s. silich et al- on the rapidly cooling interior of supergalactic winds

8/3/2019 S. Silich et al- On the rapidly cooling interior of supergalactic winds

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arXiv:astro-ph/0303235v111Mar2003

On the rapidly cooling interior of supergalactic winds

S. Silich 1,2, G. Tenorio-Tagle 1 and C. Munoz-Tunon 3

ABSTRACT

Here we present the steady state numerical solution and two dimensional hydrodynamic cal-culations of supergalactic winds, taking into consideration strong radiative cooling. The twopossible outcomes: quasi-adiabatic and strongly radiative flows are thoroughly discussed, to-gether with their implications on the appearance of supergalactic winds both in the X-ray andvisible line regimes.

Subject headings: Galaxies: superwinds, Starbursts: optical and X-ray emissions, general - starburstgalaxies

1. Introduction

Massive starbursts, well localized short episodesof violent star formation, are among the intrinsiccharacteristics of the evolution of galaxies. Theyare found both at high and intermediate redshifts(Dawson et al., 2002; Ajiki et al., 2002; Pettini etal., 1998) as well as in galaxies in the local universe(Marlowe et al., 1995, Cairos et al., 2001).

It has usually been assumed that the energy

deposition occurs within a region of about 100 pc,the typical size of a starburst. However recent op-tical, radio continuum and IR observations (Ho1997; Johnson et al. 2001, Gorjian et al. 2001)revealed a number of unusually compact youngstellar clusters. These overwhelmingly luminousconcentrations of stars present a typical radius ofabout 3 pc, and a mass that ranges from a fewtimes 104M to 10

6M. Clearly these units ofstar formation (super-star clusters) are very differ-ent from what was usually assumed to be a typicalstarburst, and we shall put a special emphasis onthe outflows expected from them.

The large kinetic luminosity produced by vio-lent bursts of star formation is well known to dras-tically affect the surrounding interstellar medium,

1Instituto Nacional de Astrofsica Optica y Electronica,

AP 51, 72000 Puebla, Mexico2Main Astronomical Observatory National Academy of

Sciences of Ukraine, 03680, Kiev-127, Golosiiv, Ukraine3Instituto de Astrofisica de Canarias, E 38200 La La-

guna, Tenerife, Spain

generating the giant superbubbles and supershells,detected in a large sample of star-forming galaxies(Bomans, 2001). In other cases, the energy inputrate is able to drive their associated shock wavesto reach the outskirts of their host galaxy, lead-ing, in these cases, to the development of a super-galactic wind with outflow rates of up to severaltens of solar masses per year (see Heckman 2001for a complete review). One of the main impli-cations of such outflows is the clear contamina-

tion of the intergalactic medium with the metalsrecently processed by the massive starburst. Inboth cases it is usually assumed that at the heartof the starburst, within the region that encom-passes the recently formed stellar cluster (RSB ),the matter ejected by strong stellar winds and su-pernova explosions is fully thermalized. This gen-erates the large central overpressure responsiblefor the mechanical luminosity associated with thenew starburst. Within the starburst region, it isthe mean total mechanical energy LSB and massMSB deposition rates that control, together withthe actual size of the star forming region RSB ,

the properties of the resultant outflow. The totalmass and energy deposition rates define the cen-tral temperature TSB and thus the sound speedcSB at the cluster boundary. As shown by Cheva-lier & Clegg (1985; hereafter referred to as CC85)at the boundary r = RSB , the thermal and kineticenergy flux amount exactly to 9/20 and 1/4 of the

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total energy flux:

Fth/Ftot =

1

1P

u2

2 +

1

P

=9

20

, (1)

Fk/Ftot =u2/2

u2

2+ 1

P

=1

4. (2)

There is however a rapid evolution as matterstreams away from the central starburst. Aftercrossing r = RSB the gas is immediately acceler-ated by the steep pressure gradients and rapidlyreaches its terminal velocity (V 2 cSB ). Thisis due to a fast conversion of thermal energy,into kinetic energy in the resultant wind. In thisway, as the wind takes distance to the star clus-

ter boundary, its density, temperature and ther-mal pressure will drop as r2, r4/3 and r10/3,respectively (CC85). Previous analysis by Heck-man et al. (1990) showed that thermal pressureradial distributions inside starburst galaxies M82and NGC 3256 are in a good agreement with theCC85 model. However Martin et al. (2002) foundthat X-ray surface brightness and radial tempera-ture gradient observed by Chandra in NGC 1569are inconsistent with CC85 predictions.

Note that the wind is exposed to the appear-ance of reverse shocks whenever it meets an ob-stacle cloud or when its thermal pressure becomes

lower than that of the surrounding gas, as is thecase within superbubbles. There, the high pres-sure acquired by the swept up ISM becomes largerthan that of the freely expanding free wind re-gion (FWR), a situation that rapidly leads to thedevelopment of a reverse shock, the thermalizationof the wind kinetic energy and to a much reducedsize of the FWR. Thus for the FWR to extendup to large distances away from the host galaxy,the shocks would have had to evolve and displaceall the ISM, leading to a free path into the in-tergalactic medium and to a supergalactic windwith properties similar to those derived by CC85.

Here we study the true physical properties of suchwell developed FWRs, taking into considerationstrong radiative cooling. Section 2 compares theadiabatic solution of CC85 with our steady statesolution where radiative cooling is considered. Insection 2 we also develop an easy criterion to de-fine in which cases radiative cooling is to becomedominant. Section 3 displays two dimensional cal-culations that use CC85 as the initial condition

which evolves until a new steady state is reached.Section 4 discusses some of the observational con-sequences of such outflows.

2. The steady state solution

Following CC85 we assume a spherically sym-metric wind, unaffected by the gravitational pullcaused by the central star cluster or its associateddark matter component. The equations that gov-ern the steady outflow away from the star formingregion are:

1

r2d

dr

ur2

= 0, (3)

udu

dr=

dP

dr, (4)

1

r2d

dr

ur2

u2

2+

1

P

= Q, (5)

where r is the spherical radius, u(r), (r) and P(r)are the wind velocity, density and thermal pres-sure, respectively. Q is the cooling rate (Q = n2,where n is the wind number density and isthe interstellar cooling function, Raymond et al.1976). At the boundary of the star cluster (RSB )we use the solution of CC85

MSB = (0.1352)

2LSB

c2SB , (6)

P = 0.0338M1/2SB L

1/2SBR

2

SB , (7)

T =0.299

k

LSB

MSB, (8)

u = cSB =

kT

1/2, (9)

=MSB

4R2SBcSB, (10)

where is the mean mass per wind particle, kis the Boltzmann constant, = 5/3 is the ratioof specific heats and cSB is the sound speed at r= RSB , and then solve equations (3)-(5) numeri-cally. Note that at r = RSB the wind Mach num-ber Mw = 1. Therefore we use the wind velocityas an independent variable at the vicinity of thesonic point. Our numerical solutions for Q = 0,fully reproduce CC85 adiabatic results.

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2.1. Radiative cooling in supergalactic

winds

A first order of magnitude estimate of whetheror not radiative cooling could affect the thermody-namics of superwinds, results from a comparisonof the radiative cooling time scale

cool(r) =3kT

n, (11)

with the characteristic dynamical time scale

dyn(r) =

rRSB

dr

u(r). (12)

The wind density, which, as it streams away, de-creases as (1/r2), in combination with the inter-

stellar cooling curve, fully define locally the ratioofcool/dyn. One can infer then that if the ratio ofthe above two quantities becomes smaller than 1,radiative cooling sets in, affecting the thermody-namical properties of the flow. These simple esti-mates indicate that radiative cooling may becomemore efficient the more compact a star cluster is.In fact, it is the density of the free wind what re-ally matters. For the same total starburst energy,the more compact a starburst is, the larger thewind density value and thus the larger the coolingrate. The temperature profiles for a 1041 erg s1

starburst with a radius RSB = 5 pc and differ-

ent metallicities of the wind material are shown inFigure 1, for both the adiabatic and the radiativecases. Note that for compact starbursts radiativecooling sets in within a radius 10 RSB . Despitethe rapid drop in temperature the velocity andthe density distributions remain almost unaffectedby radiative cooling. In all cases the thermal en-ergy is rapidly transformed into kinetic energy ofthe wind in the close vicinity of the sonic point.This leads to a fast gas acceleration that allows thewind gas to rapidly approach its terminal velocityV 2 cSB . At the same time, if radiative cool-ing is considered, the temperature profile strongly

deviates away from the adiabatic solution forcingthe gas to soon reach temperature values of theorder of 104 K.

One can establish an approximate boundarythat separates the adiabatic from the strongly ra-diative cases, from the condition that cool be-comes equal to dyn. The corresponding curves fordifferent energy input rates, wind terminal veloc-ities and wind metallicities, as a function of RSB ,

are shown in Figure 2. If the initial wind param-eters (LSB and RSB ) intersect below the corre-sponding metallicity curve, cooling will be ineffi-

cient and deviations from the adiabatic solutionwould be negligible. On the other hand, if theinitial wind parameters intersect above the corre-sponding metallicity curve, radiative cooling is ex-pected to become important. Note that the largerthe wind terminal velocity is, the smaller the re-gion of the parameter space covered by the coldwind solution.

3. The time dependent solution

Several two dimensional calculations usingCC85 as the initial condition adiabatic flows have

been performed with the Eulerian code describedby Tenorio-Tagle & Munoz Tunon (1997, 1998).This has been adapted to allow for the continu-ous injection in the most central zones, of windswith a variety of LSB and MSB values. The timedependent calculations also account for radiativecooling and display the evolution from the adi-abatic regime to the more realistic final steadystate solution when radiative cooling is consid-ered. There is an excellent agreement between thetime dependent calculations and the steady statesolutions displayed in section 2.

Figure 3 displays isotemperature contours and

the velocity field within the central 100 pc2 of asupergalactic wind driven by an LSB = 10

42 ergs1, cSB = 500 km s

1 or a V = 1000 km s1,

emanating from an RSB = 20 pc. The solutionfor Z = Z, as expected from Figure 2, is wellinto the strongly radiative regime. Figure 3 showsthe rapid increase in velocity from its central valueto the terminal speed 2 cSB . The upper panelshows the run of temperature for the correspond-ing CC85 adiabatic solution, our initial condition,while the central panels depict how radiative cool-ing proceeds within the supersonic outflow, lead-ing to the formation of cool parcels of gas (T 104

K) within rapidly expanding shells of cooling gas.After a few 104 years a new steady state solutionhas been reached (lower panel). There the temper-ature of the fast moving wind suddenly plummetsfrom 107 K to 104 K at a distance of 37 pc fromRSB . Cooling takes place in a catastrophic man-ner, a fact that made us search for possible signs offragmentation, however, the sudden pressure gra-

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dients resulting from cooling are inhibited by thestrongly diverging flow, leaving both the densityand the velocity fields almost unperturbed. Sim-

ilar results were obtained when higher metallic-ity outflows were assumed. The high metallicitiesare indeed expected from the large inflow of newmetals into the superwind (see Silich et al., 2001).Figure 4 shows the final steady-state solution fora wind with RSB = 5 pc, LSB = 10

41 erg s1 andV = 1000 km s

1 when the assumed metallicityof the wind is equal to 1Z, 3Z, 5Z and 10Z.Clearly the impact of this variable is to favor ra-diative cooling even closer to the RSB surface, factthat can be also noticed in Figure 1.

4. The structure of supergalactic winds

The results from sections 2 and 3 imply that thestructure of supergalactic winds aught to be re-vised, particularly in the case of powerful sourceswith a small value of RSB in which radiative cool-ing reduces the spatial extent of the X-ray emit-ting region. In such cases, the only possibilityfor the origin of an extended hot gas componentarises from shock heated ISM overrun by the cen-tral wind. On the other hand, in lower luminos-ity and/or widely spread starbursts, the extendedhot wind region may also contribute significantlyto the total soft X-ray emission. Here we center

our attention on very massive and centrally con-centrated starbursts, entities that leave no doubtthat their newly processed elements will sooner orlater be driven into the IGM. In such cases thecentral wind is affected by radiative cooling andthe extended structure of such winds will be un-detected in the X-ray regime.

Supergalactic winds present a four zone struc-ture: 1) A central starburst region (a source ofhard and soft X-rays). 2) A soft X-ray emittingzone. 3) The line cooling zone. 4) A region of re-combined gas, exposed to the UV radiation fromthe central star cluster.

Figure 5 displays the radial structure of super-galactic winds powered by low (LSB = 10

41 ergs1) and high (LSB = 10

43 erg s1) luminositystarbursts as a function of RSB . In all cases wehave assumed a free wind region terminal velocityequal to 1000 km s1 and a 1Z metal abundance.Solid lines mark the distance at which a 1041ergs1 superwind acquires a temperature of 5105K

and 104K for an adiabatic solution. Dashed linespresent the modified location of the two tempera-ture boundaries provided by gas cooling. Dotted

lines mark the position of the two temperatureboundaries for energetic starbursts (1043erg s1).Note that in both high and low luminosity cases wehave assumed the same central temperature, andthus the same central sound velocity (cSB ), bothcases develop the same terminal speed, leading inthe adiabatic regime to the same temperature ra-dial structure. For the low luminosity radiativecases (heavy dashed lines) significant departuresfrom the adiabatic solution occur for highly con-centrated starbursts (say RSB 20 pc) bringingthe zone of rapid radiative cooling (104 K T 5 105 K) closer to the starburst surface. On

the other hand, the radiative solution for the ener-getic cases (dotted lines) shows how both temper-ature limits here considered move much closer tothe starbursts, reducing significantly the extent ofthe X-ray and the line cooling zones. The effect isnoticeable for all RSB (from 1pc to 100 pc) valueshere considered, a fact that ought to be taken intoaccount in full numerical simulations.

4.1. The impact of photo-ionization and

the expected Halpha luminosity

Figure 5 shows that powerful and compact star-

bursts are to be surrounded by extended, cold andfast expanding envelopes. This continuously in- jected halo, however, becomes an easy target ofthe UV photons escaping from the central starforming regions, and as it presents an R2 den-sity distribution it should be completely ionizedby the stellar radiation. This is simply becausethe number of recombinations in such a densitydistribution is, as shown by Franco et al. 1990,unable to trap the ionization front. As shown inFigure 5, the size of the X-ray and line coolingzones become strongly affected by radiative cool-ing reducing largely their dimensions in favor of a

closer development of the outer photo-ionized re-gion 4. Note that the recombining zone 3 is alsoan additional source of UV photons capable of ion-izing the wind outer extended halo. The numberof recombinations per unit time expected in thephoto-ionized, outer free wind region is:

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dNrecdt

= 4R24n(R4)Vw(R4) +

4

R4

n2(r)r2dr =Mwa

+M2w

4V2t 2aR4

, (13)

where the first term in the right hand side refersto the number of recombinations in the rapidlycooling zone and the second one is related to thenumber of recombinations in the outer cold enve-lope (zone 4). Recombinations should lead to Hand Ly emission. One then can estimate the Hluminosity LH = 1.36 1012Nrec (Leitherer &Heckman, 1995) and Ly luminosity LLy 8.74LH (Brocklehurst, 1971). The expected H lu-

minosities calculated for radiative winds poweredby 1041 erg s1 and 1043 erg s1 starbursts arepresented in Figure 6 as a function of RSB .

4.2. The X-ray luminosity

The X-ray luminosity from the hot wind withdensity distribution n(r) = Mw/4au(r)r2 is

Lx = 4

RxRSB

n2x(T, Zw)r2dr, (14)

where x(T, Zw) is the hot gas X-ray emissiv-

ity and Rx is the X-ray emission cutoff radiusthat corresponds to the cutoff temperature Tcut 5 105K. This is shown in Figure 5. We thenuse a model velocity field u(r) and the cutoff ra-dius Rx to calculate a wind soft (0.1kev - 2.4kev)X-ray luminosity. The results of the calculationsfor Lw = 10

41 erg s1 and Lw = 1043 erg s1

superwinds are shown in Figure 6. We have toconclude that the inconsistency between the freewind model predictions and observed superwindX-ray luminosities, mentioned by Strickland &Stevens (2000), becomes even larger if one takesinto account the modifications provided by radia-

tive cooling. That is, in the standard approachthe free wind material itself cannot be the mainsource of diffuse superwind X-ray emission.

5. Conclusions

We have reanalyzed the physical properties (ve-locity, density and temperature) of supergalacticwinds powered by a constant energy input rate,

taking radiative cooling into account. Three in-put parameters control the properties of the wind:the total energy input rate LSB , the characteris-

tic scale of star formation (RSB), and a thermal-ized gas temperature TSB (or initial wind veloc-ity cSB). We have revealed two possible outflowregimes: a hot wind, which due to its low powerand low density remains unaffected by cooling, andthus as found by CC85 behaves adiabatically. Onthe other hand, winds driven by powerful and/orcompact starbursts become rapidly dominated bycatastrophic radiative cooling.

Superwinds driven by compact and powerfulstarbursts (see Figure 2) undergo catastrophiccooling close to their sources, and establish a tem-perature distribution radically different from those

obtained in adiabatic calculations. At the sametime, both velocity and density radial distribu-tions remain almost unchanged given the speedof the rapidly diverging flow.

The rapid fall in temperature as a function ofr reduces the size of the zone radiating in X-raysand decreases the superwind X-ray luminosity. Atthe same time, cooling brings the 104 K boundarycloser to the wind center, and promotes the estab-lishment of an extended ionized fast moving enve-lope. This should show up as a weak and broad( 1000 km s1) line emission component at the

base of the much narrower line caused by the cen-tral HII region.

The authors highly appreciated the friendlyhospitality of A. DErcole, F. Brighenti, M. Tosiand F. Matteucci at the superwind 2002 work-shop in Bologna, where this study was initi-ated. They thank the referee for helpful com-ments and Jeff Wagg for his careful reading ofthe manuscript. This study has been supportedby CONACYT - Mexico, research grant 36132-Eand by the Spanish Consejo Superior de Investi-gaciones Cientficas, grant AYA2001 - 3939.

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Fig. 1. The intrinsic temperature profile of su-perwinds. The dash-dotted line shows the tem-perature distribution derived from the adiabatic

solution of CC85. Other curves show the effects ofradiative cooling for different superwind metallic-ities.

Fig. 2. Adiabatic versus radiative superwinds.The lines divide the region defined by the pa-rameter space into strongly radiative superwinds(above the lines) and adiabatic solutions (belowthe lines), for different values of the terminal ve-locity (V) and metallicity.

Fig. 3. Two dimensional superwinds. Isotem-perature contours, with a separation logT = 0.1and the velocity field (longest arrow = 1000 kms1) within the central 100 pc2 of a superwindpowered by a 1042 erg s1 starburst with a radiusRSB = 20pc. The evolution starts from (a) theadiabatic solution of CC85 and continues at (b) t= 1.3 104yr, (c) 1.6 104yr and (d) 1.9 104yrwhen a new steady state solution is reached. In thebottom panel the gas temperature falls to 104Kbefore reaching 40pc from the center. Distancebetween consecutive tick mark = 25pc in all fig-ures.

Fig. 4. The metallicity effects. The sameas figure 3 for a 1041erg s1 superwind with anRSB = 5pc. The panels show the final temper-ature and velocity distributions for the radiativesteady state solution for (a) Z = Z, (b) 3Z, (c)5Z and (d) 10Z.

Fig. 5. The internal structure of free wind re-gions. Solid lines mark the distance at whicha 1041erg s1 superwind, with a velocity V =1000km s1, acquires a temperature of 5 105Kand 104K as a function of the initial radius RSB ,for an adiabatic solution. Dashed lines present themodified location of the two temperature bound-aries provided by gas cooling (Z = Z). Dottedlines mark the position of the two temperatureboundaries for energetic starbursts (1043erg s1).

Fig. 6. Observational appearance of free windregions. The expected X-ray and H luminosityof superwinds as a function of the starburst powerand the radius RSB .

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s. silich et al- on the rapidly cooling interior of supergalactic winds

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