Probing the mass and anisotropy of the Milky Way gaseous halo: sight-lines toward Mrk 421 and PKS 2155-304

Abstract

We recently found that the halo of the Milky Way contains a large reservoir of warm-hot gas that accounts for large fraction of the missing baryons from the Galaxy. The average physical properties of this circumgalactic medium (CGM) are determined by combining average absorption and emission measurements along several extragalactic sightlines. However, there is a wide distribution of both, the halo emission measure and the O vii column density, suggesting that the Galactic warm-hot gaseous halo is anisotropic. We present Suzaku observations of fields close to two sightlines along which we have precise O vii absorption measurements with Chandra. The column densities along these two sightlines are similar within errors, but we find that the emission measures are different: 0.0025±0.0006 cm⁻⁶ pc near the Mrk 421 direction and 0.0042±0.0008 cm⁻⁶ pc close to the PKS 2155-304 sightline. Therefore the densities and pathlengths in the two directions must be different, providing a suggestive evidence that the warm-hot gas in the CGM of the Milky Way is not distributed uniformly. However, the formal errors on derived parameters are too large to make such a claim. In the Mrk 421 direction we derive the density of $1.6^{+2.6}_{-0.8} \times 10^{-4}~\mbox{cm}^{-3}$ and pathlength of $334^{+685}_{-274}~\mbox{kpc}$. In the PKS 2155-304 direction we measure the gas density of $3.6^{+4.5}_{-1.8} \times10^{-4}~\mbox{cm}^{-3}$ and path-length of $109^{+200}_{-82}~\mbox{kpc}$. Thus the density and pathlength along these sightlines are consistent with each other within errors. The average density and pathlength of the two sightlines are similar to the global averages, so the halo mass is still huge, over 10 billion solar masses. With more such studies, we will be able to better characterize the CGM anisotropy and measure its mass more accurately. We can then compare the observational results with theoretical models and investigate if/how the CGM structure is related to the larger scale environment of the Milky Way.

We also show that the Galactic disk makes insignificant contribution to the observed O vii absorption; a similar conclusion was also reached by Henley and Shelton (2013) about the emission measure. We further argue that any density inhomogeneity in the warm-hot gas, be it from clumping, from the disk, or from a non-constant density gradient, would strengthen our result in that the Galactic halo path-length and the mass would become larger than what we estimate here. As such, our results are conservative and robust.

Appendix

Here we show explicitly how a two component density distribution affects the resultant halo path-length and mass.

Let us assume that there is a high density component with n(High)=1×10⁻³ cm⁻³ and pathlength L(High)=1 kpc. We can identify this component with the Galactic disk, but that is not important. Let us also say there is a halo of density n(Low)=1×10⁻⁵ cm⁻³.

The column density of the high density component is then N_H=3×10¹⁸ cm⁻² and the emission measure EM(High)=n(High)² L(High)=3×10¹⁵ in units of cm⁻⁵.

The EM would be strongly biased by the high density component, so let us assume it contributes 90 % to the total emission measure. Therefore the total EM=3.3×10¹⁵ in the same units.

By construction, the EM from the low density component is only 10 %, that is EM(Low)=3.3×10¹⁴ in the same units. Given this EM(Low) and n(Low) we can now calculate the path-length of the low density component: L(Low)=300 kpc. And its column density N_H(Low)=3×10¹⁹ cm⁻².

The total disk + halo column density is then N_H=3.3×10¹⁹cm⁻². Thus we have completely defined a two component medium, with the high density component (disk) dominating the observed EM while the low density component (halo) dominating the observed column density. The EM we measure is EM=3.3×10¹⁵ cm⁻⁵ and the total column density we measure is N_H=3.3×10¹⁹ cm⁻².

If we now make the assumption of a single density medium, and derive density and pathlength from the total observed EM and N_H, the values we get are as follows. The average density is n=EM/N_H=1×10⁻⁴ cm⁻³ and the average pathlength L=N_H/n=110 kpc. Thus, under the assumption of a single density plasma, the derived density is an order of magnitude higher and the derived pathlength is about a factor of three lower than the actual density and pathlength of the halo.

The actual mass of the halo (low density component) is M(Low)=n(Low)L(Low)³=7.3×10⁶⁶ in dimensionless units (ignoring constants). The derived mass under the single component assumption, however, is M=nL³=3.6×10⁶⁶ in the same dimensionless units. Thus the mass derived assuming a single density component is a factor of two lower than the actual mass.

Thus, the assumption of a single density halo underpredicts the halo pathlength and mass. We have explicitly presented a two component system here for simplicity, but it shows that any density gradient would similarly strengthen our results. In this example, we have considered that the high density component contributes 90 % to the total EM. Higher contribution to the EM would make the halo even more extended. We thus conclude that any disk contribution, clumping, and/or a declining density profile would make the halo more extended and more massive, thus strengthening our result.