Spectroscopic active galactic nucleus survey at z ∼ 2 with NTT/SOFI for GRAVITY+ observations

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Table B.1.

Results of fitting the BLR model to the line profiles.

ID	Model	Tied?	HαR_BLR [ld]	β	ϵ	i [°]	θ₀ [°]	κ	γ	ξ	f_flow	f_ellip	θ_e [°]	Δϕ_peak
					× 10⁻³
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)	(14)	(15)
1	F	-	$2442_{- 1582}^{+ 1123}$ $2442_{-1582}^{+1123}$	${1.36}_{- 0.21}^{+ 0.18}$ ${1.36}_{-0.21}^{+0.18}$	${+ 4.20}_{- 8.27}^{+ 0.69}$ ${+4.20}_{-8.27}^{+0.69}$	$55_{- 27}^{+ 23}$ ${55}_{-27}^{+23}$	$25_{- 6}^{+ 23}$ ${25}_{-6}^{+23}$	${- 0.39}_{- 0.02}^{+ 0.74}$ ${-0.39}_{-0.02}^{+0.74}$	${3.92}_{- 1.81}^{+ 0.48}$ ${3.92}_{-1.81}^{+0.48}$	${0.45}_{- 0.31}^{+ 0.33}$ ${0.45}_{-0.31}^{+0.33}$	${0.43}_{- 0.27}^{+ 0.26}$ ${0.43}_{-0.27}^{+0.26}$	${0.17}_{- 0.08}^{+ 0.27}$ ${0.17}_{-0.08}^{+0.27}$	$19_{- 7}^{+ 35}$ ${19}_{-7}^{+35}$	${9.3}_{- 7.9}^{+ 7.3}$ ${9.3}_{-7.9}^{+7.3}$
2	C	-	$1128_{- 554}^{+ 457}$ $1128_{-554}^{+457}$	${1.86}_{- 0.31}^{+ 0.07}$ ${1.86}_{-0.31}^{+0.07}$	${- 0.34}_{- 0.56}^{+ 0.45}$ ${-0.34}_{-0.56}^{+0.45}$	$43_{- 19}^{+ 16}$ ${43}_{-19}^{+16}$	$61_{- 24}^{+ 17}$ ${61}_{-24}^{+17}$							${4.6}_{- 2.5}^{+ 4.2}$ ${4.6}_{-2.5}^{+4.2}$
3	C	-	$348_{- 229}^{+ 248}$ $348_{-229}^{+248}$	${1.56}_{- 0.92}^{+ 0.20}$ ${1.56}_{-0.92}^{+0.20}$	${0.22}_{- 1.34}^{+ 0.74}$ ${0.22}_{-1.34}^{+0.74}$	$53_{- 27}^{+ 24}$ ${53}_{-27}^{+24}$	$67_{- 43}^{+ 12}$ ${67}_{-43}^{+12}$							${0.3}_{- 0.3}^{+ 1.2}$ ${0.3}_{-0.3}^{+1.2}$
4	C	-	$597_{- 373}^{+ 400}$ $597_{-373}^{+400}$	${1.83}_{- 0.48}^{+ 0.03}$ ${1.83}_{-0.48}^{+0.03}$	${- 0.12}_{- 0.55}^{+ 0.46}$ ${-0.12}_{-0.55}^{+0.46}$	$25_{- 10}^{+ 20}$ ${25}_{-10}^{+20}$	$50_{- 23}^{+ 18}$ ${50}_{-23}^{+18}$							${0.9}_{- 0.6}^{+ 1.9}$ ${0.9}_{-0.6}^{+1.9}$
5	F	-	$1899_{- 1175}^{+ 974}$ $1899_{-1175}^{+974}$	${1.76}_{- 0.21}^{+ 0.13}$ ${1.76}_{-0.21}^{+0.13}$	${+ 0.91}_{- 1.84}^{+ 1.09}$ ${+0.91}_{-1.84}^{+1.09}$	$37_{- 20}^{+ 27}$ ${37}_{-20}^{+27}$	$49_{- 23}^{+ 28}$ ${49}_{-23}^{+28}$	${- 0.01}_{- 0.34}^{+ 0.36}$ ${-0.01}_{-0.34}^{+0.36}$	${2.69}_{- 1.12}^{+ 1.48}$ ${2.69}_{-1.12}^{+1.48}$	${0.48}_{- 0.31}^{+ 0.37}$ ${0.48}_{-0.31}^{+0.37}$	${0.35}_{- 0.24}^{+ 0.38}$ ${0.35}_{-0.24}^{+0.38}$	${0.41}_{- 0.27}^{+ 0.34}$ ${0.41}_{-0.27}^{+0.34}$	$36_{- 25}^{+ 35}$ ${36}_{-25}^{+35}$	${3.6}_{- 2.7}^{+ 3.4}$ ${3.6}_{-2.7}^{+3.4}$
6	C	Y	$1552_{- 335}^{+ 1316}$ $1552_{-335}^{+1316}$	${1.76}_{- 0.21}^{+ 0.13}$ ${1.76}_{-0.21}^{+0.13}$	${- 0.11}_{- 0.23}^{+ 0.21}$ ${-0.11}_{-0.23}^{+0.21}$	$33_{- 9}^{+ 20}$ ${33}_{-9}^{+20}$	$50_{- 11}^{+ 24}$ ${50}_{-11}^{+24}$							${9.6}_{- 4.2}^{+ 9.4}$ ${9.6}_{-4.2}^{+9.4}$
7	C	-	$905_{- 378}^{+ 1058}$ $905_{-378}^{+1058}$	${1.48}_{- 0.32}^{+ 0.35}$ ${1.48}_{-0.32}^{+0.35}$	${- 0.05}_{- 0.88}^{+ 1.07}$ ${-0.05}_{-0.88}^{+1.07}$	$37_{- 14}^{+ 33}$ ${37}_{-14}^{+33}$	$53_{- 25}^{+ 25}$ ${53}_{-25}^{+25}$							${6.2}_{- 4.3}^{+ 9.5}$ ${6.2}_{-4.3}^{+9.5}$
8	C	-	$1492_{- 632}^{+ 1074}$ $1492_{-632}^{+1074}$	${1.56}_{- 0.28}^{+ 0.28}$ ${1.56}_{-0.28}^{+0.28}$	${- 0.32}_{- 0.55}^{+ 0.54}$ ${-0.32}_{-0.55}^{+0.54}$	$38_{- 16}^{+ 23}$ ${38}_{-16}^{+23}$	$56_{- 21}^{+ 23}$ ${56}_{-21}^{+23}$							${7.7}_{- 4.9}^{+ 8.6}$ ${7.7}_{-4.9}^{+8.6}$
9	C	Y	$2931_{- 1089}^{+ 2272}$ $2931_{-1089}^{+2272}$	${1.80}_{- 0.28}^{+ 0.11}$ ${1.80}_{-0.28}^{+0.11}$	${- 0.23}_{- 0.36}^{+ 0.55}$ ${-0.23}_{-0.36}^{+0.55}$	$34_{- 12}^{+ 22}$ ${34}_{-12}^{+22}$	$52_{- 17}^{+ 24}$ ${52}_{-17}^{+24}$							${25.3}_{- 16.4}^{+ 19.0}$ ${25.3}_{-16.4}^{+19.0}$
10	C	Y	$5199_{- 2373}^{+ 3995}$ $5199_{-2373}^{+3995}$	${1.87}_{- 0.29}^{+ 0.07}$ ${1.87}_{-0.29}^{+0.07}$	${- 0.44}_{- 0.68}^{+ 0.68}$ ${-0.44}_{-0.68}^{+0.68}$	$33_{- 14}^{+ 18}$ ${33}_{-14}^{+18}$	$48_{- 17}^{+ 25}$ ${48}_{-17}^{+25}$							${21.5}_{- 14.0}^{+ 30.0}$ ${21.5}_{-14.0}^{+30.0}$
11	C	-	$525_{- 339}^{+ 955}$ $525_{-339}^{+955}$	${1.23}_{- 0.76}^{+ 0.50}$ ${1.23}_{-0.76}^{+0.50}$	${- 0.50}_{- 2.50}^{+ 2.93}$ ${-0.50}_{-2.50}^{+2.93}$	$53_{- 6}^{+ 29}$ ${53}_{-6}^{+29}$	$44_{- 26}^{+ 33}$ ${44}_{-26}^{+33}$							${1.1}_{- 0.9}^{+ 4.2}$ ${1.1}_{-0.9}^{+4.2}$
12	C	-	$252_{- 161}^{+ 338}$ $252_{-161}^{+338}$	${0.94}_{- 0.45}^{+ 0.80}$ ${0.94}_{-0.45}^{+0.80}$	${- 0.06}_{- 2.18}^{+ 1.67}$ ${-0.06}_{-2.18}^{+1.67}$	$37_{- 10}^{+ 39}$ ${37}_{-10}^{+39}$	$70_{- 50}^{+ 7}$ ${70}_{-50}^{+7}$							${0.9}_{- 0.7}^{+ 2.6}$ ${0.9}_{-0.7}^{+2.6}$
13	C	N	$1354_{- 717}^{+ 1017}$ $1354_{-717}^{+1017}$	${1.64}_{- 0.31}^{+ 0.22}$ ${1.64}_{-0.31}^{+0.22}$	${- 0.28}_{- 0.54}^{+ 0.37}$ ${-0.28}_{-0.54}^{+0.37}$	$34_{- 16}^{+ 21}$ ${34}_{-16}^{+21}$	$53_{- 22}^{+ 23}$ ${53}_{-22}^{+23}$							${6.3}_{- 3.7}^{+ 10.2}$ ${6.3}_{-3.7}^{+10.2}$
14	C	-	$330_{- 220}^{+ 423}$ $330_{-220}^{+423}$	${1.39}_{- 0.77}^{+ 0.38}$ ${1.39}_{-0.77}^{+0.38}$	${- 0.14}_{- 1.98}^{+ 2.14}$ ${-0.14}_{-1.98}^{+2.14}$	$48_{- 23}^{+ 27}$ ${48}_{-23}^{+27}$	$59_{- 40}^{+ 18}$ ${59}_{-40}^{+18}$							${1.0}_{- 1.0}^{+ 1.2}$ ${1.0}_{-1.0}^{+1.2}$
15	C	Y	$1273_{- 664}^{+ 776}$ $1273_{-664}^{+776}$	${1.68}_{- 0.35}^{+ 0.13}$ ${1.68}_{-0.35}^{+0.13}$	${0.65}_{- 0.80}^{+ 0.39}$ ${0.65}_{-0.80}^{+0.39}$	$35_{- 16}^{+ 28}$ ${35}_{-16}^{+28}$	$60_{- 29}^{+ 19}$ ${60}_{-29}^{+19}$							${6.1}_{- 4.1}^{+ 6.8}$ ${6.1}_{-4.1}^{+6.8}$
16	C	Y	$2339_{- 1202}^{+ 2263}$ $2339_{-1202}^{+2263}$	${1.46}_{- 0.27}^{+ 0.39}$ ${1.46}_{-0.27}^{+0.39}$	${- 0.51}_{- 0.80}^{+ 0.78}$ ${-0.51}_{-0.80}^{+0.78}$	$41_{- 19}^{+ 27}$ ${41}_{-19}^{+27}$	$59_{- 29}^{+ 19}$ ${59}_{-29}^{+19}$							${8.9}_{- 6.1}^{+ 17.4}$ ${8.9}_{-6.1}^{+17.4}$
17	C	Y	$1151_{- 533}^{+ 718}$ $1151_{-533}^{+718}$	${1.44}_{- 0.28}^{+ 0.33}$ ${1.44}_{-0.28}^{+0.33}$	${- 0.53}_{- 0.77}^{+ 0.59}$ ${-0.53}_{-0.77}^{+0.59}$	$39_{- 18}^{+ 18}$ ${39}_{-18}^{+18}$	$53_{- 18}^{+ 25}$ ${53}_{-18}^{+25}$							${5.8}_{- 2.9}^{+ 5.8}$ ${5.8}_{-2.9}^{+5.8}$
18	C	Y	$2746_{- 1140}^{+ 1645}$ $2746_{-1140}^{+1645}$	${1.79}_{- 0.20}^{+ 0.11}$ ${1.79}_{-0.20}^{+0.11}$	${- 0.07}_{- 0.30}^{+ 0.26}$ ${-0.07}_{-0.30}^{+0.26}$	$32_{- 12}^{+ 12}$ ${32}_{-12}^{+12}$	$47_{- 14}^{+ 18}$ ${47}_{-14}^{+18}$							${15.6}_{- 6.8}^{+ 16.4}$ ${15.6}_{-6.8}^{+16.4}$
19	C	-	$1072_{- 1140}^{+ 1645}$ $1072_{-1140}^{+1645}$	${1.56}_{- 0.98}^{+ 0.22}$ ${1.56}_{-0.98}^{+0.22}$	${+ 0.95}_{- 2.93}^{+ 4.44}$ ${+0.95}_{-2.93}^{+4.44}$	$36_{- 10}^{+ 40}$ ${36}_{-10}^{+40}$	$53_{- 32}^{+ 24}$ ${53}_{-32}^{+24}$							${3.8}_{- 3.1}^{+ 18.6}$ ${3.8}_{-3.1}^{+18.6}$
20	C	Y	$1150_{- 620}^{+ 1150}$ $1150_{-620}^{+1150}$	${1.40}_{- 0.55}^{+ 0.40}$ ${1.40}_{-0.55}^{+0.40}$	${- 1.60}_{- 1.22}^{+ 1.20}$ ${-1.60}_{-1.22}^{+1.20}$	$42_{- 20}^{+ 26}$ ${42}_{-20}^{+26}$	$51_{- 25}^{+ 25}$ ${51}_{-25}^{+25}$							${3.6}_{- 2.5}^{+ 10.6}$ ${3.6}_{-2.5}^{+10.6}$
21	C	Y	$5510_{- 3670}^{+ 2999}$ $5510_{-3670}^{+2999}$	${1.69}_{- 0.44}^{+ 0.18}$ ${1.69}_{-0.44}^{+0.18}$	${- 0.05}_{- 0.64}^{+ 0.51}$ ${-0.05}_{-0.64}^{+0.51}$	$40_{- 23}^{+ 13}$ ${40}_{-23}^{+13}$	$55_{- 31}^{+ 17}$ ${55}_{-31}^{+17}$							${19.8}_{- 12.8}^{+ 35.1}$ ${19.8}_{-12.8}^{+35.1}$
22	C	Y	$1776_{- 946}^{+ 956}$ $1776_{-946}^{+956}$	${1.79}_{- 0.19}^{+ 0.14}$ ${1.79}_{-0.19}^{+0.14}$	${- 0.004}_{- 0.292}^{+ 0.296}$ ${-0.004}_{-0.292}^{+0.296}$	$37_{- 18}^{+ 22}$ ${37}_{-18}^{+22}$	$55_{- 23}^{+ 22}$ ${55}_{-23}^{+22}$							${12.8}_{- 7.8}^{+ 12.8}$ ${12.8}_{-7.8}^{+12.8}$
23	C	Y	$333_{- 162}^{+ 297}$ $333_{-162}^{+297}$	${1.61}_{- 0.45}^{+ 0.22}$ ${1.61}_{-0.45}^{+0.22}$	${- 0.33}_{- 0.55}^{+ 0.75}$ ${-0.33}_{-0.55}^{+0.75}$	$38_{- 16}^{+ 31}$ ${38}_{-16}^{+31}$	$55_{- 25}^{+ 22}$ ${55}_{-25}^{+22}$							${1.5}_{- 1.1}^{+ 3.7}$ ${1.5}_{-1.1}^{+3.7}$
24	C	Y	$4651_{- 1185}^{+ 1307}$ $4651_{-1185}^{+1307}$	${1.65}_{- 0.11}^{+ 0.11}$ ${1.65}_{-0.11}^{+0.11}$	${- 0.26}_{- 0.19}^{+ 0.17}$ ${-0.26}_{-0.19}^{+0.17}$	$40_{- 9}^{+ 9}$ ${40}_{-9}^{+9}$	$54_{- 10}^{+ 14}$ ${54}_{-10}^{+14}$							${25.4}_{- 7.8}^{+ 14.2}$ ${25.4}_{-7.8}^{+14.2}$
25	C	Y	$4252_{- 2029}^{+ 4221}$ $4252_{-2029}^{+4221}$	${1.79}_{- 0.49}^{+ 0.11}$ ${1.79}_{-0.49}^{+0.11}$	${- 0.15}_{- 0.66}^{+ 0.67}$ ${-0.15}_{-0.66}^{+0.67}$	$33_{- 13}^{+ 26}$ ${33}_{-13}^{+26}$	$54_{- 26}^{+ 22}$ ${54}_{-26}^{+22}$							${21.1}_{- 13.3}^{+ 28.6}$ ${21.1}_{-13.3}^{+28.6}$
26	C	-	$606_{- 430}^{+ 518}$ $606_{-430}^{+518}$	${1.48}_{- 0.96}^{+ 0.26}$ ${1.48}_{-0.96}^{+0.26}$	${- 0.55}_{- 2.63}^{+ 3.29}$ ${-0.55}_{-2.63}^{+3.29}$	$48_{- 22}^{+ 28}$ ${48}_{-22}^{+28}$	$61_{- 41}^{+ 16}$ ${61}_{-41}^{+16}$							${0.6}_{- 0.5}^{+ 1.7}$ ${0.6}_{-0.5}^{+1.7}$
27	C	Y	$2112_{- 1083}^{+ 2855}$ $2112_{-1083}^{+2855}$	${1.61}_{- 0.68}^{+ 0.21}$ ${1.61}_{-0.68}^{+0.21}$	${0.08}_{- 0.98}^{+ 0.89}$ ${0.08}_{-0.98}^{+0.89}$	$38_{- 16}^{+ 33}$ ${38}_{-16}^{+33}$	$69_{- 41}^{+ 9}$ ${69}_{-41}^{+9}$							${11.1}_{- 7.1}^{+ 35.5}$ ${11.1}_{-7.1}^{+35.5}$
28	C	Y	$351_{- 277}^{+ 515}$ $351_{-277}^{+515}$	${1.56}_{- 1.07}^{+ 0.21}$ ${1.56}_{-1.07}^{+0.21}$	${- 0.02}_{- 2.09}^{+ 1.56}$ ${-0.02}_{-2.09}^{+1.56}$	$35_{- 14}^{+ 30}$ ${35}_{-14}^{+30}$	$43_{- 18}^{+ 33}$ ${43}_{-18}^{+33}$							${0.3}_{- 0.3}^{+ 1.9}$ ${0.3}_{-0.3}^{+1.9}$
29	C	N	$436_{- 256}^{+ 359}$ $436_{-256}^{+359}$	${1.73}_{- 0.52}^{+ 0.12}$ ${1.73}_{-0.52}^{+0.12}$	${+ 23.32}_{- 0.73}^{+ 0.41}$ ${+23.32}_{-0.73}^{+0.41}$	$44_{- 18}^{+ 33}$ ${44}_{-18}^{+33}$	$51_{- 42}^{+ 25}$ ${51}_{-42}^{+25}$							${1.1}_{- 0.8}^{+ 3.7}$ ${1.1}_{-0.8}^{+3.7}$

Note: The columns show (1) the ID number, (2) the model used (C for circular, F for full), (3) whether the central wavelength of Hβ and Hγ was tied to that of Hα whenever the other Balmer lines are available, (4) the Hα BLR size in ld, (5) the shape parameter of the radial cloud distribution, (6) the amount of shift on the central wavelength of the Balmer line(s), (7) inclination angle, (8) position angle, (9) anisotropy parameter, (10) vertical distribution of clouds, (11) midplane obscuration, (12) binary switch for inflowing (f_flow < 0.5) and outflowing (f_flow > 0.5) radial motion, (13) fraction of clouds in circular/bound orbits, (14) angular location for radial orbit distribution, and (15) the peak expected differential phase. All errors are 1σ uncertainties. More details about the BLR model parameters are discussed in Sect. 5, while the calculation of the peak expected differential phase is shown in Sect. 6.

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