The density profile of Milky Way dark matter halo constrained from the OGLE microlensing sky map

Open Access

Table 1.

Density profile and velocity profile for each type of lens, where α = d_l/d_s, κ = 5.625 × 10⁻³ km/s/pc, λ = 3.75 × 10⁻³ km/s/pc, δ = (8000 − x) pc, K₀(x) is the modified Bessel function, and $R = {(x^{2} + y^{2})}^{\frac{1}{2}}$ $R=(x^2+\mathit{y}^2)^\frac{1}{2}$ , s⁴ = R⁴ + (z/0.61)⁴, r² = x² + y² + z².

Lens’ kind	Density profile ρ[M_⊙/pc³]	Velocity profile(μ, σ) [km/s]
Bulge	$1.04 \times 10^{6} {(\frac{s}{0.482 pc})}^{- 1.85}$ $1.04\times10^6\left(\frac{s}{0.482\,\mathrm{pc}}\right)^{-1.85}$ , (s < 938pc)	$f_{y} : {- 220 (1 - α), 100 \sqrt{1 + α^{2}}}$ $f_{\mathit{y}} : \{-220(1-\alpha),100\sqrt{1+\alpha^2}\}$
	3.53 $K_{0} (\frac{s}{667 pc})$ $K_0\left(\frac{s}{667\,\mathrm{pc}}\right)$ , (s ≥ 938 pc)	$f_{z} : {0, 100 \sqrt{1 + α^{2}}}$ $f_z : \{0,100\sqrt{1+\alpha^2} \}$

Disk	$0.06 \times \exp [- {\frac{R - 8000}{3500} + \frac{z}{325}}]$ $0.06\times\mathrm{exp}[-\{\frac{R-8000}{3500}+\frac{z}{325}\}]$	$f_{y} : {220 α, \sqrt{{(κ δ + 30)}^{2} + {(100 α)}^{2}}}$ $f_{\mathit{y}} : \{220\alpha, \sqrt{(\kappa\delta+30)^2+(100\alpha)^2}\}$
		$f_{z} : {0, \sqrt{{(λ δ + 30)}^{2} + {(100 α)}^{2}}}$ $f_z : \{0, \sqrt{(\lambda\delta+30)^2+(100\alpha)^2}\}$

MDMS	Cusp: $4.88 \times 10^{- 3} \frac{1}{(r / r_{s}) {(1 + r / r_{s})}^{2}}$ $4.88\times10^{-3}\frac{1}{(r/r_{\mathrm{s}})(1+r/r_{\mathrm{s}})^2}$	$f_{y} : {- 220 (1 - α), \sqrt{220^{2} + {(100 α)}^{2}}}$ $f_{\mathit{y}} : \{-220(1-\alpha),\sqrt{220^2+(100\alpha)^2}\}$
	Core: $\frac{ρ_{b}}{(1 + r / r_{b}) (1 + {(r / r_{b})}^{2})}$ $\frac{\rho_{\mathrm{b}}}{(1+r/r_{\mathrm{b}})(1+(r/r_{\mathrm{b}})^2)}$	$f_{z} : {0, \sqrt{220^{2} + {(100 α)}^{2}}}$ $f_z: \{0,\sqrt{220^2+(100\alpha)^2}\}$

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