Correction: Godzieba, D.A.; Radice, D. High-Order Multipole and Binary Love Number Universal Relations. Universe 2021, 7, 368

Daniel A. Godzieba; David Radice

doi:10.3390/universe7120456

and

¹

Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA

²

Institute for Gravitation & The Cosmos, The Pennsylvania State University, University Park, PA 16802, USA

³

Department of Astronomy & Astrophysics, The Pennsylvania State University, University Park, PA 16802, USA

^*

Author to whom correspondence should be addressed.

Universe2021, 7(12), 456;https://doi.org/10.3390/universe7120456

This article belongs to the Special Issue Properties and Dynamics of Neutron Stars and Proto-Neutron Stars

Version Notes

Order Reprints

The authors wish to make the following corrections to their paper []:

In Section 4, we accidentally swapped the numerators in the definitions of the fitting functions

α (x)

and

β (x)

in Equation (8). The definitions are corrected as

α (x) = \frac{\sum_{k = 0}^{3} p_{k} x^{k}}{\sum_{k = 0}^{2} q_{k} x^{k}} km and β (x) = \frac{\sum_{k = 0}^{2} p_{k} x^{k}}{\sum_{k = 0}^{2} q_{k} x^{k}},

(8)

where

x = (M / M_{⊙} - μ_{M}) / σ_{M}

,

μ_{M} = 1.1537

, and

σ_{M} = 0.15927

.

As a consequence of this error, Table 3 in Section 4 has the fitting parameters for

α (x)

and

β (x)

incorrectly labelled. Additionally, it was not originally made clear in the table that we fix

q_{2} = 1

for all fits. The table is corrected to Table 3. All other results are unaffected by these corrections. The authors would like to apologize for any inconvenience caused to the readers by these changes.

Table 3. Fitting parameters

\vec{p} = {p_{k}}

and

\vec{q} = {q_{k}}

for

α

and

β

as functions of

x = (M / M_{⊙} - μ_{M}) / σ_{M}

, where

μ_{M} = 1.1537

and

σ_{M} = 0.15927

for several values of M. The fitting functions are given in Equation (3).

Reference

Godzieba, D.A.; Radice, D. High-Order Multipole and Binary Love Number Universal Relations. Universe 2021, 7, 368. [Google Scholar] [CrossRef]

Table 3. Fitting parameters

\vec{p} = {p_{k}}

and

\vec{q} = {q_{k}}

for

α

and

β

as functions of

x = (M / M_{⊙} - μ_{M}) / σ_{M}

, where

μ_{M} = 1.1537

and

σ_{M} = 0.15927

for several values of M. The fitting functions are given in Equation (3).

Table 3. Fitting parameters

\vec{p} = {p_{k}}

and

\vec{q} = {q_{k}}

for

α

and

β

as functions of

x = (M / M_{⊙} - μ_{M}) / σ_{M}

, where

μ_{M} = 1.1537

and

σ_{M} = 0.15927

for several values of M. The fitting functions are given in Equation (3).

$M / M_{⊙}$		$p_{0}$	$p_{1}$	$p_{2}$	$p_{3}$	$q_{0}$	$q_{1}$	$q_{2}$
1.4	$β (x)$	$404.40$	$- 96.991$	$26.475$	-	$65.755$	$- 15.259$	1
	$α (x)$	$224.75$	$- 24.553$	$11.832$	$- 1.8434$	$19.758$	$- 1.9914$	1
1.5	$β (x)$	$502.01$	$- 119.44$	$32.193$	-	$79.153$	$- 16.598$	1
	$α (x)$	$282.86$	$- 29.568$	$12.893$	$- 2.2628$	$24.833$	$- 2.3357$	1
1.6	$β (x)$	$642.10$	$- 152.88$	$40.447$	-	$98.054$	$- 18.391$	1
	$α (x)$	$386.63$	$- 42.102$	$14.780$	$- 3.0054$	$33.942$	$- 3.2743$	1
1.7	$β (x)$	$877.56$	$- 210.98$	$54.468$	-	$129.67$	$- 21.419$	1
	$α (x)$	$598.97$	$- 73.554$	$18.854$	$- 4.5818$	$52.655$	$- 5.7193$	1
1.8	$β (x)$	$1442.2$	$- 356.28$	$88.775$	-	$206.20$	$- 29.608$	1
	$α (x)$	$1291.3$	$- 192.50$	$32.831$	$- 10.064$	$113.87$	$- 15.207$	1
1.9	$β (x)$	$2734.1$	$- 709.62$	$174.36$	-	$380.72$	$- 46.815$	1
	$α (x)$	$3282.2$	$- 592.78$	$80.705$	$- 27.980$	$291.00$	$- 48.054$	1
2	$β (x)$	63,061	$- 19,071$	$3663.7$	-	$8959.4$	$- 1478.5$	1
	$α (x)$	$9986.9$	$- 2011.9$	$232.61$	$- 82.091$	$887.58$	$- 167.09$	1
2.14	$β (x)$	93,209	$- 34,415$	$6102.8$	-	12,686	$- 2286.4$	1
	$α (x)$	58,353	$- 18,272$	$1904.6$	$- 609.58$	$5234.8$	$- 1543.2$	1

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Correction: Godzieba, D.A.; Radice, D. High-Order Multipole and Binary Love Number Universal Relations. Universe 2021, 7, 368

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