Revisiting INTEGRAL/SPI observations of 44Ti from Cassiopeia A
Thomas Siegert, Roland Diehl, Martin G. H. Krause, Jochen Greiner
AAstronomy & Astrophysics manuscript no. CasA˙44Ti˙revisit˙2.6.2˙arxiv c (cid:13)
ESO 2018July 26, 2018
Revisiting INTEGRAL/SPI observations of Ti from Cassiopeia A
Thomas Siegert (cid:63) , Roland Diehl , , Martin G. H. Krause , , , and Jochen Greiner , Max-Planck-Institut f¨ur extraterrestrische Physik, D-85741 Garching, Germany Excellence-Cluster “Origin & Structure of Universe”, D-85748 Garching, Germany Universit¨ats-Sternwarte Ludwig-Maximilians-Universit¨at, D-81679 M¨unchen, GermanyReceived February 12, 2015; accepted May 20, 2015
ABSTRACT
Context.
The 340-year old supernova remnant Cassiopeia A, located at 3.4 kpc distance, is the best-studied young core-collapsesupernova remnant. Nucleosynthesis yields in radioactive isotopes have been studied with di ff erent methods, in particular, methodsfor production and ejection of Ti and Ni, which originate in the innermost regions of the supernova. Ti was first discovered inthis remnant, but is not seen consistently in other core-collapse sources.
Aims.
We aim to measure radioactive Ti ejected in Cassiopeia A and to place constraints on velocities of these ejecta by determiningX- and γ -ray line-shape parameters of the emission lines. Methods.
We analyzed the observations made with the SPI spectrometer on INTEGRAL together with an improved instrumentalbackground method, to achieve a high spectroscopic resolution that enables interpretation for a velocity constraint on Ti ejecta fromthe 1.157 MeV γ -ray line of the Sc decay.
Results.
We observe both the hard X-ray line at 78 keV and the γ -ray line at 1157 keV from the Ti decay chain at a combinedsignificance of 3.8 σ . Measured fluxes are (2 . ± .
4) 10 − ph cm − s − and (3 . ± .
2) 10 − ph cm − s − , which corresponds to(1 . ± .
4) 10 − and (2 . ± .
9) 10 − M (cid:12) of Ti, respectively. The measured Doppler broadening of the lines implies expansionvelocities of 4300 and 2200 km s − , respectively. By combining our results with previous studies, we determine a more preciseestimate of ejected Ti of (1 . ± .
19) 10 − M (cid:12) . Conclusions.
The measurements of the two lines are consistent with previous studies. The flux in the line originating from excited Ca is significantly higher than the flux determined in the lines from Sc. Cosmic-ray acceleration within the supernova remnantmay be responsible for an additional contribution to this line from nuclear de-excitation following energetic particle collisions in theremnant and swept-up material.
Key words. (Stars:) supernovae: individual: Cas A – Nuclear reactions, nucleosynthesis, abundances – Stars: massive – ISM: super-nova remnants – Gamma rays: ISM – Techniques: spectroscopic
1. Introduction
Cassiopeia A (Cas A) is the closest young remnant of a core-collapse supernova and therefore a prominent study object inmany wavelength regimes. It may have been seen in AD 1680by Flamsted (Ashworth 1980; Green 2002), but was not as brightas expected from its proximity of 3.4 + . − . kpc (Reed et al. 1995).Apparently, the supernova itself was occulted by interstellar dustand gas, and its brightness and Ni production are therefore onlyinferred indirectly (Eriksen et al. 2009). The date of the event isnot precisely settled; Thorstensen et al. (2001) inferred the su-pernova event at AD 1671.3 ± Ti decay had been reported (Iyudinet al. 1994); this line arises from de-excitation of Ca, thefinal daughter nucleus in the decay chain Ti → Sc → Ca.Later measurements focused on the equally bright lines fromthe first stage in the Ti decay chain, the de-excitation of Sc.In particular, the studies with INTEGRAL / IBIS (Renaud et al.2006) and NuStar (Grefenstette et al. 2014) settled the amountof Ti to (cid:39) − M (cid:12) (IBIS: 1.6 + . − . − M (cid:12) ; NuStar: (cid:63) E-mail: [email protected] (1.25 ± − M (cid:12) ). This is significantly higher than the yieldspredicted for typical supernova models, which suggested thatCas A represents a rare subclass of Ti ejecting supernovae, andexplosion asymmetries have been thought to cause such anoma-lies (Nagataki et al. 1998; The et al. 2006). The Ti image re-cently obtained by the NuStar hard X-ray telescope (Grefenstetteet al. 2014) has shown that Cas A ejecta carrying Ti appearin clumps, re-a ffi rming that Cas A did not explode as a spheri-cally symmetric supernova. Other observations had shown thisbefore from X-ray measurements, for example, and especiallyfrom optical / IR light echo spectra, revealing this asymmetry inthe supernova photosphere. Furthermore, it was shown by theselight echoes that Cas A exploded as a type IIb supernova (Krauseet al. 2005, 2008; Rest et al. 2008, 2011, see also discussionby Wheeler et al. (2008)).Earlier gamma-ray spectroscopy with INTEGRAL / SPI hadprovided some velocity constraints on the radioactive ejectafrom the inner supernova, with a lower limit on Ti ejecta of500 km s − from a nondetection of the high-energy line at 1.157MeV, which was attributed to Doppler broadening (Martin et al.2007). Doppler broadening is proportional to photon energy;therefore, a background dominated measurement such as withSPI would be more sensitive to a low-energy line, while thehigh-energy line would drown in the background, especially ifpart of the Ti ejecta were moving at high velocities. NuStardetectors also provide a su ffi ciently high spectral resolution for a r X i v : . [ a s t r o - ph . H E ] J u l homas Siegert et al.: Revisiting INTEGRAL / SPI observations of Ti from Cassiopeia A velocity information. Grefenstette et al. (2014) reported an over-all velocity of fastest Ti clumps of (5350 ± − ,simultaneous to a bulk line-of-sight velocity in the range of2000 km s − . The NuStar result is only based on the detection ofthe 68 keV line, although both hard X-ray lines have been mea-sured. Our recently improved method for handling instrumen-tal background suggested re-analysis of INTEGRAL data fromCas A with the aim to revisit and refine velocity constraints fromhigh-resolution spectroscopy with the SPI instrument of all threelines resulting from the Ti decay chain. Ti and Ni arise from nuclear burning in the innermostparts of supernovae very close to the mass-cut separating ejectafrom the compact remnant (Diehl & Timmes 1998). Therefore Ti and Ni are expected to also be co-spatial when they de-cay in the expanding SNR (The et al. 1998; Ho ff man et al.2010; Magkotsios et al. 2010). But as this inner region is prob-ably characterized by dynamical instabilities and simultaneousinflows and outflows of material, it remains unclear how andwhere this separation between material accreting onto the com-pact remnant and the ejecta occurs, and thus how much of the Ti can end up in the ejecta (Fryer et al. 2008; Wongwathanaratet al. 2013; Popov et al. 2014). Ni radioactive decay occurs with a first decay to Co after τ (cid:39) ffi ciently dense to absorb even gamma-rays at MeV ener-gies and convert this radioactivity energy into thermal emission,which makes supernovae shine at UV to IR wavelengths (Isernet al. 2008; R¨opke et al. 2012). As the supernova envelope be-comes more transparent, fewer gamma-rays thermalize, in par-ticular when the second decay stage from Co to Fe at τ (cid:39) Ti has a considerably longerdecay lifetime, and thus gamma-rays will escape readily. Tidecays to Sc within τ (cid:39)
86 years (Ahmad et al. 1998; G¨orreset al. 1998; Norman et al. 1998; Wietfeldt et al. 1999; Hashimotoet al. 2001; Ahmad et al. 2006). In this first decay stage, gamma-rays of 67.87 and 78.36 keV are emitted. The subsequent decayof Sc to Ca occurs after τ (cid:39) β + decays.For SN1987A, this has been investigated: The study of thelate light-curve in SN1987A (Lundqvist et al. 2001; Fransson& Kozma 2002; Jerkstrand et al. 2011) obtained an inferred Ti mass from optical and infrared spectra of SN1987A to(1.5 ± − M (cid:12) . The Ti that mainly powers the late light-curve (years after the explosion) has a direct e ff ect on the to-tal absolute flux level of the optical-to-infrared spectra, but alsodepends on the estimated extinction. Corresponding gamma-rayemission has recently been detected by Grebenev et al. (2012)with IBIS; this direct measurement constrained the Ti massof SN1987A to (3.1 ± − M (cid:12) (see, however, Seitenzahlet al. (2014), who obtained (0.55 ± − M (cid:12) from a de-tailed, multi-component light-curve model). Beyond SN1987A,the Cas A SNR is the only other core-collapse event where thisconsistency between nucleosynthesis radioactive elements andobserved emission can be studied. Fig. 1.
Exposure map of the sky with the SPI telescope onINTEGRAL for the data used in this analysis (Mar 2003 –Jan 2014). Cas A is marked with a star at its position ( l / b ) = (111 . ◦ / − . ◦ ). The total exposure time in the PCFOV is10.84 Ms, while Cas A was seen fully coded within an exposureof 5.15 Ms.
2. Data and analysis
The INTEGRAL space gamma-ray observatory (Winkler et al.2003) carries the spectrometer instrument SPI as one of its twomain instruments, measuring gamma-rays in the energy rangeof 20 keV to 8 MeV with a spectral resolution of ∼ . ∼ ◦ steps in a certain sky region around the targetof interest. For our analysis, we used exposures in which CasA was at least in the partially coded field of view (PCFOV) ofSPI of 34 ◦ × ◦ accumulated over almost eleven years of theINTEGRAL mission. Solar flares mainly a ff ect the backgroundrate and are di ffi cult to model. We therefore excluded data of anyorbit in which a solar flare occurred until the overall backgroundreturned to normal. Perigee passages around Earth, involvinga higher radiation dose when the satellite is passing the VanAllen radiation belts, additionally a ff ect the background rate,and we consequently chose data from orbital phases [0 . , . / SPI observations of Ti from Cassiopeia A quacy of the fit (mainly background) and the scientific question(sky components). Hence, data d k of energy bin k are modeledas a linear combination of the N I sky model components M i j asconvolved with the instrument response matrix R jk , and the N B background components B jk : d k = (cid:88) j R jk N I (cid:88) i = θ i M i j + N I + N B (cid:88) i = N I + θ i B jk . (1)The comparison between scaled models and measurements isperformed in data space, which consists of the counts per energybin k measured in each of the SPI detectors j for each single tele-scope pointing as part of the complete observation. Our adoptedsky intensity distribution for Cas A is a point source, given theSPI imaging resolution of 2.7 degrees and the total SNR diam-eter of ∼ . Sc, to be the same as for the high-energy line (1157 keV)from excited Ca. For example, cosmic-ray (CR) collisions withambient Ca at several tens of MeV / nucleon e ff ectively pro-duce nuclear excitation, followed by de-excitation photons at1.157 MeV. Because Sc is short lived, no corresponding excita-tion of Sc will occur through this cosmic-ray process, meaningthat no additional emission is produced in the 68 and / or 78 keVlines. We therefore treat the hard X-ray lines and the gamma-rayline indepedently. In earlier SPI analyses, the detailed background line informa-tion was neglected or used only indirectly as background trac-ers, obtained from cosmic-ray intensity variations or from adja-cent energy bands, for example. These were separately adjustedby a set of fit parameters for each energy bin in the measuredspectra (Wang et al. 2007, 2009). To improve the spectroscopicsensitivity compared to previous SPI analysis results, we im-plemented a new approach for modeling the instrumental back-ground.We now investigate the spectroscopic signatures of nuclearreaction physics that occur in the instrument and satellite in greatdetail by separately tracking the shape and intensity variationsof characteristic lines in each Ge detector. First, a high-precisioncumulative spectrum is used in the two energy bands, rangingfrom 60 keV to 85 keV, and from 1143 keV to 1175 keV, re-spectively, to also identify the weak instrumental line signatures.Then, a three-day integration is used to obtain su ffi cient statis-tical precision to determine spectral shape parameters of eachidentified background component for all detectors by fitting thespectra using a Metropolis-Hastings algorithm in a Monte CarloMarkov chain. We then fix the shapes of the spectral templatesduring one orbit of the selected data set and scale the ampli-tude of each component for the entire Ge camera by pointingto properly trace intensity variations of each background com-ponent. Long-term investigations showed that the relative inten-sities of a particular spectral background feature present in onedetector with respect to the mean intensity of the same featurein all detectors (detector ratios) are constant in time and thus aremaximally independent of possible celestial signals (Diehl et al. 2014, 2015) . Therefore, the spectral shape and detector ratioconstancy that is expected for each individual background com-ponent is imprinted onto the short-term (pointing-to-pointing)variations, while the mean amplitude (over all detectors) of aparticular spectral feature is still allowed to vary to normalizethe predicted background count rate.In principle, each background component may have its ownproperties, and in particular, detector-to-detector intensity ratio,but we clearly identify physically plausible classes: Ge back-ground lines provide a higher count rate in the inner Ge detec-tor elements which are surrounded by Ge, while Bi backgroundlines provide a lower count rate in the inner Ge detector elementsbecause the BGO anticoincidence shield surrounds the Ge cam-era. For details see Siegert et al., in preparation (2015).The instrument spectral response is represented as a pa-rameterized semi-analytic function, that is, the convolution ofa Gaussian with an exponential tail toward lower energies to de-scribe the line shape. The spectral model we use in our line fit-ting consists of a linear continuum C j ( E ; C , j , C , j ) = C , j + C , j · E (2)and a set of instrumental lines at positions E , i j , which areneeded to characterize the spectrum. Each Gaussian line iG i j ( E ; A , i j , E , i j , σ i j ) = A , i j · exp − ( E − E , i j ) · σ i j (3)is convolved with an exponential tail function T i j ( E ; τ i j ) = τ i j exp (cid:18) − τ i j E (cid:19) (4)that describes the impact of cosmic radiation that gradually de-teriorates the charge collection e ffi ciency of each detector j . Theraw spectra of SPI are background dominated; the instrumentalbackground is more than 99% of the total, with a small contri-bution from a celestial signal. Fitting the raw spectra for eachdetector and a three-day cumulative sample results in a very pre-cise spectrum of what is observed from instrumental backgroundgamma-ray lines and continuum. This ”continuum” includes theinstrumental background continuum ( > ff set from zero in the finally derivedspectra can be considered as a measure of systematics of thiscontinuum treatment. For each energy bin, a discrete backgrounddetector pattern (in time and position in the sky) is predicted,which serves as the only background component B jk in Eq. (1).The degradation of Ge detectors from cosmic-ray irradiation andtheir restoration in annealings results in a time-variable widthand asymmetry of the spectral response. This variation domi-nates all other spectral changes and is found consistent acrossthe SPI energy range.
3. Results and discussion Ti gamma-ray line measurements
Our analysis shows the expected signature of a (Gaussian-shaped) line at the expected energies for the two independent This is true for the time during one camera configuration. Withinthese 11 years of data, 4 detectors out of 19 have failed in flight, thusleading to a new camera configuration - in total, five di ff erent configu-rations. 3homas Siegert et al.: Revisiting INTEGRAL / SPI observations of Ti from Cassiopeia A spectra. The significances of the lines are 2.2 σ (1157 keV)and 3.1 σ (78 keV), with a combined Ti detection signifi-cance of 3 . σ . Unfortunately, systematic e ff ects due to strongbackground features below 70 keV cannot be reliably modeled;therefore no constraint on the 68 keV line could be obtained.The mean reduced χ of the derived fit per energy bin is 1.06( χ = = (cid:39) ± .
6) keV and broadened with respect to theinstrumental resolution. We obtain a total flux of F = F l u x [ − ph c m − s − k e V − ] c t s b i n − Fig. 2.
Spectrum obtained from a source at the position of Cas Aat 1157 keV (black crosses, 2.5 keV energy bins). The spectrumhas been fitted by a constant plus a Gaussian that is centered at(1158 ± .
6) keV and broadened (8 . ± .
42) keV (FWHM).The derived expansion velocity of the Ti ejecta is (2200 ± − . The measured flux is (3 . ± .
2) 10 − ph cm − s − , which can be converted to an observable Ti mass of(2 . ± .
9) 10 − M (cid:12) at the time of the explosion. The cumula-tive long-time spectrum (mainly background) is shown as a grayhistogram. The laboratory-determined energy of the excited Caline is marked with an arrow.(3 . ± .
2) 10 − ph cm − s − from this fit. This can be trans-lated into an observable Ti mass at the time of the explosion( t =
0) of (2 . ± .
9) 10 − M (cid:12) , by M Ti ( t = (cid:27) π d F ( t ) · m u · τ Ti · exp( t /τ Ti ) / W , (5)taking into account that the characteristic lifetime of Sc(5 .
73 h) is much shorter than of Ti (86 a). In Eq. (5), d = . + . − . kpc is the distance to the SNR, t = (337 . ± .
4) a its age,incorporating the eleven-year observation time span, F ( t ) themeasured flux in the 1157 keV line today, m u the atomic massunit, τ Ti = (86 ± .
5) a the characteristic lifetime of the Tidecay, and W = .
9% the respective branching ratio.The uncertainty on this Ti mass value is mainly due tothe distance to Cas A and the measured flux. In addition, the Ti half-life time has an impact on the derived mass; its uncer-tainty is taken into account above. Because statistical fluctua-tions in the measured spectra are large, the fit and the resultingmass might su ff er from systematic e ff ects in the assumed spec-tral shape (constant plus Gaussian); we estimate this e ff ect by
70 75 80 85051015 70 75 80 85Energy [keV]051015 F l u x [ − ph c m − s − k e V − ]
70 75 80 85Energy [keV] 0.11.010.0100.0 c t s b i n −
74 76 78 80 82 84Energy [keV]−15−10−50510 F l u x [ − ph c m − s − k e V − ] Fig. 3.
Same as Fig. 2, but at 78 keV (1.5 keV energy bins).The best-fit values are (78 . ± .
5) keV for the centroid,(1 . ± .
6) keV for the width (FWHM), yielding an expansionvelocity of (4300 ± − , and (2 . ± .
4) 10 − ph cm − s − for the flux, which is equivalent to (1 . ± .
4) 10 − M (cid:12) of Ti.The raw count spectrum (gray) increases by two orders of mag-nitude below 70 keV with respect to 80 keV, which introducesstrong systematic e ff ects.determining an upper limit of the constant o ff set, which wouldthen reduce the derived mass by about 33%.The high-energy Ti decay line has a FWHM of (8 . ± .
42) keV and is thus broadened with respect to the instrumen-tal resolution at 1.157 MeV of (cid:39) . Ti ejecta of (2200 ± − . Thisvalue is significantly lower than values reported in recent pa-pers (Renaud et al. 2006; Grefenstette et al. 2014). The linecentroid is found as (1158 . ± .
6) keV and thus agrees withthe laboratory-determined energy, suggesting only minor bulkaverage motion of Ti in Cas A relative to the solar system,( v Bulk = ( − ± − ).For the 78 keV line (Fig. 3), we obtain a line flux of F = (2 . ± .
4) 10 − ph cm − s − . Using Eq. (5) and replac-ing W with W = F is converted to a Ti mass of(1 . ± .
4) 10 − M (cid:12) . Within uncertainties, the two derived Timasses are consistent. The 78 keV line is not significantly shiftedeither, confirming absence of average bulk motion. The mea-sured Doppler broadening of (1 . ± .
6) keV (FWHM) yields anexpansion velocity of (4300 ± − for the Ti ejecta.This value is consistent with the result from the 1157 keV lineand also with the value measured by NuStar. The apparent dif-ferences between values derived for the 78 and 1157 keV linesreflect the energy dependence of the resolving power of the SPIinstrument: While at 78 . R = . / . =
49, it is R = / . =
482 at1157 keV, meaning that SPI derives better line width constraintsat higher energies; this adds to the linear energy dependence ofthe Doppler e ff ect. Figure 4 shows the 2 σ upper limit on theexpansion velocity assuming the best-fit values for flux and cen-troid for the two detected lines. While the constraint from the78 keV line is rather flat with a shallow minimum (gray linein the figure), the 1157 keV line (black line) provides a well-defined minimum or constraint.Representing the line shapes by Gaussians is an empiri-cal approach. Alternatively, a physical model can be adapted: / SPI observations of Ti from Cassiopeia A km s −1 ]024681012 ∆ χ
78 keV line1157 keV line
Fig. 4. ∆ χ vs. expansion velocity for the two detected lines, in-dividually. The values are calculated assuming the best-fit val-ues in each case, only letting the Gaussian width vary. Becauseof the higher resolving power of SPI at 1 MeV with respect tolower energies, the value for the expansion velocity derived formthe high-energy line (solid black) is more constrained than thatfrom the low-energy line (solid gray). For comparison, the 2 σ limits are indicated by the thick dashed line.Assuming a homogeneously expanding thin shell where the shellradius is much larger than the distance to the observer, the ex-pected ideal line shape can be described by a tophat function S ( E ; F , E , ˙ R ) = F · Θ (cid:32)(cid:12)(cid:12)(cid:12) ˙ R (cid:12)(cid:12)(cid:12) − (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) c (cid:32) EE − (cid:33)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:33) · c RE , (6)where F is the measured flux, E the bulk motion, ˙ R the ex-pansion velocity, and c the speed of light (Kretschmer, K. A.2011). This line shape has to be convolved with the spectral re-sponse function of SPI (see Eqs. (3) and (4)). Fitting the spec-tra using Eq. (6) leads to lower velocities in both cases, thatis, (3900 ± − (78 keV) and (1500 ± − (1157 keV), respectively. The measured expansion velocities,however, are similar to those from a Gaussian fit, and system-atic di ff erences are smaller than uncertainties from statistics.When the results of The et al. (1996) obtained with OSSEon CGRO with the COMPTEL result by Iyudin et al. (1997), theBeppoSAX result (Vink et al. 2001), the INTEGRAL / IBIS re-sult (Renaud et al. 2006), and the NuStar result (Grefenstetteet al. 2014) are combined with our work through a weightedmean (weighted by the inverse variance of each measurement),the Ti mass is (1 . ± .
19) 10 − M (cid:12) . We note that the high-energy line appears to yield a systemat-ically higher Ti mass, both from our analysis and in Iyudinet al. (1994) and Iyudin et al. (1997), with respect to the hard X-ray line based Ti mass determinations. Our derived Ti massfrom the 78 keV line is consistent with other published studiesthat measured the low-energy lines. The derived Ti mass perinstrument is shown in Fig. 5 together with the weighted meanof all measurements (hatched area). This systematic di ff erence in Ti flux values becomes even more obvious when the measure-ments of the Sc and Ca lines, taken with di ff erent instrumentsin the past two decades, are compared and plotted on a time axis T i m a ss [ - M O • ] OSSECOMPTEL BeppoSAX ISGRI NuStar SPI(This work)
68 keV line ( Ti(EC) Sc * ) 78 keV line ( Ti(EC) Sc * )1157 keV line ( Sc(EC) Ca * ) Fig. 5.
Derived Ti masses of di ff erent instruments. All databars are drawn from the measurements with only the given in-strument (no combinations), including the uncertainties in half-life time and explosion date. The OSSE and COMPTEL valuesare corrected for the distance to Cas A. Upper limits (if given)are shown as dashed lines. The yields measured by COMPTELand SPI using the 1157 keV line are systematically higher thanvalues using the low-energy lines. The calculated weighted meanof all shown measurements is illustrated as the hatched area andis (1 . ± .
19) 10 − M (cid:12) . −5 −4 −5 −4 F l u x [ ph c m − s − ] Flux from high−energy line (1157 keV)Flux from low−energy lines (68 keV, 78 keV) C O M P T E L S P I O S S E B eppo
S A X I S G R I N u S t a r Fig. 6.
Compilation of γ -ray flux measurements in Cas A fromdi ff erent instruments during the years 1992 to 2014 (see text).To each family of lines (low- and high-energy), an exponentialdecay function has been fitted, fixing the half-life time of Tito 86 a and the explosion date to AD 1671 (solid lines). The 1 σ uncertainties are separately shown by dashed gray lines for eachfit. The discrepancy can be expressed as a constant flux level of(2 . ± .
62) 10 − ph cm − s − .(Fig. 6). The values in Fig. 6 are taken from The et al. (1996,Table 3) with OSSE, Iyudin et al. (1997) with COMPTEL, Vinket al. (2001, Table 1) with BeppoSAX, Renaud et al. (2006, Table1) with IBIS, this work with SPI, and Grefenstette et al. (2014,Table ED2) with NuStar (from left to right). These values onlyconsider the value measured with the mentioned instrument it-self, hence no double-counting of flux values. The 1157 keV fluxvalues (Iyudin et al. (1997) and our study) are found to be sig-nificantly higher than the low-energy line flux measurements. / SPI observations of Ti from Cassiopeia A
We investigated this systematic by treating the measurementsof the hard X-ray lines independently of the 1157 keV gamma-ray line. We performed an F-test to check whether the derivedspectra can be represented by only one flux value (case I) or ifthe preference is for two values (case II). The corresponding χ values are χ I = .
14 (16 dof), and χ II = .
27 (15 dof), re-spectively. The F-value of this test is F = . , for which the F-statistic gives a probability of ∼ . σ , thatthe two spectra cannot be represented by the same flux value.Alternatively, we fixed the explosion date to AD 1671 and thecharacteristic lifetime of Ti to 86 years and then fit an expo-nential decay function to only the flux measurements of the low-energy lines. This yields a Ti mass of (1 . ± .
14) 10 − M (cid:12) .The same fitting procedure applied to the 1157 keV gamma-ray line flux measurements (COMPTEL and SPI) results in a Ti mass of (2 . ± .
43) 10 − M (cid:12) . Using the first value as anestimate for the real observable Ti mass seen to decay, thatis, uncontaminated by possible secondary processes that mightmimic additional Ti, we evaluated an additional flux level of(2 . ± .
62) 10 − ph cm − s − by fitting the high-energy mea-surements with a constrained Ti mass. This discrepancy has astatistical significance of 3 σ .About 340 years after the explosion, the expected flux ratio F / F is ∼
1, the measured flux ratio is ∼ .
5. This wouldimply an e ffi ciency (number of photons per decay) error of 50%and is excluded by several measurements (Norman et al. 1998;Wietfeldt et al. 1999; Ahmad et al. 2006). We speculate that this discrepancy may be due to an additionalnuclear de-excitation component originating from acceleratedparticles colliding with Ca ∗ in the remnant and swept up in-terstellar medium. CRs are thought to be accelerated in SNRs bydi ff usive shock acceleration (Baade & Zwicky 1934), in partic-ular in Cas A (Berezhko & V¨olk 2004; Aharonian et al. 2001).Only the 1157 keV line from excited Ca will have an addi-tional contribution from nuclear excitation (see Sect. 2.1). Theadditional gamma-ray line flux originating from the isotope Cacan be estimated by F γ = (4 π d ) − · n ( Ca) · (cid:90) Q P ( p ) σ ( p ) v ( p ) d p , (7)where d is the distance to Cas A, n ( Ca) the mean density of Ca atoms in the medium where the interaction takes place, Q P ( p ) the proton acceleration spectrum , σ ( p ) the cross sectionof the reaction Ca( p , p (cid:48) ) Ca ∗ , and v ( p ) the velocity of accel-erated protons. The product of n ( Ca) by the integral, I ( Ca) inEq. (7) describes the collision frequency and includes the present Ca abundance in the interaction region (Ramaty et al. 1979;Summa et al. 2011).With Eq. (7), the Ca density required in front of the shockto produce this gamma-ray flux can be estimated. The meancross sections of the reactions C( p , p (cid:48) ) C ∗ by Ramaty et al.(1979), and Ca( p , p (cid:48) ) Ca ∗ by Mitchell et al. (1982) havethe same order of magnitude. With the solar abundance ratio Ca / C = . · ≈ · − by Lodders (2003), the inte-gral I ( Ca) can be estimated to be 2 · − I ( C). I ( C) was The proton acceleration spectrum, Q P ( p ) ∝ p − . , was chosen fol-lowing Summa et al. (2011) to meet the FERMI-LAT constraints on theenergy content of the cosmic rays that were measured by Abdo et al.(2010), about 3 − erg. calculated from the values given in Summa et al. (2011). The re-sulting Ca density is about 10 - 10 cm − . This value is veryhigh compared to densities of the interstellar medium, but mayreflect the swept-up density in front of the forward shock (“snowplough”). If the measurements of presolar grains by Nittler et al.(1996), Clayton et al. (1997), and Hoppe et al. (2000) are takeninto account, which suggest that the ratio Ca / Ca can be morethan 100 times higher than solar, the forward-shock Ca densityis scaled down correspondingly to 10 - 10 cm − . Although thisdensity range appears plausible for optical knots and might evenbe consistent with expectations (Fesen et al. 2006; Docenko &Sunyaev 2010), the estimated values appear extreme: Assuminga volume of the swept-up material near the Cas A SNR of ∼ cm , and a density of ∼ cm − , the estimated Camass would be of the order 10 M (cid:12) . Therefore, the ejecta fromCas A alone cannot explain this mass; adding the swept-up in-terstellar material cannot explain the additional flux either. Themorphology of the swept-up material possibly di ff ers from theexpectations, or the physics of nuclear excitation may not beproperly treated in our simple estimate. It would be interestingto investigate the nuclear de-excitation lines from C and O inCas A because these lines are expected to be more luminous.Additional support for our speculated nuclear de-excitationcomponent is the measured Doppler velocity of the 1157 keVline: It is lower than the one derived from the 78 keV line. Whilethe emission originating in the decay of Ti to Sc (78 keVline) follows the kinematics of the expanding SNR, the 1157 keVline emission might have two components, one resembling thekinematics ( (cid:39) − ) from the Sc decay to Ca, andanother one incorporating the nuclear de-excitation of Ca ∗ inthe swept-up material in front of the shock at zero velocity.However, we do not know where the interaction takes place andcan also assume that a measurement of the 1157 keV line sam-ples another volume element of Cas A than the 78 keV line.Milisavljevic & Fesen (2015) illustrated the bubble-like behaviorof the interior of Cas A that naturally shows velocities of about2000 km s − near the expansion center and up to 5000 km s − farther outside.
4. Conclusions and discussion
Revisiting the 340 year old supernova remnant CassiopeiaA with eleven years of data from the spectrometer SPI onINTEGRAL, we detected two gamma-ray lines originating inthe Ti decay chain Ti → Sc → Ca. One of the low-energylines from the process Ti → Sc at 78 keV was detected, whilethe adjacent line at 68 keV coincides with a major and di ffi cultinstrumental-background feature and cannot be measured. The78 keV line parameters are consistent with other measurementsconstraining the Ti mass and kinematics in the supernova rem-nant, ((1 . ± .
4) 10 − M (cid:12) , and v exp (cid:39) (4300 ± − ). Thesecond decay step in the Ti decay chain, Sc → Ca, occursonly a few hours after the Ti decay and produces character-istic 1157 keV gamma-rays that were also detected and ana-lyzed independently. The Ti mass from the 1157 keV line is(2 . ± .
9) 10 − M (cid:12) , while Doppler broadening here implies anexpansion velocity of (2200 ± − .The kinematic information of the Cas A SNR by mea-suring emission lines is not unique. In particular, fast-movingO-rich knots at velocities of around 8000 km s − have beenfound (Fesen et al. 2006). From Chandra measurements, char-acteristic X-ray lines of Si and Fe have been mapped. An inver-sion of the classical onion-shell structure had been inferred, as / SPI observations of Ti from Cassiopeia A
Fe X-ray emission clumps have been found outside the Si X-ray emitting regions more central to the remnant (Hwang et al.2004). From the NuStar image and the more central location of Ti clumps (Grefenstette et al. 2014), this inversion hypothe-sis may be recognized as a misinterpretation of the Fe line X-ray emission, which is driven by the ionization state of rem-nant gas; Fe in the central region thus may escape X-ray linedetection. The forward shock reached a diameter of 5 arcminand appears to currently move at 5000 km s − , while the X-raybright regions predominantly are beyond the inner 2 arcmin, andin the jet regions at radial distances above 3 arcmin from thecentral compact object (Hwang et al. 2004). Thus the reverseshock has progressed about half into the remnant (inner diame-ter ∼ Ti nucleosynthesis yields in core-collapse supernovae isone of the questions we wish to address; they could rangeup to several 10 − M (cid:12) (Timmes et al. 1996; The et al. 2006;Magkotsios et al. 2010), while for thermonuclear supernovae(SN Ia) only a rare subtype is considered a plausible Ti source,but then also with yields of up to several 10 − M (cid:12) (Woosley &Weaver 1994), see also The et al. (2006). Nuclear burning insupernova explosions occurs at high densities and temperatures,and thus those sites are closest to conditions of equilibrium burn-ing, where nucleons find their most stable arrangement withinatomic nuclei. The binding energy of nucleons is maximized for Ni, and nuclear statistical equilibrium (NSE) appears to be agood description of plasma conditions for the brief moment ofthe supernova explosion when nucleosynthesis occurs. Here allnuclear reactions except weak-force reactions are in thermal bal-ance. As the explosion site is diluted and cools, the first nuclearreactions falling out of such equilibrium are three-body reactionssuch as the 3 α conversion of helium to carbon. Here, the condi-tions are better described by an overabundance of α particlesover NSE. This is called α - rich freeze-out, and nucleosynthesisproductions emerging from these conditions are characterized byoverabundances of nuclei that are multiples of α particles result-ing from successive captures of α s on nuclei (Bodansky et al.1968; Woosley et al. 1973). Ca and Ti are among the most-massive of such products; note that Ni is an α -multiple nucleusas well. It has been considered plausible, therefore, that super-novae that produce major amounts of Ni are also sources ofsignificant amounts of Ti.When the measurements taken by various instruments dur-ing the last 20 years are combined, the Ti mass seen to decayis (1 . ± .
19) 10 − M (cid:12) . But we find a significant di ff erence(3 σ ) in flux, resulting Ti mass, and velocity from the mea-surements of the Ca versus Sc lines (high- and low-energylines, respectively). We argue that the low-energy line measure-ments (68 keV and / or 78 keV) reflect the true Ti content andkinematics, and an additional component with a flux level of(2 . ± .
62) 10 − ph cm − s − is found in the 1157 keV line flux.We speculate that this excess is due to the nuclear de-excitationof Ca ∗ in the remnant and swept-up interstellar medium, ex-cited by cosmic rays that are expected to be accelerated in theyoung remnant by di ff usive shock acceleration. Acknowledgements.
This research was supported by the German DFG cluster ofexcellence “Origin and Structure of the Universe”. The INTEGRAL / SPI projecthas been completed under the responsibility and leadership of CNES; we aregrateful to ASI, CEA, CNES, DLR, ESA, INTA, NASA and OSTC for supportof this ESA space science mission.
References
Abdo, A. A., Ackermann, M., Ajello, M., et al. 2010, ApJ, 710, L92Aharonian, F., Akhperjanian, A., Barrio, J., et al. 2001, A&A, 370, 112Ahmad, I., Bonino, G., Castagnoli, G. C., et al. 1998, Physical Review Letters,80, 2550Ahmad, I., Greene, J. P., Moore, E. F., et al. 2006, Phys. Rev. C, 74, 065803Ashworth, Jr., W. B. 1980, Journal for the History of Astronomy, 11, 1Atti´e, D., Cordier, B., Gros, M., et al. 2003, A&A, 411, L71Audi, G., Bersillon, O., Blachot, J., & Wapstra, A. H. 2003, Nuclear Physics A,729, 3Baade, W. & Zwicky, F. 1934, Contributions from the Mount WilsonObservatory, vol. 3, pp.79-83, 3, 79Berezhko, E. G. & V¨olk, H. J. 2004, A&A, 419, L27Bodansky, D., Clayton, D. D., & Fowler, W. A. 1968, ApJS, 16, 299Clayton, D. D., Amari, S., & Zinner, E. 1997, Ap&SS, 251, 355da Cruz, M. T. F., Chan, Y., Larimer, R.-M., et al. 1992, Phys. Rev. C, 46, 1132Diehl, R., Siegert, T., Hillebrandt, W., et al. 2014, Science, 345, 1162Diehl, R., Siegert, T., Hillebrandt, W., et al. 2015, A&A, 574, A72Diehl, R. & Timmes, F. X. 1998, PASP, 110, 637Docenko, D. & Sunyaev, R. A. 2010, A&A, 509, A59Eriksen, K. A., Arnett, D., McCarthy, D. W., & Young, P. 2009, ApJ, 697, 29Fesen, R. A., Hammell, M. C., Morse, J., et al. 2006, ApJ, 636, 859Fransson, C. & Kozma, C. 2002, New A Rev., 46, 487Fryer, C., Young, P., Bennet, M. E., et al. 2008, in Nuclei in the Cosmos (NICX), 101Funck, E., Sch¨otzig, U., Woods, M. J., et al. 1992, Nuclear Instruments andMethods in Physics Research A, 312, 334G¨orres, J., Meißner, J., Schatz, H., et al. 1998, Physical Review Letters, 80, 2554Grebenev, S. A., Lutovinov, A. A., Tsygankov, S. S., & Winkler, C. 2012,Nature, 490, 373Green, D. A. 2002, Highlights of Astronomy, 12, 350Grefenstette, B. W., Harrison, F. A., Boggs, S. E., et al. 2014, Nature, 506, 339Grefenstette, B. W., Reynolds, S. P., Harrison, F. A., et al. 2015, ArXiv e-prints,1502.03024Hashimoto, T., Nakai, K., Wakasaya, Y., et al. 2001, Nuclear Physics A, 686,591Ho ff man, R. D., Sheets, S. A., Burke, J. T., et al. 2010, ApJ, 715, 1383Hoppe, P., Strebel, R., Eberhardt, P., Amari, S., & Lewis, R. S. 2000, Meteoriticsand Planetary Science, 35, 1157Hwang, U., Laming, J. M., Badenes, C., et al. 2004, ApJ, 615, L117Isern, J., Bravo, E., & Hirschmann, A. 2008, New A Rev., 52, 377Iyudin, A. F., Diehl, R., Bloemen, H., et al. 1994, A&A, 284, L1Iyudin, A. F., Diehl, R., Lichti, G. G., et al. 1997, in ESA Special Publication,Vol. 382, The Transparent Universe, ed. C. Winkler, T. J.-L. Courvoisier, &P. Durouchoux, 37Jerkstrand, A., Fransson, C., & Kozma, C. 2011, A&A, 530, A45Krause, O., Birkmann, S. M., Usuda, T., et al. 2008, Science, 320, 1195Krause, O., Rieke, G. H., Birkmann, S. M., et al. 2005, Science, 308, 1604Kretschmer, K. A. 2011, Dissertation, Technische Universit¨at M¨unchen,M¨unchenLodders, K. 2003, ApJ, 591, 1220Lundqvist, P., Kozma, C., Sollerman, J., & Fransson, C. 2001, A&A, 374, 629Magkotsios, G., Timmes, F. X., Hungerford, A. L., et al. 2010, ApJS, 191, 66Martin, P., Kn¨odlseder, J., & Vink, J. 2007, in ESA Special Publication, Vol. 622,ESA Special Publication, 105Milisavljevic, D. & Fesen, R. A. 2015, ArXiv e-prints, 1501.07283Mitchell, L. W., Anderson, M. R., Kennett, S. R., & Sargood, D. G. 1982,Nuclear Physics A, 380, 318Nagataki, S., Hashimoto, M.-a., Sato, K., Yamada, S., & Mochizuki, Y. S. 1998,ApJ, 492, L45Nittler, L. R., Amari, S., Zinner, E., Woosley, S. E., & Lewis, R. S. 1996, ApJ,462, L31Norman, E. B., Browne, E., Chan, Y. D., et al. 1998, Phys. Rev. C, 57, 2010Popov, M. V., Filina, A. A., Baranov, A. A., Chardonnet, P., & Chechetkin, V. M.2014, ApJ, 783, 43Ramaty, R., Kozlovsky, B., & Lingenfelter, R. E. 1979, ApJS, 40, 487Reed, J. E., Hester, J. J., Fabian, A. C., & Winkler, P. F. 1995, ApJ, 440, 706Renaud, M., Vink, J., Decourchelle, A., et al. 2006, ApJ, 647, L41Rest, A., Foley, R. J., Sinnott, B., et al. 2011, ApJ, 732, 3Rest, A., Welch, D. L., Suntze ff , N. B., et al. 2008, ApJ, 681, L81R¨opke, F. K., Kromer, M., Seitenzahl, I. R., et al. 2012, ApJ, 750, L19Roques, J. P., Schanne, S., von Kienlin, A., et al. 2003, A&A, 411, L91Seitenzahl, I. R., Timmes, F. X., & Magkotsios, G. 2014, ApJ, 792, 10Summa, A., Els¨asser, D., & Mannheim, K. 2011, A&A, 533, A13The, L.-S., Clayton, D. D., Diehl, R., et al. 2006, A&A, 450, 1037The, L.-S., Clayton, D. D., Jin, L., & Meyer, B. S. 1998, ApJ, 504, 500The, L.-S., Leising, M. D., Kurfess, J. D., et al. 1996, A&AS, 120, C357 / SPI observations of Ti from Cassiopeia A
Thorstensen, J. R., Fesen, R. A., & van den Bergh, S. 2001, AJ, 122, 297Timmes, F. X., Woosley, S. E., Hartmann, D. H., & Ho ff man, R. D. 1996, ApJ,464, 332Vedrenne, G., Roques, J.-P., Sch¨onfelder, V., et al. 2003, A&A, 411, L63Vink, J., Laming, J. M., Kaastra, J. S., et al. 2001, ApJ, 560, L79Wang, W., Harris, M. J., Diehl, R., et al. 2007, A&A, 469, 1005Wang, W., Lang, M. G., Diehl, R., et al. 2009, A&A, 496, 713Wheeler, J. C., Maund, J. R., & Couch, S. M. 2008, ApJ, 677, 1091Wietfeldt, F. E., Schima, F. J., Coursey, B. M., & Hoppes, D. D. 1999,Phys. Rev. C, 59, 528Winkler, C., Courvoisier, T. J.-L., Di Cocco, G., et al. 2003, A&A, 411, L1Wongwathanarat, A., Janka, H.-T., & M¨uller, E. 2013, A&A, 552, A126Woosley, S. E., Arnett, W. D., & Clayton, D. D. 1973, ApJS, 26, 231Woosley, S. E. & Weaver, T. A. 1994, ApJ, 423, 371man, R. D. 1996, ApJ,464, 332Vedrenne, G., Roques, J.-P., Sch¨onfelder, V., et al. 2003, A&A, 411, L63Vink, J., Laming, J. M., Kaastra, J. S., et al. 2001, ApJ, 560, L79Wang, W., Harris, M. J., Diehl, R., et al. 2007, A&A, 469, 1005Wang, W., Lang, M. G., Diehl, R., et al. 2009, A&A, 496, 713Wheeler, J. C., Maund, J. R., & Couch, S. M. 2008, ApJ, 677, 1091Wietfeldt, F. E., Schima, F. J., Coursey, B. M., & Hoppes, D. D. 1999,Phys. Rev. C, 59, 528Winkler, C., Courvoisier, T. J.-L., Di Cocco, G., et al. 2003, A&A, 411, L1Wongwathanarat, A., Janka, H.-T., & M¨uller, E. 2013, A&A, 552, A126Woosley, S. E., Arnett, W. D., & Clayton, D. D. 1973, ApJS, 26, 231Woosley, S. E. & Weaver, T. A. 1994, ApJ, 423, 371