利用下一代地基探测器网络估算中质量黑洞二元参数

IF 5 2区 物理与天体物理 Q1 Physics and Astronomy
Luca Reali, Roberto Cotesta, Andrea Antonelli, Konstantinos Kritos, Vladimir Strokov, Emanuele Berti
{"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;\\\" 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comparable mass systems. 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引用次数: 0

摘要

质量范围在102𝑀⊙≲𝑀≲106𝑀⊙的中等质量黑洞(IMBHs)的形成和演化的天体物理情景仍不确定,但未来的地基引力波(GW)干涉仪将探测IMBH质量范围的低端。我们研究了 IMBH 双星合并的可探测性,以及利用由宇宙探测器(CE)和爱因斯坦望远镜(ET)干涉仪的不同组合组成的下一代地基探测器网络对其参数的可测量性。我们发现,对于成分质量𝑚1,2∼1000𝑀⊙的双星,最佳的3探测器网络可以在𝑧=0.5(𝑧=2)时以误差≲0.1%(≲1%)来约束质量,在𝑧≲2时可以以百分级或更高的精度测量源红移。即使在𝑧=10的条件下,较轻的双星(𝑚1,2≲300𝑀⊙)的红移测量精度仍然可以达到𝒪(10)%。对于𝑚1,2≲1000𝑀⊙的双星,𝑧≲0.5的定位精度在1度以内,对于质量相当的系统,定位精度在0.1度以内。天空定位足够好,可以将全球变暖搜索与星系目录进行交叉关联,并搜索 IMBH 合并的电磁对应物。我们还指出,探测器的低频灵敏度对于 IMBH 的探测和参数估计至关重要。将我们的结果与种群合成代码结合起来使用,以约束天体物理IMBH形成模型,将是很有意义的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Intermediate-mass black hole binary parameter estimation with next-generation ground-based detector networks
Astrophysical scenarios for the formation and evolution of intermediate-mass black holes (IMBHs) in the mass range 102𝑀𝑀106𝑀 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 𝑚1,21000𝑀, an optimal 3-detector network can constrain the masses with errors 0.1% (1%) at 𝑧=0.5 (𝑧=2), and the source redshift can be measured with percent-level accuracy or better at 𝑧2. The redshift of lighter binaries (𝑚1,2300𝑀) can still be measured with 𝒪(10)% accuracy even at 𝑧=10. Binaries with 𝑧0.5 can be localized within 1deg2 for 𝑚1,21000𝑀, and within 0.1deg2 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.
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来源期刊
Physical Review D
Physical Review D 物理-天文与天体物理
CiteScore
9.20
自引率
36.00%
发文量
0
审稿时长
2 months
期刊介绍: Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics. PRD covers experimental and theoretical results in all aspects of particle physics, field theory, gravitation and cosmology, including: Particle physics experiments, Electroweak interactions, Strong interactions, Lattice field theories, lattice QCD, Beyond the standard model physics, Phenomenological aspects of field theory, general methods, Gravity, cosmology, cosmic rays, Astrophysics and astroparticle physics, General relativity, Formal aspects of field theory, field theory in curved space, String theory, quantum gravity, gauge/gravity duality.
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