A single HII region model of the strong interstellar scattering towards Sgr A*
aa r X i v : . [ a s t r o - ph . GA ] D ec MNRAS , 1–6 (2015) Preprint 28 July 2018 Compiled using MNRAS L A TEX style file v3.0
A single HII region model of the strong interstellarscattering towards Sgr A*
Egid Sicheneder ⋆ and Jason Dexter † Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Until recently, the strong interstellar scattering observed towards the Galactic center(GC) black hole, Sgr A*, was thought to come from dense gas within the GC region.The pulse broadening towards the transient magnetar SGR J1745-2900 near Sgr A*has shown that the source of the scattering is instead located much closer to Earth,possibly in a nearby spiral arm. We show that a single HII region along the line ofsight, 1 . − . n e of a few ≃
100 cm − and radius R ≃ . − . .
10 pc should show the same scattering origin as the magnetar andSgr A*, while the nearest known pulsars with separations >
20 pc should not. Theradio spectrum of Sgr A* should show a cutoff from free-free absorption at 0 . . ν . B ≃ − µ G, the HII region could produce therotation measure of the magnetar, the largest of any known pulsar, without requiringthe gas near Sgr A* to be strongly magnetised.
Key words:
Galaxy: centre — pulsars: individual (J745-2900) — scattering — HIIregions
Interstellar scattering by electron density fluctuations alongthe line of sight blurs radio images and pulsar emission pro-files (angular and temporal broadening). Certain lines ofsight through the Galaxy show anomalously strong scatter-ing, notably towards the Galactic center (GC) black hole,Sgr A*, whose image has been broadened to a constant 1GHz size of ≃ ≃
40 years of observations (e.g.,Backer 1978; Krichbaum et al. 1993; Lo et al. 1993, 1998;Shen et al. 2005; Bower et al. 2006, 2014b).The origin of the strong scattering towards the GC re-mains uncertain. From the lack of free-free absorption of theSgr A* spectrum, van Langevelde et al. (1992) argued thatthe scattering source should be located ∆ &
200 pc fromSgr A*. From a decrease in the number density of extra-galactic background sources near Sgr A*, Lazio & Cordes(1998) found a best fit location of ∆ ≃ −
300 pc. Produc-ing the large observed image of Sgr A* from turbulent gasso close to the GC would require either extreme turbulent ⋆ E-mail: [email protected] † [email protected] energy densities or a special scattering geometry (Lithwick2002; Goldreich & Sridhar 2006).A prediction of this scattering model was that radiopulsars in the GC should be rendered undetectable due tothe spread of arrival times of their pulses becoming longerthan their pulse periods. Recently, a rare transient magne-tar SGR J1745-2900 was discovered ≃ . ≃ . − . ± . . . c (cid:13) Sicheneder & Dexter
Litvak 1971; Little 1973; Dennison et al. 1984). Here we as-sess the physical conditions required to produce the observedscattering towards Sgr A* in terms of a simple model of tur-bulent, ionized gas in such an HII region ( § § § We use the thin screen approximation (e.g., Ishimaru 1977;Blandford & Narayan 1985; van Langevelde et al. 1992) tocalculate the angular broadening associated with a givenspectrum of density fluctuations arising from an HII region.
Turbulent, free electrons scatter electromagnetic radiationstrongly, since the electron density fluctuates. The electrondensity fluctuations are described by (Cordes et al. 1985), h δn e i = Z P δn e ( q ) d q , (1)with the Kolmogorov spectrum, P δn e ( q ) = C n ( x ) · q − ; for q ≪ q ≪ q , (2)where q denotes the wavenumber, and q = 2 π/l and q =2 π/l correspond to the inner and outer scales of the turbu-lenct spectrum, l and l . Assuming isotropic turbulence, thevisibility V ( ρ ; L ) is given by (van Langevelde et al. 1992), V ( ρ ; D ) = exp ( − D Φ / , (3) D Φ ( ρ ) = 8 πr e λ Z D d x Z d q q [1 − J ( qρ )] P δn e ( q ) , (4)where ρ is the baseline length, D is the distance from the ob-server to the source and J ( qρ ) a Bessel function. The phasestructure function D Φ specifies the statistical properties ofthe turbulent medium.For ρ < π/l = q , the visibility has a Gaussian profile: V ( ρ ; D ) = exp (cid:0) − ρ /ρ C (cid:1) , (5) ρ C = (cid:20) π λ r e L ( D ) q (cid:21) − , (6)as is observed for Sgr A*. Here r e is the classical electronradius. The function L ( D ) takes into account the strengthand position of the turbulent medium along the line of sight, L ( D ) = Z D C n ( x ) (cid:16) xD (cid:17) d x ≃ C n γ H, (7)where x is the distance of the screen from the source and γ ≡ ∆ /D the relative screen location. The second step comesfrom taking C n ( x ) to be constant across the HII region andassuming the cloud thickness H is small ( H ≪ D ).The apparent image size θ and ρ C are related by, ρ C = λ · p π · θ . (8)We express the structure constant in terms of the outer scale l (Cordes et al. 1985), C n = δn e π (cid:18) πl (cid:19) / . (9)Using the thin screen approximation and equations 6-9, wecan write the image size as, θ = 2 √ ln 2 r e λ δn e γH / l / l / . (10) We consider a uniform distribution of free electrons con-tained in a single HII region, with a size given by its Str¨om-gren radius R S , R S = (cid:18) N Ly πα H n e (cid:19) ≃ . (cid:16) n e
100 cm − (cid:17) − / · N / Ly,f pc , (11)for an ionizing photon rate N Ly = 5 × N Ly,f s − , scaledto a value appropriate for a bright O star. The scaling factor N Ly,f is a model parameter, with N Ly,f = 1 in the fiducialcase. At the radius R S , the photoionization is in equilibriumwith the recombination, characterized by the volumetric re-combination rate α H ≃ × − cm − s − .We connect the properties of the turbulent fluctua-tions with the density and size of the HII radius by as-suming the line of sight passes through a cloud thickness H = 4 / R S , the average value for a line of sight througha sphere, and parameterize the fluctuations as δn e = fn e ,with f ≤
1. We further assume an inner scale l = 10 km(e.g., Wilkinson et al. 1994) and an outer scale comparableto the cloud radius: l = f R S with f ≤
1. With thesescalings, we re-write equation 10 as, θ ≃ . γ f − / f (cid:16) n e
100 cm − (cid:17) (cid:18) R S (cid:19) / (cid:18) λ
30 cm (cid:19) arcsec . (12)where γ = ∆ /D is the relative screen location along the lineof sight defined in terms of the screen-source (∆) and total( D ) distance. The same cloud properties produce a largerimage when located closer to the observer. Due to scattering, different light rays reach the observerat different times. The width of the resulting broadenedpulse depends on the image size and the thin screen locationas(e.g., Cordes & Lazio 1997), t PB ≃ D · ln (2) · c − γγ · θ sec , (13)called pulse broadening. MNRAS , 1–6 (2015)
II region model of GC scattering n e i n [ c m - ] n e DM0 0.2 0.4 0.6 0.8 1 γ D M i n [ c m - p c ] DM Limit
Figure 1.
To account for the observed angular broadening of SgrA*, the electron density (blue line and left axis) and dispersionmeasure (red line and right axis) must increase with decreasingdistance between the model HII region and Galactic center. Thehorizontal line marks our assumed upper limit on the contribu-tion to the dispersion measure of J1745-2900 from the HII region,DM
Limit = 1000pc cm − , in turn constraining the screen location γ & . With a cloud size R s and location γ , our model givesthe mean angular separation θ sep of two sources, such thatthey can not be scattered by the same cloud: θ sep ≃ R S D − ∆ = R S D − γ , (14) θ sep ≃ . · N Ly,f − γ (cid:16) n e
100 cm − (cid:17) − deg . (15)Second, the Earth rotates around the Galactic center ata speed v Orb ≃
220 km/s. We can calculate in our frameworkhow long it takes for the earth to pass the cloud, changingthe observed scattering properties: t pass = R S v Orb DD − ∆ = R S v orb γ , (16) t pass = 21000 · N Ly,f γ (cid:16) n e
100 cm − (cid:17) − yr . (17) We calculate the electron density n e and corresponding ra-dius R S required to produce the observed angular broad-ening of Sgr A* and J1745-2900 ( θ = 945 mas at 1 GHz,Bower et al. 2014a) from equation (12) as a function of thescreen location γ along the line of sight: n e ≃ · f · f − · γ − · N − / Ly,f cm − , (18) R S ≃ . · f · f − · N / Ly,f · γ pc , (19)From the cloud density and radius, we calculate its con-tribution to the magnetar dispersion and rotation measures: R M i n [ r ad · m - ] RM β =1 t PB γ -4 -2 P u l s e B r oaden i ng i n [ s e c ] shouldhave beendetectedpreviouslyallowed solutionsDM too large Figure 2.
Rotation measure (RM, blue line and left axis) andpulse broadening (red line and right axis) versus the relative po-sition of the HII region. Solid lines show the allowed solutionsand the horizontal lines show the limits for DM and the pulsebroadening. For clouds close to the GC ( γ . . τ ff .A cloud close to Earth ( γ & .
8) likely would have been detectedalready and so is not considered viable.
DM = Z L n e ( x ) d x ≃ (cid:16) n e
100 cm − (cid:17) / · N / Ly,f pc cm − , (20)RM = 0 . Z L n e ( x ) · B d x ≃ · (cid:16) n e
100 cm − (cid:17) / · (cid:18) B || µ G (cid:19) · N / Ly,f rad m − (21) B || ≃ · β − · T e, · (cid:16) n e
100 cm − (cid:17) / µ G (22)Using equation (18), we can re-write these in terms of thelocation γ of the cloud:DM ≃ · f · f − · γ − · N / Ly,f pc cm − , (23)RM ≃ , · β − / · T / e, · f · f · γ − · N / Ly,f · rad m − , (24)where β is the ratio of the thermal to magnetic pressure and T e, = T e / K is the electron temperature. We set the pa-rameters f , f and N Ly,f (introduced in section § n e and DM as a function of the screen location.Both quantities increase for screens closer to the GC, whereproducing the observed angular size requires large values of C n .We also calculate the free-free optical depth τ ff (Rybicki & Lightman 1979) through the cloud: τ ff ≃ . · T − / e, · N Ly,f · (cid:16) n e
100 cm − (cid:17) / (cid:16) ν (cid:17) − ≃ . · f · f − · T − e, γ − N / Ly,f , (25)where we use ν = 1 GHz and set the Gaunt factor g ff ≃ MNRAS , 1–6 (2015)
Sicheneder & Dexter for this frequency (Karzas & Latter 1961). Finally, the geo-metric quantities are given as, θ sep ≃ . · f − · f · γ − γ · N Ly,f deg , (26) t pass = 16 , · f · f − · N / Ly,f · γ − γ yr . (27)We compare these model values to the measured quan-tities from the line of sight towards Sgr A* / J1745-2900.We use upper limits of DM < − , τ ff < t pass >
40 yr, θ sep > . − Eatough et al. 2013). We use it asa limit because it is comparable to both the observed DMvalues toward the nearest pulsars to the GC (Johnston et al.2006; Deneva et al. 2009), and to the Galactic disc compo-nent of the DM along this line of sight in the NE2001 model(e.g., the ∆DM between lines of sight with l = 0 ◦ and l = 2 ◦ with b = 0 ◦ , Cordes & Lazio 2002).Screens with γ . . γ & . D − ∆ > . . ± . β = 1). At γ ≃ . ≃ . · rad m − (Eatough et al. 2013) towards J1745-2900, the largest of anypulsar. The magnetic field strength at γ ≃ . B || ≃ µ G(see equation (22) with β = 1). Towards γ ≃ . B || ≃ µ G. This is fur-ther shown in figure 3, which shows RM vs. t PTD for ourmodel with different assumed field strengths compared tothe observed values from J1745-2900. Except for very lowfield strengths (e.g., Harvey-Smith et al. 2011), the allowedmodels contribute significantly to the observed RM.
The recently discovered GC magnetar SGR J1745-2900, ≃ . − Pulse Broadening in [sec] R M i n [ r ad · m - ] RM Limit RM β =1 RM β =10 RMMagnetar
Figure 3.
Rotation measure (RM) versus the pulse broaden-ing. A magnetised cloud (cyan and purple lines) can produce theobserved RM ≃ . · rad m − (red star, see (Eatough et al.2013)) which was previously thought to require a dynamically im-portant magnetic field in gas falling onto Sgr A* (Eatough et al.2013). N L y ( s - ) γ l o w e r li m i t DM too large τ ff toolarge Figure 4.
Lower limit on screen distance from the GC ( γ ) as afunction of the ionizing photon rate N Ly and fluctuation strength f . The relevant constraints are DM < − , τ ff < θ sep > . f = 1, N Ly = 5 × s − . At large N Ly , low f models overproduce the observed DM, while at low N Ly theoptical depth is too large. In the lower right region, the limit on γ comes from forcing the cloud to be large enough to produce boththe magnetar and Sgr A* images. The white region shows modelswhere all γ are excluded, placing a constraint f & .
1. The rangeof allowed screen locations we find is generic to a large part ofthe parameter space. Screens close to the GC ( γ & .
05) wouldrequire a weak ionizing source driving strong turbulence, and areonly possible in a narrow range of parameter space. orders of magnitude smaller than predicted (Bower et al.2014a; Spitler et al. 2014). The combination of these mea-surements implies that the turbulent gas producing the ob-served image is located far from the GC.HII regions have long been candidates for the observedstrong interstellar scattering towards the Galactic plane. Wehave shown that for typical properties, n e ≃
100 cm − , R S ≃ MNRAS000
100 cm − , R S ≃ MNRAS000 , 1–6 (2015)
II region model of GC scattering S g r A * c u t o ff f r e qu e n cy ( G H z ) Melia & Falcke 2001An+2005
Figure 5.
Predicted cutoff frequency (where τ ff = 1) for the ra-dio spectrum of Sgr A* as a function of the fluctuation strength f , assuming a screen location γ = 0 .
75 found by Bower et al.(2014a). Detections of Sgr A* below 1 GHz constrain f & . ≃
200 MHz, in agreement with low frequency spectral mea-surements (Nord et al. 2004; An et al. 2005). . − . . − . γ . .
4) overproduces the observed DM ofthe magnetar, and for screens close to the GC ( γ . .
1) alsothe free-free optical depth towards Sgr A*. This constrainton the location of the scattering medium is independent of,and consistent with, the geometric result γ ≃ .
75 foundby combining the angular and temporal broadening of themagnetar (equation 13, Bower et al. 2014a).We have assumed a uniform HII region with a size andparticle density related by the Str¨omgren radius for an as-sumed rate of ionizing photons, N Ly = 5 × s − , andfluctuation strength δn e = fn e with f = 1. Figure 4 showshow our lower limit on the screen location, γ , depends onthese parameters. Decreasing the turbulent scaling, f , in-creases the required particle density to produce the angularbroadening of Sgr A*. This in turn increases the DM and τ ff at each location, and so requires the screen to be locatedfarther from the GC. A similar effect results from increasing N Ly . This causes the HII region to be larger for fixed δn e ,and increases the DM since its weighting with R is strongerthan that of C n . The combination of these effects means thatthe model is only compatible with the observed DM and τ ff ( γ <
1) for strong turbulence, f & .
1, and N Ly . s − .In models of MHD turbulence, it is sometimes assumed that f ≃ β − (e.g., Goldreich & Sridhar 2006). Our limit on f could then favor a relatively large value of B , which in turnleads to a larger contribution of the HII region to the ob-served RM.A successful model of scattering towards the mag-netar also needs to account for its temporal broadening,1 . ± .
2s at 1 GHz (Spitler et al. 2014), which fixes γ ≃ . n e ≃
200 cm − , R S ≃ ≃
800 pc cm − , τ ff ≃ . ν − , θ sep ≃ −
15 arcminutes from Sgr A* ( ≃
25 pc at the distanceof the GC, Johnston et al. 2006; Deneva et al. 2009). All ofthese GC pulsars show large pulse broadening, and so mea-surements of their radio images can constrain the screen lo-cation γ in the same fashion as done by Bower et al. (2014a)for SGR J1745-2900. A prediction of our model is that thesingle HII region is unlikely to cover all of these pulsars, sothat their values of γ should be different than that of themagnetar. This prediction is consistent with recent measure-ments of angular broadening for the other GC pulsars (Dex-ter et al., in prep.). Significant angular broadening of OH/IRstars is seen on larger scales . . τ ff = 1) at & . f = 1, whilevalues f . . −
100 cm (100 −
866 MHz), consistent with ourprediction. Measuring the low-frequency cut off shape of theSgr A* spectrum would help to directly measure the fluctu-ation strength and further constrain the model.The RM of the magnetar is an order of magnitude largerthan that of any other pulsar, and for this reason was previ-ously thought to come from gas local to the GC. To producethe observed RM, this gas would need to be threaded byvery strong, uniform magnetic fields (Eatough et al. 2013).As an alternative, we show that for magnetic field strengths ≃ − µ G a single HII region can produce much orall of the observed RM (figure 3). This field strength islarge, but within the range of observed HII region values ofboth B (e.g., Heiles et al. 1981; Rodr´ıguez et al. 2012) and β (Harvey-Smith et al. 2011). Therefore we caution that theRM of the magnetar does not necessarily require that the gasnear Sgr A* be highly magnetised. The HII region cannothowever produce the order of magnitude larger RM seen to-wards Sgr A* itself, which is thought to arise within the sur-rounding accretion flow (Bower et al. 2003; Marrone et al.2007).Schnitzeler et al. (2016) measured the RM towardsthe other GC pulsars and found two others with RM ≃ rad m − . If the very large RM for SGR J1745-2900 isproduced from extremely strong, ordered fields within thecentral parsec, it seems strange that smaller but compara-ble RMs would be found for these other objects much furtheraway. The mean field strength estimated from RM / DM ≃ µ G for these pulsars is similar to that of SGR J1745-2900, and so distant HII regions with mean field strengthslike we require could be a more natural explanation. Onthe other hand, the RM towards the magnetar and otherGC pulsars is an order of magnitude higher than for otherknown pulsars, while our model should apply to many heav-ily scattered lines of sight in the inner Galaxy. This suggeststhat other heavily scattered lines of sight either have weaker
MNRAS , 1–6 (2015)
Sicheneder & Dexter field strengths (e.g. the HII regions towards the GC wouldhave to be uncomfortably “special”), are preferentially notdetected by pulsar surveys (preventing detections of largeRMs away from the GC), or that the GC environment onscales of tens of pc does in fact produce the large observedRMs as suggested by Schnitzeler et al. (2016).In this scenario for the scattering towards Sgr A*,the small HII region is aligned with Sgr A* by chanceand does not cover the entire GC. The chance probabil-ity of this occurrence is small unless lines of sight withsuch strong scattering are common. A significant fraction( & ∼
100 cm − is seen stronglyin emission towards the inner Galaxy at the radial veloc-ity corresponding to the Scutum spiral arm (Langer et al.2016). A handful of lines of sight with very strong scatter-ing are known (e.g., Rodriguez et al. 1982; Wilkinson et al.1994) and many extragalactic background sources behindthe Galactic plane are known to be heavily scattered (e.g.,Lazio et al. 1999; Claussen et al. 2002; Beasley et al. 2002;Pushkarev & Kovalev 2015). If such lines of sight are com-mon, then HII regions as modeled here should contributesignificantly to the observed DM and RM towards heavilyscattered objects. Lower limits on the DM, and thereforerevised pulsar distance estimates, can be inferred from ourmodel in cases where the properties of the intervening HIIregion can be measured. ACKNOWLEDGEMENTS
We thank E. Quataert, F. Eisenhauer, S. Gillessen, R.Herrera-Camus, G. Bower, and R. Wharton for useful dis-cussions. This work was supported by a Sofja KovalevskajaAward from the Alexander von Humboldt Foundation ofGermany.
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