A&A 450, 1037–1050 (2006) Astronomy DOI: 10.1051/0004-6361:20054626 & ⃝c ESO 2006 Astrophysics 44 ⋆ Are Ti-producing supernovae exceptional? 1 1 2 1 2,3 1 L.-S. The , D. D. Clayton , R. Diehl , D. H. Hartmann , A. F. Iyudin , M. D. Leising , 1 4 2 B. S. Meyer , Y. Motizuki , and V. Schönfelder 1 Department of Physics and Astronomy, Clemson University, Clemson, SC 29634-0978, USA e-mail: 44 1038 L.-S. The et al.: Ti supernova remnants 44 4. Nucleosynthesis of Ti is primarily from α-rich freeze-out of nuclear statistical equilibrium and secondarily from sili- con burning. 44 5. The origin of abundant cosmic Ca occurs mainly through 44 Ti nucleosynthesis. 44 6. Ti traces have been found in pre-solar grains which have been attributed to condensation within core-collapse Fig. 1. Maximum-entropy map of the Galactic plane (within latitude supernovae. ±30◦) in the 44Ti energy window (1.066–1.246 MeV) for the combi- nation of CGRO observations from 0.1 to 617.1. Two crosses mark the 44 In this paper we estimate what the gamma-ray sky of Ti positions of Cas A and GRO J0852-4642. This figure is adopted from sources would be expected to look like by adopting an average Iyudin (1999). 44 Ti source model having a characteristic source event recur- 44 rence rate, Ti yield per event, and spatial distribution. We compare this to the present-day gamma-ray survey and find weak signal from the Per OB2 association (Dupraz et al. 1997). apparent and serious conflicts. Then we analyze whether de- 44 Apparently, no bright young Ti emitting supernova remnants viations from these average expectations can occur from the are found in the inner region of the Galaxy (see Fig. 1). known or expected variability of models and parameters in- What do we expect the Galaxy to look like in volved. We use a Monte Carlo simulation of the expected sky 44 Ti emission? image within reasonable distributions of parameters for that purpose. This leads us to discuss each of the relevant param- 44 44 2.1. Ti from supernovae eters, which may explain an anomalous Ti sky; these are, specifically: Supernova observations directly demonstrate that these events 44 – the gamma-ray survey quality; are at the origin of Ti production: the 1.157 MeV γ-ray line 44 following Ti decay has been detected in the 340-year old – statistical effects of small samples; – the adopted supernova rates; Galactic supernova remnant Cas A (Iyudin et al. 1994; Vink – the supernova explosion and nucleosynthesis models; et al. 2001). Furthermore, SN1987A’s late light curve, observed in unique detail over more than 15 years, appears powered by – the spatial distribution of supernova events; 44 −4 – the deviations from smooth chemical evolution; a similar amount of Ti (0.2–2.0 × 10 M⊙), from modeling – the supernova origin of Galactic and solar 44Ca. of radioactive energy deposition and photon transport in the SNR (Woosley et al. 1989; Fransson & Kozma 2002). Gamma- ray detection and proof of this interpretation is still lacking, 44 2. Ti and supernovae in the Galaxy but INTEGRAL’s recent observations may prove sufficiently Supernova rates in the Galaxy can be inferred from differ- sensitive. ent observables. But observational incompleteness and bias re- Presolar grains have been identified in meteoritic sam- quires that several assumptions are an essential part of such ples through their unusual isotopic abundance patterns, and 44 inferences. We compare here the observed Ti sky with expec- hold rich isotopic abundance detail for characterizing their con- 44 tations for the occurrences of young Ti emitting supernova densation environments (e.g. Clayton & Nittler 2004; Zinner remnants, as they result from astrophysical assessments of su- 1998). SiC grains of the X-type are attributed to core-collapse pernova characteristics for our Galaxy. We choose a time inter- supernovae from their large excesses in characteristic isotopes 44 44 val unit of 100 years for comparison of chemical history with (Nittler et al. 1996). Ti-produced overabundance of Ca is 44 supernova event rates. The extrapolation of the past history and found in these SiC X grains, indicating presence of Ti at 44 44 40 yields of Ti-ejecting supernova events should give a produc- their time of condensation. Measured Ca/ Ca ratios are large tion rate which can be compared with recent supernova rates, (Nittler et al. 1996; Clayton et al. 1997a; Hoppe et al. 2000). 44 as no other source of Ca has yet been identified. This proves their supernova origin, on one hand, and likewise 44 44 Have the Ca-producing supernovae been typical; is all it proves that dust-producing supernovae may eject Ti in sig- 44 44 of Ca produced through radioactive Ti; or do exceptional nificant amounts. Their attribution to core collapse supernovae 44 44 events contribute most of the Ti? Gamma-ray surveys for Ti rather than supernovae of type Ia (Nittler et al. 1996) is plausi- sources, and presolar supernova grains provide ways to address ble, if we believe that core collapse supernovae probably dom- 44 this question. inate Ti production and because there is no direct evidence of In the following section we will then examine each of the dust condensation in thermonuclear supernovae (Dwek 1998). critical assumptions in more detail. It is likely that all of the observed X grains sample both differ- 44 For a Ti sky reference, we adopt the result from ent condensation environments and different production events. 44 COMPTEL’s survey in the 1.157 MeV band, which is the Therefore, their Ca abundances cannot be interpreted in ab- 44 most complete survey to date (Dupraz et al. 1997; Iyudin solute terms as a measure of the mass of Ti ejected per super- et al. 1999). In this survey, one object has been clearly de- nova. tected (340-year-old Cas A at a distance of 3.4 kpc), candidates The most plausible cosmic environment for production of 44 at lower significance have been discussed (most prominently Ti is the α-rich freeze-out from high-temperature burning GRO J0852-4642 in the Vela region, Iyudin et al. 1999), and a near Nuclear Statistical Equilibrium (e.g. Woosley et al. 1973; 44 L.-S. The et al.: Ti supernova remnants 1039 Arnett 1996). The required high values for the entropy are calculation (Timmes et al. 1995) upward by a factor of three found in core-collapse supernovae. Therefore the simplest to achieve the solar abundance, we infer a production rate of 44 −6 −1 plausible assumption is that core-collapse supernovae are re- Ca of about 3.6 × 10 M⊙ yr . Other considerations us- 44 sponsible for any substantial sources of Ti. ing different chemical evolution models (see Appendix C) 44 44 It is likewise plausible that traditional SNIa do not add sig- lead from the Ca abundance to a current Ti production 44 −6 −1 nificantly to nucleosynthesis at mass A= 44, specifically no rate: p( Ti) = 5.5 × 10 M⊙ yr , with full uncertainty range 44 Ti, since their NSE freeze-out conditions will not be favor- 1.2–12 × 10−6 M⊙ yr−1 (see Appendix C). 44 able for Ti production (Timmes et al. 1995). We consider the symbiotic-star scenario as a rare subclass of SNIa, even though 44 2.3. Supernova rates their Ti yields may be large (Woosley & Weaver 1994); so 44 they indeed would be rare outliers, rather than typical Ti pro- Direct supernova rate measures have been made through cor- ducing supernovae. We will discuss uncertainties in each of relations between supernova activity and other tracers of the these sites in more detail below (see Sect. 3.5). massive star content of a galaxy. van den Bergh (1991) finds 2 −1 (2.62 ± 0.8) h 100 SN century . For h100 = 0.75, the rate −1 2.2. Ca from supernovae is 1.5 ± 0.8 SN century . This rate is based on a com- bined study of galactic supernova remnants, historical SNe, Measurements of cosmic isotopic abundances can be converted and novae in M 31 and M 33. Cappellaro et al. (1993) refer into isotope production rates; however, for all long-lived iso- to this rate as the best estimate. van den Bergh & Tammann topes models of chemical evolution have to be applied (e.g. (1991) find SNR= 4.0 SN century−1. The authors review su- Clayton 1988; Pagel 1997; Timmes et al. 1995; Matteucci pernova rates in external galaxies and derive a specific su- 44 2003). How can we use these for predicting the shortlived Ti pernova frequency, in units of 1 SNu= one SN per century source appearance in gamma-rays? Its lifetime is too short for per 1010 L ⊙(B), for various galaxy types. If one assumes that mean chemical evolution arguments. the Galaxy is intermediate between types Sab-Sb and types 2 Over the time scale of chemical evolution of the Galaxy, the Sbc-Sd, the specific rate is 3 h SNu. For a Galactic blue- 100 10 cumulative and averaging effects of different explosion types band luminosity of L(B) = 2.3 × 10 L⊙(B) (their Table 11) −1 would integrate to a smooth pattern of “standard abundances”, and h100 = 0.75 we infer SNR=4.0 SN century . Their re- as they are observed throughout the universe. Evolutionary view paper also discusses estimates from internal tracers in pathways for individual elements can be associated with the the Milky Way: from radio supernova remnant (RSNR) statis- −1 evolution of metallicity and the rates of different supernova tics they infer SNR= 3.3 ± 2.0 SN century . From the historic 44 types. The abundance of Ca in solar-system matter thus can record of nearby (<a few kpc) supernovae in the past millen- −1 be translated through models of chemical evolution into a cur- nium they find SNR= 5.8 ± 2.4 SN century . The large ex- −4 44 rent average production rate of ≃3 × 10 M⊙ of Ti per 100 y tinction corrections in the galactic plane make this small sam- (Leising & Share 1990, see below). ple highly incomplete, which results in large uncertainties in Chemical evolution calculations (Timmes et al. 1995) us- extrapolations to the full galactic disk. The authors also re- ing computed ejecta masses (Woosley & Weaver 1995) were view efforts based on the pulsar birth rate, but extensive ob- shown to account reasonably for most solar abundances, in- servational selection effects in combination with the strong and cluding specifically 40Ca, but failing by a factor of three for poorly understood evolution of luminosity and beaming geom- 44 Ca; this fact is also evident from the ratio of 44Ti to Fe in cc- etry (see Lyne & Graham-Smith 1998; and Lorimer & Kramer SN models. But over short time scales where only a limited 2004) renders this method impractical for estimating the galac- number of source events contribute, great variability among tic SNR. Continuing the studies of van den Bergh & Tammann, −1 sources would present a significant difference of the present- Cappellaro et al. (1993) find SNR= 1.4 ± 0.9 SN century , day picture from the average. Therefore we may compare the when scaling to external galaxies of similar type. The sample is expectations from long-term averaged 44Ti production to the obtained from surveys carried out at the Asiago and Sternberg present-day 44Ti source record imaged in gamma-rays, allow- Observatories. The authors provide an extensive discussion ing for the short-term fluctuations with Monte-Carlo realiza- of the uncertainties of this method, which can exceed 200% tions of the sources. for some late type galaxies. More recently, van den Bergh & 2 44 McClure (1994) find SNR= (2.4–2.7) h events per century. The solar-system Ca abundance is rooted plausibly in 75 44 This estimate is based on re-evaluation of the extra-galactic Ti nucleosynthesis (Woosley et al. 1973; Clayton 1982), and SN rates obtained from Evans’ 1980–1988 observations. This is a result of the integrated Galactic nucleosynthesis prior to method depends on a somewhat uncertain type of the Galaxy formation of the solar system. Given a time-dependence of and the value of its blue-band luminosity, while the uncertainty the production rate, it can be normalized to the rate required due to the Hubble constant is now very small. Given the error to give precisely the measured solar abundance 4.5 Gyr ago, analysis in the paper, the rate is uncertain by at least 30%. which also fixes the long-term average production rate to- day. Models of galactic chemical evolution, constrained by van den Bergh & McClure (1994) in studying the supernova a number of observables, provide us with that time depen- rates of local spiral galaxies of types Sab-Sd of Evans’ observa- dence, albeit subject to a number of assumptions and param- tions estimated that 80%–90% of supernova in that galaxies are 44 eter choices. Adjusting the Ti yield in the aforementioned of types Ibc and II. Recently Cappellaro (2003) combining five 44 1040 L.-S. The et al.: Ti supernova remnants SN searches to include 137 SNe in 9346 galaxies estimates the standard core collapse events but not to standard thermonuclear SN type ratios in the Galaxy to be Ia:Ib/c:II = 0.22:0.11:0.67. supernovae. Is this correct? From these observations, one infers a ratio of core-collapse If true, the location of 44Ti sources should match the lo- to thermonuclear supernova of R = (II+Ibc)/Ia= 3.5. However, cations of young massive stars which have rather short life- note that the Galactic historical record in the last millennium times. There is substantial evidence that massive star forma- shown in Table B.1 contains only two type Ia SNR out of tion occurs in spiral arms and predominantly in the inner six SNRs. An often used alternative distribution over types Galaxy (Elmegreen et al. 2003; Scoville et al. 2001; Kennicutt is Ia:Ib/c:II = 0.1:0.15:0.75 (Hatano et al. 1997; Dawson & 1998). Massive stars can be observed directly in the infrared Johnson 1994; Tammann et al. 1994; Hartmann et al. 1993), (e.g. Maeder & Conti 1994), though extinction corrections which implies a three times higher cc-SN fraction. In this are large in regions of dense clouds. Possibly an even better work, we adopt this set of parameters, and note that the small (though more indirect) massive-star census can be derived from 44 Ti yield of type Ia renders our results insensitive to this ratio. 26Al decay γ-rays (Diehl et al. 1995; Prantzos & Diehl 1996; 26 Knödlseder 2000; Diehl et al. 2005). Al is understood to orig- Over the last millennium, the historic record contains six inate predominantly from massive stars and γ-rays easily pen- events (see Appendix B.4), which implies a rather low rate at etrate even dark clouds in star forming regions. So, do we see face value. However Galactic extinction at visible wavelengths 44 the Ti sources in regions where we expect them to occur? Or and embedded supernovae will lead to large occultation bias, do other factors which are not yet understood conspire to make and with extinction models plus Monte Carlo simulations this 44 Ti ejection a phenomenon of core collapse events occurring historic record can be assessed to approximately agree with ex- in special regions and environments? tragalactic rate determinations (see Sect. 3 and Appendix A.2). An often cited rate of galactic cc-SN of three per century is consistent both with astronomical arguments (van den Bergh 44 2.5. Estimating the Ti sky appearance & McClure 1990) and with the rate inferred by Timmes et al. 44 (1995) from their chemical evolution model that produces solar If we want to estimate how the Ti sky should appear in a abundances successfully. We adopt a supernova recurrence rate gamma-ray survey, we need to follow a statistical approach, 44 of 30 years as a baseline for our Ti sky expectations. due to the rare occurrence of supernovae. We therefore apply a Monte Carlo approach of sampling plausible probability distri- 44 butions for supernova rates, their Ti yields, and their Galactic 2.4. Supernova locations distribution, thus calculating a large statistical sample of possi- 44 ble appearances of the Ti sky. 44 The 1.157 MeV γ-ray line following Ti decay has been de- tected in the 340-year old Galactic supernova remnant Cas A – The mean rate of supernovae in our Galaxy is taken as one (Iyudin et al. 1994; Vink et al. 2001). COMPTEL’s survey event in 30 years. (Dupraz et al. 1997; Iyudin et al. 1999) has resulted in other 44 – Ti producing supernova events can be of type Ia, Ib/c, candidate sources, such as the so-called Vela junior SNR or II SNe. For this study, we choose a supernova type ra- (Iyudin et al. 1998). INTEGRAL’s inner-Galaxy survey has tio, Ia:Ib/c:II= 0.10:0.15:0.75 (Dawson & Johnson 1994; been studied with IBIS Imager data, which did not reveal a Hatano et al. 1997). new source in this region (Renaud et al. 2004). The difficulties 44 – Supernovae are then assumed to produce Ti according 44 of MeV observations have thus not led to convincing new Ti to models of that type. In our models, type II supernova rich supernova remnants, especially in the inner Galaxy region yields are generated according to stellar mass, which is ◦ ◦ (l = 0 ± 30 ) where observations are deepest. Yet, Cas A seems drawn from a Salpeter-type initial mass distribution for 44 an established Ti detection in COMPTEL (Schönfelder et al. 44 M ≥ 8 M⊙; the Ti yields per mass of the star are taken 2000) and Beppo-Sax (Vink et al. 2001) and INTEGRAL/IBIS from Table 1 of Timmes et al. (1996). A typical yield is (Vink 2005) measurements, while OSSE (The et al. 1996) −5 3 × 10 M⊙ for M = 25 M⊙, but variations with mass are and RXTE (Rothschild & Lingenfelter 2003) measurements 44 about a factor 2. The Ti yields of type Ib SNe are uni- of Cas A were not sufficiently sensitive. There exist no well- −5 −5 formly distributed between 3 × 10 M⊙ and 9 × 10 M⊙ understood supernova remnants other than Cas A where the −5 44 with typical values of 6 × 10 M⊙ (Timmes et al. 1996). Ti production issue can be tested. It is apparently the only su- 44 The Ti yields of type Ia SNe are uniformly distributed 44 pernova whose yield, age, and nearness makes Ti visible in −6 −5 between 8.7 × 10 M⊙ and 2.7 × 10 M⊙ so this range gammas. Naturally we ask ourselves if Cas A is a typical su- 44 covers the Ti yield in the deflagration W7 model, the 44 pernova or an anomalous case of a high- Ti yield supernova? delayed detonation WDD2 model, and the late detonation 44 Current supernova models predict an amount of Ti which W7DT model of Nomoto et al. (1997). But instead of 44 is of the same order than what these observations suggest, adopting the Ti ejecta masses directly from these mod- though generally slightly less. Can we take this as a satisfactory els, we uniformly increase these by a factor 3 in order that confirmation of our understanding of core collapse supernova chemical evolution calculations reproduce the known solar 44 44 40 44 44 Ti production? These two identified core collapse events and Ca/ Ca ratio. This assumes that Ti and Ca nucleosyn- 44 their association with Ti production appear to be in line with thesis are directly related and that some unknown physics 44 44 models which attribute Ti production to the more frequent factor causes the computed Ti masses to be uniformly low 44 L.-S. The et al.: Ti supernova remnants 1041 Fig. 2. The expected Ti sky of 10 simulated galaxies of model A where the supernova recurrence time is taken to be 30 years and the supernovae 5 −5 −2 −1 ratio of Ia:Ib:II = 0.10:0.15:0.75. Simulating a 10 galaxy sky, a gamma-ray detector with a detection limit of 10 cm s would have a 44 −5 −2 −1 probability of detecting 0, 1, and 2 Ti sources of 0.0017, 0.012, and 0.037, respectively. A slightly better instrument than the 10 cm s 44 detection limit would detect several Ti sources. 44 5 by a factor three. Note that Ti yields and supernova rate Randomly selected sample results from 10 such realizations 44 44 determine the brightness scale of our Ti sky expectations. of an expected Ti sky are shown in Fig. 2, to be compared – For each supernova type, we then adopt a parent spatial dis- with the observed 1.157 MeV COMPTEL image shown in tribution, from which we draw random samples to deter- Fig. 1 (Iyudin et al. 1999). We illustrate how typical these ex- mine the location of the event. The spatial distribution for pected images would be, by showing the distribution of source core-collapse supernovae (types Ib/c and II) is taken, from brightnesses over a much larger number of Monte Carlo sam- 44 either an exponential disk with scale radii between 3.5 and ples (Fig. 3, left): a Ti flux above a representative limit of −5 −2 −1 44 5 kpc, or from a Gaussian-shaped ring at 3.7 kpc radius 10 ph cm s occurs in 19% of our Ti gamma-line flux 44 with a thickness of 1.3 kpc, both placing young stars in the distribution. The expected number of Ti point sources per inner region of the Galaxy as suggested by many observ- galaxy lies above the gamma-ray survey sensitivity limit, i.e., 44 ables. Thermonuclear supernovae (type Ia) are assumed to we do expect typically 5–6 positive detections of Ti sources arise from an old stellar population, hence we adopt the (see Fig. 3 right). distribution of novae as our parent Galactic distribution for It is immediately evident from Figs. 2 and 3 that expecta- those rare events. We adopt the composite disk-spheroid tions based on such seemingly plausible assumptions look very 44 nova model from Higdon & Fowler (1987) (see Appendix different than the observed Ti sky: Fig. 2 shows ∼4–7 observ- 44 A for more detail on the variety of modeled distributions). able Ti sources in an area of the Galaxy that contained none – We then randomly choose the individual supernova age (see Fig. 1) above the observable flux limit used for compari- 44 within the last millennium, for deriving its Ti decay son. The brightest source in that realization (large-filled circles) −4 −2 −1 gamma-ray brightness. This assumes that the factors gov- has I γ ∼ 10 cm s , which would have been seen as a ∼10 σ erning the mean recurrence rate have not changed in the source by COMPTEL, and would have been detected already in 3 past 10 yr. INTEGRAL’s inner-Galaxy survey (Vink 2004). The majority of our calculated samples lead to this same type of conflict (see 44 1042 L.-S. The et al.: Ti supernova remnants 44 −12 −2 −1 Fig. 3. Cumulative Ti gamma-ray line flux distribution of supernovae with fγ >1×10 cm s according to our Model A (see Appendix 44 A.2) with supernovae type ratio of Ia:Ib:II = 0.1:0.15:0.75 (left). Expected average number of supernovae per sample galaxy with their Ti gamma-line fluxes above detection limits, for a supernova recurrence time of 30 yr, irrespective of their position in the sky (right). The detection limit of COMPTEL instrument is shown as a dotted line. – supernovae of each given type sample a relatively narrow 44 range of the Ti yield, i.e., we do not consider extreme outliers event (nor do we consider a rare but superhigh yield source class); – the locations of core collapse supernovae is axisymmet- ric i.e., we assume star formation in spiral arms is not dominant. In the following we examine these questions, and seek possible explanations for the apparent conflict. 44 3. Resolving the Ti sky conflict 3.1. Gamma-ray observations 44 The Ti gamma-ray sky can be studied in lines from the pri- Fig. 4. The longitude distribution of supernovae for four 44Ti gamma- mary decay to 44Sc at 67.9 and 78.4 keV and from the following ray line flux bandwidths in Model A of Appendix A.2 with supernovae 44 decay to Ca at 1.157 MeV. In this latter line, the COMPTEL type ratio of Ia:Ib:II = 0.1:0.15:0.75. The equal-bin width is 20 degrees 44 imaging telescope had reported the pioneering detection of Ti −6 −2 −1 in longitude. Only the fγ < 1×10 cm s distribution is normalized from Cas A (Iyudin et al. 1994), clearly showing a point source and multiplied by a factor of 0.298. image at 1.157 MeV as well as the line in a spectrum from this source. This detection had initially created some contro- versy because other gamma-ray instruments apparently did not Fig. 3). The probability of having no sources within the central see it (The et al. 1996; Rothschild et al. 1998). We now be- galaxy is small for current surveys, as illustrated in Fig. 4 (for −5 −2 −1 lieve that this is due to the high initially-reported COMPTEL model A): for a survey down to Iγ ∼ 10 cm s , ∼12% of su- ◦ gamma-ray flux value, reduced later with better statistical ac- pernovae appear within longitudes 0±60 , whereas only 72% of curacy of the measurement (Iyudin et al. 1999; Dupraz et al. supernovae is within that volume. An interesting feature, how- −5 −2 −1 1997). The independent detections with BeppoSax (Vink et al. ever, is that the longitude distribution for fγ < 1×10 cm s 2001) and with INTEGRAL/IBIS (Vink 2005) in both lower- is dominated by sources from type Ia (the bulge) and farther −5 −2 −1 energy lines (Beppo-SAX) and in the 67.9 keV line (IBIS) away SNe, while the distribution for fγ > 1 × 10 cm s 44 now consolidate the Ti detection from Cas A, but also sug- is dominated by sources from type Ib and type II (disk) and 44 gest that indeed the Ti gamma-ray flux of Cas A is in a nearby SNe. This feature also can be seen in Fig. 3, where −5 −2 −1 −5 −2 −1 range between 0.8 and 3.5 × 10 ph cm s ; an “average” around fγ ≃ 1×10 cm s the distribution changes its slope. −5 −2 −1 of (2.6 ± 0.4 ± 0.5)× 10 ph cm s has been derived (Vink It is clear that something is wrong with at least one of these 2005). An upper limit from INTEGRAL/SPI reported from first assumptions: studies is consistent with this flux value, and may suggest that 44 −1 – the rate of core collapse supernovae in the Galaxy is the Ti line is broader than 1000 km s (Vink 2005). 3/100 y; COMPTEL’s sky survey allowed for mapping of the −4 44 44 – a core collapse supernova produces ≃10 M⊙ of Ti; plane of the Galaxy in the Ti line (Dupraz et al. 1996; 44 L.-S. The et al.: Ti supernova remnants 1043 Iyudin et al. 1999). Secondary features in these COMPTEL should be rather well-behaved and useful for our study. Note 44 Ti maps kept the discussion about statistical significances and that the first inner-Galaxy survey from INTEGRAL (longitudes ◦ systematic uncertainties alive (see Schönfelder et al. 2000, for a of ±20 around the GC) (Renaud 2004) is consistent with our comparison of Cas A to RX J0852, a promising second source dataset in that also there no source is found to flux levels of −5 −2 −1 candidate, Iyudin et al. 1998). The COMPTEL point source 10 ph cm s (Renaud 2005). detection algorithm (de Boer et al. 1992) has been tested with simulations over the full sky: likelihood statistics has been veri- 3.2. Galactic supernova rate fied to reproduce the expected number of artificial sources for a full sky survey, as the noise level is approached. The problem is Many determinations of the galactic star formation rate (SFR) 44 that in the range of all the Ti gamma-ray lines, all gamma-ray and supernova rate (SNR) have been made in past decades (see telescopes suffer from a large background from local radioac- Diehl et al. 2005 for a compilation of estimates, and Stahler tivity induced by cosmic-ray bombardment of the instruments & Palla 2005 on general astrophysical aspects of star forma- (Gehrels & Michelson 1999; Weidenspointner et al. 2002). 44 tion). In this work we are concerned with the Ti from super- Determination of this background is crucial. For an imaging in- novae, so we need the formation rate of massive stars (above, strument, this can be done rather well by interpolation of imag- say, 10 M⊙). The conversion between SNR and SFR is a sen- ing signatures from adjacent energies. But furthermore, for sitive function of the Initial Mass Function (IMF), and values 44 COMPTEL the 1.157 MeV line of Ti is not far above its lower given in the literature thus vary depending on the author’s cho- energy threshold, and in fact imaging selections strongly affect sen IMF. For a generic transformation equation, we use the the sensitivity of the instrument up to ≃1.5 MeV. Nevertheless, calibration from McKee & Williams (1997): SFR= 196 SNR, imaging analysis in adjacent energy bands should all experi- −1 where the SFR is measured in M⊙ yr and the SNR in events ence similar problems, and therefore differences between im- −1 44 per year. A star formation rate of 4 M⊙ yr thus corresponds to ages in the Ti band and in neighboring energy bands can be a supernova rate of two events per century. These rates only in- 44 attributed to Ti rather than continuum sources or instrumental clude core collapse supernovae (type II and Ibc), but not SNIa. artifacts, once they are confirmed to be point-like sources (in- Generally these supernova rates are averages over time scales strumental background lines would in general spread over data 44 much longer than Ti decay. space and hence lead to extended or large-scale artifacts in the Many papers discuss the star formation (rate) history (SFH) image, hence impact on the flux measurement rather than on in relative terms, or the star formation rate surface density point source detection). Detailed comparisons of results for dif- −1 −2 (M⊙ yr kpc ) in the solar neighborhood and its radial depen- ferent energy bands, data subsets, and selections have led to the dence. None of these papers is useful (for our purpose) without more cautious report about the Vela-region source (Schönfelder 44 an absolute calibration, based on a model of the galactic distri- et al. 2000), so that still no convincing second Ti source bution of star formation. clearly above the noise level is claimed. The INTEGRAL lim- 44 Generically, the SFR is obtained from a tracer that can be its for Ti lines from the Vela region source are now close to corrected for observational selection effects and is understood the reported COMPTEL flux value for this candidate source well enough so that possible evolutionary effects can be taken (Renaud 2004; von Kienlin et al. 2004) and we therefore con- 44 into account. One either deals with a class of residual objects, sider only one single Ti source (Cas A) as being detected −5 −2 −1 such as pulsars or supernova remnants, or with reprocessed down to flux levels of 10 ph cm s . light, such as free-free, H-alpha, or IR emission that follows For the low-energy lines measured by other instruments, in from the ionization and heating of interstellar gas and its dust addition to the instrumental background the underlying contin- content in the vicinity of the hot and luminous stars. One must uum (see The et al. 1999 for Cas A) presents a major source be careful to include time-dependent effects, as the afterglow of uncertainty (see Vink et al. 2001; Vink & Laming 2003; of an instantaneous starburst behaves differently than the steady Vink 2005). This becomes even more of a problem for recom- 44 state output from a region with continuous star formation. Here, bination line features from Sc at 4.1 keV, which have been we are concerned with an average star formation rate. studied with ASCA (Tsunemi et al. 2000; Iyudin et al. 2005), yet without clear detections (though tantalizing hints have been To set the stage, let us collect SFR values from the lit- −1 discussed for the Vela-region source). erature. Smith et al. (1978) concluded SFR= 5.3 M⊙ yr , 44 −1 For our quantitative comparisons of the Ti supernova rate while Talbot (1980) finds a very low value SFR= 0.8 M⊙ yr , with the historical record of supernovae in the last millen- and Guesten & Mezger (1982) report a very high value of −1 nium (see Appendix B.2), we make use of the COMPTEL SFR= 13.0 M⊙ yr . Later papers appear to converge on a −1 survey. We avoid the regions where reduced exposure might median value: Turner (1984) finds SFR= 3.0 M⊙ yr , and −1 eventually lead to increased artifact levels, and concentrate on Mezger (1987) finds 5.1 M⊙ yr . Measurements in the past the inner Galaxy where exposure for the COMPTEL sky sur- decade confirm this moderate rate: McKee (1989) derives −1 vey is deep and homogeneous. We also avoid using data af- SFR= 3.6 M⊙ yr from the analysis of thermal radio emission ter the second re-boost of the satellite, whereafter the activa- (free-free) from HII regions around massive stars. This emis- 22 tion level of Na had increased substantially (Weidenspointner sion is directly proportional to the production rate of ionizing et al. 2002). This leaves us with a dataset covering the sky photons, which in turn is directly proportional to the SFR. He ◦ ◦ range of |l| ≤ 90 , |b| ≤ 30 using 7 years of the 9-year sky pointed out that this method is very sensitive to the slope of 44 survey. In these gamma-ray data, the Ti source sensitivity the high-mass IMF. We also note that the method depends on 44 1044 L.-S. The et al.: Ti supernova remnants stellar model atmospheres in conjunction with models for mas- limit). The OB-star catalog of the author was used to perform sive stars, which change with treatments of mass loss, rotation, a modified V/Vmax test to obtain a present-day star count as and convection. This paper also briefly discusses the use of the a function of absolute V-band magnitude. From the stellar life far-IR luminosity, due to warm dust heated by the absorption of times, and the assumption of steady state, the local birthrate fol- photons from massive stars. The author uses the measured IR lows. A double exponential model (in galactocentric radius and 9 luminosity of the Galaxy of 4.7 × 10 L⊙ (from Mezger 1987) scale height above the plane) of the spatial distribution of these −1 to derive SFR=2.4 M⊙ yr . stars (which includes an inner hole of radius R = 4.25 kpc) We must convert between star formation rate (SFR) and ultimately leads to a total birthrate of 1.14 OB stars per cen- supernova rate (SNR) (see above). McKee & Williams (1997) tury. Variations in the size of the hole change this number −1 promote the value SFR= 4.0 M⊙ yr , and based on the Scalo’s significantly, which leads the author to finally claim a rate of IMF (Scalo 1986) convert this rate into a total number rate 1–2 supernovae per century. of 7.9 stars per year. They assume that all stars above 8 M⊙ In the context of our interpretation of the 44Ti observa- become supernovae, corresponding to a supernova fraction of tions, we would argue that Supernova rates between one and −3 2.6 × 10 . The mean stellar mass is ⟨m⟩ = 0.51 M⊙. The three cc-SNe per century are consistent with the large set of corresponding cc-SN rate is 2 per century. This value is also 44 studies reviewed above. To solve the Ti Sky conflict with supported by a completely independent method, based on the a choice of the SNR (or SFR), an extremely low rate outside 26 production of radioactive Al in cc-SNe, which can be traced 44 this range would of course explain the absence of Ti gamma- though its gamma-ray line at 1.809 MeV. Timmes et al. (1997) ray line sources in the sky. However, chemical evolution ar- −1 use this method and conclude SFR= (5 ± 4) M⊙ yr , utilizing guments for 44Ca would then require correspondingly higher 26 the Al line flux derived from COMPTEL. The steady-state 44 Ti yields which are not supported by explosive nucleosynthe- 26 mass of Al obtained in their work is in the range 0.7–2.8 M⊙, sis studies (as discussed below) and which in any case would consistent with the value presented in the recent study by Diehl lead to higher fluxes from supernova remnants and thus again to et al. (2005). Based on the Salpeter IMF in the range 0.1– a source count that exceeds the observed count of ∼1. The ob- 26 40 M⊙ and the Al yields from Woosley & Weaver (1995) servational constraints are on the product of rate and yield. The [which do not include contributions from the Wolf-Rayet wind natural solution to the problem may be the very rare events with phase] the authors derive the above quoted SFR and an asso- extremely high yields, which is discussed below. In that case it ciated cc-supernova rate of 3.4 ± 2.8 per century. They ne- is of course totally unclear what to use for the spatial distribu- 26 glect hydrostatically produced Al that is injected into the ISM tion of these events, and “unusual” positions of a gamma-ray in massive star winds, which causes their SFR to be overesti- line source on the sky (such as that of Cas A) would be hard to mated. The large uncertainty is mostly due to the steady-state interpret. 26 mass of Al inferred from the COMPTEL flux. INTEGRAL But perhaps we have overlooked another option. We know data presented by Diehl et al. (2005) have significantly reduced that the galactic star formation process is strongly correlated the error in this key quantity, and with wind yields included in space and time (Elmegreen et al. 2003). Could it be that the the latter study finds SNR=1.9 ± 1.1 supernovae per century, Galaxy just had a brief hiatus in its SFR? It would not take too −1 which corresponds to SFR= 3.8 ± 2.2 M⊙ yr , similar to the much of a pause (say a few centuries) to explain the absence of value given in McKee & Williams (1997). This SFR is very 44 bright Ti sources if the past few centuries were very untypical similar to the one obtained for M 51 (Calzetti et al. 2005), and with respect to the SFR (or SNR). This possibility is included thus places the Galaxy in the group of quiescently star-forming in our Monte Carlo simulations, which show that this is not a galaxies. likely solution when one simply considers Poisson fluctuations. The most recent paper addressing this issue is by Reed This solution is thus not acceptable, unless one can point out a (2005), who does not derive the SFR, but states that the galactic physical cause of the hiatus in the recent SFR. supernova rate is estimated as probably not less than 1 nor more than 2 per century. Using the conversion factors from McKee & Williams (1997), one infers that the SFR is in the range 3.3. Galactic supernovae locations −1 2–4 M⊙ yr . Reed uses a sample of a little over 400 O3-B2 dwarfs within 1.5 kpc of the Sun to determine the birthrate of Likewise, we may wonder about the possibility of very large stars more massive than 10 M⊙. The galaxy wide rate is derived spatial fluctuations. Could it be that the recent Galaxy ex- from this local measurement by extrapolation based on models hibits an average star formation, rate-wise, but a lopsided dis- for the spatial distribution of stars, a model for galactic extinc- tribution in space. If the opposite side of the Galaxy currently tion (to accomplish corrections for stellar magnitudes), and a forms stars, and regions in the solar sector are relatively in- ◦ model of stellar life times. Reed emphasizes various sources of active (l = 90−270 ), we expect to detect fewer gamma-ray errors, such as lacking spectral classifications of some bright line sources (because of their somewhat larger average dis- OB stars, the (poorly known) inhomogeneous spatial structure tances). But at the same time the supernovae would also suf- of extinction as well as stellar density, and non-unique connec- fer from enhanced extinction, and matching the historic SN tion between mass and spectral type. Finally, Reed also draws record would require a much higher rate. We have simulated attention to the fact that one would have to include B3 dwarfs the effects of a lopsided profile with a von Mises Distribution, as well, if the lower mass limit for supernovae is 8 M⊙ and the analog of a Gaussian distribution for circular data (Mardia not 10 M⊙ (see Heger et al. (2003) for comments on this mass 1975; Fisher 1996). This function allows us to change from an 44 L.-S. The et al.: Ti supernova remnants 1045 axis-symmetric galactic distribution to a one-parameter distri- implemented by Hakkila et al. (1997) in addition to some other bution (measured by a parameter k, where k = 0 corresponds to restricted surveys. However this extinction map is reliable only the uniform circular distribution) in a chosen direction which for solar neighborhood within 6 kpc. Another large scale three- ◦ we choose it to be the longitude l = 0 direction. We re- dimensional model of Galactic extinction based on the Galactic 5 simulated the 10 Galaxies sample as described in Sect. 2.5, dust distribution of Drimmel et al. (2003) has been shown to and find that the detection probabilities (stated in the caption give a good agreement with the empirical extinction derived of Fig. 2) change to 0.0042, 0.023, and 0.062 for parameter from NIR color–magnitude diagrams within 0.05 mag and fur- k = 0.5 and 0.0068, 0.035, and 0.087 for parameter k = 1.0, thermore it is reliable for a distance up to ≃8 kpc. This extinc- 44 respectively. The probability curves for Ti γ-line source de- tion model gives a larger magnitude of extinction than that of ◦ tection (see Fig. B.4) are shifted towards higher rates, as ex- Hakkila et al. (1997) for longitude |l| ≤ 1.5 and for most point- pected, but the overall likelihood of these models decreases. ing directions from the Sun for distance larger than 6 kpc. For The constraint from the historic record demands new rates that distance less than 5 kpc, the extinction of this map is smaller are even larger, as the extinction correction affects the results than that of Hakkila et al. (1997) which could give a better −2 more strongly than the D distance effect for the flux. The agreement between the SN rates of the historical record and of combination of these two constraints make lopsided models the COMPTEL’s gamma-ray map. less acceptable than axis-symmetric ones. A lopsided model would also make Cas A even more spe- 3.5. The SN model cial, regarding its unexpected location on the sky. To alleviate this problem we simulated lopsided star-forming galaxies in 44 3.5.1. Lifetime of Ti which the solar sector was the more active. The detection prob- 44 44 abilities of 0, 1, and 2 Ti sources of this model are 0.0005, Although the lifetime of Ti measured in laboratories had ex- 0.003, and 0.012 for parameter k = 1.0, respectively. This hibited a large uncertainty since its first measurement in 1965, 44 shows that the number of the most probable Ti γ-line source a compilation of five recent experiments performed after 1998 detection in the Galaxy is >2 detections and the model is less gives an averaged lifetime of 87 ± 1 yr, where the quoted error probable than the model used for Fig. 2 for consistency with is of statistical and of one standard deviation (see, e.g., Fig. 5 of 44 the observed Ti sky. Hashimoto et al. 2001 and also Görres et al. 1998). Apparently, 44 Is it reasonable at all to consider one-sided star forming this small uncertainty in the measured Ti lifetime does not galaxies? That major merger events should be able to tidally affect the discrepancy discussed here. induce a lopsided starburst activity is perhaps obvious, but the It is noted that the above-mentioned lifetime measured in 44 Galaxy is not undergoing such an event. However, Rudnick laboratories is for neutral atoms. Since Ti is a pure orbital- et al. (2000) have shown that even minor mergers (Ibata et al. electron-capture decay isotope, its lifetime depends on the elec- 1995) generically termed “weak interactions” may lead to a tronic environment in the evolutional course of a supernova 44 boost in the star formation rate correlated with their lopsid- remnant. For example, a fully-ionized Ti is stable, and the 44 edness. Another mechanism for the creation of non-symmetric lifetime of Ti in the Hydrogen-like ionization state becomes 44 star formation patterns is the interaction between odd numbers longer by a factor of 2.25 than that of the neutral Ti (see of spiral density waves, as it may be at work in M 51 (Henry Motizuki & Kumagai 2004). Let us briefly consider the effect 44 et al. 2003). We do not advocate such an asymmetry for our of Ti ionization on our problem. Galaxy, but just wanted to consider this real possibility as one In young supernova remnants, the reverse shock propagates 44 of the potential fixes for the Ti sky problem. Our simulations inward through the ejecta and the resulting increase in temper- indicate that even such an extreme solution does not work, as ature and density may lead to highly ionized ejecta material the various combined constraints operate against each other. through thermal collisions with free electrons. A high-degree While a lopsided Galaxy helps on the gamma-ray source count 44 of ionization may then result in a longer lifetime of Ti, which side, the historic record is harder to explain if recent supernovae 44 would significantly alter the inferred Ti mass. In fact, H-like are located preferentially on the far-side. and He-like Fe ions have been observed in Cas A (see, e.g., Hwang et al. 2004). Because the electron binding energies of Ti are smaller than those of Fe, it is easier to ionize Ti than Fe. 3.4. Galactic extinction map 44 Accordingly, Ti atoms in Cas A may be expected to be in such high ionization states at least in part if they are accompa- Analyzing the consistency of the supernova rates derived from 44 nied by the highly ionized Fe (this is expected because Ti is the Galactic historical record and the COMPTEL’s gamma- 56 synthesized at the same location as where Ni is also produced ray map (Appendix B.4), the consistency would improve if the in the innermost region of a supernova). SN rate from historical record is smaller. This could be real- ized if the true Galactic extinction map is lower than the vi- Since the present-day radioactivity was entirely affected sual extinction map we used here. Recently there are two pub- by the history of various ionization stages and their dura- 44 lished Galactic extinction maps that are useful for the type of tion time for which the Ti has experienced through the evo- study of this paper. The optical reddening model of Mendez lution, detailed discussion requires numerical simulations as & van Altena (1998), which is based on Galactic dust dis- was done by Mochizuki et al. (1999) and Mochizuki (2001). tribution model, makes use of the same optical sky surveys However, we can get a rough idea of the ionization effect on the 44 1046 L.-S. The et al.: Ti supernova remnants radioactivity by using the result of simple linear analysis, i.e., individual rates varied upwards and downwards by a factor of Eq. (7) of Motizuki & Kumagai (2004): 100 from their reference values. The results were that the pro- 44 duction of Ti was most sensitive to the rates for the follow- ∆Fγ/Fγ = (t/τ − 1)∆τ/τ, (1) 44 47 12 44 48 ing reactions: Ti(α, p) V, α(2α, γ) C, Ti(α, γ) Cr, and 45 46 where we have replaced the radioactivity A and the decay rate λ V(p, γ) Cr for matter with equal numbers of neutrons and appeared in Eq. (7) of Motizuki & Kumagai (2004) with the γ- protons (η = 0). For neutron excess η greater than zero, the 44 45 46 ray flux Fγ and the Ti lifetime τ, respectively. In Eq. (1), t is importance of the reaction V(p, γ) Cr drops, but other reac- the age of a SNR, ∆Fγ is the change of the flux by ionization, tions become more important. In particular, these reactions are 12 16 40 44 27 30 30 33 ∆τ is that of the lifetime. C(α, γ) O, Ca(α, γ) Ti, Al(α, n) P, and Si(α, n) S. Note that ∆τ is always positive because the ionization al- For our purposes, the relevant question is how much the ways increases its lifetime. As was pointed out by the above 44 Ti may vary from current supernova models given these authors, the sign of ∆Fγ is then determined by that of the term uncertainties. Motivated by the work of The et al. (1998), in the parenthesis in the right-hand side of Eq. (1). This means Sonzogni et al. (2000) measured the cross section for the that the flux is enhanced by the ionization when a SNR is older 44 47 Ti(α, p) V reaction at the astrophysically relevant energies. 44 than the Ti lifetime, and that the flux is reduced when it is They found that the experimental cross section for this reac- younger. tion was a factor of two larger than in the rate compilation of Our concern here is whether the effect of ionization on the Thielemann et al. (1987) used in the The et al. (1998) calcula- 44 lifetime of Ti in SNRs can reduce the disagreement between tions. From this result, Sonzogni et al. (2000) inferred a 25% 44 the observed Ti Galactic map and the model’s map or not. 44 reduction in the amount of Ti produced in alpha-rich freeze- From the above arguments, we can easily understand that the outs in supernovae. Other of the key reactions found by The discrepancy may be diminished if the γ-line fluxes in Fig. 2 44 et al. (1998) had similar sensitivities of Ti yield to reaction could be smaller which may be realized if most of the γ-ray rates; therefore, if other experimental reaction rates are also 44 detected SNRs in Fig. 2 are younger than the Ti lifetime. a factor of ∼2 different from the theoretical calculations, we To get a rough idea, we performed a calculation in which 44 can expect similar ∼25% effects on the Ti yield. From these all parameters are the same as employed for Fig. 2 except 1) 44 results, we might thus conservatively expect the Ti yield to the fluxes are multiplied by a factor 0.5 for SNRs with ages be uncertain by less than a factor of ∼2 due to reaction rate less than 100 y, and 2) the fluxes are multiplied by a factor 2 uncertainties. Such a conclusion is supported by the study of for SNRs with ages between 200 and 400 y. The selection of the reaction rate sensitivity of nucleosynthesis yields in core- 200–400 years old SNRs as enhanced targets here is because the collapse supernovae by Hoffman et al. (1999). These authors effect of the ionization due to the reverse shock is considered compared the yields from core-collapse supernova models us- to be distinguished for these ages and the further inclusion of ing two different reaction rate libraries. For the 15 M⊙ stellar the enhanced-flux effect on SNRs older than 400 y only makes 44 model studied, the two calculations gave Ti yields that agreed the discrepancy larger (see Mochizuki et al. 1999 for details). to within 20%, in spite of the fact that many individual nuclear 5 Simulating a 10 galaxy sky, we found that a γ-ray detector reaction rates differed by a factor of two or more between the −5 −2 −1 with a detection limit of 1 × 10 ph cm s would have a two rate compilations. 44 probability of detecting 0, 1, 2 Ti sources of 0.0012, 0.008, On the other hand, Nassar et al. (2005) have recently mea- and 0.026, respectively. Therefore, from this simple analysis it 40 44 sured the Ca(α, γ) Ti reaction cross section in the energy is suggested that the disagreement cannot be compensated by range for nucleosynthesis in supernovae. In that energy range, the ionization effect; in effect it becomes worse in our simple the authors find that the reaction rate is 5–10 times larger than calculations above than the reference calculations of Fig. 2. the previously used theoretical rate calculated from a statistical A more precise estimate requires the knowledge of the tem- model (Rauscher et al. 2000). This large difference between perature and the density evolution of a supernova remnant, and 44 the experimental rate and the theoretical rate may be due to the the distribution of Ti in it. However, any detailed calculations 44 fact that the low level density in the Ti compound nucleus 44 taking into account the retardation of Ti decay due to ion- limits the applicability of the statistical model for theoretical ization will not alter the situation better: in any case, the older predictions for the rate of this reaction. In any event, the larger SNRs whose fluxes may be enhanced always dominate in num- 44 rate increases the yield of Ti by a factor of ∼2 in the stellar ber the younger SNRs whose fluxes may be decreased. models Nassar et al. (2005) explored. Such a large increase in 40 44 the Ca(α, γ) Ti reaction rate may allow normal core-collapse 44 3.5.2. Nucleosynthesis reaction rates supernovae to account for the solar system’s supply of Ca; however, this result would worsen the discrepancy between the 44 Estimates of yields of Ti from nucleosynthesis in super- 44 observed Galactic Ti gamma-ray flux and our predictions. novae depend crucially on key nuclear reaction rates, and uncertainties in these rates limit our ability to constrain the supernova rate. The et al. (1998) studied the sensitivity of 3.5.3. The supernova explosion model 44 Ti yields in alpha-rich freezeouts to uncertainties in nu- 44 clear reaction rates. They did this by computing the alpha- In core-collapse supernovae, Ti production occurs by the rich freezeout with reference values for the reaction rates and alpha-rich freezeout near the mass cut. The location of the mass 44 then comparing these results with ones from calculations with cut in the star will then certainly affect the Ti yield. Also