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However, such simple models may mislead us if the real mass distribution is more complicated than that in the assumed models. In particular, assumptions on mass models are crucial in studying flux ratio anomalies that have been suggested as evidence for a cold dark-matter substructure. We reinvestigated four quadruple lens systems using power-law Fourier models, which have advantages of clear physical meanings and the applicability of a linear method, as well as a simple singular isothermal elliptical density model. We also investigated the effect of external perturbations, including a singular isothermal sphere, lowest-order expansion, and next-order expansion. We have found that the $\\cos3\\theta$ terms of the primary galaxy and/or of external perturbation significantly reduce the \\chi^2 in PG 1115+080 and B1422+231. In particular, we could reproduce the flux ratios of B1422+231 with next-order external perturbation assuming 5% flux uncertainties, suggesting that external perturbation cannot be described by a simple singular isothermal sphere approximation. On the other hand, we could not fit B0712+472 and B2045+265 very well even with our models, although the \\chi^2 were reduced compared with the case of using simple models. Our results clearly demonstrate that both the primary lens galaxy and the external perturbation are often more complicated than we usually assume. ", "subitem_description_type": "Abstract"}]}, "item_10001_relation_14": {"attribute_name": "DOI", "attribute_value_mlt": [{"subitem_relation_name": [{"subitem_relation_name_text": "10.1093/pasj/56.2.253"}], "subitem_relation_type": "isVersionOf", "subitem_relation_type_id": {"subitem_relation_type_id_text": "https://doi.org/10.1093/pasj/56.2.253", "subitem_relation_type_select": "DOI"}}]}, "item_10001_relation_17": {"attribute_name": "関連サイト", "attribute_value_mlt": [{"subitem_relation_name": [{"subitem_relation_name_text": "Copyright"}], "subitem_relation_type_id": {"subitem_relation_type_id_text": "http://arxiv.org/help/general", "subitem_relation_type_select": "URI"}}]}, "item_10001_rights_15": {"attribute_name": "権利", "attribute_value_mlt": [{"subitem_rights": "© Y. Kawano et al."}]}, "item_10001_source_id_9": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "00046264", "subitem_source_identifier_type": "ISSN"}]}, "item_10001_version_type_20": {"attribute_name": "著者版フラグ", "attribute_value_mlt": [{"subitem_version_resource": "http://purl.org/coar/version/c_ab4af688f83e57aa", "subitem_version_type": "AM"}]}, "item_creator": {"attribute_name": "著者", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "KAWANO, Yozo"}], "nameIdentifiers": [{"nameIdentifier": "740", "nameIdentifierScheme": "WEKO"}]}, {"creatorNames": [{"creatorName": "OGURI, Masamune"}], "nameIdentifiers": [{"nameIdentifier": "741", "nameIdentifierScheme": "WEKO"}]}, {"creatorNames": [{"creatorName": "MATSUBARA, Takahiko"}], "nameIdentifiers": [{"nameIdentifier": "742", "nameIdentifierScheme": "WEKO"}]}, {"creatorNames": [{"creatorName": "IKEUCHI, Satoru"}], "nameIdentifiers": [{"nameIdentifier": "734", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "ファイル情報", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2013-03-08"}], "displaytype": "simple", "download_preview_message": "", "file_order": 0, "filename": "56022559.pdf", "filesize": [{"value": "119.9 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_11", "mimetype": "application/pdf", "size": 119900.0, "url": {"label": "56022559", "url": "https://ir.soken.ac.jp/record/3293/files/56022559.pdf"}, "version_id": "26520f80-ba49-4cb7-a3d3-c17e90b43896"}]}, "item_language": {"attribute_name": "言語", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"resourcetype": "journal article", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "Galaxy structures and external perturbations in gravitational lenses", "item_titles": {"attribute_name": "タイトル", "attribute_value_mlt": [{"subitem_title": "Galaxy structures and external perturbations in gravitational lenses"}, {"subitem_title": "Galaxy structures and external perturbations in gravitational lenses", "subitem_title_language": "en"}]}, "item_type_id": "10001", "owner": "21", "path": ["95", "274"], "permalink_uri": "https://ir.soken.ac.jp/records/3293", "pubdate": {"attribute_name": "公開日", "attribute_value": "2012-12-13"}, "publish_date": "2012-12-13", "publish_status": "0", "recid": "3293", "relation": {}, "relation_version_is_last": true, "title": ["Galaxy structures and external perturbations in gravitational lenses"], "weko_shared_id": 21}