Challenges In Stellar Pulsation

Pulsating stars in the hot upper main sequence

Author(s): Luis A. Balona

Pp: 25-55 (31)

DOI: 10.2174/978160805185411001010025

* (Excluding Mailing and Handling)

Abstract

Although periodic light variability is rare among O-type stars, periodic line pro le variations are more common. The modes in these stars are probably all of high degree and the visibility may be a ected by obscuration. The observed frequencies in β Cep stars cover a wider range than predicted. This is a major unsolved problem which may point to problems in the current opacities. Observations of these stars in low-metallicity environments also present a challenge. Asteroseismology of these stars not been very successful due to the e ect of rotation and the fact that some observed modes are stable in the models. For the SPB stars, the decrease in amplitude with rotation is unexplained. The Be stars are clearly multiperiodic variables, but most of the periods are unresolved. Recent space observations suggest that some of the variability is probably due to rotational modulation. An alternative view is that the light and line pro le variations are due to obscuring clouds locked into co-rotation by a magnetic eld. The fact that the rotational velocities of early type Be stars are in general well below the critical velocity suggest that pulsation is not the trigger for mass loss. Recent space observations suggest that there may exist pulsating stars in the region between the SPB and δ Scuti instability strips. Models of pulsating supergiants are located in a high-luminosity extension of the β Cep and SPB instability strips, but observations do not support these calculations. Models of Wolf-Rayet stars invariably predict instability due to the strange mode mechanism, but like the O-type stars, observations of periodic variations are almost entirely absent.

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      • 13. app/Models/UserAccess/UserAccess.php:1266
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      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Trial Access" as access_base_text, CASE j.type WHEN 111 THEN true ELSE false END as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_trail` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59780576 and j.to_ip >=59780576 )) and ((j.from_date <= 1739847152 and j.to_date >= 1739847152 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 1593) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Subscribed" as access_base_text, false as terms_popup, "S" as content_download_type, null as restricted_user_access_key, null as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_corporate` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59780576 and j.to_ip >=59780576 )) and ((j.from_date <= 1739847152 and j.to_date >= 1739847152 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 1593) union (select j.user_access_id,j.volume_id,j.user_id,j.from_ip,j.to_ip,j.type,j.track,"Token Based Access" as access_base_text, false as terms_popup, "R" as content_download_type, j.uc_id as restricted_user_access_key, "v" as restricted_user_access_type, CASE j.track WHEN 0 THEN false ELSE true END as tracksAccessByVolume,"chapter" as access_level, j.chapter_id from `user_access_chapter_token` as `j` inner join `user_access_info` as `info` on `j`.`user_access_id` = `info`.`user_access_id` where ((j.from_ip <= 59780576 and j.to_ip >=59780576 )) and ((j.from_date <= 1739847152 and j.to_date >= 1739847152 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 1593)
      720μsalphaeurekaselec_live_10_06_2022UserAccess.php#1266
      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 906 and `b`.`banner_from_date` <= 1739847152 and `b`.`banner_to_date` >= 1739847152 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.45msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 906
      • 3: 1739847152
      • 4: 1739847152
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='cd360af337fbcf79f9e8211fd45f43ce'
      340μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Keywords
    1Keywords.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        ONG7UjYVP5cY635Gs4Rj2WFrTw2DjjTeCFr6Ahde
        uc_cart_id
        cd360af337fbcf79f9e8211fd45f43ce
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/1593" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/1593
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "x-https" => array:1 [ 0 => "1" ] "host" => array:1 [ 0 => "alpha.eurekaselect.com" ] "priority" => array:1 [ 0 => "u=0, i" ] "cookie" => array:1 [ 0 => "wayfindertarget=eyJpdiI6IndXTFNWUnlvUEVWTnBIWXoydGRzZ0E9PSIsInZhbHVlIjoiWjlmWGdtYlBSd01vdjcrMHE4Q1lDUzlhbTdXczg2cHM0YVhydlJqTDFtMD0iLCJtYWMiOiJjZjg2Mjk0NzkwMTNmODBhNTY5OGYxM2RkOTI2NWM1YjQ5NTQ1MjYzZTJlMjVjZDgyODEyNGViYjczMmYxZjUzIiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6IndXTFNWUnlvUEVWTnBIWXoydGRzZ0E9PSIsInZhbHVlIjoiWjlmWGdtYlBSd01vdjcrMHE4Q1lDUzlhbTdXczg2cHM0YVhydlJqTDFtMD0iLCJtYWMiOiJjZjg2Mjk0NzkwMTNm" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] ]
        request_cookies
        0 of 0
        array:1 [ "wayfindertarget" => null ]
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Tue, 18 Feb 2025 02:52:32 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InRtRy9LamdnbXZxMjVJVGptZHMrUVE9PSIsInZhbHVlIjoielRqMUwvVUo3S1pqbVZhMkpoL1dLY2RTb0pNbWlGL0lDTDFOWFFpMGRqVEVIaXRXRnVxYkMwRzNoOWE1VndycHRma2JxT3pKTllnQzhmblh6bkZwdGRSdG9UOU9TdGNpWTZEK0czK3psRGx5QXpiNFJOc2xKVmlBb1ZjZHcwczciLCJtYWMiOiI0MzA4ZDFmMWYyYjA4MDc0ODQwZDllOGM3NTFlZjI2OTk0OTdlODgxMTQxZTg3NjhhOWUzZTk0OTliODRjYTFjIiwidGFnIjoiIn0%3D; expires=Thu, 20 Feb 2025 14:52:32 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6InRtRy9LamdnbXZxMjVJVGptZHMrUVE9PSIsInZhbHVlIjoielRqMUwvVUo3S1pqbVZhMkpoL1dLY2RTb0pNbWlGL0lDTDFOWFFpMGRqVEVIaXRXRnVxYkMwRzNoOWE1VndycHRma2JxT" 1 => "alphaeurekaselectnet_session=eyJpdiI6IllEaFJQbFR3ZCtwUXk4a2ROVzNScGc9PSIsInZhbHVlIjoiL1RCYXo3b2dvZXRKbEpoVHJPNUd4VC9ZMmZvdjVGQnUwamI2MjlYZ0Nvbnd2bnZHdFYybjNZYkdJSExaZnRqTTJoMHN3THdmMEl4eXJsRG55bkd2NG9ydVpIVjR2UFZVbnNtWmd5MklQU3AvTEJxSEFGZ2NQRVh3L2cyNGx5OWkiLCJtYWMiOiI3NGExMzU1NzJhMGUwY2IyNjU5N2U1MTY5ZWVhODUwOThiYmQyNzc4ZDdkMWIzNDZjNGYzYzdjNzUzNTgwYmExIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6IllEaFJQbFR3ZCtwUXk4a2ROVzNScGc9PSIsInZhbHVlIjoiL1RCYXo3b2dvZXRKbEpoVHJPNUd4VC9ZMmZvdjVGQnUwamI2MjlYZ0Nvbnd2bnZHdFYybjNZYkd" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6InRtRy9LamdnbXZxMjVJVGptZHMrUVE9PSIsInZhbHVlIjoielRqMUwvVUo3S1pqbVZhMkpoL1dLY2RTb0pNbWlGL0lDTDFOWFFpMGRqVEVIaXRXRnVxYkMwRzNoOWE1VndycHRma2JxT3pKTllnQzhmblh6bkZwdGRSdG9UOU9TdGNpWTZEK0czK3psRGx5QXpiNFJOc2xKVmlBb1ZjZHcwczciLCJtYWMiOiI0MzA4ZDFmMWYyYjA4MDc0ODQwZDllOGM3NTFlZjI2OTk0OTdlODgxMTQxZTg3NjhhOWUzZTk0OTliODRjYTFjIiwidGFnIjoiIn0%3D; expires=Thu, 20-Feb-2025 14:52:32 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6InRtRy9LamdnbXZxMjVJVGptZHMrUVE9PSIsInZhbHVlIjoielRqMUwvVUo3S1pqbVZhMkpoL1dLY2RTb0pNbWlGL0lDTDFOWFFpMGRqVEVIaXRXRnVxYkMwRzNoOWE1VndycHRma2JxT" 1 => "alphaeurekaselectnet_session=eyJpdiI6IllEaFJQbFR3ZCtwUXk4a2ROVzNScGc9PSIsInZhbHVlIjoiL1RCYXo3b2dvZXRKbEpoVHJPNUd4VC9ZMmZvdjVGQnUwamI2MjlYZ0Nvbnd2bnZHdFYybjNZYkdJSExaZnRqTTJoMHN3THdmMEl4eXJsRG55bkd2NG9ydVpIVjR2UFZVbnNtWmd5MklQU3AvTEJxSEFGZ2NQRVh3L2cyNGx5OWkiLCJtYWMiOiI3NGExMzU1NzJhMGUwY2IyNjU5N2U1MTY5ZWVhODUwOThiYmQyNzc4ZDdkMWIzNDZjNGYzYzdjNzUzNTgwYmExIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6IllEaFJQbFR3ZCtwUXk4a2ROVzNScGc9PSIsInZhbHVlIjoiL1RCYXo3b2dvZXRKbEpoVHJPNUd4VC9ZMmZvdjVGQnUwamI2MjlYZ0Nvbnd2bnZHdFYybjNZYkd" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "ONG7UjYVP5cY635Gs4Rj2WFrTw2DjjTeCFr6Ahde" "uc_cart_id" => "cd360af337fbcf79f9e8211fd45f43ce" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/1593" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-18 02:52:32GET/chapter/1593112193