[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-141381-105":59,"doc-detail-141381-en":134},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":127,"head_meta":129,"extra_data":131,"updated_unix":133},105,"en","the-exomoon-corridor-half-of-all-exomoons-exhibit-ttv-frequencies-within-a-narrow-window-due-to-aliasing","The Exomoon Corridor - Half of all exomoons exhibit TTV frequencies within a narrow window due to aliasing","","Exomoons are expected to generate transit timing variations (TTVs) for their parent planets, but separating moon-induced signals from other causes—especially planet–planet interactions—has limited exomoon identification. A core challenge is that exomoon TTV periods are systematically undersampled because observations occur only once per transit/planetary period. This work derives an analytic description of the aliased TTV periodicity in terms of planet and moon periods, then studies the resulting inversion degeneracies. The analysis shows a distinctive prediction: 50% of exomoons yield aliased TTV periods between 2 and 4 cycles, enabling a simple probabilistic way to prioritize exomoon candidates. Applying the approach to Kepler-1625b i shows its TTV periodicity aligns with the exomoon median expectation.",{"@graph":69,"@context":126},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/the-exomoon-corridor-half-of-all-exomoons-exhibit-ttv-frequencies-within-a-narrow-window-due-to-aliasing/141381/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/the-exomoon-corridor-half-of-all-exomoons-exhibit-ttv-frequencies-within-a-narrow-window-due-to-aliasing/141381.png","ImageObject",300,407,{"name":92,"@type":93},"Logic","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-06","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118,122],{"name":109,"@type":110,"acceptedAnswer":111},"为什么由外行星卫星（exomoon）引起的TTV周期难以被可靠测定？","Question",{"text":112,"@type":113},"由于卫星绕行周期通常远短于行星的观测采样间隔，而TTV只会在每次凌日时被间接采样，因此周期会出现欠采样。欠采样导致TTV周期不能被直接唯一确定，只会对应一组谐波频率的别名。","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"本文如何解析“别名（aliasing）”导致的TTV周期？",{"text":117,"@type":113},"作者给出外行星与卫星周期之间的解析表达，把欠采样产生的别名周期写成行星与卫星周期的函数。随后讨论从别名周期反推真实卫星周期会出现大量谐波模态，使反演变得困难。",{"name":119,"@type":110,"acceptedAnswer":120},"别名TTV在区分exomoon与行星-行星相互作用方面有什么关键特征？",{"text":121,"@type":113},"尽管别名反推存在许多谐波模态，但文中发现别名周期会稳定地出现在较短周期区域，与所假设的卫星群体模型几乎无关。具体预测是：约50%的exomoons会产生落在2到4个cycle之间的TTV别名周期，而行星-行星相互作用很少在该范围内显现。",{"name":123,"@type":110,"acceptedAnswer":124},"这种方法如何应用到Kepler-1625b i？",{"text":125,"@type":113},"作者将上述识别思路用于候选天体Kepler-1625b i，结果显示其TTV周期集中在文中预测的exomoons中位周期附近。","https://schema.org",{"og:url":83,"og:type":128,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":130,"canonical":83},"index,follow",{"doc_id":132,"site_id":62},141381,1787655135,{"code":4,"msg":5,"data":135},{"doc_id":132,"user_id":136,"nickname":92,"user_avatar":137,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":138,"file_id":139,"file_url":140,"file_type":141,"file_size":142,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":143,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":144,"faqs":145,"seo_title":146,"seo_description":67,"update_tm":133,"read_time":46},1099513958762,"https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253","arXiv :2012 .00764v1 [ astro-ph .EP] 1 Dec 2020  \nThe Exomoon Corridor: Half of all exomoons exhibit TTV frequencies within a narrow window due to aliasing  \nDavid Kipping 1 ;2?  \n1 Dept. of Astronomy, Columbia University, 550 W 120th Street, New York NY 10027  \n2 Center for Computational Astrophysics, Flatiron Institute, 162 5th Av. , New York, NY 10010  \nAccepted . Received ; in original form  \nABSTRACT  \nExomoons are expected to produce potentially detectable transit timing variations (TTVs) upon their parent planet. Unfortunately, distinguishing moon-induced TTVs from other sources, in particular planet-planet interactions, has severely impeded its usefulness as a tool for identifying exomoon candidates. A key feature of exomoon TTVs is that they will always be undersampled, due to the simple fact that we can only observe the TTVs once per transit/planetary period. We show that it is possible to analytically express the aliased TTV periodicity as a function of planet and moon period. Further, we show that inverting an aliased TTV period back to a true moon period is fraught with hundreds of harmonic modes. However, a unique aspect of these TTV aliases is that they are predicted to occur at consistently short periods, irrespective of what model one assumes for the underlying moon population. Speci􀀌 -cally, 50% of all exomoons are expected to induce TTVs with a period between 2 to  \n4 cycles, a range that planet-planet interactions rarely manifest at. This provides an exciting and simple tool for quickly identifying exomoons candidates and brings the TTV method back to the fore as an exomoon hunting strategy. Applying this method to the candidate, Kepler-1625b i, reveals that its TTV periodicity centers around the median period expected for exomoons.  \nKey words: planets and satellites: detection | methods: analytical  \n1 INTRODUCTION  \nOne of the 􀀌rst methods proposed to look for moons of extrasolar planets, exomoons, is through transit timing variations (TTVs; Sartoretti & Schneider 1999) . The amplitude of these variations is proportional to satellite-to-planet mass ratio, (MS=MP) , multiplied by the moon's semi-major axis (aS ), and can anywhere from less than a second to up to an hour (Kipping & Teachey 2020) .  \nUnfortunately, the detection of such signals is frustrated by two major obstacles. First, planet-planet interactions area frequent source of TTVs (e.g. Holman et al. 2010; Nesvorn􀀓yet al. 2014; Hadden & Lithwick 2017), making it di􀀎cult to assess whether a given TTV signal is truly caused by a satellite (e.g. see Szab􀀓o et al. 2013; Kipping et al. 2014) . Second, any satellite orbiting within the Hill sphere will have an orbital period much shorter than the planetary period-which represents the sampling rate via transits. Accordingly, the signal is undersampled, as 􀀌rst proved in Kipping (2009a) . A key conclusion of that work was that \\the period of the  \n? E-mail: [dkipping@astro.columbia.edu](dkipping@astro.columbia.edu)  \nexomoon cannot be reliably determined from TTVs, only a set of harmonic frequencies\".  \nDespite the awareness of this issue since 2009, there has been no e􀀋ort (that we are aware of) to actually predict what this aliasing looks like. This is important because characteristics of this aliasing may present a means of distinguishing, even if only in a probabilistic sense, exomoon-induced TTVs versus planet-planet interactions. At the most basic level, such an investigation provides at lease some insight as to how exomoons should be expected to manifest in the frequency domain of TTVs.  \nThis is perhaps a product of the availability of other proposed methods to distinguish between moons and planets in the literature at the time. For example, several authors had expected that transits of the moons themselves would be likely detected in conjunction with the TTVs (Brown et al. 2001; Szab􀀓o et al. 2006; Simon et al. 2007), which would indeed permit a unique inversion (Kipping 2011), as well o􀀋ering","cbCaipPjhyZ4j0b6","https://ap.wps.com/l/cbCaipPjhyZ4j0b6","pdf",1001158,"English","# Abstract\n# 1 Introduction\n## Transit timing variations and obstacles\n## Undersampling and aliasing motivation\n# 2 Theory\n## Why moons are always undersampled","[{\"question\":\"为什么由外行星卫星（exomoon）引起的TTV周期难以被可靠测定？\",\"answer\":\"由于卫星绕行周期通常远短于行星的观测采样间隔，而TTV只会在每次凌日时被间接采样，因此周期会出现欠采样。欠采样导致TTV周期不能被直接唯一确定，只会对应一组谐波频率的别名。\"},{\"question\":\"本文如何解析“别名（aliasing）”导致的TTV周期？\",\"answer\":\"作者给出外行星与卫星周期之间的解析表达，把欠采样产生的别名周期写成行星与卫星周期的函数。随后讨论从别名周期反推真实卫星周期会出现大量谐波模态，使反演变得困难。\"},{\"question\":\"别名TTV在区分exomoon与行星-行星相互作用方面有什么关键特征？\",\"answer\":\"尽管别名反推存在许多谐波模态，但文中发现别名周期会稳定地出现在较短周期区域，与所假设的卫星群体模型几乎无关。具体预测是：约50%的exomoons会产生落在2到4个cycle之间的TTV别名周期，而行星-行星相互作用很少在该范围内显现。\"},{\"question\":\"这种方法如何应用到Kepler-1625b i？\",\"answer\":\"作者将上述识别思路用于候选天体Kepler-1625b i，结果显示其TTV周期集中在文中预测的exomoons中位周期附近。\"}]","The Exomoon Corridor - Half of all exomoons exhibit TTV frequencies within a narrow window due to aliasing | PDF"]