Comparing the space densities of millisecond-spin magnetars and fast X-ray transients

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Volume 700 (August 2025)

A&A, 700 (2025) A161

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Table 1.

Volumetric rates calculated using SFR density (ℛ_SFR) and galaxy SMD (ℛ_SMD) methods at different redshifts for various MW event rates, r_MW [yr⁻¹].

z	r_MW = 10⁻³	r_MW = 10⁻⁴	r_MW = 10⁻⁵	r_MW = 10⁻⁶
ℛ_SFR (Gpc⁻³ yr⁻¹)
z = 0.3	$(1 . 71_{- 0.44}^{+ 0.92}) \times 10^{4}$ $(1.71^{+0.92}_{-0.44}) \times 10^4$	$(1 . 71_{- 0.44}^{+ 0.92}) \times 10^{3}$ $(1.71^{+0.92}_{-0.44}) \times 10^3$	$(1 . 71_{- 0.44}^{+ 0.92}) \times 10^{2}$ $(1.71^{+0.92}_{-0.44}) \times 10^2$	$(1 . 71_{- 0.44}^{+ 0.92}) \times 10^{1}$ $(1.71^{+0.92}_{-0.44}) \times 10^1$
z = 1.0	$(4 . 38_{- 1.14}^{+ 2.36}) \times 10^{4}$ $(4.38^{+2.36}_{-1.14}) \times 10^4$	$(4 . 38_{- 1.14}^{+ 2.36}) \times 10^{3}$ $(4.38^{+2.36}_{-1.14}) \times 10^3$	$(4 . 38_{- 1.14}^{+ 2.36}) \times 10^{2}$ $(4.38^{+2.36}_{-1.14}) \times 10^2$	$(4 . 38_{- 1.14}^{+ 2.36}) \times 10^{1}$ $(4.38^{+2.36}_{-1.14}) \times 10^1$
z = 2.0	$(6 . 58_{- 1.70}^{+ 3.54}) \times 10^{4}$ $(6.58^{+3.54}_{-1.70}) \times 10^4$	$(6 . 58_{- 1.70}^{+ 3.54}) \times 10^{3}$ $(6.58^{+3.54}_{-1.70}) \times 10^3$	$(6 . 58_{- 1.70}^{+ 3.54}) \times 10^{2}$ $(6.58^{+3.54}_{-1.70}) \times 10^2$	$(6 . 58_{- 1.70}^{+ 3.54}) \times 10^{1}$ $(6.58^{+3.54}_{-1.70}) \times 10^1$
z = 3.0	$(4 . 42_{- 1.15}^{+ 2.38}) \times 10^{4}$ $(4.42^{+2.38}_{-1.15}) \times 10^4$	$(4 . 42_{- 1.15}^{+ 2.38}) \times 10^{3}$ $(4.42^{+2.38}_{-1.15}) \times 10^3$	$(4 . 42_{- 1.15}^{+ 2.38}) \times 10^{2}$ $(4.42^{+2.38}_{-1.15}) \times 10^2$	$(4 . 42_{- 1.15}^{+ 2.38}) \times 10^{1}$ $(4.42^{+2.38}_{-1.15}) \times 10^1$
z = 4.0	$(2 . 61_{- 0.68}^{+ 1.41}) \times 10^{4}$ $(2.61^{+1.41}_{-0.68}) \times 10^4$	$(2 . 61_{- 0.68}^{+ 1.41}) \times 10^{3}$ $(2.61^{+1.41}_{-0.68}) \times 10^3$	$(2 . 61_{- 0.68}^{+ 1.41}) \times 10^{2}$ $(2.61^{+1.41}_{-0.68}) \times 10^2$	$(2 . 61_{- 0.68}^{+ 1.41}) \times 10^{1}$ $(2.61^{+1.41}_{-0.68}) \times 10^1$
ℛ_SMD (Gpc⁻³ yr⁻¹)
z = 0.3	$(1 . 59_{- 0.14}^{+ 0.15}) \times 10^{4}$ $(1.59^{+0.15}_{-0.14}) \times 10^4$	$(1 . 59_{- 0.14}^{+ 0.15}) \times 10^{3}$ $(1.59^{+0.15}_{-0.14}) \times 10^3$	$(1 . 59_{- 0.14}^{+ 0.15}) \times 10^{2}$ $(1.59^{+0.15}_{-0.14}) \times 10^2$	$(1 . 59_{- 0.14}^{+ 0.15}) \times 10^{1}$ $(1.59^{+0.15}_{-0.14}) \times 10^1$
z = 1.0	$(1 . 67_{- 0.12}^{+ 0.13}) \times 10^{4}$ $(1.67^{+0.13}_{-0.12}) \times 10^4$	$(1 . 67_{- 0.12}^{+ 0.13}) \times 10^{3}$ $(1.67^{+0.13}_{-0.12}) \times 10^3$	$(1 . 67_{- 0.12}^{+ 0.13}) \times 10^{2}$ $(1.67^{+0.13}_{-0.12}) \times 10^2$	$(1 . 67_{- 0.12}^{+ 0.13}) \times 10^{1}$ $(1.67^{+0.13}_{-0.12}) \times 10^1$
z = 2.0	$(5 . 80_{- 0.58}^{+ 0.60}) \times 10^{3}$ $(5.80^{+0.60}_{-0.58}) \times 10^3$	$(5 . 80_{- 0.58}^{+ 0.60}) \times 10^{2}$ $(5.80^{+0.60}_{-0.58}) \times 10^2$	$(5 . 80_{- 0.58}^{+ 0.60}) \times 10^{1}$ $(5.80^{+0.60}_{-0.58}) \times 10^1$	$(5 . 80_{- 0.58}^{+ 0.60}) \times 10^{0}$ $(5.80^{+0.60}_{-0.58}) \times 10^0$
z = 3.0	$(2 . 79_{- 0.30}^{+ 0.28}) \times 10^{3}$ $(2.79^{+0.28}_{-0.30}) \times 10^3$	$(2 . 79_{- 0.30}^{+ 0.28}) \times 10^{2}$ $(2.79^{+0.28}_{-0.30}) \times 10^2$	$(2 . 79_{- 0.30}^{+ 0.28}) \times 10^{1}$ $(2.79^{+0.28}_{-0.30}) \times 10^1$	$(2 . 79_{- 0.30}^{+ 0.28}) \times 10^{0}$ $(2.79^{+0.28}_{-0.30}) \times 10^0$
z = 4.0	(8.70 ± 0.80)×10²	(8.70 ± 0.80)×10¹	(8.70 ± 0.80)×10⁰	(8.70 ± 0.80)×10⁻¹

Notes. ℛ_SFR values are derived assuming SFR_MW = 2.0 ± 0.7 M_⊙ yr⁻¹.

ℛ_SMD values are calculated using ρ^* values from Table C.1 in Weaver et al. (2023).

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