Challenges In Stellar Pulsation

roAp stars

Author(s): Luis A. Balona

Pp: 86-109 (24)

DOI: 10.2174/978160805185411001010086

* (Excluding Mailing and Handling)

Abstract

Rapidly pulsating Ap stars present the widest range of physical phenomena in any pulsating star. It seems probable that most of the driving is due to the κ mechanism in the H ionization zone in which convection is suppressed by the magnetic eld. Recent attempts to model some stars show that driving by this mechanism is sometimes insu cient and that another unknown mechanism is also at work. This is also indicated by the fact that the predicted instability strip for the κ mechanism is much hotter than observed. Much progress has occurred in the last decade and we now have a good understanding of the cyclic frequency jumps that occur in models as the magnetic eld is changed. Coupling of the pulsation with the magnetic eld induces a slow wave which is thought to damp δ Scuti pulsations in these stars. However, recent space observations have shown that in at least one roAp star a low frequency mode is also present, presenting a challenge to this idea. The eigenfunctions are far from simple spherical harmonics, considerably complicating mode identi cation. Observations indicate the presence of pulsational nodes in the atmosphere and variations in amplitude and phase shifts between di erent atomic species. This appears to be the result of chemical strati cation and running waves. The line pro le variations are axisymmetric except in the uppermost atmospheric layers. The non-axisymmetric variations are not understood, but may be a result of turbulence in the atmosphere or shock waves.

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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 <= 51271243 and j.to_ip >=51271243 )) and ((j.from_date <= 1739848348 and j.to_date >= 1739848348 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 1596) 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 <= 51271243 and j.to_ip >=51271243 )) and ((j.from_date <= 1739848348 and j.to_date >= 1739848348 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 1596) 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 <= 51271243 and j.to_ip >=51271243 )) and ((j.from_date <= 1739848348 and j.to_date >= 1739848348 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 1596)
      920μsalphaeurekaselec_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` <= 1739848348 and `b`.`banner_to_date` >= 1739848348 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.56msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 906
      • 3: 1739848348
      • 4: 1739848348
      • 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='1d0e88177ad923aba3e70878ce500cc6'
      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
        mp3Nrsuy8B3VjaWPA26APFw0X4LelqtuQiWetzoQ
        uc_cart_id
        1d0e88177ad923aba3e70878ce500cc6
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/1596" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/1596
        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=eyJpdiI6IjliNWUxMlRwRnJZdXlueUxMYXFEMVE9PSIsInZhbHVlIjoiZEJDZ1JZbGxDRkM4enFUdWZHdWJSM0lqMEZXTWJGK2NPYmFPYkNRYWFFbz0iLCJtYWMiOiI2OTg4MzkyODAxNTQwMmRiZDI2MzJkZjk0ZjkzMjRmYmMxZGNhZDcyNjRlMjA2YjRhOWQ2NGU2MDc5MjAwZTg0IiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6IjliNWUxMlRwRnJZdXlueUxMYXFEMVE9PSIsInZhbHVlIjoiZEJDZ1JZbGxDRkM4enFUdWZHdWJSM0lqMEZXTWJGK2NPYmFPYkNRYWFFbz0iLCJtYWMiOiI2OTg4MzkyODAxNTQw" ] "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 03:12:28 GMT" ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImxBL2hCV040WTRpSFI4dnlKU284ekE9PSIsInZhbHVlIjoiRng1anE4TkwybmtmWUh4VGROaGJpL2lwdGJzcE8wUXJPSnVrcHgxWnF4TmtLWStmaWN2YTBnNk1NQlJiNkpiaGx5aXJwbnZiQ2xaYW5oU3Z5Qlp6K3VWNW5HMnU5eUZ6N0l1SnVwYk1LSVRXV2pXZHZzSmJxT0dFUzltNWVGYWEiLCJtYWMiOiIwNmRhZTk1ZWMwOWYwM2E5ZWNlNDEwYzBhZDZlNmFlZjlmNjNhNjdlNzIwOGVhYmM1Yjk5ZjY3NzVhMzhmZmNjIiwidGFnIjoiIn0%3D; expires=Thu, 20 Feb 2025 15:12:28 GMT; Max-Age=216000; path=/; secure; samesite=laxXSRF-TOKEN=eyJpdiI6ImxBL2hCV040WTRpSFI4dnlKU284ekE9PSIsInZhbHVlIjoiRng1anE4TkwybmtmWUh4VGROaGJpL2lwdGJzcE8wUXJPSnVrcHgxWnF4TmtLWStmaWN2YTBnNk1NQlJiNkpiaGx5aXJwb" 1 => "alphaeurekaselectnet_session=eyJpdiI6InQyWG9MUWxDTEJZY1BZWjBZcE1Lanc9PSIsInZhbHVlIjoiVnVzYkY2Y1EvSmVqNmVZVkN6eXY1RWd2dDVSZzhXT2FyMFNpSFBYZDlnZFE2b1JzY2tPRThpMThCdTRVc0czQXBza0o4ZHUzQUNwWE5jTDJDNHlXM1QrWk9VNE9Dc1RGQmNOWmhnSWtlVkJTMElxQ0VqODFPQzBVRkErU3VLMS8iLCJtYWMiOiI5NDVjMDIyNDNhOTQ4YzUzZTY1N2M5MTM3YjFiYjdiNjJlODgyZGI2YmIyNjEyYzYyMTk1ZTQzZDM1ZGJkZjJkIiwidGFnIjoiIn0%3D; path=/; secure; httponly; samesite=laxalphaeurekaselectnet_session=eyJpdiI6InQyWG9MUWxDTEJZY1BZWjBZcE1Lanc9PSIsInZhbHVlIjoiVnVzYkY2Y1EvSmVqNmVZVkN6eXY1RWd2dDVSZzhXT2FyMFNpSFBYZDlnZFE2b1JzY2tPRThpMTh" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImxBL2hCV040WTRpSFI4dnlKU284ekE9PSIsInZhbHVlIjoiRng1anE4TkwybmtmWUh4VGROaGJpL2lwdGJzcE8wUXJPSnVrcHgxWnF4TmtLWStmaWN2YTBnNk1NQlJiNkpiaGx5aXJwbnZiQ2xaYW5oU3Z5Qlp6K3VWNW5HMnU5eUZ6N0l1SnVwYk1LSVRXV2pXZHZzSmJxT0dFUzltNWVGYWEiLCJtYWMiOiIwNmRhZTk1ZWMwOWYwM2E5ZWNlNDEwYzBhZDZlNmFlZjlmNjNhNjdlNzIwOGVhYmM1Yjk5ZjY3NzVhMzhmZmNjIiwidGFnIjoiIn0%3D; expires=Thu, 20-Feb-2025 15:12:28 GMT; path=/; secureXSRF-TOKEN=eyJpdiI6ImxBL2hCV040WTRpSFI4dnlKU284ekE9PSIsInZhbHVlIjoiRng1anE4TkwybmtmWUh4VGROaGJpL2lwdGJzcE8wUXJPSnVrcHgxWnF4TmtLWStmaWN2YTBnNk1NQlJiNkpiaGx5aXJwb" 1 => "alphaeurekaselectnet_session=eyJpdiI6InQyWG9MUWxDTEJZY1BZWjBZcE1Lanc9PSIsInZhbHVlIjoiVnVzYkY2Y1EvSmVqNmVZVkN6eXY1RWd2dDVSZzhXT2FyMFNpSFBYZDlnZFE2b1JzY2tPRThpMThCdTRVc0czQXBza0o4ZHUzQUNwWE5jTDJDNHlXM1QrWk9VNE9Dc1RGQmNOWmhnSWtlVkJTMElxQ0VqODFPQzBVRkErU3VLMS8iLCJtYWMiOiI5NDVjMDIyNDNhOTQ4YzUzZTY1N2M5MTM3YjFiYjdiNjJlODgyZGI2YmIyNjEyYzYyMTk1ZTQzZDM1ZGJkZjJkIiwidGFnIjoiIn0%3D; path=/; secure; httponlyalphaeurekaselectnet_session=eyJpdiI6InQyWG9MUWxDTEJZY1BZWjBZcE1Lanc9PSIsInZhbHVlIjoiVnVzYkY2Y1EvSmVqNmVZVkN6eXY1RWd2dDVSZzhXT2FyMFNpSFBYZDlnZFE2b1JzY2tPRThpMTh" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "mp3Nrsuy8B3VjaWPA26APFw0X4LelqtuQiWetzoQ" "uc_cart_id" => "1d0e88177ad923aba3e70878ce500cc6" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/1596" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-18 03:12:28GET/chapter/1596112193