Shock acceleration of relativistic particles in galaxy-galaxy collisions
aa r X i v : . [ a s t r o - ph . C O ] A p r Shock acceleration of relativistic particles ingalaxy-galaxy collisions
Heinrich J. Völk ∗ a and Ute Lisenfeld b a Max-Planck-Institut für Kernphysik, Heidelberg, Germany b Departamento de Física Teórica y del Cosmos, and Instituto ‘Carlos I’ de Física Teórica yComputacional, Universidad de Granada, SpainE-mail:
[email protected] ; [email protected] All galaxies without a radio-loud AGN follow a tight correlation between their global FIR andradio synchrotron luminosities, which is believed to be ultimately the result of the formation ofmassive stars. Two face-on colliding pairs of galaxies, UGC12914/5 and UGC 813/6 deviate fromthis correlation and show an excess of radio emission which in both cases originates to a largeextent in a gas bridge connecting the two galactic disks. The radio synchrotron emission expectedfrom the bridge region is calculated, assuming that the kinetic energy liberated in the predom-inantly gas dynamic interaction of the respective interstellar media (ISM) has produced shockwaves that efficiently accelerate nuclei and electrons to relativistic energies. A simple model forthe acceleration of relativistic particles in these shocks is presented together with a calculation ofthe resulting radio emission, its spectral index and the expected high-energy gamma-ray emission.This process is not related to star formation. It is found that the nonthermal energy produced inthe collision is large enough to explain the radio emission from the bridge between the two galax-ies. The calculated spectral index at the present time also agrees with the observed value. Theexpected gamma-ray emission, on the other hand, is too low by a factor of several to be detectableeven with foreseeable instruments like CTA. ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/ hock acceleration in galaxy-galaxy collisions
Heinrich J. Völk
1. Introduction
The universal, tight correlation between the spatially integrated far-infrared (FIR) luminositiesand the monochromatic radio continuum emissions from late type galaxies without a bright, radio-loud AGN (de Jong et al. 1985, Helou et al. 1985) has been known for a long time. It is believed tobe ultimately a result of the formation of massive stars and also holds for most interacting galaxies.It is therefore quite unusual that Condon et al. (1993), hereafter referred to as CHS, and Condon etal. (2002) found two clear exceptions to this rule. This concerns two face-on colliding spiral galaxysystems where at the present time, presumably some 30 Myr after the interaction, the respectivepairs of galaxy disks are again well separated from each other optically, but are connected by aradio continuum-bright “bridge” of gas, suggested to be stripped from the interpenetrating disks.The two systems show overall a significant excess, by a factor of about two, of the radio continuumemission relative to the FIR-radio continuum ratio expected from the FIR-radio correlation forsingle galaxies. CHS interpreted the finding as the result of general electron escape from galaxies,in this case into the bridge connecting the pair.In the present paper the dynamical effects of such galaxy-galaxy collisions on the interstellargas are investigated. It is argued that the interstellar media of the respective galaxies will undergoa largely gas dynamic interaction, where the low-density parts exchange momentum and energythrough the formation of large-scale shock waves in the supersonic collision. A simple modelfor the acceleration of relativistic particles is presented and the synchrotron emission from therelativistic electron component is calculated, as well as the expected gamma-ray emission fromrelativistic nuclei and electrons. The model is shown to be able to explain the radio continuumemission observed from the bridge between the galaxies. For details, see Lisenfeld & Völk (2010),hereafter referred to as LV.
2. Further properties of the colliding systems
The spectral index of the radio emission between 1.49 and 4.9 GHz steepens gradually fromthe stellar disks with values of 0.7–0.8 to values of 1.3–1.4 in the middle of the connecting gasbridge. This steep spectral index will be argued to be indicative of dominant synchrotron andinverse Compton losses suffered by the relativistic electrons. Apart from the sychrotron emittingelectrons the bridge in the system UGC 12914/5 contains also large amounts of atomic (CHS)and molecular (Braine et al. 2003) gas, where practically no star formation is taking place. Thisis interpreted as an essentially complete hydrodynamic removal of the more diffuse atomic andmolecular gas from the galaxies. Most likely, only the dense cloud cores – capable of forming stars– have remained within the stellar disks together with the stars. The other system, UGC 813/6, wasdescribed in the later paper by Condon et al. (2002). Since it is very similar, the discussion herewill be limited to UGC 12914/5.
3. Acceleration model
In a face-on collision the stellar disks interpenetrate each other without being too much altered.However, the diffuse gas and part of the gas clouds interact hydrodynamically and exchange energyand momentum. 2 hock acceleration in galaxy-galaxy collisions
Heinrich J. Völk
If one assumes that half of the gas, which is now present in the bridge, was previously in onegalaxy, and the other half in the other galaxy, then the total energy liberated in a fully inelasticinteraction is the kinetic energy of the gas mass: E k in = M gas (cid:16) v coll (cid:17) , (3.1)where M gas is the total gas mass in the bridge and v coll denotes the velocity difference of the gasat collision. The factor 1/2 converts this velocity to the velocity difference in the center of masssystem (assuming that both gas disks are equally massive). The relative velocity between thegalaxies, v coll ≈
600 km/s, in the case of UGC 12914/5 has been derived by CHS from a analysisof the HI line and of the galaxy masses. M gas and E kin are estimated as ( − ) × M ⊙ andtherefore ( . − . ) × erg, respectively.At the collision of the two ISM, a tangential discontinuity will form and two strong shockswill propagate in opposite directions with velocities v shock , communicating the interaction to largerand larger fractions of the colliding interstellar gas masses. The space in between these shocks isfilled with post-shock gas. Fig. 1 shows the idealized picture of this interaction, the basis of thepresent model, in the reference frame of the motion normal to this tangential discontinuity, whichis also the center of mass system. In this frame, the post-shock normal velocity v post vanishes andthe preshock normal velocity of the gas is v pre = v coll . The contact discontinuity is stationary andsituated in the middle between the galaxies (at x = × ( v post − v shock ) = ( v pre − v shock ) . With v post =
0, this yields v shock = v coll . The shock velocity V s , relative to the unperturbed ISM gas,is then V s = v shock + v coll = v coll = 400 km/sec. From Fig. 1 in CHS one can estimate that theshocks are at present close to the galaxy disks so that practically the entire bridge is expected to befilled with post-shock gas.The Mach number of the shocks produced in this collision is like in middle-aged supernovaremnants in the Sedov phase. Roughly speaking, the particle acceleration efficiency of such shockswill therefore be similar to that of a supernova remnant, i.e. of the order of 10 −
30% (e.g. Berezhko& Völk 1997). This is a basic assumption for the present paper.The source function Q ( E ) , i.e. the number of relativistic particles produced by the shock perenergy and time interval is given by: Q ( E ) = f acc ( E ) v shock A , where A is the area covered bythe shock (roughly the area of the galaxy disks). The factor 2 is due to the fact that the shockspropagate into two, opposite directions. f acc ( E ) is the downstream, uniform number of relativisticparticles of rest mass m , produced per volume and energy interval at the shocks: f acc ( E ) = f (cid:18) Emc (cid:19) − g . (3.2)Here, g is the spectral index of the differential relativistic particle source spectrum, taken to be g = . f can be determined by requiring that the total energy converted into relativistic particlesduring the entire duration of the interaction, T , is equal to E acc = Q × E kin , where Q = . − . hock acceleration in galaxy-galaxy collisions Heinrich J. Völk
Galaxy 1 Galaxy 2X=0v shock v shock v coll /2v coll / shock /TX=-v shock /T Figure 1:
Schematic illustration of the shock in the bridge region, in the center of mass system. E acc = Z ¥ E min E Q ( E ) T dE = Z ¥ E min E f (cid:18) Em p c (cid:19) − g v shock A T dE = f ( m p c ) g − (cid:18) E min m p c (cid:19) − g + v shock A T , for g >
2. Here, E min is the minimum energy of relativistic protons of mass m p accelerated, takenas E min = f = E acc T A v shock ( g − )( m p c ) (3.3)In the Galactic cosmic rays, at a given energy, the number of relativistic electrons is about 1%of that of the protons at GeV energies, and the source spectra for electrons and protons are probablysimilar (Müller 2001). Assuming that this electron-to-proton ratio is also representative for thesource spectra in the galaxies considered here, implying that the electron and proton source spectraare the same, for the source function of the relativistic electrons Q e ( E ) = Q ( E ) × .
01 is adopted,which means that their source distribution is f acc , e = f , e ( E / ( m p c )) − g , with f , e = f × .
4. Relativistic electron density and synchrotron emission
In order to calculate the synchrotron emission from the bridge the time-dependent propagationequation for the electron particle density f e ( t , x , E ) is solved. Due to the spatial symmetry of thesituation, a one-dimensional approximation is appropriate, where x is the coordinate in the directionalong which the galaxies separate (see Fig. 1). In addition, the diffusion of relativistic electrons isneglected because the typical spatial scales which are relevant on the time-scales discussed here,3 × yr, are < ¶ f e ( t , x , E ) ¶ t = q e ( t , x , E ) + ¶¶ E (cid:26) b E f e ( t , x , E ) (cid:27) , (4.1)4 hock acceleration in galaxy-galaxy collisions Heinrich J. Völk where q e ( t , x , E ) = Q e A (cid:0) d ( x − v shock t ) + d ( x + v shock t ) (cid:1) (4.2)is the local source strength (in units of relativistic electrons produced per energy interval per timeand per volume). This source strength describes two shocks that start at t = x = v shock . Eq.(4.1) takes into account the electron acceleration inthe shocks together with the radiative energy losses of these CR electrons due to Inverse Comptonand synchrotron losses; up to the present epoch, adiabatic losses can be disregarded. Then: (cid:18) d E d t (cid:19) rad = − bE = − s T c (cid:18) Em e c (cid:19) ( U B + U rad ) , (4.3)where s T is approximated by the Thompson scattering cross section, B the magnetic field strength, U B its energy density and U rad is the energy density of the radiation field. Neglecting adiabaticlosses is consistent with the fact that the distribution of the synchrotron spectral index a ( . , . ) ,between 1.49 and 4.86 GHz, has an integrated value a ( . , . ) > m Gin the bridge of UGC 12914/5 (CHS), which implies U B = . − . The total radiationfield density from (in essentially equal amounts) the blue magnitude, the FIR, and the CosmicMicrowave Background (CMB) amounts to U rad ≈ .
76 eV cm − (LV).The solution of eq. (4.1) is: f e ( E , | x | , t ) = f , e (cid:18) E m c (cid:19) − g (cid:26) − E b (cid:18) t − | x | v shock (cid:19)(cid:27) g − , (4.4)for t > | x | / v shock and t − | x | / v shock < t loss and f e ( E , | x | , t ) = , for t < | x | / v shock and t − | x | / v shock > t loss , (4.5)with t loss = ( Eb ) − being the life-time of a relativistic electron against radiative energy losses.This expression can also be integrated over the volume of the bridge to obtain the total number ofrelativistic electrons in the bridge F e ( E , t ) . The result is: F e ( E , t ) = A f , e (cid:18) E m p c (cid:19) − g v shock t loss g − (cid:8) − ( − t / t loss ) g − (cid:9) , for t < t loss (4.6)and F e ( E , t ) = A f , e (cid:18) E m p c (cid:19) − g v shock t loss g − , for t > t loss (4.7)The synchrotron spectrum is obtained by convolving f e ( E , x , t ) , respectively F e ( E , t ) , with the syn-chrotron emission spectrum of a single electron.This solution allows a theoretical prediction for the total radio flux density specifically at1 .
49 GHz and of the radio spectral index between 1 .
49 and 4 .
86 GHz. Both values are in satisfac-tory agreement with the observations (LV). Clearly also the radio spectral index increases towardsthe center of the bridge. The model calculations therefore show that acceleration by large-scale5 hock acceleration in galaxy-galaxy collisions
Heinrich J. Völk shocks caused by the galaxy-galaxy interaction is indeed able to explain the radio emission fromthe bridge both in intensity and spectral morphology.The two interacting galaxy pairs studied here, are possibly examples of what might have hap-pened much more frequently at early stages of structure formation, when primordial galaxies hadalready developed magnetic fields as a consequence of early star formation, but when they werestill likely to interact strongly with neighboring structures of a similar character.
5. High-energy gamma-ray emission
Although not the primary topic of this paper, it is clear that the interaction of galaxies con-sidered here will also lead to the acceleration of gamma-ray producing very high-energy particles,both nuclei and electrons, in the form of the distribution f acc , cf. eq. (3.2). The visibility of theacceleration process also in high-energy gamma rays would be an independent argument for themodel presented. In the following a rough estimate will be given.The shock system which characterizes the face-on interaction of the two spiral galaxies canto first approximation be considered as plane parallel, with constant speed shocks; the energeticparticles remain confined in the growing interaction region until the interaction is completed. As-suming the diffusion coefficient to be as low as the Bohm diffusion coefficient (e.g Kang 2007)one can approximately calculate the maximum proton energy achieved at the present epoch as E max ≈ . × eV. This very high energy is the result of the long life-time ( T = . × yrs)of the shocks, inspite of their comparatively moderate speed of ≈
400 km sec − . The situationis rather different for the energetic electrons because of their radiative losses. Even disregardingany magnetic field amplification at the shocks due to the accelerating particles, the maximum elec-tron energy is only ∼
10 TeV. For the IC gamma-ray emission in the sub-TeV region mainly theCMB counts. In contrast to the great majority of the radio electrons, however, all gamma-ray emit-ting electrons are “old” as a result of postshock radiative losses. As a consequence their energyspectrum is softened with a correspondingly reduced IC gamma-ray emission.When the shocks have gone through the interacting ISM of the two galaxies, which is the caseat about the present epoch, the kinetic energy E kin = ( .
49 to 1 . ) × erg has been transformedinto thermal and nonthermal particle energy. This corresponds to E acc ∼ erg, predominantly inrelativistic nuclei, which is roughly 10 times more energy than available from a single supernovaremnant.The bridge volume V is reasonably estimated as V ≈ p R , where the disk radius R ≈
10 kpc(CHS). This implies a mean gas density of 0 .
05 to 0 .
14 cm − , which is an order of magnitudesmaller than the typical density in the plane of spiral galaxies and more than three orders of mag-nitude smaller than the density in the starburst nucleus of e.g. the galaxy NGC 253.An analytical estimate for the integral hadronic gamma-ray emission, from p -production bycollisions of energetic protons with gas nuclei and subsequent decay into two gamma rays, is givenin Eq. (9) of Drury et al. (1994) for gamma energies E large compared to 100 MeV: F ( > E , t = T ) ≈ × − Q (cid:18) E (cid:19) − . (cid:18) E kin erg (cid:19) (cid:18) d1kpc (cid:19) − × (cid:16) n − (cid:17) photons cm − s − hock acceleration in galaxy-galaxy collisions Heinrich J. Völk
Inserting the values E kin = erg, d =
61 Mpc, Q = .
1, and n = .
05 to 0 .
14 cm − results in ( − ) E ¶ F ( > E ) ¶ E ≈ ( ) × − erg cm − s − , (5.1)approximately independent of energy up to about 10 eV.For the IC emission of the electrons at high gamma-ray energies the distribution F e ( E , t ) for t > t loss in eq. 4.7 is relevant. For g ≈ ∼ × − erg cm − s − .Thus the IC gamma-ray energy flux is of the same order as the hadronic gamma-ray energyflux in the region of energy overlap, even for the radiatively cooled electrons. This is a consequenceof the low mean gas density in the bridge. On the other hand, the lowest TeV photon flux from anastrophysical source detected until now was F ( >
220 GeV ) = . × − photons cm − s − . Fora flat spectral energy density this corresponds to 8 . × − erg cm − s − . The measurement wasmade with the H.E.S.S. telescope system for the nearby starburst galaxy NGC253 (Acero 2009).Taking this result as a yard stick, the expected hadronic flux from UGC 12914/5 at gamma-rayenergies above 1 TeV is still two orders of magnitude below this minimum flux. The expectedminimum detectable energy flux for the future Cherenkov Telescope Array (CTA) is as low as ≈ × − erg cm − s − in the TeV region, and at least one order of magnitude higher at 50GeV (CTA 2010). Therefore the gamma-ray flux is also below the detection capabilities of CTA.To this extent the more optimistic expectation by LV is corrected here. This flux is also expectedto be too low for the detection capabilities with the LAT instrument on Fermi at lower gamma-ray energies. The same source at the distance of NGC 253 would be detectable even for presentNorthern Hemisphere ground-based TeV gamma-ray instruments like VERITAS and MAGIC, andat GeV energies for
Fermi . Ultimately the reason for the low gamma-ray fluxes from these distantinteracting systems is their low gas density and their comparatively high age, despite the largeoverall nonthermal energy they contain.
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