Five-hundred-meter Aperture Spherical Telescope
|Location(s)||Jinke Village, Pingtang County, People's Republic of China|
|Coordinates||25°39′11″N 106°51′24″E / 25.6531°N 106.8567°ECoordinates: 25°39′11″N 106°51′24″E / 25.6531°N 106.8567°E|
|Wavelength||0.10 m (3.0 GHz)–4.3 m (70 MHz)|
|First light||3 July 2016|
|Telescope style||radio telescope|
|Diameter||500 m (1,640 ft 5 in)|
|Illuminated diameter||300 m (984 ft 3 in)|
|Collecting area||196,000 m2 (2,110,000 sq ft)|
|Illuminated area||70,690 m2 (760,900 sq ft)|
|Focal length||140 m (459 ft 4 in)|
|Related media on Commons|
The Five-hundred-meter Aperture Spherical radio Telescope (FAST; Chinese: 五百米口径球面射电望远镜), nicknamed Tianyan (天眼, lit. "Sky's/Heaven's Eye"), is a radio telescope located in the Dawodang depression (大窝凼洼地), a natural basin in Pingtang County, Guizhou, southwest China. FAST has a 500 m (1,600 ft) diameter dish constructed in a natural depression in the landscape. It is the world's largest filled-aperture radio telescope and the second-largest single-dish aperture, after the sparsely-filled RATAN-600 in Russia.
It has a novel design, using an active surface made of 4,500 metal panels which form a moving parabola shape in real time. The cabin containing the feed antenna, suspended on cables above the dish, can move automatically by using winches to steer the instrument to receive signals from different directions. It observes at wavelengths of 10 cm to 4.3 m.
Construction of FAST began in 2011. It observed first light in September 2016. After three years of testing and commissioning, it was declared fully operational on 11 January 2020.
The telescope made its first discovery, of two new pulsars, in August 2017. The new pulsars PSR J1859-01 and PSR J1931-02—also referred to as FAST pulsar #1 and #2 (FP1 and FP2), were detected on 22 and 25 August 2017; they are 16,000 and 4,100 light years away, respectively. Parkes Observatory in Australia independently confirmed the discoveries on 10 September 2017. By September 2018, FAST had discovered 44 new pulsars, and by 2021, 500.
The telescope was first proposed in 1994. The project was approved by the National Development and Reform Commission (NDRC) in July 2007. A 65-person village was relocated from the valley to make room for the telescope and an additional 9,110 people living within a 5 km radius of the telescope were relocated to create a radio-quiet area. The Chinese government spent around $269 million in poverty relief funds and bank loans for the relocation of the local residents, while the construction of the telescope itself cost US$180 million.
On 26 December 2008, a foundation laying ceremony was held on the construction site. Construction started in March 2011, and the last panel was installed on the morning of 3 July 2016.
Originally budgeted for ¥700 million RMB,: 49  the final cost was ¥1.2 billion RMB (US$180 million). Significant difficulties encountered were the site's remote location and poor road access, and the need to add shielding to suppress radio-frequency interference (RFI) from the primary mirror actuators. The actuators were redesigned to meet shielding efficiency requirements and their installation was completed in 2015. Interference from the actuators has not been detected since.
Testing and commissioning began with first light on 25 September 2016. The first observations are being done without the active primary reflector, configuring it in a fixed shape and using the Earth's rotation to scan the sky. Subsequent early science took place mainly in lower frequencies while the active surface is brought to its design accuracy; longer wavelengths are less sensitive to errors in reflector shape. It took three years to calibrate the various instruments so it can become fully operational.
Local government efforts to develop a tourist industry around the telescope are causing some concern among astronomers worried about nearby mobile telephones acting as sources of RFI. A projected 10 million tourists in 2017 will force officials to decide on the scientific mission versus the economic benefits of tourism.
The primary driving force behind the project was Nan Rendong, a researcher with the Chinese National Astronomical Observatory, part of the Chinese Academy of Sciences. He held the positions of chief scientist and chief engineer of the project. He died on 15 September 2017 in Boston due to lung cancer.
On 14 June 2022, astronomers, working with China's FAST telescope, reported the possibility of having detected artificial (presumably alien) signals, but cautioned that further studies are required to determine if some kind of natural radio interference may be the source. More recently, on 18 June 2022, Dan Werthimer, chief scientist for several SETI-related projects, noted, "These signals are from radio interference; they are due to radio pollution from earthlings, not from E.T."
FAST has a reflecting surface 500 meters in diameter located in a natural sinkhole in the karst rock landscape, focusing radio waves on a receiving antenna in a "feed cabin" suspended 140 m (460 ft) above it. The reflector is made of perforated aluminium panels supported by a mesh of steel cables hanging from the rim.
FAST's surface is made of 4450 triangular panels, 11 m (36 ft) on a side, in the form of a geodesic dome. 2225 winches located underneath make it an active surface, pulling on joints between panels, deforming the flexible steel cable support into a parabolic antenna aligned with the desired sky direction.
Above the reflector is a lightweight feed cabin moved by a cable robot using winch servomechanisms on six support towers.: 13 The receiving antennas are mounted below this on a Stewart platform which provides fine position control and compensates for disturbances like wind motion.: 13 This produces a planned pointing precision of 8 arcseconds.
The maximum zenith angle is 40 degrees when the effective illuminated aperture is reduced to 200 m, while it is 26.4 degrees when the effective illuminated aperture is 300 m without loss.: 13
Although the reflector diameter is 500 m (1,600 ft), only a circle of 300 m diameter is used (held in the correct parabolic shape and "illuminated" by the receiver) at any one time.: 13 The telescope can be pointed to different positions on the sky by illuminating a 300-meter section of the 500 meter aperture. [As such FAST has a smaller effective aperture than the Jicamarca Radio Observatory, which has a filled aperture of equivalent diameter of 338 m].
Its working frequency ranges from 70 MHz to 3.0 GHz, with the upper limit set by the precision with which the primary can approximate a parabola. It could be improved slightly, but the size of the triangular segments limits the shortest wavelength which can be received. The original plan was to cover the frequency range with 9 receivers. During the construction phase, a commissioning ultra-wide band receiver covering 260 MHz to 1620 MHz was proposed and built, which produced the first pulsar discovery from FAST. At the moment, only the FAST L-band Receiver-array of 19 beams (FLAN) is installed and is operational between 1.05 GHz and 1.45 GHz.
The Next Generation Archive System (NGAS), developed by the International Centre for Radio Astronomy Research (ICRAR) in Perth, Australia and the European Southern Observatory will store and maintain the large amount of data that it collects.
A five-kilometre zone near the telescope forbids tourists from using mobile phones and other radio-emitting devices.
The FAST website lists the following science objectives of the radio telescope:
- Large scale neutral hydrogen survey
- Pulsar observations
- Leading the international very long baseline interferometry (VLBI) network
- Detection of interstellar molecules
- Detecting interstellar communication signals (Search for extraterrestrial intelligence)
- Pulsar timing arrays
The FAST telescope joined the Breakthrough Listen SETI project in October 2016 to search for intelligent extraterrestrial communications in the Universe.
In February 2020, scientists announced the first SETI observations with the telescope.
China's Global Times reported that its 500-meter (1,600 foot) FAST telescope will be open to the global scientific community starting in April 2021 (when applications will be reviewed), and becoming effective in August 2021. Foreign scientists will be able to submit applications to China's National Astronomical Observatories online.
Comparison with Arecibo Telescope
The basic design of FAST is similar to the former Arecibo Telescope. Both designs had reflectors installed in natural hollows within karst limestone, made of perforated aluminium panels with a movable receiver suspended above; and both have an effective aperture smaller than the physical size of the primary. There are however significant differences in addition to the size.
First, Arecibo's dish was fixed in a spherical shape. Although it was also suspended from steel cables with supports underneath for fine-tuning the shape, they were manually operated and adjusted only during maintenance. It had a fixed spherical shape with two additional suspended reflectors in a Gregorian configuration to correct for spherical aberration.
Second, Arecibo's receiver platform was fixed in place. To support the greater weight of the additional reflectors, the primary support cables were static, with the only motorised portion being three hold-down winches which compensated for thermal expansion.: 3 The antennas could move along a rotating arm below the platform, to allow limited adjustment of azimuth,: 4 although Arecibo was not limited in azimuth, only in zenith angle: The smaller range of motion limited it to viewing objects within 19.7° of the zenith.
Third, Arecibo could receive higher frequencies. The finite size of the triangular panels making up FAST's primary reflector limits the accuracy with which it can approximate a parabola, and thus the shortest wavelength it can focus. Arecibo's more rigid design allowed it to maintain sharp focus down to 3 cm wavelength (10 GHz); FAST is limited to 10 cm (3 GHz). Improvements in position control of the secondary might be able to push that to 6 cm (5 GHz), but then the primary reflector becomes a hard limit.
Fourth, the FAST dish is significantly deeper, contributing to a wider field of view. Although 64% larger in diameter, FAST's radius of curvature is 300 m (980 ft),: 3 barely larger than Arecibo's 270 m (870 ft), so it forms a 113° arc: 4 (vs. 70° for Arecibo). Although Arecibo's full aperture of 305 m (1,000 ft) could be used when observing objects at the zenith, this was only possible with the line feed which had a very narrow frequency range and had been unavailable due to damage since 2017. Most Arecibo observations used the Gregorian feeds, where the effective aperture was approximately 221 m (725 ft) at zenith.: 4
Fifth, Arecibo's larger secondary platform also housed several transmitters, making it one of the few instruments in the world capable of radar astronomy. (Planetary radar is also possible at the Jicamarca and Millstone and Altair observatories.) The NASA-funded Planetary Radar System allowed Arecibo to study solid objects from Mercury to Saturn, and to perform very accurate orbit determination on near-earth objects, particularly potentially hazardous objects. Arecibo also included several NSF funded radars for ionospheric studies (ionosondes). Such powerful transmitters are too large and heavy for FAST's small receiver cabin, so it will not be able to participate in planetary defense although in principle it could serve as a receiver in a bistatic radar system. (Arecibo has been used in several multi-static experiments with an auxiliary 100 meter dish, including S-band radar experiments in the stratosphere, and ISAR mapping of Venus.)
In popular culture
It appeared in the episode "The Search for Intelligent Life on Earth" of the 2020 television series Cosmos: Possible Worlds presented by Neil deGrasse Tyson.
- Chinese space program
- KARST – a 1990s Chinese proposal to host the SKA
- List of telescope types
- Square Kilometre Array – a proposed 1 km2 telescope array in Australia and South Africa
- ^ "中国"天眼"能不能发现外星人？" [Can Chinese Tianyan find aliens?] (in Chinese). Xinhua News Agency. 22 February 2016. Archived from the original on 4 March 2016. Retrieved 27 February 2016.
- ^ Brinks, Elias (11 July 2016). "China Opens the Aperture to the Cosmos". The Conversation. U.S. News & World Report. Archived from the original on 26 August 2016. Retrieved 12 August 2016.
- ^ a b c Nan, Rendong (April 2008). Project FAST – Five hundred meter Aperture Spherical radio Telescope (PDF). China-US Bilateral Workshop on Astronomy. Beijing. Archived (PDF) from the original on 7 August 2016. Retrieved 4 July 2016.
- ^ "China starts building world's biggest radio telescope". New Scientist. 8 June 2011. Archived from the original on 8 December 2015. Retrieved 19 October 2015.
- ^ a b c d e f Normile, Dennis (26 September 2016). "World's largest radio telescope will search for dark matter, listen for aliens". Science News. doi:10.1126/science.aah7346. Archived from the original on 1 October 2016. Retrieved 28 September 2016.
- ^ a b NAN, RENDONG (2011). "The Five-Hundred-Meter Aperture Spherical Radio Telescope (Fast) Project". International Journal of Modern Physics D. Key Laboratory for Radio Astronomy, Chinese Academy of Sciences. 20 (6): 989–1024. arXiv:1105.3794. Bibcode:2011IJMPD..20..989N. doi:10.1142/S0218271811019335. S2CID 26433223. Archived from the original on 15 June 2022. Retrieved 25 January 2021.
- ^ a b Li, Di (2018). "FAST in Space: Considerations for a Multibeam, Multipurpose Survey Using China's 500-m Aperture Spherical Radio Telescope (FAST)". IEEE Microwave Magazine. National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China. 19 (3): 112–119. arXiv:1802.03709. Bibcode:2018IMMag..19..112L. doi:10.1109/MMM.2018.2802178. S2CID 4595986. Archived from the original on 4 May 2022. Retrieved 25 January 2021.
- ^ Xinhua (25 September 2016). "Xi commends launch of world's largest radio telescope in China". Archived from the original on 11 October 2017. Retrieved 10 October 2017 – via China Daily.
- ^ "FAST Homepage in English". Archived from the original on 16 March 2017. Retrieved 15 January 2017.
- ^ "World's largest radio telescope starts formal operation". Xinhua. 11 January 2020. Archived from the original on 13 January 2020. Retrieved 13 January 2020.
- ^ Jones, Andrew (10 October 2017). "China's huge new FAST radio telescope discovers two new pulsars". GBTimes. Archived from the original on 11 October 2017. Retrieved 10 October 2017.
- ^ McGlaun, Shane (11 October 2017). "Chinese FAST telescope finds multiple pulsars in early use". slashgear. Archived from the original on 11 October 2017. Retrieved 11 October 2017.
- ^ Jones, Andrew. "China's FAST radio telescope detects three more pulsars". gbtimes. Archived from the original on 17 September 2018. Retrieved 14 December 2017.
- ^ "China's FAST telescope identifies 44 pulsars". scio.gov.cn. Archived from the original on 17 September 2018. Retrieved 12 September 2018.
- ^ "China's FAST telescope detects over 500 new pulsars - People's Daily Online". Archived from the original on 16 December 2021. Retrieved 16 December 2021.
- ^ Jin, Nan & Gan 2007.
- ^ a b c d e "Xinhua Insight: Installation complete on world's largest radio telescope". Xinhua. 3 July 2016. Archived from the original on 3 July 2016. Retrieved 4 July 2016.
- ^ De Jesus, Cecille (26 September 2016). Caughill, Patrick (ed.). "The Quest For Life Beyond Earth: The World's Largest Radio Telescope Just Went Online". Futurism. Archived from the original on 12 April 2019. Retrieved 19 February 2017.
- ^ "中国科学院·贵州省共建国家重大科技基础设施500米口径球面射电望远镜（ＦＡＳＴ）项目奠基" (in Chinese). Guizhou Daily. 27 December 2008. Archived from the original on 12 January 2009. Retrieved 28 December 2008.
- ^ a b Quick, Darren (16 June 2011). "China building world's biggest radio telescope". gizmag. Archived from the original on 19 November 2012. Retrieved 13 August 2012.
- ^ a b c d e f g Rendong Nan; Di Li; Chengjin Jin; Qiming Wang; Lichun Zhu; Wenbai Zhu; Haiyan Zhang; Youling Yue; Lei Qian (20 May 2011). "The Five-Hundred-Meter Aperture Spherical Radio Telescope (FAST) Project". International Journal of Modern Physics D. 20 (6): 989–1024. arXiv:1105.3794. Bibcode:2011IJMPD..20..989N. doi:10.1142/S0218271811019335. S2CID 26433223.
- ^ "China completes installation of world's largest telescope". The BRICS Post. 3 July 2016. Archived from the original on 19 April 2019. Retrieved 3 July 2016.
- ^ a b McKirdy, Euan (12 October 2015). "China looks to the stars with creation of world's largest radio telescope". CNN News. Archived from the original on 19 October 2015. Retrieved 19 October 2015.
- ^ Shen, Alice (31 October 2018). "Wanted: Researchers for China's mega telescope to interpret signals from across the universe". South China Morning Post. Archived from the original on 9 January 2020. Retrieved 8 November 2018.
- ^ Zhang, Hai-Yan; Wu, Ming-Chang; Yue, You-Ling; Gan, Heng-Qian; Hu, Hao; Huang, Shi-Jie (1 April 2018). "EMC design for actuators in the FAST reflector". Research in Astronomy and Astrophysics. 18 (4): 048. arXiv:1802.02315. Bibcode:2018RAA....18...48Z. doi:10.1088/1674-4527/18/4/48. ISSN 1674-4527. S2CID 116359320. Archived from the original on 15 June 2022. Retrieved 12 June 2022.
- ^ a b Morelle, Rebecca (25 September 2016). "China's colossal radio telescope begins testing". BBC News. Archived from the original on 25 September 2016. Retrieved 25 September 2016.
- ^ Yue, Youling; Li, Di; Nan, Rendong (20–31 August 2012). FAST low frequency pulsar survey. Neutron Stars and Pulsars: Challenges and Opportunities after 80 years. arXiv:1211.0748. doi:10.1017/S174392131300001X. Archived from the original on 30 May 2017. Retrieved 26 September 2016.
- ^ Li, Di; Nan, Rendong; Pan, Zhichen (20–31 August 2012). The Five-hundred-meter Aperture Spherical Radio Telescope Project and its Early Science Opportunities. Neutron Stars and Pulsars: Challenges and Opportunities after 80 years. arXiv:1210.5785. doi:10.1017/S1743921312024015. Archived from the original on 30 May 2017. Retrieved 26 September 2016. Video available at http://www.pulsarastronomy.net/IAUS291/video/DiLi/ Archived 24 August 2018 at the Wayback Machine
- ^ Chen, Zhou; Gang, Wu. "Scientists Concerned About Plans to Make Telescope a Tourist Attraction". Caixin Online. Archived from the original on 18 November 2016. Retrieved 26 September 2016.
- ^ Chen, Stephen (24 August 2017). "How noisy Chinese tourists may be drowning out alien signals at the world's biggest telescope". South China Morning Post. Archived from the original on 24 August 2017. Retrieved 24 August 2017.
- ^ "中国天眼"首席科学家南仁东病逝 享年72岁". China News Service (in Simplified Chinese). 16 September 2017. Archived from the original on 29 June 2019. Retrieved 17 September 2017.
- ^ Byrd, Deborah (4 June 2022). "Has China's FAST telescope detected alien intelligence?". Earth & Sky. Archived from the original on 15 June 2022. Retrieved 15 June 2022.
- ^ Ling Xin (15 June 2022). "Alien hunters detect mystery radio signal from direction of Earthlike planet". South China Morning Post.
Narrowband signal picked up from direction of the Kepler-438 star meets initial criteria for extraterrestrial intelligence, preprint says; orbiting Kepler-438 in its habitable zone is one of the most Earthlike planets ever found outside the solar system.
- ^ Overbye, Dennis (18 June 2022). "A Chinese Telescope Did Not Find an Alien Signal. The Search Continues. China's astronomers have been initiated into the search for extraterrestrial intelligence with the kind of false alarm that others in the field have experienced for decades". The New York Times. Retrieved 19 June 2022.
- ^ "China assembles world's largest telescope in Guizhou". Xinhua. 24 July 2015. Archived from the original on 23 August 2018. Retrieved 6 July 2016 – via China.org.cn.
- ^ a b c d e f Williams, R.L. II (July 2015). Five-Hundred Meter Aperture Spherical Radio Telescope (FAST) Cable-Suspended Robot Model and Comparison with the Arecibo Observatory (PDF) (Report). Ohio University. Archived from the original (PDF) on 22 October 2016. Retrieved 6 July 2016. Although this source contains wealth of detail, its reliability is questionable. It describes in some detail (at the end of p. 4) the fact that FAST's dish is actually 519.6 m in diameter; papers published by the project scientists, who would presumably know, are explicit that the dish extends "up to a girder ring of exactly 500 m diameter".
- ^ Jin Chengjin; et al. (23 October 2013). "The optics of the Five-hundred-meter Aperture Spherical radio Telescope" (PDF). International Symposium on Antennas and Propagation. Archived (PDF) from the original on 16 August 2016. Retrieved 9 July 2016.
- ^ "Receiver Systems". FAST Home Page. National Astronomical Observatories, Chinese Academy of Sciences. Archived from the original on 17 October 2017. Retrieved 28 June 2014.
- ^ Qian, Lei (May 2019). "The first pulsar discovered by FAST". Science China Physics, Mechanics & Astronomy. CAS Key Laboratory of FAST, National Astronomical Observatories, Chinese Academy of Sciences. 62 (5): 4 pp. arXiv:1903.06318. Bibcode:2019SCPMA..6259508Q. doi:10.1007/s11433-018-9354-y. S2CID 119479606. 959508. Archived from the original on 15 June 2022. Retrieved 25 January 2021.
- ^ "FAST Radio Telescope Open for Business". Sky & Telescope. 27 September 2016. Archived from the original on 10 October 2016. Retrieved 10 October 2016.
- ^ "China Finds Phone-Wielding Tourists and Telescopes Don't Mesh". Wired. ISSN 1059-1028. Archived from the original on 26 April 2021. Retrieved 26 April 2021.
- ^ "Science". Archived from the original on 18 November 2019. Retrieved 19 February 2017.
- ^ Hobbs, G.; Dai, S.; Manchester, R.N.; Shannon, R.M.; Kerr, M.; Lee, K.J.; Xu, R. (1 July 2014). "The Role of FAST in Pulsar Timing Arrays". arXiv:1407.0435 [astro-ph.IM].
- ^ "National Astronomical Observatories of China, Breakthrough Initiatives Launch Global Collaboration in Search for Intelligent life in the Universe" (Press release). Breakthrough Initiatives. 12 October 2016. Archived from the original on 15 June 2022. Retrieved 24 August 2017 – via Astrobiology Web.
- ^ Zhang, Zhi-Song; Werthimer, Dan; Zhang, Tong-Jie; Cobb, Jeff; Korpela, Eric; Anderson, David; Gajjar, Vishal; Lee, Ryan; Li, Shi-Yu; Pei, Xin; Zhang, Xin-Xin (17 March 2020). "First SETI Observations with China's Five-hundred-meter Aperture Spherical radio Telescope (FAST)". The Astrophysical Journal. 891 (2): 174. arXiv:2002.02130. Bibcode:2020ApJ...891..174Z. doi:10.3847/1538-4357/ab7376. ISSN 1538-4357. S2CID 211043944. Archived from the original on 29 August 2021. Retrieved 29 August 2021.
- ^ Dent, Steve (4 January 2021). "China's huge FAST telescope will open to scientists globally in April". Engadget (via Yahoo! Finance). Archived from the original on 4 January 2021. Retrieved 5 January 2021.
- ^ "China's FAST telescope will be available to foreign scientists - Xinhua | English.news.cn". www.xinhuanet.com. Archived from the original on 4 January 2021. Retrieved 4 January 2021.
- ^ Jin, Chengjin; Zhu, Kai; Fan, Jin; Liu, Hongfei; Zhu, Yan; Gan, Hengqian; Yu, Jinglong; Gao, Zhisheng; Cao, Yang; Wu, Yang (23 October 2013). The optics of the Five-hundred-meter Aperture Spherical radio Telescope (PDF). International Symposium on Antennas and Propagation. Nanjing: National Astronomical Observatories, Chinese Academy of Sciences. Archived (PDF) from the original on 16 August 2016. Retrieved 9 July 2016.
- ^ Qiu, Yuhai H. (11 December 1998). "A novel design for a giant Arecibo-type spherical radio telescope with an active main reflector". Monthly Notices of the Royal Astronomical Society. Beijing Astronomical Observatory, The Chinese Academy of Sciences. 301 (3): 827–830. Bibcode:1998MNRAS.301..827Q. doi:10.1111/j.1365-8711.1998.02067.x.
- ^ Cortés-Medellín, Germán (13 September 2010). AOPAF: Arecibo Observatory Phased Array Feed (PDF) (Report). National Astronomy and Ionosphere Center, Cornell University. Archived (PDF) from the original on 8 May 2018. Retrieved 27 September 2016.
- ^ a b "Arecibo: General statistical information on the antenna". National Astronomy and Ionosphere Center. 3 January 2005. Archived from the original on 18 August 2016. Retrieved 5 July 2016.
- ^ a b "The Arecibo observatory and its telescope". Archived from the original on 10 September 2019. Retrieved 1 December 2020.
- Nan, R.; et al. (16 June 2002). "Kilometer-square Area Radio Synthesis Telescope – KARST" (PDF). Archived from the original (PDF) on 29 October 2006.
- Jin, C. J.; Nan, R. D.; Gan, H. Q. (October 2007). "The FAST telescope and its possible contribution to high precision astrometry" (PDF). Proceedings of the International Astronomical Union. 3 (S248): 178–181. Bibcode:2008IAUS..248..178J. doi:10.1017/S1743921308018978.
- Li, Di; Pan, Zhichen (30 December 2016). "The Five-hundred-meter Aperture Spherical Radio Telescope (FAST) Project". Radio Science. 51 (7): 1060–1064. arXiv:1612.09372. Bibcode:2016RaSc...51.1060L. doi:10.1002/2015RS005877. S2CID 119363387.