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SARAO News #02 2018

The South African Radio Astronomy Observatory, through its Hartebeesthoek Radio Astronomy Observatory in Gauteng, has been instrumental in the adoption of the Third realisation of the International Celestial Reference Frame (ICRF-3), adopted at the International Astronomical Union (IAU) General Assembly held in Vienna, Austria last month.

HartRAO provided essential geometric coverage and is one of only two observatories in the Southern Hemisphere covering two of the three wavelengths (“colours”) for the ICRF-3.

“South Africa constantly tries to profile the utilitarian value of radio astronomy and the ICRF-3 provides such an opportunity where geophysicists can use the improved celestial positional grid to understand a number of phenomena such as plate tectonics, earthquakes, sea level rise, and processes that affect our planet’s orientation in space,” says Dr Alet de Witt, a member of the IAU working group for the ICRF-3.

Climate change is a major concern to society. In particular, current projections predict alarming rises in sea levels caused by climate change. The ICRF-3 provides the long term stability needed to monitor and understand sea level rise with its potential to affect millions of people.

Chris Jacobs, NASA Deep Space navigation Engineer and first chair of the ICRF-3 says: “The ICRF-3 provides the stable platform from which we can monitor the dynamic changes of the Earth with unprecedented levels of accuracy of a few parts in 10 billion – about the size of a tennis ball at the moon. This is achieved by using quasars powered by supermassive black holes to provide radio beacons which do not change their positions even after decades.”

This also allows the ICRF-3 to monitor plate tectonics with extreme accuracy and thus better understand the natural hazards from earthquakes and other geological processes.

It enables radio astronomers to provide the data on the Earth’s rotation which is essential for stabilizing global navigation satellite systems (GPS, GLONASS, Galileo) which are widely used by the public for navigation and hundreds of related uses. A GPS device gets its stability by connecting people to the stars.

Read more about the ICRF-3



For more information contact Dr Alet de Witt on alet@hartrao.ac.za

Nineteen students graduated from the third African Very Long Baseline Interferometry Network training held at the Hartebeesthoek Radio Astronomy Observatory during March 2018.

The students, all hailing from Botswana, Zambia and Namibia, participated in the training which took place from 26 February to 23 March 2018.

The training is part of the Development in Africa with Radio Astronomy (DARA) project, which seeks to provide people in the targeted countries with training to use radio telescopes. The first four-week training at the Hartebeesthoek Radio Astronomy Observatory (HartRAO) took place in 2016, focusing on Observational and Technical Training.

It also has an outreach programme to encourage young people to study the technological aspects of radio astronomy and pursue science, technology, engineering and mathematics subjects. The project is funded by the DARA Newton Fund.

Since 2016 a training school was held every year, and this year two schools are taking place – one in March and another in April.

Dr Alet de Witt, Operations Astronomer at HartRAO and coordinator of the training programme, says that since the programme started, more hands-on practicals have been added and more demonstrations take place during lectures.

“We focus on keeping each lecture as interactive as possible. This hands-on experience and interactive teaching style is a great tool to stimulate discussion and to promote an atmosphere of attention and participation where students can test their skills in applying knowledge,” says De Witt.

“Since the inception of the DARA project we have made various upgrades to existing training instruments at HartRAO as well as investments in new training instruments, for example, our two-element interferometer. We also upgraded our lecture room to a state-of-the art training facility, with 40 computers dedicated to student training. To date we have trained more than 60 students from various African SKA Partner Countries,” continues De Witt.

By the end of April, another 20 students from Madagascar and Mozambique will be able to add this excellent training opportunity to their resumés.

The main focus of the training this year is the observational and technical side of radio astronomy. The Centre for High Performance Computing (CHPC) also participated this year and presented a week’s training in Linux and Python during the first week of the school at HartRAO.

Several international scholars have been invited to and have been involved in the AVN training since 2016. This includes Chris Jacobs (NASA/Jet Propulsion Laboratory, USA in 2016, 2017 and 2018); Dr Michael Bietenholz (York University, Canada in 2016, 2017 and 2018); Dr Christina Garcia Miro (SKA International in 2017); Daniel Hayden (SKA International in 2018); David Mayer (Vienna University of Technology in 2016, 2017 and 2018); Matthias Schartner (Vienna University of Technology in 2017 and  2018); and Andreas Hellerschmied (Vienna University of Technology in 2016), among others.

The graduation ceremony, which took place on Friday, 23 March 2018 at Hartebeestpoort Dam, was preceded by a talk by Chris Jacobs on Stellar GPS: Navigating the solar system, at HartRAO. Thereafter the students travelled to a venue at the Dam, where they graduated.

Professor Justin Jonas, Chief Technologist and Acting Managing Director of HartRAO, said that it is important to note that the course is ‘an old fashioned course in radio astronomy’.

“In this new age of millennials, everybody wants to get onto the new next biggest best thing as soon as possible. Unfortunately, there is a new generation of radio astronomers who have never seen a radio telescope and everything they do is from their laptop. They have never actually done a very fundamental observation with a radio telescope. The only way to understand any science, and radio astronomy in particular, is to go right back to the fundamentals,” said Prof. Jonas.

“I am very grateful to Alet and the others who are involved in putting this course together, for taking you right back to those fundamentals, to the first principles of physics and mathematics so that you have that grounded understanding of where you get your data from,” Prof. Jonas continued.

Chileshe Mutale, a 23-year old Physics and Geology student from Zambia, said that the course has expanded new horizons for her.

“This course has has really been really great – not only the course, but the people as well. In school they put you in a box, but when I saw this course, I decided to try it. It has opened my horizons.”

De Witt herself is a former recipient of an SKA bursary through its Human Capital Development Programme. She commenced her PhD studies in Astronomy and Astrophysics from 2006 and attended the very first SKA Postgraduate Bursary Conference as a postdoctoral student that same year.

“I joined HartRAO in 2012 as a postdoctoral student and in 2013 I was appointed as Operations Astronomer. I have been involved in training activities at HartRAO since 2013 and was involved in the DARA project since its inception,” says De Witt.

She completed her PhD in Radio Astronomy with a focus on celestial reference frames and calibrator sources for Very Long Baseline Interferometry (VLBI). Her research is focused on fundamental astronomy, in particular celestial reference frames.

De Witt is also part of the International Astronomical Union (IAU) working group on the realisation of the next generation International Celestial Reference Frame (ICRF-3) to be adopted at the XXXth General Assembly of the IAU in 2018. One of the goals of the ICRF-3 was the extension of the ICRF to higher radio frequencies, such as the K-band (22 GHz) reference frame.

De Witt is the principal investigator of the K-band celestial reference frame project and this project has received to date more than 600 hours of observing time on the Very Long Baseline Array (VLBA) and equal amounts of time on Southern VLBI instruments.

She is also the principal investigator and scheduler for the majority of the Southern Hemisphere astrometric and geodetic VLBI sessions operated through the International VLBI Service for Geodesy and Astrometry (IVS). The IVS is an international collaboration of organisations which operate VLBI components in support of geodetic and astrometric research and operational activities and to integrate VLBI into a global Earth observing system.

A starquake on one of the littlest stars, 1500 light years away, caused some excitement among radio astronomers from South Africa and Australia.

The star “the Vela Pulsar” is no ordinary star. Compressed to the size of Johannesburg by a massive supernova explosion, it now drifts through space spinning eleven times a second and flashing like a cosmic emergency light. Pulsars are the next best thing to black holes, and Vela is an unusual adolescent version, not yet settled down into middle age, it suffers from rotational stresses that build up to cause the starquakes.

Sarah Buchner of the Hartebeesthoek Radio Astronomy Observatory near Krugersdorp, and Claire Flanagan of the Johannesburg Planetarium at the University of the Witwatersrand, have been watching Vela closely, hoping to catch a starquake. Richard Dodson uses a telescope in Hobart, Tasmania, to do the same. Yesterday, after a four-and-a-half year wait, it happened – Vela “glitched”! Both telescopes are watching the pulsar recover, hoping to learn something new about what’s going on inside it.

For nearly thirty years, Vela was the most highly-stressed pulsar known. Recently, another twenty or so more “adolescents” have been discovered. All are in the southern skies. South Africa recently joined the international team to design the Square Kilometre Array, radio astronomers’ dream telescope of the future. One reason for building an SKA is to study pulsars – gravitational monsters that help us understand our universe.

This was the formal announcement of the discovery:

PSR 0833-45

R. Dodson, Institute of Space and Astronautical Science; S. Buchner, Hartebeesthoek Radio Astronomy Observatory (HartRAO); B. Reid and D. Lewis, University of Tasmania; and C. Flanagan, Johannesburg Planetarium, report observing a sudden spin-up (“glitch”) in the Vela pulsar (cf. IAUC 7347) on July 7.09 UT. Preliminary model fitting gives a fractional decrease of 2.1 x 10**-6 in the rotation period. The jump was first detected by the HartRAO 26-m telescope and observed at three frequencies (635.034, 990.25, and 1390.64 MHz) with the Mount Pleasant 14-m dish.

Photographs of the meeting may be viewed.
Abstracts of the presentations are given below.

The full text of the articles is available at the African Skies web edition. Note that you must click on the article names on the second (contents) page of this pdf file to reach the articles.

Programme 3rd Dec 2001


Binary evolution: Spin-up, spin-down and non-thermal (thermal) emission from accreting compact objects.

 Author: Hannes Calitz  
 e-mail: calitzjj@sci.uovs.ac.za 

 Affiliation: Department of Physics, University of the Free State, 
              Bloemfontein, South Africa
 Co-Author: Pieter.J. Meintjies 
 e-mail: MeintjPJ@sci.uovs.ac.za

 Affiliation: Department of Physics, University of the Free State, 
              Bloemfontein, South Africa

 Abstract: The spin-up or spin-down of accreting objects can be used as a
 diagnostic tool to investigate the mass transfer mechanism between the
 primary and secondary star in binary systems, as well as the evolution of
 the system. This can put tight contstraints on the non-thermal and thermal
 emission in the system. By getting a global view of system, potential
 non-thermal emitters can be identified for future studies by HESS and other
 new-generation gamma-ray telescopes.  

AE Aquarii, the “binary milli-second radio pulsar” of Cataclysmic Variables

 Author: Pieter.J. Meintjies  
 e-mail: MeintjPJ@sci.uovs.ac.za

 Affiliation: Department of Physics, University of the Free State, 
              Bloemfontein, South Africa
 Abstract: This is an investigation of the evolution of the binary system  
 AE Aquarii and the relation it has on the spin-up and spin-down of the
 compact companion of the system, as well as the thermal and non-thermal
 emission in the system. The mechanisms causing the rapid non-thermal
 outbursts are investigated and constraints are put on the binary system

Observations, Past and Future, of X-ray pulsars from South Africa

 Author: David A.H. Buckley  
 e-mail: dibnob@saao.ac.za

 Affiliation: South African Astronomical Observatory, Cape Town,        
              South Africa

 Abstract: This talk covers two separate, but related, topics concerning
 X-ray emitting pulsars. Most of the talk concentrates on a description of an
 on-going optical/IR/Xray observational program on Be/X-ray binaries: early
 type Be stars whose mass loss powers the accretion energy of X-ray pulsars.
 This class of object is the most common of early spectral type X-ray
 binaries. Optical spectroscopy and IR photometry can help probe the
 circumstellar disks of Be stars, which are the mass "reservoirs" powering
 the accreting neutron stars. Understanding the states of these disks can
 help predict the X-ray activity of these, often transient, sources. Unlike
 the more massive systems, where Roche lobe overflow powers the accretion,
 neutron stars in Be/X-ray binaries are principally accreting from either a
 strong stellar wind or a circumstellar disk. In eccentric systems, the
 accretion rate can vary significantly over the orbit. Similarly the extent
 of the disk itself determines the X-ray properties. Recent work on these
 sources in the Magellanic Clouds will be discussed, particularly in
 relevance to the apparent discrepancies in populations between the two

 The second part of the talk covers the interesting group of isolated
 accreting neutron stars, as typified by the 8.39 s spin period system, RX
 J0720.4-3125. This nearby system, although sharing some properties of the
 "anomolous 6 s pulsars", is clearly much less luminous and accreting from
 the ISM, rather than a remnant Thorne-Zytkow object, as proposed for the
 latter. Optical counterparts to this object, and a similar, but non-pulsing
 object (RX J1856.5-3754), have recently been identified. The paucity of
 similar objects has been at odds with the predictions of ~2000 isolated
 neutron stars supposed to be detectable from their hot thermal (soft X-ray)
 emission. I end with a discussion of the future role of SALT in this
 research, and the possible capabilities of instruments, including new
 generation photon detectors, with energy discrimination, like
 Superconduction Tunnel Junction (STJ) devices. 

Neutron Star Magnetic Field Evolution

 Author: Legesse W. Kebede  
 e-mail: Observatory.aau@telecom.net.et (Subject of mail must be Legesse
         Kebede as the address is shared with others.)

 Affiliation: Department of Physics, Addis Ababa University, Ethiopia

 Abstract: Based on the relativistic plasma diffusion theory for neutron
 star magnetic fields developed by the author, the evolution of surface
 magnetic fields of neutron stars is discussed. It is particularly shown that
 neutron star magnetic fields are temperature dependent and hence dissipate
 as a result of neutrino and photon cooling mechanisms. The decay law for the
 process seems to give results which are in good agreement with observations.
 Consequences of the decay law in relation to certain important astrophysical
 measurements are also discussed. 

Implications of time dependant parameters for braking indices

 Author: Adrian Tiplady  
 e-mail: g9731642@campus.ru.ac.za

 Affiliation: Physics Department, Rhodes University, Grahamstown, South

 Co-Author: Fabio Frescura   
 e-mail: frescura@physnet.phys.wits.ac.za 

 Affiliations: Research Fellow in the Department of Physics, Rhodes University,
               Grahamstown, South Africa;  Centre of Theoretical Physics,
               University of the Witwatersrand, South Africa; Research
               Associate at the Hartebeesthoek Radio Astronomy Observatory.

 Abstract: The determination of braking indices via experimental results has
 been allowed by a certain degree of assumption. An analytical approach is
 taken in exploring the nature of the braking index and its possible
 different forms by introducing a time varying parameter. This is a first
 step into understanding the reason for our measurement of differing braking

Radio Observations and the Challenges of the Neutron Star Interior

 Author: Johnson O. Urama presented by Augustine E. Chukwude  
 e-mail: johnsonurama@yahoo.com

 Affiliation: Department of Physics and Astronomy, University of Nigeria, 
              Nsukka, Nigeria 
 Abstract: Radio pulsars are, by far, the most common observable
 manifestation of the fascinating neutron star. The timing observations of
 the emitted radio pulses remain one of the best probes of the neutron star
 interior. Such observations have led to a number of models describing the
 various components of the neutron star interior and the manner in which
 they couple with each other. This paper discusses the progress made in this

The HartRAO Glitch-Monitoring Project: Part I – Catching Glitches

 Author: Claire Flanagan   
 e-mail: 111flan@cosmos.wits.ac.za    

 Affiliation: Johannesburg Planetarium, University of the Witwatersrand,
              South Africa and the Hartebeesthoek Radio Astronomy 
              Observatory, South Africa

 Abstract: The HartRAO glitch-monitoring project was set up in 1984, in
 response to the need for good observational coverage of the response of the
 Vela pulsar to spin-ups. We describe the (at the time unique) technique used
 to obtain post-glitch observations (commencing in one case within seven
 minutes of a glitch). New insight into the interior of the pulsar obtained
 from these observations is presented, and value of extending the project
 into the future is discussed. 

Ground Based Observations with Third Generation Ground-Based Gamma-Ray Telescopes

 Author: Okkie C. de Jager  
 e-mail: okkie@fskocdj.puk.ac.za

 Affiliation: School of Physics, Potchefstroom University, South Africa

 Co-Authors: The MAGIC Pulsar Working Group (Magic-pulsar@ulises.gae.ucm.es)
             and the H.E.S.S. Pulsar Working Group (HESS-all@mpi-hd.mpg.de)

 Abstract: Pulsar polar cap models predict gamma-ray/pair cascades resulting
 in a high multiplicity of pairs in the pulsar magnetosphere. This large
 multiplicity is also required to explain the plerionic emission from such
 systems. The consequence is that emergent gamma-ray energies are
 constrained to be well below a TeV. Emergent maximum energies up to 30 GeV
 (pulsed photons) were seen by EGRET from PSR B1706-44 and PSR B1951+32,
 whereas observations above these energies by past ground-based pulsars only
 resulted in upper limits, which confirm the existence of such spectral

 The next generation telescopes such as MAGIC (La Palma) and H.E.S.S.
 (Namibia) should have low enough thresholds to detect the high energy tails
 of pulsed emission from some of these pulsars. This opens a new window on
 Pulsar Astronomy, since the main contribution to the photon luminosity will
 be measured by such telescopes. This talk reviews the sensitivities of
 H.E.S.S., MAGIC and 5@5 for such detections within a single night of

HartRAO Long-term Pulsar Timing Observations – Relevance and Prospect

 Author: Augustine E. Chukwude  
 e-mail:aus_chukwude@yahoo.com; austine@hartrao.ac.za (until 21 Dec 2001)
 Affiliation: Department of Physics and Astronomy, University of Nigeria, 
              Nsukka, Nigeria; Hartebeesthoek Radio Astronomy Observatory, 
              South Africa

 Abstract: Regular timing observations of some radio pulsars have now been
 conducted at the Hartebeesthoek Radio Astronomy Observatory (HartRAO) for 
 more than a decade. Here we present some of the results of our current 
 work on timing activity in radio pulsars. Our results highlight the 
 relevance of such long-term timing program in our quest for better 
 understanding of the dynamical behaviour of neutron stars. Arguments are 
 also presented for the continuation and improvement of the current HartRAO 
 pulsar monitoring program.

Programme 4th Dec 2001


Effects of Pulsar Timing Noise and Glitches on Gamma-Ray Pulsar Observations

 Author: E. de Ona-Wilhelmi 
 e-mail: fskeow@puknet.puk.ac.za

 Affiliation: School of Physics, Potchefstroom University, South Africa
 Co-Authors: The MAGIC Pulsar Working Group (Magic-pulsar@ulises.gae.ucm.es)

 Abstract: Pulsed emission from a few Gamma-Ray pulsars may be detectable
 with Ground-Based Gamma-Ray Telescopes. The pulsar ephemerides from the
 archival data of HARTRAO and Princeton (between 1989 and 1998) provide an
 excellent opportunity to study the accuracy of extrapolations of such
 ephemerides to the present moment, if an appropriate time shift is
 introduced. The aim of this study is to investigate the smear in the
 gamma-ray pulse profile during a single night of observations, given the
 absence of contemporary radio pulsar observations during ON-line analyses
 when "quick look" procedures must be employed to determine the status of a
 candidate. Pulsars with typical gamma-ray parameters on the (P, Pdot)
 diagram will be employed in this study.   

Constraining Pulsar Pair Production Multiplicity and Wind Magnetization Parameters with Multiwavelength Observations.

 Authors: Rocky R. Sefako (fskrrs@puknet.puk.ac.za) 
          Okkie C. de Jager (okkie@fskocdj.puk.ac.za)

 Affiliation: School of Physics, Potchefstroom University, South Africa

 Co-Authors: A. Konopelko, R.A. Burger

 Affiliation: School of Physics, Potchefstroom University, South Africa

 Abstract: The pair cascade above the pulsar polar cap, combined with the
 energy from the pulsar wind, results in a pair plasma which is injected into
 the environment around a pulsar. This wind, which consists of particles and
 fields, is shocked by the environment, resulting in synchrotron emission
 from "thermalized" pairs. We see this as a typical compact X-ray nebula which
 may extend into the optical part of the spectrum, depending on the pair
 multiplicity, spindown power and wind magnetization parameter. We review
 these parameters for the Crab Nebula, but show how such parameters are
 derived for the Vela and PSR B1706-44 pulsars. The multiplicity derived for
 these two pulsars agree with the theoretical predictions. We also show how
 the total number of pairs contribute to the diffuse gamma-ray signal through
 inverse Compton scattering of the Cosmic Microwave Background, galactic dust
 emission and optical starlight emission. With these target photon fields
 known, we can verify the injection rate of pairs into the "plerion" by
 measuring the high energy to very high energy gamma-ray spectrum. We will
 apply this to three pulsars and show that such TeV signals should be
 detectable from a few pulsar/plerion systems with the H.E.S.S. Telescope

Pulsars and Precession

 Author: Fabio Frescura 
 e-mail: frescura@physnet.phys.wits.ac.za 

 Affiliation: Research Fellow in the Department of Physics, Rhodes      
              University, Grahamstown, South Africa; Centre of Theoretical 
              Physics, University of the Witwatersrand, South Africa; 
              Research Associate at the Hartebeesthoek Radio Astronomy 

 Abstract: We consider the implications of precession for pulsar timing

Cyclic behaviour in rotation and DM of PSR B1557-50

 Author: Augustine Chukwude
 e-mail:aus_chukwude@yahoo.com; austine@hartrao.ac.za (until 21 Dec 2001)
 Affiliation: Department of Physics and Astronomy, University of Nigeria, 
              Nsukka, Nigeria; Hartebeesthoek Radio Astronomy Observatory, 
              South Africa

 Abstract: Analysis of pulsar timing data collected at regular intervals over 
 a long timescale remains one the best probes of the long-term rotational 
 behaviour of neutron stars. Here we summarize results of the analysis of 
 13 years of pulse arrival time data of the pulsar PSR 1557-50 collected at 
 the Hartebeesthoek Radio Astronomy Observatory (HartRAO) between 1986 August 
 and 1999 May. Our results show that over this period, both the timing 
 residuals and dispersion measure of this pulsar exhibit sustained cyclic 
 variations. No few than two cycles with peak-to-peak separation of about 
 1500 days are evident in our data. The DM variation is more than 60% 
 anticorrelated with rotation parameters. The results are discussed in the 
 context of our current understanding of the dynamics of neutron stars.  

The HartRAO Glitch-Monitoring Project: Part II – Glitch-Monitoring By-Products

 Author: Claire Flanagan  
 e-mail: 111flan@cosmos.wits.ac.z
 Affiliation: Johannesburg Planetarium, University of the Witwatersrand,  
              South Africa and the Hartebeesthoek Radio Astronomy 
              Observatory, South Africa

 Abstract: The glitch-monitoring project described in an earlier paper
 results in the collection of a massive amount of data, whereas the
 targetted glitch transients endure for a few days or weeks once every three
 years or so. The insight this additional data gives us into the timing noise
 and underlying spin-down forces in the Vela pulsar is discussed. 

Future Radio Pulsar Observing – Threats and Opportunities

 Author: Michael J Gaylard   
 e-mail: mike@hartrao.ac.za

 Affiliation: Hartebeesthoek Radio Astronomy Observatory, South Africa
 Abstract: The increasing use being made of the existing 26-m radio telescope
 at Hartebeesthoek has steadily reduced the time available for pulsar
 observing. Even greater pressure on pulsar observing time is forseen from

 It is therefore appropriate to investigate the possibilities for a new radio
 telescope optimised for pulsar research, as part of strategic planning for
 the future of astronomy in South Africa. This is particularly relevant in
 view of the increasing number of people in Africa involved in pulsar

 Technically, a telescope optimised for pulsar studies would likely operate
 at frequencies below the 1.6 GHz lower end of the 26-m telescope. We
 investigate the sensitivity required for observing different types of
 pulsars and look at trade-offs in telescope design that could produce an
 instrument that is desirable and useful but affordable in the face of the
 massive expenditure on SALT.  

Enabling Technologies for Radio Astronomy

 Author: Justin Jonas 
 e-mail: j.jonas@ru.ac.za

 Affiliation: Physics Department, Rhodes University, Grahamstown, 
              South Africa

 Abstract: Recent advances in digital electronics, photonics and material
 science have provided the radio astronomy community with new tools for the
 implementation of new generation telescopes. Artificial magneto-electric
 materials allow the fabrication of novel low-cost antennas. Fibre optic
 technology and versatile, high-speed digital electronic devices facilitate
 the implementation of "large-N" interferometric arrays. The applicability of
 various new technologies to a pulsar telescope will be discussed. A dominant
 topic will be the use of digital electronics in radio astronomy receivers. 

Development of a Digital Pulsar Timer

 Author: Adrian Tiplady  
 e-mail: g9731642@campus.ru.ac.za

 Affiliation: Physics Department, Rhodes University, Grahamstown, 
              South Africa

 Abstract: A new, digital pulsar timer which will replace the existing one at
 HartRAO is presently being developed at Rhodes University. The timer makes
 use of cell phone technology and FGPAs, allowing for relatively cheap and
 simple implementation as well as the possibility of replacing existing,
 expensive equipment with affordable circuitry. The modularised system is
 generalised in order to allow for easy, limitless expansion at any time
 without further design adjustments while the use of new signal processing
 techniques allows for maximum bandwidth usage and efficiency.