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TRACING GALACTIC STAR FORMATION WITH RADIOACTIVITIES
Dieter H. Hartmann(1), Joshua Molgaard(1), Roland Diehl
(1 ) (2)

Clemson University, Department of Physics and Astronomy, Kinard Lab of Physics, Clemson, SC 29634-0978 (USA) E-mail: hdieter@clemson.edu (2 ) Max-Planck-Institut fЭr extraterrestrische Physik, Postfach 1312, D-85741Garching (Germany), E-mail: rod@mpe.mpg.de

ABSTRACT The galactic star formation rate is a key parameter in the description of the structure and evolution of the interstellar medium (ISM), and further determines the present-day global luminosity of the Milky Wa y in various bands. Determinations of the star formation rate are based on several distinct tracers: The stellar light component is reprocessed to IR emission by the dust content of the ISM, recombination radiation leads to H emission, and particle acceleration in supernova remnant (SNR) shocks leads to a -ray continuum. Stellar ejection of radioactive material adds a -ray line glow that can be utilized to measure the star formation activity on a galaxy-wide scale. We promote using the 1.809 MeV gamma-ray line due to the deca y of 26Al as a powerful technique to measure the global (the Galaxy is transparent to MeV gamma-rays) l ong-term average (the mean life of 26Al is ~ 1 Myr) star formation rate. This method is compared to standard approaches that rely on scaling the supernova rates in external galaxies to the Milky Wa y, or the modelling of tracer objects that require significant corrections for evolution, or extinction. We describe the value and limitations of the "26Al-method", which may prove to be one of the most accurate methods once reliable yields are available. 1. SFR/SNR ESTIMATES IN CONTEXT

extrapolation from a very local star formation tracer to a global model. We advocate an approach based on ray line measurements; these are well suited for a galaxy-wide estimate, as the MeV band does not suffer from extinction, and yield a time average on scales that are long in comparison to the typical times between events, thus minimizing the effects of small number statistics. Before presenting the key features of this "26Al-method", and the recent results obtained from its application to INTEGRAL data, we will briefl y review some of the methods that have been used in the past (as summarized in the table). Generically, the star formation rate (SFR, expressed in solar masses per year, M y-1) is obtained from a tracer that can be corrected for observational selection effects and is understood well enough so that evolutionary effects can be taken into account. One either deals with a class of residual objects, such as pulsars or supernova remnants, or with reprocessed light, such as free-free, H, or IR emission that follows from ionization and heating of interstellar gas and its dust content in the vicinity of hot and luminous stars. In some cases one should include time-dependent effects, because the observational phenomena are caused by processes which include their own characteristic evolution with time. The "after-glow" of an instantaneous starburst behaves differently than the steady state output from a region with continuous star formation. Here we are concerned with an average (steady state) star formation rate, where "average" is to be understood as spatial (galaxy-wide) and temporal, over long enough time scales to avoid distortion from fluctuations and not too long for galactic evolution to matter (i.e., <108 y, which would be a t ypical time for morphological changes in the Galaxy itself).

A survey of the literature demonstrates that measures of the star formation rate and its associated corecollapse supernova rate are currently uncertain by at least a factor two. When one considers these values without taking into account method-specific (i.e. "systematic") uncertainties, one might conclude that we don't know the Galactic SFR to better than an order of magnitude. However, there is some convergence in recent estimates, and we argue that the star formationand the related supernova rates are now established to within less than a factor 2. Still, further improvements in the measurement of this important quantity are possibl e. We are concerned about systematic effects in methods using indirect scaling to rates of external galaxies, or

To give a sense of how the measurements of the SFR have evolved over time, we present a Table of values that were drawn from the literature over nearly the past three decades. This selected set of citations is not meant to be complete, but a representative sample. A graphic rendering of this table is presented at the end of this paper.

_____________________________________________________________________ Proc. 6th INTEGRAL Workshop `The Obscured Universe', Moscow, 3-7 July 2006 (ESA S P-622)


Authors
Smith et al. 1978 Talbot 1980 Guesten et al. 1982 Turner 1984 Mezger 1987 McKee 1989 van den Bergh 1990 Van den Bergh & Tammann 1991 Supernov a Remants Historic SN Record Cappellaro et al. 1993 Van den Bergh & McClure 1994 Pagel 1994 McKee & W illiams 1997 Timmes, et al. 1997 Reed 2005 Diehl et al. 2005

SFR
(M /yr) 5.3 0.8 13.0 3.0 5.1 3.6 (R) 2.4 (IR) 2.9 7.8 6.5 +/- 3.9 11.4 +/- 4.7 2.7 +/- 1.7 4.9 +/- 1.7 6.0 4.0 5.1 +/- 4 2-4 3.8 +/- 2.2


(century -1) 2.7 0.41 6.6 1.53 2.6 1.84 1.22 1.5 +/- 0.8 4 3.3 +/- 2.0 5.8 +/- 2.4 1.4 +/- 0.9 2.5 +/- 0.9 3.1 2.0 2.6 +/- 2.0 1-2 1.9 +/- 1.1

SNR

Supernovae onl y trace stars from the upper IMF, thus statements about the SFR (including all stars) are sensitive to the full mass range of the IMF employed. On the other had, some quantities, such a supernova yi elds and ionizing fluxes, are only sensitive to assumptions about the IMF above about 10 M . To enable a direct comparison of published results we normalize to [12]. Uncertainties in each quantity should be treated separately, as methods that directly determine the SNR yield a less accurate SFR due to the added uncertainties for the low mass IMF. Many papers discuss the Star Formation (rate) History (SFH) in relative terms (studies not concerned with the absolute value of the SFR, but with the relative history of the rate), or the star formation rate surface density (M y-1 kpc-2) in the solar neighborhood, and possibl y its radial dependence. Papers are not listed if the global SFR was not explicitly addressed or is only derivable with model assumptions not provided in the original work. Our first reference is to Smith, Biermann, and Mezger [1], who studied HII regions and estimated the number of Lyman continuum photons required to maintain the ionization of these regions. They find SFR = 5.3 Mo/yr. Following the footsteps of [1] Talbot [2] investigated the rate of star formation with observed intensities of CO and HI emission in the Milky Wa y (and M83) and finds SFR = 0.8 Mo/yr. GЭsten and Metzger's luminosity obtained fr implies a SFR of 13.0 +/- 4) M /yr to spiral [3] estimate of the total ionizing om observations of HII regions Mo/yr, of which they attribute (5 arm activity.

Turner [4] reviews the observational data pertaining to regions of star formation, in particular in radio bands, and advocates SFR = 3.0 Mo/yr. Mezger [5] continuum the mass di SFR of 5.1 constrains SFR estimates from the Lyman photon production rate with estimates of stribution of the galactic disk, and finds a Mo/yr.

We briefl y discuss some of the methods used to estimate the galaxy-wide star formation rate. Related quantities of interest, such as the production rate of stars (in units of stars per year) or the type-II (and Ibc) core-collapse supernova rate (in units of events per century) are provided, if given in the original paper. If only the supernova rate (SNR) or the star formation rate (SFR) is given, we convert one quantity to the other by using the specific initial mass function (IMF) "calibration" used by McKee and Williams [12]: SFR = 1.96 SNR, in units defined above.

With a model for the rate of low-mass star formation in molecular clouds McKee [6] finds a SFR of 3.6 M /yr from the analysis of thermal radio emission from HII regions, which is proportional to the production rate of ionizing photons, which in turn is proportional to the SFR. It is pointed out that this method is sensitive to the slope of the high-mass IMF. It also must be noted that the method depends on stellar atmosphere models in conjunction with models for massive stars, which change with treatments of mass loss, rotation, and convection. This paper also briefl y discusses the use of


the far-IR luminosity, due to warm dust heated by the absorption of photons from massive stars. The author uses the measured IR luminosity of the Galaxy of 4.7 109 Lo (from [5]) to derive a SFR of 2.4 Mo/yr. At this point we introduce the first reference to work in which the primary focus was a direct estimate of the supernovae rate (in our context we are only interested in the core-collapse rate (Types II, and Ibc) . Van den Bergh [7] finds (2.62 +/- 0.8) h1002 century-1. For h100 = 0.75, the rate is 1.5 +/- 0.8 century-1. This rate is based on a combined study of Galactic supernova remnants, the small set of historical SNe, and supernovae in M31 and M33. Cappellaro et al. [9] later refer to this rate as "the best estimate" Van den Bergh and Tammann [8] find a SNR of ~4 per century. The authors review supernova rates in external galaxies and derive a specific supernova frequency, in units of 1 SNu = 1 SN per century per 1010 L (B), for various galaxy t ypes. If one assumes that the Galaxy is intermediate between types Sab-Sb and types Sbc-Sd, the specific rate is ~3 h1002 SNu. For a Galactic blueband luminosity of L(B) = 2.3 1010 Lo(B) (their Table 11) and h100 = 0.75 we infer a SNR of 4 per century. They also discusses estimates from internal Galactic tracers: from radio supernova remnant (SNR) statistics they infer a SNR of 3.3 +/- 2.0 century-1. The historic record of nearby (< a few kpc) supernovae in the past millennium they (Tammann) argue for a SNR of 5.8 +/- 2.4 century-1. Large extinction corrections in the galactic plane render this sample highly incomplete, which results in very large uncertainties when one extrapolates to the full galactic disk. The authors also review efforts based on the pulsar birth rate, but their extensive observational selection effects together with strong (and poorly understood) evolution of luminosity and beaming renders this method impractical for estimating the galactic SNR. Along these lines of studies, Cappellaro et al. [9] find a SNR of 1.4 +/- 0.9 century-1 based on scaling the rate in the Galaxy to that in external galaxies of similar type. Their sample is obtained from surveys carried out at the Asiago and Sternberg Observatories. The authors provide an extensive discussion of the uncertainties of this method, which can exceed 200% for some late type galaxies. Subsequently, van den Bergh and McClure [10] find a SNR of 2.4-2.7 h752 century-1, after re-evaluating extragalactic SN rates obtained from Evans's 1980-1988 observations. This result relies on extrapolation from other galaxies, and thus a proper evaluation of the type and B-band luminosity of the Galaxy. The uncertainty due to the Hubble constant is now very small. Given

the error analysis in the paper, the rate is uncertain by at least 34%. We enter 2.5 +/- 0.9 century-1 in the table. In Pagel's [11] textbook on galactic chemical evolution we find a SFR of 6.0 M /yr. McKee and Williams [12] study the galactic luminosity distribution of giant OB associations, and infer a SFR of 4.0 M y-1, and based on the Scalo-IMF convert this rate into a total number rate of 7.9 stars per year. They assume that all stars above 8 Mo become supernovae, corresponding to a supernova fraction of fSN = 2.6 10-3. With a mean stellar mass of = 0.51 M , the corresponding cc-supernova rate is thus 2 per century. As mentioned above, we use this study for calibration SFR(M y-1)=fSN-1 SNR = 1.96 SNR(century-1). (1) Timmes, Diehl, and Hartmann [13] applied the "26Almethod", described in the next section, to the data from COMPTEL and obtain a SFR of 5.1 +/- 4 M /yr. For the steady state equilibrium mass of 26Al in the presentday ISM they obtained a range 0.7 ­ 2.8 M , based on the Salpeter IMF (0.1 M - 40 M ) and 26Al yields from Woosley and Weaver [15] [which do not include the contributions from Wolf-Ra yet winds]. Their SFR implies a cc-supernova rate of 2.6 +/- 2 century-1. The neglect of hydrostatically produced 26Al injected into the ISM by winds from massive stars, caused their SFR to be overestimated. The large uncertainty in the final result for the SFR is due to large uncertainties in the observed COMPTEL flux. Recent INTEGRAL observations have significantly reduced the error in this key quantity and also provided support for the basic idea that 26Al is indeed distributed globally in the ISM. Diehl et al. [14] use INTEGRAL measurements to obtain a SNR of 1.9 ± 1.1 century-1, corresponding to a SFR of 3.8 ± 2.2 M y-1, as discussed bel ow. Recently, Reed [16] estimate the birthrate of stars with masses in excess of 10 M using a sample of local OB stars. He does not state a value for the SFR, but states "... the galactic supernova rate is estimated as probabl y not less than 1 nor more than 2 per century". Using the conversion factors from [12] one thus infers a SFR in the range 2-4 M y-1. Reed uses a sample of about 400 O3-B2 dwarfs within a heliocentric distance of 1.5 kpc, and then extrapolates based on models for the spatial distribution of stars, galactic extinction, and stellar life times. Reed emphasizes various sources of errors, such as lacking spectral classifications of some bright OB stars, the (unknown) inhomogeneous spatial structure of extinction as well as stellar density, and non-unique connection between mass and spectral type, and draws attention to the fact that one would have to include B3 dwarfs as well, if the lower mass limit for supernovae


is 8 M instead of 10 M (e.g., [17]). The OB-star catalog of the author was used t o perform a modified V/Vmax test to obtain a present-day star count as a function of absolute V-band magnitude. From the stellar life times and the assumption of steady state the local birthrate follows. A double exponential model (in galactocentric radius and scale height above the plane) of the spatial distribution of these stars (which includes an inner "hole" of radius R = 4.25 kpc) ultimately leads to a total birthrate of about one OB stars per century. Variations in the size of the hole change this number significantly, which leads the author to finally derive a rate of 1-2 supernovae per century. Extrapolating star counts in the solar vicinity to the global count clearly is sensitive to the spiral model one uses for the nonsymmetric part of the galactic star formation pattern. Molgaard, Hartmann, and Diehl [18] carried out Monte Carlo simulations to address this issue, and find that pulsar-based distribution models from [19,20] imply an additional uncertainty of at least a factor of two. With future astrometry missions such as GAIA we should significantly improve the understanding of the global distribution of stars in the Galaxy, and thus reduce this source of uncertainty. Presently we should regard starcount measurements of the SFR as rather uncertain. Figure 1 shows the SFR values discussed a bove (and a few more we did not describe in detail), demonstrating that, with few exceptions, the SFR estimate converged to a range of 2-4 M y-1. From eq. (1) we thus infer that the galactic core collapse rate should be in the range of 1-2 per century, a value that is now commonly used. The pulsar-historic-SN-based estimate in the recent textbook Astrophysics (Kundt 2004, Springer Verlag) is significantly higher than this advocated value, but, as pointed out above, uncertainties due t o assumptions about extinction, pulsar beaming and lifetime are large. 2. RESULTS FROM THE AL METHOD
26 26

average amount of a few solar masses in the ISM. The diffuse -ray line glow from this smoothly distributed trace element results in a total flux of

F1.8 ~ 1.510 -4 M 26 D -2 ( / cm 2 s ),

(2)

where D is an effective distance, normalized to an assumed distance RGC = 8.5 kpc to the Galactic Center. The value of D is dependent on the assumed overall scale of the galaxy and the relative distribution of 26Al sources (traced by a com bination of massive, young stars and an older nova population). The steady state mass of 26Al (in solar masses, M )

M

26

=< Y > R

SN

= 1.410 -4 M 0 R

SN

(3)

is given by the product of mean yield, , the ccSN rate RSN (which we wish to obtain), and the mean life (26Al) = 1.03 106 yrs, which is well established and thus does not contribute much to the error budget. The largest source of uncertainty is due t o , which has two contributing sources, the IMF for masses above mSN ~ 8-10 M , and the model-dependent yields as a function of progenitor mass, m. For the purpose of this study one must combine 26Al mass (yields) ejected in the Wol f-Ra yet wind phase prior to the supernova and the explosive yi eld. Diehl et al. [14] compiled the theoretical Y26(m) predictions from several groups, and derived the high-mass IMF-averaged yield used in eq. 3. With this value of , the INTEGRAL flux in the 1.809 MeV -ray line from the inner Galaxy implies (from eq. 2) a SNR of 2 ± 1 ccSNe century-1, and a SFR of 4 ± 2 M y-1. Eq. 3 then implies that the diffuse glow of the Milky Wa y in the 1.809 MeV -ray line stems from the decay of about 3 M of 26Al. 3. THE 60Fe AND 44Ti METHODS

Using -rays from radioactive Al ejected galaxy-wide by massive stars, we established an alternative method [13,14] to obtain a global measure of the galactic SNR (and thus the SFR). This is made possible because 26Al gamma-ray line emission is observable throughout the Galaxy, and the decay of 26Al occurs in the interstellar medium on a characteristic time scale long compared to that of 26Al ejection events and the dynamics of individual stellar explosions, sampling over 10,000 such events. A key advantage of the "26Al method" is the fact that our Milky Wa y is basically transparent to 1.8 MeV photons from the decay of this isotope, and that the yields are now reasonabl y well known [21]. Production of 26Al in ccSNe is abundant (about 10-4 Mo on average), so that the approximately 10,000 events per mean life of ~106 yrs accumulate a steady-state

A similar method for estimating the star formation rate of the Milky Wa y can be based on other -ray line tracers, as long as the yields are large enough to allow detection. Isotopes with long decay times, compared to the time between source events, result in a diffuse glow of the galactic plane from a large number of sources that contribute in a few mean deca y times (~10,000 in the case of 26Al). In case of a short decay time, one deals with a small number of sources, which must be detectable individually. The former category includes gamma-ray lines from the isotope 60Fe, which is coproduced with 26Al in ccSNe with similar yields [15, 21, 22], and the latter category includes 44Ti, which has yi elds similar to 26Al and 60Fe, but a short decay time of ~ 85 yrs, so that -ray surveys have only been able to establish one source with high significance, Cas A [23, 24].


Fig. 1: A comparison of the star formation rate estimates presented in Table 1 and discussed in the text. Our estimate based on 26Al radioactivity gamma-rays is consistent with results from alternative, albeit more indirect methods. Once nucleosynthetic yields of massive stars are better constrained, this could be one of the more precise approaches to determine the star formation rate throughout our own Galaxy. The discover y with COMPTEL [23] of the 1.157 MeV -ray line from 44Ca in the decay chain 44Ti 44Sc 44 Ca from the young (~ 335 years) and relativel y far (3.4 kpc) SNR Cas A suggested that deeper surveys would yield further detections from other supernova remnants. Despite initially promising candidates, this expectation has not yet been fulfilled [25], and The et al. [26] interpret the surprising absence of additional ray det ectable supernovae from the past three centuries as an indication that either core collapse supernovae have been improbabl y rare in recent times, or that 44Tiproducing supernovae are atypical events. Resol ving this question with still deeper -ray surveys will require a next generation instrument with at least one order of magnitude improvement in the flux limits [26]. A spatially resolved flux map like the one for 26Al does not yet exist for 60Fe. However, the presence of 60Fe in the ISM has now been detected with RHESSI [27-29] and also SPI/INTEGRAL [30]. The flux ratio of their respective lines, F60/F26 = F(1.17 or 1.33 MeV)/F(1.809 MeV), is in the range 01.-0.3 [31], and thus consistent with the predicted value of 0.15 [13]. However, the interpretation of this flux ratio is hampered by large uncertainties in the yields [21, 32] (mostly from stellar model assumptions about mass loss, rather than the uncertainties in the nuclear physics). Progress on this frontier will require a 60Fe map with a quality similar to the one accomplished for 26Al, rather than just the flux ratio. The detection of the longer-lived 60Fe isotope is opening the door to comparative studies in which the dynamic evolution of the radioactivities in the ISM can be studied. 4. CONCLUSIONS

We used the observed galactic 1.8 MeV flux measured by INTEGRAL to estimate the Galactic production rate of this isotope, and thereby inferred the average, global star formation rate. We found that about 4 ± 2 M of gas is converted to stars each year. This value assumes the IMF used in [12], corresponding to the conversion SFR = 1.96 SNR. The supernova rate SNR = 1.9 ± 1.1 events per century is the primary result of the 26Almethod, and follows from the total 1.8 MeV flux in conjunction with distribution models for massive stars and isotopic yields provided by theoretical studies of hydrostatic and explosive nuclear burning in presupernova stars and their subsequent explosions. Here we used the IMF-averaged yield that discussed in [14]. The "26Al-method" offers a unique and powerful wa y for measuring the global Galactic star formation rate, a quantity that plays a key role in Galactic astrophysics.


5. 1. 2. 3. 4. 5.

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