Leonard–Merritt mass estimator

In astronomy, the Leonard–Merritt mass estimator is a formula for estimating the mass of a spherical stellar system using the apparent (angular) positions and proper motions of its component stars. The distance to the stellar system must also be known.

Like the virial theorem, the Leonard–Merritt estimator yields correct results regardless of the degree of velocity anisotropy. Its statistical properties are superior to those of the virial theorem. However, it requires that two components of the velocity be known for every star, rather than just one for the virial theorem.[1]

The estimator has the general form

The angle brackets denote averages over the ensemble of observed stars. M(r) is the mass contained within a distance r from the center of the stellar system; R is the projected distance of a star from the apparent center; VR and VT are the components of a star's velocity parallel to, and perpendicular to, the apparent radius vector; and G is the gravitational constant.

Like all estimators based on moments of the Jeans equations, the Leonard–Merritt estimator requires an assumption about the relative distribution of mass and light. As a result, it is most useful when applied to stellar systems that have one of two properties:

  1. All or almost all of the mass resides in a central object, or,
  2. the mass is distributed in the same way as the observed stars.

Case (1) applies to the nucleus of a galaxy containing a supermassive black hole. Case (2) applies to a stellar system composed entirely of luminous stars (i.e. no dark matter or black holes).

In a cluster with constant mass-to-light ratio and total mass MT, the Leonard–Merritt estimator becomes:

On the other hand, if all the mass is located in a central point of mass M0, then:

In its second form, the Leonard–Merritt estimator has been successfully used to measure the mass of the supermassive black hole at the center of the Milky Way galaxy.[2][3]

See also

References

  1. ^ Leonard, Peter; Merritt, David (10 April 1989). "The Mass of the Open Star Cluster M35 as Derived from Proper Motions". The Astrophysical Journal. 339: 195–208. Bibcode:1989ApJ...339..195L. doi:10.1086/167287.
  2. ^ Schödel, R; Ott, T; Genzel, R; Eckart, A; Mouawad, N; Alexander, T (1 October 2003). "Stellar Dynamics in the Central Arcsecond of Our Galaxy". The Astrophysical Journal. 596 (2): 1015–1034. arXiv:astro-ph/0306214. Bibcode:2003ApJ...596.1015S. doi:10.1086/378122. S2CID 17719367.
  3. ^ Schödel, Rainer; Merritt, David; Eckart, Andreas (1 July 2009). "The nuclear star cluster of the Milky Way: proper motions and mass". Astronomy and Astrophysics. 502 (1): 91–111. arXiv:0902.3892. Bibcode:2009A&A...502...91S. doi:10.1051/0004-6361/200810922. S2CID 219559.

Read other articles:

Vidhichathum Kothichathum

1982 Indian filmVidhichathum KothichathumPosterDirected byT. S. MohanWritten byT. S. MohanScreenplay byT. S. MohanProduced byT. S. MohanStarringMammoottyAdoor BhasiJoseKrishnachandranCinematographyB.R. RamakrishnaEdited byBalanMusic byRaveendranProductioncompanyVimal PicturesRelease date 17 September 1982 (1982-09-17) CountryIndiaLanguageMalayalam Vidhichathum Kothichathum is a 1982 Indian Malayalam-language film, directed and produced by T. S. Mohan. The film stars Vincent, V...

 

كليمان توربان

كليمان توربان (بالفرنسية: Clément Turpin)‏  معلومات شخصية الميلاد 16 مايو 1982 (العمر 41 سنة)فرنسا الجنسية فرنسا الحياة العملية المهنة حكم كرة قدم  الرياضة كرة القدم[1]  بلد الرياضة فرنسا  تعديل مصدري - تعديل   كليمان توربان (بالفرنسية: Clément Turpin)‏ (المولود 16 مايو 1982) هو �...

 

Bahrullah Akbar

Bahrullah Akbar Wakil Ketua Badan Pemeriksa Keuangan Republik Indonesia ke-9Masa jabatan26 April 2017 – 24 Oktober 2019 PendahuluSapto Amal DamandariPenggantiAgus Joko Pramono Informasi pribadiLahir23 Maret 1959 (umur 65)JakartaSunting kotak info • L • B Prof. Dr. Drs. H. Bahrullah Akbar, B.Sc., S.E., M.B.A. (lahir 23 Maret 1959) merupakan Guru Besar Keuangan Publik Institut Pemerintahan Dalam Negeri (IPDN) dan juga Anggota Badan Pemeriksa Keuangan Republik I...

District of Columbia Voting Rights Amendment

Not to be confused with Twenty-third Amendment to the United States Constitution. Proposed U.S. constitutional amendment This article is part of a series on theConstitutionof the United States Preamble and Articles Preamble I II III IV V VI VII Amendments to the Constitution I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX XX XXI XXII XXIII XXIV XXV XXVI XXVII Unratified Amendments: Congressional Apportionment Titles of Nobility Corwin Child Labor Equal Rights D.C. Voting...

 

Vienne (département)

Pour les articles homonymes, voir Vienne. Vienne Administration Pays France Région Nouvelle-Aquitaine Création du département 4 mars 1790 Chef-lieu(Préfecture) Poitiers Sous-préfectures ChâtelleraultMontmorillon Président duconseil départemental Alain Pichon (LR) Préfet Jean-Marie Girier[1] Code Insee 86 Code ISO 3166-2 FR-86 Code Eurostat NUTS-3 FR534 Démographie Gentilé Poitevins Population 439 385 hab. (2021) Densité 63 hab./km2 Géographie Coordonnées 46°...

 

Congregation of Mary Immaculate Queen

Sedevacantist organization Congregation of Mary Immaculate QueenCongregatio Mariae Reginae ImmaculataeAbbreviationCMRIFormation1967; 57 years ago (1967)TypeSedevacantist Catholic religious congregationHeadquartersOmaha, Nebraska, U.S.Superior GeneralMark PivarunasKey peopleFrancis Schuckardt (founder)Denis ChicoineM. Benedict HughesCasimir M. PuskoriusMark Pivarunas (current Superior General and bishop)Websitecmri.org Our Mother of Perpetual Help Church: CMRI church in Sulph...

العلاقات الأرمينية الشمال مقدونية

العلاقات الأرمينية الشمال مقدونية أرمينيا شمال مقدونيا   أرمينيا   شمال مقدونيا تعديل مصدري - تعديل   العلاقات الأرمينية الشمال مقدونية هي العلاقات الثنائية التي تجمع بين أرمينيا وشمال مقدونيا.[1][2][3][4][5] مقارنة بين البلدين هذه مقارنة عامة...

 

Motore a getto preraffreddato

Il motore a getto preraffreddato è una soluzione studiata per raggiungere alte velocità con motori turbogetto che sfrutta il preraffreddamento dell'aria in ingresso immediatamente a valle della presa d'aria mediante uno scambiatore di calore raffreddato dal combustibile criogenico. Dopo aver sottratto calore all'aria mediante l'evaporazione nello scambiatore, il combustibile (in genere H2) viene bruciato in camera di combustione. Motori a getto preraffreddati non hanno ancora volato, ma, su...

 

巴育·占奥差

將軍巴育·占奥差ประยุทธ์ จันทร์โอชา上將 MPCh MWM TChW 泰國樞密院議員现任就任日期2023年11月29日君主拉瑪十世議長素拉育·朱拉暖 泰國第29任總理任期2022年9月30日復職—2023年8月22日君主拉瑪十世副總理（英语：Deputy Minister of Thailand） 列表 巴威·翁素万塔那塞·巴滴玛巴功（英语：Thanasak Patimaprakorn） 威沙努·革岸（英语：Wissanu Krea-ngam） 比蒂耶�...

Muskerry West

Muskerry West (Irish: Múscraí Thiar[l 1]) is one of the baronies of Ireland, a historical geographical unit of land. Its chief town is Macroom. It is one of 24 baronies in the county of Cork. It may also be viewed as a half barony because sometime before the 1821 census, it was divided from its other half – Muskerry East. Other neighbouring baronies include Duhallow to the north (whose chief town is Newmarket) and the Barony of Carbery East (West Division) to the south (whose chi...

 

Edward C. Prado

American judge and ambassador (born 1947) Edward C. PradoUnited States Ambassador to ArgentinaIn officeMay 15, 2018 – January 20, 2021PresidentDonald TrumpPreceded byNoah MametSucceeded byMarc StanleyJudge of the United States Court of Appeals for the Fifth CircuitIn officeMay 5, 2003 – April 2, 2018Appointed byGeorge W. BushPreceded byRobert Manley ParkerSucceeded byAndrew OldhamJudge of the United States District Court for the Western District of TexasIn officeMarch 30...

 

Mudflow

Form of mass wasting Mudslide redirects here. For other uses, see Mudslide (disambiguation). Mailboxes caught in a mudflow following the May 1980 Mount St. Helens volcanic eruption. A mudflow, also known as mudslide or mud flow, is a form of mass wasting involving fast-moving flow of debris and dirt that has become liquified by the addition of water.[1] Such flows can move at speeds ranging from 3 meters/minute to 5 meters/second.[2] Mudflows contain a significant proportion o...

Sue Wicks

American basketball player and aquaculture farmer See also: Susan Wicks Sue WicksSue Wicks, being honored at Rutgers-UConn gamePersonal informationBorn (1966-11-26) November 26, 1966 (age 57)Center Moriches, New York, U.S.Listed height6 ft 3 in (1.91 m)Listed weight174 lb (79 kg)Career informationHigh schoolCenter Moriches(Center Moriches, New York)CollegeRutgers (1984–1988)WNBA draft1997: 1st round, 6th overall pickSelected by the New York LibertyPlaying caree...

 

Celilo Village, Oregon

Unincorporated community in Oregon, United States Location of Celilo Village Modern Native American Longhouse in Celilo Village with the Columbia River and Oregon Trunk Rail Bridge in the background Native Americans drying salmon at Celilo Falls, circa 1900 Celilo Village, Oregon is an unincorporated Native American community on the Columbia River in northeastern Wasco County in the U.S. state of Oregon.[1] It is near Lake Celilo, the former site of Celilo Falls; it is just south of t...

 

List of Cultural Properties of the Philippines in Pinamalayan, Oriental Mindoro

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: List of Cultural Properties of the Philippines in Pinamalayan, Oriental Mindoro – news · newspapers · books · scholar · JSTOR (February 2022) (Learn how and when to remove this message) This is a list of Cultural Properties of the Philippines in Pinamalayan, O...

List of Playboy Playmates of 1958

The following is a list of Playboy Playmates of 1958. Playboy magazine names its Playmate of the Month each month throughout the year. January Elizabeth Ann RobertsPersonal detailsBorn (1941-08-04) August 4, 1941 (age 82)Chicago, Illinois, U.S. Main article: Elizabeth Ann Roberts Elizabeth Ann Roberts (born August 4, 1941) is an American model. She was Playboy magazine's Playmate of the Month for the January 1958 issue. Her centerfold was photographed by Arthur James and Mike Shea, when...

 

IMI SR-99

IMI SR-99 Jenis Senapan runduk Negara asal  Israel Sejarah produksi Produsen IMI Spesifikasi Berat 5,08 kg (11,1 lbs) Panjang laras 508 mm (20 in) Peluru 7,62 x 51 mm NATO Amunisi Magazen box isi 10, 20, 25 butir Alat bidik Bidikan teleskopik, Bidikan besi sebagai cadangan. IMI SR-99 atau SR-99 adalah senapan runduk peluru 7,62 x 51 mm NATO buatan IMI, Israel. Senapan ini merupakan pengembangan dari senapan runduk sebelumnya yaitu IMI Galil Sniper (Galat’z). Perbedaan m...

 

Self-publishing

Publication of a book or other publications by the author or authors For book building by artisans for collectors and patrons, see Private press. Private publishing redirects here. For low-volume regular publishing, see Privishing. For Wikipedia's policy on self-published sources, see Wikipedia:Self-published sources. This article is written like a manual or guide. Please help rewrite this article and remove advice or instruction. (December 2020) Self-publishing is the publication of media by...

1885 Princeton Tigers football team

American college football season 1885 Princeton Tigers footballNational championConferenceIndependentRecord9–0Head coachNoneCaptainC. M. DeCampSeasons← 18841886 → 1885 college football records vte Conf Overall Team W   L   T W   L   T Princeton   –   9 – 0 – 0 Michigan   –   3 – 0 – 0 Colorado College   –   1 – 0 – 0 Yale   –   7 – 1 –...

 

Castello Charles

Castello Charles(FR) Château CharlesUna facciata del castello CharlesStato Contea di Savoia Stato attuale Italia RegioneValle d'Aosta CittàPerloz Coordinate45°37′N 7°49′E45°37′N, 7°49′E Informazioni generaliTipoCasaforte CostruzioneXVII secolo-XVII secolo MaterialePietra, legno [1] voci di architetture militari presenti su Wikipedia Modifica dati su Wikidata · ManualeIl castello Charles (pron. fr. AFI: [ʃaʁl] - in francese, Château Charles) è una casaforte medieva...