Luca Reali, Roberto Cotesta, Andrea Antonelli, Konstantinos Kritos, Vladimir Strokov, Emanuele Berti
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{"title":"利用下一代地基探测器网络估算中质量黑洞二元参数","authors":"Luca Reali, Roberto Cotesta, Andrea Antonelli, Konstantinos Kritos, Vladimir Strokov, Emanuele Berti","doi":"10.1103/physrevd.110.103002","DOIUrl":null,"url":null,"abstract":"Astrophysical scenarios for the formation and evolution of intermediate-mass black holes (IMBHs) in the mass range <mjx-container ctxtmenu_counter=\"57\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"16,7,18\" data-semantic-content=\"6,8\" data-semantic- data-semantic-owns=\"16 6 7 8 18\" data-semantic-role=\"inequality\" data-semantic-speech=\"10 squared upper M Subscript circled dot Baseline less than or equivalent to upper M less than or equivalent to 10 Superscript 6 Baseline upper M Subscript circled dot\" data-semantic-structure=\"(19 (16 (2 0 1) 15 (5 3 4)) 6 7 8 (18 (11 9 10) 17 (14 12 13)))\" data-semantic-type=\"relseq\"><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"2,5\" data-semantic-content=\"15\" data-semantic- data-semantic-owns=\"2 15 5\" data-semantic-parent=\"19\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\"><mjx-msup data-semantic-children=\"0,1\" data-semantic- data-semantic-owns=\"0 1\" data-semantic-parent=\"16\" data-semantic-role=\"integer\" data-semantic-type=\"superscript\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">1</mjx-c><mjx-c style=\"padding-top: 0.642em;\">0</mjx-c></mjx-mn><mjx-script style=\"vertical-align: 0.369em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"2\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"16\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"16\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.045em;\"><mjx-mo data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" size=\"s\"><mjx-c>⊙</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-mrow><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,≲\" data-semantic-parent=\"19\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"19\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\" space=\"4\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,≲\" data-semantic-parent=\"19\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"11,14\" data-semantic-content=\"17\" data-semantic- data-semantic-owns=\"11 17 14\" data-semantic-parent=\"19\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" space=\"4\"><mjx-msup data-semantic-children=\"9,10\" data-semantic- data-semantic-owns=\"9 10\" data-semantic-parent=\"18\" data-semantic-role=\"integer\" data-semantic-type=\"superscript\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">1</mjx-c><mjx-c style=\"padding-top: 0.642em;\">0</mjx-c></mjx-mn><mjx-script style=\"vertical-align: 0.369em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"11\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>6</mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"18\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"12,13\" data-semantic- data-semantic-owns=\"12 13\" data-semantic-parent=\"18\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"14\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.045em;\"><mjx-mo data-semantic- data-semantic-parent=\"14\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" size=\"s\"><mjx-c>⊙</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> remain uncertain, but future ground-based gravitational-wave (GW) interferometers will probe the lower end of the IMBH mass range. We study the detectability of IMBH binary mergers and the measurability of their parameters with next-generation ground-based detector networks consisting of various combinations of Cosmic Explorer (CE) and Einstein Telescope (ET) interferometers. We find that, for binaries with component masses <mjx-container ctxtmenu_counter=\"58\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"5,12\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"5 6 12\" data-semantic-role=\"equality\" data-semantic-speech=\"m Subscript 1 comma 2 Baseline tilde 1000 upper M Subscript circled dot\" data-semantic-structure=\"(13 (5 0 (4 1 2 3)) 6 (12 7 11 (10 8 9)))\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,4\" data-semantic- data-semantic-owns=\"0 4\" data-semantic-parent=\"13\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑚</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"1,2,3\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"1 2 3\" data-semantic-parent=\"5\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"4\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,∼\" data-semantic-parent=\"13\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>∼</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"7,10\" data-semantic-content=\"11\" data-semantic- data-semantic-owns=\"7 11 10\" data-semantic-parent=\"13\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" space=\"4\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"12\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">1</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c style=\"padding-top: 0.642em;\">0</mjx-c></mjx-mn><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"12\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"8,9\" data-semantic- data-semantic-owns=\"8 9\" data-semantic-parent=\"12\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.045em;\"><mjx-mo data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" size=\"s\"><mjx-c>⊙</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>, an optimal 3-detector network can constrain the masses with errors <mjx-container ctxtmenu_counter=\"59\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"4,2\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"4 2\" data-semantic-role=\"endpunct\" data-semantic-speech=\"less than or equivalent to 0.1 percent sign\" data-semantic-structure=\"(5 (4 3 0 1) 2)\" data-semantic-type=\"punctuated\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"3,1\" data-semantic-content=\"0\" data-semantic- data-semantic-owns=\"3 0 1\" data-semantic-parent=\"5\" data-semantic-role=\"inequality\" data-semantic-type=\"relseq\" inline-breaks=\"true\"><mjx-mrow data-semantic-added=\"true\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"unknown\" data-semantic-type=\"empty\"></mjx-mrow><mjx-break size=\"0\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,≲\" data-semantic-parent=\"4\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"float\" data-semantic-type=\"number\" space=\"4\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">.</mjx-c><mjx-c style=\"padding-top: 0.642em;\">1</mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"punctuation\"><mjx-c>%</mjx-c></mjx-mo></mjx-math></mjx-container> (<mjx-container ctxtmenu_counter=\"60\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"4,2\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"4 2\" data-semantic-role=\"endpunct\" data-semantic-speech=\"less than or equivalent to 1 percent sign\" data-semantic-structure=\"(5 (4 3 0 1) 2)\" data-semantic-type=\"punctuated\"><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"3,1\" data-semantic-content=\"0\" data-semantic- data-semantic-owns=\"3 0 1\" data-semantic-parent=\"5\" data-semantic-role=\"inequality\" data-semantic-type=\"relseq\" inline-breaks=\"true\"><mjx-mrow data-semantic-added=\"true\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"unknown\" data-semantic-type=\"empty\"></mjx-mrow><mjx-break size=\"0\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,≲\" data-semantic-parent=\"4\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c>1</mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"5\" data-semantic-role=\"unknown\" data-semantic-type=\"punctuation\"><mjx-c>%</mjx-c></mjx-mo></mjx-math></mjx-container>) at <mjx-container ctxtmenu_counter=\"61\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"equality\" data-semantic-speech=\"z equals 0.5\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑧</mjx-c></mjx-mi><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"3\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"float\" data-semantic-type=\"number\" space=\"4\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">.</mjx-c><mjx-c style=\"padding-top: 0.642em;\">5</mjx-c></mjx-mn></mjx-math></mjx-container> (<mjx-container ctxtmenu_counter=\"62\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"equality\" data-semantic-speech=\"z equals 2\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑧</mjx-c></mjx-mi><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"3\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c>2</mjx-c></mjx-mn></mjx-math></mjx-container>), and the source redshift can be measured with percent-level accuracy or better at <mjx-container ctxtmenu_counter=\"63\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"inequality\" data-semantic-speech=\"z less than or equivalent to 2\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑧</mjx-c></mjx-mi><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,≲\" data-semantic-parent=\"3\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c>2</mjx-c></mjx-mn></mjx-math></mjx-container>. The redshift of lighter binaries (<mjx-container ctxtmenu_counter=\"64\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"5,12\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"5 6 12\" data-semantic-role=\"inequality\" data-semantic-speech=\"m Subscript 1 comma 2 Baseline less than or equivalent to 300 upper M Subscript circled dot\" data-semantic-structure=\"(13 (5 0 (4 1 2 3)) 6 (12 7 11 (10 8 9)))\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,4\" data-semantic- data-semantic-owns=\"0 4\" data-semantic-parent=\"13\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑚</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"1,2,3\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"1 2 3\" data-semantic-parent=\"5\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"4\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,≲\" data-semantic-parent=\"13\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"7,10\" data-semantic-content=\"11\" data-semantic- data-semantic-owns=\"7 11 10\" data-semantic-parent=\"13\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" space=\"4\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"12\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">3</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.644em;\">0</mjx-c><mjx-c style=\"padding-top: 0.644em;\">0</mjx-c></mjx-mn><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"12\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"8,9\" data-semantic- data-semantic-owns=\"8 9\" data-semantic-parent=\"12\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.045em;\"><mjx-mo data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" size=\"s\"><mjx-c>⊙</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>) can still be measured with <mjx-container ctxtmenu_counter=\"65\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"7,4\" data-semantic-content=\"4\" data-semantic- data-semantic-owns=\"7 4\" data-semantic-role=\"endpunct\" data-semantic-speech=\"script upper O left parenthesis 10 right parenthesis percent sign\" data-semantic-structure=\"(8 (7 0 6 (5 1 2 3)) 4)\" data-semantic-type=\"punctuated\"><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:simple\" data-semantic-children=\"0,5\" data-semantic-content=\"6,0\" data-semantic- data-semantic-owns=\"0 6 5\" data-semantic-parent=\"8\" data-semantic-role=\"simple function\" data-semantic-type=\"appl\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"script\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"7\" data-semantic-role=\"simple function\" data-semantic-type=\"identifier\"><mjx-c>𝒪</mjx-c></mjx-mi><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"appl\" data-semantic-parent=\"7\" data-semantic-role=\"application\" data-semantic-type=\"punctuation\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-children=\"2\" data-semantic-content=\"1,3\" data-semantic- data-semantic-owns=\"1 2 3\" data-semantic-parent=\"7\" data-semantic-role=\"leftright\" data-semantic-type=\"fenced\"><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"5\" data-semantic-role=\"open\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>(</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">1</mjx-c><mjx-c style=\"padding-top: 0.642em;\">0</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"fenced\" data-semantic-parent=\"5\" data-semantic-role=\"close\" data-semantic-type=\"fence\" style=\"vertical-align: -0.02em;\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"8\" data-semantic-role=\"unknown\" data-semantic-type=\"punctuation\"><mjx-c>%</mjx-c></mjx-mo></mjx-math></mjx-container> accuracy even at <mjx-container ctxtmenu_counter=\"66\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"equality\" data-semantic-speech=\"z equals 10\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑧</mjx-c></mjx-mi><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,=\" data-semantic-parent=\"3\" data-semantic-role=\"equality\" data-semantic-type=\"relation\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"integer\" data-semantic-type=\"number\" space=\"4\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">1</mjx-c><mjx-c style=\"padding-top: 0.642em;\">0</mjx-c></mjx-mn></mjx-math></mjx-container>. Binaries with <mjx-container ctxtmenu_counter=\"67\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"0,2\" data-semantic-content=\"1\" data-semantic- data-semantic-owns=\"0 1 2\" data-semantic-role=\"inequality\" data-semantic-speech=\"z less than or equivalent to 0.5\" data-semantic-structure=\"(3 0 1 2)\" data-semantic-type=\"relseq\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑧</mjx-c></mjx-mi><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,≲\" data-semantic-parent=\"3\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"3\" data-semantic-role=\"float\" data-semantic-type=\"number\" space=\"4\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">.</mjx-c><mjx-c style=\"padding-top: 0.642em;\">5</mjx-c></mjx-mn></mjx-math></mjx-container> can be localized within <mjx-container ctxtmenu_counter=\"68\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"0,1,2,5\" data-semantic-collapsed=\"(9 (c 6 7 8) 0 1 2 5)\" data-semantic- data-semantic-owns=\"0 1 2 5\" data-semantic-role=\"text\" data-semantic-speech=\"1 degree squared\" data-semantic-structure=\"(9 0 1 2 (5 3 4))\" data-semantic-type=\"punctuated\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>1</mjx-c></mjx-mn><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"space\" data-semantic-type=\"text\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 3px;\" variant=\"-explicitFont\"> </mjx-utext></mjx-mtext><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"space\" data-semantic-type=\"text\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 3px;\" variant=\"-explicitFont\"> </mjx-utext></mjx-mtext><mjx-msup data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"9\" data-semantic-role=\"prefix function\" data-semantic-type=\"superscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">d</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">e</mjx-c><mjx-c style=\"padding-top: 0.706em;\">g</mjx-c></mjx-mi><mjx-script style=\"vertical-align: 0.433em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-math></mjx-container> for <mjx-container ctxtmenu_counter=\"69\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math breakable=\"true\" data-semantic-children=\"5,12\" data-semantic-content=\"6\" data-semantic- data-semantic-owns=\"5 6 12\" data-semantic-role=\"inequality\" data-semantic-speech=\"m Subscript 1 comma 2 Baseline less than or equivalent to 1000 upper M Subscript circled dot\" data-semantic-structure=\"(13 (5 0 (4 1 2 3)) 6 (12 7 11 (10 8 9)))\" data-semantic-type=\"relseq\"><mjx-msub data-semantic-children=\"0,4\" data-semantic- data-semantic-owns=\"0 4\" data-semantic-parent=\"13\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑚</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em;\"><mjx-mrow data-semantic-children=\"1,2,3\" data-semantic-content=\"2\" data-semantic- data-semantic-owns=\"1 2 3\" data-semantic-parent=\"5\" data-semantic-role=\"sequence\" data-semantic-type=\"punctuated\" size=\"s\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\"punctuated\" data-semantic-parent=\"4\" data-semantic-role=\"comma\" data-semantic-type=\"punctuation\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"4\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-break size=\"4\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\"relseq,≲\" data-semantic-parent=\"13\" data-semantic-role=\"inequality\" data-semantic-type=\"relation\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\"true\" data-semantic-annotation=\"clearspeak:unit\" data-semantic-children=\"7,10\" data-semantic-content=\"11\" data-semantic- data-semantic-owns=\"7 11 10\" data-semantic-parent=\"13\" data-semantic-role=\"implicit\" data-semantic-type=\"infixop\" space=\"4\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"12\" data-semantic-role=\"integer\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">1</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c style=\"padding-top: 0.642em;\">0</mjx-c></mjx-mn><mjx-mo data-semantic-added=\"true\" data-semantic- data-semantic-operator=\"infixop,\" data-semantic-parent=\"12\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\"8,9\" data-semantic- data-semantic-owns=\"8 9\" data-semantic-parent=\"12\" data-semantic-role=\"latinletter\" data-semantic-type=\"subscript\"><mjx-mi data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"italic\" data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"latinletter\" data-semantic-type=\"identifier\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-script style=\"vertical-align: -0.15em; margin-left: -0.045em;\"><mjx-mo data-semantic- data-semantic-parent=\"10\" data-semantic-role=\"multiplication\" data-semantic-type=\"operator\" size=\"s\"><mjx-c>⊙</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>, and within <mjx-container ctxtmenu_counter=\"70\" ctxtmenu_oldtabindex=\"1\" jax=\"CHTML\" overflow=\"linebreak\" role=\"tree\" sre-explorer- style=\"font-size: 100.7%;\" tabindex=\"0\"><mjx-math data-semantic-children=\"0,1,2,5\" data-semantic-collapsed=\"(9 (c 6 7 8) 0 1 2 5)\" data-semantic- data-semantic-owns=\"0 1 2 5\" data-semantic-role=\"text\" data-semantic-speech=\"0.1 degree squared\" data-semantic-structure=\"(9 0 1 2 (5 3 4))\" data-semantic-type=\"punctuated\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"float\" data-semantic-type=\"number\"><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">0</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.642em;\">.</mjx-c><mjx-c style=\"padding-top: 0.642em;\">1</mjx-c></mjx-mn><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"space\" data-semantic-type=\"text\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 3px;\" variant=\"-explicitFont\"> </mjx-utext></mjx-mtext><mjx-mtext data-semantic-annotation=\"clearspeak:unit\" data-semantic- data-semantic-parent=\"9\" data-semantic-role=\"space\" data-semantic-type=\"text\" style='font-family: MJX-STX-ZERO, \"Helvetica Neue\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 3px;\" variant=\"-explicitFont\"> </mjx-utext></mjx-mtext><mjx-msup data-semantic-children=\"3,4\" data-semantic- data-semantic-owns=\"3 4\" data-semantic-parent=\"9\" data-semantic-role=\"prefix function\" data-semantic-type=\"superscript\" space=\"2\"><mjx-mi data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"prefix function\" data-semantic-type=\"function\"><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">d</mjx-c><mjx-c noic=\"true\" style=\"padding-top: 0.706em;\">e</mjx-c><mjx-c style=\"padding-top: 0.706em;\">g</mjx-c></mjx-mi><mjx-script style=\"vertical-align: 0.433em;\"><mjx-mn data-semantic-annotation=\"clearspeak:simple\" data-semantic-font=\"normal\" data-semantic- data-semantic-parent=\"5\" data-semantic-role=\"integer\" data-semantic-type=\"number\" size=\"s\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-math></mjx-container> for comparable mass systems. The sky localization is good enough that it may be possible to cross-correlate GW searches with galaxy catalogs and to search for electromagnetic counterparts to IMBH mergers. We also point out that the low-frequency sensitivity of the detectors is crucial for IMBH detection and parameter estimation. It will be interesting to use our results in conjunction with population synthesis codes to constrain astrophysical IMBH formation models.","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"127 1","pages":""},"PeriodicalIF":5.0000,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Intermediate-mass black hole binary parameter estimation with next-generation ground-based detector networks\",\"authors\":\"Luca Reali, Roberto Cotesta, Andrea Antonelli, Konstantinos Kritos, Vladimir Strokov, Emanuele Berti\",\"doi\":\"10.1103/physrevd.110.103002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Astrophysical scenarios for the formation and evolution of intermediate-mass black holes (IMBHs) in the mass range <mjx-container ctxtmenu_counter=\\\"57\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"16,7,18\\\" data-semantic-content=\\\"6,8\\\" data-semantic- data-semantic-owns=\\\"16 6 7 8 18\\\" data-semantic-role=\\\"inequality\\\" data-semantic-speech=\\\"10 squared upper M Subscript circled dot Baseline less than or equivalent to upper M less than or equivalent to 10 Superscript 6 Baseline upper M Subscript circled dot\\\" data-semantic-structure=\\\"(19 (16 (2 0 1) 15 (5 3 4)) 6 7 8 (18 (11 9 10) 17 (14 12 13)))\\\" data-semantic-type=\\\"relseq\\\"><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"2,5\\\" data-semantic-content=\\\"15\\\" data-semantic- data-semantic-owns=\\\"2 15 5\\\" data-semantic-parent=\\\"19\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\"><mjx-msup data-semantic-children=\\\"0,1\\\" data-semantic- data-semantic-owns=\\\"0 1\\\" data-semantic-parent=\\\"16\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"superscript\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">1</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">0</mjx-c></mjx-mn><mjx-script style=\\\"vertical-align: 0.369em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"2\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"16\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"3,4\\\" data-semantic- data-semantic-owns=\\\"3 4\\\" data-semantic-parent=\\\"16\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em; margin-left: -0.045em;\\\"><mjx-mo data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" size=\\\"s\\\"><mjx-c>⊙</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-mrow><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,≲\\\" data-semantic-parent=\\\"19\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"19\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\" space=\\\"4\\\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,≲\\\" data-semantic-parent=\\\"19\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"11,14\\\" data-semantic-content=\\\"17\\\" data-semantic- data-semantic-owns=\\\"11 17 14\\\" data-semantic-parent=\\\"19\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\" space=\\\"4\\\"><mjx-msup data-semantic-children=\\\"9,10\\\" data-semantic- data-semantic-owns=\\\"9 10\\\" data-semantic-parent=\\\"18\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"superscript\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">1</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">0</mjx-c></mjx-mn><mjx-script style=\\\"vertical-align: 0.369em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"11\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c>6</mjx-c></mjx-mn></mjx-script></mjx-msup><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"18\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"12,13\\\" data-semantic- data-semantic-owns=\\\"12 13\\\" data-semantic-parent=\\\"18\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"14\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em; margin-left: -0.045em;\\\"><mjx-mo data-semantic- data-semantic-parent=\\\"14\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" size=\\\"s\\\"><mjx-c>⊙</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container> remain uncertain, but future ground-based gravitational-wave (GW) interferometers will probe the lower end of the IMBH mass range. We study the detectability of IMBH binary mergers and the measurability of their parameters with next-generation ground-based detector networks consisting of various combinations of Cosmic Explorer (CE) and Einstein Telescope (ET) interferometers. We find that, for binaries with component masses <mjx-container ctxtmenu_counter=\\\"58\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"5,12\\\" data-semantic-content=\\\"6\\\" data-semantic- data-semantic-owns=\\\"5 6 12\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"m Subscript 1 comma 2 Baseline tilde 1000 upper M Subscript circled dot\\\" data-semantic-structure=\\\"(13 (5 0 (4 1 2 3)) 6 (12 7 11 (10 8 9)))\\\" data-semantic-type=\\\"relseq\\\"><mjx-msub data-semantic-children=\\\"0,4\\\" data-semantic- data-semantic-owns=\\\"0 4\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑚</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mrow data-semantic-children=\\\"1,2,3\\\" data-semantic-content=\\\"2\\\" data-semantic- data-semantic-owns=\\\"1 2 3\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"sequence\\\" data-semantic-type=\\\"punctuated\\\" size=\\\"s\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"comma\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,∼\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>∼</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"7,10\\\" data-semantic-content=\\\"11\\\" data-semantic- data-semantic-owns=\\\"7 11 10\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\" space=\\\"4\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">1</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">0</mjx-c></mjx-mn><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"8,9\\\" data-semantic- data-semantic-owns=\\\"8 9\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em; margin-left: -0.045em;\\\"><mjx-mo data-semantic- data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" size=\\\"s\\\"><mjx-c>⊙</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>, an optimal 3-detector network can constrain the masses with errors <mjx-container ctxtmenu_counter=\\\"59\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"4,2\\\" data-semantic-content=\\\"2\\\" data-semantic- data-semantic-owns=\\\"4 2\\\" data-semantic-role=\\\"endpunct\\\" data-semantic-speech=\\\"less than or equivalent to 0.1 percent sign\\\" data-semantic-structure=\\\"(5 (4 3 0 1) 2)\\\" data-semantic-type=\\\"punctuated\\\"><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-children=\\\"3,1\\\" data-semantic-content=\\\"0\\\" data-semantic- data-semantic-owns=\\\"3 0 1\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relseq\\\" inline-breaks=\\\"true\\\"><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"empty\\\"></mjx-mrow><mjx-break size=\\\"0\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,≲\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">.</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">1</mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c>%</mjx-c></mjx-mo></mjx-math></mjx-container> (<mjx-container ctxtmenu_counter=\\\"60\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"4,2\\\" data-semantic-content=\\\"2\\\" data-semantic- data-semantic-owns=\\\"4 2\\\" data-semantic-role=\\\"endpunct\\\" data-semantic-speech=\\\"less than or equivalent to 1 percent sign\\\" data-semantic-structure=\\\"(5 (4 3 0 1) 2)\\\" data-semantic-type=\\\"punctuated\\\"><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-children=\\\"3,1\\\" data-semantic-content=\\\"0\\\" data-semantic- data-semantic-owns=\\\"3 0 1\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relseq\\\" inline-breaks=\\\"true\\\"><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"empty\\\"></mjx-mrow><mjx-break size=\\\"0\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,≲\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c>1</mjx-c></mjx-mn></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c>%</mjx-c></mjx-mo></mjx-math></mjx-container>) at <mjx-container ctxtmenu_counter=\\\"61\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 2\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"z equals 0.5\\\" data-semantic-structure=\\\"(3 0 1 2)\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑧</mjx-c></mjx-mi><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">.</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">5</mjx-c></mjx-mn></mjx-math></mjx-container> (<mjx-container ctxtmenu_counter=\\\"62\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 2\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"z equals 2\\\" data-semantic-structure=\\\"(3 0 1 2)\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑧</mjx-c></mjx-mi><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c>2</mjx-c></mjx-mn></mjx-math></mjx-container>), and the source redshift can be measured with percent-level accuracy or better at <mjx-container ctxtmenu_counter=\\\"63\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 2\\\" data-semantic-role=\\\"inequality\\\" data-semantic-speech=\\\"z less than or equivalent to 2\\\" data-semantic-structure=\\\"(3 0 1 2)\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑧</mjx-c></mjx-mi><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,≲\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c>2</mjx-c></mjx-mn></mjx-math></mjx-container>. The redshift of lighter binaries (<mjx-container ctxtmenu_counter=\\\"64\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"5,12\\\" data-semantic-content=\\\"6\\\" data-semantic- data-semantic-owns=\\\"5 6 12\\\" data-semantic-role=\\\"inequality\\\" data-semantic-speech=\\\"m Subscript 1 comma 2 Baseline less than or equivalent to 300 upper M Subscript circled dot\\\" data-semantic-structure=\\\"(13 (5 0 (4 1 2 3)) 6 (12 7 11 (10 8 9)))\\\" data-semantic-type=\\\"relseq\\\"><mjx-msub data-semantic-children=\\\"0,4\\\" data-semantic- data-semantic-owns=\\\"0 4\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑚</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mrow data-semantic-children=\\\"1,2,3\\\" data-semantic-content=\\\"2\\\" data-semantic- data-semantic-owns=\\\"1 2 3\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"sequence\\\" data-semantic-type=\\\"punctuated\\\" size=\\\"s\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"comma\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,≲\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"7,10\\\" data-semantic-content=\\\"11\\\" data-semantic- data-semantic-owns=\\\"7 11 10\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\" space=\\\"4\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.644em;\\\">3</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.644em;\\\">0</mjx-c><mjx-c style=\\\"padding-top: 0.644em;\\\">0</mjx-c></mjx-mn><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"8,9\\\" data-semantic- data-semantic-owns=\\\"8 9\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em; margin-left: -0.045em;\\\"><mjx-mo data-semantic- data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" size=\\\"s\\\"><mjx-c>⊙</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>) can still be measured with <mjx-container ctxtmenu_counter=\\\"65\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-children=\\\"7,4\\\" data-semantic-content=\\\"4\\\" data-semantic- data-semantic-owns=\\\"7 4\\\" data-semantic-role=\\\"endpunct\\\" data-semantic-speech=\\\"script upper O left parenthesis 10 right parenthesis percent sign\\\" data-semantic-structure=\\\"(8 (7 0 6 (5 1 2 3)) 4)\\\" data-semantic-type=\\\"punctuated\\\"><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-children=\\\"0,5\\\" data-semantic-content=\\\"6,0\\\" data-semantic- data-semantic-owns=\\\"0 6 5\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"simple function\\\" data-semantic-type=\\\"appl\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"script\\\" data-semantic- data-semantic-operator=\\\"appl\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"simple function\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝒪</mjx-c></mjx-mi><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"appl\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"application\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c></mjx-c></mjx-mo><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-children=\\\"2\\\" data-semantic-content=\\\"1,3\\\" data-semantic- data-semantic-owns=\\\"1 2 3\\\" data-semantic-parent=\\\"7\\\" data-semantic-role=\\\"leftright\\\" data-semantic-type=\\\"fenced\\\"><mjx-mo data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"open\\\" data-semantic-type=\\\"fence\\\" style=\\\"vertical-align: -0.02em;\\\"><mjx-c>(</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">1</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">0</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"fenced\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"close\\\" data-semantic-type=\\\"fence\\\" style=\\\"vertical-align: -0.02em;\\\"><mjx-c>)</mjx-c></mjx-mo></mjx-mrow></mjx-mrow><mjx-mo data-semantic- data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"8\\\" data-semantic-role=\\\"unknown\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c>%</mjx-c></mjx-mo></mjx-math></mjx-container> accuracy even at <mjx-container ctxtmenu_counter=\\\"66\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 2\\\" data-semantic-role=\\\"equality\\\" data-semantic-speech=\\\"z equals 10\\\" data-semantic-structure=\\\"(3 0 1 2)\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑧</mjx-c></mjx-mi><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,=\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"equality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>=</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">1</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">0</mjx-c></mjx-mn></mjx-math></mjx-container>. Binaries with <mjx-container ctxtmenu_counter=\\\"67\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"0,2\\\" data-semantic-content=\\\"1\\\" data-semantic- data-semantic-owns=\\\"0 1 2\\\" data-semantic-role=\\\"inequality\\\" data-semantic-speech=\\\"z less than or equivalent to 0.5\\\" data-semantic-structure=\\\"(3 0 1 2)\\\" data-semantic-type=\\\"relseq\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑧</mjx-c></mjx-mi><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,≲\\\" data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"3\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\" space=\\\"4\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">.</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">5</mjx-c></mjx-mn></mjx-math></mjx-container> can be localized within <mjx-container ctxtmenu_counter=\\\"68\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-children=\\\"0,1,2,5\\\" data-semantic-collapsed=\\\"(9 (c 6 7 8) 0 1 2 5)\\\" data-semantic- data-semantic-owns=\\\"0 1 2 5\\\" data-semantic-role=\\\"text\\\" data-semantic-speech=\\\"1 degree squared\\\" data-semantic-structure=\\\"(9 0 1 2 (5 3 4))\\\" data-semantic-type=\\\"punctuated\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c>1</mjx-c></mjx-mn><mjx-mtext data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic- data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"space\\\" data-semantic-type=\\\"text\\\" style='font-family: MJX-STX-ZERO, \\\"Helvetica Neue\\\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\\\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 3px;\\\" variant=\\\"-explicitFont\\\"> </mjx-utext></mjx-mtext><mjx-mtext data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic- data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"space\\\" data-semantic-type=\\\"text\\\" style='font-family: MJX-STX-ZERO, \\\"Helvetica Neue\\\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\\\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 3px;\\\" variant=\\\"-explicitFont\\\"> </mjx-utext></mjx-mtext><mjx-msup data-semantic-children=\\\"3,4\\\" data-semantic- data-semantic-owns=\\\"3 4\\\" data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"prefix function\\\" data-semantic-type=\\\"superscript\\\" space=\\\"2\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"prefix function\\\" data-semantic-type=\\\"function\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.706em;\\\">d</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.706em;\\\">e</mjx-c><mjx-c style=\\\"padding-top: 0.706em;\\\">g</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: 0.433em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-math></mjx-container> for <mjx-container ctxtmenu_counter=\\\"69\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math breakable=\\\"true\\\" data-semantic-children=\\\"5,12\\\" data-semantic-content=\\\"6\\\" data-semantic- data-semantic-owns=\\\"5 6 12\\\" data-semantic-role=\\\"inequality\\\" data-semantic-speech=\\\"m Subscript 1 comma 2 Baseline less than or equivalent to 1000 upper M Subscript circled dot\\\" data-semantic-structure=\\\"(13 (5 0 (4 1 2 3)) 6 (12 7 11 (10 8 9)))\\\" data-semantic-type=\\\"relseq\\\"><mjx-msub data-semantic-children=\\\"0,4\\\" data-semantic- data-semantic-owns=\\\"0 4\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑚</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em;\\\"><mjx-mrow data-semantic-children=\\\"1,2,3\\\" data-semantic-content=\\\"2\\\" data-semantic- data-semantic-owns=\\\"1 2 3\\\" data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"sequence\\\" data-semantic-type=\\\"punctuated\\\" size=\\\"s\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c>1</mjx-c></mjx-mn><mjx-mo data-semantic- data-semantic-operator=\\\"punctuated\\\" data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"comma\\\" data-semantic-type=\\\"punctuation\\\"><mjx-c>,</mjx-c></mjx-mo><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"4\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c>2</mjx-c></mjx-mn></mjx-mrow></mjx-script></mjx-msub><mjx-break size=\\\"4\\\"></mjx-break><mjx-mo data-semantic- data-semantic-operator=\\\"relseq,≲\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"inequality\\\" data-semantic-type=\\\"relation\\\"><mjx-c>≲</mjx-c></mjx-mo><mjx-mrow data-semantic-added=\\\"true\\\" data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic-children=\\\"7,10\\\" data-semantic-content=\\\"11\\\" data-semantic- data-semantic-owns=\\\"7 11 10\\\" data-semantic-parent=\\\"13\\\" data-semantic-role=\\\"implicit\\\" data-semantic-type=\\\"infixop\\\" space=\\\"4\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">1</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">0</mjx-c></mjx-mn><mjx-mo data-semantic-added=\\\"true\\\" data-semantic- data-semantic-operator=\\\"infixop,\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\"><mjx-c></mjx-c></mjx-mo><mjx-msub data-semantic-children=\\\"8,9\\\" data-semantic- data-semantic-owns=\\\"8 9\\\" data-semantic-parent=\\\"12\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"subscript\\\"><mjx-mi data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"italic\\\" data-semantic- data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"latinletter\\\" data-semantic-type=\\\"identifier\\\"><mjx-c>𝑀</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: -0.15em; margin-left: -0.045em;\\\"><mjx-mo data-semantic- data-semantic-parent=\\\"10\\\" data-semantic-role=\\\"multiplication\\\" data-semantic-type=\\\"operator\\\" size=\\\"s\\\"><mjx-c>⊙</mjx-c></mjx-mo></mjx-script></mjx-msub></mjx-mrow></mjx-math></mjx-container>, and within <mjx-container ctxtmenu_counter=\\\"70\\\" ctxtmenu_oldtabindex=\\\"1\\\" jax=\\\"CHTML\\\" overflow=\\\"linebreak\\\" role=\\\"tree\\\" sre-explorer- style=\\\"font-size: 100.7%;\\\" tabindex=\\\"0\\\"><mjx-math data-semantic-children=\\\"0,1,2,5\\\" data-semantic-collapsed=\\\"(9 (c 6 7 8) 0 1 2 5)\\\" data-semantic- data-semantic-owns=\\\"0 1 2 5\\\" data-semantic-role=\\\"text\\\" data-semantic-speech=\\\"0.1 degree squared\\\" data-semantic-structure=\\\"(9 0 1 2 (5 3 4))\\\" data-semantic-type=\\\"punctuated\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"float\\\" data-semantic-type=\\\"number\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">0</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.642em;\\\">.</mjx-c><mjx-c style=\\\"padding-top: 0.642em;\\\">1</mjx-c></mjx-mn><mjx-mtext data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic- data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"space\\\" data-semantic-type=\\\"text\\\" style='font-family: MJX-STX-ZERO, \\\"Helvetica Neue\\\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\\\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 3px;\\\" variant=\\\"-explicitFont\\\"> </mjx-utext></mjx-mtext><mjx-mtext data-semantic-annotation=\\\"clearspeak:unit\\\" data-semantic- data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"space\\\" data-semantic-type=\\\"text\\\" style='font-family: MJX-STX-ZERO, \\\"Helvetica Neue\\\", Helvetica, Roboto, Arial, sans-serif;'><mjx-utext style=\\\"font-size: 90.6%; padding: 0.828em 0px 0.221em; width: 3px;\\\" variant=\\\"-explicitFont\\\"> </mjx-utext></mjx-mtext><mjx-msup data-semantic-children=\\\"3,4\\\" data-semantic- data-semantic-owns=\\\"3 4\\\" data-semantic-parent=\\\"9\\\" data-semantic-role=\\\"prefix function\\\" data-semantic-type=\\\"superscript\\\" space=\\\"2\\\"><mjx-mi data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"prefix function\\\" data-semantic-type=\\\"function\\\"><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.706em;\\\">d</mjx-c><mjx-c noic=\\\"true\\\" style=\\\"padding-top: 0.706em;\\\">e</mjx-c><mjx-c style=\\\"padding-top: 0.706em;\\\">g</mjx-c></mjx-mi><mjx-script style=\\\"vertical-align: 0.433em;\\\"><mjx-mn data-semantic-annotation=\\\"clearspeak:simple\\\" data-semantic-font=\\\"normal\\\" data-semantic- data-semantic-parent=\\\"5\\\" data-semantic-role=\\\"integer\\\" data-semantic-type=\\\"number\\\" size=\\\"s\\\"><mjx-c>2</mjx-c></mjx-mn></mjx-script></mjx-msup></mjx-math></mjx-container> for comparable mass systems. The sky localization is good enough that it may be possible to cross-correlate GW searches with galaxy catalogs and to search for electromagnetic counterparts to IMBH mergers. We also point out that the low-frequency sensitivity of the detectors is crucial for IMBH detection and parameter estimation. It will be interesting to use our results in conjunction with population synthesis codes to constrain astrophysical IMBH formation models.\",\"PeriodicalId\":20167,\"journal\":{\"name\":\"Physical Review D\",\"volume\":\"127 1\",\"pages\":\"\"},\"PeriodicalIF\":5.0000,\"publicationDate\":\"2024-11-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review D\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevd.110.103002\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevd.110.103002","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
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