early‐Type Galaxies: The Gravitational Lens System MG 2016+112 at z = 1.004
journal, August 2002
- Treu, Tommaso; Koopmans, Leon V. E.
- The Astrophysical Journal, Vol. 575, Issue 1
Detecting strongly lensed supernovae at z ∼ 5–7 with LSST
journal, November 2019
- Rydberg, Claes-Erik; Whalen, Daniel J.; Maturi, Matteo
- Monthly Notices of the Royal Astronomical Society, Vol. 491, Issue 2
Hubble constant hunter’s guide
journal, February 2020
- Knox, L.; Millea, M.
- Physical Review D, Vol. 101, Issue 4
Search for Gravitational Lensing Signatures in LIGO-Virgo Binary Black Hole Events
journal, March 2019
- Hannuksela, O. A.; Haris, K.; Ng, K. K. Y.
- The Astrophysical Journal, Vol. 874, Issue 1
Multiple images of a highly magnified supernova formed by an early-type cluster galaxy lens
journal, March 2015
- Kelly, P. L.; Rodney, S. A.; Treu, T.
- Science, Vol. 347, Issue 6226
The Atacama Cosmology Telescope: DR4 maps and cosmological parameters
journal, December 2020
- Aiola, Simone; Calabrese, Erminia; Maurin, Loïc
- Journal of Cosmology and Astroparticle Physics, Vol. 2020, Issue 12
HOLISMOKES: I. Highly Optimised Lensing Investigations of Supernovae, Microlensing Objects, and Kinematics of Ellipticals and Spirals
journal, December 2020
- Suyu, S. H.; Huber, S.; Cañameras, R.
- Astronomy & Astrophysics, Vol. 644
On the Accuracy of Time-delay Cosmography in the Frontier Fields Cluster MACS J1149.5+2223 with Supernova Refsdal
journal, July 2020
- Grillo, C.; Rosati, P.; Suyu, S. H.
- The Astrophysical Journal, Vol. 898, Issue 1
Observational selection biases in time-delay strong lensing and their impact on cosmography
journal, July 2016
- Collett, Thomas E.; Cunnington, Steven D.
- Monthly Notices of the Royal Astronomical Society, Vol. 462, Issue 3
Particle swarm optimization
conference, January 1995
- Kennedy, J.; Eberhart, R.
- Proceedings of ICNN'95 - International Conference on Neural Networks
Projected Cosmological Constraints from Strongly Lensed Supernovae with the Roman Space Telescope
journal, February 2021
- Pierel, J. D. R.; Rodney, S.; Vernardos, G.
- The Astrophysical Journal, Vol. 908, Issue 2
HOW TO FIND GRAVITATIONALLY LENSED TYPE Ia SUPERNOVAE
journal, December 2016
- Goldstein, Daniel A.; Nugent, Peter E.
- The Astrophysical Journal, Vol. 834, Issue 1
STRIDES: a 3.9 per cent measurement of the Hubble constant from the strong lens system DES J0408−5354
journal, March 2020
- Shajib, A. J.; Birrer, S.; Treu, T.
- Monthly Notices of the Royal Astronomical Society, Vol. 494, Issue 4
H0LiCOW – IV. Lens mass model of HE 0435−1223 and blind measurement of its time-delay distance for cosmology
journal, November 2016
- Wong, Kenneth C.; Suyu, Sherry H.; Auger, Matthew W.
- Monthly Notices of the Royal Astronomical Society, Vol. 465, Issue 4
TDCOSMO: V. Strategies for precise and accurate measurements of the Hubble constant with strong lensing
journal, May 2021
- Birrer, Simon; Treu, Tommaso
- Astronomy & Astrophysics, Vol. 649
Planck 2018 results: VI. Cosmological parameters
journal, September 2020
- Aghanim, N.; Akrami, Y.; Ashdown, M.
- Astronomy & Astrophysics, Vol. 641, A6
H0LiCOW – IX. Cosmographic analysis of the doubly imaged quasar SDSS 1206+4332 and a new measurement of the Hubble constant
journal, January 2019
- Birrer, S.; Treu, T.; Rusu, C. E.
- Monthly Notices of the Royal Astronomical Society, Vol. 484, Issue 4
HOLISMOKES: III. Achromatic phase of strongly lensed Type Ia supernovae
journal, February 2021
- Huber, S.; Suyu, S. H.; Noebauer, U. M.
- Astronomy & Astrophysics, Vol. 646
H0LiCOW. VI. Testing the fidelity of lensed quasar host galaxy reconstruction
journal, November 2016
- Ding, Xuheng; Liao, Kai; Treu, Tommaso
- Monthly Notices of the Royal Astronomical Society, Vol. 465, Issue 4
Chromatic Microlensing Time Delays
journal, August 2020
- Liao, Kai
- The Astrophysical Journal, Vol. 899, Issue 2
Cosmic Distances Calibrated to 1% Precision with Gaia EDR3 Parallaxes and Hubble Space Telescope Photometry of 75 Milky Way Cepheids Confirm Tension with ΛCDM
journal, February 2021
- Riess, Adam G.; Casertano, Stefano; Yuan, Wenlong
- The Astrophysical Journal, Vol. 908, Issue 1
Searching for supernovae in the multiply-imaged galaxies behind the gravitational telescope A370
journal, June 2018
- Petrushevska, T.; Goobar, A.; Lagattuta, D. J.
- Astronomy & Astrophysics, Vol. 614
Time delay lens modelling challenge
journal, February 2021
- Ding, X.; Treu, T.; Birrer, S.
- Monthly Notices of the Royal Astronomical Society, Vol. 503, Issue 1
TDCOSMO: I. An exploration of systematic uncertainties in the inference of H 0 from time-delay cosmography
journal, July 2020
- Millon, M.; Galan, A.; Courbin, F.
- Astronomy & Astrophysics, Vol. 639
The internal structure of the lens PG1115+080: breaking degeneracies in the value of the Hubble constant
journal, September 2002
- Treu, T.; Koopmans, L. V. E.
- Monthly Notices of the Royal Astronomical Society, Vol. 337, Issue 2
Measuring the Value of the Hubble Constant “à la Refsdal”
journal, June 2018
- Grillo, C.; Rosati, P.; Suyu, S. H.
- The Astrophysical Journal, Vol. 860, Issue 2
H0LiCOW – XIII. A 2.4 per cent measurement of H0 from lensed quasars: 5.3σ tension between early- and late-Universe probes
journal, September 2019
- Wong, Kenneth C.; Suyu, Sherry H.; Chen, Geoff C-F
- Monthly Notices of the Royal Astronomical Society, Vol. 498, Issue 1
What Do Gravitational Lens Time Delays Measure?
journal, October 2002
- Kochanek, C. S.
- The Astrophysical Journal, Vol. 578, Issue 1
Magnification, dust and time-delay constraints from the first resolved strongly lensed Type Ia supernova iPTF16geu
journal, October 2019
- Dhawan, S.; Johansson, J.; Goobar, A.
- Monthly Notices of the Royal Astronomical Society
Strongly lensed repeating fast radio bursts as precision probes of the universe
journal, September 2018
- Li, Zheng-Xiang; Gao, He; Ding, Xu-Heng
- Nature Communications, Vol. 9, Issue 1
Strong gravitational lensing of explosive transients
journal, November 2019
- Oguri, Masamune
- Reports on Progress in Physics, Vol. 82, Issue 12
Lens modelling of the strongly lensed Type Ia supernova iPTF16geu
journal, June 2020
- Mörtsell, E.; Johansson, J.; Dhawan, S.
- Monthly Notices of the Royal Astronomical Society, Vol. 496, Issue 3
How Does the Earth’s Rotation Affect Predictions of Gravitational Wave Strong Lensing Rates?
journal, April 2019
- Yang, Lilan; Ding, Xuheng; Biesiada, Marek
- The Astrophysical Journal, Vol. 874, Issue 2
Strong gravitational lensing of gravitational waves in Einstein Telescope
journal, October 2013
- Piórkowska, Aleksandra; Biesiada, Marek; Zhu, Zong-Hong
- Journal of Cosmology and Astroparticle Physics, Vol. 2013, Issue 10
Gravitational lensing
journal, November 2010
- Bartelmann, Matthias
- Classical and Quantum Gravity, Vol. 27, Issue 23
Ambiguities in gravitational lens models: impact on time delays of the source position transformation
journal, September 2018
- Wertz, Olivier; Orthen, Bastian; Schneider, Peter
- Astronomy & Astrophysics, Vol. 617