text:
How to listen to Radiohead in chronological order
By Andrew Murphy published 5 June 20
All the albums, EPs, soundtracks and solo works
(Image credit: Radiohead)
If you're one of those who takes delight in traversing a band's catalogue to witness some kind of sonic evolution, then you'll find few as sprawling and diverse as that of Radiohead.
This Oxfordshire quintet – formed of Thom Yorke, Jonny Greenwood, Ed O'Brien, Colin Greenwood and Philip Selway – have become undeniably one of the most successful bands in the world, and if not definitively the best then certainly in the top one.
Their canon can be rather daunting to a first-time listener, however. It is vast, not exactly teeming with hit singles – despite six UK No1 albums, Radiohead have never topped the singles charts – and its stylistic reach is about as wide as you can get without sounding disjointed. And that's before you get to all the solo work, soundtracks and the attic full of B-sides.
That's why we put together this guide, as recently we did for the music of David Bowie, to hold your hand along a journey from 1992 to the present day. We'll cover every release from every member of the band and, while some aren't available on streaming services, any that are have made their way to our dedicated Spotify and Tidal Radiohead playlists.
So whether this is your first time listening to something other than Creep, or you're just here to pick up a little trivia on your favourite album, make yourself comfortable. We've a lot to get through.
Listen to Radiohead in chronological order on Spotify or Tidal.
Test your Radiohead knowledge by completing the lyrics to these singles
TL;DR: a brief introduction to Radiohead
Don't fancy tackling Radiohead's entire catalogue in one go? These ten tracks will introduce you to the band's nine albums.
Creep (1992) Preceded only by a 3000 CD run of the Drill EP earlier in 1992, Creep became an anthem for the alienated, peaking at No7 in the UK charts, and in truth still stands out for its combination of complexity and melody among Radiohead's earliest work.
My Iron Lung (1994) A first taste of The Bends, a decidedly more accomplished, mature and complete second album. Not stylistically dissimilar from what came before, but a more spacious and careful set of arrangements.
Talk Show Host (1996) Undoubtedly Radiohead's most famous B-side, Talk Show Host appeared on Street Spirit (Fade Out) and hinted in January 1996 at some of the experimentation and dark minimalism to be expected from OK Computer and beyond.
No Surprises (1997) The first track recorded for OK Computer, and the version used is the very first take. The group's trademark dissonance is evident in the pitch-black lyrics set against a cradling lullaby.
Kid A (2000) The album Kid A was hugely experimental and heavily reliant on electronics, and was not promoted by any singles. Its title track here is about as far from the mainstream as the group could imaginably veer.
I Might Be Wrong (2001) Proof of the band's ability to be playful with instrumentation and arrangement while still delivering an infectious hook, I Might Be Wrong featured on Amnesiac, released only eight months after Kid A.
There, There (2003) The lead single from the album Hail To The Thief, in many ways signaling Radiohead's return to a more familiar, guitar-led sound – or at least weaving it in more generously to the sound developed on their previous two records.
Reckoner (2007) Some spacious arrangements and light-fingered production benefited a collection of songs that had debuted on a tour leading up to the release of Radiohead's seventh album, In Rainbows. None more typified the approach than Reckoner, easily a standout track with its gliding melody and communal percussion.
Bloom (2011) Ensuring fans couldn't assume the band were mellowing after a fifth No1 album, Radiohead returned with perhaps their most aggressively experimental record to date when they released The King Of Limbs, its opener being Bloom.
True Love Waits (2016) First performed way back in 1995, True Love Waits was an unreleased live favourite for more than two decades before a studio recording finally appeared on A Moon Shaped Pool – at the fourth time of asking.
Pablo Honey (1993)
The story of Radiohead really goes back as far as 1985, when the group first began rehearsing at Abingdon School in Oxfordshire. Thom Yorke and bassist Colin Greenwood were friends in the same school year, guitarist Ed O'Brien and dummer Philip Selway were in the year above and Jonny Greenwood – Colin's brother – was two years below.
Initially named On A Friday, after the afternoon on which they'd rehearse, their performances and demo albums were enough to attract the ear of Parlophone Records in 1991, and on 5 May the following year the band released their first EP under their new, Talking Heads-inspired moniker.
The lead track from the Drill EP, Prove Yourself, did receive some national radio play, but its 3000-strong CD release meant most people wouldn't hear its contents until three of the four songs were included on Radiohead's debut album.
Far more enduringly popular was the band's second release, Creep, though Radiohead's biggest-selling single only made its way to No78 in the UK charts after an initial release in September 1992 – not entirely aided by minimal radio play due to its depressing nature.
In fact, Radiohead would have to release the single Anyone Can Play Guitar, debut album Pablo Honey and non-album single Pop Is Dead – all in 1993 – before a rerelease of Creep in September finally became the group's first top 10 entry when it reached No7.
That in turn helped with sales of Pablo Honey, which peaked at No22 – and but for the release in some territories of Stop Whispering as a single in October, and the Japan-only Itch EP in June 1994, it was rapidly onto the next chapter as far as the band was concerned.
Radiohead releases 1992-1994 (Albums and singles/EPs)
Drill EP; Creep; Anyone Can Play Guitar; Pablo Honey; Pop Is Dead; Stop Whispering; Itch EP.
The Bends (1995)
There was definitely something other about My Iron Lung when it was issued as a first taste of Radiohead's second album in September 1994.
There wasn't so much a change of direction, but a more mature and careful crafting of the songs, along with John Leckie's surer and more spacious production, made for the sound of a band seemingly more comfortable in its skin.
Fans would have to wait another five months before more music was released, though. High and Dry and Planet Telex became a lead double A-side on 27 February but on 13 March both second album The Bends and debut live film Live at the Astoria made the wait worthwhile.
Becoming the band's highest-charting release when it peaked at No4, The Bends is also significant for being the first Radiohead album to feature cover art created by Stanley Donwood.
As with Nigel Godrich – who's first production credit with the band would come two years later – Donwood's work has been present on every one of the band's releases since.
Three more tracks from the album were released as singles over the following year: Fake Plastic Trees (a song written by Yorke pre-Radiohead), Just and Street Spirit (Fade Out).
Not only did that last score the band their first top five single – only four more have followed since – but it included Talk Show Host as one of its B-sides. Sparse and darkly minimal, in hindsight it was perhaps the most explicit indication of what was about to come.
My Iron Lung EP; High and Dry / Planet Telex; The Bends; Fake Plastic Trees; Just; Street Spirit (Fade Out).
OK Computer (1997)
On 21 May 1997, Radiohead released OK Computer. Produced by Nigel Godrich, it shifted the band's positioning from slightly obscure, relatively complex five-piece guitar music to a more daring and inventive sound rife with creativity while still melodious enough to conquer a world stage.
Indeed, Radiohead were no longer mainly a UK-based success. OK Computer topped the charts at home, but also reached No21 in the USA and won the Grammy for Best Alternative Album.
A few days later came the release of Paranoid Android as the record's lead single – which achieved the band's highest chart position to date when it reached No3 – and then in August Karma Police, which as one of its B-sides contained Meeting In The Aisle, Radiohead's first-ever instrumental offering.
A combination of diversity and the strength of every song on the album meant different tracks could be used as singles worldwide; Lucky was released in France in December 1997, while the No Surprises / Running From Demons EP was used to promote the band's upcoming tour in Japan.
This was also the period during which Yorke's voice was beginning to be heard on other artists' material – firstly on a collaboration with Sparklehorse for EMI's 1997 Come Again compilation that celebrated the label's biggest releases. Yorke sang his part of Wish You Were Here down the phone while on tour, and the Pink Floyd cover also appeared as a B-side to Sparklehorse's Maria's Little Elbows in 1998.
After Radiohead released No Suprises worldwide in January 1998, Yorke was again heard on someone else's track in April – this time Drugstore's El President, released the day before an EP of OK Computer B-sides – then again in August on UNKLE's Rabbit In Your Headlights.
In October, the UK first saw Todd Haynes's glam-rock movie Velvet Goldmine, which was produced and featured a curated soundtrack by R.E.M.'s Michael Stipe. Having toured with Radiohead, Stipe got Yorke and Jonny Greenwood to collaborate with Suede's Bernard Butler and Andy Mackay of Roxy Music to cover five of the latter's songs.
Yorke was in fact also approached to write the score for David Fincher's adaptation of the Chuck Palahniuk novel Fight Club, but declined to recover from promoting and touring OK Computer.
The madness and wonder of that period is well encapsulated in the documentary film Meeting People Is Easy – released on 30 November 1998, losing out to Jimi Hendrix for the Best Music Film Grammy – a toll it would take more than a year to pay.
OK Computer; Paranoid Android; Karma Police; Lucky; No Surprises / Running From Demons; Airbag / How Am I Driving? EP.
Kid A (2000)
The new millennium began with Radiohead having been dormant for more than a year, and when they did return it was with the resolve to do pretty much the opposite of what happened with OK Computer.
After Yorke had given his voice to I've Seen It All in July – a track from Björk's Dancer In The Dark soundtrack – Radiohead released Kid A on 2 October 2000.
A potentially alienating array of experimentation and heavy use of electronics, with no promotional singles or music videos, it inevitably shot straight to No1 in both the UK and the States and scooped a second Best Alternative Album award at the Grammys.
It wasn't that Radiohead tried to release this record under the radar, though; they were simply using means that at the time were extremely forward-thinking. Namely, the internet.
The album was available to stream online, along with some short animated films including the album's music and artwork, while bootlegs of early performances were up on file-sharing websites and the record was also leaked early.
Later the same month PJ Harvey would release her album Stories From The City, Stories From The Sea, which featured Yorke singing on three tracks – This Mess We're In, One Line and Beautiful Feeling – and beat Radiohead's Amnesiac to win the Mercury Music Prize the following year.
Radiohead releases 2000 (Albums and singles/EPs)
Kid A.
Amnesiac (2001)
Eight months is all we had to wait for Radiohead's next record, Amnesiac.
Often regarded as a kind of sister album to Kid A, it continued challenging listeners with its experimental arrangements but without forgoing deep hooks and often hauntingly beautiful melodies.
Preceded by the single release of Pyramid Song a couple of weeks earlier, Amnesiac became Radiohead's third UK No1 album and reached No2 in the US when it came out on 4 June 2001.
The only other official release from the album was Knives Out in August, but the band released their first live album – a collection of performances of songs from Kid A and Amnesiac – in November.
Alongside those album tracks – including a stunning piano version of Like Spinning Plates – I Might Be Wrong: Live Recordings closed with a performance in Oslo of live favourite True Love Waits, its first inclusion on any release.
Though there would be no further Radiohead releases for another two years, Ed O'Brien and Philip Selway featured in Neil Finn's 7 Worlds Collide project, a collective that released a self-titled live album in November 2001 – and who would enter the studio a few years later.
Pyramid Song; Amnesiac; Knives Out; I Might Be Wrong: Live Recordings.
Hail To The Thief (2003)
Those disappointed by Amnesiac, having hoped for a return to Radiohead's more guitar-led roots, are likely to have been delighted when There, There became the lead single from the band's sixth album, Hail To The Thief.
The single reached No4 in the UK – the last time to date Radiohead have broken the top ten – but was not wholly telling of the record that was to follow. Rather than a regression to a previous style, Hail To The Thief married live band recordings – as opposed to overdubs – with the synthesized sounds that had dictated their previous two albums.
Alongside it came The Most Gigantic Lying Mouth Of All Time. Brought out on DVD on 1 December 2004, this collection of 24 short films directed by Chris Bran was designed initially for a four-episode run on regular TV. Instead, Radiohead launched their own online TV channel on 26 May 2003, with the episodes beginning on the hour – those who turned up late would be faced with a test card and 1970s-style intermission music.
The album, released on 9 June, debuted at No1 in the UK and No3 in the States, with Go To Sleep and 2 + 2 = 5 both charting as singles later in the year.
The year is also significant in the career of Jonny Greenwood specifically, being the year he released his first film score – for Simon Pummell's BAFTA-winning documentary Bodysong – before a 2004 EP featuring the B-sides and outtakes from Hail To The Thief, named COM LAG (2plus2isfive), was the final Radiohead release for another three years.
After a fallow year in 2005, but for the inclusion of I Want None Of This on the War Child charity album Help: A Day In The Life, Radiohead fans were at least treated to some solo work before Radiohead's next album.
On 10 July 2006 came Thom Yorke's solo debut, The Eraser. Charting at No3 in the UK and No2 in the US, its connection to Radiohead is strengthened by Nigel Godrich's production and artwork by Stanley Donwood, but there is an intimacy that distinguishes this electronics-led record from the band's catalogue.
Two tracks – Harrowdown Hill and Analyse – were released as singles, and their B-sides were included on the Spitting Feathers EP that November. Yorke also featured on Modeselektor's Happy Birthday! album in 2007, on the track The White Flash, shortly before Radiohead released their first album since leaving Parlophone.
There, There; Hail To The Thief; Go To Sleep; 2 + 2 = 5; COM LAG (2plus2isfive) EP.
In Rainbows (2007)
Without a label, having left EMI-owned Parlophone Records, Radiohead were free to release In Rainbows whenever they wanted – 10 October 2006, as it happens – and fans were free to pay whatever they wanted for it.
Initially self-released online on a pay-what-you-like basis, lore is that In Rainbows was actually more financially successful than major-released Hail To The Thief – even before it was afforded a physical form by XL Recordings the following year.
Parlophone, who still owned the band's back catalogue at the time, also released the Radiohead Box Set – all previous albums on seven CDs or a 4GB USB stick – on 10 December 2007 to piggyback on XL's physical release.
Despite no singles having been released at this point, the songs on In Rainbows were far from alien to fans, with Radiohead having performed most of them on a tour leading up to the album's release, and the record duly topped the charts on both sides of the Atlantic.
Also making waves in December 2007 was Paul Thomas Anderson's There Will Be Blood, a period film based on Upton Sinclair's novel Oil!, for which Jonny Greenwood wrote the score – starting a hugely fruitful partnership between the Oscar-nominated director and Radiohead guitarist.
It was largely a year of promotion in 2008, with the band now backed by XL, with Jigsaw Falling Into Place and Nude put out as singles. For the latter, the band made stems available online so fans could remix the track at home – something they would do again later in the year for the release of Reckoner.
Between those two singles, though – after another Parlophone-released Best Of album and DVD – was a first proper peak inside Radiohead's natural habitat with the release of In Rainbows: From The Basement, as well as collection of remixes from Yorke's The Eraser.
Yorke and Björk collaborated again on the latter's charity single Náttúra in October 2008, before Radiohead released two new singles in August the following year.
The first was Harry Patch (In Memory Of), a £1 digital download with all proceeds going to the Royal British Legion, and that was followed by a free download of These Are My Twisted Words.
Also that month came the debut studio record from the 7 Worlds Collide collective. Titled The Sun Came Out, it again featured performances by Selway and O'Brien as well as songs written by the pair.
Ed O'Brien wrote Learn To Crawl for the album with Johnny Marr and Liam and Neil Finn, as well as Bodhisattva Blues again with Liam Finn; Philip Selway wrote and sang The Ties That Bind Us and The Witching Hour, and wrote 3 Worlds Collide with Glenn Kotche and Neil Baldock.
The torch passed once again to Yorke in September, who gave us the singles Feeling Pulled Apart By Horses – a track of which an early version became Reckoner – and Hearing Damage, written for the Twilight soundtrack. In May 2010 he teamed up for the first time with Flying Lotus, co-writing the track ...And The World Laughs With You for the American musician's album Cosmogramma.
Also in 2010 came Selway's first solo releases with the single By Some Miracle and subsequent album Familial, before the year closed with another Jonny Greenwood score – this time for Tran Anh Hung's Norwegian Wood.
In Rainbows; Jigsaw Falling Into Place; Nude; Reckoner; Harry Patch (In Memory Of); These Are My Twisted Words.
The King Of Limbs (2011)
Having released probably their most mainstream-friendly album since 1997's OK Computer when they brought out In Rainbows, Radiohead again turned their back on the popular vote with probably their least accessible record to date.
Debuting on 18 February 2011, The King Of Limbs is far from being bereft of melody or traditional structure, but its sprawling rhythms and off-kilter arrangements are not exceedingly radio friendly.
There were no singles as such, and it became the first Radiohead album since 1995's The Bends not to top the UK charts. It was also the first to do better in the USA than on home soil, ranking four places higher at No3 on the Billboard list.
Those singles were effectively replaced by remixes. After Yorke had released the double A-side Ego / Mirror with Burial and Four Tet, and Radiohead's Supercollider / The Butcher came out for 2011's Record Store Day, TKOL RMX1 began a series of eight remix releases.
Compiled on the record TKOL RMX1234567, tracks from The King Of Limbs were reworked by producers and collaborators such as Caribou, Nathan Fake, Four Tet, Jamie xx and Objekt, cementing the record's status as music for musicians.
Also providing a TKOL RMX were Modeselektor, who invited Thom Yorke to feature on two tracks – Shipwreck and This – from their album Monkeytown, which came out that September. That was followed the next month by yet another impeccable Jonny Greenwood score, for We Need To Talk About Kevin.
A prolific year ended with a double release: The Daily Mail / Staircase single and another live video, The King Of Limbs: From The Basement.
The first Radiohead-related release of 2012 was a collaboration between Jonny Greenwood and Polish composer Krzysztof Penderecki. Recordings of Penderecki's early 1960s pieces Threnody for the Victims of Hiroshima and Polymorphia are each followed by Greenwood's responses, Popcorn Superhet Receiver and 48 Responses to Polymorphia respectively.
And more Greenwood shortly followed, with his score for Paul Thomas Anderson's The Master, before we were first introduced to Atoms For Peace.
A band formed to perform Thom Yorke's solo work on tour, and eventually named after one of those songs, Atoms For Peace features Red Hot Chili Peppers bassist Flea and Radiohead producer Nigel Godrich on keys.
The collective released their first single Default in September 2012 – a week before Yorke and Jonny Greenwood appeared on Flying Lotus's album Until The Quiet Comes – and followed it up with Judge, Jury and Executioner in January. Their first and to date only album, Amok, was released on 25 February 2013, peaking at No5 in the UK and No2 in the US charts.
There were three Radiohead solo projects in 2014: first Thom Yorke released his second album Tomorrow's Modern Boxes, followed by Philip Selway's Weatherhouse and Jonny Greenwood's Inherent Vice score, before Yorke sandwiched those with the single YouWouldn'tLikeMeWhenI'mAngry.
Perhaps the most interesting and even most accomplished of Greenwood's non-Radiohead work came when the guitarist travelled to India to work with Israeli composer Shye Ben Tzur and local folk group the Rajasthan Express.
Released in November 2015, Junun was recorded at Mehrangarh Fort in Rajasthan, fusing the influence of all three components for an album that sounds far more cohesive than describing it would have you believe. Produced again by Godrich, it was also filmed by Paul Thomas Anderson for a worthy documentary release.
One track you won't hear on film, however, is Radiohead's Spectre. Recorded to lead the soundtrack for the James Bond film of the same name, after OK Computer outtake Man Of War was rejected due to being ineligible for a Best Original Song Oscar, it was discarded for being too melancholy and replaced by an offering from Sam Smith.
Nonetheless, the band let it out as a free download on Christmas day 2015.
The King Of Limbs; Supercollider / The Butcher; TKOL RMX1234567; The Daily Mail / Staircase; Spectre.
A Moon Shaped Pool (2016)
Within the space of a week at the beginning of May 2016, Radiohead collectively returned with the singles Burn The Witch and Daydreaming, and their ninth studio album A Moon Shaped Pool.
It provided a sixth UK No1 for the band, also charting high at No3 in the US, no doubt helped by its more accessible lead singles and the long five years since The King Of Limbs.
The highlight for many fans, however, was the inclusion of True Love Waits. More than 20 years after it was first performed – and after failed attempts to include it on OK Computer, Kid A and Amnesiac – the band and Godrich had finally found an arrangement that worked not only for the song but also for the temperament of the album.
Thom Yorke appeared on the track Beautiful People for Mark Pritchard's album Under The Sun a week later, before global touring meant another year-long wait for anything new from the band.
And when it came, it was another victory for those yearning for older tracks. Celebrating the 20th anniversary of their third record, OK Computer OKNOTOK 1997-2017 was released on 23 June. It included the original album, all the B-sides from the album's singles alongside previously unreleased outtakes I Promise, Man Of War and Lift.
Between that and the band's next release – the single Ill Wind in January 2011 – attention turned to a number of soundtracks. First came Philip Selway's for Let Me Go, then was a double of You Were Never Really Here and Phantom Thread from Jonny Greenwood, before Thom Yorke's first score the remake of cult horror classic Suspiria.
After Ill Wind, Yorke released a download-only EP of outtakes from his Suspiria soundtrack before his computer was hacked and hours of Radiohead demos, performances and rehearsals were distributed online.
It led to Minidiscs (Hacked), an official download of all the stolen files made available for 18 days via Bandcamp with all proceeds going to Extinction Rebellion, at the end of which Yorke released his third solo album ANIMA on 27 June 2019.
ANIMA was teased with cryptic posters in around the world advertising Anima Technologies, a company claiming to be able to recover lost dreams. Calling the advertised number led to a prerecorded message that said Anima Technologies had been seized after unlawful activities, before playing part of the track Not the News.
Whether that advertising was successful or not, Yorke made it to No5 in the UK album charts, and backed it with a Not The News Rmx EP on 2 August. A final release of 2019 featured on the soundtrack to Motherless Brooklyn, another collaboration with Chili Peppers bassist Flea on Daily Battles.
And so we arrive at the latest installment of this group's vast and running catalogue. On 4 October 2019, the track Santa Teresa was released under the name EoB – namely the long-awaited solo debut of guitarist Ed O'Brien.
His album Earth was released on 17 April 2020, featuring a certain Colin Greenwood playing bass on the single Brasil as well as turns from artists such as Omar Hakim and Laura Marling.
As for Radiohead, Selway has been quoted as saying the group planned to work away from each other in 2020 – something which became inevitable due to the global pandemic – so it is likely to be next year at least before this list is added to with any new material.
That said, with Radiohead, you never really know.
Radiohead releases 2016-present (Albums and singles/EPs)
Burn The Witch; Daydreaming; A Moon Shaped Pool; I Promise; Man Of War; OK Computer OKNOTOK 1997-2017; Ill Wind.
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Wyldehoarne is een in aanbouw zijnde woonwijk in Joure uit de jaren 2000 en jaren 10 van de 21e eeuw. In de toekomst moet de wijk het gebied beslaan tussen de Koarte Ekers, Wildehornstersingel, Haskerveldweg en de wijk Skipsleat. De naam van de wijk betekent "wilde hoek".

Geschiedenis
In 1997 komt de gemeente Skarsterlân een nieuwe woonwijk aan ten oosten van Skipsleat. De wijk wordt genoemd naar het gehucht Wildehorne of Wildehornsterpolder dat oorspronkelijk tussen Haskerhorne en Westermeer lag. Het is de bedoeling dat in de wijk 500 tot 600 woningen gebouwd worden. De nadruk zal meer op groen liggen dan op water, zoals in Skipsleat. Ook komen de huizen dichter op elkaar te staan.

Op het moment dat de plannen voor Wyldehoarne gemaakt worden, is de vraag naar woningen hoog. Bij de bouw van Wyldehoarne in 2002, zakt de woningmarkt in. De plannen worden op een lager pitje gezet. De woningmarkt trekt later weer iets aan, maar aan het eind van het decennium ontstaat de kredietcrisis waardoor de woningverkoop op slot komt te zitten. In 2009 wordt de bouw van de volgende fasen van Wyldehoarne voor onbepaalde tijd afgeblazen.

Waterwoningen
In 2001 worden plannen gepresenteerd voor 48 waterwoningen in Wyldehoarne. Het is op dat moment een uniek project in Friesland en trekt de aandacht van verschillende media.  De meeste huizen in dit plan staan op palen, hebben geen tuin en zijn enkel per loopplank bereikbaar. Zes van deze woningen drijven daadwerkelijk. Het is een duidelijke breuk met de bouwstijl van de voorgaande wijk Skipsleat. De huizen in dit plan zouden gebouwd worden aan drie pieren die een gebogen vorm hadden. Toch is er weinig animo voor de geplande waterwoningen. In 2004 maakt de gemeente bekend dat er "een minder ambitieus plan" voor het gebied is ontworpen. Dit wordt de straat It Reidlân waarin twee-onder-een-kapwoningen met tuin komen te staan.

De wijk
De wijk bestaat uit verschillende deelgebieden met elk een eigen karakter. Aan de zuidwestkant van Wyldehoarne speelt water een grote rol, aan de oostkant voert groen de boventoon. Het stratenpatroon is rechtlijniger dan eerdere wijken als het Schepenkwartier en Skipsleat. De voornaamste verkeersader in Wyldehoarne is Oer de Feart (Fries voor "aan de andere kant van het water"). Dit is de enige weg die verschillende deelgebieden met elkaar verbindt. Bij voltooiing van de wijk, moet Oer de Feart een driehoeksvorm krijgen.

In het deelgebied in het zuidwesten hebben straten Friestalige namen als De Bleek en It Hiem. Huizen in dit gebied zijn vrijstaande- of twee-onder-een-kapwoningen. Ten noorden hiervan ligt een deelgebied dat omsloten wordt door water. Straatnamen zijn Nederlandstalig en bestaan uit een vrouwennaam met het achtervoegsel -hoeve, zoals Aliehoeve en Jannahoeve. In dit deelgebied staan onder meer huizen aan het water en rijtjeswoningen.

Vogelbuurt

Aan de noordkant van de wijk ligt een vijftal eilanden. Elk eiland is genoemd naar een vogel, zoals De Mosk en De Markol. De gemeente Skarsterlân wilde dat de buurt de meest vogelvriendelijke van Friesland werd. Om dat te bewerkstelligen waren nieuwe bewoners verplicht drie nestkasten in hun gevels te verwerken en kregen ze een lidmaatschap van de Vogelbescherming Nederland. Ook werd in de buurt een 30 meter lange oeverzwaluwwand geplaatst. De buurt werd in 2009 genomineerd voor de Stadsvogelprijs van de Vogelbescherming Nederland. De prijs ging uiteindelijk naar Leiden.

De buurt, die rond 2008 gebouwd is, staat bekend als duurzaam. Autowassen is er verboden, regen stroomt via goten terug naar het oppervlaktewater en huizen worden verwarmd door aardwarmte en zijn daarom niet aangesloten op het aardgasnet. Bewoners kregen snel een goedkope bouwvergunning van de gemeente als ze beloofden hun woning milieuvriendelijk te bouwen.

Voorzieningen
Wyldehoarne beschikt over weinig eigen voorzieningen. Er is bijvoorbeeld geen school in de wijk. Waarschijnlijk zal die er ook niet komen. Wel horen het Jouster strandje en naastgelegen fierljepschans, die al bij de bouw van Skipsleat zijn aangelegd, sinds enkele jaren officieel bij Wyldehoarne.

Galerij

Wijk in De Friese Meren

redpajama_set_name: RedPajamaWikipedia


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I remember with my first child, knowing the exact day that I could start using some new piece of equipment. For example, the bumbo seat has a manufacturer suggested age of 1 month, or when a child can support their own head. With my oldest, that thing would have put away until the second she turned 1 month and then she'd be in it. Not a day before, not a date late.
This go 'round I totally forgot about the bumbo seat. The other day I happen to see one in a picture and I thought to myself, "OH YEAH!! I totally forgot about that, I wonder when Lizzie can go in it". So off to google I went and lo and behold she could have been in it like 2 months earlier. Woops. Not that that's a bad thing, I just forgot.
But she likes it, see... even if I am a little late.
After that revelation I asked myself what else I needed to get out of the attic.
The exersaucer, of course! My other two LIVED in that thing!
So off to google again I went to see the age range on that thing... approximately 4 months to walking.
Which clearly means nothing to me because I decided to put her in it with a towel wrapped around her to keep her steady. (shh don't tell). See, back with child #1 I wouldn't think of putting my child in early; "oh no! But it clearly says 4 months, my daughter isn't 4 months yet, so I can't!".
Along the same lines, but not "equipment"-wise; I was at a birthday party today with all 3 girls and when it came time to feed Lizzie, I got my nursing cover and started to feed her. Until I didn't want to miss out on all the conversations so I got up and was feeding Lizzie while walking around (with the nursing cover).
One of the mom commented that she could tell I was on #3 because with #1, breastfeeding would require the glider, with the gliding foot rest, and the boppy.... by #3 you are so practiced that you can do it while walking around keeping an eye on your other children at a birthday party. I just smiled; you do what you have to do.
JUST like the Luvs diapers commercials - 1st child vs 2nd child. PS - love these commercials!
So true, and what's perhaps even more devastating is that there's been so little support to help the community rebuild.Cruise Tips.
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text:
En programmation informatique, un bug logiciel inhabituel est un bug considéré comme très difficile à détecter et à réparer. Il en existe plusieurs types souvent désignés d'après le nom de scientifiques qui ont découvert des principes non intuitifs.

Selon la nature, la probabilité d'apparition ou la gravité, on trouve ainsi :
 Schrödinbug ;
 Heisenbug ;
 Bohr bug ;
 Mandelbug.

Schrödinbug
Un schrödinbug (ou schroedinbug, graphie beaucoup plus courante en anglais) est un bug qui n'est pas découvert et non gênant pour les utilisateurs, mais qui apparaît après que quelqu'un a relu le code source ou utilise le logiciel d'une façon non habituelle.

Un autre cas de schrödinbug peut se produire lorsque le programme de débogage comporte lui-même un léger bug, et, lorsqu'il est utilisé pour tester un programme, donne le résultat qu'un bug est présent dans le programme testé, alors qu'en mode de fonctionnement effectif, ce bug n'existe pas. À l'inverse, il arrive qu'un bug, détecté lors d'un traitement effectif, n'apparaisse plus lorsqu'il est testé au moyen d'un programme de débogage.

Étymologie
Le mot schrödinbug est un mot-valise composé de « Schrödinger », nom du physicien inventeur du concept du Chat de Schrödinger, et de «  ».

Heisenbug
Un Heisenbug est un bug difficile à localiser parce qu'il ne se manifeste pas lorsque des outils de détection sont utilisés pour le rechercher. En électronique, le terme traditionnel est effet de sonde.

En pratique, on retrouve l'un des trois cas suivants :
 le programme tourne sous le débogueur, mais pas sur la ligne de commande
 le programme fonctionne compilé en mode normal, mais pas lors d'une compilation avec optimisation
 le programme marche quand on rajoute des affichages pour déboguer, mais pas quand on les enlève

Une cause courante est la présence d'une situation de compétition, un ralentissement de tout ou partie de l'exécution pouvant conduire à déséquilibrer la compétition, qui est alors masquée, et le problème avec.

Un Heisenbug peut aussi apparaître si le principe de séparation requête-action n'est pas respectée, une routine appelée plusieurs fois peut alors retourner des valeurs différentes, créant alors une situation de compétition pouvant être difficile à reproduire.

Une autre source est l'oubli d'initialisation de variables locales. En mode débogage, les valeurs seront par exemple placées sur la pile, alors qu'en mode optimisé, elles seront placées directement dans les registres du processeur. Une variable qui est utilisée avant d'être assignée aura alors un état indéfini, mais différent dans les deux cas. Les effets peuvent être indirects, par exemple un indice de tableau incorrectement initialisé (mais correct en termes d'étendue, par exemple un zéro), pourra entraîner une écriture dans une mauvaise cellule, ce qui déclenchera le bug plus tard au cours de l'exécution.

Dans les langages à gestion de mémoire manuelle, un Heisenbug peut provenir d'une gestion de la mémoire incorrecte, propice aux fuites de mémoires et à l'écrasement éventuel de données. Les données écrasées seront alors « circonstancielles ». Il s'agit d'une cause commune dans les langages tels que C++.

Exemple
Sous Visual C++, il existe un mode debug (pour la mise au point d'un programme) et un mode release (la version de production généralement). Le mode debug a la fonction de réserver plus de mémoire qu'il n'en faut réellement. Ce comportement implique que le programme en mode debug plantera rarement, alors qu'en mode release, le programme plantera systématiquement à cause d'un débordement de pile. Il s'agit d'un Heisenbug car lorsqu'on veut l'analyser, il faut passer en mode debug, ce qui le fait disparaître…

Étymologie
Le nom Heisenbug est inspiré du principe d'incertitude d'Heisenberg, défini en physique quantique, qui constate qu'observer une structure modifie son état.

Bohr bug
Un Bohr bug est un bug qui, à la différence des heisenbugs, ne disparaît ni n'a ses caractéristiques modifiées lorsqu'il est recherché.

Étymologie
Un Bohr bug est persistant et appelé du nom du modèle atomique de Niels Bohr.

Mandelbug
Un mandelbug est un bug dont les causes sont si complexes que son comportement apparaît chaotique; il le reste tant que le testeur n'arrive pas à établir précisément un comportement déterministe d'apparition du bogue. L'emploi de ce terme signifie également qu'il est plus probablement un Bohr bug qu'un heisenbug.

On peut avancer, d'après le même principe que celui du test de Turing, que s'il n'y a aucun moyen de juger si le comportement d'un bogue apparaît seulement chaotique ou est réellement chaotique, alors il n'y a pas de pertinence dans la distinction entre un Bohr bug et un heisenbug, puisqu'on ne peut pas les déterminer.

Étymologie
Le mot est issu de la fusion de « Mandelbrot », nom de l'inventeur des fractales variables, et de « bug ».

Notes et références

Articles connexes
 Bug (informatique)
 Hacker

Bug
Jargon informatique
Terminologie de l'informatique


text:
Q: Aggregate JSON values by keys I have a bunch of dynamic survey results stored in a table with a JSON column that looks like so:
{"regional":"never","local":"sometimes","personal":"often","bike":"field_4","walk":"field_5","carpool":"field_4","carshare":"often","rideshare":"sometimes"}

The keys are values that exist dynamically throughout the dataset. I need to find an efficient way to aggregate the keys and count the correlated results. This data represents a Likert scale survey question ie.
"How often do you go to the bus station? Not Often, Sometimes, Very Often"
The resulting dataset I'd like to produce is:
{
    "regional": { "sometimes": 20, "often": 10, "never": 5 },
    "bike": { "sometimes": 20, "often": 10, "never": 5 }
    "walk": { "sometimes": 20, "often": 10, "never": 5 }
}

I've attempted JSON_EACH to break the values into key/value pairs but I'm now having trouble aggregating the keys and frequency of potential results. This is what I have so far:
  SELECT
    json_data.key,
    json_data.value
  FROM
    "SubmissionData" AS sd,
    JSON_EACH_TEXT(sd.data) AS json_data
  WHERE
    sd.key = 'transit'

Definitely hit a roadblock here though.
Thanks.

A: Use json_object_agg(), e.g.:
with my_table(data) as (
values
    ('{"regional":"never","local":"sometimes","personal":"often"}'::json),
    ('{"regional":"often","local":"sometimes","personal":"often"}'::json)
)

select json_object_agg(key, vals)
from (
    select key, json_object_agg(value, count) vals
    from (
        select key, value, count(*)
        from
            my_table,
            json_each_text(data)
        group by 1, 2
        ) s
    group by 1
    ) s;

                                              json_object_agg
------------------------------------------------------------------------------------------------------------
 { "regional" : { "never" : 1, "often" : 1 }, "personal" : { "often" : 2 }, "local" : { "sometimes" : 2 } }
(1 row)

redpajama_set_name: RedPajamaStackExchange


text:
Homexbox series sXbox Series S | One Week Later
Xbox Series S | One Week Later
Sri Kandula November 17, 2020
Launch week has come and gone, leaving a few people happy as hell about their brand new consoles and a lot more people angry about low stock in stores, online waiting lines, and bloodthirsty scalpers. The GW&CO team has been lucky enough to pick up an Xbox Series S and a PlayStation 5 to ensure we have full coverage of the latest generation of systems so whether you already picked one up or are waiting until the next restock, you can still be a part of the conversation. Now, personally speaking, I got my Xbox Series S on launch day, November 10, and while I don't think one week is enough time to accurately review an entire system, I still wanted to share my thoughts on this tiny new Xbox that a lot of media outlets seem to be overlooking despite it being the console that I'd bet most average consumers have an interest in. So here are my initial thoughts on the Xbox Series S, one week after release.
To start off, let's talk about hardware. The Xbox Series S is a really nice looking console and it's apparent right from the unboxing experience. The matte white is the same color as the Xbox One S and just like its predecessor, the Series S stands out against a lineup of black consoles, TVs, and monitors. The console can be sat both vertically and horizontally, though the Xbox logo on the power button suggests that it's meant to really be horizontal. That being said, due to the arrangement of my desk, I have to put the system standing up and it still looks fine despite what the speaker memes said. Microsoft has been marketing the Series S as the smallest Xbox ever and a byproduct of that is a super portable yet confidently dense console. It really is impressive the performance that is packed into this small machine and I occasionally pick it up from my desk just to feel its premium build quality.
On the note of build quality, I have two gripes with the physical system. The first is that the back corner panel has some give. I first noticed this when setting up my console on launch day and it's one of those things you can't unsee once you know it's there. Pressing against this particular part of the console makes the panel flex. This is more jarring considering how sturdy the rest of the system is. Another thing that I can't quite unsee, and is more of a problem for me and not for someone who has the system all the way across the room under their TV, is that due to the ventilation holes on the right side of the console (when placed horizontally) the light from the Xbox power button often shines through. This is even more noticeable when I'm playing games with the lights turned off. I have the system arranged in a way that I can't see the lit-up Xbox logo when turned on but I can still see the light seeping through the holes and it makes me wish they just put a small panel there to prevent that light leak.
Moving over to the controller, the Xbox Series X|S controller is not a substantial redesign from the Xbox One version, and for most players, that's not a bad thing. This new controller has a new d-pad, reminiscent of the one seen on the Xbox Elite Controller, and a textured grip added to the back and triggers. There are some small design changes to make it a bit sleeker and it has a USB-C port instead of micro-USB. Personally, there are two notable changes that I really like with this iteration of the controller. The first is overall build quality which no longer feels loose or plasticy like on the last-gen controller. The other is the share button, a feature that is coming late to Xbox with both DualShock 4 and Joy-Cons from last generation systems having a designated button. As someone who often stops to stare at the views in games, I take so many more photos and videos thanks to the new button. My only negative in regards to the controller has to do with the Series S controller specifically because while an all-white controller may look great right out the box, it also gets noticeably dirtier faster.
That's all well and good but most people are going to spend more time playing on the console than staring at it like me. Luckily, in that department, the system is just as impressive. Though the Series S is less powerful than its older brother, the Series X, it still takes advantage of many of the same features like Quick Resume and fast load times thanks to an internal SSD. Quick Resume is really something that you have to see in person to appreciate and while a lot of players remain skeptical of its practicality, I can say that it has already been useful for me. I often have four games I switch between at any given time, one game that I'm reviewing (Observer: System Redux), one game from my backlog to enjoy on my own time (Far Cry 4), one game to play mindlessly while watching TV (Forza Horizon 3) and one game to play with friends (none at the moment), and going from racing around the streets of Australia in Forza to shooting up Pagan Min's goons in Far Cry 4 in a matter of seconds is truly mind-boggling. And that's not even taking into account the faster load times when booting up a game for the first time. Forza Horizon 3, which normally takes a minute to go from menu to gameplay, takes 36 seconds on Series S. These seconds and minutes may not seem important at the moment, but in the long run, that time adds up.
That isn't to say that there are no hitches. Quick resuming into a game will occasionally cause the game to freeze for a few moments. In Far Cry 4, that freeze is common every time I load into the game. And on one instance, loading in caused a bug where I could not move from where I was. The left analog stick remained functional in menus and I could look around using the right stick, but no amount of button flicking gave me walking controls. This required a restart of the game. And in my first few times of playing Observer, every time I tried to quick resume back into the game it would load from the menu as if I had just opened the game for the first time. This has since been fixed and Quick Resume does now work as advertised with the game. None of these are game-breaking bugs either, other than Far Cry 4 at times though I'm fairly certain some of the bugs I've come across in that game are the game's fault and not the system, and none of those issues have detracted from my overall positive gaming experience.
Okay, now onto how the games look and play. I don't need to reiterate the fact that the Xbox launch line-up isn't too amazing. So the only true "Optimized for Series X|S" game I got to play was Observer: System Redux. Now I'm no Digital Foundry so I can't speak to performance on a technical level, but I can say from just playing the game that it looks really great and plays super smooth. The Series X does have the added benefit of 4K and ray tracing, something that isn't quite there on Series S, but despite that omission, Observer is a really stunning game with some super detailed textures and no performance hiccups to speak of. As for the backward compatibility side of things, Far Cry 4, which I am having a great time with, loads super fast on the Series S. (Which is a good thing because I die a lot in that game.) As someone who has played a lot of open-world games in the past, I'm used to long load times. In fact, every time I hit a load screen I usually put down my controller and pick up my phone to check messages or emails. The first time I really noticed the impact of next-gen was in Far Cry 4 when I picked a fast travel location on the other side of the map and by the time my controller even touched the desk it already loaded. Both in Far Cry and in Forza the performance is great and there are no dropped frames that I noticed.
On top of all that, even while playing those games, the Series S is inaudible. Unless you're right next to the console you will not hear the fan's noise even in heavy loads and with headphones or from across the room it's pretty much nonexistent. That being said, the system does get very hot and as someone who has their system on the desk, its heat can be felt from around a foot away from the black exhaust vent. Because of this, I would suggest you follow Microsoft's guidelines of having a few inches of clearance to the system on all sides. Something I found interesting in my time with the Series S so far was that the night I got it, after installing all the games and testing out a few, I turned off the console (in Instant-On mode), placed the controller on top of the vent, and went to bed. The next morning, when I picked up the controller, it was warm to the touch. This means that even when turned off, the system does occasionally turn on its fans for some reason or another. And even now as I write this, having not used the console in over 12 hours, placing my hand near the vent is a bit warmer than touching my now unplugged Xbox One S.
The last thing I want to bring up is storage. While the Xbox Series S box advertises 512GB storage, in reality, after OS and system functions are taken into account, there is a mere 364GB storage on the system for games. This is an even bigger problem considering the Series S is an all-digital system. Like it or not, you will have to download games and due to the size, you'll also have to manage your resources to decide what stays on the SSD and what gets deleted or booted to an external hard drive. I currently have 7 games installed on my system (Fallout: New Vegas, Far Cry 4, Forza Horizon 3, Nexomon: Extinction, Observer: System Redux, The Witcher 3: Wild Hunt, and Tomb Raider: Definitive Edition) and I have 196GB free space remaining. While I don't have games like Call of Duty: Modern Warfare installed, with its 100GB+ file size, I still have games like The Witcher 3 which comes in at 40GB. For me, the storage on Series S is not an issue and I do have a 1TB hard drive on standby if I need to use it to offload my backward compatible games. That being said, if you think that from your current Xbox One storage situation, 364GB is not enough for you, then I would not recommend the proprietary storage expansion card that costs $219 and instead suggest you just cash out for the Series X. You'll be paying around the same amount in the end plus you'll have a substantially more powerful system with a 4K blu-ray player.
Now usually, in my conclusions, I would summarize the article for those too lazy to read it entirely. But this time around I wanted to throw out a theory. Yes, I do think the Series S is an impressive system but it's severely underpowered when compared to other next-gen consoles. This, along with the two-year plan for Xbox All-Access, leads me to believe that in two to three years, we will see a new Xbox system. It may not be an Xbox Series H (or some other letter) and could simply be an Xbox Series S2, but the idea of Microsoft putting out an upgraded system that, while not entirely up to par with PS5 specs, will put the system at least closer to Xbox One X in terms of GPU power and be a reason for All-Access members to continue their membership for another two years much like phone plans lines up with the games as a service route Xbox is headed in. But until then, as it is now, I can say that the Series S is a tiny gaming machine that is not for the enthusiasts, especially for those who like physical media, but for casual games or PS5 owners who want to play Xbox Game Studios titles via Game Pass, it's a great package with lots of value for its size and price.
favorites first impressions games xbox series s
Posted by Sri Kandula
Sri Kandula is a filmmaker and co-creator of Great White & Co. Former writer for The Daily Collegian and former host of Pop Culture Corner on PSNtv.

redpajama_set_name: RedPajamaCommonCrawl


Kate Walsh fragrance and perfume list.
Kate Walsh fragrances: Kate Walsh in an American actress, who launched her debut fragrance in 2010.
Kate Walsh, born October 13, 1967, is an American actress known for her role as Dr. Addison Montgomery on ABC's Grey's Anatomy and Private Practice, playing the estranged wife of Derek Shepherd played by Patrick Dempsey. She starred in the movies, Bewitched, Under the Tuscan Sun, and The Perks of Being a Wallflower. Kate Walsh founded her beauty and lifestyle company, Boyfriend LLC, in 2010, launching her first fragrance Boyfriend in November 2010 on HSN. She launched her 2nd celebrity fragrance, Billionaire Boyfriend, on July 9, 2012.


text:
Dear Boy aka LA's best kept secret light's up the Teragram Ballroom
Dear Boy at the Teragram Ballroom — Photo by David Fisch
I've been singing the praises of LA's Dear Boy since the release of their first EP back in 2013, and it's been a real treat to see how much they've shaped and refined their sound since then. With a few smashing singles under their belt and a new EP out this year, The Strawberry EP, they have come into their own as LA's best kept secret, a band that confidently taps into influences of the last few decades of punk and pop and coming out roundly vivid and refreshing as a result.
The quartet performed last Thursday at the Teragram Ballroom as a headlining homecoming show, and they milked every minute of that hour-long set. Singer and guitarist Ben Grey opened the set by welcoming the crowd as a family and closed it as such, opening his arms in embrace and practically hugging the air as he swiftly and rather majestically entered into "Limelight," setting the tone for the rest of the evening.
Even with production sounding great and feeling whole on record, it's another thing to see the band perform tracks like "Hesitation Waltz" and "Semester" and "Alluria" live, when their lyrics ranging from light and dark translate harmoniously in the lighting schemes and the musicianship on stage, with each performer sinking into and leaping out of their respective instruments. It's also particularly interesting to see the band essentially extend their songs with dive's into instrumental jams, all of which are performed pretty valiantly.
If you aren't on the Dear Boy train yet, what will it take to convince you?
LA up-and-comers LAUNDER opened for the band, who delivered a pretty compelling set of shoegaze tunes. Given that it was their first show with a new drummer, I can forgive the few onstage mess-ups.
LAUNDER at the Teragram Ballroom — Photo by David Fisch
More Photos: Dear Boy, LAUNDER at Teragram Ballroom
This entry was posted in Live Concerts and tagged Dear Boy, downtown la, indie rock, Launder, Teragram Ballroom, The Strawberry EP on October 14, 2019 by David Fisch.


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In our family, the game of dodgeball has become a kind of moral and ethical template by which we judge people's character.
Last Sunday I was reading the Woman's Sports Pages in the New York Times. For the uninitiated, that's the wedding section; the part where a happy duo smiles blithely and innocently from their cropped photo on the page.
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text:
Last modified 1965 days ago (Feb. 26, 2014)
MCC conforter blitz begins March 10
The Kansas Friends of Mennonite Central Committee will sponsor a comforter blitz again March 10 and 11 at the Journey at Yoder campus one mile north of Yoder.
Participants will tie comforters to be sent overseas. Hand quilting also will be offered.
The blitz runs from noon to 9 p.m. March 10 and from 9 a.m. to 5 p.m. March 11, so those planning to attend through a meal should bring a sack lunch. Donations will be accepted for a chili supper Monday, as well as for sloppy joe sandwiches at lunch on Tuesday.
Participants are encouraged to bring their own scissors, thimbles, needles, and comforter tops and backs, but some supplies will be provided. For comforters, the 60-by-80 inch size is preferred, and the backs should be at least 4 inches larger than the tops.
Baby-sitting is available by reservation. For more information, call Carol Peters at (316) 283-4232 or Lois Leinbach at (620) 327-4119.
Last modified Feb. 26, 2014


text:
\section{Introduction}
The existence of the supermassive black holes, whose masses
range from $\sim 10^6 M_\odot$ to $\sim 10^9 M_\odot$, that
reside in the centers of disk galaxies is gaining a firm
basis observationally (\cite{magorrian98,tremaine02,mh03,
marconi03,hr04,atkinson05,pastorini07,beifiori09,siopis09}).
Such a large-mass black hole (BH) could dissolve a bar
in a barred galaxy that embraces it, as a dynamical
consequence.  This kind of bar dissolution was first
studied by \citet{hn90}, who examined the stellar
orbits moving in combined fixed potentials of a rotating
bar and a central BH in two-dimensional configurations.
Next, \citet{hpn93} extended that work to three-dimensional
configurations.  Both studies showed that central mass
concentrations like massive central BHs can destroy a bar
by converting bar-supporting orbits into chaotic ones.

Although such orbital studies mentioned above are useful
for understanding the mechanism of bar destruction, they
cannot provide answers to the questions of how much BH mass
is needed, and how long it takes, precisely to destroy a bar.
As a helpful tool for resolving these issues, self-consistent
$N$-body simulations have played an important role in
investigating the detailed evolution of a bar under the
influence of a massive central BH.  As pioneering work on
$N$-body studies, \citet{nsh96} explored the evolution of
a Kuzmin-Toomre \mbox{(K-T)} disk \citep{kuzmin56,toomre63}
both in two- and three-dimensional configurations in which
a bar was formed by the bar instability, and then a BH was
added at the center of the disk as an external field.  They
showed that regardless of disk geometries, the minimum BH
mass required for bar destruction is $4-5$\% of the disk
mass.  Subsequently, \citet{ss04} have obtained a similar
BH mass to destroy a bar with high-quality $N$-body simulations
using a three-dimensional \mbox{K-T} disk embedded in a halo.

Unfortunately, K-T disks are inadequate in that real disk
galaxies are well-described by exponential surface-density
distributions \citep{freeman70}.  Then, \authorcite{hh05}
(\yearcite{hh05}, hereafter HH) adopted a two-dimensional
exponential disk and examined the effect of a central BH
on a bar generated in that disk.  Although the motions of
stars in their simulations are restricted to a single plane,
they have demonstrated that a BH with a mass of only 0.5\%
of the disk mass is sufficient for bar dissolution.  This BH
mass is about an order of magnitude smaller than that obtained
by Norman \etal\ (\yearcite{nsh96}) and that by \citet{ss04}.
Concerning this difference, HH argued that since exponential
disks are more centrally concentrated than K-T disks, central
BHs could have a more destructive impact on a bar in the former
than in the latter, and that as a result, bars in exponential
disks could be destructed more easily.  However, \authorcite{ald05}
(\yearcite{ald05}, hereafter ALD) have shown that complete bar
destruction needs a BH with a mass of at least 5\% of the disk
mass even for more realistic models that are composed of an
exponential disk and its surrounding live halo.  Their result
suggests that the difference in the minimum BH mass does not
necessarily originate from the difference in the mass profile
of the disks.  Consequently, the discrepancy in the minimum BH
mass still remains unexplained, although the difference in disk
geometry and situation between the two studies might be related
to that difference in the BH mass: HH used a two-dimensional
disk without a halo, while ALD adopted a three-dimensional
disk with a live halo.

If the BH mass required for destroying a bar is at least about
5\% of the disk mass, bar dissolution of the kind stated here
would be practically impossible.  This is because the corresponding
BH mass amounts to approximately $10^{9.5} M_\odot$ for a typical
disk galaxy, while the largest BH mass derived observationally
from nearby spiral galaxies is about $10^9 M_\odot$
\citep{kormendy88,koretal96,mh03}.  On the other hand,
if that mass is around 0.5\% of the disk mass, we can expect
the existence of bar-dissolved galaxies in the real Universe.
In this case, as \citet{larson10} has argued, dissolving a bar
could weaken and ultimately cease the central activities of
disk galaxies, since a barred structure is considered effective
in fueling gas into the nucleus and this gas inflow could drive
such activities.  Therefore, also from this viewpoint, it is
significant to determine the precise lower limit of the BH mass
for bar destruction in order to reveal the secular evolution of
the barred galaxies that harbor central BHs.  However, it is
conceivable that the BH mass needed to destroy a bar depends
on the characteristics of the bar.  Indeed, the bars formed by
the bar instability will have a diversity of shapes and structures
that arise from the difference in the kinematic structure of the
disk like that represented by \citet{toomre64} $Q$ profile, even
though its mass profile is fixed.  Nevertheless, in the previous
$N$-body studies noted above, the kinematic structure of the disk
for a given mass profile was never changed systematically, with
other parameters of the system intact.  Instead, some parameters
included in the system such as a BH mass and a BH softening length
were surveyed systematically for a disk with given mass and velocity
profiles.

In this paper, we examine what type of bar is destroyed easily
by a massive central BH, and thereby aim at understanding what
causes that difference in the minimum BH mass required for bar
dissolution which has been described above.  In section 2, we
show disk models with different kinematic structures for given
mass profiles in order to produce a wide variety of bars.  In
addition, a BH model is also provided.  Our numerical method is
described in section 3.  In section 4, we present the evolution
of the disk models, in which bars form spontaneously and then
they are deformed by adding a BH at the center of the disk.
The properties of the bars are disclosed as well.  In section
5, we discuss destructible bars under the dynamical influence
of a massive central BH.  Conclusions are given in section 6.

\section{Models}
\begin{figure*}
\centerline{\FigureFile(140mm,40mm){figure1.eps}}
\caption{Toomre's $Q$ parameters as a function of radius
for (a) models E1, E2, and E3 of the exponential disks,
(b) models TK6, TK8, and TK10 of the Kuzmin-Toomre disks
with Kalnajs's distribution functions, and (c) models TM3,
TM4, and TM5 of the Kuzmin-Toomre disks with Miyamoto's
distribution functions.  Note that $Q$ values at small radii
for model E1 are smaller than those for model E2.  Here, the
radius is normalized by the exponential scale length $h$.}
\label{fig:Q_profile}
\end{figure*}

We adopt infinitesimally thin stellar disks in order to
avoid another damaging influence on a bar arising from
the fire-hose instability inherent in three-dimensional
disks \citep{raha91,debattista04,mvs04}.  In addition,
we do not include bulge and halo components.  Two
different mass profiles for such flat disks are employed,
that is, exponential and Kuzmin-Toomre disks that are
globally unstable to the formation of a bar.  On the
other hand, as an external field, we model a BH that
is placed at the center of the disk after the full
growth of a bar.

\subsection{Exponential Disks}
The surface-density distributions of exponential disks,
$\mu_{\rm exp}$, are given by
\begin{equation}
\mu_{\rm exp}(R)=\frac{M_d}{2\pi h^2}\exp(-R/h),
\end{equation}
where $M_d$ is the mass of the disk, $h$ is the scale
length, and $R$ is the distance from the center of the
disk.  The disks are truncated at $R=10h$.  As adopted
by HH, the full phase space is realized with the method
devised by \citet{hernquist93}, in which the velocity
structure is approximated using moments of the collisionless
Boltzmann equation.  In so doing, following the observations
of disk galaxies \citep{vdks81,lf89}, we determine the square
of the radial velocity dispersion, ${\sigma_R}^2$, so as to be
proportional to the surface density such that
\begin{equation}
{\sigma_R}^2(R)={\sigma_0}^2\exp(-R/h),
\label{eq:radial_disp}
\end{equation}
where $\sigma_0$ is the radial velocity dispersion at the center.
Although the initial models thus constructed are not based on
exact equilibrium distribution functions, we did not see any
violent changes in the early stages of evolution.  This behavior
indicates that these models are sufficiently close to exact
dynamical equilibrium.

We set up three models that have different \citet{toomre64}
$Q$ profiles shown in figure \ref{fig:Q_profile}a.  These
models are named models E1, E2, and E3, whose reference $Q$
values at the supposed solar radius, 2.43$h$ (8.5 kpc, see
below), are 1.2, 0.91, and 0.64, respectively.  As explained
by \citet{hernquist93}, there is difficulty in completely
fulfilling the ${\sigma_R}^2$ distribution given by equation
(\ref{eq:radial_disp}) near the center, so that some reduction
in ${\sigma_R}^2$ is needed within a certain radius.  As a
result, the ${\sigma_R}^2$ profiles of the models created
here are not shifted vertically to one another at small radii.
This behavior applies also to the $Q$ profiles of the models,
taking into consideration the definition of the $Q$ parameter.
Accordingly, model E1 has a rather different $Q$ profile at
small radii than models E2 and E3.  Thus, in this disk model
group, except at small radii, the functional form of the
velocity structure is the same, and the radial velocity
dispersion at each radius is different from model to model
by a constant factor.

\subsection{Kuzmin-Toomre Disks}
The surface-density distributions of Kuzmin-Toomre (K-T)
disks, $\mu_{\rm KT}$, are provided by
\begin{equation}
\mu_{\rm KT}(R)=\frac{M_d}{2\pi h^2}
  \left(1+\frac{R^2}{h^2}\right)^{-3/2}.
\label{eq:sd_disk}
\end{equation}
The disks are again truncated at $R=10h$.

In contrast to the exponential disks, the K-T disks are
known to possess exact equilibrium distribution functions
(DFs), $F_0$, in analytical forms.  In general, for a flat
axisymmetric galaxy, the equilibrium DF of directly rotating
stars, $F^+$, is composed of the energy, $\varepsilon$,
and angular momentum, $j$, of a star per unit mass.  This
prograde part of the equilibrium DF, $F^+(\varepsilon, j)$,
has been given by \citet{kalnajs76} and by \citet{miya71}.
Here, we use both of the DFs.

On the other hand, there is no definite way of prescribing
the distribution of retrograde stars.  Then, we introduce
them in the same manner as that adopted by \citet{nishida84}.
Consequently, the equilibrium DF is written as
\begin{equation}
F_0(\varepsilon,j)=\left\{
  \begin{array}{ll}
    (1/2)F_0^+(\varepsilon)+F_1^+(\varepsilon,j) & j\ge 0,\\
    (1/2)F_0^+(\varepsilon) & j<0,
  \end{array}\right.
\label{DF}
\end{equation}
where the functions $F_0^+(\varepsilon)$ and $F_1^+(\varepsilon,j)$
are derived from the expansion of $F^+(\varepsilon,j)$ as
\begin{equation}
F^+(\varepsilon,j)=F_0^+(\varepsilon)+F_1^+(\varepsilon,j).
\end{equation}

The two types of DF described above involve a model parameter that
assigns the kinematic structure to the disk.  When denoting this
parameter as $m_{\rm K}$ for Kalnajs's DFs and as $m_{\rm M}$ for
Miyamoto's DFs, we take $m_{\rm K}=6, 8,$ and 10, which are termed
models TK6, TK8, and TK10, respectively, and $m_{\rm M}=3, 4,$
and 5, which are named models TM3, TM4, and TM5, respectively.
We present the $Q$ profiles for models TK6, TK8, and TK10 in
figure \ref{fig:Q_profile}b, and those for models TM3, TM4, and
TM5 in figure \ref{fig:Q_profile}c.  The models generated from
Kalnajs's DFs have slightly declining $Q$ distributions with
radius except for model TK6 that shows a slight increase in
$Q$ from $R\sim 1.3h$ with radius, while those from Miyamoto's
DFs yield steeply rising $Q$ distributions with radius.  At any
rate, as the model parameters, $m_{\rm K}$ and $m_{\rm M}$,
increase, the $Q$ values at all radii decrease for both DFs.

In these disk models, the functional form of the velocity
structure is completely different between these two types
of DF.  For Miyamoto's DFs, the square of the radial velocity
dispersion is represented by
\begin{equation}
{\sigma_R}^2(R)=-\frac{\Phi_{\rm KT}(R)}{2m_{\rm M}+4},
\end{equation}
where $\Phi_{\rm KT}$ is the potential of the K-T disk.
Thus, in this disk model group, the radial velocity dispersion
at each radius is different from model to model by a constant
factor that depends on the model parameter $m_{\rm M}$, so
that the $Q$ profiles are shifted vertically to one another,
as is obvious in figure \ref{fig:Q_profile}c.  On the other
hand, Kalnajs's DFs lead to rather complicated functional forms
of the radial velocity dispersion.  Even so, the resulting $Q$
profiles show sequential changes designated by the model parameter
$m_{\rm K}$, as seen from figure \ref{fig:Q_profile}b.

\subsection{Black Hole}\label{subsec:BH}
A black hole (BH) model is the same as that employed by HH.
That is, a BH is represented by a softened point-mass using
a spline-kernel \citep{hk89}, and its scale length is set to
be $0.01h$.

The BH is added at time $t_{\rm BH}$ after a bar is fully
developed.  To avoid a sudden change in the dynamical state
of the disk caused by an addition of the BH, we increase the
BH mass, $M_\bullet(t)$, from 0 to $M_{\rm BH}$ gradually with
time $t$ as follows:
\begin{equation}
M_\bullet(t)=\left\{
  \begin{array}{ll}
    M_{\rm BH}\tau^2(3-2\tau) & 0 \le \tau \le 1,\\
    M_{\rm BH} & \tau > 1,
  \end{array}\right.
  \label{bhmass}
\end{equation}
where $\tau=(t-t_{\rm BH})/t_{\rm grow}$, and $t_{\rm grow}$
is the time for the BH to attain to its preassigned mass
$M_{\rm BH}$.  Thus, the BH is made to grow adiabatically
by taking $t_{\rm grow}$ to be sufficiently long.  In our
dimensionless system of units described in the next section,
we choose $t_{\rm grow}$ to be 100, and set $t_{\rm BH}$ to
be 200.

According to recent observations, the Sa galaxy NGC 4594
\citep{kormendy88,mh03} and the S0 galaxy NGC 3115 \citep{koretal96}
are thought to harbor a central BH with a mass of approximately
$10^9 M_\odot$, which is the largest BH mass inferred in nearby
spirals.  Since this BH mass is close to 1\% of the disk mass for
a typical disk galaxy, we set $M_{\rm BH}=0.01 M_d$.  With this
choice, we can evaluate the largest impact of a central BH on a
bar from a realistic point of view.

\section{Method}
We use a self-consistent field (SCF) method (Hernquist \& Ostriker
\yearcite{ho92}) to follow the evolution of the disks constructed
in the previous section and that of the systems including the BH.
In this approach, Poisson's equation is solved by expanding the
surface density, $\mu$, and potential, $\Phi$, of the disk in a
bi-orthogonal basis set such that
\begin{equation}
  \mu(\mbox{\boldmath $R$})=
    \sum_{nm} A_{nm}(t)\mu_{nm}(\mbox{\boldmath $R$})
  \label{muexpand}
\end{equation}
and
\begin{equation}
  \Phi(\mbox{\boldmath $R$})=
  \sum_{nm} A_{nm}(t)\Phi_{nm}(\mbox{\boldmath $R$}),
  \label{phiexpand}
\end{equation}
where $\mu_{nm}$ and $\Phi_{nm}$ are, respectively, the
surface-density and potential basis functions, $A_{nm}$
are the expansion coefficients, and $\mbox{\boldmath $R$}$
is the position vector.  In the SCF code, we adopt \citet{ai78}
basis set that is suitable for flat stellar disks.  The outline
of SCF simulations is explained by \citet{ho92} and by
\citet{hozumi97}.  In addition, the computational details
concerning the simulations presented here are described by HH.

The disks are realized with $N=1,000,000$ particles of equal mass.
The equations of motion are integrated in Cartesian coordinates
with a time-centered leapfrog algorithm (e.g., \cite{press86}).
We present results in the system of units such that $G=M_d=h=1$,
where $G$ is the gravitational constant.  These units can be scaled
to physical values appropriate for the Milky Way using $h=3.5$ kpc
and $M_d=5.6\times 10^{10} M_\odot$, with the result that unit time
and velocity are $1.31\times 10^7$ yr and 262 km s$^{-1}$,
respectively.

We set the maximum numbers of radial and azimuthal expansion
terms in the SCF code, $n_{\rm max}$ and $m_{\rm max}$,
respectively, to be $n_{\rm max}=24$ and $m_{\rm max}=12$.
In imposing these numbers of the expansion terms on each model,
we save only even $m$-values to avoid a sizable disagreement
between the center of the bar and the position of the BH
caused by asymmetric features that would originate from
odd $m$-values.  Again, the computational details are
taken over from those stated by HH.

Although our present simulations include a wide range of timescales
after introducing the BH, we use a fixed time step that is made
as small as possible.  In order to reduce computation times, we
have parallelized the SCF code in accordance with the prescription
provided by \citet{hsb95} (see also \cite{kelly01}).  The time
steps adopted are $\Delta t=0.05$ and $\Delta t=0.002$ before and
after the addition of the BH, respectively.  With these choices of
time step, the relative energy error of the system after the full
growth of the BH was, in all cases, smaller than $7.2\times 10^{-6}$.

\section{Results}

\subsection{Evolution of Bars}
\begin{figure}
\centerline{\FigureFile(70mm,150mm){figure2.eps}}
\caption{Time evolution of the bar amplitude before and after
the addition of the black hole (solid lines) for (a) models E1,
E2, and E3 of the exponential disks, (b) models TK6, TK8, and
Tk10 of the Kuzmin-Toomre disks with Kalnajs's distribution
functions, and (c) models TM3, TM4, and TM5 of the Kuzmin-Toomre
disks with Miyamoto's distribution functions.  The black hole
is added at $t=200$, and grows up fully at $t=300$.  The bar
evolution without the black hole after $t=200$ is also shown
with dashed lines for each model.}
\label{fig:baramp}
\end{figure}

\begin{figure*}
\centerline{\FigureFile(150mm,60mm){figure3.eps}}
\caption{Density contours in barred structures at the time
just before the addition of the black hole ($t=200$) and at
the end of the simulations ($t=800$) for (a) models E1, E2,
and E3 of the exponential disks, (b) models TK6, TK8, and
TK10 of the Kuzmin-Toomre disks with Kalnajs's distribution
functions, and (c) models TM3, TM4, and TM5 of the Kuzmin-Toomre
disks with Miyamoto's distribution functions.  The bar major
axis is aligned to the $y$ axis.  The contour levels are drawn
at the 90, 80, 70, $\cdots$, and 30\% of the peak amplitude on
logarithmic scales.  Black hole growth starts at $t=200$ and
ends at $t=300$.  All patterns rotate counterclockwise.}
\label{fig:contour}
\end{figure*}

As the disks are evolved forward in time, linearly growing
two-armed spiral modes excited in the disks are deformed
into bars in nonlinear regimes through the bar instability.
We evaluate the bar amplitude by the absolute value of the
expansion coefficient, $|A_{22}(t)|$, which corresponds to
the amplitude of the fastest growing two-armed mode (see HH).
Figure \ref{fig:baramp} shows the time evolution of the bar
amplitude for each model of the three disk model groups.
From this figure, we find that all bars are fully developed
at least by $t=200$, and that their amplitudes are practically
held constant over time to the end of the simulations unless
the BH is added, although in an exact sense, some bars grow
in amplitude very slightly with time and others show small
decrements in amplitude with time, in response to a way of
redistributing the angular momentum of a bar.  We have thus
chosen the time of adding the BH to be $t_{\rm BH}=200$, as
mentioned in section \ref{subsec:BH}.  We notice from figure
\ref{fig:baramp}, along with figure \ref{fig:Q_profile}, that
in each disk model group, the bar amplitude becomes lower
as the disk is colder in the sense of typical $Q$ values.
Concerning the exponential disks, the bar amplitude of model
E1 is larger than that of model E2, while $Q$ values at
small radii for model E1 are slightly smaller than those for
model E2 as expressed in figure \ref{fig:Q_profile}.  This fact
implies that the bar amplitude would not be sensitive to the
inner velocity structures but to the relatively outer ones.

Once the BH is added at $t=t_{\rm BH}$, the bar amplitudes start
to decrease with time, as demonstrated in figure \ref{fig:baramp}.
After the full growth of the BH, the bar amplitudes continue
to decay almost exponentially with time till the end of the
simulations.  Consequently, the bars become very round in the
final stages as found from a comparison between the density
contours at $t=t_{\rm BH}$ and those at the end of the
simulations, which are illustrated in figure \ref{fig:contour}.
To quantify to what degree the bars are made round, we evaluate
the axis ratios of the bars along radius at these two times
by calculating the principal moment of inertia tensor for
particles included in a specified radius, the value of which
is regarded as the axis ratio at that radius.  Resulting
axis-ratio profiles are presented in figure \ref{fig:axisratio}.
We can see from this figure, together with figure \ref{fig:contour},
that in each disk model group, the bar is more easily deformed
into a rounder shape as the smallest axis ratio along radius is
larger, that is, the bar is rounder when the BH is added, or as
the bar half-length, estimated here to be a distance from the
center to the radius of the smallest axis ratio, is shorter.

Since the final axis ratios of the bars exceed about 0.9 at all
radii except for the bar of model TM3 (the final axis ratio is
0.86), irrespective of the mass and velocity profiles, it follows
that a BH with a mass of 1\% of the disk mass can destroy almost
completely, or in some cases appreciably, the bars formed by the
bar instability.  Furthermore, when we take into account the $Q$
profiles shown in figure \ref{fig:Q_profile}, the runs of the final
axis ratios in figure \ref{fig:axisratio} indicate that in each
disk model group, the bars originating from the colder disks
are destroyed more easily by the BH.

\subsection{Characteristics of Bars}
We describe the characteristics of the bars before the BH acts
on them to unravel what type of bar is more destructible under
the dynamical influence of a massive central BH.

Figure \ref{fig:sd} presents the surface-density profiles
of the bars along the major and minor axes at $t=t_{\rm BH}$
just before the BH is added.  Except for models E1 and
TK6, there is no noticeable change in the density slope
on logarithmic scales from the center towards the bar
ends along the major axis.  On the other hand, models E1
and TK6 show a bend in the surface-density distribution
along the major axis at around an intermediate position
between the center and the bar end, although the bend for
model TK6 is rather gentle as compared to that for model E1.
The surface-density profiles along the minor axis for these
two models are close to those of the rest of the models.

\begin{figure}
\centerline{\FigureFile(70mm,150mm){figure4.eps}}
\caption{Axis ratio of bars as a function of radius for (a) the
exponential disks, (b) the Kuzmin-Toomre disks with Kalnajs's
distribution functions, and (c) the Kuzmin-Toomre disks with
Miyamoto's distribution functions.  Dashed lines show the axis
ratios of the bars just before the black hole is added ($t=200$),
while solid lines represent those at the end of the simulations
($t=800$).}
\label{fig:axisratio}
\end{figure}

\begin{figure*}
\centerline{\FigureFile(140mm,70mm){figure5.eps}}
\caption{Surface-density profiles along the major (solid lines)
and minor (dashed lines) axes at the time just before the black
hole is added ($t=200$) for (a) models E1, E2, and E3 of the
exponential disks, (b) models TK6, TK8, and TK10 of the
Kuzmin-Toomre disks with Kalnajs's distribution functions,
and (c) models TM3, TM4, and TM5 of the Kuzmin-Toomre disks
with Miyamoto's distribution functions.}
\label{fig:sd}
\end{figure*}

To examine the structures of the bars in detail, we analyze
the surface-density profiles by calculating their Fourier
components along radius, $I_m(R)$, where $m=2, 4, 6,$ and 8.
These Fourier components are normalized by the $m=0$ component,
$I_0$, of the disk being analyzed.  The resulting relative
Fourier amplitudes of each model at $t=t_{\rm BH}$ are displayed
in figure \ref{fig:fourier}.  Here, we calculate the Fourier
components in the same manner as that done by \citet{ohw90}
and by \citet{am02}.  This figure indicates that for the hottest
models in each disk model group from a viewpoint of typical $Q$
values, that is, for models E1, TK6, and TM3, the amplitudes for
the $m=4$ and $m=6$ components are large in magnitude as well as
for the $m=2$ component, while for the rest of the models they
are small, and, in particular, the amplitudes for the $m=6$
component are negligibly small.  In addition to this property
of the hottest models, taking into account the $Q$ profiles
presented in figure \ref{fig:Q_profile}, together with figure
\ref{fig:sd}, we can see that a bend in the surface-density
distribution of the bar along the major axis is produced for
the models that have relatively high $Q$ values near the center
as for models E1 and TK6.

\begin{figure*}
\centerline{\FigureFile(140mm,70mm){figure6.eps}}
\caption{Fourier amplitudes of the surface-density distribution,
$I_m$, for the $m=2$ (red lines), 4 (blue lines), 6 (green lines),
and 8 (black lines) components normalized by the $m=0$ component
at the time just before the black hole is added ($t=200$) as a
function of radius for (a) models E1, E2, and E3 of the exponential
disks, (b) models TK6, TK8, and TK10 of the Kuzmin-Toomre disks
with Kalnajs's distribution functions, and (c) models TM3, TM4,
and TM5 of Kuzmin-Toomre disks with Miyamoto's distribution
functions.}
\label{fig:fourier}
\end{figure*}

To further characterize the bars, we measure the size of the bar
region at $t=t_{\rm BH}$, following Ohta \etal\ (\yearcite{ohw90}),
who defined the bar region to be the region where the value of
$(I_0+I_2+I_4+I_6)/(I_0-I_2+I_4-I_6)$ exceeds 2.0.  In figure
\ref{fig:barsize}, the measured size of the bar region (bar
half-size) is plotted against the bar amplitude that is
normalized by the amplitude of the ring mode ($m=0$),
$|A_{22}|/|A_{00}|$, at $t=t_{\rm BH}$ in order to be compared
among the disk models with the different mass and velocity profiles.
This figure reveals that the bar size is approximately proportional
to the normalized bar amplitude.

As another ingredient for featuring the bars, the smallest axis
ratio along radius at $t=t_{\rm BH}$, as a measure of the degree
of elongation, is plotted against the normalized bar amplitude
in figure \ref{fig:barshape}.  We can find from this figure that
on the whole, the roundness of the bar decreases monotonically
with increasing normalized bar amplitude.

\section{Discussion}
We have obtained a wide variety of bars from the exponential
and K-T disks to which various velocity distributions are
assigned.  The amplitude of these bars continues to decay
exponentially with time till the end of the simulations
after the full growth of the BH that is added at the center
of the disk.  When we pay attention to the three models of
each disk model group, the final axis-ratio profiles in
figure \ref{fig:axisratio} show that the BH can make the
bar rounder as the bar amplitude becomes lower.  To be sure,
it may be no wonder that lower-amplitude bars are destructed
more easily by a given mass BH.  The important thing is that
this fragility of low-amplitude bars originates from the
bar properties exposed in figures \ref{fig:barsize} and
\ref{fig:barshape} that the normalized bar amplitude is
related to the size and shape of a bar.  Therefore, the
precise explanation is that since lower-amplitude bars are
shorter in length and rounder in shape, a given mass BH can
provide a more destructive impact on shorter bars that lie
more deeply inside the BH's ``sphere of influence", and can
increase the roundness more easily for rounder bars over a
given period.

\begin{figure}
\centerline{\FigureFile(70mm,50mm){figure7.eps}}
\caption{Bar half-size as a function of bar amplitude normalized
by the amplitude of the ring mode excited in each model disk.
The bar half-size and the amplitudes of the bar and ring modes
are calculated at the time just before the addition of the black
($t=200$).  The definition of the bar half-size is described
in the text.}
\label{fig:barsize}
\end{figure}

\begin{figure}
\centerline{\FigureFile(71.186mm,53.5mm){figure8.eps}}
\caption{Axis ratio of bars as a function of bar amplitude
normalized by the amplitude of the ring mode excited in each
model disk.  The axis ratio means the smallest axis ratio along
radius for each model.  The axis ratio and the amplitudes of
the bar and ring modes are calculated at the time just before
the addition of the black hole ($t=200$).}
\label{fig:barshape}
\end{figure}

We should mention the bar properties extracted in the present
study from an observational point of view.  \citet{elmegreen07}
have found from $K_s$-band images of barred galaxies that longer
bars have higher bar amplitudes.  On the other hand, analyzing
near-infrared images of nearby barred galaxies, \citet{menendez07}
have indicated a weak tendency that the bar ellipticity is larger
for longer bars.  Here, the bar ellipticity is defined as $1-b/a$,
where $b/a$ is the axis ratio of a bar.  Also, very recently,
\citet{hoyle11} have presented a similar correlation between the
bar ellipticity and bar length from an analysis of bar length
measurements in local disk galaxies.  Then, if we are allowed to
combine these two kinds of observed results, we are led to the
conclusion that the bar ellipticity increases with increasing bar
amplitude.  In fact, the bar ellipticity is often used as a measure
of the bar strength: larger bar ellipticities mean higher bar
amplitudes \citep{chapelon99, laine02, laurikainen02}.  Therefore,
the properties that we have uncovered for the simulated bars are
consistent with those of real barred galaxies.  Although the
correlation of the bar length and ellipticity with the bar
amplitude has thus far been explained from a viewpoint
of secular evolution \citep{elmegreen07, menendez07, hoyle11},
we will demonstrate in a future paper that these bar properties
are closely related to the properties of the fastest growing,
globally unstable two-armed modes excited in stellar disks,
which finally lead to bars in nonlinear regimes.

We have also found that the lower-amplitude bars are generated
from the colder disks in each disk model group, although the
physical origin of this finding is unclear at the moment (we
will mention it also in that future paper).  Consequently,
once the functional form of the velocity distribution is
assigned, the degree of the coldness of a disk determines
the fragility of a bar under the dynamical influence of a
massive central BH at least for two-dimensional disks.  If
this property is applicable to bars formed in three-dimensional
disks, the discrepancy that HH's minimum BH mass necessary
for bar dissolution in the exponential disk is about an
order of magnitude smaller than ALD's one might have arisen
partly from the difference in the coldness, more precisely,
the $Q$ profile of the disk.  However, it is uncertain whether
the relation between the coldness of a disk and the amplitude
of a bar holds for bars produced in three-dimensional disks,
because the fire-hose instability intrinsic in such disks
\citep{raha91,debattista04,mvs04} and bar-halo interactions
(\cite{lia02}; Athanassoula \& Misiriotis \yearcite{am02}),
both of  which are not included in the present study, might
distort those properties of the bars which have been obtained
in flat disks.  Thus, we need to investigate the validity of this
relation using realistic disk galaxy models in three-dimensional
configurations.

Note that the relation between the coldness of a disk and the
fragility of a bar mentioned above is obtained by ignoring the
effects of gas components on the bar instability, because our
simulations are based on pure stellar dynamics.  In general,
if gas components are added to a stellar disk, the system
will become colder on account of their low velocity dispersions.
Then, we could expect a lower-amplitude bar in such a system
that would suffer a more violent bar instability.  In a case
where a large gas mass fraction is included in a disk, \citet{sn93}
demonstrated that the bar instability in the disk is damped heavily.
Even in this situation, it can be interpreted apparently that an
extremely weak bar or bar-like structure is formed in an exceedingly
cold disk owing to a large amount of gas.  Thus, in principle, our
finding that colder disks lead to lower-amplitude bars might hold
even for the disks that contain gas components, regardless of
their amount.

Figures \ref{fig:sd} and \ref{fig:fourier} have indicated
that robust bars against the dynamical influence of a massive
central BH have relatively larger Fourier amplitudes for the
$m=4$ and $m=6$ components (models E1, TK6, and TM3), and that
for the models whose $Q$ values are somewhat large near the
center (models E1 and TK6), the bars represented by these Fourier
components exhibit a bend in the surface-density profile along
the major axis.  These two features appear similar to those of
the MH-type models, employed by \citet{lia02} and by \citet{am02},
whose halos are characterized by small core radii.  On the other
hand, the surface-density profiles of the models other than models
E1 and TK6 have no noticeable change in density slope along the bar
major axis.  This feature corresponds to that obtained from the
MD-type models, also used by \citet{lia02} and by \citet{am02},
whose halos are depicted by large core radii.  ALD have reported
that for a given mass central BH, bars formed in the MH-type
models are less destructible than those in the MD-type models.
Interestingly, ALD mentioned that the disks in the MH-type models
have $Q=1.4$, while those in the MD-type models have $Q=1$.  Thus,
this relation between the degree of bar destruction and the typical
$Q$ value is in concord with our claim that bars formed in colder
disks are more destructible.  It is true that we cannot compare
directly between their results and ours, since the disks in their
MH- and MD-type models are three-dimensional and their halos are
self-gravitating, while our models are two-dimensional and have
no halos.  Nevertheless, our models seem to reflect the
characteristics possessed by the bars in their MH- and MD-type
models.  This finding may imply that the velocity structure of
the disk affects more substantially the characteristics of the bars
formed by the bar instability than the difference in the central
concentration of self-gravitating halos.  Therefore, we should
examine the bar properties for both MH- and MD-type models that
have a wide variety of velocity structures in the disks, and
evaluate the minimum BH mass needed to dissolve the bars formed
spontaneously.  This line of investigation will enable us to
confirm whether the discrepancy in the minimum BH mass between
HH's study and the others is due to the difference in the velocity
structure of the disk.

HH argued that the destructive effect of a central BH on a
bar could be considered stronger for more centrally concentrated
disks.  Although Norman \etal\ (1996) used a K-T disk and ALD
adopted an exponential disk, both studies resulted in a similar
BH mass that is about 5\% of the disk mass as the minimum value
required for bar dissolution, in spite of the fact that exponential
disks are more centrally concentrated than K-T disks.  This result
might suggest that the velocity structure is more significant to
bar dissolution than the degree of mass concentration of the disk,
because our simulations have shown that the vulnerability of a bar
to a given mass central BH depends on the velocity structure of the
disk.  Furthermore, we have found from figures \ref{fig:barsize}
and \ref{fig:barshape} that the size and roundness of a bar
are determined by the normalized bar amplitude, irrespective
of the mass profile of the disk, and that the strength of this
amplitude is connected to the destructibility of a bar.  However,
we cannot answer exactly whether these bar properties
depend on the degree of mass concentration of the disk, since
it is prohibitively difficult to construct such models that
have the same velocity structure for different mass profiles.
Therefore, we cannot conclude definitely that the bars generated
in more centrally concentrated disks are destroyed more easily
by a given mass central BH.

We have found that the bar amplitude continues to decrease
almost exponentially with time for 500 time units after the
full growth of the BH.  This simulated period corresponds to
about 7 Gyr, if the time unit is represented by the physical
value appropriate for the Milky Way.  We have also found that
the bars formed in the exponential disks have been practically
destroyed within that period by the BH whose mass is 1\%
of the disk mass.  This BH mass is reduced to be approximately
$10^9 M_\odot$ for a typical disk galaxy, and so, it is
comparable to the largest mass for central BHs in nearby
spirals \citep{kormendy88,koretal96,mh03}.  Therefore,
our simulations suggest that bar dissolution induced by
a massive central BH could occur in the real Universe, if
galaxy disks are relatively cold at birth.  However, the
frequency of such bar dissolution would be rare, since the
minimum BH mass examined by HH (about $10^{8.5} M_\odot$)
as well as the BH mass in this work are close to the upper
bound of the observationally derived BH masses.  Consequently,
the bar fraction would be declined to a negligible degree,
if any, as the Universe evolves, by the bar dissolution
mechanism studied here.  In fact, \citet{elmegreen04}
and \citet{jogee04} found that the observed bar fraction
is nearly constant, and recently, \citet{sheth08} have
shown that it even increases with time over the last 7
Gyr (see also \cite{abraham99,vdB02}).

\section{Conclusions}
We have examined the properties of the bars formed by the bar
instability in the exponential disks with approximate equilibrium
velocity distributions and the Kuzmin-Toomre disks with two
different types of exact equilibrium DF in two-dimensional
configurations, and the damaging impact of a massive central
BH on these bars.  Then, we have found that lower-amplitude
bars, that is, weaker bars are destroyed more easily by a given
mass central BH, because the bar formed by the bar instability
is shorter in length and rounder in shape as the bar amplitude
decreases, thereby being more susceptible to the dynamical
influence of that BH.

In addition, we have also found that lower-amplitude bars are
generated from colder disks for a given functional form of the
velocity distribution.  This finding suggests that destructible
bars under the dynamical influence of a given mass central BH
are determined by the kinematic properties of disks, like those
specified by typical $Q$ values, at the formation epoch, once
the functional form of the velocity distribution is assigned.
Thus, it is likely that the discrepancy in the lowest BH mass
required for bar dissolution found in the previous simulations
might have resulted from the difference in the velocity structure
of the disk.

When scaling the dimensionless units to appropriate physical
values, we have shown that the bar amplitude continues to
decrease almost exponentially with time for about 7 Gyr after
the full growth of a BH, and that the bars formed in the relatively
cold exponential disks have resulted in practical dissolution for
a BH with a mass of approximately $10^9 M_\odot$, a likely largest
BH mass derived observationally from nearby spirals.  We thus infer
that bar dissolution induced by a massive central BH could occur in
the real Universe, if galaxy disks are formed in a rather cold state.

\bigskip
The author is indebted to Dr.\ K.\ Nitadori for optimizing the
two-dimensional SCF code for parallelization.  He would also
like to thank the anonymous referee for the valuable comments
that have called the author's attention to the connection of
the present work to observations, which have helped improve
the manuscript.  Numerical computations were carried out on
the PC cluster and Cray XT4 at the Center for Computational
Astrophysics (CfCA), the National Astronomical Observatory
of Japan.

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