GN-z11-flash: A shock-breakout in a Population III supernova at Cosmic Dawn?
DDraft version February 1, 2021
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GN-z11-flash: A shock-breakout in a Population III supernova at Cosmic Dawn?
Hamsa Padmanabhan and Abraham Loeb D´epartement de Physique Th´eorique, Universit´e de Gen`eve24 quai Ernest-Ansermet, CH 1211 Gen`eve 4, Switzerland Astronomy department, Harvard University60 Garden Street, Cambridge, MA 02138, USA
ABSTRACTWe discuss the possible interpretation of the recently observed transient, GN-z11-flash as originatingfrom a shock-breakout in a Population III supernova occurring in the GN-z11 galaxy at z ∼
11. Wefind that the parameters of the explosion are fully consistent with those expected from the shockbreakout associated with a Type II supernova of a progenitor star of ∼
300 solar masses in this galaxy,with of order unity such events expected over an observing timescale of a few years. We forecast theexpected number of such transients from z >
10 galaxies as a function of their host stellar mass andstar formation rate.
Keywords: galaxies: high-redshift – stars: Population III – (stars:) supernovae: general INTRODUCTIONRecently, Jiang et al. (2020a) reported the detectionof a rest-frame ultraviolet flash with an observed du-ration of a few hundred seconds from GN-z11, a lumi-nous, star forming galaxy situated at z ∼
11. Here, weexamine the scenario in which this transient originatedfrom the shock breakout following the Type II super-nova explosion of a massive Population III (Pop III)star in the galaxy. The observed star formation rate(Jiang et al. 2020b; Oesch et al. 2016) of the GN-z11galaxy ( ∼ M (cid:12) /yr) with a top heavy IMF is con-sistent with ∼ luminosity of the flare(1 . × ergs/s) and the expected energetics of theshock breakout, we estimate the mass of the breakoutshell ( ∼ − M (cid:12) ) and the total energy of the explosion( ∼ × ergs) for a typical Pop III mass of ∼ M (cid:12) and radius R ∗ ∼ R (cid:12) , which are fully consistent withtheoretical predictions (Nakar & Sari 2010) for a PopIII star with a polytropic index of γ p = 3. We fore-cast the expected number of such transients expectedfrom future surveys based on extrapolating the empiri-cally constrained star formation rates and stellar mass [email protected], [email protected] We use this value as representative of the ‘initial luminosity’ ofthe flare considered by Nakar & Sari (2010), although it is a lowerlimit on the inferred νL ν . functions at lower redshifts. The alternative explana-tion of a gamma-ray burst afterglow is much less likelygiven the much lower rate of occurrence for such events(Jiang et al. 2020a). SHOCK BREAKOUT SCENARIOGN-z11 is a luminous galaxy at z ∼
11 with an in-trinsic star formation rate of 26 M (cid:12) /yr. We begin byestimating the rate of Type II supernovae in this galaxyby using the relation from lower redshift observationscalibrated in Melinder et al. (2012): R = k SFR( z )where R is the intrinsic supernova (SN) rate for a galaxywith star-formation rate SFR( z ) at redshift z , and theconstant k is the percentage of stars that explode as su-pernovae per unit mass. At low redshifts, it is foundthat k = 0 . /M (cid:12) , a typical value for the flattest ini-tial mass function (IMF) as adopted by Hopkins & Bea-com (2006). However, for Pop III stars at early times,the findings of Pan et al. (2012) predict a core collapseSN rate of 10 − yr − Mpc − for Pop III stars, for a starformation rate of 0.01 M (cid:12) Mpc − yr − . This leads toa proportionality constant of k PopIII ∼ . /M (cid:12) , whichmay be nearly an order of magnitude higher than forgalaxies in the lower-redshift universe. For the case ofGN-z11, this corresponds a near-unity detection of the a r X i v : . [ a s t r o - ph . GA ] J a n supernova rate when observations are made over a pe-riod of a few years. The breakout of a shock (e.g., Chevalier 1976; Colgate1974) from a Type II supernova associated with a Popu-lation III star in GN-z11 would be detectable in the UVto gamma-ray bands. We can estimate the energy re-leased in the shock breakout by connecting the observedluminosity of the flare (Jiang et al. 2020a), the time ofthe shock breakout and the radius of the star. We beginwith the connection between the peak observed lumi-nosity of the flare, L obs , the radius of the star, R ∗ andthe internal energy of the breakout shell, E : E cR ∗ ≡ L obs = 1 . × ergs/s (1)The timescale of the observed flare is given by t s = R ∗ /v ∼
35 s, where v is the velocity of the shock whenit breaks out. We can relate v to E by invoking theenergy released when the star collapses to form a blackhole. This energy is delivered to the mass of the stellarenvelope, m , through the radiative shock which heatsit up (e.g., Nakar & Sari 2010). When the shock reachesthe surface of the star, it heats the surface layer as well.The observer sees the flash only from the surface layer atan optical depth τ = c/v and all the radiation lockedinterior to that takes a long time to diffuse out. Theflash represents the energy that can immediately leakout during the flash, defined by E ∼ m v , where m and v are the mass and velocity of the breakout shellrespectively.Population III stars are held against their self-gravityby radiation pressure, which maintains their radiationfield at the Eddington luminosity. For a surface temper-ature of T eff ∼ K, their radius R ∗ and mass m ∗ canbe connected by: R ∗ ≈ . × cm × (cid:18) m ∗ M (cid:12) (cid:19) / (2)A typical value of the star’s mass for this kind of explo-sion (Schaerer 2002) is m ∗ ∼ M (cid:12) , above the pairinstability regime, giving R ∗ ∼ R (cid:12) . From Eq. (1),we find E ∼ × ergs. We have v ∼ R ∗ / ∼ . c , which then leads to the mass of the shell, m ∼ × g ∼ − m ∗ . A similar proportionality factor is predicted from the model ofMebane et al. (2018), with the SN rate of about 10 − yr − Mpc − for a Population III IMF, with the corresponding SFR being10 − M (cid:12) Mpc − yr − , again leading to of order unity supernovaeover a few years’ observation time. We have used the observed time, t s , obs = 424 s scaled down bythe redshift dilation factor (1 + z ) ∼ Given a power-law behaviour of the stellar density pro-file with the radial distance, ρ ∼ ( R ∗ − r ) n , we can relatethe mass of the shell and the stellar parameters by gen-eralizing the treatment in Nakar & Sari (2010): m = 4 πm ∗ ( n + 1) (cid:34) A (cid:18) m E (cid:19) / ( n + 1) R ∗ κ m ∗ (cid:35) β ( n +1) /n (3)where β = 1 / (( n + 1) /n − . , A = c/ (1800 km s − ) =166 .
7, and κ = 0 . X ) where X = 0 .
76 is themass fraction of hydrogen (Bromm et al. 2001). Inthe above expression, m = ( m ∗ / M (cid:12) ) and E =( E/ ergs) where E is the total energy of the explo-sion. The exponent n is related (Calzavara & Matzner2004) to the polytropic index γ p for the star as γ p =1 + (1 /n ), giving n = 0 . γ p = 3. From this, we can relate thevalue of m to the total energy of the explosion, as m ∼ . × − E − . M (cid:12) , thus inferring E ∼ . m . This value of E is alsofully consistent with the expected energetics of this kindof explosion. DISCUSSIONWe have explored the scenario in which the observedflare from the GN-z11 galaxy at z ∼
11 arises as a resultof the shock breakout from a supernova explosion in aPop III star located in this galaxy. A top heavy IMFpredicts enough supernova events to be observed giventhe observed SFR of this galaxy. The simplest modelis that of a Pop III star with mass ∼ M (cid:12) and ra-dius ∼ R (cid:12) , which core collapses to make a black hole,releasing a total energy E ∼ × ergs from the ac-cretion of the core mass into the black hole. The partof the energy associated with the flash at the surfacelayer (with mass m ∼ − M (cid:12) ) leads to the observedluminosity of 1 . × ergs/s. This event may thuspresent the first observational evidence for the death ofvery massive stars at z (cid:38) z ∼
11. To do this, we use the empirically derivedstellar mass - star formation rate connection (Behrooziet al. 2019) for z (cid:38)
10 galaxies, and combine this withthe comoving number density of such galaxies expectedat these epochs (Davidzon et al. 2017) assuming negligi-ble evolution of the stellar mass function from z ∼ − . ± . × M (cid:12) ] and star formation rate(26 ± M (cid:12) yr − ) of GN-z11 overplotted as the red lines.The top x -axis in the right panel also shows the corre-sponding observed supernova rate per year expected for log ( M ∗ /M (cid:12) ) − l og S F R ( M (cid:12) y r − ) Model expectations GN − z SFR ( M (cid:12) yr − ) − − − φ S F R ( d e x − c M p c − ) GN − z R SN (yr − ) Figure 1.
Left panel:
Stellar mass to star formation rate relation for galaxies at z (cid:38)
10 (blue solid curve) and its associateduncertainty based on current observations (Behroozi et al. 2019; Matthee & Schaye 2019) extrapolated to the observed stellarmass range of GN-z11. The inferred stellar mass and star formation rate of GN-z11 are shown by the red solid lines (with theiruncertainties indicated by the dashed lines).
Right panel:
Comoving number density of galaxies per dex of SFR obtained bycombining the stellar mass function (Davidzon et al. 2017), assuming negligible evolution, with the stellar mass - SFR relationin the left panel. The top x -axis shows the corresponding (observed) number of Type II supernovae per year expected for a PopIII IMF at z ∼ a Pop III IMF, as discussed in Sec. 2, consistent withthe estimate of ∼ z >
10 in low-metallicity galax-ies. Flares such as GN-z11-flash from supernovae at Cos-mic Dawn (Loeb & Furlanetto 2013) could make galax-ies that are otherwise too faint, detectable, leading to anew method to flag z >
10 galaxies by monitoring flaresfrom them. Searching for flaring z >
10 galaxies by tak-ing multiple snapshots of the same region of the sky will thus be extremely important in the context of upcomingobservations with the
James Webb Space Telescope , andwould lead to a detailed understanding of the propertiesof their progenitor stars.ACKNOWLEDGEMENTSHP acknowledges support from the Swiss Na-tional Science Foundation under the Ambizione GrantPZ00P2 179934. The work of AL was partially sup-ported by Harvard’s Black Hole Initiative, which isfunded by grants from JTF and GBMF.REFERENCES