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Hoe kan die Event Horizon Telescope Sgr A * beeld as dit nie sigbaar is vanaf alle terreine nie?

Hoe kan die Event Horizon Telescope Sgr A * beeld as dit nie sigbaar is vanaf alle terreine nie?


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Ek het na https://eventhorizontelescope.org/array gegaan en gelees van die tien webwerwe wat gelys word as deel van die EHT. Hieronder sien ek 'n fyn skermfoto van hulle.

Ek het 'n teks gemaak wat ook hieronder getoon word met benaderde koördinate en gesien dat Sgr A * 'n afname van ongeveer -29,5 grade (Suid) het. Ek het dit om die aarde gedraai, die puntproduk bereken tussen elkeen van die posisies se vektore en alle normale wat na Sgr A * wys terwyl dit om die aarde draai.

Ek teken toe die hoogtehoek bo die horison vir al tien plekke. Ek was nogal verbaas!

  1. Sgr A * is nooit bo die horison vir die Groenlandse teleskoop nie!
  2. Sgr A * is nooit gelyktydig sigbaar nie, selfs nie vir al die oorblywende nege teleskope nie

Het ek 'n fout gemaak? Indien nie, hoe kombineer hierdie tien webwerwe hul data met Sgr A *?

class Site (object): def __init __ (self, name, lat, lon, alt): self.name = str (name) self.lat = rads * float (lat) self.lon = rads * float (lon) self. alt = km * float (alt) (clat, slat), (clon, slon) = [[f (x) for f in (np.cos, np.sin)] for x in (self.lat, self.lon )] self.norm = np.array ([clon * clat, slon * clat, slat]) data = (('Northern Extended Millimeter Array', (44.634, 5.908, 2550.)), ('IRAM 30 meter teleskoop' , (37.066, -3.393, 2850.)), ('The Greenland Telescope now near Thule Air Base', (76.531, -68.703, 10.)), ('Combined Array for Research in Millimeter-wave Astronomy CARMA', ( 37.280, -118.142, 2196.)), ('Kitt Peak National Observatory 12 meter Submillimeter Telescope (SMT)', (1.9583, -111.5967, 2096.)), ('Mt. Graham International Observatory 12 meter ALMA prototye', ( 32.701, -109.892, 3191.)), ('The Large Millimeter Telescope Alfonso Serrano', (18.985, -97.315, 4600.)), ('ALMA', (-22.971, -67.703, 4800.)), (' Caltech Submillimeter Observatory ', (19.823, -155.476, 4140.)), (' Suidpool Teleskoop ', (-90.0, 0.0, 2800.))) # https://eventhorizontelescope.org/array # / questions / 26413 / wiskunde-agter-a-uv-plot-in-interferometrie datadict = dict (data) invoer gevoelloos soos np invoer matplotlib.pyplot as plt vanaf skyfield.api invoer Topos, Loader, EarthSatellite vanaf mpl_toolkits.mplot3d invoer Asse3D halfpi, pi, twopi = [f * np.pi vir f in (0.5, 1, 2)] degs, rads = 180 / pi, pi / 180 km = 0.001 sites = [Site (a, * b) vir a, b in datadict.items ()] Des = rads * -29.5 # SgrA_star cDec, sDec = [f (Des) vir f in (np.cos, np.sin)] th = twopi * np.linspace (0, 1, 100001) [: - 1] cth, sth = [f (th) vir f in (np.cos, np .sin)] zth, oth = np.zeros_like (th), np.ones_like (th) SgrA_star = np.stack ([cDec * cth, cDec * sth, sDec * oth], axis = 1) vir werf in webwerwe: site.elev = np.arcsin (np.dot (SgrA_star, site.norm)) as Waar: vir werf in webwerwe: plt.plot (degs * site.elev) plt.plot (zth, '-k', linewidth = 2) plt.ylim (-90, 90) plt.ylabel ('elevation (deg)', lettergrootte = 16) plt.show ()

Ek dink nie dit is nodig dat al die teleskope die teiken gelyktydig besigtig as u die aanname kan maak dat die bron wat u waarneem slegs op tydskale wissel nie, aangesien dit nodig is om deur al die teleskope sigbaar te wees. Sekerlik, die maksimum basislyn wat u kan kry sal word gedefinieër deur die teleskope wat die terselfdertyd waargeneem word, die mees afgeleë, maar dit verhinder u om foto's wat op ander tye geneem is bymekaar te tel.

Dit is heel waarskynlik die rede waarom M87 die eerste beeld is wat deur die EHT aangebied word. Die tydskaal vir beduidende wisselvalligheid rondom hierdie (groot) swart gat sal 'n paar keer van orde wees $ 2GM / c ^ 2 $, wat 'n paar dae vir die M87-swartgat is. Imaging Sgr A * gaan moeiliker wees (of ten minste vaager) omdat die veranderlike tydskaal minute is.

Dit lyk (uit die datareduksiepapier) dat die eerste stappe behels dat elke basislyn op 'n paar wyse (soos ek hierbo voorgestel het) behandel word en dit dan oor die netwerk gekombineer word, met die basislyne wat destyds waargeneem is, om data te gee op die verrassende (vir my) hoë tydresolusie van tien.


  1. Sgr A * is nooit bo die horison vir die Groenlandse teleskoop nie!

Wel, Sgr A * is nie die enigste fokus van EHT nie; die webwerf noem dat dit ook ander voorwerpe soos die M87-sterrestelsel in Maagd bestudeer, wat teen + 12 ° deklinasie is sigbaar vanaf Groenland.

  1. Sgr A * is nooit gelyktydig sigbaar nie, selfs nie vir al die oorblywende nege teleskope nie

Baie lang basisinterferometrie kombineer net die resultate van die teleskope wat kan (en is op 'n spesifieke tydstip op 'n spesifieke teiken gewys (plus of minus 'n paar nanosekondes, omdat sommige teleskope dalk verder van die teiken af ​​is as ander, en die lig neem dit effens langer of korter om dit te bereik). Dit sal dus nooit die volle potensiaal van al die teleskope in die skikking gelyktydig benut nie.

Op die plek van die korrelator word die data gespeel. Die tydsberekening van die afspeel word aangepas volgens die atoomklokseine op die (bande / skyfaandrywers / optiese vesel sein) en die geskatte tye van aankoms van die radiosein by elk van die teleskope. 'N Reeks afspeel-tydsberekeninge oor 'n reeks nanosekondes word gewoonlik getoets totdat die regte tydsberekening gevind is.


Die onlangs aangekondigde M87-waarnemings het slegs 8 van die tien terreine gebruik. Hierdie vraestel bevat hierdie diagram. Al lyk dit asof die Suidpool-instrument slegs vir kalibratioom (die stippellyne) gebruik is.


Wetenskaplikes onthul die eerste beeld van die swart gat in al sy donker glorie

'N Virtuele teleskoop so groot soos die planeet Aarde het die eerste direkte beeld van 'n swart gat vasgelê 'n eeu nadat Einstein se vergelykings die bestaan ​​van swart gate voorspel het. Spesifiek, die beeld wat deur die Event Horizon Telescope vasgelê is, was die geheimsinnige streek wat gedefinieer is deur die gebeurtenishorison van die gat, die punt waarbinne niks & mdash nie eens lig & mdash kan ontsnap nie.

"Ons het gesien wat ons dink onsigbaar was," het Shep Doeleman, 'n radiosterrekundige by die Harvard Smithsonian Center for Astrophysics en direkteur van die Event Horizon Telescope-projek, gesê. "Ons het 'n swart gat gesien en 'n foto daarvan geneem. Dit is 'n besonderse prestasie."

Die teiken was 'n enorme swart gat, 6,5 miljard keer massiewer as die son, in die kern van M-87, 'n reuse elliptiese sterrestelsel ongeveer 55 miljoen ligjare weg in die sterrebeeld Maagd. 'N Bekende teiken vir amateur-sterrekundiges, M-87 is een van die helderste radiobronne in die lug, met 'n groot hoeveelheid materiaal wat van die kern af strek, aangedryf deur die gulsige swart gat. Die swart gat se ses-en-'n-half miljard sonmassas word in 'n gebied ongeveer so groot soos 'n sonnestelsel ingedruk.

Hierdie beeld wat Woensdag 10 April 2019 deur Event Horizon Telescope vrygestel is, toon 'n swart gat. Wetenskaplikes het die eerste beeld wat ooit gemaak is van 'n swart gat onthul nadat hulle data versamel het wat deur 'n netwerk radioteleskope regoor die wêreld versamel is. Event Horizon Telescope Collaboration / Maunakea Observatories via AP

Die beeld wat deur die Event Horizon Telescope vasgelê is, wys 'n swart kern en die gebeurtenishorison en die skerm omring deur 'n skewe ligring wat uitgestraal word deur deeltjies wat teen die spoed van die lig rondhardloop. Dit lyk baie soos wat sterrekundiges verwag het op grond van simulasies wat die vergelykings van Einstein se algemene relatiwiteitsteorie gebruik.

"Ons het nou visuele bewyse vir 'n swart gat," het Doeleman gesê. "Ons weet nou dat 'n swart gat wat 6,5 miljard keer weeg wat ons son doen, in die middel van M-87 bestaan. Dit is die sterkste bewys wat ons tot nog toe het vir die bestaan ​​van swart gate. Dit is ook in ooreenstemming met Einstein se voorspellings. . "

Daniel Marrone, 'n sterrekundige aan die Steward Observatory van die Universiteit van Arizona, het gesê: "Vandag het algemene relatiwiteit nog 'n belangrike toets geslaag. Die voorwerp in die hart van M-87 is 'n swart gat soos dié wat deur algemene relatiwiteit beskryf word."


Hoe die Event Horizon Telescope ons 'n swart gat gewys het

Op 10 April 2019 het die Event Horizon Telescope (EHT) die allereerste beeld van 'n swart gat van 'n swart gat gekry. Hierdie merkwaardige tegnologiese prestasie is moontlik gemaak deur die gesamentlike pogings van honderde astrofisika, ingenieurs en rekenaarwetenskaplikes. Hulle het gereelde tydelike waarnemings van hul teiken met veelvuldige teleskope regoor die wêreld gereël en die data tussen die instrumente gekorreleer om die skepping van 'n planeetgrootte teleskoop effektief te bewerkstellig. Die data is dan verwerk om die beeld wat ons in die nuus gesien het, te maak.

Maar het ons 'n swart gat regtig 'gesien' toe ons 'net' 'n digitale beeld gewys het? En hoe is dit moontlik om 'n teleskoop op aarde te skep?

Laat ek begin deur te verduidelik waarom EHT werklik 'n teleskoop op aarde benodig. Daar is 'n oorvloed stof tussen ons teleskope en die waargenome swart gate. Hierdie stof absorbeer elektromagnetiese straling van kort golflengtes soos sigbare lig (ongeveer 5,5 x 10 -7 m), infrarooi lig (ongeveer 10 -6 m), ensovoorts. Die straling van golflengtes van ongeveer 1 millimeter (10 -3 m) en groter word egter nie deur die stof beïnvloed nie. Die hoekoplossing van 'n teleskoop is eweredig aan die waargenome golflengte gedeel deur die deursnee van die teleskoop. 'N Lang golflengte het 'n laer resolusie, terwyl 'n groter teleskoopspieël 'n hoër resolusie verseker. ETH moes dus 'n golflengte van ongeveer 1 mm waarneem. (Hulle het 1,3 mm waargeneem.) Hierdie golflengte het egter ook geïmpliseer dat hulle 'n teleskoop nodig het wat soortgelyk is aan die deursnee van ons planeet om die skaduwee van swart gate op te los. Dit is nie prakties moontlik om 'n spieël van so 'n grootte te konstrueer nie, maar ons kan steeds die vereiste resolusie bereik met behulp van die interferometer-tegniek. Om dit te verduidelik, sal ons 'n reeks analogieë gebruik.

Eerste analogie: Stel u 'n regte teleskoopspieël voor wat gelyk is aan die grootte van die planeet Aarde en plaas dan 'n swart lap met verskeie gate daaroor. Die lap sal die vermoëns van die teleskoop beperk en die ligversamelingsarea verminder, maar ons sal steeds 'n magtige planeetgrootte teleskoop met hoë resolusie-vermoëns hê.

Tweede analogie: Stel jou voor 'n handvol klein spieëls. 'N Mens kan hulle styf bymekaar plaas en 'n mooi mediumgrootte teleskoopspieël konstrueer. Maar 'n mens kan ook kies om hulle oor 'n groter gebied te versprei. Elke klein spieël verteenwoordig 'n plek waar die stof van die eerste analogie 'n gaatjie het. As 'n mens dus 'n slim manier vind om die klein spieëls te verbind en die gegewens wat elkeen versamel, saam te ontleed, kan dit moontlik wees om die vermoëns (veral die resolusie) van die groot spieël weer te gee, soortgelyk aan die grootte in die wat die spieëls verstrooi het. As u klein stukke rondbeweeg, bedek u ook meer en meer die oppervlak van die groot spieël en kom u al hoe nader aan sy volle vermoëns.

Dit is 'n illustrasie van hoe 'n interferometer werk. EHT versamel gelyktydig die data van verskeie teleskope wat oor ons planeet versprei is en korreleer en analiseer die data dan gesamentlik. Die betrokke teleskope verander ook hul relatiewe posisies ten opsigte van die teiken as gevolg van die rotasie van die aarde wat groter dele van die aarde-grootte spieël bedek.

In die geskiedenis van sterrekundige waarnemings het ons geleer om tegnologie te gebruik en vertrou om ons te help om die lug te bestudeer. Die eerste waarnemings is slegs met blote oë gedoen. Toe vergroot die optiese teleskope die beeld en vergroot die ligversamelarea vanaf die pupilgrootte tot die grootte van die lens (en later die spieël), sodat kleiner en flouer voorwerpe in detail sigbaar word. Die films (en ander ontvangers) het ons baie langer blootstelling gegee as wat die menslike oog kan doen. Die films en ontvangers het ons ook in staat gestel om buite die sigbare spektrum te kyk, wat uiters nuttig was vir die bestudering van hemelse voorwerpe. (As die produk van evolusie op ons bepaalde planeet, is ons oë strategies ontwerp om sensitief te wees vir die straling van die son, sonder om te kyk of dit 'n goeie frekwensie is vir die studie van die res van die heelal.) Interferometers is net die volgende stap in die ontwikkeling van visuele hulpmiddels. Daarom het ons inderdaad 'n swart gat 'gesien' alhoewel ons 'net 'n na-verwerkte digitale beeld gewys is.

Dit is waar dat wetenskaplik die beeld van M87 se swart gat ons niks onverwags geleer het nie. Dit het presies gelyk soos voorspel. Maar miskien is dit nie 'n slegte ding nie. Toe die Large Hadron Collider in CERN begin werk, moes hy al die deeltjies wat voorheen ontdek is, herontdek. Eers dan kon vertrou word om na onbekende deeltjies te soek en nuwe fisika te ondersoek. Die eerste EHT-beeld was 'n bewys van die waarde van nuwe tegnologie, en dit het die toets geslaag. As die beeld wat daarna vrygestel word, iets onverwags en nuut toon, sal ons meer geneig wees om die fisiese implikasies daarvan in te duik eerder as om te bevraagteken wat met die waarneming verkeerd geloop het. (So ​​'n ontdekking, wat so goed ooreenstem met die voorspellings, het ook hopelik aan die wêreld bewys in hierdie era van anti-wetenskap dat kenners ook vertrou moet word.)

Wat is volgende vir die EHT? Die ander lang verwagte, en ek sou aanvoer, meer opwindende teiken, is ons eie swart gat in die middel van ons Melkwegstelsel bekend as Boogskutter A * (Sgr A *) - die onderwerp van my eie navorsing aan die Instituut. Sgr A * is die naaste supermassiewe swart gat aan die aarde. Dit is 26 000 ligjare weg en het 'n massa van 4.000.000 keer die son. Daarteenoor is M87 se swart gat 2 000 keer verder weg en is dit 1600 keer massiewer, maar die grootte van die skaduwees van die swart gate is soortgelyk. Die massa van Sgr A * is afgelei van die wentelbane van die nabygeleë sterre, wat vyf en twintig jaar lank gevolg is, en wetenskaplikes het tot die gevolgtrekking gekom dat die voorwerp waarom hulle wentel so massief en so klein is dat dit niks anders as 'n swart gat kan wees nie . (Professor Scott Tremaine het meer oor hierdie onderwerp geskryf in sy artikel “The Odd Couple: Quasars and Black Holes” vir die Institute Letter in 2015).

'N Verrassende kant van die gedrag van Sgr A * is die aanwas daarvan, naamlik die gedrag van inkomende gas. Hier wil ek daarop wys dat die swart gat geen materiaal insuig nie. Die materiaal val vanself daarin. Op dieselfde manier suig die aarde nie die Internasionale Ruimtestasie op nie, wat dit noukeurig wentel. Die stasie ervaar wrywing met die buitenste lae van die atmosfeer van die planeet, wat dit vertraag, wat veroorsaak dat sy baan laer sak om in die ruimte te bly, dit moet weer versterk word, dit wil sê, gereeld na 'n hoër baan geskuif word. Die gaswolke wat om die swart gat wentel, ervaar ook dieselfde wrywing, word verhit, vertraag en beweeg al hoe nader aan die agterste gat totdat dit inval. Hulle bedek die swart gat, om dit te sê. Die gaswolke straal ook die oormatige hitte uit terwyl hulle afwaarts draai, en produseer dus die emissie wat ons swartgatstraling noem. (Die Hawking-straling van die swart gate word hopeloos oorweldig deur die bestraling van die aanwasgas.)

Die hoeveelheid warm gas (ongeveer tien miljoen Kelvin), wat aan Sgr A * gebind is, is goed beperk deur X-straalwaarnemings. As hierdie gas die swart gat op die gewone manier gevoer het, sou ons 'n paar ordes meer bestraling sien as wat ons werklik waarneem. Daar is dus tot die gevolgtrekking gekom dat dit vinniger in die swart gat inskakel as wat dit die hitte kan uitstraal, omdat die digtheid van die gas laag is en dat die hoeveelheid wat aan die swart gat gevoer word, groter kan wees as wat ons normaalweg sou kon aflei uit die hoeveelheid waargenome bestraling. Die spesifieke besonderhede van die proses is egter nog onseker. Ons weet nog steeds nie of daar 'n radiale uitvloei van Sgr A * is nie, of dit strale het wat die snelheid van die gas rondom dit is en die rigting van die vloei in die verskillende strale is, of die vloei 'n skyf vorm of nie, hoe die digtheid is en die temperatuur van die gas en die sterkte van magnetiese velde verander met die afstand vanaf die swart gat en hoeveel van die gas, wat te koel is om X-strale uit te straal, is naby die swart gat aanwesig. Die laaste gebied is die onderwerp van my eie studies.

Daar is verskeie onopgeloste vrae rakende die voer van ons supermassiewe swart gat, wat EHT-waarnemings kan help beantwoord. Ons sal byvoorbeeld leer oor die aan- of afwesigheid van Sgr A * -strale en die rigting van die gasvloei-rotasie en die neiging daarvan bevestig (daar is onlangs beweer dat dit op die gesig staar). Oor die algemeen sou dit 'n heeltemal nuwe hoofstuk in die bestudering van fisika in swart gate open. Al met al is dit 'n ware voorreg om in so 'n opwindende en dinamiese tyd vir hierdie wonderlike veld te leef.

Niemand kan voorspel waarheen die dieper begrip van fundamentele wette wat hierdie wêreld regeer ons sal lei en watter deure hulle sal oopmaak nie, maar dit is altyd onverwags en opwindend. Dit is die moeite werd om te onthou dat die studie van elektrisiteit eens as 'n heeltemal onpraktiese poging beskou is, wat nooit bruikbare toepassings sou hê nie. Nou belas ons dit.

Elena Murchikova, Bezos-lid van die Skool vir Natuurwetenskappe, werk aan die koppelvlak tussen teoretiese astrofisika en waarnemingsterrekunde. Haar navorsingsinteresse bestudeer studies van die Melkweg se galaktiese middelgat swart gat met die ALMA-teleskoop, die teorie vir die aanwas van swart gate, die binnekant van neutronsterre en kosmiese snare.


2. ALGEMENE DEFINISIES EN OORWEGINGS

2.1. Die sentrale swart gat

Optiese / IR-waarnemings van die wentelbane van sterre in die omgewing van Sgr A * het gelei tot 'n meting van die massa en afstand van die Aarde, D. Die onsekerhede in die twee metings is betekenisvol en sterk gekorreleer (Ghez et al. 2008 Gillessen et al. 2009b). Vanweë die aanwysings van hierdie korrelasies is die onsekerheid in die skynbare grootte van die swartgatskadu, wat die mees relevante hoeveelheid vir die EHT-waarnemings is, aansienlik kleiner. In die volgende bespreking stel ons die massa van Sgr A * op en die afstand daarvan op D = 8,3 kpc (Reid et al. 2014), sodat die oënskynlike openingshoek van een gravitasieradius () op die afstand van Sgr A * gelyk is aan en ooreenstem met die waarskynlikste waarde afgelei van huidige waarnemings (Psaltis et al. 2015b).

Vanweë die groot baanafstande van die tans bekende optiese / IR-sterre rondom Sgr A * was daar geen dinamiese metings van die draaigrootte nie, χ, of oriëntasie. Vergelykings van aanwasvloeimodelle met spektroskopiese en EHT-beeldwaarnemings dui op lae draaie wanneer semi-analitiese modelle gebruik word (bv. Broderick et al. 2011), of relatief hoë draaie wanneer GRMHD-modelle gebruik word (bv. Dexter et al. 2010 Chan et al. 2015). Boonop ondersteun die klein afgeleide grootte van die 1,3 mm-beeld van Sgr A * die aanname dat die draai van die swart gat geneig is met betrekking tot die siglyn en in lyn is met die hoekmomentvektor van die stertskyf by

3 boogsek weg van die swart gat (Psaltis et al. 2015a). Vir die doeleindes van hierdie artikel stel ons die draai van Sgr A * op, wat ooreenstem met 'n Kerr-kwadrupmoment van. Ons het hierdie waardes so gekies dat die effekte van die draai sowel as die kwadrupoolmoment moontlik waarneembaar is, sonder dat dit maksimaal is. Dit is duidelik dat ons slegs die stelling sonder hare kan toets as die swart gat in die middel van die Melkweg draai.

2.2. Die innerlike groep sterre-massa voorwerpe

Vooruitgang in adaptiewe optika het 'n groot aantal sterre in 'n wentelbaan rondom Sgr A * geopenbaar (sien Genzel et al. 2010 Ghez et al. 2012). Een van hierdie sterre is gevolg vir ten minste een volledig geslote baan (Ghez et al. 2008 Gillessen et al. 2009a) en die omwentelingsparameters van verskeie ander (S0-16, S0-102 en S0-104) sal uiteindelik plaas hulle binne 'n paar duisend gravitasieradiusse vanaf die swart gat (bv. Meyer et al. 2012). Alhoewel die monitering van hierdie wentelbane in die nabye toekoms waarskynlik sal lei tot die opsporing van periapsis-presessie, sal addisionele relativistiese effekte wat die stelling van geen hare kan toets, te klein wees om te bespeur of gemasker deur ander astrofisiese ingewikkeldhede.

Daar word verwag dat waarnemings met toekomstige instrumente, soos die adaptiewe-optiese geassisteerde interferometer GRAVITY op die Very Large Telescope (Eisenhauer et al. 2011) en die nuwe generasie adaptiewe optika-instrumente op 'n 30 m-teleskoop (Weinberg et al. 2005) , sal lei tot die ontdekking van sterre met nouer wentelbane. Die monitering van die presessie van hul wentelbane en hul baanvlakke sal die moontlikheid bied om die draai en die kwadrupoolmoment van die swart gat te meet en dus die stelling sonder hare te toets (Will 2008).

Die verspreiding van sterre-massa-voorwerpe binne enkele duisende gravitasieradiusse vanaf Sgr A * is op hierdie punt baie moeilik waarnemend af te lei (sien die gedetailleerde bespreking in Merritt 2010). Vir die doeleindes van die huidige studie sal ons Merritt et al volg. (2010) en stel die verdeling van die halforbitale asse van sterre voorwerpe om die swart gat so in

Ons skryf ons uitdrukkings in die algemene geval van, maar evalueer dit in die ooreenstemmende syfers vir (Merritt et al. 2010) en (Bahcall & amp Wolf Wolf 1976), om die effek van hierdie veronderstelde parameter te kwantifiseer. Vereis dat die totale massa sterre binne die kenmerkende wentelskeiding a0 is gelyk aan M*, d.w.s.

ons verkry vir die normaliseringskonstante

en vir die totale aantal sterre binne 'n baan met 'n halfas a

Die kenmerkende waardes vir die massa m* van elke voorwerp en die totale massa M* ingeslote binne 'n orbitale skeiding a0 is ook swak beperk deur huidige waarnemings. Ons sal hier 'n konserwatiewe stel waardes aanneem (Merritt et al. 2010) waarvoor, pc, en.

Ons kan hierdie verdeling gebruik om die massa, hoekmomentum en kwadrupoolmoment te bereken as gevolg van die sterreswerm wat in 'n baan van 'n gegewe halfas geleë is. Die verhouding van hierdie hoeveelhede tot die swartgatmassa, hoekmomentum en kwadrupoolmoment sal die beperkende akkuraatheid voorstel waarop hierdie eienskappe van swartgatte afgelei kan word met behulp van waarnemings van wentelbane van sterre en pulse.

Die massa sterre binne 'n sirkelvormige baan met 'n halfas a,

en die relatiewe bydrae tot die massa van die swart gat is

waar in die laaste uitdrukking wat ons gestel het.

Die ingeslote hoekmomentum as gevolg van die sterregroep hang af van die relatiewe oriëntasie van die wentelbane en die verspreiding van hul eksentrisiteite. Ons kan 'n boonste limiet vir die ingeslote hoekmomentum verkry deur aan te neem dat alle wentelbane sirkelvormig en in lyn is. In hierdie geval is die ingeslote hoekmomentum

Die dimensionele draaihoekmomentum van die swart gat is (vgl. Vergelyking (1)) en daarom is die grootte van die relatiewe bydrae tot die hoekmomentum as gevolg van die sterregroep die

waar in die laaste uitdrukking wat ons gestel het.

Die ingeslote kwadrupmoment as gevolg van die sterregroep hang ook af van die oriëntasie van die wentelbane. As ons 'n asimmetriese hoekafhanklikheid by die verspreiding van wentelbane voeg, d.w.s. om hierdie verdeling aan te dui, dan word die kwadrupoolmassamoment van die stergroep

Die dimensionele kwadrupoolhoekmomentum van die swart gat is (vgl. Vergelyking (2)) en daarom is die grootte van die relatiewe bydrae tot die kwadrupoolmoment as gevolg van die stergroep

waar in die laaste uitdrukking wat ons gestel het.

Die breukbydraes tot die massa, hoekmomentum en kwadrupoolmoment wat binne 'n wentelbaan van 'n halfas geleë is a word getoon in Figuur 1. Ons doel is om wentelbane van sterre en pulse te gebruik om die kwadrupoolmoment van die swart gat te meet en die stelling sonder hare te toets. Deur net die vereiste op te stel dat die sterreswerm nie die kwadrupoolmoment van die gravitasieveld domineer nie, word ons gedwing om sirkelbane te gebruik met wentelskeidings (of gelykstaande elliptiese wentelbane met periapsis-afstande) wat binne 'n paar keer is (sien ook Merritt et al. 2010 ). Vir pulse in hoogs eksentrieke wentelbane (), soos ons in Afdeling 4 sal demonstreer, het ons, behalwe vir die sekulêre proses van die baan, 'n addisionele ondersoek na die relativistiese effekte via die periodieke bydraes byna periapsis, wat minder geraak word deur eksterne versteurings .

Figuur 1. Fraksionele bydrae tot die swartgatmassa, hoekmomentum en kwadrupolmassamoment binne 'n baan as gevolg van die ingeslote verspreiding van voorwerpe. Hierdie breukbydraes verteenwoordig die beperkte akkuraatheid waarop die ooreenstemmende swartgat-eienskappe afgelei kan word met behulp van waarnemings van wentelbane van sterre en pulse. Die soliede lyne stem ooreen met 'n sterverdeling met terwyl die stippellyne ooreenstem met Die verskillende ander veronderstelde parameters van die sterregroep word in vergelykings (8), (10) en (13) gegee.

2.3. Pulsars in die Galaktiese sentrum

Vir 'n aantal waarnemings- en teoretiese oorwegings verwag ons 'n groot aantal neutronsterre in die sentrale deel van die Melkweg. Vir 'n omvattende oorsig van die waarnemingsbewyse en verwante teoretiese oorwegings, verwys ons na Wharton et al. (2012) en verwysings daarin. Op grond van bewyse vir byvoorbeeld die sterre-vormingstempo in die verlede, die verwagte aanvanklike stermassafunksie in die Galactic Center-omgewing en die waarnemings van massiewe sterre en sterreste, in totaal moet daar tot 100 normale pulse en 1000 millisekonde pulse verwag word. innerlike parsec. Faucher-Giguère & amp Loeb (2011) het vroeër daarop gewys dat die hoë sterldigtheid in die streek ook die effektiewe skepping van eksotiese binaries moontlik maak, soos millisekonde pulsar-sterre swartgatbinaries, wat opwindende laboratoriums in hul eie reg sou wees (Wex & amp Kopeikin 1999 Liu et al. 2014).

Millisekonde pulse is ou, herwinde pulse, wat tipiese periodes tussen 1,4 en 30 ms vertoon, terwyl normale pulse gemiddelde periodes van 0,5-1 s het. Millisekonde-pulse het ook spin-down-tempo's en geskatte sterkte van die magnetiese veld wat gewoonlik drie ordes kleiner is as dié van normale (nie-herwinde) pulse. Hierdie eienskappe maak Millisekonde pulse superieure - en dus verkieslik - klokke in pulsar tydsberekening eksperimente. Vir 'n normale pulsar is die tipiese presiese tydsberekening ongeveer 100 μs, terwyl 'n mens 'n tydsberekening van net soveel as 100 ns of beter kan kry vir die beste Millisekonde-pulse. In albei gevalle hang die finale tydsberekening van die pulsar self af (bv. Die skerpte van sy polsvorm, die intrinsieke rotasiestabiliteit) en die sterkte van die pulsar, aangesien die fout op 'n individuele TOA-meting skaal met die sein-na- geraasverhouding (S / N) van die waarneming (sien Lorimer & amp Kramer 2004 vir verdere besonderhede oor pulseienskappe en tydmetodes).

Ondanks gekonsentreerde pogings en toegewyde soektogte in die Galactic Center-streek, was die opbrengs teleurstellend laag gegewe die ramings. Tot 2013 is slegs vyf pulse binne Sgr A * gevind, met die naaste hiervan, dit wil sê op 'n geprojekteerde afstand van ongeveer 25 stuks (Johnston et al. 2006 Deneva et al. 2009 Bates et al. 2011). Al hierdie was stadige pulse met verspreidingsmaatreëls tot 1500 stuks cm3. Gegewe hul afstande tot Sgr A *, is geen van hierdie geskik vir die eksperimente wat hieronder beskryf word nie.

Die gevolglike vermeende tekort aan Galactic Center-pulse is verklaar as gevolg van hipersterk verspreiding van die radiogolwe by die onstuimige inhomogene interstellêre plasma in die streek. Die verstrooiing lei tot tydelike verbreding van die pulse met verwagte tydskale van minstens 2000 (ν/ 1 GHz) −4 s (Cordes & amp Lazio 2002), wat die opsporing daarvan onmoontlik maak by tipiese soekfrekwensies, ongeveer 1–2 GHz. Om hierdie rede is in die verlede 'n aantal hoëfrekwensie-soektogte gedoen (Kramer et al. 2000 Klein et al. 2004 Johnston et al. 2006 Deneva et al. 2009 Macquart et al. 2010 Bates et al. 2011 Eatough et al. 2013 Siemion et al. 2013) teen frekwensies so hoog as 26 GHz. Selfs in hierdie soektogte is geen pulser in die sentrale parsek gevind nie. Die huidige beste limiet (Jy vir a) word voorsien deur waarnemings met die 100 m Effelsberg-teleskoop teen 19 GHz (R. P. Eatough et al. 2015, ter voorbereiding).

Die onlangse ontdekking van radio-emissie deur die magnetar SGR J1745–29 deur Eatough et al. (2013 sien ook Shannon & amp Johnston 2013), wat die eerste keer by X-strale geïdentifiseer is (Kennea et al. 2013 Mori et al. 2013), bied 'n onverwagse ondersoek na die Galactic Centre-medium en die plaaslike polsbevolking. Die bron wat met verbeterde posisie-presisie nou PSR J1745–2900 heet, is geleë binne 24 (of 0,1 stuks geprojekteer) van Sgr A * (Bower et al. 2015) en is sterk genoeg dat selfs enkele pulse opgespoor kan word vanaf 'n frekwensie van enkele GHz (Spitler et al. 2014) tot 'n ongekende 154 GHz (Torne et al. 2015). Onder 1.1 GHz voorkom die tydelike verbreding 'n opsporing van die bron (Spitler et al. 2014), terwyl gepulseerde radio-emissie tot 225 GHz opgespoor word, wat die hoogste frekwensie is waarteen radio-emissie van 'n neutronster tot dusver opgespoor is. (Torne et al. 2015). Die verspreidingsmaat en die rotasiemaat van PSR J1745–2900 is die grootste in die Melkweg (slegs die rotasiemaat van Sgr A * self is groter Eatough et al. 2013 Shannon & amp Johnston 2013), terwyl die hoekverbreding van die bron konsekwent is met dié van Sgr A * (Bower et al. 2014, 2015), wat bewys lewer vir die nabyheid van die magnetar tot die Galactic Centre. Alhoewel die rotasie-stabiliteit ongelukkig nie voldoende is om eksperimente met presiese tydsberekening uit te voer nie, kan ons die vraag na die verborge pulsarpopulasie weer besigtig.

Radio-emitterende magnetare is 'n baie seldsame tipe neutronster en voorheen was daar slegs drie daarvan bekend in die Melkweg, dit wil sê minder as 0,2% van alle radio-harde neutronsterre (Olausen & amp Kaspi 2014). Die ontdekking van so 'n seldsame voorwerp langs Sgr A * ondersteun daardeur die idee dat daar nog baie gewone radiopulsars moet wees (Eatough et al. 2013 Chennamangalam & amp Lorimer 2014). 'N Verrassende aspek van die magnetar-ontdekking is die relatiewe klein verspreiding wat waargeneem word (Spitler et al. 2014). Met 'n polsperiode van 3,75 s, moet die radio-uitstoot daarvan nie waarneembaar wees teen frekwensies van so laag as 1,1 GHz nie, as daar wel 'n hipersterk verspreiding was.

Beeldwaarnemings (Bower et al. 2015) het gelei tot die meting van 'n behoorlike beweging wat ons nog nie kan aflei of die pulsar aan Sgr A * gebonde is nie. Dit is moontlik dat PSR J1745–2900 en die ander vyf nabygeleë pulse van 'n sterskyf afkomstig is (sien ook Johnston et al. 2006) en dat 'n sentrale populasie pulse nog steeds verborge is. Indeed, Chennamangalam & Lorimer (2014) argue that, even if the lower-than-expected scattering in the direction of PSR J1745–2900 is representative of the entire inner parsec, the potentially observable population of pulsars in the inner parsec still has a conservative upper limit of members. They conclude that it is premature to assume that the number of pulsars in this region is small.

In contrast, Dexter & O'Leary (2014) come to a different conclusion. They also revisited the question about the central pulsar population given the new constraints provided by the magnetar and the non-detection of previous high-frequency surveys. Considering various effects like depletion of the pulsar population due to kick velocities exceeding the central escape velocity, pulsar spectra, and the apparent reduced scattering indicated by the magnetar observations (Spitler et al. 2014), they argue in favor of a "missing pulsar problem." They also concluded that the magnetar discovery in the center may imply, in turn, an efficient birth process for magnetars in the central region. Similarly, others suggested that normal pulsars are not formed since they may collapse into black holes on comparably short timescales by accreting of dark matter (Bramante & Linden 2014).

At the core of deciding between these possibilities is our ability to properly model and account for all selection effects in the previous surveys. There are in fact indications that this is not the case. First, continued monitoring of the scattering timescales for the magnetar indicates that the scattering time is highly variable. While it remains well below the prediction of hyper-strong scattering, it varies by a factor of 2–4 on timescales of months at frequencies between 1.4 and 8 GHz (L. G. Spitler et al. 2015, in preparation). This suggests that local "interstellar weather" certainly plays a role and that nearby scattering screens also affect the observed emission, making the resulting ability to observe sources overall line of sight dependent, especially at lower frequencies. This is not unexpected given the properties of the turbulent interstellar medium in the Galactic Center. Rather than dealing with a uniform single screen, it is likely that we see the effects of multiple finite screens. In this case, second, one expects a much shallower frequency dependence of the scattering time than the canonical values (Cordes & Lazio 2001). This is indeed seen for high-DM pulsars (Löhmer et al. 2001, 2004), where the scattering index is typically around for large dispersion measures. L. G. Spitler et al. (2015, in preparation) find similar values for the magnetar. If this is indeed representative for a possible central pulsar or millisecond pulsar population, then the remaining scattering at 5, 14, or even 19 GHz would be underestimated in the analysis by Macquart et al. (2010) or Dexter & O'Leary (2014) by factors of 2.2, 3.7, or 4.3 respectively, when extrapolating from 1 GHz. Löhmer et al. (2001) measured even flatter frequency dependencies, which would make the discrepancy between real and estimated scattering times even larger. Unless more scatter broadening times in the Galactic Center are measured, this issue is difficult to settle. However, there is yet another, third effect that has usually been neglected in sensitivity calculations of pulsar surveys. As shown very recently by Lazarus et al. (2015) for the P-ALFA survey, red noise present in pulsar search data due to radio interference (RFI), receiver gain fluctuations, and opacity variations of the atmosphere cause a significant decrease in sensitivity for pulsars with periods above 100 ms or so, when compared to the standard radiometer-based equation (see their Figure 11). This would affect in particular a search for young pulsars, but also, of course, magnetars, which are nevertheless still easier to detect at high frequencies due to their much flatter flux density spectrum (Torne et al. 2015). This selection effect in particular would favor the detection of magnetars over that of normal, young pulsars and may explain in some respects the peculiarities of the current observational situation pointed out by Dexter & O'Leary. The work by Lazarus et al. demonstrates that the various selection effects are highly dependent on the individual surveys and that much more work is needed to understand the impact on the resulting search sensitivities.

Finally, none of the previous high-frequencies surveys has, to our knowledge, applied a fully coherent acceleration search. Such an acceleration search may be needed to account both for the movement of the pulsar around the central black hole, as well as for the presence of a binary companion. Indeed, due to the high stellar density, even exotic systems (e.g., millisecond pulsar-stellar mass BH binary) may be expected (Faucher-Giguère & Loeb 2011). An acceleration search is usually very computationally expensive, especially for long integration times as employed in the high frequency searches (e.g., by Macquart et al. 2010 or R. P. Eatough et al. 2015, in preparation), since the parameter range to be searched scales as . The lack of such an acceleration search contributes as a selection effect to the present non-detection of fast-spinning pulsars.

In order to model the selection effects (red noise, acceleration, scattering etc.) a more detailed study, taking the orientation of the possible orbits and the change in acceleration into account, is needed. This is beyond the scope of this paper and will be presented elsewhere. It is clear, however, that selection effects are not adequately modeled so far and that more work is required.

We conclude that three scenarios are still possible: (a) the scattering seen for the Galactic Center magnetar is representative of the inner parsec. In this case, the pulsar population may be dominated by Millisecond pulsars, for which this moderate scattering would still have prevented their detection at previous search frequencies. Higher frequency searches may therefore even allow the discovery and hence the exploitation of Millisecond pulsars orbiting Sgr A* (see also Macquart & Kanekar 2015). We note in passing that the discovery of a Millisecond pulsar population may settle an ongoing debate about a possible excess of GeV gamma ray photons from the Galactic Center. It is being discussed whether such an excess could arise from the presence of dark matter or a central population of unresolved young or Millisecond pulsars (see e.g., O'Leary et al. 2015 and references therein). Any pulsar discovery in the Galactic Center would make a dark matter discovery less likely. (b) There is a reduced number of pulsars in the Galactic Center region that is consistent with selection effects. For example, the lack of dispersion makes the discovery of unknown pulsars actually more difficult at high frequencies, as the signals are more difficult to distinguish from radio interference (see R. P. Eatough et al. 2015, in preparation), or (c) PSR J1745–2900 is indeed in front of a much more severe scattering screen but the scattering properties for particular lines of sight are changing with time due to "local weather" effects, signs of which have been already detected (L. G. Spitler et al. 2015, in preparation). In this case, search observations at even higher frequencies are required and still promising.

Given that we cannot distinguish between these scenarios based on the available data, high frequency searches will continue. The use of more sensitive instruments than available in the past, e.g., ALMA or the Square Kilometre Array (SKA), may therefore lead to the discovery of normal pulsars and even Millisecond pulsars. In considering how they can be used to measure the properties of Sgr A*, we will therefore assume a variety of obtainable timing precisions. For details, we refer the reader to Liu et al. (2012), who demonstrated possible precision levels as a function of observing frequency for the SKA and 100-m class telescopes. In their arguments, Liu et al. (2012) only considered normal pulsars and also assumed a hyper-strong scattering. If the latter is not present as we have discussed above, Millisecond pulsars may be detectable (although this may require proper acceleration searching). Hence, for the discussion of the measurable effects, we will also allow for this possibility that Millisecond pulsars will be detected.

There are a number of Millisecond pulsars in globular clusters at distances that are signifantly larger than that of the Galactic Center. It is not uncommon to achieve a timing precision of about 10 μs for these distant sources. The exact precision mainly depends on the strength of the pulsar signal and the sensitivity of the telescope, as well as the sharpness of some of the detetable profile features. If we need to go to high radio frequencies in order to beat interstellar scattering to see pulsars in the center of the Milky Way, the flux density decreases and timing precision decreases accordingly. This can be compensated by larger bandwidth or bigger telescopes. As shown in Eatough et al. (2015), a timing precision of 1 μs should be routinely possible with the SKA, even at distances of the Galactic Center at higher frequencies. Such a precision is certainly more challenging with existing instruments. Overall, in order to cover all three plausible scenarios discussed above, we will assume, in the following, that a Galactic Center pulsar can be timed with a precision of 1, 10, and 100 μs. As, in principle, only one pulsar is needed to extract the black hole parameters, we consider this to be a useful range to demonstrate the effects that we can expect to measure.

2.4. Relativistic Orbital Effects

In describing the orbit of a stellar-mass object around Sgr A*, we will use the coordinate system and notation shown in Figure 2. In particular, we will denote by m* the mass of the orbiting object and by a en e the semimajor axis and eccentricity of its orbit. We will use the vector to define the black hole spin and the vector to denote the line of sight unit vector pointing from the Earth to the black hole. We will also denote the longitude of the periapsis of the orbit with respect to the equatorial plane of the black hole by ω, the location of the ascending node by , and the inclination of the orbit with respect to the black hole spin axis by Θ.

Figuur 2. Coordinate system and notation used in defining an orbit of a stellar-mass object around Sgr A*. The vector denotes the spin of Sgr A* and is the line of sight unit vector pointing from the Earth to the black hole. The longitude of the periapsis of the orbit is ω, the location of the ascending node is , and the inclination of the orbit with respect to the black hole spin axis is Θ. The angle i, between and the orbital angular momentum is the inclination of the orbit with respect to the observer.

With these definitions, the Newtonian period of the orbit is

Eccentric orbits of stars and pulsars precess on the orbital plane (relativistic periapsis precession). The leading term comes from the mass-monopole and corresponds to the relativistic precession of the Mercury orbit (Einstein 1915). The advance of periapsis per orbit is , where

This corresponds to a characteristic timescale for this precession of (see Merritt et al. 2010 for the definition, who denote this by )

In this expression, we have neglected the small contributions of the spin and of the quadrupole of the black hole.

Orbits with angular momenta that are not parallel to the spin of the black hole show a precession of the orbital angular momentum around the direction due to frame dragging (Lense–Thirring precession of the nodes). The location of the ascending node of the orbit, , advances per orbit by

is the Lense–Thirring frequency. The characteristic timescale for this process is (Merritt et al. 2010)

Finally, tilted orbits also precess because of the quadrupole moment of the spacetime with a characteristic timescale (Merritt et al. 2010)

Figure 3 shows the characteristic timescales of these relativistic orbital effects as a function of the semimajor axes and orbital periods of the orbits. A number of additional relativistic effects related to time dilation and photon propagation (Shapiro delay) can also be detected during timing observations of pulsars. We will discuss these effects and their dependence on the pulsar orbital parameters in Section 4.

Figuur 3. Characteristic timescales for various relativistic and astrophysical effects that alter the orbits of stars around Sgr A*. The three blue lines correspond to the periapsis precession ( ), and orbital plane precession due to frame dragging ( ) and due to the quadrupole of the black hole ( ), for orbits with eccentricities of e = 0.5 (solid) and e = 0.8 (dashed), respectively the spin of Sgr A* is set to The green line corresponds to the orbital decoherence timescale ( ) due to the interactions with other objects in the stellar cluster. The black curve ( ) corresponds to the orbital evolution timescale due to the launching of a stellar wind. The red curves correspond to the orbital evolution due to the tidal dissipation of orbital angular momentum for two eccentricities. Stars in orbits with semimajor axes comparable to 1000 gravitational radii are optimal targets for observing post-Schwarzschild relativistic effects.

2.5. Optimal Orbital Parameters for Stars and Pulsars

Performing tests of the no-hair theorem with orbits is hampered by a number of astrophysical complexities caused by non-relativistic phenomena that affect, in principle, the orbits. These included the self-interaction between the stars in the stellar cluster (Merritt et al. 2010 Sadeghian & Will 2011), the hydrodynamic drag between the stars and the accretion flow (Psaltis 2012), as well as stellar winds and tidal deformations (Psaltis et al. 2013). In order to identify the orbital parameters of stars that are optimal for performing the test of the no-hair theorem, we will first summarize and combine the results of these studies.

Interactions with Other Stars. Merritt et al. (2010) and Sadeghian & Will (2011) explored the decoherence of the orbit of a star (or pulsar) due to Newtonian gravitational interactions within the inner stellar cluster. They obtained an approximate expression for the decoherence timescale given by

where is the average ratio of the mass of a star (or compact object) in the cluster to that of Sgr A*, and N(a) is the number of stars inside the orbit of the object under consideration.

Using Equations (6), (14), and (21), we obtain for the decoherence timescale of orbits due to the self interaction between objects in the stellar cluster

Figure 3 compares the Newtonian decoherence timescale with those of the three relativistic effects discussed in Section 2. For the parameters of Sgr A* and of the stellar cluster around it, stars with orbital periods less than year are required in order for the Newtonian interactions not to mask the orbital plane precession due to frame dragging (see a more detailed discussion and simulations in Merritt et al. 2010).

Hydrodynamic Interactions with the Accretion Flow. In Psaltis (2012) we investigated the changes in the orbits of stars and pulsars caused by the hydrodynamic and gravitational interactions between them and the accretion flow around Sgr A*. For all cases of interest, we found that the hydrodynamic drag is the dominant effect. However, as we will show below, even the hydrodynamic drag is negligible for the orbital separations considered here.

When a star of mass m* and radius R* plows through the accretion flow of density ρ with a relative velocity , it feels an effective acceleration equal to

We can use this acceleration to define a characteristic timescale for the change of the orbital parameters as

Setting the relative velocity equal to the orbital velocity of a circular orbit, and the density of the accretion flow to

which has been inferred observationally (see discussion in Psaltis 2012), we obtain

Here, is the mass of the proton and we assumed for simplicity that the orbit is circular. This timescale is significantly larger than all other timescales shown in Figure 3.

Stellar Winds. In Psaltis (2012) we explored the change in the orbital parameters of stars due to the launching of a wind that carries a fraction of the orbital energy and angular momentum. The semimajor axis and the eccentricity of the orbit change at a timescale comparable to , where is the rate of wind mass loss, i.e.,

where we have used the subscript " " to denote the exponent in the wind mass loss rate. As shown in Figure 3, the evolution of the stellar orbit due to the launching of a stellar wind is always negligible compared to the effects of the Newtonian interactions with the other stars in the cluster.

Tidal Evolution. Finally, in Psaltis (2013) we also explored the evolution of a stellar orbit due to the tidal dissipation of orbital energy during the periapsis passages. Even though tidal dissipation does not cause a significant precession in the orbit (see Sadeghian & Will 2011), it leads to an evolution of the semimajor axis that may be misinterpreted (due to the expected low signal-to-noise in the observations) as a change in the projected orbital separation caused by orbital precession.

The characteristic timescale for orbital evolution due to tidal dissipation is

where the quantity is defined and calculated in Psaltis et al. (2013). Also, if the star at periastron reaches inside the tidal radius

it gets disrupted. Both these effects, for two different orbital eccentricities, are shown in Figure 3.

Optimal parameters. Comparing the various constraints shown in Figure 3 to the characteristic timescales of the three relativistic effects allows us to identify the optimal orbital parameters of stars and pulsars for measuring the black hole spin and for testing the no-hair theorem.

Using the orbital precession of stellar orbits to measure the spin of Sgr A* simply requires sub-year orbital periods for the effects of the stellar perturbations to become negligible (as previously discussed in Merritt et al. 2010). On the other hand, measuring the black hole quadrupole requires stars in much tighter orbits ( yr), for the stellar perturbations to be negligible, but with moderate eccentricities ( ), for tidal effects to not interfere with the measurements of the relativistic precessions (see also Will 2008).

For the case of pulsar timing, tidal effects do not alter the orbits and therefore only stellar perturbations can limit our ability to observe relativistic precessions. If we were to use pulsar timing to measure the black hole quadrupole by observing the pulsar orbital plane precess, we would still be limited to using only rather tight orbits ( yr). However, in defining the characteristic timescale for quadrupole effects on the pulsar orbits (Equation (20)), we have only considered the secular precession of the orbit. The most promising way to extract the quadrupole moment from timing observations is through the periodic effects in the orbital motion of the pulsar caused by the quadrupolar structure of the gravitational field of Sgr A* (Wex & Kopeikin 1999 Liu et al. 2012). This is not only the case for the quadrupole but also for the relativistic precession of the periapsis due to the mass monopole (Damour & Deruelle 1985) and the precession of the orbit due to the frame dragging (Wex 1995). (See also the discussion in Angélil & Saha 2014). As argued by Liu et al. (2012), such unique periodic features in the timing of a pulsar around Sgr A* provide a powerful handle to correct for external perturbations. As we will demonstrate with mock data simulations in Section 4, timing a pulsar only during a small number of successive periapses passages is sufficient to measure both the spin and the quadrupole moment of Sgr A*.


New analysis of black hole reveals a wobbling shadow

In 2019, the Event Horizon Telescope Collaboration delivered the first image of a black hole, revealing M87*—the supermassive object in the center of the M87 galaxy. The team has now used the lessons learned last year to analyze the archival data sets from 2009-2013, some of them not published before.

The analysis reveals the behavior of the black hole image across multiple years, indicating persistence of the crescent-like shadow feature, but also variation of its orientation—the crescent appears to be wobbling. The full results appeared today in The Astrofisiese joernaal.

The Event Horizon Telescope is not one singular telescope, but a global partnership of telescopes—including the UChicago-led South Pole Telescope—which performs synchronized observations using the technique of Very Long Baseline Interferometry. Together they form a virtual Earth-sized radio dish, providing a uniquely high image resolution.

"The Event Horizon Telescope is giving us a new tool to study black holes and gravity in ways that were never before possible," said Bradford Benson, an associate professor of astronomy and astrophysics at UChicago. "As members of the South Pole Telescope (SPT) collaboration and the EHT network, we look forward to contributing to future studies—in particular on Sgr A*, the black hole at the center of the Milky Way galaxy, which we have a unique view of given SPT's location at the geographical South Pole."

The first image of a black hole, revealed in 2019, has helped researchers analyze archival data sets. Those findings could help scientists formulate new tests of the theory of general relativity. Krediet: EHT-samewerking

"With the incredible angular resolution of the Event Horizon Telescope, we could observe a billiard game being played on the Moon and not lose track of the score!" said Maciek Wielgus, an astronomer at Center for Astrophysics | Harvard & Smithsonian, Black Hole Initiative Fellow, and lead author of the new paper.

"Last year we saw an image of the shadow of a black hole, consisting of a bright crescent formed by hot plasma swirling around M87*, and a dark central part, where we expect the event horizon of the black hole to be," said Wielgus. "But those results were based only on observations performed throughout a one-week window in April 2017, which is far too short to see a lot of changes."

But from 2009 to 2013, researchers had taken data of M87* with early prototype arrays before the full complement of telescopes joined. They could tap that data to find out if the crescent size and orientation had changed.

The 2009-2013 observations consist of far less data than the ones performed in 2017, making it impossible to create an image. Instead, the EHT team used statistical modeling to look at changes in the appearance of M87* over time.

Snapshots of the M87* black hole obtained through imaging / geometric modeling, and the EHT array of telescopes in 2009-2017. The diameter of all rings is similar, but the location of the bright side varies. Credit: M. Wielgus, D. Pesce and the EHT Collaboration

Expanding the analysis to the 2009-2017 observations, scientists have shown that M87* adheres to theoretical expectations. The black hole's shadow diameter has remained consistent with the prediction of Einstein's theory of general relativity for a black hole of 6.5 billion solar masses.

But while the crescent diameter remained consistent, the EHT team found that the data were hiding a surprise: The ring is wobbling, and that means big news for scientists. For the first time they can get a glimpse of the dynamical structure of the accretion flow so close to the black hole's event horizon, in extreme gravity conditions. Studying this region holds the key to understanding phenomena such as relativistic jet launching, and will allow scientists to formulate new tests of the theory of general relativity.

The gas falling onto a black hole heats up to billions of degrees, ionizes and becomes turbulent in the presence of magnetic fields. "Because the flow of matter is turbulent, the crescent appears to wobble with time," said Wielgus. "Actually, we see quite a lot of variation there, and not all theoretical models of accretion allow for so much wobbling. What it means is that we can start ruling out some of the models based on the observed source dynamics."

An animation representing one year of M87* image evolution according to numerical simulations. Measured position angle of the bright side of the crescent is shown, along with a 42 microarcsecond ring. For a part of the animation, image blurred to the EHT resolution is shown. Credit: G. Wong, B. Prather, C. Gammie, M. Wielgus & the EHT Collaboration

"These early-EHT experiments provide us with a treasure trove of long-term observations that the current EHT, even with its remarkable imaging capability, cannot match," said Shep Doeleman, the founding director of EHT. "When we first measured the size of M87 in 2009, we couldn't have foreseen that it would give us the first glimpse of black hole dynamics. If you want to see a black hole evolve over a decade, there is no substitute for having a decade of data."

EHT project scientist Geoffrey Bower added: "Monitoring M87* with an expanded EHT array will provide new images and much richer data sets to study the turbulent dynamics. We are already working on analyzing the data from 2018 observations, obtained with an additional telescope located in Greenland. In 2021 we are planning observations with two more sites, providing extraordinary imaging quality. This is a really exciting time to study black holes!"


How can the Event Horizon Telescope image Sgr A* when it's not visible from all sites at one time? - Sterrekunde

The center of the Milky Way galaxy, with the supermassive black hole Sagittarius A* (Sgr A*) located in the middle, is revealed in these images. As described in our press release, astronomers have used NASA's Chandra X-ray Observatory to take a major step in understanding why gas around Sgr A* is extraordinarily faint in X-rays.

The large image contains X-rays from Chandra in blue and infrared emission from the Hubble Space Telescope in red and yellow. The inset shows a close-up view of Sgr A* only in X-rays, covering a region half a light year wide. The diffuse X-ray emission is from hot gas captured by the black hole and being pulled inwards. This hot gas originates from winds produced by a disk-shaped distribution of young massive stars observed in infrared observations (mouse over the image for the distribution of these massive stars).

These new findings are the result of one of the biggest observing campaigns ever performed by Chandra. During 2012, Chandra collected about five weeks worth of observations to capture unprecedented X-ray images and energy signatures of multi-million degree gas swirling around Sgr A*, a black hole with about 4 million times the mass of the Sun. At just 26,000 light years from Earth, Sgr A* is one of very few black holes in the Universe where we can actually witness the flow of matter nearby.

The authors infer that less than 1% of the material initially within the black hole's gravitational influence reaches the event horizon, or point of no return, because much of it is ejected. Consequently, the X-ray emission from material near Sgr A* is remarkably faint, like that of most of the giant black holes in galaxies in the nearby Universe.

The captured material needs to lose heat and angular momentum before being able to plunge into the black hole. The ejection of matter allows this loss to occur.

This work should impact efforts using radio telescopes to observe and understand the "shadow" cast by the event horizon of Sgr A* against the background of surrounding, glowing matter. It will also be useful for understanding the impact that orbiting stars and gas clouds might make with the matter flowing towards and away from the black hole.


Title: HIGH-RESOLUTION LINEAR POLARIMETRIC IMAGING FOR THE EVENT HORIZON TELESCOPE

Images of the linear polarizations of synchrotron radiation around active galactic nuclei (AGNs) highlight their projected magnetic field lines and provide key data for understanding the physics of accretion and outflow from supermassive black holes. The highest-resolution polarimetric images of AGNs are produced with Very Long Baseline Interferometry (VLBI). Because VLBI incompletely samples the Fourier transform of the source image, any image reconstruction that fills in unmeasured spatial frequencies will not be unique and reconstruction algorithms are required. In this paper, we explore some extensions of the Maximum Entropy Method (MEM) to linear polarimetric VLBI imaging. In contrast to previous work, our polarimetric MEM algorithm combines a Stokes I imager that only uses bispectrum measurements that are immune to atmospheric phase corruption, with a joint Stokes Q and U imager that operates on robust polarimetric ratios. We demonstrate the effectiveness of our technique on 7 and 3 mm wavelength quasar observations from the VLBA and simulated 1.3 mm Event Horizon Telescope observations of Sgr A* and M87. Consistent with past studies, we find that polarimetric MEM can produce superior resolution compared to the standard CLEAN algorithm, when imaging smooth and compact source distributions. As an imaging framework, MEM is highlymore » adaptable, allowing a range of constraints on polarization structure. Polarimetric MEM is thus an attractive choice for image reconstruction with the EHT. « less


Photographing a Black Hole: Historic Campaign Now Underway

The campaign to capture the first-ever image of a black hole has begun.

From today (April 5) through April 14, astronomers will use a system of radio telescopes around the world to peer at the gigantic black hole at the center of the Milky Way, a behemoth called Sagittarius A* (Sgr A*) that's 4 million times more massive than the sun.

The researchers hope to photograph Sgr A*'s event horizon — the "point of no return" beyond which nothing, not even light, can escape. (The interior of a black hole can never be imaged, because light cannot make it out.) [The Strangest Black Holes in the Universe]

"These are the observations that will help us to sort through all the wild theories about black holes — and there are many wild theories," Gopal Narayanan, an astronomy research professor at the University of Massachusetts Amherst, said in a statement. "With data from this project, we will understand things about black holes that we have never understood before."

The project, known as the Event Horizon Telescope (EHT), links up observatories in Hawaii, Arizona, California, Mexico, Chile, Spain and Antarctica to create the equivalent of a radio instrument the size of the entire Earth. Such a powerful tool is necessary to view the event horizon of Sgr A*, which lies 26,000 light-years from our planet, EHT team members said.

"That's like trying to image a grapefruit on the surface of the moon," Narayanan said.

During the current campaign, EHT is also eyeing the supermassive black hole at the core of the galaxy M87, which lies 53.5 million light-years from Earth. This monster black hole's mass is about 6 billion times that of the sun, so its event horizon is larger than that of Sgr A*, Narayanan said.

These observations should help astronomers determine the mass, spin and other characteristics of supermassive black holes with better precision, team members said. The researchers also aim to learn more about how material accretes into disks around black holes, and the mechanics of the plasma jets that blast from these light-gobbling giants.

EHT could also reveal more about the "information paradox" — a long-standing puzzle about whether information about the material gobbled up by black holes can be destroyed — and other deep cosmological mysteries, team members said.

"At the very heart of Einstein's general theory of relativity, there is a notion that quantum mechanics and general relativity can be melded, that there is a grand, unified theory of fundamental concepts," Narayanan said. "The place to study that is at the event horizon of a black hole."

Though the current observing campaign will be over soon, it will take a while for astronomers to piece together the images. For starters, so much information will be collected by the participating telescopes around the world that it will be physically flown, rather than transmitted, to the central processing facility at the Massachusetts Institute of Technology's Haystack Observatory.

Then, the data will have to be calibrated to account for different weather, atmospheric and other conditions at the various sites. The first results from the campaign will likely be published next year, EHT team members said.


Title: A GENERAL RELATIVISTIC NULL HYPOTHESIS TEST WITH EVENT HORIZON TELESCOPE OBSERVATIONS OF THE BLACK HOLE SHADOW IN Sgr A*

The half opening angle of a Kerr black hole shadow is always equal to (5 ± 0.2)GM/Dc, where M is the mass of the black hole and D is its distance from the Earth. Therefore, measuring the size of a shadow and verifying whether it is within this 4% range constitutes a null hypothesis test of general relativity. We show that the black hole in the center of the Milky Way, Sgr A*, is the optimal target for performing this test with upcoming observations using the Event Horizon Telescope (EHT). We use the results of optical/IR monitoring of stellar orbits to show that the mass-to-distance ratio for Sgr A* is already known to an accuracy of ∼4%. We investigate our prior knowledge of the properties of the scattering screen between Sgr A* and the Earth, the effects of which will need to be corrected for in order for the black hole shadow to appear sharp against the background emission. Finally, we explore an edge detection scheme for interferometric data and a pattern matching algorithm based on the Hough/Radon transform and demonstrate that the shadow of the black hole at 1.3 mm can be localized, in principle, to within ∼9%. All these results suggest thatmore » our prior knowledge of the properties of the black hole, of scattering broadening, and of the accretion flow can only limit this general relativistic null hypothesis test with EHT observations of Sgr A* to ≲10%. « less


Title: THE EVENT HORIZON OF SAGITTARIUS A*

Black hole event horizons, causally separating the external universe from compact regions of spacetime, are one of the most exotic predictions of general relativity. Until recently, their compact size has prevented efforts to study them directly. Here we show that recent millimeter and infrared observations of Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, all but require the existence of a horizon. Specifically, we show that these observations limit the luminosity of any putative visible compact emitting region to below 0.4% of Sgr A*'s accretion luminosity. Equivalently, this requires the efficiency of converting the gravitational binding energy liberated during accretion into radiation and kinetic outflows to be greater than 99.6%, considerably larger than those implicated in Sgr A*, and therefore inconsistent with the existence of such a visible region. Finally, since we are able to frame this argument entirely in terms of observable quantities, our results apply to all geometric theories of gravity that admit stationary solutions, including the commonly discussed f(R) class of theories.