The Milky Way's Hot Gas Kinematics: Signatures in Current and Future OVII Absorption Line Observations

5.6 MB·

by  Matthew J. Miller

Draft version January 27, 2016
PreprinttypesetusingLATEXstyleemulateapjv.01/23/15
THE MILKY WAY’S HOT GAS KINEMATICS: SIGNATURES IN CURRENT AND FUTURE OVII
ABSORPTION LINE OBSERVATIONS
Matthew J. Miller, Edmund J. Hodges-Kluck, & Joel N. Bregman
DepartmentofAstronomy,UniversityofMichigan,AnnArbor,MI48104,USA
Draft version January 27, 2016
ABSTRACT
Detections of z ≈ 0 oxygen absorption and emission lines indicate the Milky Way hosts a hot (∼
106 K), low-density plasma extending (cid:38)50 kpc into the Mily Way’s halo. Current X-ray telescopes
6
cannot resolve the line profiles, but the variation of their strengths on the sky constrains the radial
1
0 gas distribution. Interpreting the O VII Kα absorption line strengths has several complications,
2 including optical depth and line of sight velocity effects. Here, we present model absorption line
profiles accounting for both of these effects to show the lines can exhibit asymmetric structures and
n
be broader than the intrinsic Doppler width. The line profiles encode the hot gas rotation curve, the
a
netinfloworoutflowofhotgas,andthehotgasangularmomentumprofile. Weshowhowlineofsight
J
velocity effects impact the conversion between equivalent width and the column density, and provide
5
modifiedcurvesofgrowthaccountingfortheseeffects. Asanexample, weanalyzetheLMCsightline
2 pulsar dispersion measure and OVII equivalent width to show the average gas metallicity is (cid:38)0.6Z
andb(cid:38)100kms−1. Determiningthesepropertiesoffersvaluableinsightsintothedynamicalstateo(cid:12)f
]
A the Milky Way’s hot gas, and improves the line strength interpretation. We discuss future strategies
to observe these effects with an instrument that has a spectral resolution of about 3000, a goal that
G
is technically possible today.
h. Keywords: Galaxy: halo – ISM: structure – line: profiles – X-rays: diffuse background – X-rays: ISM
p
-
o 1. INTRODUCTION traviolet absorption line surveys probing gas at T ∼105
r K have also revealed absorbers at a wide range of Local
t The observed dynamics of stars and gas in galaxies
s haveplayedvitalrolesininterpretingthecontent, struc- Standard of Rest (LSR) velocities. Absorbers observed
[a ture, and formation of galaxies. Baryons respond to the at |vLSR| (cid:46) 100 km s−1 are typically associated with a
total galactic gravitational field, implying the observed warm-ionized atmosphere corotating with the disk (e.g.,
1 velocitystructureprobestheunderlyingdarkmatterdis- Savageetal.2003;Bowenetal.2008),whileabsorbersat
v tribution. Measurements of the H I rotation curves of |vLSR| (cid:62) 100 km s−1 are interpreted as discrete clouds
7 late-type galaxies (e.g., Kent 1987; de Blok et al. 2008), or complexes of material, commonly referred to as high
9 thestellarvelocitydispersionsofearlytypegalaxies(e.g., velocityclouds(e.g., Wakker&vanWoerden1997;Sem-
7 Bernardietal.2005;Matkovi´c&Guzm´an2005),andthe bach et al. 2003). The clouds’ origins are still debated,
6 orbits of satellite galaxies (e.g., Boylan-Kolchin et al. withtheleadingtheoriesincludinggalacticfountainpro-
0 2013) have all been crucial in understanding how and cesses in the Galactic disk, material stripped from orbit-
1. why galaxies form the way they do. Additionally, kine- ingsatellitegalaxies,ormaterialcondensedoutofahot-
0 maticobservationsandsimulationsshowinflowsandout- terphaseofhalogas(seereviewby Putmanetal.2012).
6 flowsofmultiphasegasareprevalentinthegalaxyevolu- Regardless of their origins, the clouds’ characteristic ve-
1 tionprocess(e.g., Kaufmannetal.2006;Coiletal.2011; locities imply they can supply a substantial amount of
: Kacprzaketal.2012). Thelatterprobegalacticfeedback neutral gas to the H I disk and that the clouds interact
v
mechanisms while the former probe the accretion of gas with the surrounding hot gas material.
i
X ontogalaxiesthatcangeneratefuturestarformationac- The Milky Way and Milky Way-like galaxies also host
r tivity. Allofthesemethodsprovideauniqueviewofthe hotgasdistributionsbetween106 -107 K(Spitzer1956),
a galaxy formation and evolution process, and help shape which formed either from supernova explosions in the
the view of the Milky Way. disk(e.g., Joung&MacLow2006;Hilletal.2012)orgas
There has been extensive work on the Milky Way’s thatwasshock-heatedtotheMilkyWay’svirialtempera-
neutralandwarmionizedgaskinematics,providingvalu- tureasitaccretedontothedarkmatterhalo(e.g., White
able information on the Milky Way’s total H I content & Frenk 1991; Cen & Ostriker 2006; Fukugita & Peebles
and interplay between the Galactic disk and halo. In 2006). Like the cooler gas, the hot gas responds to the
the Galactic disk, all-sky maps of 21 cm emission line Milky Way’s gravitational field, implying any kinematic
radiationrevealemissionacrossarangeofvelocitiesasa structure is connected with its formation and evolution.
function of Galactic longitude (e.g., Westerhout 1957). These motions include global rotation from residual or
Decoding the emission strength as a function of l and injectedangularmomentum, turbulence, bulkflows, and
v implies the existence of a HI disk corotating with the net inflow (accretion) or outflow (wind), all of which re-
stellardiskandwith∼10%itsmassalongwithnumerous late to how the galaxy has formed and evolved. How-
spiral arm structures (see review by Burton 1976). Ul- ever, the large spatial extent of the hot gas ((cid:38)10 kpc
from the Sun) combined with current observational ca-
[email protected],[email protected],[email protected]
2
pabilities limit constraints on hot gas dynamics. This ratio targets. In particular, Hodges-Kluck et al. (2016)
is important since the gas velocity structure can impact utilized the improved calibration for sun angle and he-
hotgasobservablesandtheinferredstructure,similarto liocentric motion in XMM-Newton RGS observations to
the HI analyses discussed above. significantly improve the precision for line centroid mea-
The Milky Way’s hot gas distribution is volume-filling surements. Thisupdatedcalibrationresultedinasample
on(cid:38)10kpcscales,hasdensityestimatesrangingbetween of37OVIIabsorptionlinecentroidsfromarchivalXMM-
10−5 −10−3 cm−3, and a temperature characteristic of Newton RGS data with uncertainties ranging from ≈25-
theMilkyWay’svirialtemperature, ≈2×106 K.Acolli- 400 km s−1. The measured values are inconsistent with
sionally ionized plasma at this temperature emits in the a stationary hot gas halo, and suggest the hot rotates
soft X-ray band, 0.5 - 2.0 keV, making it the dominant in the same direction as the disk. This analysis high-
source of the ROSAT 3/4 keV background (Snowden lights that high resolution absorption line observations
etal.1997). All-skymapsfromtheROSAT All-skySur- areusefulprobesoftheMilkyWay’shotgaskinematics.
vey constrained the characteristic densities and temper- Here, we present model absorption line profiles for dif-
ature of the plasma, but higher resolution spectroscopic ferent hot gas velocity structures and analyze their ef-
observations with current X-ray telescopes provide addi- fects on current and future high resolution absorption
tional constraints on the gas structure and origin. lineobservations. Themodelingisanalogoustothelong-
Recent work on hot gas in the Milky Way has relied established work on the Milky Way’s H I structure and
on OVII and OVIII emission and absorption line obser- kinematics discussed above, however the hot gas system
vations characteristic of a 106 - 107 K plasma (Paerels we consider is extended and spherical out to the Milky
& Kahn 2003). The emission lines are observed in ∼ Way’s virial radius. For velocity profiles, we explore
1000 blank fields of view using either sounding rocket the effects of gas rotation in the same direction as the
experiments (McCammon et al. 2002), or the CCDs on disk and global inflows/outflows of gas. We show that
boardcurrentX-raytelescopes(e.g., Yoshinoetal.2009; the absorption lines can exhibit significant asymmetries,
Henley & Shelton 2012). The number of bright X-ray broadeningbeyondthe Dopplerwidth, and differentline
point sources in the soft X-ray band limits the number centers depending on the underlying velocity structure.
of absorption line measurements, but they are detected These model line centroids complement the work dis-
in about 40 active galactic nuclei (e.g., Nicastro et al. cussed above, but observing the profile shapes requires
2002; Rasmussen et al. 2003; Wang et al. 2005; Breg- a higher resolution X-ray spectrograph. We discuss the
man & Lloyd-Davies 2007; Yao & Wang 2007; Gupta instrumentrequirementstoobservesucheffectsandhow
et al. 2012; Miller & Bregman 2013; Fang et al. 2015) futureobservationswillprovideadditionalconstraintson
and X-ray binary (Yao & Wang 2005; Hagihara et al. the Milky Way’s hot gas kinematics and baryon content
2010)spectra. Interpretingthelinestrengthshasseveral (see discussion by Bregman et al. 2015).
difficulties: (1) weak detections of O VII Kβ absorption Inadditiontothelineprofilecalculations,weshowhow
lines suggest some of the lines may not be optically thin opticaldepthandkinematiceffectsimpactongoingwork
(τ (cid:46)2; Williams et al. 2005; Gupta et al. 2012; Fang ontheMilkyWay’shotgasstructure. Accountingforve-
o
et al. 2015), (2) the Sun exists within the Local Hot locity flows in the halo can broaden the total absorption
Bubble, which is 100-300 pc in size and has signatures line profile in velocity space, which impacts the conver-
in the soft X-ray band (e.g., Snowden et al. 1990, 1993; sionbetweenobservedequivalentwidthsandtheinferred
Kuntz & Snowden 2000; Lallement et al. 2003; Smith column densities. We present curves of growth that ac-
et al. 2007; Welsh & Shelton 2009; Smith et al. 2014a), count for these velocity effects along with the plasma
(3) solar wind charge exchange emission can add signif- opticaldepth,providingmoreaccurateinferencesforthe
icant time-varying emission to individual emission line gas density structure.
observations (e.g., Snowden et al. 2004; Koutroumpa The rest of the paper is structured as follows. In Sec-
et al. 2007; Carter & Sembay 2008; Carter et al. 2011; tion 2,wedescribeourlineprofilecalculation,including
Galeazzi et al. 2014; Henley & Shelton 2015). Analyses a discussion on the inferred hot gas density and velocity
of the line strengths that account for these issues sug- structures. Thisalsoincludesthealteredconversionsbe-
gestthegasstructureisanextended,sphericalcoronaas tween equivalent widths and column densities. Section
opposed to a flattened disk-like morphology (Fang et al. 3includesadiscussionandsummaryofourresults, with
2013; Miller & Bregman 2013, 2015). additional implications for future X-ray missions.
The above studies focused primarily on the line
strengths since the lines are unresolved with current X- 2. CALCULATIONSOFLINESHAPESANDEQUIVALENT
raytelescopes, howeverrecentdatareductiontechniques WIDTHS
and improved calibration allow the line centroids to be The calculation and interpretation of absorption line
measuredwithhighprecisionaswell. Theemissionlines shapes is analogous to the Galactic H I distribution. In
aresignificantlyblendedatCCDresolution(EPIC-MOS these studies, resolved HI 21 cm emission line measure-
FWHM ∼50 eV ∼25,000 km s−1 at 0.6 keV; Sembay ments in velocity space constrain the neutral hydrogen
et al. 2004), implying they do not encode hot gas kine- distribution and kinematics in the Galactic disk (e.g.,
matic information. The absorption lines are also unre- Kalberla et al. 2007). These methods involve analyzing
solved at current grating resolutions (Reflection Grat- the amount of emission received at different velocities
ing Spectrometer FWHM ∼2 eV∼1000 km s−1 at 0.6 and different Galactic longitudes. Here, we make sim-
keV; den Herder et al. 2003), but the higher resolution ilar predictions for the hot gas absorption line profiles,
compared to the CCDs yields accurate equivalent width but assuming different underlying hot gas density and
and line centroid measurements in high signal-to-noise velocity profiles compared to the neutral hydrogen dis-
tribution. Theprimarydifferencehereistheassumption
3
thatthehotgasisavolume-filleddistributionofmaterial Hodges-Kluck et al. 2016). Additional work by Fang
extendingtotheMilkyWay’svirialradiusasopposedto et al. (2013) explored more sophisticated spherical, ex-
only being confined to the Galactic disk. Similarly, we tended density models (an adiabatic profile and a cuspy
explore different large-scale velocity profiles for the hot NFW profile) and an exponential disk model to com-
gas that deviate from simple corotating motion with the pare with other observed constraints, such as the resid-
disk. These factors imply that different density and ve- ual pulsar dispersion measure toward the Large Mag-
locityprofilesproduceuniquelineshapesandlinecenter ellanic Cloud (LMC) (Anderson & Bregman 2010) and
shifts for different l,b coordinates. We explore these ef- ram-pressurestrippingofdwarfspheroidalgalaxies(e.g.,
fects and estimate their impact on current and future Grcevich & Putman 2009). They found the spherical,
absorption line measurements. extended models were consistent with these constraints,
while the exponential disk model was not. Therefore, an
2.1. Model Assumptions extended, spherical density morphology appears to be
consistent with several observed hot gas properties, and
We make several assumptions for the hot gas density,
a simple power law can reproduce how the observed line
temperature, and metallicity distribution based on pre-
strengths vary across the sky.
vious observational and theoretical analyses. Most of
Theβ-modelisalsousedforfittingtheobservedX-ray
theseassumptionsarebasedontheresultsfromMiller&
surface brightness profiles around nearby galaxies. This
Bregman (2013, 2015), and we refer the reader to these
has historically been done for ≈50 early-type galaxies,
studies for a more detailed description. Here, we out-
withfittedβvaluesrangingbetween0.4-1.0foratypical
line the most important assumptions and any caveats in
early-type galaxy (Forman et al. 1985; O’Sullivan et al.
termsofhowtheycouldaffectourabsorptionlineprofile
2003). More recently, there have been detections of dif-
calculations.
fuse X-ray halos around massive (∼10 times larger than
We assume the hot gas density distribution follows a
the Milky Way) late-type galaxies within ∼70 kpc (An-
modifiedsphericalβ-modelextendingtotheMilkyWay’s
derson & Bregman 2011; Dai et al. 2012; Bogd´an et al.
virial radius. The β-model has the following functional
2013a,b; Anderson et al. 2016). Although there are only
form:
fourlate-typegalaxieswherethesecoronaearedetected,
their fitted β values are also comparable to the results
n(r)=n (1+(r/r )2)−3β/2, (1)
o c from early-type galaxy surveys. This further motivates
where n is the core density, r is the core radius, and our initial choice to use a β model as our underlying
o c
β controls the slope at r (cid:29) r . The Milky Way’s ex- Milky Way hot gas density profile.
c
pected r is ((cid:46)5 kpc), a region that is not well sampled We also assume that the hot gas temperature, oxy-
c
by absorption or emission line observations. To account gen abundance, and metallicity are constant with ra-
for this, Miller & Bregman (2013) defined a modified β- dius. Observationally, the Milky Way’s hot gas temper-
model in the limit where r (cid:29)r : ature is inferred from a combination of fitting soft X-ray
c
background (SXRB) spectra with thermal plasma mod-
n r3β els, or comparing the O VII to O VIII absorption line
n(r)≈ o c , (2)
ratio in individual sight lines where both lines are de-
r3β
tected. Both methods indicate that the hot gas temper-
where norc3β is the density normalization and -3β is the atureis≈2×106K,withthelattermethodprovidingthe
slope. This density profile is effectively a power law de- most current observational constraints. Henley & Shel-
scribing the Milky Way’s hot gas distribution. Unless ton(2013)fitthe0.5-2.0keVbandof110SXRBspectra
otherwisestated,weassumedensityparametersofnorc3β with multiple thermal APEC plasma models to measure
= 1.3×10−2 cm−3 kpc3β and β = 0.5 based on results the Milky Way’s hot halo emission measure and temper-
from Miller & Bregman (2015). ature distribution. The found the halo gas temperature
This model, although simple, is not arbitrarily cho- shows little variation across the sky with a median value
sen, and has successfully reproduced several Milky Way of 2.22×106 K and interquartile region of 0.63×106 K.
hot gas observables. Most recent studies on the Milky The fact that this value is consistent across the sky im-
Way’s hot gas structure follow a general methodology. pliesthegasisclosetoisothermal. Therefore,weassume
One assumes one of two types of underlying density dis- aconstanthalogastemperatureof2×106 K,resultingin
tributions: an exponential disk with scale height of 5-10 anOVIIionfractionof0.5(Sutherland&Dopita1993).
kpc, oralower-density, sphericalmodelextendingtothe There is less certainty when considering the hot gas
virialradius. Givenamodelchoice, onecomparesmodel metallicity and oxygen abundance since there are no di-
observations to measured observations and determines if rect observational constraints on these values. The re-
the model is consistent with the data. The primary ob- ported solar oxygen abundance relative to hydrogen has
servablesoftheMilkyWay’shotgasareOVIIandOVIII varied in the literature, but we assume a value of 5.49
absorption and emission line strengths (e.g., Paerels & × 10−4 Holweger (2001). Galaxy evolution simulations
Kahn 2003; Rasmussen et al. 2003). Several analyses ar- suggest halo gas metallicities can range between ≈0.05
gue that an exponential disk-like morphology can repro- - 2 Z depending on the stellar feedback prescription,
(cid:12)
duce the line strengths for individual sight lines (Yao & with a typical value of ≈0.3Z (Toft et al. 2002; Cen &
(cid:12)
Wang2007;Hagiharaetal.2010). However,independent Ostriker 2006; Marinacci et al. 2014). This is consistent
analyses on all-sky samples of absorption and emission with the model-dependent constraint Miller & Bregman
line strengths suggest a density model like Equation 2 (2015) placed on the hot gas metallicity in order to not
reproduces the global line strength trends better than overproduce the pulsar dispersion measure in the LMC
a disk-like morphology (Miller & Bregman 2013, 2015; direction, Z ≥ 0.3Z . Miller & Bregman (2015) also
(cid:12)
4
estimated a model-dependent hot gas metallicity profile wherev followsaflatrotationcurvesimilartothedisk,
φ
by comparing their emission line fitting results (sensi- andv /v arenetflowsintherˆ/zˆdirectionsrespectively.
r z
tive to n n ) with absorption line results (sensitive to Therefore, positive v /v values assume flows away from
e ion r z
n ) from Miller & Bregman (2013). They found ev- the Galactic center (v ) or Galactic plane (v ). We also
ion r z
idence for a shallow metallicity gradient of Z ∝ r−0.2 considermodelswithaconstantmassinflow/outflowrate
with Z = 0.26Z(cid:12) at r = 10 kpc, although the uncer- by allowing vr(r) to not be a constant. The mass flux
tainty in the relation was consistent with a constant gas depends on the density and radial velocity, and is repre-
metallicity. Thus,weassumeaconstantmetallicityvalue sented by the following equation:
of 0.3Z , which still results in (cid:38)50% of the absorption
(cid:12)
coming from (cid:38)5 kpc of the Sun and (cid:38)90% coming from M˙ (r)=4πr2ρ(r)v (r)rˆ=constant, (6)
r r
(cid:46)50 kpc (Hodges-Kluck et al. 2016).
It is worth noting that these hot gas distribution as- where ρ(r) is the mass density as a function of radius. If
sumptionsareallbroadlyconsistentwiththetheoretical ρ(r) ∝ n(r) ∝ r−3β, this implies vr(r) ∝ r3β−2 in order
predictionthatthehotgasformedviaanaccretionshock for M˙ to be constant.
r
and is in hydrostatic equilibrium with the Milky Way’s Optical depth effects and the assumed absorption line
dark matter potential well. Our density parametrization Dopplerwidthplayanimportantrolewheninferringcol-
of a power law is the simplest functional form that can umn densities from measured equivalent widths. The
remain in hydrostatic equilibrium with the dark matter observed absorption lines are never broader than the in-
potential well at large radii, with β = 0.5 implying the strumental line widths of current X-ray spectrographs
gas should be close to hydrostatic equilibrium. Given (the Chandra Low-energy Transmission Grating has a
this type of distribution and formation mechanism, one FWHM of ≈0.05 ˚A ). This sets an upper limit on the
expects the gas temperature to be close to the Galactic Doppler width of (cid:46)550 km s−1. Given these spectral
virial temperature of 2 × 106 K. This prediction is con-
resolutions, it becomes difficult to quantify deviations
sistentwiththeobserved,andthereforeassumedhotgas
from an optically thin plasma. There have been several
temperature. The global hot gas distribution adopted
detections of the O VII Kβ transition along with the
here has a reasonable theoretical basis, and is also con-
O VII Kα line, suggesting Doppler widths ranging from
sistent with multiple types of observations. the thermal width (≈45 km s−1 at 2×106 K) to ≈150
Finally, our calculations depend on several Milky Way
km s−1 (Williams et al. 2005; Gupta et al. 2012; Fang
parametersthathavebeenmeasuredfromdifferenttech-
etal.2015). Galaxyformationandevolutionsimulations
niques. For the Milky Way’s size and geometry, we as-
predict a similar range of b values with a characteristic
sumeasolardistancetotheGalacticcenterofR =8.34
(cid:12) valueof85kms−1 (Cen2012). Theadditionalturbulent
kpc, a solar rotation velocity around the Galactic center
velocitycanarisefromavarietyofsources,includingtur-
of v = 240 km s−1 (Reid et al. 2014), and an average
(cid:12) bulentmixinglayers,satellitegalaxyorbits,bulkflowsof
virial radius of r = 250 kpc (Klypin et al. 2002; Loeb
v materialinandoutofthedisk,etc. (e.g., Kwak&Shel-
et al. 2005; Shattow & Loeb 2009). The former do not
ton2010;Cen2012;Hilletal.2012). Weadoptabvalue
affect our overall line shapes, but act as a net shift in
of 85 km s−1 for our initial line profile calculations, but
wavelength/velocity space for the line profiles. We ex-
explore how the Doppler width compares with different
trapolate our model profiles and calculations to r , how-
v velocity flows.
evergaswithin≈50kpcoftheSundominatesourcolumn
Given a density profile, velocity profile, and Doppler
densitiesandequivalentwidths(Miller&Bregman2013;
width for the absorbing medium, we calculate model
Hodges-Kluck et al. 2016). This implies that our choice
absorption line profiles for different sight lines in the
for r has a negligible impact on our results, and that
v Galaxy. For a given l,b coordinate, we divide the line of
our model profiles are explicitly valid within ≈50 kpc.
sight into cells with densities and Galactic standard of
2.2. Velocity Profile and Line Profile Calculation rest (GSR) velocities dependent on the cells’ locations
in the Galaxy. The coordinate transformations between
We consider bulk rotation motion, radial in-
the line of sight position, s, and Galactic coordinates is:
flow/outflow, and flows perpendicular to the Galactic
disk for our velocity profiles. A net rotational flow (de- R2 =R2 +s2cos(b)2−2sR cos(b)cos(l) (7)
notedastheφˆdirectionhenceforth)isexpectedifthegas (cid:12) (cid:12)
z2 =s2sin(b)2 (8)
has residual angular momentum from the Milky Way’s
formation. The radial and perpendicular flows (rˆand zˆ r2 =R2+z2 (9)
directions) are considered as a net accretion of material
onto the Galactic disk or a net ejection of material from Thedensityineachcellcomesfromthecells’r positions
the Galactic disk. We assume constant flow velocities and using Equation (2). The conversions between
as a function of R, z, or r, depending on the flow type, GSR and LSR velocities for our velocity models are
where R is the distance from the rotation axis, z is the represented by the following equations:
distanceperpendiculartotheGalacticplane,andristhe (cid:18) v v (cid:19)
galactocentric radial distance. These are represented by vs,φ(s)= R(φs) − R(cid:12) R(cid:12)sin(l)cos(b), (10)
the following equations: (cid:12)
v
v (s)= r [sin(|b|)z(s)
vφ(R)=vφφˆ=constant, (3) s,r r(s) (11)
v (r)=v rˆ=constant, (4) +(scos(b)−R cos(l))cos(b)],
r r (cid:12)
v (z)=v zˆ=constant, (5) v (s)=v sin(|b|), (12)
z z s,z z
5
l = 0± l = 45± l = 90± l = 135± l = 180±
v = 0, v = 0
vvÁÁÁ == 214800z,,= vvrzr ==r =-2 00 F / F¸¸;c b = 90±
1.0
0.8
F / F¸¸;c00..64 b = 60±
0.2
0.0
1.0
0.8
F / F¸¸;c00..64 b = 30±
0.2
0.0
1.0
0.8
F / F¸¸;c00..64 b = 0±
0.2
0.0
−400 −200 0 200 400 −400 −200 0 200 400 −400 −200 0 200 400 −400 −200 0 200 400 −400 −200 0 200 400
v (km s¡1) v (km s¡1) v (km s¡1) v (km s¡1) v (km s¡1)
Figure 1. Model absorption line profiles, normalized to the continuum, for different positions on the sky and velocity profiles. Each
model spectrum assumes the gas density follows a modified β-model (Equation 2 with β = 0.5) and that the gas is either stationary
(red),corotatingwiththedisk(blue),orlaggingbehindthediskwithamodestradialinflowvelocity(green). Themodelprofilesexhibit
asymmetricshapesandvaryinglinecentroids(verticaldottedlines)dependingontheobservedpositionandunderlyingvelocityprofile.
where R(s), z(s), and r(s) are the Galactic coordinates ¸ (Å)
21.57 21.58 21.59 21.60 21.61 21.62
alongthesightlines, v aretheGSRflowvelocities,
φ/r/z
and v are the LSR velocities for each cell. We
s,φ/r/z 1.0
generate a Voigt profile for each cell that is shifted to
the cell’s LSR velocity and weighted by the density, or
0.8
optical depth, in the cell. The cell line center optical
depth is defined as:
¸;c0.6
F
τ =.015×n(s)fλb−1ds, (13) / ¸
o F
0.4
wheren(s)isthenumberdensityofabsorbersinthecell, vÁ = 0, vz=r = 0
f is the transition oscillator strength (f = .6945 for the 0.2 vÁ = 240, vz=r = 0
O VII Kα transition), λ is the transition wavelength in vÁ = 180, vr = -20
centimeters, b is the Doppler width of the plasma in cm vÁ = 180, M_r = -1
0.0
s−1, .015 is a constant with units cm2 s−1, and ds is −500 −400 −300 −200 −100 0 100 200
the cell path length in centimeters. The total model line v (km s¡1)
opticaldepth,τ orτ ,isthesumofeachcell’slineprofile
v λ Figure 2. Same model spectra as Figure 1, except focusing on
out to the Milky Way’s virial radius with the resultant an l,b = 90◦, 0◦ sight line. The velocity effects are apparent,
absorption line profile following the usual definition: where the corotating line profile (blue) is much broader than the
stationary line profile (red). The additional orange line is for a
Fv/λ =e−τv/λ, (14) cmoinnsotrandtiffreardeinaclemsafrsosmflutxhemcoodnesltwanitthvMr˙mro=de-1l.MT(cid:12)heydr−as1h,ewdhviecrhtihcaasl
Fv/λ,c bluelinerepresentsthetangentpointvelocityforthissightline(0
kms−1),althoughthereisstillabsorptionatv>0kms−1 dueto
where Fv/λ is the source flux in velocity or wavelength theinferredbvalueof85kms−1.
space and F is the continuum flux.
v/λ,c
The resultant model line profiles include asymmetric ourabsorptionlinecalculationsforagridof0◦≤l≤180◦
line shapes, widths broader than the plasma Doppler and 0◦ ≤ b ≤ 90◦ coordinates. The velocity profiles in-
width, and significant line center shifts. Figure 1 shows cludeastationaryhotgasmodel(v =v =0kms−1),
φ r/z
6
100 10-5 1.0
Left Axis Right Axis
50 vÁ;vz=r = 0, 0 Line of Sight Density 10-6 0.8 106 50 32 23 18 14 11 9 7 5 3 0
0 vÁ;vz=r = 240, 0 2¡
1)¡ −50 10-7 3m)¡ cm0.6
(km sv−−115000 10-8 (cnOVII 15=10OVII0.4
N
−200 10-9 0.2
−250
10-10 0.0
0 50 100 150 200 250 −250 −200 −150 −100 −50 0 50
Line of Sight Distance (kpc) v (km s¡1)
Figure 3. Thel,b=90◦,0◦ lineofsightdensity(dashedline)andvelocity(solidlines)profiles(left)andOVIIcolumndensityin10km
s−1 binsalongthelineofsight(right). Inthestationarycase(red),allofthegasisatthereflexvelocityoftheSunaroundtheGalactic
center, -240 km s−1 (the column density bin goes above the plot limits to a value of 8.4 in order to emphasize the corotating velocity
effects). In the corotating case (blue), the column density is spread out in velocity space, with the black horizontal scale indicating the
median line of sight distance in kpc for every other velocity bin. Material near the Sun produces ≈0 km s−1 absorption while material
furtherinthehaloproduces≈-200kms−1 absorption.
ahotgasdistributioncorotatingwiththedisk(v =240 alter the inferred conversion between measured equiva-
φ
km s−1, v = 0 km s−1), and a profile similar to the lent width and column density.
r/z
best-fitmodelfromHodges-Klucketal.(2016)thatbest
reproducesasampleofobservedlinecentroids(vφ =180 2.3. Model Line Strengths
kms−1,v =-20kms−1). Oneimmediatelyseestheline
r Theselineofsightvelocityeffectshaveimportantcon-
profiles can be highly asymmetric or broadened beyond
sequences when analyzing the absorption line strengths.
theassumed85kms−1 forobservationsnearl≈90◦ and
Specifically, these effects impact observable quantities
for b(cid:46)30◦. Figure 2 shows a detailed plot of the model
(equivalent widths, resolved line profiles, etc.) and how
profiles toward the l,b = 90◦, 0◦ direction, where the
we infer the gas column density. This is not a new con-
velocity effects will be strongest. This figure includes a
cept in the broad field of absorption line analysis, but
constantM˙r modellineprofilewithvφ=180kms−1,M˙r these large scale velocity flows have never been consid-
= -1 M(cid:12) yr−1. There are minor differences between the ered when analyzing the Milky Way’s O VII absorbers.
line shapes and centroids (≈15 km s−1) for this model Here, we discuss how these effects impact current line
and the v = -20 km s−1 model, so we only consider the strength interpretations when the lines are unresolved
r
constant v model for the rest of the analysis. andpotentialfutureanalysesifthelinescanbepartially
r
Thereareseveralapparenttrendsseeninthesefigures. resolved.
If the halo gas is stationary, all of the absorption occurs Modeling the line of sight velocity flows and corre-
atthereflexmotionoftheSun’sorbitaroundtheGalac- sponding line profiles leads to a more accurate conver-
tic center, v = −v sin(l)cos(b). If instead the hot gas sionbetweenmeasuredabsorptionlineequivalentwidths
s (cid:12)
corotates with the disk, the absorption can be spread and the inferred column densities. The measured equiv-
out between ±v depending on the direction observed alent widths are currently the best way to measure the
(cid:12)
(Figure 3). The resultant density-weighted LSR veloci- absorption line strengths since the lines are unresolved
ties create the asymmetric line profiles and significantly by current X-ray spectrographs. The inferred column
broader lines compared to the stationary plasma results. densities are usually determined from a curve of growth
Forexample,thecorotatingmodellinewidth(definedas analysis with various assumptions for the plasma optical
the full width at half the line depth) for the l,b = 90◦, depth. Velocity flows alter this conversion by spreading
0◦ direction in Figure 2 is 326 km s−1 compared to 200 out the absorption in velocity space, producing larger
km s−1 for the stationary model, a 63 % increase. Fur- equivalent widths for a given column density. To quan-
thermore, the absorption line centroids depend on the tifythestrongestvelocitycorrections,wegeneratemodel
underlying velocity profile (vertical dotted lines in Fig- line spectra in the l,b = 90◦, 0◦ direction, for a range of
ures 1 and 2). The stationary plasma halo produces the column densities and Doppler b values, and for a coro-
strongest deviations from the rest wavelength, or 0 km tating halo. We vary the column density by changing
s−1, since alloftheabsorptionisatthesame velocity. If the halo normalization parameter in Equation 2, thus
the gas is corotating with the disk, one expects weaker keeping the gas distribution the same with β = 0.5. We
line shifts since dense gas near the Galactic disk pro- create curves of growth with velocity effects by calculat-
duces v ≈0 km s−1 absorption, while gas futher in the ing equivalent widths for each line profile/column den-
s
halo produces absorption at |v |(cid:38)100 km s−1. Flows in sity. Figure 4 shows these new growth curves, where the
s
the r or z directions produce similar net velocity shifts, solid lines represent traditional curve of growth calcula-
although flows in these directions have stronger effects tions with no velocity effects and the opposite edges of
near the Galactic center, anti-center, and poles. These the shaded regions represent our curves of growth with
effects imply that the hot gas kinematics produce ob- rotational velocity effects. Therefore, the shaded regions
servable signatures on the absorption line centroids, and represent the range of possible velocity corrections, de-
pending on the true halo velocity structure.
7
log(Nthin (cm¡2))
15.2 15.4 15.6 15.8 16.0 16.2
optically thin
1.6 b = 45 km s¡1
))Å1.4 102 bb == 8155 0k mkm s ¡s1¡1
m n
EW (OVII11..02 /NNtruethi101
g( optically thin
lo0.8 b = 45 km s¡1
b = 85 km s¡1
0.6 b = 150 km s¡1 100
15.0 15.5 16.0 16.5 17.0 0.6 0.8 1.0 1.2 1.4 1.6
log(NOVII (cm¡2)) log(EWOVII (mÅ))
Figure 4. ConversionsbetweentheobservedequivalentwidthsandcolumndensitiesfordifferentDopplervaluesandwithvelocityeffects
alonganl,b=90◦,0◦ lineofsight. Theleft panelshowscurvesofgrowth,wherethecoloredsolidlinesrepresentnormalgrowthcurvesfor
differentbvalues(orequivalentlyastationaryhalo),andtheupperboundariesoftheshadedregionsrepresentthegrowthcurvesassuming
acorotatingvelocityprofile. Theright panelisthesameastheleft panel,butwiththecolumndensitiesnormalizedtotheopticallythin
values. ThedashedlinesrepresentthemedianequivalentwidthsfromtheMiller&Bregman(2013)(black)andFangetal.(2015)(yellow)
samples,indicatingtheopticaldepthandvelocityeffectscanbesubstantial.
These velocity effects have a significant impact on the cult because it is intrinsically weaker than the Kα tran-
inferred column densities, with potentially large devia- sitionandthereisanRGSinstrumentalfeaturenearthe
tions from optically thin values. Here, we examine cor- transition1. Thus, this method will be useful if we ob-
rections to the inferred optically thin column densities tainabsorptionlineobservationswithahigherresolution
withandwithoutconsideringvelocityeffectsandfordif- spectrograph (see Section 3.2).
ferentbvalues. TherighthandpanelofFigure4rescales
the curves of growth in the left hand panel into the ra- 3. DISCUSSIONANDCONCLUSIONS
tio between the true and optically thin column density We have shown that the Milky Way’s hot gas kine-
for a given equivalent width. The Doppler b value plays maticsproducesignaturesintheintrinsicabsorptionline
a critical role when inferring the correct column density shapes and centroids. Bulk velocity flows in the disk ro-
foragivenmeasuredequivalentwidth,wherecorrections tation direction along with a net inflow or outflow of gas
without velocity effects range between ≈50% to over an canproducestrongasymmetricallineshapesandsignifi-
order of magnitude for b between 45 and 150 km s−1 cantlinecentroiddeviationsfromthetheabsorptionline
and a typical equivalent width measurement of 20 m˚A . rest wavelength. These results alter the conversion be-
Thevelocityeffectsdiscussedabovemitigatethesediffer- tweenequivalentwidthsandcolumndensities,producing
ences,butstillcausesignificantdeviationsfromoptically significant deviations from both optically thin and zero
thinvalues. Forexample,theratiobetweenthetrueand velocityassumptions,butalsoimplythelineshapes(not
optically thin column ranges from a factor of ≈2 if the currently observable) and observed centroids encode in-
halo has is corotating to a factor of ≈5 without velocity formation on the Milky Way’s hot gas kinematics. The
effects for b = 85 km s−1 and a 20 m˚A equivalent width. new velocity considerations presented here motivate fu-
Thisimpliesthatvelocityeffectsresultinsmaller column ture analyses on the Milky Way’s hot gas structure and
densitiesthanwouldbeinferredfromatraditionalcurve kinematics.
ofgrowthconversion. Theseresultsareusefulinthecur-
rent limit where the lines are unresolved, but there are 3.1. Implications for the Milky Way
alternative approaches if the lines are partially resolved.
The model line calculations presented in this paper
A useful approach for future analyses on these ab-
form the basis for the Hodges-Kluck et al. (2016) anal-
sorption lines will be the apparent optical depth method
ysis on the Milky Way’s hot gas kinematics. Their
(Savage & Sembach 1991). In this method, one decom-
non-parametric statistical tests concluded that the ob-
poses the observed line profile into an apparent opti-
servedlinecentroidmeasurementswereinconsistentwith
cal depth function τ (v) and converts this into an ap-
a a stationary hot gas profile (a result not requiring addi-
parent column density function N (v), which can be
a tionalmodelingorassumptionsforthegasdistribution),
integrated to determine a total column density. This
whereas corotating model centroids from calculations in
method makes no assumption for the underlying line
Section 2.2 were more consistent with the data. Fig-
of sight density or line of sight velocity profile, but it
ure 5 shows their observed centroid distribution on the
would be useful to reconstruct a column density distri-
skywithmapsofthemodellinecentroiddistributionsfor
bution similar to our Figure 3. The reason this method
the stationary and corotating profiles to illustrate how
is not used in current analyses on the O VII absorbers
themodelscomparewiththedata. Theyalsousedpara-
is because: 1) the lines need to be at least partially re-
metric modeling techniques with v as a free parameter
solved (FWHM(instrument) (cid:46) 2FWHM(line)) and 2) it φ
to show that a velocity profile lagging behind the disk
requires multiple lines of the same species with different
with v = 183 ± 41 km s−1 is most consistent with the
fλproductstoestimatesaturationeffects. Thelinesare φ
completelyunresolvedwithcurrentX-raytelescopesand
1 http://xmm.esac.esa.int/external/xmm user support/
detecting the O VII Kβ transition at 18.63 ˚A is diffi- documentation/uhb/rgsmultipoint.html
8
Figure 5. Absorption line centroids in single-hemisphere Aitoff projections. The upper-left panel shows the observed line centroid
distribution from Hodges-Kluck et al. (2016) where the point sizes are inversely proportional to their measurement errors. The bottom
panels represent model centroid calculations for a cororating (left) and stationary (right) halo gas distribution. The upper-right panel
shows the absolute difference between the stationary and corotating model, indicating where on the sky one has the greatest leverage to
differentiatebetweenmodels.
observed line centroid distribution. The v and v flow tential in the following way:
z r
parameters were also included, but the constraints were
within 1σ of 0 km s−1. These results are the first con- (cid:90) R
straints on the Milky Way’s T ∼106 K gas kinematics, Φeff =Φ− Ω2(R(cid:48))R(cid:48)dR(cid:48), (16)
and they depend on the absorption line profile calcula- Ro
tions presented here. The inferred velocities also have where Ro is an arbitrary radius for normalization, Ω(R)
implications for other inferred hot gas properties, such is the angular rotation profile, and Φeff is the effective
as the density distribution and metallicity. potential (see Equation (8) in Barnab`e et al. 2006). In-
Significant hot gas rotation velocities can change the serting the effective potential into Equation 15 for flat
net potential well affecting the hot gas, resulting in a rotation curves can alter the initial spherical profile into
flattened or “bow-tie” morphology. The prediction of a flattened morphology.
hot, extendedcoronaearoundlate-typegalaxiesisbased Tovisualizethiseffect,wecalculateaneffectivepoten-
on the assumption that the shock-heated gas exists in tial profile for a static potential and flat rotation curve
hydrostatic equilibrium with the dark matter potential weimposeonthegas. Weassumethestaticpotentialin-
well. If the dark matter distribution is approximately cludes a dark matter NFW profile (Navarro et al. 1997)
spherical on large galactic scales and the gas is isother- withascaleradiusof12kpcandvirialmassof1.8×1012
mal, hydrostatic equilibrium implies a spherical power M andathinstellardiskprofilewithscaleradiusof3.2
(cid:12)
law distribution for the hot gas: kpc and total surface density of 536 M pc2 (Binney &
(cid:12)
Tremaine 2008). These assumptions do not account for
the triaxiality of the Milky Way’s dark matter distribu-
tion (Loebman et al. 2014) and the vertical structure of
(cid:18) (cid:19)
Φ
thestellardisk,butthesecalculationsaremeanttoshow
n∝exp − , (15)
c2 thecharacteristiceffectthatrotationhasonthehotgas.
T
We also point out that the baryonic components con-
tributeverylittletothepotentialforr (cid:38)5kpc,implying
where Φ is the potential (Φ ∝ ln(r) for an isothermal the details of their assumed profile do not significantly
sphere) and c2 = 2kT/µm . Rotation modifies the po- affect our calculations. The results of these calculations
T p
9
50 50
v = 0 km s 1 v = 100 km s 1
Á ¡ Á ¡
40 40
30 30
) )
c c
p p
k k
( (
z z
20 20
10 10
0 0
0 10 20 30 40 50 0 10 20 30 40 50
R (kpc) R (kpc)
Figure 6. Isodensitycontoursforstationaryhotgasdistribution(left)andadistributionwithaflat100kms−1 rotationcurve(right).
The contours are normalized to the maximum density values, and are log-spaced with a 0.5 interval between -3 through -5.5. Including
rotationleadstoacharacteristicflattenedmorphology.
for a stationary halo and a modest flat rotation curve of structure in the hot gas, regardless of the assumed den-
v = 100 km s−1 are seen in Figure 6. One sees that sity profile. This appears to be a valuable first step in
φ
the isodensity contours are constant with r for the sta- this type of analysis, especially since there is little ob-
tionary halo, but become flattened with the inclusion of servational or theoretical background for the expected
rotation. We also point out that these calculations and kinematic structure of this gas phase. The line profiles
general results are consistent with those found by Mari- presentedherearedesignedtohighlighthowwecanlearn
nacci et al. (2011), who estimated these same effects of about the Milky Way’s hot gas kinematics, and show
coronal rotation on the underlying morphology. how the hot gas kinematics can potentially impact the
In contrast with these model predictions, several inferred hot gas structure.
observation-based lines of evidence suggest the Milky One example of how these line profile calculations can
Way’s hot gas distribution is not significantly flattened. improve constraints on the hot gas structure is with a
As discussed in Section 2.1, analyses on large samples more accurate conversion between measured equivalent
of line strength measurements, pulsar dispersion mea- width and the column density. The velocity calculations
sures, and X-ray surface brightness measurements sug- presentedinSection2.3implythatvelocityflowsmodify
gest a spherical morphology can better reproduce these the curve of growth analysis depending on the observed
observables than a disk-like morphology. In particular, direction. Thus, one needs to account for bulk velocity
themodelsconsideredinMiller&Bregman(2013,2015) flows to infer an accurate column density from a mea-
includedaflattened,extendeddistribution. However,the suredequivalentwidth. Theseeffectshavenotbeencon-
modelfittingresultsforthisflattenedmodel(withanad- sidered in previous analyses of the Milky Way’s hot gas,
ditional parameter and thus one less degree of freedom) and impact inferred hot gas properties.
were not a significant improvement in fitting the data As an example application of the improved equivalent
compared to a spherical model. The analysis showed width-column density conversion, we examine the hot
that a flattened halo was not required to fit the line gas metallicity based on the observed O VII equivalent
strength measurements. Also, observations of hot gas width toward the LMC direction and the hot gas disper-
in other galaxies do not indicate rotation significantly sion measure in this direction. We convert the observed
impacts their morphologies. The examples discussed in O VII equivalent width for the LMC X-3 X-ray binary
Section 2.1 found that the extended X-ray halos around intoOVIIcolumndensitiesfordifferentbvalueswithand
both early- and late-type galaxies are typically fit well withoutvelocityeffects. Thesecolumndensitiesarethen
with spherical β models. Additional analyses on higher- converted to dispersion measures, which depend on the
resolution X-ray images of early-type galaxies indicate gas metallicity, and compared to the observed residual
anyX-rayobservedellipticitydoesnotcorrelatewiththe hot gas dispersion measure toward the LMC direction.
galaxies’ rotation velocities, implying rotation does not The dispersion measure is the integral of free electrons
(cid:82)s
drive their morphologies (Diehl & Statler 2007). Thus, along the line of sight, n(s)ds, which relates to the
0
the balance of observational evidence suggests the ex- OVII column density as follows:
tended hot gas distributions around the Milky Way and
other galaxies is approximately spherical.
The observed line centroids from Hodges-Kluck et al.
(2016)combinedwiththemodelsoutlinedin Section2.2
lead to the robust result that there is global kinematic
10
2.0 Figure 7 shows the lines where the calculated dispersion
measure equals 23 cm−3 pc.
There are several key results to note from the calcula-
1.5 tions represented in Figure 7. Increasing the b value de-
creases the O VII column density required to match the
observed equivalent width. Therefore, increasing the b
¯
Z 1.0 valuerequiresadecreaseinmetallicityinordertomatch
=
Z the observed dispersion measure. For a stationary halo,
thetransitionbetweensolarandsub-solarmetallicityoc-
0.5 cursatb=130kms−1. Includingvelocityeffectsbroad-
Stationary ensthelineprofileinthisdirection,whichfurtherreduces
Corotating theOVIIcolumndensityrequiredtomatchtheobserved
0.0 equivalent width. The transition between solar and sub-
60 80 100 120 140 160 180 200
Doppler b (km s¡1) solar metallicity is at 100 km s−1 in this case. For both
the stationary and corotating cases, the metallicity ap-
Figure 7. ThehotgasmetallicityandDopplerbvaluesrequired proachesalimitof≈0.6Z asbincreasesbeyond200km
for the observed LMC X-3 OVII equivalent width to equal a dis- s−1. These results imply(cid:12)that the gas metallicity should
persionmeasureof23cm−3 pc(solidlines). Thedashedlinesin-
corporatethe90%uncertaintyonthemeasuredequivalentwidth. be(cid:38)0.6Z(cid:12) ifbislessthanthesoundspeed,butalsothat
The red shaded region assumes a stationary halo for the column b(cid:38) 100 km s−1 if the gas metallicity is not greater than
densityconversion(orastandardcurveofgrowth)whiletheblue solar. This analysis provides important constraints on
shadedregionassumesacorotatingvelocityprofile.
theaveragehotgasmetallicityalongtheLMCsightline,
however it also illustrates how the halo gas kinematics
can impact inferred hot gas properties.
N
DM=1.2 OVII 3.2. Future Applications
f A Z
OVII O
These velocity considerations have important applica-
=14.2(cid:18) NOVII (cid:19)(cid:18)fOVII(cid:19)−1 (17) tions for future analyses on the Milky Way’s hot gas
1016cm−2 0.5 structure. We have discussed several problems and ini-
(cid:18) A (cid:19)−1(cid:18) Z (cid:19)−1 tialattemptstosolvethem,suchastheMilkyWay’shot
× O cm−3pc, gaskinematicstructure,therelationbetweenthehotgas
5.49×10−4 Z(cid:12) kinematics and density structure, and how to accurately
interpret current hot gas observables. Here, we discuss
where f is the O VII ion fraction, A is the fixed
OVII O strategiestosolvetheseissuesinthefuture,andhighlight
solar oxygen abundance relative to hydrogen (Holweger
how our velocity calculations will be useful.
2001), and Z is the gas metallicity. Thus, we infer an
WecanbetterconstraintheMilkyWay’shotgaskine-
average hot gas metallicity by equating the inferred dis-
matic structure by targeting sight lines that predict the
persion measure from the OVII measurement to the in-
largest differences between model line centroid values.
dependently observed value.
These regions provide the most leverage when validat-
The inferred metallicity depends on an accurate con-
ing or excluding different types of velocity flows. As an
versionbetweentheobservedOVIIequivalentwidthand
example,theupper-rightpanelinFigure5showstheab-
true column density, which we calculate above, and the
solute difference between the predicted line centroids for
residual dispersion measure due to hot gas. For the lat-
a stationary and corotating halo. Clearly, the regions
ter, analyses on LMC pulsars suggest the Milky Way’s
near l = 90◦ and 270◦ show the largest differences of
hotgascontributes23cm−3 pctothetotalobserveddis-
(cid:38)100 km s−1, while regions near the Galactic pole and
persionmeasures(Anderson&Bregman2010;Fangetal.
anticenter have differences of ≈0 km s−1. Although we
2013). Independent analyses report a consistent O VII
donotshowamapwithav orv flow,theGalacticpole
equivalentwidth for theLMC X-3spectrum, with Wang r z
and anticenter are ideal locations to probe those effects
et al. (2005) suggesting a value of 20±6 m˚A and Breg-
sincerotationproducesanegligibleshiftintheseregions.
man & Lloyd-Davies (2007) suggesting a value of 21±5
We also point out that a rotating gas profile predicts a
m˚A (90% confidence regions). Here, we use a more cur- distinctive line centroid feature near the Galactic cen-
rent measurement with improved calibration from the ter, in that the centroid switches sign for |l| (cid:46) 30◦. It
Hodges-Kluck et al. (2016) analysis, 22+6 m˚A. We also is possible that this effect could be observed, although
−4
assumealloftheabsorptionarisesfromtheMilkyWay’s the Galactic center is a complex region with other kine-
hot gas distribution, as opposed to a distribution asso- matic features due to the Fermi bubbles (Su et al. 2010;
ciated with the LMC or intrinsic to the LMC X-3 X-ray Foxetal.2015). Regardlessofthesecomplications,these
binary. This appears to be a valid assumption since the models should be used to motivate the most informative
OVIIcentroidisinconsistentwiththeLMCsystemicve- observations.
locity(∼300kms−1)ortheX-raybinaryescapevelocity Interpreting current and future absorption line obser-
(∼103 km s−1) (Wang et al. 2005; Yao et al. 2009). We vations requires a better estimate for the plasma optical
convert this equivalent width to a column density using depth, or b value. Figure 4 indicates optical depth ef-
our curves of growth for the LMC direction, a range of fects and line of sight kinematics introduce significant
plausible b values, and assuming either a stationary or corrections to the equivalent width-column density con-
corotating halo. We then use Equation 17 to convert version. The plasma b value is usually determined by
these to dispersion measures for different metallicities. the O VII Kβ to Kα ratio, but weak Kβ detections in-