arXiv subjects

Evgenii O. Vasiliev

Publications and source records attributed to Evgenii O. Vasiliev.

At least 19 recordsLinked to original sources

arXiv2026

Large dust grains escaping from a supernova remnant

Dust grains produced in the supernova (SN) ejecta at early ages are partially destroyed in hot gas of the SN remnant. Large grains owing to their inertia can overtake the forward shock front of the remnant and move through the ambient interstellar medium. Using one-dimensional gas dynamics including the dust destruction we study the transport of dust grains inside the SN remnant and the ambient medium. Here we estimate the surviving and escaping mass fractions depending on the cut-off (maximum) size in a power-law distribution of grain sizes. We found that these fractions follow closely each other at late age of the SN remnant, i.e. almost all grains, which have survived in the remnant, leave it for the ambient interstellar medium. At the age of 30 kyr -- the onset of the radiative phase with density $n\sim 1$ cm$^{-3}$ with solar metallicity -- the escaping/surviving mass fractions for the cut-off size of several microns reach about $0.7-0.8$. The major part of these grains have size larger than $1~μ$m and initially located at distances $\gtrsim 0.2$ of the ejecta core radius. Later dust grains at velocity of several hundreds km/s escaping the remnant continue to be destroyed due to kinetic sputtering in the interstellar medium. Grains with sizes of several microns are destroyed marginally and therefore will survive in the interstellar gas. After decelerating of grains in the medium the surviving mass fraction of grains produced in the SN remnant, which evolves in an ambient gas with $n$ from 1 to 100 cm$^{-3}$, is from $\sim 0.5$ to $\sim 0.3$, respectively, for the cut-off grain size $a_{cut} = 10~μ$m. A decrease of the cut-off size in the distribution results in lower surviving mass fraction.

astro-ph.GA↗

arXiv2026

High velocity dust grains produced by a supernova explosion

Motivated by the discovery of a meteor with velocity more than 300~km/s (Afanasiev et al. 2007) we study how dust grains formed in the supernova (SN) ejecta at its free-expansion phase can keep their high velocity obtained from the gas, where these grains were born. Using a one-dimensional spherically symmetric Lagrangian approach we follow the dynamics of grains during the interaction of a SN ejecta with the ambient interstellar gas. We found that grains larger $\sim 0.3~μ$m can cross the SN forward shock front and reach the ambient interstellar medium. They are destroyed inefficiently, thus, their sizes remain close to the initial ones. In a diffuse interstellar gas of density $\lesssim 1$ cm$^{-3}$ grains larger as $\gtrsim 1~μ$m move with velocity around $1-2$ thousand km/s and spread over distances exceeding $\sim 40-90$ pc from the SN origin within tens of kiloyears. In dense environment the propagation of grains is significantly suppressed: even large grains do not spread over distances greater than 50% of the current SN remnant size. Grains born close to the edge of the SN ejecta core in less-massive ejecta reach greater distances. Thus, high-velocity grains are expected to be formed in this part of the ejecta with mass lower than $\sim 3~M_\odot$ of the SN remnant evolving in a diffuse gas with density $\lesssim 1$ cm$^{-3}$. We discuss possible consequences for dust transport out from galactic disks.

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arXiv2026

Dust destruction in bubbles driven by multiple supernovae explosions

Dust lifetime derived from an isolated supernova (SN) evolution in the interstellar medium is known to be an order of magnitude shorter than the time needed to replenish dust mass by its production in various Galactic sources. We show, using 3-D numerical hydrodynamical simulations, that destruction of dust in the case of multiple SNe in a star cluster is markedly different from that in an isolated SN. We find that the mass of dust destroyed in the bubble does not grow for a considerable time, while SNe continue to explode. This regime is attained at saturation timescale, which is proportional to SNe rate in cluster. We show that the mass of dust destroyed in bubble per SN decreases for higher SN rate. Thus, the destruction efficiency -- defined as the ratio of the the total mass of dust destroyed by clustered SNe to that destroyed by the same number of isolated SNe -- in bubbles evolved in a homogeneous medium drops for massive clusters, e.g. around clusters with $M_\ast \gtrsim 4\times 10^4 M_\odot$ it is less $0.4$\%. For lower mass clusters, the efficiency is proportional to the average time delay between SNe. We found that each cluster with $M_\ast \lesssim 4\times 10^4 M_\odot$ destroys the same mass of dust as a single isolated SN. In a clumpy medium in bubbles formed around clusters with $M_\ast \sim 4\times 10^4 M_\odot$ and up to 4 times around $M_\ast \sim 8\times 10^5 M_\odot$. We argue that the interstellar dust swept up by multiple SNe almost completely survives in the shells of bubbles around such massive clusters. Therefore, the destruction of the interstellar dust is controlled by SNe in low-mass clusters. We point out that the interstellar dust lifetime for a given SN rate is at least a factor $\sim 10$ longer as compared to the estimates derived from an isolated SN. (abridged)

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arXiv2026

Destruction of the interstellar dust by a supernova

Destruction of the interstellar dust proceeds primary behind supernova shocks. The previous estimates of the mass of the interstellar dust destroyed in the SN remnant do not take into account the physical properties of the ambient medium. Here we consider how some parameters, i.e. gas density and metallicity, can influence the destruction of the interstellar dust. We show that there are two regimes of the interstellar dust grains destruction in SN remnants: rapid and almost complete in compact low-mass SN remnants expanding in dense medium, and gradual and weak destruction in massive remnants evolving in the low-dense environment. When time for thermal sputtering is close to the dynamical one, i.e. to the SN remnant age, the mass of the interstellar dust destroyed in the SN remnant reaches its maximum value. We find that change of the ambient gas density results in the reduction of the dust mass logarithmically. We argue that dust cooling suppresses the interstellar dust destruction up to a factor of 1.6 by mass. This factor decreases for higher density of the ambient medium. We found that the dust mass depends linearly on gas metallicity as ${\rm log}~M_d \sim {\rm [Z/H]}$ or, in other words, on the dust-to-gas ratio as $M_d \sim ζ_d$. In turn, the destruction efficiency is higher in low-metallicity environments due to relatively longer adiabatic phase. We point out that the mass of the interstellar dust destroyed per one SN in a high density environment of the high star formation regions like in local ultraluminous infrared and high-redshift massive galaxies is about several times smaller than that in the Milky Way diffuse medium.

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arXiv2024

Inhibited destruction of dust by supernova in a clumpy medium

The decrease rate of dust mass due to strong shock waves ($v_s\geq 150$ km s$^{-1}$) from supernovae (SNe) estimated for the Milky Way interstellar medium significantly exceeds the overall production rate by both asymptotic giant branch stars and core collapse SNe. The interplay between the production and destruction rates is critically important for evaluation of the net dust outcome from SNe at different conditions. In light of this, we study the dynamics of initially polydisperse dust grains pre-existing in an ambient medium swept up the SN shock front depending on magnitude of inhomogeneity (clumpiness) in the medium. We find that dust destruction inside the bubble is inhibited in more inhomogeneous medium: the larger amount of dust survives for the higher dispersion of density. This trend is set by the interrelation between radiative gas cooling and dust sputtering in different environment. After several radiative times the mass fraction of the survived dust saturates at the level almost independent on the gas mean density. We note that for more clumpy medium the distributions of dust over thermal phases of a gas inside the bubble and over sizes are smoother and flatter in comparison with those in a nearly homogeneous medium.

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arXiv2023

Dust evolution in a supernova interacting with the ISM

Supernovae (SN) explosions are thought to be an important source of dust in galaxies. At the same time strong shocks from SNe are known as an efficient mechanism of dust destruction via thermal and kinetic sputtering. A critically important question of how these two hypotheses of SNe activity control the dust budget in galaxies is still not quite clearly understood. In this paper we address this question within 3D multi-fluid hydrodynamical simulations, treating separately the SNe injected dust and the dust pre-existed in ambient interstellar gas. We focus primarily on how the injected and the pre-existing dust is destroyed by shock waves and hot gas in the SN bubble depending on the density of ambient gas. Within our model we estimate an upper limit of the SN-produced dust mass which can be supplied into interstellar medium. For a SN progenitor mass of 30 $M_\odot$ and the ejected dust mass $M_d=1~M_\odot$ we constrain the dust mass that can be delivered into the ISM as $\geq 0.13~M_\odot$, provided that the SN has injected large dust particles with $a\geq 0.1~μ$m.

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arXiv2023

Dust-free starburst galaxies at redshifts $z>10$

One of the most distant galaxies GN-z11 was formed when the Universe was $\le$ 400 Myr old, and it displays a burst-like star formation rate $\sim 25~M_\odot$ yr$^{-1}$ with a metallicity $Z\sim 0.2\pm 0.1Z_\odot$. It resembles $z=2-3$ galaxies (at ``cosmic noon") except for the fact that the measured reddening $E(B-V)=0.01\pm 0.01$ indicates the presence of little or no dust. This marked absence of dust hints towards violent dynamical events that destroy or evacuate dust along with gas out of the galaxy on a relatively short time scale and make it transparent. We apply a 3D numerical model to infer possible physical characteristics of these events. We demonstrate that the energetics of the observed star formation rate is sufficient to tear apart the dusty veil on time scales of $20-25$ Myr. This can explain the apparent lack of evolution of UV luminosity function of galaxies between and $z\ge 10$ and $z\sim 7$, by compensating for the lower galaxy masses at higher redshift by the absence of dust. We show, however, that this is a temporary phenomenon and soon after the last of the supernovae explosions have taken place, the expanding shell shrinks and obscures the galaxy on time scales of $\approx 5-8$ Myr.

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arXiv2023

Disc-halo gas outflows driven by stellar clusters as seen in multiwavelength tracers

We consider the dynamics of and emission from growing superbubbles in a stratified interstellar gaseous disc driven by energy release from supernovae explosions in stellar clusters with {masses $M_{cl}= 10^5-1.6\times 10^6~M_\odot$}. Supernovae are spread randomly within a sphere of $r_c=60$ pc, and inject energy episodically with a specific rate $1/130~M_\odot^{-1}$ proportional to the star formation rate (SFR) in the cluster. Models are run for several values of SFR in the range $0.01$ to $0.1~M_\odot$ yr$^{-1}$, with the corresponding average surface energy input rate $\sim 0.04-0.4$ erg cm$^{-2}$ s$^{-1}$. We find that the discrete energy injection by isolated SNe are more efficient in blowing superbubbles: asymptotically they reach heights of up to 3 to 16 kpc for $M_{cl}=10^5-1.6\times 10^5~M_\odot$, correspondingly, and stay filled with a hot and dilute plasma for at least 30 Myr. During this time they emit X-ray, H$α$ and dust infrared emission. X-ray liminosities $L_X\propto {\rm SFR}^{3/5}$ that we derive here are consistent with observations in star-forming galaxies. Even though dust particles of small sizes $a\leq 0.03~μ$m are sputtered in the interior of bubbles, larger grains still contribute considerably ensuring the bubble luminosity $L_{\rm IR}/{\rm SFR}\sim 5\times 10^7 L_\odot M_\odot^{-1} ~{\rm yr}$. It is shown that the origin of the North Polar Spur in the Milky Way can be connected with activity of a cluster with the stellar mass of $\sim 10^5~M_\odot$ and the ${\rm SFR}\sim 0.1~M_\odot$ yr$^{-1}$ some 25--30 Myr ago. Extended luminous haloes observed in edge-on galaxies (NGC 891 as an example) can be maintained by disc spread stellar clusters of smaller masses $M_\ast \simlt 10^5~M_\odot$.

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arXiv2022

Dust in Clusters of Galaxies

The presence of dust in the intracluster medium (ICM) has been a long-standing problem that is still awaiting elucidation. Direct observational diagnostics are rather challenging (though not impossible) either because of a sparse distribution of dust in the intracluster space that makes extinction measurements difficult or because of a low surface brightness of infrared emission from dust. Complex indirect approaches are currently available that can overcome uncertainties and provide a reasonable understanding of the basic regulations of the physical state of dust in the ICM. Contrary to the common opinion that the hot ICM does not allow dust to survive and manifest, many sparse observational data either directly point out that dust exists in the intracluster space or its presence is consistent with the data. Highly divergent data in direct evidence and highly uncertain indirect indicators are often connected either with dust fragility in a hot environment, the possible compactness of spatial (clumpy) dust distribution in the ICM, or dynamical features of dust transport. The source of dust is obviously connected with galaxies, and it turns out that in most cases, dust is carried from galaxies into the ICM while being thermally and dynamically shielded against the hostile influence of high-energy ions. In this review, we briefly discuss related issues from observational and theoretical points of view, including the transport of dust into the ICM, and the associated destructive and protective mechanisms and their characteristic time scales.

astro-ph.GA↗

arXiv2020

Far-infrared nebular spectral features from growing massive black holes

Supermassive black holes (BHs) and their host galaxies are interlinked by virtue of feedbacks and are thought to be co-eval across the Hubble time. This relation is highlighted by an approximate proportionality between the BH mass $M_\bullet$ and the mass of a stellar bulge $M_\ast$ of the host galaxy. However, a large spread of the ratio $M_\bullet/M_\ast$ and a considerable excess of BH mass at redshifts $z\sim8$, indicate that the coevolution of central massive BHs and stellar populations in host galaxies may have experienced variations in its intensity. These issues require a robust determination of the relevant masses (BH, stars and gas), which is difficult in the case of distant high-redshift galaxies that are unresolved. In this paper, we seek to identify spectral diagnostics that may tell us about the relative masses of the BH, the gas mass and stellar mass. We consider general features of SEDs of galaxies that harbour growing massive BHs, forming stars and interstellar/circumgalactic gas. We focus on observational manifestations of possible predominances or intermittent variations in evolutionary episodes of growing massive BHs and forming stellar populations. We consider simplified scenarios for star formation and massive BHs growth, and simple models for chemical composition of gas, for dust free gas as well as for gas with dust mass fraction of $1/3$ of the metal content. We argue that wideband multi-frequency observations (X-ray to submillimeter) of the composite emission spectra of growing BH, stellar population and nebular emission of interstellar gas are sufficient to infer their masses.

astro-ph.GA↗

arXiv2019

Submillimeter signatures from growing supermassive black holes before reionization

The presence of supermassive black holes (SMBHs) with masses up to $M_\bullet\sim10^9M_\odot$ at redshifts $z\simeq7.5$ suggests that their seeds may have started to grow long before the reionization in ambient medium with pristine chemical composition. During their latest 500Myr episode of growing from $z\geq10$ to $z\sim7$ the black holes shine as luminous as $10^{11}\hbox{--}10^{12}L_\odot$, with a cumulative spectrum consisting of the intrinsic continuum from hot accretion disk, nebular hydrogen and helium spectral lines and free-free continuum from gas of host halos. Here we address the question of whether such a plain spectrum would allow us to trace evolution of these growing SMBHs. In our calculations we assume that host galaxies have stellar populations with masses smaller than the mass of their central black holes -- the so-called obese black hole galaxies. Within this model we show that for a sufficiently high mass of gas in a host galaxy -- not smaller than the mass of a growing black hole, the cumulative spectrum in the far-infrared reveals a sharp transition from a quasi-blackbody Rayleigh-Jeans spectrum of the black hole $\proptoλ^{-2}$ to a flat free-free nebular continuum $λ^{0.118}$ on longer wavelength limit. Once such a transition in the spectrum is resolved, the black hole mass can be inferred as a combination of the observed wavelength at the transition $λ_k$ and the corresponding spectral luminosity. Possible observability of this effect in spectra of growing high-$z$ SMBHs and determination of their mass with the upcoming JWST and the planned space project Spektr-M is briefly discussed.

astro-ph.GA↗

arXiv2019

Probing primordial $^3$He from hyperfine line afterglows around supercritical black holes

We consider the possibility of the detection of $^3$HeII hyperfine line (rest frequency, $8.67 \, \rm GHz$) emission from ionized zones around accreting black holes (BHs) formed at high redshifts, $z=15\hbox{--}30$. We show that the brightness temperature in 8.67GHz line increases and reaches a peak value after the accretion onto the BH exhausts and HeIII recombines into HeII. This period of brightening last up to 40~million years. We find that during this period the maximum brightness temperature reaches $\simeq 0.2\hbox{--}0.5 μ$K, depending on the epoch when such a black hole starts growing. The maximum angular size of the region emitting in the hyperfine line is around $0.5'$. The flux from such a region ($\simeq 0.3 \, \rm nJy$) is too small to be detected by SKA1-MID. The RMS of the collective flux from many emitting regions from a volume bounded by the synthesized beam and the band-width of SKA1-MID might reach 100~nJy, which is potentially detectable by SKA1-MID.

astro-ph.CO↗

arXiv2019

Launching of hot gas outflow by disc-wide supernova explosions

Galactic gas outflows are driven by stellar feedback with dominant contribution from supernovae (SN) explosions. The question of whether the energy deposited by SNe initiates a large scale outflow or gas circulation on smaller scales -- between discs and intermediate haloes, depends on SN rate and their distribution in space and time. We consider here gas circulation by disc-wide unclustered SNe with galactic star formation rate in the range from {$\simeq 6\times 10^{-4}$ to $\simeq 6\times 10^{-2}~M_\odot$~yr$^{-1}$~kpc$^{-2}$, corresponding to mid-to-high star formation observed in galaxies. We show that such disc-wide SN explosion regime can form circulation of warm ($T\sim 10^4$ K) and cold ($T<10^3$ K) phases within a few gas scale heights, and elevation of hot {($T>10^5$ K)} gas at higher ($z>1$ kpc) heights. We found that the threshold energy input rate for hot gas outflows with disc-wide supernovae explosions is estimated to be of the order $\sim 4\times 10^{-4}$~erg~s$^{-1}$~cm$^{-2}$. We discuss the observational manifestations of such phenomena in optical and X-ray bands. In particular, we found that for face-on galaxies with SF ($Σ_{_{\rm SF}}>0.02~M_\odot$~yr$^{-1}$~kpc$^{-2}$), the line profiles of ions typical for warm gas show a double-peak shape, corresponding to out-of-plane outflows. In the X-ray bands, galaxies with high SF rates ($Σ_{_{\rm SF}}>0.006~M_\odot$~yr$^{-1}$~kpc$^{-2}$) can be bright, with a smooth surface brightness in low-energy bands ($0.1\hbox{--}0.3$~keV) and patchy at higher energies ($1.6\hbox{--}8.3$~keV).}

astro-ph.GA↗

arXiv2018

Observing the influence of growing black holes on the pre-reionization IGM

We consider cosmological implications of the formation of first stellar size black holes (BHs) in the universe. Such BHs form and grow by accretion in minihaloes of masses $\simeq 10^5-10^7~M_\odot$, and emit non-thermal radiation which impact the ionization and thermal state of the IGM. We compute the implications of this process. We show that the influence regions for hydrogen increase to 10kpc (physical length) for non-growing BHs to more than 0.3--1Mpc for accreting BHs, the influence regions are ten times smaller for singly ionized helium. We consider three possible observables from the influence zones around accreting BHs during $8.5<z<25$: HI 21cm line, hyperfine line of $^3$HeII, and HI recombination lines. We show that the 21cm emitting region around a growing BH could produce brightness temperatures $\simeq 15$mK across an evolving structure of 1Mpc in size with hot, ionized gas closer to the BH and much cooler in outer regions. We show that the ongoing and upcoming radio interferometers such as LOFAR and SKA1-LOW might be able to detect these regions. $^3$HeII emission from regions surrounding the growing BH is weak: the corresponding brightness temperatures reaches tens of nano-Kelvin, which is below the range of upcoming SKA1-MED. We show that for growing BHs H$α$ line could be detected by JWST with $S/N=10$ in $10^4$~seconds of integration. In light on the recent EDGES result, we show that with additional cooling of baryons owing to collision with dark matter the HI signal could be enhanced by more than an order of magnitude.

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arXiv2017

Evolution of clustered supernovae

We study the merging and evolution of isolated supernovae (SNe) remnants in a stellar cluster into a collective superbubble, with the help of 3-D hydrodynamic simulations. We particularly focus on the transition stage when the isolated SNe remnants gradually combine to form a superbubble. We find that when the SN rate is high ($ν_{\rm sn}\sim 10^{-9}$ pc$^{-3}$ yr$^{-1}$), the merging phase lasts for $\sim 10^4$ yr, for $n=1\hbox{--}10$ cm$^{-3}$, and the merging phase lasts for a longer time ($\sim 0.1$ Myr or more) for lower SN rates ($ν_{\rm sn}\le 10^{-10}$ pc$^{-3}$ yr$^{-1}$). During this transition phase, the growing superbubble is filled with dense and cool fragments of shells and most of the energy is radiated away during this merging process. After passing through the intermediate phase, the superbubble eventually settles on to a new power-law wind asymptote that is smaller than estimated in a continuous wind model. This results in a significant (more than {\it several times}) underestimation of the mechanical luminosity needed to feed the bubble. We determine the X-ray and H$α$ surface brightnesses as functions of time for such merging SNe in a stellar cluster and find that clusters with high SN rate shine predominantly in soft X-rays and H$α$. In particular, a low value of the volume averaged H$α$ to H$β$ ratio and its large spread can be a good indicator of the transition phase of merging SNe.

astro-ph.GA↗

arXiv2017

A Kennicutt-Schmidt relation at molecular cloud scales and beyond

Using N-body/gasdynamic simulations of a Milky Way-like galaxy we analyse a Kennicutt-Schmidt relation, $Σ_{SFR} \propto Σ_{gas}^N$, at different spatial scales. We simulate synthetic observations in CO lines and UV band. We adopt the star formation rate defined in two ways: based on free fall collapse of a molecular cloud - $Σ_{SFR, cl}$, and calculated by using a UV flux calibration - $Σ_{SFR, UV}$. We study a KS relation for spatially smoothed maps with effective spatial resolution from molecular cloud scales to several hundred parsecs. We find that for spatially and kinematically resolved molecular clouds the $Σ_{SFR, cl} \propto Σ_{\rm gas}^N$ relation follows the power-law with index $N \approx 1.4$. Using UV flux as SFR calibrator we confirm a systematic offset between the $Σ_{\rm UV}$ and $Σ_{\rm gas}$ distributions on scales compared to molecular cloud sizes. Degrading resolution of our simulated maps for surface densities of gas and star formation rates we establish that there is no relation $Σ_{\rm SFR, UV} - Σ_{\rm gas}$ below the resolution $\sim 50$ pc. We find a transition range around scales $\sim 50-120$ pc, where the power-law index $N$ increases from 0 to 1-1.8 and saturates for scales larger $\sim 120$ pc. A value of the index saturated depends on a surface gas density threshold and it becomes steeper for higher $Σ_{gas}$ threshold. Averaging over scales with size of $>150$ pc the power-law index $N$ equals 1.3-1.4 for surface gas density threshold $\sim 5 M_\odot$pc$^{-2}$. At scales $>120$ pc surface SFR densities determined by using CO data and UV flux, $Σ_{\rm SFR, UV}/Σ_{\rm SFR, cl}$, demonstrate a discrepancy about a factor of 3. We argue that this may be originated from overestimating (constant) values of conversion factor, star formation efficiency or UV calibration used in our analysis.

astro-ph.GA↗

arXiv2014

Ionized gas velocity dispersion and multiple supernova explosions

Using 3D numerical simulations we study the evolution of the H$α$ intensity and velocity dispersion for single and multiple supenova (SN) explosions. We find that the $I_{\rm Hα}-σ$ diagram obtained for simulated gas flows is similar in shape to that observed in dwarf galaxies. We conclude that colliding SN shells with significant difference in age are resposible for high velocity dispersion that reaches values high as $\simgt 100$kms$^{-1}$. Such a high velocity dispersion could be hardly got for a single SN remnant. Peaks of velocity dispersion on the $I_{\rm Hα}-σ$ diagram may correspond to several stand-alone or merged SN remnants with moderately different ages. The procedure of the spatial resolution degrading in the H$α$ intensity and velocity dispersion maps makes the simulated $I_{\rm Hα}-σ$ diagrams close to those observed in dwarf galaxies not only in shape, but also quantitatively.

astro-ph.GA↗

arXiv2014

Evolution of multiple supernova remnants

(Abridged) Heating of the interstellar medium by multiple supernovae (SNe) explosions is at the heart of producing galaxy-scale outflows. We use hydrodynamical simulations to study the efficiency of multiple SNe in heating the interstellar medium (ISM) and filling the volume with gas of high temperatures. We argue that it is important for SNe remnants to have a large filling factor {\it and} a large heating efficiency. For this, they have to be clustered in space and time, and keep exploding until the hot gas percolates through the whole region, in order to compensate for the radiative loss. In the case of a limited number of SNe, we find that although the filling factor can be large, the heating efficiency declines after reaching a large value. In the case of a continuous series of SNe, the hot gas ($T \ge 3 \times 10^6$ K) can percolate through the whole region after the total volume filling factor reaches a threshold of $\sim 0.3$. The efficiency of heating the gas to X-ray temperatures can be $\ge 0.1$ after this percolation epoch, which occurs after a period of $\approx 10$ Myr for a typical starburst SNe rate density of $ν_{\rm SN} \approx 10^{-9}$ pc$^{-3}$ yr$^{-1}$ and gas density of $n\approx 10$ cm$^{-3}$ in starburst nuclei regions. This matches the recent observations of a time delay of similar order between the onset of star formation and galactic outflows. The efficiency to heat gas up to X-ray temperatures ($\ge 10^{6.5}$ K) roughly scales as $ν_{\rm SN}^{0.2} n^{-0.6}$. For a typical SNe rate density and gas density in starburst nuclei, the heating efficiency is $\sim 0.15$, also consistent with previous interpretations from X-ray observations. We discuss the implications of our results with regard to observational diagnostics of ionic ratios and emission measures in starburst nuclei regions.

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