Constraining the nature of the most extreme Galactic particle accelerator - H.E.S.S. observations of the microquasar V4641 Sgr

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Table 2.

Best-fit values and confidence intervals (C.I.) for the parameters of the hadronic and a selection of the leptonic spectral models.

Parameter	Best-fit value	68% C.I.	95% C.I.
leptonic model, t_inj = 2 × 10² yr

B (μG)	2.72	(2.11, 3.26)	(1.31, 3.82)
α_e (% of L_Edd)	2.13	(1.45, 5.13)	(1.10, 8.59)
Γ_e	1.85	(1.70, 2.01)	(1.47, 2.07)
$E_{cut}^{e}$ $E_{\mathrm{cut}}^{e}$ (PeV)	0.49	(0.33, 0.86)	(0.21, 1.46)
$u_{tot}^{e}$ $u_{\mathrm{tot}}^{e}$ (eV cm⁻³)	0.08	(0.06, 0.20)	(0.04, 0.33)
$u_{B} / u_{tot}^{e}$ $u_B/u_{\mathrm{tot}}^{e}$	2.22	–	–

leptonic model, t_inj = 2 × 10³ yr

B (μG)	2.87	(2.26, 3.45)	(1.48, 3.96)
α_e (% of L_Edd)	0.33	(0.20, 1.41)	(0.13, 3.52)
Γ_e	1.93	(1.82, 2.12)	(1.59, 2.19)
$E_{cut}^{e}$ $E_{\mathrm{cut}}^{e}$ (PeV)	0.99	(0.59, 11.59)	(0.31, 68.41)
$u_{tot}^{e}$ $u_{\mathrm{tot}}^{e}$ (eV cm⁻³)	0.13	(0.08, 0.55)	(0.05, 1.37)
$u_{B} / u_{tot}^{e}$ $u_B/u_{\mathrm{tot}}^{e}$	1.59	–	–

leptonic model, t_inj = 2 × 10⁴ yr

B (μG)	1.91	(1.54, 2.66)	(1.1, 3.5)
α_e (% of L_Edd)	0.04	(0.03, 0.06)	(0.02, 0.1)
Γ_e	1.81	(1.59, 1.87)	(1.39, 1.98)
$E_{cut}^{e}$ $E_{\mathrm{cut}}^{e}$ (PeV)	20.31	(2.58, 49.09)	(0.88, 90.95)
$u_{tot}^{e}$ $u_{\mathrm{tot}}^{e}$ (eV cm⁻³)	0.16	(0.12, 0.23)	(0.08, 0.39)
$u_{B} / u_{tot}^{e}$ $u_B/u_{\mathrm{tot}}^{e}$	0.58	–	–

leptonic model, t_inj = 7 × 10⁴ yr

B (μG)	2.84	(2.11, 3.42)	(1.4, 3.99)
α_e (% of L_Edd)	0.03	(0.02, 0.09)	(0.01, 0.19)
Γ_e	< 1.0	(1.0, 1.43)	(1.0, 1.62)
$E_{cut}^{e}$ $E_{\mathrm{cut}}^{e}$ (PeV)	1.74	(1.45, 28.2)	(1.16, 78.09)
$u_{tot}^{e}$ $u_{\mathrm{tot}}^{e}$ (eV cm⁻³)	0.41	(0.27, 1.22)	(0.14, 2.58)
$u_{B} / u_{tot}^{e}$ $u_B/u_{\mathrm{tot}}^{e}$	0.49	–	–

hadronic model

Γ_p	1.49	(1.24, 1.64)	(1.04, 1.79)
$E_{tot}^{p}$ $E_{\mathrm{tot}}^{p}$ ( $10^{50} \times n_{0.2 {cm}^{- 3}}^{- 1}$ $10^{50}\times \mathrm{n}^{-1}_{0.2\,\mathrm{cm}^{-3}}$ erg)	8.0	(7.17, 8.76)	(6.57, 10.31)
$u_{tot}^{p}$ $u_{\mathrm{tot}}^{p}$ (n $_{0.2 {cm}^{- 3}}^{- 1}$ $^{-1}_{0.2\,\mathrm{cm}^{-3}}$ keV cm⁻³)	0.49	(0.44, 0.54)	(0.40, 0.63)
$E_{cut}^{p}$ $E_{\mathrm{cut}}^{p}$ (PeV)	1.74	(1.00, 2.69)	(0.72, 4.99)

Notes. The normalisation parameter α_e is given as a percentage of L_Edd and not fraction. The energy densities of protons ( $u_{tot}^{p}$ $u_{\mathrm{tot}}^{p}$ ) and electrons ( $u_{tot}^{p}$ $u_{\mathrm{tot}}^{p}$ ) assume a cylindrical geometry, but we note that the depth of the emission region is completely unconstrained. Cooling and escape were ignored when deriving the energy densities. The magnetic field strengths should be interpreted as upper limits (see the discussion in the text) and, consequently, also the derived equipartition ratio $u_{B} / u_{tot}^{e}$ $u_B/u_{\mathrm{tot}}^{e}$ .

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