The Progenitors of Type Ia Supernovae: Are They Supersoft Sources?
aa r X i v : . [ a s t r o - ph . H E ] D ec THE PROGENITORS OF TYPE IA SUPERNOVAE:I. Are they Supersoft Sources?
R. Di Stefano
Harvard-Smithsonian Center for Astrophysics, 60 Garden St.. Cambridge, MA 02138
ABSTRACT
In a canonical model, the progenitors of Type Ia supernovae (SNe Ia) areaccreting, nuclear-burning white dwarfs (NBWDs), which explode when the whitedwarf (WD) reaches the Chandrasekhar mass, M C . Such massive NBWDs are hot( k T ∼
100 eV), luminous ( L ∼ erg s − ), and are potentially observable asluminous supersoft X-ray sources (SSSs). During the past several years, surveysfor soft X-ray sources in external galaxies have been conducted. This papershows that the results falsify the hypothesis that a large fraction of progenitorsare NBWDs which are presently observable as SSSs. The data also place limitson sub- M C models. While ⁀ M C . Subject headings: binaries:close; ISM:planetary nebulae:general; stars:evolution;X-rays:stars; X-rays:general
1. Introduction
Type Ia supernovae (SNe Ia) help us to explore the history of the cosmos (see, e.g.,Riess et al. 2007; Kuznetsova et al. 2008). Yet we still know little about their progenitors.There are two classes of progenitor models. (See Kotak 2009 and Branch et al. 1995 forreviews.) In “single degenerate” models, the progenitors are accreting white dwarfs (WDs).In “double-degenerate” models, the explosion is initiated through mass transfer betweenand/or the merger of two WDs. This paper is devoted to searching for the progenitors.In § years. In § Chandra place strict limits on the numbers of Type Ia progenitors that 2 –are detected as SSSs. In section § ⁀
2. The Numbers of Accreting WD Progenitors
In single-degenerate models, a WD must accrete and retain matter. Let M representthe initial mass of the WD. An explosion occurs when the mass has increased to a value M f . We start with models in which M f is the Chandrasekhar mass, M C ≈ . M ⊙ . The WD musthave a donor that can contribute the requisite mass. In addition, the rate of mass infall,˙ M in , must be large enough that accreted matter can be burned and retained. The rate ofgenuine mass increase, ˙ M W D , is determined by the rate of infall to the WD and a retentionfactor β ( M W D , ˙ M in ). ˙ M W D = β ( M W D , ˙ M in ) ˙ M in (1)The top panel of Figure 1 illustrates that mass retention requires mass donation rates ina narrow range between ˙ M in,min ( M W D ) (roughly 10 − M ⊙ yr − for a solar-mass CO WD),and ˙ M in,max ( M W D ), which is generally a few times larger than ˙ M in,min ( M W D ). This rangecorresponds to rates of infall for which accreting matter can undergo quasisteady nuclearburning. For ˙ M in > ˙ M in,max , not all of the incoming matter can be burned, and β declines.For ˙ M in < ˙ M in,min , incoming matter accumulates and burns episodically. For rates just below˙ M in,min ( M W D ) , the explosions are frequent (separated by decades) and weak, correspondingto recurrent novae (RNe); β can be close to unity. The lower the rate of infall, the moreviolent are the explosions produced by nuclear burning, and the more matter is ejected fromthe system. In some cases, more matter may be ejected than is accumulated between novae; β is negative. Most of the accreting WDs already identified are cataclysmic variables withaccretion rates typically two orders of magnitude or more below the rate required for steadyburning. Binaries can produce the requisite high rates, however (van den Heuvel et al. 1992).The duration, τ acc , of the accretion phase is τ acc = Z M f M dM ˙ M in β ( M W D , ˙ M in ) (2)There may be long periods in which the mass transfer period is too low (or too high) formass retention. In this paper we are concerned primarily with the interval during which the Note that even within the so-called steady-burning region , β need not be equal to unity. For example,some of the infalling mass may be driven from the white dwarf in the form of winds. M in is large enough that infalling mass is burned and retained. The approximateduration of this interval can be written as follows. τ acc = 5 × yrs (cid:16) ∆ M . M ⊙ (cid:17)(cid:16) × − M ⊙ yr − β ˙ M in (cid:17) . (3)where the value of β ˙ M in represents an average during the epoch when the WD’s mass ischanging.The rate of SNe Ia in galaxies is roughly 0 . L ⊙ in blue luminosity(Cappellaro et al. 1993; Turatto et al. 1994). In a galaxy with blue luminosity L B , thenumber, N acc , of accreting progenitors within 0 . M ⊙ of M C is roughly N acc = 1500 (cid:18) ∆ M . M ⊙ (cid:19)(cid:18) × − M ⊙ yr − β ˙ M in (cid:19)(cid:18) L B L ⊙ (cid:19) . (4)To determine the expected range of values of N acc , we assess the range of likely values of eachfactor. The amount of mass, ∆ M, that the white dwarf must gain is constrained from belowby the requirement that the accretor must start as a CO white dwarf, while white dwarfsborn with the highest mass start as O-Ne-Mg white dwarfs, which undergo accretion-inducedcollapse (AIC) upon achieving M C (see, e.g., Nomoto et al. 1979). The value of ∆ M cantherefore not be smaller than 0 . − . M ⊙ . Furthermore, the numbers of high-mass whitedwarfs are constrained by two considerations. First the initial mass function favors low-mass stars (Miller & Scalo 1979; Salpeter 1955). Second, low-mass stars produce low-masswhite dwarfs (Kalirai et al. 2008; Catal´an et al. 2009 ; Dobbie et al. 2006; Williams 2007;Weideman & Koester 1983). Therefore ∆ M is almost certainly in the range: 0 . − . M ⊙ ,consistent with N acc in the range 750 − M to besmall enough to place N acc below 750, the relationship between a star and the mass and/orcomposition of the remnant would have to be different from current models. Alternatively,part of the answer could be that O-Ne-Mg white dwarfs produce ⁀ β ˙ M in is larger than 8 × − M ⊙ yr − , this would reduce the valueof N acc . Higher rates of nuclear burning will, however, produce luminosities that exceed theEddington luminosity. It is more likely that the average rate at which mass is accretedis actually smaller, producing larger values of N acc . Note in addition that calculations bydifferent groups agree on the general range of ˙ M in needed for high-mass white dwarfs to burnaccreting matter (see, e.g., Nomoto 1982; Iben 1982, Fujimoto 1982; Shen & Bildsten 2008and references therein).The third factor influencing the value of N acc is proportional to L B . This factor isincluded because observations find that the rate of Type Ia supernova scales with L B . As 4 –more ⁀
1e are discovered in more galaxies, this rate is becoming better measured. (See, e.g.,Dilday et al. 2008; Graham et al. 2008; Kuznetsova et al. 2008; Poznanski et al. 2008;Panagia et al. 2007.) It is unlikely that the estimated rates will change enough to reduceor enhance the predicted values of N acc by a factor as large as 2.Therefore, taking into account the range of possible values of the factors in Equation 4,we find that for spiral galaxies similar to the Milky Way and M31 (and even for ellipticals,with a lower rate of SNe Ia), N acc cannot be much smaller than several hundred, and is likelyto be significantly larger. The assumptions that lead to to these predictions are that (1) thesingle-degenerate channel produces the majority of ⁀
3. Detecting the Progenitors3.1. The High Luminosity of Progenitors
The crucial point is that nuclear-burning, either episodic or quasisteady, appears to benecessary for the retention of matter by WDs. The burning of matter releases a great dealof energy. L NB = 2 . × erg s − (cid:18) η . (cid:19) (cid:18) f . (cid:19) (cid:18) β ˙ M in × − M ⊙ yr − (cid:19) (5)In this equation, L NB is the power released through the burning of accreted material; f isthe fraction of the incoming matter burned, and η is the efficiency.Consider a WD with accretion rate in the steady-burning regime. Because the massinfall rate is large, the accretion luminosity is also large, although typically less than 10% ofthe power provided by nuclear burning. If, however, the accretion rate lies slightly below thesteady-burning regime, then nuclear burning will occur only episodically, during recurrentnovae. In contrast, the accretion luminosity, which can be ∼ erg s − for high-masswhite dwarfs, could make the system appear bright even between nova explosions. Therefore,particularly when nuclear burning is occurring, but even when mass infall rates are slightlybelow the nuclear-burning limit, accreting WDs that are Type Ia progenitors should behighly luminous (second panel of Figure 1). We address the issue of the detectability of theaccretion luminosity in the companion paper (Di Stefano 2009). 5 – -9-8-7-63536373839 0.6 0.8 1 1.2 1.4050100150 Fig. 1.—
Properties of NBWDs: green point correspond to systems in which the rate of mass infall is inthe range necessary for quasisteady nuclear burning. In each panel, the green points lie between two curves;the upper (lower) curves correspond to the maximum (minimum) rate of infall consistent with quasisteadynuclear burning.
Top panel: ˙ M in is plotted against the white dwarf mass, M W D . For values of ˙ M in belowthe steady-burning region, novae are expected. The repetition frequency is highest for ˙ M in just below thesteady-burning limit, so that the novae are recurrent novae and a large fraction of the accreted matter canbe retained. For even lower accretion rates, the novae are classical novae, blasting accreted material from thebinary at intervals > years. Just above the steady burning region is the region in which mass comes intoo quickly for it all to be burned upon arrival. Unless mass transfer can be turned off during an interval inwhich all excess matter is burned, the value of β must be smaller than unity. Second panel:
The logarithmof the luminosity versus M W D . The positions of the green points are computed by assuming that 0 .
75 of theinfalling matter is burned with an efficiency of 0 . . The red points show the accretion luminosity, which wascomputed to be: ˙ M in M W D
G/R
W D . Although more than an order of magnitude lower than the luminosityderived from nuclear burning, accretion by high-mass white dwarfs is detectable in nearby external galaxies.
Third panel: k T versus M W D . The value of T was computed by assuming an effective radius equal to1 . R W D . This panel illustrates that the effective temperature is a strong function of the WD mass. ForWDs with mass near M C , k T is large enough to make x-ray detection efficiency comparable to what it wouldbe for a canonical (i.e., hard) x-ray source. As the third panel of Figure 1 shows, effective values of k T for NBWDs are expected tobe in the range of tens of eV. The x-ray missions
Einstein and
ROSAT had good low-energysensitivity and could detect soft x-ray sources in the Local Group. By the mid-1990s, morethan 30 sources with the properties expected for NBWDs had been discovered. (See Greiner2000 for a catalog and for references.) The soft emitters were dubbed luminous supersoftx-ray sources (SSSs). A natural conjecture is that the SSSs are in fact NBWDs. Some nearbySSSs are known to be hot white dwarfs post-nova, or are pre-WDs still ensconced in planetarynebulae. The binary properties of roughly half of the SSSs with optical IDs suggests thatthey might be WDs accreting at high-enough rates to burn matter in a quasisteady fashion.Soon after their discovery, it was conjectured that some SSSs could be progenitors of AIC(van den Heuvel et al. 1992) or of ⁀
1e (Rappaport, Di Stefano & Smith 1994).As Figure 1 demonstrates, the temperature is higher for WDs with higher mass. This isbecause higher-mass WDs (1) are smaller, and (2) require a higher infall rate, and thereforea higher rate of nuclear burning. In principle, NBWDs with mass close to M C can havevalues of k T near or even slightly above 100 eV.Di Stefano & Rappaport (1994) modeled the gas distribution of several galaxies to deter-mine what fraction of SSSs could be detected as a function of L and T . While only roughlya percent of low-L/low-T SSSs could be detected by ROSAT , almost all SSSs associatedwith NBWDs with mass near M C could be detected in M31, because they are both hot andbright. Figure 2 demonstrates that, with Chandra , for typical amounts of absorption, wecan expect to have a complete census of NBWDs with masses within a few tenths of M C inM31, M101, M83, and M51. In fact, with typical values of N H ∼ cm − , the Chandra exposures we analyzed should allow us to detect and identify all NBWDs with M W D largerthan 0 . − . M ⊙ (1 . − . M ⊙ ) in M31 (M81 and M83). Elliptical galaxies are good placesin which to hunt for bright SSSs because they have relatively small amounts of gas and dust.If, therefore, (1) the class of Type Ia progenitors consists primarily of accreting whitedwarfs with mass close to M C , and (2) these white dwarfs are burning the accreted matter ina quasi-steady manner, and (3) this produces luminosities and temperatures in the expectedregime, then these galaxies should each contain at least several hundred hot, bright, anddetectable SSSs. 7 – Table 1 shows the numbers of soft x-ray sources in each of six galaxies that have beencarefully studied (Di Stefano et al. 2003a, 2003b, 2004a, 2004b). M101, M83, and M51 arespiral galaxies. M104 is a bulge-dominated spiral, while both NGC4472 and NGC4697 areelliptical galaxies. Two categories of soft sources are listed.(1)
SSSs refer to sources with values of k T below 150 eV. These should encompass themajority of NBWDs, including all of the Type Ia progenitors. In each case, the numbersof SSSs actually detected are smaller than the numbers of predicted Type Ia progenitors bymore than an order of magnitude. Furthermore, only a fraction of the detected SSSs arecandidate progenitors of ⁀ M C (see, e.g., Pence et al. 2001). On the other hand, some SSSs aretoo luminous to correspond to NBWDs. Some ultraluminous SSSs, with x-ray luminositiesabove 10 erg s − , may be accreting black holes (Kong & Di Stefano 2005; Mukai et al.2005; Kong et al. 2004).(2) Quasisoft sources (QSSs) are sources that are slightly harder than SSSs, butwhich exhibit little or no emission above 2 keV (Di Stefano & Kong 2004; Di Stefano et al.2004a; Di Stefano et al. 2004b). With effective values of k T above ∼
150 eV, some couldbe NBWDs with mass near M C : the addition of a small hard component and/or high levelsof absorption could cause such a source to have a QSS spectrum. Nevertheless, many QSSsare too hard to be associated with NBWDS. At most a small fraction could be progenitorsof Type Ia SNe. Results:
At most, a modest fraction of all SSSs and QSSs could be progenitors of ⁀ and QSSs in each galaxy were progenitors, they wouldTable 1: Soft Sources in External GalaxiesGalaxy SSSs QSSs Other SourcesM101 42 21 24M83 28 26 74M51 15 21 56M104 5 17 100NGC4472 5 22 184NGC4697 4 15 72 8 –constitute less than a tenth of the total NBWDs with mass near M C needed to provide theobserved rate of ⁀ −
99% of the actively accreting progenitorsnot appearing as SSSs or QSSs. Figure 2 also indicates that the observations already placelimits on the numbers of lower-mass NBWDs in each of several galaxies.It may be important to note, however, that there is an interesting trend in the data.That is, both the rate of ⁀
1e and the number of SSSs are significantly larger in late-typegalaxies than in early-type galaxies.If the rate of mass transfer is high enough to support quasisteady-nuclear burning,then the character of the disk is remarkable, because the total accretion energy is only asmall fraction of the energy provided to the disk by the white dwarf through irradiation andheating. The inner disk itself becomes a source of supersoft x-rays. At x-ray wavelengths,the effect is therefore to make the source marginally brighter, but to likely keep it in the SSSregime. Should it b
An automated source detection and identification process was employed by Liu (2008) tostudy x-ray sources in fields containing 383 nearby galaxies. SSSs and QSSs were identifiedusing the same algorithm used for the galaxies in Table 1. Liu found that only 2 .
6% of allsources bright enough for spectral classification are SSS. For every SSS there are roughly fourQSSs. The combination of SSSs and QSSs constitute about 13% of all x-ray sources. Yet,the total numbers of x-ray sources per galaxy were generally several times smaller than theexpected population of nuclear-burning Type Ia progenitors. Thus, the discrepancy betweenthe numbers of progenitors and the total numbers of soft sources per galaxy is typicallylarger than an order of magnitude. Furthermore, a significant fraction of the soft sourceshave x-ray luminosities above 10 erg s − , and are therefore not good candidates for whitedwarf accretors.Liu created merged images to achieve effective exposure times far longer than thoseutilized in Figure 2. The total exposure time of M101, for example, is roughly ten times thevalue used to create Figure 2. This means that Liu’s catalog can be used to place stringentlimits on sub-Chandrasekhar models (with white dwarf masses as low as 0 . − . M ⊙ ) as The high ratio of QSSs to SSSs may reflect the prevalence of older stellar populations among the galaxiesin Liu’s survey.
M31 is a special case because of its proximity. A source with x-ray luminosity (0 . − erg s − , possibly corresponding to a NBWD with mass within roughly 0 . M ⊙ of M C , would produce a count rate of 0 .
04 s − in ACIS-S, or 0 .
014 s − in ACIS-I. Since mostexposures of M31 are longer than 5 ksec, these sources are readily detected and their spectracan be classified as SSS. A source which exhibits a small hard component might appear as aQSS, producing an even higher count rate. Di Stefano et al. (2004b) published a list of 42SSSs and QSSs drawn from three regions in the disk and also from the galactic bulge. Ofthese, only 4 sources (3 of them in the bulge), had count rates above 0 . s − . Most of thedetected soft sources are too dim to be high-mass NBWDs. These observations cover only afraction of the galaxy. (Note that most of the SSSs are in the center, which was well covered,so the total number of sources we expect does not scale with the area covered.) Orio (2006)identified SSSs and QSSs in M31 by using deep XMM-Newton observations that covered theentire body of the galaxy. Using x-ray spectral information alone, Orio found significantcontamination from supernova remnants. The data contained evidence for 15 SSSs and 18QSSs that were not associated with known supernova remnants. In addition, Orio foundthat about one in ten nova outbursts in M31 produces SSS-behavior post nova. The link tonovae has been studied in more detail using additional data sets (Pietsch et al. 2006; Henzeet al. 2009). della Valle & Livio (1996) have demonstrated that only ∼
10% of all novae arelikely to be RNe, retaining most of the matter they accrete. Most novae, therefore, are not ⁀ N H are ∼ cm − , we likely have a completecensus of NBWDs with mass greater than roughly 0 . M ⊙ . This places strong limits onsub-Chandrasekhar models. 10 –
Only a handful of SSSs have been discovered in the Milky Way. This small number isconsistent with the fact that absorption by the interstellar medium (ISM) in the Galacticdisk can obscure the soft radiation emanating from l-m NBWDs. If, however, the Galaxycontains 500 − −
10 of them should lie within roughly a kpc. Ifthese have values of k T in the range 75 −
100 eV and luminosities of ∼ erg s − , theywill be easily detected by ROSAT, Chandra , and
XMM-Newton .For
Chandra count rates we can scale from the numbers given in the paragraph on M31;the
XMM-Newton count rates would be ∼ ROSAT count rateswould be smaller than the
Chandra rates by a factor of ∼
2, the
All-Sky Survey could havediscovered all high-mass NBWDs within a kpc, even along directions in the sky in whichthe exposure times were shortest. The persistent SSSs discovered by
ROSAT were dimmerand cooler than high-mass NBWDs (Greiner 2000). The failure to detect bright, hot SSSsand/or QSSs in the neighborhood ( < ⁀ The most direct way to determine if ⁀
1e are generated by SSSs is to check pre-explosionx-ray images. Voss & Nelemans (2008) found 4 galaxies that had been observed by
Chandra prior to a ⁀ . ′′ from the supernova ( ∼
80 pc in projection;Roelofs et al. 2008), and was neither an SSS nor a QSS.
4. Conclusions4.1. SSSs for the Long Term?
The discovery of SSSs seemed to provide hope that Type Ia progenitors could be iden-tified in a fairly straightforward way, through the signatures of their soft x-ray emission.While some bright SSSs may be progenitors of Type Ia supernovae, we can now say con-clusively that the majority of the progenitors do not appear as bright SSSs during intervalslong enough ( ∼ yrs) to allow quasisteady burning of the necessary amounts of accretingmatter. The discrepancy is at least an order of magnitude, and may be as much as two 11 – Fig. 2.— Each panel refers to a quasi-steady NBWD with the listed mass; L and T weretaken from Iben (1982). Within each panel, each curve corresponds to a single galaxy(M31, green; M101, red; M83, magenta; M51, cyan; NGC 4697, blue); the galaxy’s distanceand the longest ACIS-S exposure we have analyzed were used to compute the numbers ofcounts. We assumed the sensitivity of Chandra’s
ACIS-S as computed by PIMMS for AO4.The horizontal dot-dashed line shown on each panel corresponds to 14 counts, the numberneeded to ascertain whether a given source can be classified as an SSS (see Di Stefano &Kong 2003). 12 –orders of magnitude.In addition, we find that existing data already place restrictions on sub-Chandrasekharmodels (Figure 2). These restrictions will be tightened as more data are analyzed, andadditional exposures with
Chandra and
XMM-Newton become available.
Although we have ruled out the possibility that the majority of ⁀ ⁀ M C can sustain mass transfer rates in the steady burning regimefor most of the mass-transfer phase. (See, e.g., van den Heuvel et al. 1992; Rappaport,Di Stefano & Smith 1994; Di Stefano & Nelson 1996; Yungelson et al. 1996; L¨u et al. 2006;Han & Podsiadlowski 2006.)It is therefore possible that a portion of the observed SSSs and QSSs are CO whitedwarfs on their way to the Chandrasekhar mass. It is important to identify candidates.Given the expected temperature range, the NBWDs that are ⁀ ∼ − M ⊙ in thermal dominant states Di Stefano et al. 2004a).The candidates that turn out to be NBWDs could be near explosion. The likelihoodthat an individual source is about to “go off” is small. Even a white dwarf within 0 . M ⊙ may take more than 1000 years to achieve M C . Nevertheless, by identifying a large pool ofcandidates, drawn from the hundreds of galaxies observed with Chandra and
XMM-Newton ,we increase the chance of having a useful pre-explosion image of a ⁀ The restrictions on the numbers of SSSs we have derived above do not necessarilytranslate into restrictions on the numbers of NBWDs. In fact, theoretical considerationspredict the presence of a population of high-mass NBWDs. First, starting with a largepopulation of binaries, a subset will pass through a phase in which a high-mass white dwarfaccretes matter at a high rate (see, e.g., Rappaport, Di Stefano & Smith 1994; Yungelsonet al. 1996). Second, we know that ⁀
1e occur, and that every evolutionary pathway toexplosion passes through channels that involve high accretion rates onto a white dwarf withmass larger than ∼ . M ⊙ . Certainly a long phase of nuclear-burning is required in single-degenerate models (Equation 3). This would be true in sub-Chandrasekhar models as well.Furthermore, we show in the companion paper that even many -.d binaries require a priorsingle-degenerate phase during which nuclear burning is expected (Di Stefano 2009).We have also found that the numbers of NBWDs needed per galaxy is large. Thus, atany given time, galaxies such as the Milky Way house ∼ M C . In sub-Chandrasekhar models, or -.d models the average mass of the NBWDs may be smaller,but nevertheless larger than 0 . M ⊙ . This increases our chances of establishing the existenceof a population of progenitors in M31 and in other nearby galaxies. Perhaps most exciting,the large number guarantees that some progenitors that are actively accreting NBWDs mustlie within a kpc of Earth. If we can identify these, we will be able to make detailed studiesof the progenitors and the processes that allow high-mass white dwarfs to grow in mass.In fact, we have almost certainly detected NBWDs that are ⁀ In the companion paper we also discuss the discovery of progenitors at other wavelengths (IR, optical,and UV) in the context of binary models.
14 –Di Stefano, Paerels & Rappaport 1995). In the companion paper (Di Stefano 2009) we linkthe possible signatures of nuclear burning to the characteristics of the binary models for ⁀ Summary:
Nuclear burning appears to be required in order for Type Ia supernovae to occur.As the companion paper shows, even many -.d progenitors of ⁀
1e are expected to pass throughan earlier single-degenerate phase in which nuclear burning occurs. We have demonstratedthat the majority of the progenitors do not appear as SSSs or QSSs during most of theall-important nuclear-burning phase. The energy must escape in other wavebands, makingit possible to detect and identify dozens of progenitors in our own Galaxy, and comparableor perhaps even larger numbers in M31 and other nearby galaxies. Given the long durationof the requisite nuclear-burning phases, it would be surprising if some progenitors do notappear as SSSs or QSSs, at least during part of their evolution. It is therefore still interestingto explore the connection between soft x-ray sources and ⁀ ⁀
1e arerare and therefore tend to occur at great distance from us, thousands of the progenitors arenearby, and are luminous enough that we can study them in detail well before they explode.
Acknowledgements:
It is a pleasure to acknowledge helpful conversations and commentsfrom many of the participants (especially Ed van den Heuvel, Lev Yungelson, and JimLiebert), of the KITP conference and workshop on
Accretion and Explosion held at UCSanta Barbara in 2007. This work was supported in part by an LTSA grant from NASA andby funding from the Smithsonian Institution.
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