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Table 4.

Simulations of the PL relations of the form M = α + β log P with input values α = −2.50 and β = −3.30.

# α β N Remarks
Using exact distance
1 −2.502 ± 0.006 −3.296 ± 0.007 426 1% error on distance
2 −2.502 ± 0.009 −3.296 ± 0.011 426 2% error on distance
3 −2.502 ± 0.018 −3.296 ± 0.020 426 5% error on distance
4 −2.504 ± 0.037 −3.294 ± 0.041 426 10% error on distance
With parallax error
5 −2.499 ± 0.006 −3.297 ± 0.007 426 1% error on distance
6 −2.500 ± 0.009 −3.294 ± 0.011 426 2% error on distance
7 −2.496 ± 0.018 −3.293 ± 0.020 426 5% error on distance
8 −2.488 ± 0.037 −3.294 ± 0.041 426 10% error on distance
9 −2.521 ± 0.021 −3.267 ± 0.022 426 Parallax error based on data
10 −2.518 ± 0.027 −3.268 ± 0.030 426 Error based on data, another random seed
11 −2.514 ± 0.023 −3.273 ± 0.025 426 Error based on data, another random seed
12 −2.511 ± 0.021 −3.276 ± 0.023 361 Error based on data, π > 0, σπ/π < 0.2
13 −2.514 ± 0.024 −3.273 ± 0.027 218 Error based on data, π > 0, σπ/π < 0.1
14 −2.557 ± 0.022 −3.295 ± 0.024 426 Error based on data, ZPoff = −0.029 mas, not in analysis
15 −2.577 ± 0.022 −3.312 ± 0.024 426 Error based on data, ZPoff = −0.046 mas, not in analysis
16 −2.521 ± 0.022 −3.267 ± 0.023 426 Error based on data, ZPoff = −0.046 mas, −0.046 in analysis
17 −2.541 ± 0.022 −3.284 ± 0.023 426 Error based on data, ZPoff = −0.046 mas, −0.029 in analysis
18 −2.565 ± 0.023 −3.319 ± 0.025 310 Error based on data, ZPoff = −0.046 mas, not in analysis, π > 0, σ π /π < 0.2
19 −2.562 ± 0.023 −3.308 ± 0.024 189 Error based on data, ZPoff = −0.046 mas, not in analysis, π > 0, σπ/π < 0.1
20 −2.572 ± 0.025 −3.271 ± 0.027 76 Error based on data, ZPoff = −0.046 mas, not in analysis, π > 0, σπ/π < 0.05
21 −2.542 ± 0.040 −3.276 ± 0.038 13 Error based on data, ZPoff = −0.046 mas, not in analysis, π > 0, σπ/π < 0.02
22 −2.575 ± 0.026 −3.273 ± 0.028 126 Error based on data, ZPoff = −0.046 mas, not in analysis, π > 0.5 mas
23 −2.570 ± 0.030 −3.257 ± 0.033 50 Error based on data, ZPoff = −0.046 mas, not in analysis, π > 1.0 mas
24 −2.539 ± 0.035 −3.279 ± 0.035 20 Error based on data, ZPoff = −0.046 mas, not in analysis, π > 1.5 mas
25 −2.515 ± 0.033 −3.288 ± 0.039 205 As (9), for realistic sample size and δPL = 0 mag
26 −2.520 ± 0.058 −3.289 ± 0.066 205 As (9), for realistic sample size and δPL = 0.066 mag

Notes.N is the number of stars in the solution.

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