C. Fromm

发表

First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

S. T. Timmer, Chih-Wei L. Huang, Alexander W. Raymond, 2019, 1906.11238.

First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, The Astrophysical Journal.

The science case and challenges of space-borne sub-millimeter interferometry

L. Gurvits, H. Falcke, L. Rezzolla, 2022, Acta Astronautica.

First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole

Chih-Wei L. Huang, Alexander W. Raymond, K. Souccar, 2019, The Astrophysical Journal.

First M87 Event Horizon Telescope Results. III. Data Processing and Calibration

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, The Astrophysical Journal.

First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, The Astrophysical Journal.

First M87 Event Horizon Telescope Results. II. Array and Instrumentation

Kevin A. Dudevoir, Daniel C. M. Palumbo, S. T. Timmer, 2019, 1906.11239.

Deep Horizon: A machine learning network that recovers accreting black hole parameters

H. Falcke, J. Davelaar, C. Fromm, 2019, Astronomy & Astrophysics.

Modeling non-thermal emission from the jet-launching region of M 87 with adaptive mesh refinement

J. Davelaar, T. Bronzwaer, C. M. Fromm, 2019, Astronomy & Astrophysics.

On the location of the supermassive black hole in CTA 102

E. Ros, J. Zensus, M. Perucho, 2014, 1412.1317.

The science case and challenges of space-borne sub-millimeter interferometry

L. Gurvits, H. Falcke, L. Rezzolla, 2022, Acta Astronautica.

Ariane 5 Performance Optimization Using Dual-Bell Nozzle Extension

Ralf Stark, Chloé Génin, Dirk Schneider, 2016 .

The current ability to test theories of gravity with black hole shadows

H. Falcke, L. Rezzolla, M. Kramer, 2018, Nature Astronomy.

First M87 Event Horizon Telescope Results. III. Data Processing and Calibration

Chih-Wei L. Huang, Alexander W. Raymond, K. Souccar, 2019, The Astrophysical Journal.

Long-term Simulations of Magnetized Disks and Jets Around Supermassive Black-hole Binaries in General Relativity

L. J. Papenfort, L. Rezzolla, R. Gold, 2021 .

THEZA: TeraHertz Exploration and Zooming-in for Astrophysics

L. Gurvits, H. Falcke, L. Rezzolla, 2021, Experimental Astronomy.

THEMIS: A Parameter Estimation Framework for the Event Horizon Telescope

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2020, The Astrophysical Journal.

Event Horizon Telescope imaging of the archetypal blazar 3C 279 at an extreme 20 microarcsecond resolution

Daniel C. M. Palumbo, S. T. Timmer, Chih-Wei L. Huang, 2020 .

Monitoring the Morphology of M87* in 2009–2017 with the Event Horizon Telescope

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2020, The Astrophysical Journal.

Gravitational Test beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2020, Physical Review Letters.

Millimeter Light Curves of Sagittarius A* Observed during the 2017 Event Horizon Telescope Campaign

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2022, The Astrophysical Journal Letters.

First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way

Marcos Emir Moreno Nolasco, Chih-Wei L. Huang, P. K. Leung, 2022, The Astrophysical Journal Letters.

First Sagittarius A* Event Horizon Telescope Results. III. Imaging of the Galactic Center Supermassive Black Hole

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2022, The Astrophysical Journal Letters.

First Sagittarius A* Event Horizon Telescope Results. II. EHT and Multiwavelength Observations, Data Processing, and Calibration

Chih-Wei L. Huang, P. K. Leung, Alexander W. Raymond, 2022, The Astrophysical Journal Letters.

Jet-torus connection in radio galaxies: Relativistic hydrodynamics and synthetic emission

L. Rezzolla, E. Ros, J. Zensus, 2017, 1705.01300.

Selective Dynamical Imaging of Interferometric Data

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2022, The Astrophysical Journal Letters.

Modelling the polarised emission from black holes on event horizon-scales

C. Fromm, Y. Mizuno, H. Olivares, 2019, Proceedings of the International Astronomical Union.

Core-Shift and Spectral Analysis

C. Fromm, 2015 .

VLBI Kinematic Analysis

C. Fromm, 2015 .

Catching the radio flare in CTA 102 - II. VLBI kinematic analysis

E. Ros, M. Lister, A. Lobanov, 2012, 1211.3606.

A sensitive study of the peculiar jet structure HST-1 in M87

M. Perucho, C. Casadio, C. Fromm, 2013, 1310.6312.

Binary black holes in nuclei of extragalactic radio sources

S. Britzen, C. Fromm, A. Caproni, 2013, 1307.3700.

Catching the radio flare in CTA 102 - III. Core-shift and spectral analysis

E. Ros, A. Lobanov, J. Zensus, 2013, 1306.6208.

Core-shift and spectral analysis of the 2006 radio flare in CTA102

E. Ros, A. Lobanov, J. Zensus, 2013, 1301.7674.

Evidence for shock-shock interaction in the jet of CTA 102

E. Ros, M. Gurwell, A. Lobanov, 2010, Proceedings of the International Astronomical Union.

State-of-the-art energetic and morphological modelling of the launching site of the M87 jet

H. Falcke, L. Rezzolla, J. Davelaar, 2021, Nature Astronomy.

First Sagittarius A* Event Horizon Telescope Results. II. EHT and Multiwavelength Observations, Data Processing, and Calibration

Chih-Wei L. Huang, P. K. Leung, Alexander W. Raymond, 2022, The Astrophysical Journal Letters.

A Universal Power-law Prescription for Variability from Synthetic Images of Black Hole Accretion Flows

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2022, The Astrophysical Journal Letters.

Characterizing and Mitigating Intraday Variability: Reconstructing Source Structure in Accreting Black Holes with mm-VLBI

Daniel C. M. Palumbo, Michael F. Wondrak, P. K. Leung, 2022, The Astrophysical Journal Letters.

First Sagittarius A* Event Horizon Telescope Results. VI. Testing the Black Hole Metric

Chih-Wei L. Huang, P. K. Leung, Alexander W. Raymond, 2022, The Astrophysical Journal Letters.

First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass

Chih-Wei L. Huang, P. K. Leung, Alexander W. Raymond, 2022, The Astrophysical Journal Letters.

First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way

Marcos Emir Moreno Nolasco, Chih-Wei L. Huang, P. K. Leung, 2022, The Astrophysical Journal Letters.

First Sagittarius A* Event Horizon Telescope Results. V. Testing Astrophysical Models of the Galactic Center Black Hole

Chih-Wei L. Huang, P. K. Leung, Alexander W. Raymond, 2022, The Astrophysical Journal Letters.

TeraHertz Exploration and Zooming-in for Astrophysics (THEZA): ESA Voyage 2050 White Paper

L. Gurvits, J. Conway, H. Falcke, 2019, 1908.10767.

The Photon Ring in M87*

D. James, L. Rezzolla, K. Menten, 2022, The Astrophysical Journal.

Resolving the Inner Parsec of the Blazar J1924–2914 with the Event Horizon Telescope

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2022, The Astrophysical Journal.

Using space-VLBI to probe gravity around Sgr A*

H. Falcke, L. Rezzolla, M. Kramer, 2021, Astronomy & Astrophysics.

Impact of non-thermal particles on the spectral and structural properties of M87

H. Falcke, L. Rezzolla, J. Davelaar, 2021, Astronomy & Astrophysics.

THE ACCELERATING JET OF 3C 279

C. Fromm, S. Bloom, E. Ros, 2012 .

Recollimation shocks in the relativistic outflows of active galactic nuclei. Doctoral Thesis Award Lecture 2014

C. Fromm, 2015 .

Accreting Black Hole Binaries

L. J. Papenfort, L. Rezzolla, R. Gold, 2021, High Performance Computing in Science and Engineering '20.

Dual-frequency VLBI study of Centaurus A on sub-parsec scales. The highest-resolution view of an extragalactic jet

U. Katz, E. Ros, P. Edwards, 2011, 1104.0804.

Sub-parsec scale imaging of Centaurus A

E. Ros, M. Kadler, J. Wilms, 2010, 1006.1486.

Light Curve Analysis

C. Fromm, 2015 .

Multi-frequency properties of synthetic blazar radio light curves within the shock-in-jet scenario

M. Perucho, L. Fuhrmann, C. Fromm, 2014, 1412.7194.

F-GAMMA: On the phenomenological classification of continuum radio spectra variability patterns of Fermi blazars

T. Krichbaum, J. Zensus, V. Pavlidou, 2011, 1202.4242.

Spectral Evolution in Blazars

C. Fromm, 2015 .

The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, The Astrophysical Journal Supplement Series.

Verification of Radiative Transfer Schemes for the EHT

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2020, The Astrophysical Journal.

Studying Black Holes on Horizon Scales with VLBI Ground Arrays

Daniel C. M. Palumbo, Alexander W. Raymond, K. Bouman, 2019, 1909.01411.

The ngEHT Analysis Challenges

Alexander W. Raymond, L. Blackburn, N. Patel, 2022, Galaxies.

Comparing accretion flow morphology in numerical simulations of black holes from the ngEHT Model Library: the impact of radiation physics

L. Blackburn, N. Patel, Michael D. Johnson, 2022, 2212.01804.

First M87 Event Horizon Telescope Results. VII. Polarization of the Ring

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2021, The Astrophysical Journal Letters.

First M87 Event Horizon Telescope Results. VIII. Magnetic Field Structure near The Event Horizon

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2021, The Astrophysical Journal Letters.

3D magnetized jet break-out from neutron-star binary merger ejecta: afterglow emission from the jet and the ejecta

L. Rezzolla, C. Fromm, O. Porth, 2020, 2009.09714.

Shedding light on the angular momentum evolution of binary neutron star merger remnants: A semi-analytic model

C. Fromm, F. Guercilena, L. Sagunski, 2020, 2010.11224.

Comparison of Kerr and dilaton black hole shadows

L. Rezzolla, C. Fromm, Y. Mizuno, 2022, Proceedings of European VLBI Network Mini-Symposium and Users' Meeting 2021 — PoS(EVN2021).

How to tell an accreting boson star from a black hole

H. Falcke, L. Rezzolla, M. Kramer, 2018, Monthly Notices of the Royal Astronomical Society.

BlackHoleCam: Fundamental physics of the galactic center

T. Bronzwaer, C. M. Fromm, S. Issaoun, 2016, 1606.08879.

Using evolutionary algorithms to model relativistic jets

L. Rezzolla, E. Ros, J. Zensus, 2019, Astronomy & Astrophysics.

Using electric propulsion for the de-orbiting of satellites

C. Fromm, A. Herbertz, 2015 .

Key Science Goals for the Next-Generation Event Horizon Telescope

Daniel C. M. Palumbo, K. Bouman, L. Blackburn, 2023, Galaxies.

The Event Horizon Telescope Image of the Quasar NRAO 530

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2023, The Astrophysical Journal.

Multifrequency Black Hole Imaging for the Next-generation Event Horizon Telescope

Michael D. Johnson, A. Chael, D. Pesce, 2022, The Astrophysical Journal.

Event Horizon Telescope observations of the jet launching and collimation in Centaurus A

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2021, Nature Astronomy.

Constraints on black-hole charges with the 2017 EHT observations of M87*

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2021, Physical Review D.

Broadband Multi-wavelength Properties of M87 during the 2017 Event Horizon Telescope Campaign

F. G. Saturni, Daniel C. M. Palumbo, Chih-Wei L. Huang, 2021, 2104.06855.

Polarimetric Properties of Event Horizon Telescope Targets from ALMA

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2021, The Astrophysical Journal Letters.

Accretion Flow Morphology in Numerical Simulations of Black Holes from the ngEHT Model Library: The Impact of Radiation Physics

Alexander W. Raymond, L. Blackburn, N. Patel, 2022, Galaxies.

Comparison of the ion-to-electron temperature ratio prescription: GRMHD simulations with electron thermodynamics

L. Rezzolla, C. Fromm, Y. Mizuno, 2021, Monthly Notices of the Royal Astronomical Society.

Constraints on blackhole charges with the 2017 EHT observations of M 87 *

Chih-Wei L. Huang, H. Falcke, T. Lauer, 2021 .

Flares in the Galactic Centre – I. Orbiting flux tubes in magnetically arrested black hole accretion discs

C. Fromm, Y. Mizuno, O. Porth, 2020, Monthly Notices of the Royal Astronomical Society.

Asymmetric jet production in the active galactic nucleus of NGC 1052

E. Ros, M. Perucho, R. Schulz, 2019, Astronomy & Astrophysics.

Plasmoid formation in global GRMHD simulations and AGN flares

L. Rezzolla, C. Fromm, Y. Mizuno, 2020, 2002.01777.

On the opening angle of magnetized jets from neutron-star mergers: the case of GRB170817A

L. Rezzolla, C. Fromm, O. Porth, 2020, 2003.03597.

First M87 Event Horizon Telescope Results and the Role of ALMA

H. Falcke, D. James, L. Rezzolla, 2019, 1910.10193.

Constrained transport and adaptive mesh refinement in the Black Hole Accretion Code

L. Rezzolla, J. Davelaar, C. Fromm, 2019, Astronomy & Astrophysics.

SYMBA: An end-to-end VLBI synthetic data generation pipeline

F. Roelofs, M. Janssen, I. Natarajan, 2020, Astronomy & Astrophysics.

First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way

Daniel C. M. Palumbo, Marcos Emir Moreno Nolasco, Michael F. Wondrak, 2023, 2311.08680.

First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, The Astrophysical Journal.

Spectral evolution of flaring blazars from numerical simulations

E. Ros, M. Perucho, C. Fromm, 2016, 1601.03181.

First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2022, The Astrophysical Journal Letters.

First Sagittarius A* Event Horizon Telescope Results. VI. Testing the Black Hole Metric

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2022, The Astrophysical Journal Letters.

First Sagittarius A* Event Horizon Telescope Results. V. Testing Astrophysical Models of the Galactic Center Black Hole

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2022, The Astrophysical Journal Letters.

First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, The Astrophysical Journal.

First Sagittarius A* Event Horizon Telescope Results. II. EHT and Multi-wavelength Observations, Data Processing, and Calibration

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2023, 2311.08679.

First M87 Event Horizon Telescope Results. II. Array and Instrumentation

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019 .

First M87 Event Horizon Telescope Results. III. Data Processing and Calibration

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, The Astrophysical Journal.

Comparison of Polarized Radiative Transfer Codes Used by the EHT Collaboration

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2023, The Astrophysical Journal.

The Variability of the Black Hole Image in M87 at the Dynamical Timescale

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2021, The Astrophysical Journal.

The Polarized Image of a Synchrotron-emitting Ring of Gas Orbiting a Black Hole

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2021, The Astrophysical Journal.

UvA-DARE Event Horizon Telescope observations of the jet launching and collimation in Centaurus A

Daniel C. M. Palumbo, Chih-Wei L. Huang, H. Falcke, 2021 .

UvA-DARE Event Horizon Telescope observations of the jet launching and collimation in Centaurus A

Daniel C. M. Palumbo, Chih-Wei L. Huang, H. Falcke, 2021 .

UvA-DARE Event Horizon Telescope observations of the jet launching and collimation in Centaurus A

Daniel C. M. Palumbo, Chih-Wei L. Huang, H. Falcke, 2021 .

Impact of radiative cooling on the magnetised geometrically thin accretion disk around Kerr black hole

C. Fromm, Y. Mizuno, Z. Younsi, 2023, 2305.09698.

Two-Temperature GRMHD simulations of black hole accretion flows with multiple magnetic loops

C. Fromm, Y. Mizuno, A. Nathanail, 2023, Monthly Notices of the Royal Astronomical Society.

Magnetic reconnection and plasmoid formation in three-dimensional accretion flows around black holes

L. Rezzolla, C. Fromm, O. Porth, 2021, 2111.03689.

Black hole parameter estimation with synthetic very long baseline interferometry data from the ground and from space

H. Falcke, L. Rezzolla, F. Roelofs, 2021, Astronomy & Astrophysics.

Catching the radio flare in CTA 102 - I. Light curve analysis

E. Ros, M. Gurwell, A. Lahteenmaki, 2011, 1105.5024.

First M87 Event Horizon Telescope Results. II. Array and Instrumentation

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, 1906.11239.

UvA-DARE (Digital Academic Repository) Broadband Multi-wavelength Properties of M87 during the 2017 Event Horizon Telescope Campaign

F. G. Saturni, Daniel C. M. Palumbo, Chih-Wei L. Huang, 2022 .

First Sagittarius A* Event Horizon Telescope Results. VI. Testing the Black Hole Metric

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2022, The Astrophysical Journal Letters.

First M87 Event Horizon Telescope Results. IX. Detection of Near-horizon Circular Polarization

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2023, The Astrophysical Journal Letters.

First Sagittarius A* Event Horizon Telescope Results. III. Imaging of the Galactic Center Supermassive Black Hole

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2022, The Astrophysical Journal Letters.

State-of-the-art energetic and morphological modelling of the launching site of the M87 jet

H. Falcke, L. Rezzolla, J. Davelaar, 2021, Nature Astronomy.

Ambilateral collimation study of the twin-jets in NGC1052

T. Krichbaum, J. Zensus, M. Perucho, 2021, Astronomy & Astrophysics.

First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, The Astrophysical Journal.

Polarimetric Geometric Modeling for mm-VLBI Observations of Black Holes

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2023, The Astrophysical Journal Letters.

Event Horizon Telescope imaging of the archetypal blazar 3C 279 at an extreme 20 microarcsecond resolution

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2020 .

Temperature properties in magnetised and radiatively cooled two-temperature accretion flows on to a black hole

L. Rezzolla, C. Fromm, Y. Mizuno, 2022, Monthly Notices of the Royal Astronomical Society.

The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, The Astrophysical Journal Supplement Series.

First M87 Event Horizon Telescope Results. III. Data Processing and Calibration

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, The Astrophysical Journal.

First M87 Event Horizon Telescope Results. VIII. Magnetic Field Structure near The Event Horizon

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2021, The Astrophysical Journal Letters.

A Search for Pulsars around Sgr A* in the First Event Horizon Telescope Data Set

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2023, The Astrophysical Journal.

Gravitational Test beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2020, Physical Review Letters.

UvA-DARE (Digital Academic Repository) Gravitational Test beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2020 .

TELAMON: Effelsberg Monitoring of AGN Jets with Very-High-Energy Astroparticle Emissions - II. Polarization properties

E. Pueschel, E. Ros, P. Edwards, 2023, Proceedings of 38th International Cosmic Ray Conference — PoS(ICRC2023).

First M87 Event Horizon Telescope Results. III. Data Processing and Calibration

Daniel C. M. Palumbo, Chih-Wei L. Huang, Alexander W. Raymond, 2019, The Astrophysical Journal.

First Sagittarius A* Event Horizon Telescope Results. V. Testing Astrophysical Models of the Galactic Center Black Hole

Daniel C. M. Palumbo, Michael F. Wondrak, Chih-Wei L. Huang, 2022, The Astrophysical Journal Letters.

Future Prospects for Constraining Black Hole Spacetime: Horizon-scale Variability of Astrophysical Jets

L. Rezzolla, C. Fromm, Y. Mizuno, 2023, The Astrophysical Journal.

First Sagittarius A* Event Horizon Telescope Results. VII. Polarization of the Ring

Chih-Wei L. Huang, K. Souccar, T. Lauer, 2024, The Astrophysical Journal Letters.