guillermo tenorio-tagle et al- on the extreme stationary outflows from super-star clusters: from...

8/3/2019 Guillermo Tenorio-Tagle et al- On the extreme stationary outflows from super-star clusters: from superwinds to supe

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arXiv:ast

ro-ph/0410638v1

26Oct2004

On the extreme stationary outflows from super-star

clusters: from superwinds to supernebulae and furthermassive star formation.

Guillermo Tenorio-Tagle, Sergiy Silich, Ary Rodrguez-GonzalezInstituto Nacional de Astrofsica Optica y Electronica, AP 51, 72000 Puebla, Mexico;

[email protected]

and

Casiana Munoz-TunonInstituto de Astrofsica de Canarias, E 38200 La Laguna, Tenerife, Spain; [email protected]

ABSTRACT

Here we discuss the properties of star cluster winds in the supercritical, catas-trophic cooling regime. We demonstrate that catastrophic cooling inhibits super-winds and after a rapid phase of accumulation of the ejected material within the

star-forming volume a new stationary isothermal regime, supported by the ion-izing radiation from the central cluster, is established. The expected appearanceof this core/halo supernebula in the visible line regime and possible late evolu-tionary tracks for super-star cluster winds, in the absence of ionizing radiation,are thoroughly discussed.

Subject headings: clusters: winds galaxies: starburst methods: numerical

1. Introduction

Within the volume occupied by a star

cluster (SC), the energy injected by stel-lar winds and supernova explosions is fullythermalized via random interactions. Thisgenerates the large central overpressurethat continuously accelerates the ejectedgas and eventually blows it out of thestar cluster volume to compose a super-

wind. In the adiabatic solution of Cheva-lier & Clegg (1985; hereafter referred toas CC85; see also Canto, et al. 2000 and

Raga et al. 2001) temperature and den-sity present almost homogeneous valueswithin the central volume, whereas theexpansion velocity grows almost linearlyfrom 0 km s1 at the center, to the soundspeed (c) at the cluster radius r = RSC.There is then a rapid evolution as mat-

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ter streams away from the star clusterand the wind parameters (velocity, den-sity, temperature and pressure) soon ap-proach their asymptotic values: Vw VA = (2LSC/MSC)1

/2 2c(RSC), w r2, Tw r

4/3 and thus Pw r10/3,

where LSC and MSC are energy and massdeposition rates.

Recent results on the outflows expectedfrom SCs have led us to realize that theadiabatic steady wind solution proposedby CC85 and followers, becomes inappli-cable in the case of massive and concen-

trated clusters. Radiative cooling stronglymodifies first the temperature distributionpredicted for adiabatic stationary winds(Tw r

4/3) bringing suddenly and withina small radius, the temperature down to104 K, restricting then the X-ray emissiv-ity of the winds to a volume much smallerthan previously thought (see Silich et al.2003 and 2004; hereafter referred to as Pa-pers I and II). Also, as shown in PaperII, for more energetic clusters, strong ra-diative cooling promotes the sudden leak-age of thermal energy right within the starcluster volume itself, and for the casesin which the radiative losses there exceed30% of the stellar energy deposition rate,when cooling becomes catastrophic, thenthe stationary superwind solution is to-tally inhibited. In this latter case, therapid drop in temperature within the SCvolume, leads to a sudden drop in central

pressure and particularly to a sudden dropin sound speed. This inhibits the fast ac-celeration predicted in the adiabatic solu-tion as required by the flow to reach itsadiabatic terminal speed (vA 103 kms1). The sudden drop in sound speed up-sets also the balance, demanded by the sta-

tionary solution, between the stellar massinput rate and the rate at which mat-ter can flow away from the cluster, ie:MSC = 4R2SCSC(RSC)c(RSC), and thisinevitably leads to mass accumulation.

Here we show how the metallicity at-tained by the ejected matter from a coevalcluster, strongly affects the limits found inPaper II bringing the energy input rate fur-ther down to much smaller values and thusaffecting even lower mass clusters. We alsoshow how after the thermal stationary su-perwinds are inhibited, and after an in-

evitably short phase of matter accumula-tion within the SC volume, a second sta-tionary solution can be found. This is onlypossible while the stellar UV flux ionizesthe deposited matter to compose a densesupernebula with an isothermal (T 104

K), slow (v 50 km s1), stationary

wind (see section 2). Finally, as the evo-lution continues and the stars producingthe UV photon output evolve into super-novae, a third quasi-adiabatic stationarystage could become possible after a sec-ond phase of matter accumulation withinthe star cluster radius. This could in prin-ciple evolve into a massive, cold, neutraloutflow, however, its maximum velocity iswell below the escape speed and thus theejected matter, unable to escape the grav-itational potential of the star cluster, willsooner or latter recolapse to cause a sec-ond major burst of star formation. Our

conclusions and the observational proper-ties of the various evolutionary phases aregiven in section 3.

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2. The properties of massive star

clusters

Superstar clusters recently found by theHubble Space Telescope in a large varietyof starburst galaxies (for a review see Ho1997 and the recent proceedings from Theformation and evolution of massive youngstar clusters, Eds. Lamers et al, 2004)present a typical half-light radius 3 -10 pc, and masses that range from severaltimes 104 M to several times 10

7 M (seeWalcher et al. 2004). These are now be-

lieved to be the unit of violent star forma-tion in starburst galaxies.

The theoretical properties of massivebursts of star formation strongly dependon the assumed stellar evolutionary tracks.Synthesis models (e.g. Leitherer & Heck-man 1995, Leitherer et al. 1999) assumefurther a stellar IMF and an upper andlower mass limit for the star formationevent. In this way one knows that a coevalburst of 106 M with a Salpeter IMF, and

stars between 100 M and 1 M, wouldproduce, through winds and supernovae(SNe), an almost constant mechanical en-ergy input rate of 31040 erg s1 for al-most 50 Myr, until the last star of 8 M ex-plodes as supernova. At the same time, theflux of ionizing radiation is to remain con-stant at 1053 photons s1 for the first 3Myr, to then steadily fall off approximatelyas t5. The above implies that the HII re-

gion phase will last for about 10 Myr, timeduring which the cluster photon flux willhave decrease by more than two and a halforders of magnitude with respect to its ini-tial value. The above values scale linearly,throughout the evolution, with the mass ofthe assumed cluster and thus the HII re-gion phase is in all coeval cases four to five

times shorter than the supernova phase.

When dealing with the outflows gener-

ated by star clusters, another important in-trinsic property is the metallicity of theirejected matter. This is a strongly varyingfunction of time, bound by the yields frommassive stars and their evolution time.Thus, once the cluster IMF and the stel-lar mass limits are defined, the resultantmetallicity is an invariant curve, indepen-dent of the cluster mass. Here we con-sider coeval clusters with a Salpeter IMF,and stars between 100 M and 1 M, as

well as the evolutionary tracks with rota-tion of Meynet & Maeder (2002) and aninstantaneous mixing of the recently pro-cessed metals with the stellar envelopesof the progenitors (see Silich et al. 2001and Tenorio-Tagle et al. 2003, for an ex-plicit description of the calculations). Thisleads to metallicity values (using oxygenas tracer) that rapidly reaches 14 Z (seeFigure 1), and although steadily decayingafterwards, the metallicity remains abovesolar values for a good deal of the evolu-tion (for more than 20 Myr), to then fallto the original metallicity of the parentalcloud. One of the main effects of an en-hanced metallicity of the ejecta is to boostits radiative cooling and in such a case,massive clusters may inevitably enter intothe catastrophic cooling regime, envisagedin Paper II, to then find their stationarysuperwinds totally inhibited. Relevant also

is to note that at the end of the SN phase,the mass reinserted into the interstellarmedium through winds and SNe amountsto about 40% of the original mass in stars(see Leitherer & Heckman 1995, their fig-ure 53). Here we address the fate of sucha vast amount of high metallicity matter.

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Fig. 1. The metallicity of the matterejected by coeval bursts of star formation.The metallicity (in solar units) of the mat-ter reinserted into the ISM by SCs is plot-ted as a function of the evolution time.The curve is derived from the metal yieldsof Meynet & Maeder (2002) stellar evo-lution models with stellar rotation, usingoxygen as a tracer. The estimate assumesa Salpeter IMF and 100 M and 1 Mupper and lower mass limit. The modelalso assumes an instantaneous mixing be-

tween the newly processed metals and theenvelopes of the progenitors. Note that un-der these assumptions the curve is indepen-dent of the cluster mass.

2.1. The limits between superwinds

and supernebulae

Figure 2 shows results from our self-consistent radiative code (see Paper II) in-dicating the limiting energy, as a function

of the size of the clusters, at which radia-tive cooling becomes catastrophic for mat-ter with metallicities similar to those ex-pected for the gas emanating from massivestellar clusters. As pointed out in Paper IIthere are three different kinds of solutions:low energy input rates, produced by low-

mass clusters, appear far from the thresh-old line that separates the catastrophiccooling regime from the stationary super-winds, and thus are to generate station-ary quasi-adiabatic winds similar to thoseproposed by CC85. More energetic (ormore massive clusters), as their energy in-put rate approaches the threshold line willproduce strongly radiative stationary su-perwinds with considerably smaller X-rayemitting volumes. Finally, cases that lieabove the threshold line in the catastrophiccooling zone, will radiate a large fraction of

the energy input rate within the star clus-ter volume and thus will be unable to gen-erate a stationary superwind.

Fig. 2. The threshold energy input rate.The limiting energy input rate above whichcatastrophic cooling inhibits the thermalstationary superwind solution for SCs withVA = 1000 km s

1, as a function of thesize of the clusters and for two different

abundances (solar and ten times solar) ofthe matter injected by the SCs.

Figure 3 incorporates the run of themetallicity of the matter injected by windsand SNe as a function of time (Figure 1)to the results from our self-consistent ra-

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diative solution (Figure 2) and plots theresultant location of the threshold line forclusters with a RSC = 3 pc (solid line) and10 pc (dashed line), the typical range ofsizes of superstar clusters, as a function oftime. As mentioned above, clusters of anygiven mass will evolve at an almost con-stant mechanical luminosity, crossing thediagram from left to right (as the 106 Mcluster shown in the figure as a solid ar-row). The figure confirms that low massclusters will produce quasi-adiabatic sta-tionary winds. However, clusters with a

mass in the range 3 105

M to 3 106

M would cross twice the threshold lineduring their evolution and thus will havetheir thermal stationary winds fully inhib-ited for a good fraction of their evolution.More massive and compact clusters, thoseinjecting more than say, 1042 erg s1 (seeFigure 3), will be unable to develop thesuperwind outflows during their evolution.

All of the latter clusters, unable to ridthemselves from the continuous input ofmatter from their stellar sources, are tocause a rapid accumulation of the cold(T 104 K) recombined ejecta, now sud-denly exposed to the UV photon flux fromthe most massive stars. As shown below,this leads to a dense and compact, highmetallicity supernebula, able to establishan isothermal stationary HII region wind.

2.2. The evolution of supernebulae

For clusters that enter the catastrophiccooling regime, matter accumulation withinthe star cluster volume, would rapidly leadto larger densities, while the stellar UVphoton flux independently will sustain thetemperature at T 104 by photoioniza-

Fig. 3. The evolution of the thresholdenergy input rate. The continuous changesin the metallicity of the ejecta (Figure 1)shift the location of the threshold line. Thefigure shows the run of the threshold en-ergy input rate for massive clusters with3 pc (solid line) and 10 pc (dashed line)radii, respectively. The horizontal solidline across the diagram indicates the en-ergy deposition rate of a 106 M cluster.The scale for different mass clusters is indi-cated on the right-hand axis. The areas oc-

cupied by the various stationary solutionsdescribed in this study are also indicatedin the figure.

tion.

The density SC will increase untilthe stationary condition MSC = 4R2SCSC(RSC)c(RSC) (where now c(RSC) =cHII 10 km s1) is once again fulfilled.Given the drastic drop in temperature of

the ejecta that results from thermaliza-tion followed by catastrophic cooling (sayfrom 107 K to 104 K), the density SC willhave to increase by one and a half ordersof magnitude to compensate the drop insound speed ( T0.5) and then meet theisothermal stationary condition. Mass ac-

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cumulation will last for a short time ()

=

4

3

(2 1)R3

SCV2

A

2LSC 105

yr. (1)

Once this happens, an isothermal, sta-tionary, photoionized wind will begin toemanate from the star cluster surface.The isothermal steady state flow equationswithin the star cluster radius (R RSC)are

duwdr

=qm

3w

1 + 3u2w/c2

HII

1 u2w/c2

HII

, (2)

w =qmr

3uw, (3)

and outside of the star cluster (R > RSC),

duwdr

=2uw

r

c2HII/u2

w

1 c2HII/u2w

, (4)

w =Msc

4uwr2, (5)

where qm is the mass deposition rate perunit volume inside a star cluster, cHII =(kTw/p)1

/2 is the isothermal sound speed,p = 14/23mH is the mean mass per par-ticle, k is the Boltzmann constant, and is the ratio of the specific heats. The windcentral temperature is supported by pho-toionization at a Tc 104 K level, and thewind central density can be found by iter-ations from the condition that the isother-mal sonic point (uw = cHII) acquires itsproper position at the star cluster surface,Rsonic = Rsc (for more details see paper II).The isothermal wind temperature, densityand velocity distributions are presented inFigure 4a-c (dashed lines).

The resultant core/halo supernebuladensity distribution (see Figure 4) can

Fig. 4. Supernebulae and massive slowneutral outflows. The stationary innerstructure (temperature, density and veloc-ity, (a-c, respectively) as a function ofR (inpc), adopted by the outflow from a 106 Mcompact (3 pc radius) cluster is shown forthe supernebula (dashed lines) and massiveslow neutral outflow phase (solid lines).

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be approximated by a constant value ncwithin RSC and by a power law (r

2) forr > RSC. In this case, the number of re-combinations per unit time throughout thesupernebula volume is:

dNrecdt

= 4

RSC0

n2(r)r2dr+

RStRSC

n2(r)r2dr

=

16

3n2cR

3

SC

1

3

4

RSCRSt

, (6)

where RSt is the Stromgren radius and is the recombination coefficient to all butthe ground level. The Stromgren radius isthen:

RSt =3

4

RSC

1 3Nrec16n2cR

3

SC

. (7)

Equation (7) implies that the supernebulashould be completely ionized by the starcluster UV radiation if the number of pho-tons per unit time exceeds the critical value

Ncrit =16

3n2cR

3

SC. (8)

The bright, centrally concentrated highmetallicity nebula and its moderate wind,causing a stationary core/halo structure,are to be maintained for as long as theyremain fully ionized. Note however that asthe flux of UV photons from an instanta-neous, or coeval, burst of star formationdeclines drastically after 3 Myr (see Lei-

therer & Heckman 1995) it would eventu-ally fall below the critical value. The con-tinuously reduced number of ionizing pho-tons, unable to balance the large numberof recombinations in the ionized volume,forces the ionization front to recede super-sonically towards the stars (see Beltram-etti et al. 1981). From equation (7) one

can show that it will reach RSC when thenumber of ionizing photons drops by a fac-tor of four below the critical value. At thistime the central HII region will begin toloose its identity and uniform structure, toevolve finally into a collection of individ-ual ultracompact HII regions around themost massive members left within the co-eval star cluster.

Taking into account that the superneb-ula central density c = MSC/4R2SCcHIIand that the star cluster mechanical lumi-nosity LSC =

1

2MSCV2A,, where VA, is

the adiabatic wind terminal speed in thehypothetical absence of radiative cooling,one can rewrite equation (8) in the form:

Ncrit =4L2SC

32aRSCV6

A,

VA,cHII

2

=

M2SC32aRSCc

2

HII

(9)

where a is the mean mass per atom (a =14/11mH) and the supernebula isothermalsound speed cHII 11.6 km s1. In sucha case, our standard 106 M, RSC = 3 pccluster and its supernebula will require ofan Ncrit 1.7 1052 s

1. This value isalmost an order of magnitude below themaximum number of UV photons emittedinitially by our example 106 M star clus-ter. The UV flux from the aging clusterwould however reach the critical value af-ter 4 Myr and 5 Myr, depending if one

assumes solar or 0.1 solar as the originalcluster metallicity (see Leitherer & Heck-man, 1995; their Figure 37), and the UVradiation a couple of Myr after this willnot suffice to sustain even the star clustervolume fully ionized. This brings the su-pernebula phase to an end, while restrict-ing the ionized volume to ultracompact HII

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regions around the most massive sourcesleft in the cluster. Without the sufficientUV photons to maintain the SC volumefully ionized and at a temperature 104

K, the stationary isothermal wind condi-tion is inhibited and a new phase of matteraccumulation will start.

Figure 5 displays the H luminosity ofour 106 M cluster that injects 3 1040

erg s1 within a RSC = 3 pc and thus ini-tially, while the metallicity remains belowZ, it produces a strongly radiative sta-tionary superwind (follow the horizontal

line in Figure 3). The stationary stronglyradiative solution leads to a temperature 5 105 K at a distance of 17.5 pcand thus at this radius the streaming windmatter recombines and is exposed to thestellar UV photon output. Photoioniza-tion causes in such a case, a thin station-ary shell with the matter that continuouslystreams with large speeds ( 103 km s1)across the recombining radius and leadsthus to a top-hat line profile (Rodrguez-Gonzalez et al. 2004; Owocki & Cohen,2001; Dessart & Owocki, 2002) shown bydotted line in Figure 5. This is very differ-ent to the calculated Gaussian line profileproduced during the supernebular phase,which displays a linewidth of the order of100 km s1 (FWZI) and, given the largedensities, has an intensity several ordersof magnitude larger than that of the top-hat line profile produced during the initial

superwind stage. The total integrated in-tensity over the line profiles is: 5.3 1040

erg s1 for the supernebula stage and 6.91034 erg s1 for the strongly radiative su-perwind.

2.3. Gravitationally bound massive

neutral outflows.

The lack of sufficient UV photons tokeep the supernebula phase at work, in-evitably leads to a further accumulation ofthe ejected matter within the star clustervolume, until the density there raises byanother order of magnitude and compen-sates in this way the drop in temperature(say, from 104 K to 100 K) and a stationaryflow can once again be established. Thistime however, the quasi-adiabatic flow isvery massive and very slow (v 2 kms1 2cH2). Figure 4 a-c (solid lines) dis-play the properties (the run of tempera-ture, density and velocity as a function ofdistance to the star cluster center) of suchstationary flow.

Figure 4 compares the isothermal (T104 K) high metallicity supernebula out-flow with the late massive adiabatic neu-tral flow. In both cases the density dropsas r2 and thanks to the continuous en-

ergy input rate through photoionizationthe supernebula is able to expand with in-creasingly larger velocities (up to 50 kms1). The adiabatic dense outflow casereaches instead a maximum outflow veloc-ity of only v 2c 2 km s1. This maxi-mum speed is well below the escape speed(vesc = (2GMSC/RSC)0

.5) from the centralcluster and thus is to evolve instead intoanother phase of matter accumulation, toeventually recolapse into a new generationof stars; subject of a forthcoming commu-nication.

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3. Feedback and the observational

properties of the superstar clus-

ter outflows.

Contrary to the predictions from theadiabatic solution of Chevalier & Clegg1985, we have shown here that massiveand concentrated star clusters do not nec-essarily blow a strong stationary super-wind throughout their evolution. The highmetallicity of the matter deposited throughwinds and supernovae, enhances radiativecooling within the star cluster volume, and

leads instead to two other possible typesof stationary flows emanating from mas-sive SC. These have been termed here su-pernebula and massive slow neutral out-flows. The high metallicity supernebulaewith a distinct core/halo density distribu-tion, expanding with up to 50 km s1, canonly be maintained in presence of an am-ple supply of stellar UV photons. Theseshould be able to keep, at least, the centralSC volume fully ionized. We have shown

that this phase is thus bound to the first10 Myr of the cluster evolution.

On the other hand, the slow massiveneutral flows, that follow the supernebulaphase, are to last in the case of very mas-sive clusters (M 3 10

6 M), untilthe end of the supernova phase ( 40 - 50Myr). The maximum speed of the neutraloutflows is however much slower than theescape speed from the massive clusters and

thus are to be inhibited by the potential ofthe clusters, leading instead to a furtheraccumulation of matter which may even-tually collapse and lead to a new stellargeneration.

Very massive clusters, above the thresh-old line, will enter from the start of their

evolution the supernebula phase, and willnever cause a superwind. On the otherhand, lower mass clusters will never expe-rience either the supernebula nor the mas-sive neutral stationary outflows and willestablish stationary quasi-adiabatic super-winds throughout their evolution. Notehowever, that coeval clusters with a massin the range 3 105 M to 3 10

6 Mand a RSC = 3 pc (see Figure 3) will starttheir evolution causing the developmentof a stationary strongly radiative super-wind, to then enter into the supernebulae

phase and finally, after 8 - 20 Myr, respec-tively, re-enter once again into the station-ary strongly radiative superwind regime.Clearly, this will lead to a very strong in-teraction between the new superwind andthe matter left near the cluster during thesupernebula or the massive and slow neu-tral outflow phases.

All superstar clusters will be, through-out their evolution, strong X-ray emittingsources. Clusters below the threshold line,that separates stationary superwinds andcatastrophic cooling solutions (see Figure3), are to emit copiously in X-rays bothwithin the SC central volume and in theirwinds. Clusters above the threshold line,whether experiencing the supernebula orthe massive slow neutral outflow, will alsoemit in X-rays within their central volume,as catastrophic cooling radiates away thecontinuously replenished thermal energy.

The X-ray properties of such clusters, com-pared to the X-ray emission from super-bubbles will be the subject of a forthcom-ing communication.

Our gratitude to Leticia Carigi for hersuggestions regarding the metallicity of theejected matter. We thank our anonymous

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referee for his comments and suggestions.This study has been supported by CONA-CYT - Mexico, research grant 36132-E andthe Spanish Consejo Superior de Investiga-ciones Cientficas, grant AYA2001-3939.

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This 2-column preprint was prepared with the

AAS LATEX macros v5.2.

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Fig. 5. The signature of station-ary strongly radiative superwinds and su-pernebulae. The H line profiles producedby the outflow from a compact (3 pc ra-dius), 106 M star cluster, at differentstages of its evolution. The dotted line rep-resents the low intensity, flat-top H pro-

file calculated for a strongly radiative su-perwind stage, before the metallicity of theoutflowing gas exceeds Z. In such a casestrong radiative cooling brings the super-wind temperature down to T 104 K at adistance of 17.5 pc allowing the stellar UVphoton output to ionize the rapidly movingstream, while causing a broad flat-top lineprofile. This is to be compared with theline profile calculated for the supernebulaphase (solid lines). The total integratedintensity over the line profiles is: 6.91034

erg s1 and 5.31040 erg s1, respectively.

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