Challenges In Stellar Pulsation

Review of Theoretical Concepts

Author(s): Luis A. Balona

Pp: 1-24 (24)

DOI: 10.2174/978160805185411001010001

* (Excluding Mailing and Handling)

Abstract

Fundamental aspects of pulsation theory are brie y discussed such as the solution of the hydrodynamic equations by means of perturbation theory and the important role of opacity. The concept of pressure and gravity modes is introduced. A discussion of regularities in frequency and period spacing in the asymptotic limit leads to the idea of using the large and small separations for estimating the mean density and age of the star. The Petersen diagram is often used for radial modes, but results can be a ected by metallicity and rotation. The e ects of rotation on the pulsation frequencies profound: even slow rotation can destroy the regularities in frequency and period spacing predicted by the asymptotic approximation. Nonperturbative methods of solution for models of rapidly rotating stars o er promising prospects. The excitation mechanisms at work in di erent classes of stars are discussed. The role of convection in driving and damping of pulsations is still poorly understood, in spite of recent advances. Solution of the full nonlinear pulsation equations is the ultimate goal, but at present this is still con ned to radial pulsation. Nonlinear e ects which determine the mode amplitude are brie y discussed. Much e ort has been devoted to develop methods which allow mode identi cation using multicolour photometry or high-resolution spectroscopy. The advantages and drawbacks of each method discussed. In the conclusion, the topics which require further study are highlighted and brieefly discussed.

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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 <= 316245611 and j.to_ip >=316245611 )) and ((j.from_date <= 1739848347 and j.to_date >= 1739848347 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 1591) 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 <= 316245611 and j.to_ip >=316245611 )) and ((j.from_date <= 1739848347 and j.to_date >= 1739848347 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 1591) 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 <= 316245611 and j.to_ip >=316245611 )) and ((j.from_date <= 1739848347 and j.to_date >= 1739848347 and j.perpetual= 0) or (j.from_date is null and j.to_date is null and j.perpetual= 1)) and j.chapter_id = 1591)
      890μsalphaeurekaselec_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` <= 1739848347 and `b`.`banner_to_date` >= 1739848347 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.54msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 906
      • 3: 1739848347
      • 4: 1739848347
      • 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='d578ee5fb5566c504e46e7992c03dd3d'
      360μsalphaeurekaselec_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
        uwqdM4lnWScWVEtskHR8MY8xlg4vXiQHi3f0Jc2v
        uc_cart_id
        d578ee5fb5566c504e46e7992c03dd3d
        _previous
        array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/1591" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/1591
        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=eyJpdiI6InFIc0ZOQytCSldvd3Z0aHpXZVlzWGc9PSIsInZhbHVlIjoiZjNhaUhxSmd5ek9TeVo4VFNPUkVzOFExMml6dWFoMVArazlVdlAxV1pROD0iLCJtYWMiOiJhNDA5OGFiYmFmNDUzZDcwNmNjYWJjNzU1YzQ0YTkyOWRhN2FhYTJkYzkxZjcyYmFhMzVhY2VjMGRlYjNlMTk1IiwidGFnIjoiIn0%3D; XSRF-TOKEN=eyJpdiI6IkVmRVJTdjRLTVNJSmMxNlJKbkdQT0E9PSIsInZhbHVlIjoiQ29yNnhCNjZ2TmFSYnRURXQ3RFdLS3JhaUd5RTJ6YXBZN1ZYVVZBemZNb0ZBYmJvMTFtdFBSbXVrWlo4SFlRM0kxbmoxTEp4RmJVRnV1a1k0ckEyNUxmbTZEWkJpRTJ6RjFvTkY5MHhzY3dZM0t6NGJOWnhRRk5wQWVsazJJYzEiLCJtYWMiOiI0YjY1MTVlZDkzOWM2NTJiOWU4NTEwMjk1YzA1YWQ2Yjc4Yzc3YzRiM2RhMTM0NjliMDE0YTYzMzQ3NGIyZjk5IiwidGFnIjoiIn0%3D; alphaeurekaselectnet_session=eyJpdiI6IlppUmZXYVBVSUd6V01CVEphVU5tOGc9PSIsInZhbHVlIjoiOVA1aG9GQUsxTXJtMHh3U0tkZDBYRWRDMHRZZllPNmpEYnAwRnp1VmFVOGZmZDh4REhZM2ZwNVJRY1NORWNOcnd4UzNJQ3pOY1JHTVY4bE9CczV6em5QTHlqamtvcHBBTDRsRFhsNlAvMWkwZ1JQNkdsTVpJS3BZdmYwSGM3dFYiLCJtYWMiOiJmYTllNmM2YmMzYzk5ZDcwMGNiZjhiZWE4OGJkYzRjYTFkYWY0NzlmN2VlOTgzMzllZjZkZmU3NzI3ODJkNzFjIiwidGFnIjoiIn0%3Dwayfindertarget=eyJpdiI6InFIc0ZOQytCSldvd3Z0aHpXZVlzWGc9PSIsInZhbHVlIjoiZjNhaUhxSmd5ek9TeVo4VFNPUkVzOFExMml6dWFoMVArazlVdlAxV1pROD0iLCJtYWMiOiJhNDA5OGFiYmFmNDUz" ] "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
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        response_headers
        0 of 0
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        session_attributes
        0 of 0
        array:5 [ "_token" => "uwqdM4lnWScWVEtskHR8MY8xlg4vXiQHi3f0Jc2v" "uc_cart_id" => "d578ee5fb5566c504e46e7992c03dd3d" "_previous" => array:1 [ "url" => "https://alpha.eurekaselect.com/chapter/1591" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]
        ClearShow all
        Date ↕MethodURLData
        #12025-02-18 03:12:27GET/chapter/1591112193