H3+ Spectroscopy and the Ionization Rate of Molecular Hydrogen in the Central Few Parsecs of the Galaxy
aa r X i v : . [ a s t r o - ph . GA ] M a y H + Spectroscopy and the Ionization Rate ofMolecular Hydrogen in the Central Few Parsecs ofthe Galaxy † Miwa Goto, ∗ , ‡ Nick Indriolo, ¶ T. R. Geballe, § and T. Usuda k Universitäts-Sternwarte München, Scheinerstr. 1, D-81679 Munich, Germany, Department ofPhysics and Astronomy, 3400 N. Charles St., Baltimore, MD 21218, USA, 670 North A‘ohokuPlace, Hilo, HI 96720, USA, and 650 North A‘ohoku Place, Hilo, HI 96720, USA
E-mail: [email protected]
Abstract
We report observations and analysis of infraredspectra of H + and CO lines in the Galactic cen-ter, within a few parsecs of the central black hole,Sgr A*. We find a cosmic ray ionization rate typ-ically an order of magnitude higher than outsidethe Galactic center. Notwithstanding, the elevatedcosmic ray ionization rate is 4 orders of magnitudetoo short to match the proton energy spectrum asinferred from the recent discovery of the TeV g -raysource in the vicinity of Sgr A*. Introduction H + and the cosmic ray ionization rate The ionization of molecular hydrogen by cosmicrays – mainly high energy protons, helium nu-clei, and electrons – has diverse and important † Based on data collected in the course of CRIRES Sci-ence Verification program (60.7A-9057) and open-use pro-gram (079.C-0874) at the VLT on Cerro Paranal (Chile),which is operated by the European Southern Observatory(ESO). Based also on data collected at Subaru Telescope,which is operated by the National Astronomical Observatoryof Japan. ∗ To whom correspondence should be addressed ‡ Universitäts-Sternwarte München ¶ Johns Hopkins University § Gemini Observatory k Subaru Telescope influences on the physics and chemistry of in-terstellar molecular clouds. It is a significantheat source in interstellar clouds, through the sec-ondary electrons liberated in the ionization pro-cess. If a cloud is even slightly ionized, its in-ternal motions are restricted by the ambient mag-netic field. In star forming clouds the timescale forcloud collapse is affected by the ionization frac-tion. Ion-neutral reactions, which generally pro-ceed with large Langevin rates, are the main pro-pellant of interstellar chemistry; neutral-neutral re-actions have reaction barriers and are consequentlyprohibitively slow at the low-temperatures of inter-stellar molecular clouds. Thus chemistry in molec-ular clouds is driven by the cosmic ray ionizationof H .Interstellar molecular clouds come in a range ofsizes and densities, but for many purposes may beregarded as consisting of two types: diffuse clouds(10 cm − < n < × cm − ) and dense clouds( n > × cm − ). Regardless of the cloud typethe ionization of H within a cloud occurs almostexclusively by cosmic rays collisions. Photons ca-pable of ionizing H (i.e., with E > areconsumed outside the cloud or on its surface bythe ionization of atomic hydrogen (ionization po-tential 13.6 eV) and/or absorption by dust parti-cles and thus have little or no effect on physics andchemistry in the interior. Ultraviolet photons withless than this energy penetrate diffuse clouds; as aresult hydrogen in them is only partly in molecular1orm and the abundant element carbon is mainlyatomic and singly ionized due to its low ionizationpotential (11.3 eV). In dense clouds dust does notallow near-ultraviolet radiation to penetrate. As aresult dense clouds are essentially fully molecular(e.g., virtually all H in H and all C in CO).The ionization collisional cross-section of H peaks at 70 keV and decreases to higher energyas a power law. It is thought that the cosmic raysthat contribute most significantly to the ionizationof H within clouds have energies, E <
100 MeV.Their intrinsic spectrum, however, cannot be di-rectly measured from inside the solar system, be-cause the influx of cosmic rays with E < z , either by appealing to the ener-getics of the interstellar medium, or to the chem-istry by observing the abundances of moleculesformed in reactions triggered by cosmic ray ion-ization of H , such as OH, HD, HCO + , or H + .Of these molecules H + , first detected in molecu-lar clouds 17 years ago, is the most reliable probeof the cosmic ray ionization rate of molecular hy-drogen, simply because the number of the reac-tions involved in its production is effectively theminimum, one. In a molecular cloud, once H is ionized, the reaction, H + + H → H + + H,is so rapid compared to the other competing pro-cesses that virtually all H + produced by cosmicrays quickly is converted into H + . The H + forma-tion rate is therefore directly proportional to thecosmic ray ionization rate z . Destruction of H + is dominated by fast electron dissociative recombi-nation in diffuse clouds and by chemical reactionwith CO to form HCO + in dense clouds. Both re-actions have been well studied in the laboratory.Equating creation and destruction rates one ob-tains (1) n ( H ) z = k CO n ( H + ) n ( CO ) in dense clouds and (2) n ( H ) z = k e n ( H + ) n ( e ) in diffuse clouds, where k e and k CO are the dom-inant H + destruction rate coefficients for the two types of clouds, and k e is larger than k CO byroughly two orders of magnitude at typical cloudtemperatures. In each type of cloud, however, thesteady state density of H + depends linearly on thecosmic ray ionization rate. High local cosmic ray ionization rate
Until a decade ago, z was simplistically consid-ered to be roughly uniform throughout much ofthe Galaxy, with values within a factor of 3 of3 × − s − , because the great penetrating powerof typical cosmic rays was thought to smooth outlocal influences of particle accelerators. Studiesof interstellar clouds using H + have now conclu-sively demonstrated that this is not the case. Theyhave revealed that values of z in diffuse clouds areon average an order of magnitude higher than indense molecular clouds, a finding most easilyexplained by a large and heretofore unrecognizedpopulation of low energy ( <
10 MeV) cosmic rays,which penetrate diffuse clouds much more effec-tively than dense clouds. In addition, real andlarge differences in the rates deduced for differentdiffuse clouds have been found. Finally, a directconnection between a particle acceleration sourceand the local cosmic ray ionization rate has beendemonstrated by Indriolo et al. near the super-nova remnant IC 443, where z = 2 × − s − ,an order of magnitude higher than in typical dif-fuse clouds in the Galaxy.Much higher ionization rates than those reportedabove are predicted in especially energetic envi-ronments, within galactic nuclei or near the high-est energy supernovae. Yusef-Zadeh et al. hasargued that the ionization rate could be as highas 5 × − s − near the center of the MilkyWay galaxy, in locations where high energy elec-trons that produce X-ray and non-thermal radioemission encounter dense molecular clouds. Like-wise, Tatischeff et al. estimate that the ioniza-tion rate in the Galactic center’s Arches Cluster is1 × − s − . The prediction by Becker et al. (also Black ) is even more extreme: ionizationrates of ∼ × − s − near g -ray emitting super-nova remnants, if they are the principal sources ofGalactic cosmic rays.The subject of this paper is the ionization ratein what may be the closest dense molecular cloud2o the Galactic center where H + R (2,2) l absorp-tion was first detected in the interstellar mediumby Goto et al. (2008). The ionization rate mea-sured using the new data with improved velocityresolution is compared to the ionization rates ex-pected from the X-ray and the cosmic ray flux inthe central few parsecs of the Galactic center.
The Central Molecular Zone
As suggested above, the very innermost region ofthe Galaxy is a site where one might expect tofind extreme values of z . The rate per unit vol-ume of supernova outbursts in the center is esti-mated to be 0.04 times per century, Despitethese and other violent events and the generallyhigh energy density, molecular gas is abundant inthe center. Indeed the central 200 pc of the Galaxy,known as the Central Molecular Zone, containsone tenth of the entire molecular mass of the MilkyWay in its scant 0.001% of the volume. A significant fraction of the molecular gas inthe Central Molecular Zone is found in giant anddense molecular clouds, which take up only asmall fraction of the volume of the Central Molec-ular Zone. However, spectroscopy of H + hasrecently shown that molecules also are plentifuloutside of those clouds. Indeed a large fractionof the volume of the Central Molecular Zone isfilled with warm ( ∼
250 K) and much more rari-fied ( ≤
100 cm − ) molecular gas. Within thisdiffuse molecular gas z has been estimated to be(2–7) × − s − , roughly an order of mag-nitude higher than the average value for diffuseclouds outside of the center. The central few parsecs
Here we focus on molecular gas within the centralfew parsecs of the Central Molecular Zone, a tinyregion containing a massive black hole Sgr A*, a multitude of old stars, and a "Central Cluster" of ∼ young, hot and massive stars (also knownas the nuclear star cluster ). A sketch of this"laboratory" is shown in 1. The principal gaseousstructure there is the Circumnuclear Disk, aclumpy stream of molecular clouds, with inner ra-dius 1.5 pc, orbiting Sgr A*. The gas density drops Figure 1: Schematic view of the central few par-secs of the Galaxy, showing the central black hole(Sgr A*), members of the Central Cluster of mas-sive stars, the Circumnuclear disk, and moleculargas within the Central Cavity.from 10 –10 cm − within the Disk to 10–100 cm − in the Central Cavity, the low-densityregion between Sgr A* and the inner surface ofthe Circumnuclear Disk. Gas in the Central Cavityis partly ionized by the radiation from the stars inthe Central Cluster. The high-mass stars in theCentral Cluster formed approximately 6 Myrs ago,and are now at the end of the main-sequence evolu-tionary phase. Among them, two of the brightestat mid-infrared wavelengths are GCIRS 1W andGCIRS 3. Gas in the cavity is partly ionized bythe hot stars in the Central Cluster. The radiationand the stellar winds from those stars are the mainsource of radiation and kinetic energy injected intothe Central Cavity.
The HII region of the Cen-tral Cavity together with a few distinct streamersof the molecular clouds (“Mini-spiral”) are collec-tively called Sgr A West.
Observations
Absorption spectroscopy in astronomy is similarto absorption spectroscopy in the laboratory. Ineach case the experimental setup consists of abackground light source, the spectrograph, and asample placed between the two. For this study thelight sources were GCIRS 3 and GCIRS 1W in theCentral Cluster within a few tenths of a parsec ofSgr A* as viewed in the plane of the sky. The spec-3rograph was the Cryogenic Infrared Echelle Spec-trograph (CRIRES) ( l / D l = In actuality almost all ofthe intervening gas is within the Central MolecularZone or associated with Galactic spiral arms be-tween the Central Molecular Zone and the Earth.The targeted spectral lines of H + were v vibra-tional transitions from the ( J , K )=(1,1), (3,3) and(2,2) levels at l = m m. Each of theselines is an important diagnostic. The line fromthe (1,1) level provides in a straightforward man-ner the column density in the lowest energy level.The (3,3) level, 361 K above (1,1) is metastable;when collisionally populated, as is the case in theCentral Molecular Zone, it serves as a (density-independent) thermometer. The (2,2) level, at anintermediate energy, has a lifetime against sponta-neous emission of 27 days; for temperatures notmuch lower than its excitation, 150 K, lines from(2,2) are densitometers for low density clouds. Inaddition to these lines of H + , the fundamentalband of CO at 4.7 m m was observed, in part tohelp distinguish between gas in the Central Molec-ular Zone and the foreground arms. (Lines of CO are also present but are too strong to be use-ful in this regard.)The data were obtained on several nights in2006–2008. Standard data reduction techniqueswere employed (e.g, Goto et al. 2008 ). The finalspectra, shown in Figs. 2-4, are corrected for in-strumental transmission and atmospheric absorp-tion and have been wavelength-calibrated to an ac-curacy corresponding to ± − . Results
Gas in the Central Molecular Zone
Spectra toward GCIRS 3 and GCIRS 1W of thethree H + lines and the low-lying CO P (1) lineare compared in 2. Spectra of a much wider rangeof CO lines toward GCIRS 3 are shown in 3. Ascan be seen in 2, with the exception of the density-sensitive H + R (2,2) l line, each line shows absorp-tion over a wide velocity range. From the forego- Figure 2: H + and CO v=1-0 P (1) spectra towardGCIRS 3 (blue) and GCIRS 1W (black).ing discussion the presence of the R (3,3) l line andabsence of the R (2,2) l line over much of this rangeimplies that at most velocities where warm molec-ular gas exists it is at low density.For the most part the pairs of spectra of the otherthree lines have nearly identical profiles over muchof their velocity ranges. This is not surprising,as both the Central Molecular Zone and the in-tervening Galactic arms are enormous structurescompared to the separation of the GCIRS 3 andGCIRS 1W lines of sight, ∼ + and CO lines towardthese and other infrared sources in the Galacticcenter over much wider range of sightlines thanthose shown here, together with knowledge ofGalactic structure gleaned mainly from radio ob-servations, allow one to clearly associate large por-tions of these line profiles with gas in the CentralMolecular Zone and the foreground arms. The narrow absorption features near 0, −
30 and −
50 km s − , common to the H + R (1,1) l and COlines are associated with cold and dense molecu-lar gas in the foreground Galactic arms. On theother hand, the shallow trough of absorption seen4igure 3: Spectra of individual CO v=1-0 linestoward GCIRS 3. Gaps in the individual profilescorrespond to wavelengths intervals of poor atmo-spheric transmission and/or to wavelengths where CO v=1-0 lines overlap.in the R (1,1) l line profile to extend roughly from −
200 to 0 km s − , nearly perfectly matched by thefull R (3,3) l profile, but conspicuously absent in theboth R (2,2) l and CO profiles, must be producedby warm and low-density gas which, while con-taining H (otherwise there would be no H + ), con-tains little or no CO. This description is the callingcard of diffuse molecular gas, as introduced earlierin this paper. The wide spatial and velocity extentsof these absorptions and the warm temperature ofthe gas require that the gas be located within theCentral Molecular Zone, and expanding outwardfrom the center. Figure 4: An expanded view of 2 at the positivevelocity 0–100 km s − . The velocity profile of the CO 1-0 R (4) line is shown, in place of the P (1)line. Gas in the Central Cavity
The largest differences between the line profilestoward GCIRS 1W and GCIRS 3 in 2 are at veloc-ities greater than about +
20 km s − . This velocityrange is shown in more detail in 4; note that in thisfigure we show the CO R (4) line as it is morerepresentative of the CO line profiles in this ve-locity range than the P (1) line shown in 2.In general the sightline toward GCIRS 3 pro-duces stronger absorptions than GCIRS 1W at v > +
20 km s − , but there also are differences in theshapes of the profiles between the two objects. To-ward GCIRS 3 the absorption maxima of all thethree H + lines occur at ∼ +
50 km s − . Absorp-tion by all but the lowest lying CO lines alsopeak near that velocity (see 3 and the bottom rightpanel of 4).Apart from GCIRS 1W and GCIRS 3 none of theobserved sightlines through the Central MolecularZone within 30 pc of the center produce absorptionat v > +
20 km s − in any of the H + lines. More-over, the presence of both the excited H + lines andthe CO absorption from excited rotational lev-els (see 3) implies that the absorbing gas is warm.Such absorptions cannot be produced by the coldgas of the foreground spiral arms, but instead mustarise in the Galactic center.Despite the similarity in velocities we concludethat these absorptions by H + and CO do not arise5igure 5: HCN J = (blue contours) overlaid with a VLT K -band image of the Central Cluster. The lowestcontour level is 1.6 J m beam − s − (2 s ). The dot-dash line denotes constant latitude and is parallelto the Galactic plane. Clumps H and I, as identi-fied by Montero-Castaño et al., are labeled.in the well-known “ +
50 km s − ” giant molecu-lar cloud (M − − which is locatedwithin the Central Molecular Zone, has dimen-sions of roughly 20–30 pc, and is known froma multitude of radio wavelength studies to ex-tend across the sightlines to GCIRS 1W andGCIRS 3. The large differences between the ab-sorption profiles at positive velocities in GCIRS 3and GCIRS 1W tends to rule out the absorptionoccurring in such a large cloud.This foregoing suggests that the absorption atpositive velocities occurs very close to GCIRS 3and we thus consider the possibility that the ab-sorption arises in the Circumnuclear disk and/ordense clouds that come off from the Circumnu-clear disk to the Central Cavity. 5 is a contour mapof the Circumnuclear disk in the HCN J = on which issuperimposed a K -band ( l = m m) image ofthe stars in the Central Cluster retrieved from theVLT archive. As is shown in an expanded view(6) a compact “clump I” (Montero-Castaño et al.),which may be physically connected to the Circum-nuclear disk, positionally coincides with GCIRS 3, Figure 6: Expanded view of the central part of 5.The cross is the position of Sgr A*. The positionsof the apertures where the spectra in 7 were ex-tracted are marked with gray rectangles.while the line of sight to GCIRS 1W is clear. Notethat, as n crit ∼ cm − for the HCN J = with clump I and are shown in 7. Fromthem it is clear that (1) the Circumnuclear diskgas at clump H, seen at LSR velocities of + +
60 km s − , extends inward across the sight-line to GCIRS 3 and close to clump I, but not toGCIRS 1W, and (2) clump I itself is mainly associ-ated with gas at a radial velocity of ∼ −
30 km s − .It would then appear that −
30 km s − gas in clumpI is not physically connected to the Disk. As canbe seen in 8 at GCIRS 3 the HCN emission lineprofile near +
50 km s − is an excellent matchto the H + R (2,2) l absorption line, not only in itsline center, but also in its line shape. We interpretthis as strong evidence that the absorption towardGCIRS 3 centered at +
50 km s − arises largely inthis arm of molecular gas extending inward to the6igure 7: HCN J = Temperature and density
We convert the measured equivalent widths ofthe H + absorption lines in the interval +
20 to +
80 km s − to column densities in the (1,1), (2,2)and (3,3) states using standard procedures (seeGoto et al. 2008) and utilizing the dipole transitionmoments given by Neale et al.. The absorpitonarising in the diffuse clouds at the same velocityrange, whose prsence is apparent in the spectraof GCIRS 1W, were removed by subtracting thespectra of GCIRS 1W from those of GCIRS 3 priorto the measuremment of the equivalent widths.Using the steady state analysis of Oka and Epp one can then use the relative level populations toestimate the temperature and the density in theabsorbing gas. We find 250 K < T <
350 K and >
500 cm − (9). This is sufficiently dense for thegas to be classified as a dense cloud. Unsurpris-ingly it is much warmer than the typical Galacticequivalent. The derived density is far less than thecritical density of the HCN J = + inhabits a different por- Figure 8: Comparison of the line profiles ofH + R (2,2) l and HCN J = J = R (2,2) l line.tion of the cloud than the observed HCN, perhapsthe outer layers. Detailed analysis of the CO ab-sorption feature centered at 60 km s − is compli-cated, as the individual transitions have widely dif-ferent critical densities. However, the relative linestrengths indicate temperatures exceeding 100 Kand densities of ∼ cm − (see Kramer et al. The cosmic ray ionization rate
Here we derive the cosmic ray ionization ratein the +
50 km s − gas on the line of sight toGCIRS 3. In Goto et al. 2008 z was calculatedassuming the cloud at +
50 km s − is diffuse, as inthe case for the other clouds filling the large part ofthe Galactic center. The gas likely has the proper-ties of a dense cloud (i.e, it is fully molecular), asis discussed above, and therefore we use equation(1), which can be re-expressed as z L = k ′ L N ( H + ) n C n H R x , where L is the pathlength through the cloud, N ( H + ) is the observed column density of H + , k ′ L = × − cm s − is the Langevin rate constant forthe reaction H + + CO → H + HCO + taken fromAnicich and Huntress and Klippenstein et al., and multiplied by 1.5 to take into account the7igure 9: Comparison of the relative level popula-tions of H + , n (3,3)/ n (2,2) and n (3,3)/ n (1,1) in thelines of sight to GCIRS 3 and GCIRS 1W, derivedfrom the steady state analysis by Oka and Epp. The gray dots correspond to other sightlines tosources in the Galactic center within 30 pc ofSgr A* that mostly sample the gas in the Cen-tral Molecular Zone. Note the higher temperaturesand density in the gas in front of GCIRS 3 at radialvelocities +
20 to +80 km s − (red triangle).other minor destruction paths (especially H + + O → H + OH + or → H + H O + ), n C n H | SV (= . × − ) is the fractional abundance of carbonrelative to hydrogen in the solar vicinity, and R x isthe correction factor to take into account the higherabundances of elements other than H in the Galac-tic center.We take L to be 0.1 pc, roughly half the distancebetween GCIRS 3, which lies behind the arm, andGCIRS 1W, where the cloud is absent, and R x = The total column density of H + is cal-culated by adding the column density of N (1,1), N (2,2), and N (3,3), in addition to N (1,0) publishedin Goto et al. (2008). [ N ( H + ) = × cm − ].We thus obtain z = . × − s − .We regard the above value for z as a lowerlimit, because we have used a low value for R x and also have assumed that the +
50 km s − gasis fully molecular, which may well be the case forthe dense core which produces the HCN J = + absorption is likely to occur. The valueof the ionization rate thus may not differ greatlyfrom values of (2–7) × − s − derived for theCentral Molecular Zone as a whole by Oka et al.(2005). Sources of H Ionization
These values of the ionization rate are among thehighest measured in the Galaxy. It is therefore ofinterest to consider possible sources of the ioniz-ing particles. The black hole in Sgr A*, nearby su-pernova remnants, and energetic winds from starsin the Central Cluster are all potential particle ac-celerators. We have assumed so far that cosmicray is the sole source of ionization of H . Thisis probably the case for the Central MolecularZone, where the size of the medium ( ∼
200 pc)is much larger than the range of the X-ray pho-tons ( s x ≈ − cm − at 1 keV ), therefore X-ray does not directly contribute to the ionization inmuch of the region, but need not be the case in thecentral few parsecs. There the ionization can bedue to the local sources. We discuss below the H ionization by the cosmic rays as well as by X-rays,and estimate the expected z for each mechanism. Cosmic ray ionization
The rate at which a single molecular hydrogenis ionized by an energetic proton is given by theproduct of the proton specific intensity, J p ( E ) andthe ionization cross section of H , s p ( E ) , inte-grated over energy and solid angle, z = p Z E E J p ( E ) · s p ( E ) dE . Ionization by the electron impact is neglected,since the energy loss though radiative processesas a results of the interaction with the interstellarmagnetic field, ambient photons and charged par-ticles is much faster, and since the ionization crosssection is an order of magnitude smaller than forprotons.What kind of proton spectrum one should as-sume in the central few parsecs of the Galaxy? Aclue comes from a high energy (up to ∼
10 TeV) g -ray observation. A point-like TeV g -ray source8as recently discovered in the Galactic center bythe High Energy Stereoscopic System (HESS Col-laboration) which observes optical Cherenkovlight of an electron-positron pair generated by theincidence of high energy g -rays on the Earth’s at-mosphere. The source, HESS J1745 − arguethat the most likely mechanism to produce suchhigh energy g -rays is neutral pion decay, precipi-tated by the acceleration of protons near the blackhole. When such protons encounter cold nucleiin the ambient medium, proton-proton scatteringproduces neutral pions which subsequently decayspairs of high energy g -ray photons. From the ob-served g -ray spectrum, the energy spectrum of pro-tons injected to the cold medium can be deter-mined. Chernyakova et al. calculated that theproton flux required to reproduce the observed g -ray spectrum of HESS J1745 −
290 from 0.1 GeVto 100 TeV is E F = . × erg cm − s − at 1 GeV in their representation, or 7 × par-ticles cm − s − str − (Gev/Nucleon) − . For com-parison, the standard proton flux in the Milky Wayis 0.2 particles cm − s − str − (Gev/Nucleon) − at1 GeV, which is 3 × times smaller.The collisional ionization of H occurs via pro-ton impact (H + p → H + + p + e) and elec-tron capture (H + p → H + + H) and is well un-derstood, theoretically and experimentally. Thecombined ionization cross-section is reproducedfrom Rudd et al., Padovani et al. in 10. As s p ( E ) is well understood, the cosmic ray ioniza-tion rate is virtually only dependent on the pro-ton spectrum J p ( E ) . If J p ( E ) is scaled up by3 × times from the Galactic standard, z be-comes larger by the same factor. Such a large z has never been observed, not even in the Galacticcenter; the values that we and others have reportedare only larger by factors of 10-100 than those out-side the center.There could be at least two possible explanationsfor this huge discrepancy: uncertain extrapolationof J p ( E ) to the lower energy, and the non-lineardependency of H + abundance on z for very highvalues of z .As mentioned earlier the cosmic ray spectrumcannot be directly observed in the energy rangewhere ionization of H is most efficient (1– 10 MeV), because of the solar modulation. Atmuch higher energies where direct observationsare possible, the number flux of cosmic ray protonsincreases as energy decreases from TeV to GeVaccording to a power law, J ( E ) (cid:181) E a , with a be-tween − −
3. At lower energies the best mea-surements are by the Voyagers and Pioneer space-crafts in the outer solar system.
Although theobservations are still affected by the solar modu-lation, the local interstellar cosmic ray spectrumcan be predicted using the latest solar modulationmodels.
The intrinsic cosmic ray spectra areroughly flat at 0.1–1 GeV, as is expected fromthe shorter range of the low energy cosmic rays(2 . × cm − for 1 MeV cosmic ray proton ).On the other hand, Indriolo et al. found that alow-energy turnover at 0.1–1 GeV is inconsistentwith the mean ionization rate inferred from H + spectroscopy. Instead the proton spectrum mustcontinue to increase down to 1 MeV, otherwisethe H ionization rate is too low compared to theobserved z = × − s − in diffuse clouds,an average value secured by H + spectroscopy to-ward more than a dozen of sightlines. A simi-lar conclusion is reached by Neronov et al., whoanalyzed g -ray spectra of the molecular cloudsclose to the solar system known as the Gould Beltclouds. The observed g -ray spectra were best re-produced by the cosmic-ray protons having power-law spectrum with a weak break (a change of thespectral index) at 9 GeV, but no turnover (changeof sign of the spectral index).The uncertain extrapolation of the cosmic rayspectrum from the observable ( > ∼ MeV) is the common problemwhen we calculate z directly from J p ( E ) . Guidedby Indriolo et al. and Padovani et al., we adaptedtwo extreme power-law indices a = − The latter contains a weak breakbut no turnover as is proposed by Indriolo et al.and others,
Both cases are shown in 10. Theproton injection spectrum by Chernyakova et al. iswell approximated by J p ( E ) (cid:181) E − . down to theenergy 1 GeV. The gap 0.2–1 GeV was bridgedby power-law spectrum with index a = − .
25 to9mitate a smooth break. The interval of the inte-gration [ E , E ] was arbitrarily set to 1–10 MeV.The lower cut-off energy of the integration is of-ten set at 1 MeV, because lower energy protons donot have sufficient range to affect on the global H ionization rate. However, the ionization in this par-ticular case can be local, and the cosmic rays withshort range may well contribute to z . The calcu-lation therefore provides only a lower limit for z .Integration yields z = . × − s − for thenon-turnover case with a = − . × − s − for a = z = . × − s − and z = . × − s − , respectively,if the break energy is raised to 0.4 GeV. In ei-ther case the cosmic-ray proton spectrum withouta strong turnover is 4 orders of magnitude higherthan is observed in the cloud in front of GCIRS 3.This means that, if as many relativistic protons aregenerated as the HESS TeV g -ray source implies,they must be strongly damped at low energy. Therequirement for damping is even stronger if the ac-tual cut-off energy is lower than 1 MeV.A second possible explanation for the large dis-crepancy is that the observed column density ofH + might have led to a significant underestimateof z . We have assumed that the abundance ofH + linearly increases with z , because the reac-tion of H + and H is rapid enough to justify ne-glecting other competing processes. At high z ( > − s − ), however, destructive recombinationof H + with an electron becomes non-negligible,since electrons are more populous because of thehigh z . It seems unlikely that this can com-pletely account for the discrepancy, however.Finally, another factor that may need to be takeninto account is the time-dependent formation rateof H , which would require ∼ yrs to reachan equilibrium, if the formation starts from pureatomic gas. The dynamical timescale of theGalactic center is short (the orbital period aroundthe 4 × M ⊙ black hole in Sgr A* is 10,000 yrsat 1 pc). If the formation or destruction of H istriggered by the changes of the external conditionsof the cloud, the molecular hydrogen in the cloudin front of GCIRS 3 may not have enough time toreach steady state abundances balancing formationand destruction. At the beginning of the process,the abundance of H + is less dependent on z , but more on the H abundance. z calculated on thebasis of the linear dependency on N ( H + ) may notcorrectly represent the actual cosmic ray ioniza-tion rate.Figure 10: Proton energy distribution and ioniza-tion cross section of H at 1 keV to 100 TeV. Thespectrum is obtained from Chernyakova et al. at E > J p ( E ) (cid:181) E − and J p ( E ) (cid:181) E . The spectrum from 1 GeV to0.2 GeV is bridged by J p ( E ) (cid:181) E − . to imitatea smooth break. See text for details. The ioniza-tion cross section is reproduced from Rudd et al. and Padovani et al.. X-ray ionization
Similar to the case of cosmic ray ionization, the X-ray ionization rate is the integral over energy of theproduct of the X-ray spectrum F ( E ) , and the ion-ization cross section s x ( E ) . In the X-ray regime(0.1 keV < E <
100 keV), two ionization processesmust be taken into account: photo-ionization inwhich the X-ray photon is absorbed, and Comp-ton scattering in which the photon is scattered atlower energy. In either case, the electron liberatedby the ionization is energetic enough to lead to fur-ther ionization events on H . These secondary ion-izations are far more numerous than the first ion-ization by the X-ray photon. The photo-ionizationcross section of H by X-ray s xp is taken fromYan et al. and Yan et al., and scaled by h xp according to Wilms et al. to take into accountthe contribution of the electrons produced by thephoto-ionization of heavy elements. The Comp-ton scattering cross section s xc is taken from10ubbell et al., and scaled by h xc to include theelectrons from the compton scattering on helium.The photo-ionization and compton scattering crosssections are reproduced in 11. The number of sec-ondary ionizations that follow the single primaryionization has been calculated by Dalgarno et al. as a mean energy per an ion pair W , where the totalnumber of ionization events per primary ionization N ion is given by N ion = E e / W , with E e being theenergy of the initial (secondary) electron. Follow-ing Meijerink and Spaans, we use W (1 keV) =36 eV over the entire energy range, as W asymptot-ically approaches this value for photons with E > The total X-ray ionization rate is then givenby z = Z ( s xp h xp + s xc h xc ) EW ( ) F ( E ) dE . Two possible sources of X-ray photons arepresent in the central few parsecs of the Galaxy:X-ray point sources in the Central Cavity anddiffuse X-ray emission. At least five X-raypoint sources are known within 10 arcseconds ofSgr A*, including Sgr A* and GCIRS 13, acompact star cluster that is thought to contain anintermediate-mass black hole inside. All are ofmore or less similar brightness (10 –10 erg s − at 2–10 keV) with Sgr A* slightly brighter than theothers.Here we calculate the ionization rate caused byX-ray irradiation from Sgr A* as an example. Theactual z would be a few times larger if the con-tribution of other point sources are included. Theobserved X-ray luminosity of Sgr A* at 2–10 keVis 2 . × erg s − . In order to extrapolatethe spectral range to cover 0.1 keV to 100 keV,we create a spectrum using the Raymond-Smithplasma model provided in AtomDB package with the plasma temperature kT = . and normalized tomatch the above observed luminosity. The com-plete spectrum is shown in 11. The flux of X-ray photons that the cloud at GCIRS 3 receives is F ( E ) = L ∗ ( E ) / p r , where r is the distance fromSgr A* to the cloud, assuming the X-ray emissionis isotropic and that there is no attenuation. Theresultant z is highly dependent on the distance tothe X-ray source; using the minimum linear dis- tance between GCIRS 3 and Sgr A* projected onthe sky (=0.2 pc), z is 5 . × − s − includingthe secondary ionizations, considerably larger thanthe value derived from the observed H + lines.The second possible ionizing source is thelocal diffuse X-ray emission that extends ≈
10 arcseconds of Sgr A*. According toRockefeller et al. the emission is likely thesum of the X-ray emission from the stellarwinds produced by the evolved massive starsin the Central Cluster. Its X-ray luminosity is7 . × erg s − arcsec − (2–10 keV). Theplasma temperature that best fits the observedspectrum is kT = and from the Sgr A haloemission, or from non-thermal emission from thesupernova remnant Sgr A East, which are not in-cluded in the above value.To estimate the ionization rate from the diffuseX-ray emission we assume a spherical X-ray emit-ting zone, centered on Sgr A*, of radius 1 pc,somewhat less than the inner radius of the Circum-nuclear Disk, and locate the absorbing gas in frontof GCIRS 3 on the surface of this sphere. TheX-ray luminosity per unit volume is modeled byRockefeller et al. as a function of the distancefrom Sgr A*. We integrate the luminosity per unitvolume to determine the total luminosity gener-ated within the sphere. Only the outward X-rayflux was taken into account. The calculation yields z = . × − s − including the secondary ion-izations, again considerably larger than the valuederived from the observed H + lines. We note thatit is highly dependent on the radius of the emit-ting sphere (e.g., if the cloud is closer to the center(0.2 pc), z is increased to 5 . × − s − ). Prospects and Status
With sufficient numbers of suitable backgroundsources such as GCIRS 1W and GCIRS 3 in thecentral few parsecs of the Galaxy and with a suf-ficiently extensive distribution of molecular gaswithin the Central Cavity, one should be able touse spectroscopy of H + to detect the footprintsof the ionization sources and to discriminate be-11igure 11: Calculated photon distribution of thediffuse local X-ray emission at a distance of 1 pcfrom Sgr A*, and the ionization cross section ofH , from 100 eV to 10 keV. The spectrum was cal-culated from the Raymond-Smith plasma model provided in AtomDB with the plasma temper-ature kT = . mod-eled by Rockefeller et al.. The photo-ionizationcross is taken from Yan et al. and Yan et al., and Compton scattering cross section is taken fromHubbell et al.. tween the various possibilities for ionization thathave been put forth in the previous section. IfX-rays are the main source of the ionization, z should be enhanced close to the individual X-raysources such as Sgr A* and the powerful windsource GCIRS 13. If cosmic rays (protons) are themain ionization source, z would be enhanced atthe inner wall of the Circumnuclear Disk, or on thecompact clumps, where the relativistic protons en-counter cold nuclei. Inside the Central Cavity, z would gradually decrease with the distance fromSgr A*, as the protons lose energy as they propa-gate outward. High spatial sampling of z is thekey to address the primary ionization mechanism,and the possible in situ acceleration of cosmic raysby the black hole.The Central Cluster contains hundreds of mas-sive and luminous stars whose spectra are sim-ple enough to allow quantitative spectroscopy ofthe H + lines from J =
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