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A&A 592, A129 (2016)

Applying the expanding photosphere and standardized candle methods to Type II-Plateau supernovae at cosmologically significant redshifts

The distance to SN 2013eq

E. E. E. Gall1 , 2, R. Kotak1, B. Leibundgut3 , 4, S. Taubenberger2 , 3, W. Hillebrandt2 and M. Kromer5

1 Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast, BT7 1NN, UK
e-mail: egall01@qub.ac.uk
2 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching-bei-München, Germany
3 ESO, Karl-Schwarzschild-Strasse 2, 85748 Garching-bei-München, Germany
4 Excellence Cluster Universe, Technische Universität München, Boltzmannstrasse 2, 85748 Garching-bei-München, Germany
5 The Oskar Klein Centre & Department of Astronomy, Stockholm University, AlbaNova, 106 91 Stockholm, Sweden

Received: 18 February 2016
Accepted: 22 June 2016

Abstract

Based on optical imaging and spectroscopy of the Type II-Plateau SN 2013eq, we present a comparative study of commonly used distance determination methods based on Type II supernovae. The occurrence of SN 2013eq in the Hubble flow (z = 0.041 ± 0.001) prompted us to investigate the implications of the difference between “angular” and “luminosity” distances within the framework of the expanding photosphere method (EPM) that relies upon a relation between flux and angular size to yield a distance. Following a re-derivation of the basic equations of the EPM for SNe at non-negligible redshifts, we conclude that the EPM results in an angular distance. The observed flux should be converted into the SN rest frame and the angular size, θ, has to be corrected by a factor of (1 + z)2. Alternatively, the EPM angular distance can be converted to a luminosity distance by implementing a modification of the angular size. For SN 2013eq, we find EPM luminosity distances of DL = 151 ± 18 Mpc and DL = 164 ± 20 Mpc by making use of different sets of dilution factors taken from the literature. Application of the standardized candle method for Type II-P SNe results in an independent luminosity distance estimate (DL = 168 ± 16 Mpc) that is consistent with the EPM estimate.

Key words: supernovae: individual: SN 2013eq / distance scale

© ESO, 2016

1. Introduction

Supernovae have proven to be useful as distance indicators and are pivotal to estimating fundamental cosmological parameters such as the expansion rate, geometry, age, and energy content of the Universe. Observations using thermonuclear (Type Ia) supernovae (SNe) led to the surprising conclusion that the Universe was expanding at an accelerating rate (Riess et al. 1998; Perlmutter et al. 1999; Leibundgut 2001; Goobar & Leibundgut 2011).

Although the use of SNe Ia is very well established, it is also possible to use core-collapse SNe (Hamuy & Pinto 2002). In particular, two methods for distance determinations – using Type II-Plateau (P) SNe – have received the most attention. The first is the expanding photosphere method (EPM) that was developed by Kirshner & Kwan (1974) based on a proposition by Leonard Searle, who suggested that the Baade-Wesselink method (Baade 1926; Wesselink 1946), used to determine the radii of pulsating stars, could be adapted to estimate distances to SNe. This could be done by linking the photospheric expansion to the observed expansion velocities. Thus the EPM is essentially a geometrical technique relying on the comparison between the angular size of an object and its observed flux. Over the past 40 years a variety of improvements have been suggested e.g. the introduction of distance correction factors to adjust for dilution effects in scattering atmospheres, detailed modelling of SN atmospheres, and cross-correlation techniques to measure line velocities (e.g. Wagoner 1981; Eastman et al. 1996; Hamuy et al. 2001; Dessart & Hillier 2005). A somewhat different, though related form, is the spectral-fitting expanding atmosphere method (SEAM; Baron et al. 2004), in which model fits to the SN spectra are used to determine key variables.

The other commonly used method for distance determination using SNe II-P is the standardized candle method (SCM; Hamuy & Pinto 2002). It rests on the expectation that a more energetic, and consequently more luminous explosion will produce ejecta having a higher kinetic energy per unit mass. This results in a correlation between the bolometric luminosity and the expansion velocities during the plateau phase, allowing for a normalization of the SN luminosity, yielding a distance estimate. A number of groups have further built upon the SCM, for example by simplifying extinction corrections, or exploring alternatives to the commonly employed iron lines to measure the ejecta velocities (e.g. Nugent et al. 2006; Poznanski et al. 2009). Techniques relying solely on photometric data are also being explored (de Jaeger et al. 2015). The obvious advantage of being significantly less demanding in terms of the data required, comes at the cost of lowered accuracy compared to the SCM. Indeed, the above study reports a dispersion of 0.43 mag for a colour-based distance estimation method, compared to 0.29 mag for the SCM.

Even though Type II-P SNe are intrinsically fainter than SNe Ia, and thus more challenging to observe at large distances, they occur more frequently per unit volume (e.g. Li et al. 2011), allowing the possibility of building statistically significant samples. Moreover, the EPM has the striking virtue that it is independent from local calibrations – albeit at the cost of requiring multi-epoch spectroscopy alongside photometric observations. The SCM, in comparison, is less observationally expensive requiring mainly data around the midpoint of the plateau phase, but akin to the SN Ia distance determinations, it does rely on local distance anchors. Nevertheless, both methods offer alternative distance estimates, and more importantly, are affected by different systematic effects compared to the SNe Ia.

In order to create a EPM/SCM Hubble diagram based on Type II-P SNe, distance measurements at and beyond the Hubble flow are essential. Galaxies in the local neighbourhood are affected by peculiar motions that can be difficult to model and therefore limit the precision with which cosmological redshifts can be measured.

Barring a few exceptions, applications of the EPM or its variations have remained confined to SNe within the local Universe (e.g., Hamuy et al. 2001; Leonard 2002; Elmhamdi et al. 2003; Dhungana et al. 2016). To our best knowledge the EPM has only been adopted for SNe with redshifts z > 0.01 by Schmidt et al. (1994) who performed the EPM on SN 1992am at z ~ 0.049, Eastman et al. (1996) who also included SN 1992am in their sample and Jones et al. (2009) whose sample encompassed SNe with redshifts up to z = 0.028. Schmidt et al. (1994) were the first to investigate the implications of applying the EPM at higher redshifts.

On the other hand, probably due to the relative ease of obtaining the minimum requisite data, the SCM is much more commonly applied to SNe at all redshifts 0.01 < z < 0.1 (e.g. Hamuy & Pinto 2002; Maguire et al. 2010; Polshaw et al. 2015) and even to SNe IIP at redshifts z > 0.1 (Nugent et al. 2006; Poznanski et al. 2009; D’Andrea et al. 2010).

Motivated by the discovery of SN 2013eq at a redshift of z = 0.041 ± 0.001 we undertook an analysis of the relativistic effects that occur when applying the EPM to SNe at non-negligible redshifts. As a result, we expand on earlier work by Schmidt et al. (1994), who first investigated the implications of high redshift EPM. We wish to ensure that the difference between angular distance and luminosity distance – that becomes significant when moving to higher redshifts – is well understood within the framework of the EPM.

This paper is structured as follows: observations of SN 2013eq are presented in Sect. 2; we summarize the EPM and SCM methods in Sect. 3; our results are discussed in Sect. 4.

2. Observations and data reduction

SN 2013eq was discovered on 2013 July 30 (Mikuz et al. 2013) and spectroscopically classified as a Type II SN using spectra obtained on 2013 July 31 and August 1 (Mikuz et al. 2013). These exhibit a blue continuum with characteristic P-Cygni line profiles of Hα and Hβ, indicating that SN 2013eq was discovered very young, even though the closest pre-discovery non-detection was on 2013 June 19, more than 1 month before its discovery (Mikuz et al. 2013). Mikuz et al. (2013) adopt a redshift of 0.042 for SN 2013eq from the host galaxy. We obtained 5 spectra ranging from 7 to 65 days after discovery (rest frame) and photometry up to 76 days after discovery (rest frame).

2.1. Data reduction

Optical photometry was obtained with the Optical Wide Field Camera, IO:O, mounted on the 2 m Liverpool Telescope (LT; Bessell-B and -V filters as well as SDSS-r′ and -i′ filters). All data were reduced in the standard fashion using the LT pipelines, including trimming, bias subtraction, and flat-fielding.

Point-spread function (PSF) fitting photometry of SN 2013eq was carried out on all images using the custom built SNOoPY1 package within iraf2. Photometric zero points and colour terms were derived using observations of Landolt standard star fields (Landolt 1992) in the 3 photometric nights and their averaged values where then used to calibrate the magnitudes of a set of local sequence stars as shown in Table A.1 and Fig. 1 that were in turn used to calibrate the photometry of the SN in the remainder of nights. We estimated the uncertainties of the PSF-fitting via artificial star experiments. An artificial star of the same magnitude as the SN was placed close to the position of the SN. The magnitude was measured, and the process was repeated for several positions around the SN. The standard deviation of the magnitudes of the artificial star were combined in quadrature with the uncertainty of the PSF-fit and the uncertainty of the photometric zeropoint to give the final uncertainty of the magnitude of the SN.

Fig. 1

SN 2013eq and its environment. Short dashes mark the location of the supernova at , . The numbers mark the positions of the sequence stars (see also Table A.1) used for the photometric calibrations. SDSS-i′-band image taken on 2013 August 08, 8.7 d after discovery (rest frame).

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A series of five optical spectra were obtained with the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS, grating ID R300B) mounted on the Gran Telescopio CANARIAS (GTC) and the Intermediate dispersion Spectrograph and Imaging System (ISIS, grating IDs R158R and R300B) mounted on the William Herschel Telescope (WHT).

The spectra were reduced using iraf following standard procedures. These included trimming, bias subtraction, flat-fielding, optimal extraction, wavelength calibration via arc lamps, flux calibration via spectrophotometric standard stars, and re-calibration of the spectral fluxes to match the photometry. The spectra were also corrected for telluric absorption using a model spectrum of the telluric bands.

A weak Na i D absorption, with an equivalent width of EWNa I D = 0.547 ± 0.072 Å, can be detected in the +25 d spectrum of SN 2013eq. Applying the empirical relation between Na i D absorption and dust extinction given in Poznanski et al. (2012, Eq. (9)), this translates into an extinction within the host galaxy of E(BV)host = 0.062 ± 0.028 mag. Even though the EW Na i D absorption is a commonly used diagnostic of extinction, as has been noted on numerous occasions, it is not always reliable (e.g. Poznanski et al. 2012). Given the remote location of SN 2013eq (projected distance of ~14.6 kpc from the host galaxy nucleus, assuming z = 0.041 and H0 = 70 km s-1 Mpc-1), the host extinction deduced above is likely to be an upper limit. Although one expects the local environments of core-collapse SNe to be different from those of SNe Ia, there is some indication for a positive correlation between AV and the radial position of the SN within the host galaxy (e.g. Holwerda et al. 2015). For the Galactic extinction we adopt a value of E(BV)Gal = 0.034 mag (Schlafly & Finkbeiner 2011).

The Na i D absorption lends itself to an estimate of the redshift. Applying Eq. (12) in Leonard et al. (2002, using the values for the rest wavelengths and oscillator strengths of the individual lines as given in their Table 4), and taking the rest wavelength of the Na i D λλ5890, 5896 multiplet to be λNa I D = 5891.94 Å, a comparison with the observed wavelength of the blend in our +25 d spectrum yields z = 0.041 ± 0.001. This is consistent with the redshift of 0.042 reported by Mikuz et al. (2013) for the host galaxy of SN 2013eq. As a further test we performed a series of cross correlations using SNID (Supernova Identification, Blondin & Tonry 2007). Suggested matches were scrutinized and the selected results span a range of redshifts consistent with our result. We therefore adopt z = 0.041 ± 0.001 as redshift of the SN.

2.2. Photometry

SN 2013eq was likely observed shortly after peaking in the optical bands (the light curve clearly shows a decline before settling onto the plateau), and the initial magnitudes of 18.548 ± 0.030 and 18.325 ± 0.022 measured in Bessell-B and SDSS-r′, respectively, are presumably very close to the maximum in these bands. The light curves initially decline at relatively steep rates of 3.5 ± 0.1 mag/100 d in Bessell-B, 2.1 ± 0.2 mag/100 d in Bessell-V, 2.1 ± 0.2 mag/100 d in SDSS-r′, and 3.4 ± 0.1 mag/100 d in SDSS-i′ until about 10 to 15 days after discovery. Then the decline rates slow down to 0.95 ± 0.02 mag/100 d in Bessell-V, 0.17 ± 0.02 mag/100 d in SDSS-r′, and 0.60 ± 0.03 mag/100 d in SDSS-i′ between ~25 d and ~55 d after discovery, whilst the Bessel-B light curve displays no break. Type II-P SNe display a plateau phase with almost constant brightness after a short (or sometimes negligible) initial decline (e.g. Anderson et al. 2014). Typically the plateau phase lasts up to 100 d before the light curve drops onto the radioactive tail. This transition was, however, not observed for SN 2013eq. Table A.2 shows the log of imaging observations as well as the final calibrated magnitudes. The light curve is presented in Fig. 2.

Fig. 2

Bessell-B, V, SDSS-r′, i′ light curves of SN 2013eq. The vertical ticks on the top mark the epochs of the observed spectra. The unfiltered magnitudes are from Mikuz et al. (2013).

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2.3. Spectroscopy

Table A.3 shows the journal of spectroscopic observations. In addition to the spectra obtained for our study we also included the publicly available classification spectrum3 obtained on 2013 July 31 and August 1 (Mikuz et al. 2013). The fully reduced and calibrated spectra of SN 2013eq are presented in Fig. 3. They are corrected for reddening (E(BV)tot = 0.096 mag) and redshift (z = 0.041).

Fig. 3

SN 2013eq spectroscopy. The first (+2 d) spectrum is the classification spectrum (Mikuz et al. 2013; Tomasellaet al. 2014). Flux normalized to the maximum Hα flux for better visibility of the features. The exact normalizations are: flux/1.9 for the +1 d and +7 d spectrum; flux/2.0 for +11 d; flux/2.2 for +15 d; flux/2.1 for +25 d; flux/2.3 for +65 d.

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The strongest feature in the spectra is Hα, which would be matched by the corresponding features at about 4850 Å, 4300 Å and 4100 Å in the blue to be Hβ, Hγ and Hδ. In the classification spectrum, Hα and Hβ profiles are visible though relatively weakly. They become stronger at later epochs and we can discern also Hγ, and Hδ. We can also discern a feature at about 5900 Å which is typically assigned to He i λ5876. Leonard et al. (2002) claim that it evolves into a blend with Na i D at later epochs in SN 1999em.

Finally, we can observe weak lines of iron between 4000 and 5500 Å. In particular Fe ii λ5169 which is visible in the spectra from +11 d on. Fe ii λ5018 is visible only in the +65 d spectrum. At this epoch we also see weak lines around 4450 Å and 4860 Å which have been attributed to a blend of Fe ii, Ba ii and Ti ii in SN 1999em by Leonard et al. (2002). The pseudo-equivalent width (pEW) of the Fe ii λ5018 feature can be used as a proxy for the progenitor metallicity (Dessart et al. 2014). For SN 2013eq, we measure a pEWFe II λ5018 = −13.4 ± 0.4 Å  in our 65 d spectrum, that would place it in the 0.1-0.4 Z range, provided the 15 M models are an appropriate choice for SN 2013eq. Interestingly, in their study of the potentially very low metallicity (Z ≲ 0.1 Z) Type II-P supernova, LSQ13fn, Polshaw et al. (2016) find that the SCM relation is violated.

3. Methods

3.1. The expanding photosphere method

As mentioned earlier, the EPM was originally suggested by Kirshner & Kwan (1974) and in the past decades a number of improvements and variations have been presented. In this section, however, we will only outline the most basic principle of the EPM, laying the foundation for the more detailed derivations in Sect. 3.2 regarding the application of the EPM at higher redshifts.

The photospheric angular size ϑ of a Type II supernova of redshifts z ≪ 1 can be described as4: (1)where R is the photospheric radius, D the distance to the SN, fλ the observed flux density, ζλ the distance correction factor or dilution factor, and Bλ(T) the Planck function evaluated at observed photospheric temperature T. ζλ is derived from model atmospheres and is used to correct dilution effects of scattering atmospheres meaning that a SN will not emit as a perfect black body. Approximately one day after explosion the SN achieves a state of homologous expansion and the photospheric radius of the SN at a certain time t is (2)v is the photospheric expansion velocity of the SN, t0 is the time of explosion and R0 the initial radius. Compared to the extent of the ejecta R0 becomes negligible very soon. It should be noted that neglecting R0 can introduce a small error when applying Eq. (2) at epochs within the first 1–2 weeks after explosion, where – depending on the photospheric velocities and the initial radius of a particular SN – R0 might still be in the 10% range of the photospheric radius R. Combining Eqs. (1) and (2) the relation between the photospheric angular size ϑ, the photospheric expansion velocity v, measured at time t can be expressed as (3)This means that with a minimum of two measurements spaced in time of ϑ and v, Eq. (3) can be solved for the distance D and time of explosion t0.

3.2. EPM at high redshifts

The comparison of the flux with the angular size of an object forms the cornerstone on which the concept of the EPM rests (cf. Eq. (1)). However, it is advisable to be prudent when dealing with SNe at non-negligible redshifts, where the “angular distance” and the “luminosity distance” differ by a factor of (1 + z)2 (e.g. Rich 2001): (4)While at z = 0.01 a factor of (1 + z)2 results only in a ~2% discrepancy, this effect increases quadratically and at a redshift of only 0.05 the difference between luminosity distance and angular distance is already ~10%.

Bearing in mind our derived redshift of z = 0.041 ± 0.001 for SN 2013eq, relativistic effects cannot be ignored. We therefore re-derive the basic equation for the EPM for non-negligible redshifts. In the following “” will be used to denote the SN rest frame, while “◇” will be used for variables in the observed frame.

The luminosity distance to the SN, DL, can be expressed as (5)where is the observed energy flux in the observed wavelength interval Δλ, corrected for galactic and extragalactic extinction and Lλ is the total monochromatic luminosity in the rest frame wavelength interval Δλ. The factor (1 + z) takes into account that and Lλ are given in different coordinate systems. Lλ can also be expressed in terms of the monochromatic radiation emitted in all directions: , where Bλ(T) is the Planck function evaluated at the photospheric temperature T of the SN and is the surface area of the SN with radius R. ζλ is the dilution factor in the SN rest frame. Equation (5) can therefore be rewritten as: (6)The photospheric angular size, or angular separation of the photosphere, θ5 of a SN can be expressed as (7)where Dθ is the “angular distance”.

When dealing with non-negligible redshifts, the two terms in Eqs. (6) and (7), are obviously not the same. While Eq. (1) is indeed valid for z ≪ 1 Eqs. (4), (6) and (7) can be combined to derive the correct relation between θ and the observed flux: (8)where we defined θ: = θ/ (1 + z)2. Even though θ is not an “angular size” in the mathematical sense, it corresponds6 to the “angular size”, ϑ, that was utilized for EPM in previous publications (e.g. Schmidt et al. 1994; Jones et al. 2009). Equation (3) thus transforms to (9)or (10)where t is the time in the SN rest frame.

After careful examination of the various equations finding their way into the final distance result, let us draw attention to a few particular points.

  • First, the term in Eq. (8) can be transformed to in the SN rest frame by applying a K-correction to observed flux. This was already recognized by Schmidt et al. (1994, see their Eq. (6)) who also note that their θ (which corresponds to in this paper) is not an “angular size” as in Wagoner (1977). Consequently, their distance result has to be interpreted as a luminosity distance.

  • Second, in order to determine the correct angular size, θ, of objects at non-negligible redshifts the factor of (1 + z)2 has to be taken into account.

  • Third, when calculating the luminosity distance instead of the angular distance the factors of (1 + z)2 in Eqs. (4) and (8) “cancel” each other out, resulting in Eq. (10) which is basically identical to the formulation that is commonly used (see Eq. (3)). In short, the use of θ will result in an angular distance, while the use of θ will result in a luminosity distance. This is a vital distinction that has, to our best knowledge, hitherto been ignored. Accordingly, EPM distance results in literature that follow a formulation similar to Eq. (3) – the correct high-redshift formulation of which is Eq. (10) – should be regarded as luminosity distances.

We want to emphasize that in order to correctly apply the EPM also to SNe at non-negligible redshifts the only correction to be made (compared to the low redshift EPM) is the K-correction of the observed flux. This implies the use of θ in Eq. (10) and also means that previously published applications of the EPM are correct (regarding this matter) if the resulting distances are seen as luminosity distances and K-corrections were either applied or negligible.

3.3. The standardized candle method

The SCM for Type II SNe was first suggested by Hamuy & Pinto (2002). Here however, we follow the approach of Nugent et al. (2006), who were the first to apply the SCM to SNe at redshifts of up to z ~ 0.3. The basic concept of the SCM is briefly outlined in the following.

Equation (1) in Nugent et al. (2006) describes a correlation between the rest frame I-band magnitude, MI, the rest frame (VI)-colour and the expansion velocity at 50 days after explosion: (11)with α = 5.81, MI0 = −17.52 (for an H0 of 70 km s-1 Mpc-1) and (VI)0 = 0.53. An advantage of this formulation is that no reddening correction is required for the observed photometry which can introduce an additional error if the host galaxy reddening is unknown. This works reasonably well under the assumption that the extinction laws are similar in most galaxies. Therefore the observed magnitudes only need to be transformed to the rest frame which can be easily attended to by applying a K-correction. Consequently, Eq. (11) can be adopted for local as well as more distant SNe. A practical limitation may be the spectral coverage of the rest frame I band at higher redshift needed for a precise K-correction.

The expansion velocity is typically estimated using the Fe ii λ5169 line (e.g. Hamuy & Pinto 2002; Nugent et al. 2006; Poznanski et al. 2009). As spectroscopic data 50 days after explosion might not always be available, Nugent et al. (2006) explored the time dependence of the Fe ii λ5169 velocity and found that at 50 d after explosion it can be estimated using the following relation (Nugent et al. 2006, Eq. (2)): (12)where v(t) is the Fe ii λ5169 velocity at time t after explosion.

4. Results and discussion

Measuring the distance to SN 2013eq using the EPM or SCM, requires a number of preparatory steps, like deriving the colour temperatures and velocities (for EPM) or the magnitudes and velocities at 50 days after explosion (for SCM). The EPM additionally relies on the use of appropriate dilution factors7. Eastman et al. (1996) calculated model atmospheres for Type II SNe and derived a set of dilution factors for the filter combinations {BV}, {VIC}, {BVIC} and {JHK}. Hamuy et al. (2001) later re-calculated the dilution factors for a different photometric system and expanded the number of filter combinations to {BV}, {VI}, {BVI}, {VZ}, {VJ}, {VH}, {VK}, and {JHKN} using the same atmospheric models. Dessart & Hillier (2005) also computed dilution factors for the filter sets {BV}, {VI}, {BVI} and {JHK}, based on a large set of photospheric-phase models of Type II SNe. The R-band is typically excluded due to the strong Hα contribution.

In the case of SN 1999em, the EPM distance derived by Leonard et al. (2002) using the dilution factors from Hamuy et al. (2001) was ~30 % shorter than the Cepheid distance to the host galaxy of SN 1999em, NGC 1637 (11.7 ± 1.0 Mpc, Leonard et al. 2003). This discrepancy was resolved by Dessart & Hillier (2006) who applied the dilution factors reported in Dessart & Hillier (2005); these are systematically larger than those of Hamuy et al. (2001). This resulted in a distance estimate to ~1.7% of the Cepheid value.

Here, we will use the dilution factors given by both Hamuy et al. (2001) and Dessart & Hillier (2005), for the filter combination BVI, respectively, so as to include all available data for SN 2013eq in our EPM distance estimate.

4.1. Temperature evolution

Ideally, an estimate of the photospheric temperature should be used for the EPM. In practice however, it is difficult to directly measure the photospheric temperature. Consequently, the colour temperature is commonly used for the EPM as an estimator for the photospheric temperature (e.g. Hamuy et al. 2001; Leonard et al. 2002; Dessart & Hillier 2005; Jones et al. 2009). While these are conceptionally different, this should be a reasonable approximation. In particular, the dilution factors presented in either Hamuy et al. (2001) or Dessart & Hillier (2005) are functions of specific colour temperatures. In our case we use the B, V, and I photometry to estimate the colour temperature as to be consistent with the BVI dilution factors.

This in turn requires us to transform the SDSS-i band photometry to the Johnson-Cousins Filter System used in Hamuy et al. (2001) and Dessart & Hillier (2005). Taking into consideration that the EPM requires the flux in the SN rest frame we first calculate K-corrections by using the SN 2013eq spectroscopy and the snake code (SuperNova Algorithm for K-correction Evaluation) within the S3 package (Inserra et al. 2016). For the SDSS-i filter we determine the K-correction to the rest frame Johnson-Cousins I band. Then, the uncorrected observed photometry is interpolated to the epochs of spectroscopic observations, and subsequently dereddened and K-corrected. Eventually, the adjusted B, V, and I-band magnitudes are converted into physical fluxes. The colour temperature at each epoch is derived by fitting a black body curve to the deduced fluxes and effective wavelengths of the corresponding filters.

We carried out ancillary blackbody fits and added or subtracted the uncertainties in all possible combinations. The standard deviation of the resulting range of temperatures was taken to be a conservative estimate of the uncertainty in the temperature. We adopted this approach in order to make full use of all available information across all bands.

The results are presented in Table 1.

4.2. Velocities

The knowledge of the line velocities in SN 2013eq is crucial to both the EPM and the SCM. The velocities are measured using iraf by fitting a Gaussian function to the minima of the various lines. The uncertainty in the velocity determination is presumed to be in the 5% range.

Dessart & Hillier (2005) show that the velocity measured from the Fe ii λ5169 absorption matches the photospheric velocity within 5–10%. However, they also point out that this line is only visible at later epochs. Leonard et al. (2002) and Leonard (2002) argue that lines such as Fe ii λλ5018, 5169 will overestimate the photospheric velocities and that instead weak Fe ii lines such as λλ4629, 4670, 5276, 5318 give more accurate results. An overestimation of the photospheric velocities would lead to distances that are too large for both the EPM and the SCM.

Whilst a precise stipulation of the photospheric velocity is indeed desirable we have to bear in mind that in the case of SN 2013eq, many of the weaker lines favored by Leonard et al. (2002) and Leonard (2002) for the EPM are only visible in the +65 d spectrum. However, the EPM requires measurements of the photospheric velocity for no less than two epochs. This leaves only three possible Fe ii lines that are visible in more than one spectrum of SN 2013eq: Fe ii λ5018, Fe ii λ5169 and the blended line Ba ii / Fe ii λ6147. For the purposes of the EPM an average of the measured absorption velocities from these three lines will be used (see Table 2).

For the SCM we infer the velocity at 50 days after explosion by means of the Fe ii λ5169 velocities and Eq. (12) (see Sect. 4.4 for more details).

4.3. The EPM distance to SN 2013eq

Having performed all necessary measurements we are now ready to wade into the final steps towards calculating an EPM distance for SN 2013eq. As mentioned above, we use the BVI dilution factors as given by Hamuy et al. (2001, which are based on the dilution factors calculated by Eastman et al. 1996 and Dessart & Hillier (2005). Both groups find that the dilution factor essentially is a function of the colour temperature that can be described as ζ(TS) = ∑ iaS,i(104 K /TS)i with S representing the filter subset (in our case {BVI}). The parameters aS,i are given in Appendix C, Table 14 for Hamuy et al. (2001) and Table 1 for Dessart & Hillier (2005).

In order to apply Eq. (8) to SN 2013eq we rewrite it as (13)where λ,effF is the effective wavelength of the corresponding Filter, F, in the rest frame. Note that we use θ instead of θ in our calculations in order not to introduce an additional error on the final result due to the uncertainty of the redshift.

Finally, rearranging Eq. (10) gives us: (14)For each filter B, V, and I, values of χ at the corresponding epochs are fitted linearly using DL and as parameters. The errors are estimated by executing complementary fits through the same values of χ, but adding or subtracting the uncertainties in all possible combinations. The standard deviations of the resulting range in distances as well as epochs of explosion are then employed as conservative estimates of their respective uncertainties. The results are presented in Fig. 4 and Table 3 for each set of dilution factors from Hamuy et al. (2001) and Dessart & Hillier (2005), respectively.

Note that while the derived distances and explosion epochs in the B- and I-band are very similar, the V-band distance is about 24% smaller than the I-band distance for both sets of dilution factors. Similar effects have also been observed by other groups performing the EPM. Hamuy et al. (2001), for example, find a difference of up to 20% in their distances when applying the EPM to SN 1999em for varying filter combinations and attribute these disparities to systematic errors in the dilution corrections. Jones et al. (2009) apply the EPM to 12 SNe and find varying results for for different filter combinations for all their SNe. In the case of SN 1999em the distances reported by Jones et al. (2009) differ by almost 26% between the BV and the VI filter combinations. It stands to reason that the discrepancies appearing when applying the EPM for different filter combinations are reflected also when applying it to single filters instead of filter combinations.

This disagreement could be due to the use of tabulated dilution factors. Dessart & Hillier (2006) find that when using models tailored to SN 1999em, the EPM distances derived in the different band passes are in accord with each other. An advantage of using tailored models is that the dilution factors can be evaluated alongside other EPM parameters (such as the colour temperature), and can thereby be adjusted for differences between individual SNe. For instance, our observations (Sect. 2.3) imply a subsolar metallicity for SN 2013eq, but the dilution factors are only available for solar metallicity models. Nevertheless, such tailored approaches remain currently unviable even for small sample sizes, and will be even more so for the significantly larger samples that will become available in the near future.

Our final errors on the distance are in the range of ~12% and take into account the uncertainties from the magnitudes, the redshift, the K-corrections, the velocities and the host galaxy reddening. These are propagated through all calculations and build the basis for the uncertainties of the flux, the colour temperature, and the angular size. In an attempt to estimate the global errors of their distances Jones et al. (2009) perform 1000 Monte Carlo simulations varying over parameters such as photometry, redshift, foreground & host-galaxy extinction, line expansion velocity, photospheric velocity conversion as well as dilution factors and find errors between 10 and 41% for distances to the SNe in their sample. Leonard (2002) follow a similar approach in calculating a set of simulations while varying over the velocities, magnitudes and dilution factors. They find statistical distance errors for SN 1999em of only a few percent, however they point out that the error of the EPM distance to SN 1999em is likely dominated by systematic errors as the results derived using dilution factors for different filter combinations vary by as much as 19%. Dessart & Hillier (2006) discuss potential error sources in detail. In particular, they note that the uncertainty in the angular size, propagated from the error in the flux, is temperature dependent, and that an uncertainty in the flux has a larger influence on the final error than an uncertainty in E(BV). This stems from the fact that extinction effects on the temperature estimate and the measure of the angular size will compensate each other to some extent. This has also been discussed previously by Schmidt et al. (1992), Eastman et al. (1996), and Leonard et al. (2002).

4.4. The SCM distance to SN 2013eq

Compared to the EPM the utilization of the SCM is somewhat less laborious. As mentioned in Sect. 3.3, to begin with, the magnitudes used for the SCM have to be transformed to the SN rest frame. We therefore calculate K-corrections by using the SN 2013eq spectroscopy and the snake code (SuperNova Algorithm for K-correction Evaluation) within the S3 package (Inserra et al. 2016). For the SDSS-i′ band we select the K-corrections to the rest frame Johnson-Cousins I filter. These values are then interpolated to an epoch of 50 d post-explosion.

We next need to derive the magnitude I50 and colour (VI)50 i.e., 50 d after explosion. We therefore fit low-order polynomials to the uncorrected photometry and subsequently transform it to the rest frame by applying the K-corrections. The expansion velocity is determined using the relation in Eq. (12). We then use our measured Fe ii λ5169 velocities to estimate an appropriate value for 50 d.

We repeated the above procedure three times using the epoch of explosion derived via EPM with the dilution factors from Hamuy et al. (2001) and Dessart & Hillier (2005). We additionally, estimated the explosion epoch by utilizing the average rise time for SNe II-P of 7.0 ± 0.3 as given by Gall et al. (2015) assuming that SN 2013eq was discovered close to maximum. This is likely a valid assumption given its spectral and photometric evolution. Applying, Eq. (11) – which essentially describes the relation between the I-band magnitude, the (VI)-colour and the expansion velocity 50 days after explosion – for each of the three cases, gives us MI50. Finally, the distance modulus can be calculated, μ = I50MI50, which in turn can be converted into a luminosity distance via DL [Mpc] = 10μ/ 5−5 Mpc.

Note that the uncertainty in the explosion epoch will introduce an error in all quantities derived at 50 days after explosion. An earlier explosion epoch will ultimately result in a larger distance. This has been discussed also by Nugent et al. (2006), who found that the explosion date uncertainty has the largest impact on the final error compared to other contributions, and also by Poznanski et al. (2009) who, in contrast, find that their results vary only little with the explosion epoch arguing that the magnitudes and colours are relatively constant during the plateau phase. We find that even though the explosion epoch for SN 2013eq by applying the EPM has relatively large uncertainties, this contributes only little to the uncertainties of the V- and I-band magnitudes and consequently also the (VI) colour at 50 days after explosion. These are of the same order as the original uncertainties in the photometry. The time of explosion uncertainty is, however, more significant when determining the expansion velocity at 50 days, although the error in the Fe ii λ5169 velocities and the intrinsic error in Eq. (12) also contribute to the total error.

The uncertainty in the redshift plays an almost negligible role. For completeness we did however propagate its error when accounting for time dilation. Note that Hamuy & Pinto (2002) find peculiar motions in nearby galaxies (cz< 3000 km s-1) contribute significantly to the overall scatter in their Hubble diagram; however this is not a relevant issue for SN 2013eq.

The final uncertainties in the distance modulus and the distance are propagated from the errors in MI50, v50,Fe ii and (VI)50. The derived distance moduli and luminosity distances as well as the intermediate results are given in Table 4.

4.5. Comparison of EPM and SCM distances

An inspection of Table 3 reveals that the two EPM luminosity distances derived using the dilution factors from Hamuy et al. (2001) and Dessart & Hillier (2005) give consistent values. This is no surprise, bearing in mind that the dilution factors from Hamuy & Pinto (2002) and Dessart & Hillier (2005) applied for SN 2013eq differ by only 18–27% (see Table 2). Similarly, the resulting explosion epochs are also consistent with each other.

Likewise, the SCM distances calculated utilizing the times of explosion found via EPM and the dilution factors from either Hamuy & Pinto (2002) or Dessart & Hillier (2005, see Table 4, as well as by adopting the average SN II-P rise time as given by Gall et al. (2015), are consistent not only with each other but also with the EPM results.

It is remarkable how close our outcomes are within the errors to the distance of 176 Mpc calculated from the redshift of SN 2013eq with the simple formula D = cz/H0 (for H0 = 70 km s-1 Mpc-1). While this is of course no coincidence for the SCM-distances (which are based on H0 = 70 km s-1 Mpc-1), the EPM-distance is completely independent as to any assumptions concerning the Hubble constant. This is particularly encouraging, considering the scarcity of data points for our fits stemming mostly from the difficulty of measuring the velocities of weak iron lines in our spectra. It seems that both the SCM and the EPM are surprisingly robust techniques to determine distances even at non-negligible redshifts where high cadence observations are not always viable.

5. Conclusions

We presented optical light curves and spectra of the Type II-P SN 2013eq. It has a redshift of z = 0.041 ± 0.001 which inspired us to embark on an analysis of relativistic effects when applying the expanding photosphere method to SNe at non-negligible redshifts.

We find that for the correct use of the EPM to SNe at non-negligible redshifts, the observed flux needs to be converted into the SN rest frame, e.g. by applying a K-correction. In addition, the angular size, θ, has to be corrected by a factor of (1 + z)2 and the resulting EPM distance will be an angular distance. However, when using a modified version of the angular size θ = θ/ (1 + z)2 the EPM can be applied in the same way as has previously been done for small redshifts, with the only modification being a K-correction of the observed flux. The fundamental difference is that this will result in a luminosity distance instead of an angular distance.

For the SCM we follow the approach of Nugent et al. (2006), who outline its use for SNe at cosmologically significant redshifts. Similar to the EPM their formulation of the high redshift SCM requires the observed magnitudes to be transformed into the SN rest frame, which in practice corresponds to a K-correction.

We find EPM luminosity distances of DL = 151 ± 18 Mpc and DL = 164 ± 20 Mpc as well as times of explosions of 4.1 ± 4.4 d and 3.1 ± 4.1 d before discovery (rest frame), by using the dilution factors in Hamuy et al. (2001) and Dessart & Hillier (2005), respectively. Assuming that SN 2013eq was discovered close to maximum light this would result in rise times that are in line with those of local SNe II-P (Gall et al. 2015). With the times of explosions derived via the EPM – having used the dilution factors from either Hamuy et al. (2001) or Dessart & Hillier (2005) – we find SCM luminosity distances of DL = 160 ± 32 Mpc and DL = 157 ± 31 Mpc. By utilizing the average rise time of SNe II-P as presented in Gall et al. (2015) to estimate the epoch of explosion we find an independent SCM distance of DL = 168 ± 16 Mpc.

The luminosity distances derived using different dilution factors as well as either EPM or SCM are consistent with each other. Considering the scarcity of viable velocity measurements it is encouraging that our results lie relatively close to the expected distance of ~

Table 1

Interpolated rest frame photometry and temperature evolution of SN 2013eq.

Table 2

EPM quantities for SN 2013eq.

Table 3

EPM distance and explosion time for SN 2013eq.

Table 4

SCM quantities and distance to SN 2013eq.

A&A 580, A108 (2015)

The protoMIRAX hard X-ray imaging balloon experiment

João Braga, Flavio D’Amico, Manuel A. C. Avila, Ana V. Penacchioni, J. Rodrigo Sacahui, Valdivino A. de Santiago Jr., Fátima Mattiello-Francisco, Cesar Strauss and Márcio A. A. Fialho

National Institute of Space Research – INPE, Av. dos Astronautas 1758, 12227–010 São José dos Campos, SP, Brazil
e-mail: joao.braga@inpe.br

Received: 17 April 2015
Accepted: 22 May 2015

Abstract

Context. The protoMIRAX hard X-ray imaging telescope is a balloon-borne experiment developed as a pathfinder for the MIRAX satellite mission. The experiment consists essentially in a coded-aperture hard X-ray (30–200 keV) imager with a square array (13 × 13) of 2 mm-thick planar CZT detectors with a total area of 169 cm2. The total, fully-coded field-of-view is 21° × 21° and the angular resolution is 1°43′.

Aims. The main objective of protoMIRAX is to carry out imaging spectroscopy of selected bright sources to demonstrate the performance of a prototype of the MIRAX hard X-ray imager. In this paper we describe the protoMIRAX instrument and all the subsystems of its balloon gondola, and we show simulated results of the instrument performance.

Methods. Detailed background and imaging simulations were performed for protoMIRAX balloon flights. The 3σ sensitivity for the 30–200 keV range is ~1.9 × 10-5 photons cm-2 s-1 for an integration time of 8 h at an atmospheric depth of 2.7 g cm-2 and an average zenith angle of 30°. We developed an attitude-control system for the balloon gondola and new data handling and ground systems that also include prototypes for the MIRAX satellite.

Results. We present the results of Monte Carlo simulations of the camera response at balloon altitudes, showing the expected background level and the detailed sensitivity of protoMIRAX. We also present the results of imaging simulations of the Crab region.

Conclusions. The results show that protoMIRAX is capable of making spectral and imaging observations of bright hard X-ray source fields. Furthermore, the balloon observations will carry out very important tests and demonstrations of MIRAX hardware and software in a near space environment.

Key words: stars: black holes / balloons / instrumentation: detectors / methods: laboratory: solid state / telescopes / space vehicles: instruments

© ESO, 2015

1. Introduction

Coded mask experiments have been widely used in astronomical hard X-ray (E ≳ 10 keV) observations of the sky due to several factors. First, the technology for developing focusing telescopes above these energies has only recently been mastered and implemented, especially in the NuSTAR observatory (Harrison et al. 2013). The ASTRO-H mission, expected to be launched in the near future, will also make use of focusing optics in the hard X-ray range through its Hard X-ray Telescope (HXT; Takahashi et al. 2014). While providing much higher sensitivities and better angular resolution in general, these instruments require very long focal lengths and sophisticated control and alignment systems. In addition, the highest energy achievable is still significantly below 100 keV, even though there are promising higher energy (≲600 keV) focusing techniques such as the Laues lenses being developed (Virgilli et al. 2013). Coded mask instruments, on the other hand, allow imaging over very wide fields of view (which can be a significant portion of the sky) and up to energies of several hundred keV. Another factor is that coded mask instruments can be compact and easy to implement, making them good options for wide-field hard X-ray and low-energy γ-ray monitors of the highly variable and transient source populations in this energy range. Important examples of coded mask satellite instruments that have made significant contributions to astronomy are the SIGMA (Paul et al. 1991) and ART-P (Sunyaev et al. 1990) instruments onboard GRANAT, the ASM on RXTE (Levine et al. 1996), the WFCs on BeppoSAX (Jager et al. 1997), the WFM on HETE-2 (Ricker et al. 2003), instruments on the INTEGRAL satellite (Winkler 1995), and Swift/BAT (Gehrels & Swift Team 2004).

In this paper we describe the protoMIRAX balloon experiment, a wide-field hard X-ray coded mask imager under development at the National Institute for Space Research (INPE) as a pathfinder for the MIRAX (Monitor e Imageador de Raios X) satellite mission (Braga et al. 2004). The main instrument of the balloon payload is a hard X-ray camera that employs an array of 13 × 13 CdZnTe (CZT) detectors as the position-sensitive detector plane. The experiment will be launched on a stratospheric balloon over Brazil at a latitude of ~23° S to carry out imaging spectroscopy of selected bright sources. In addition to testing the camera perfomance in a near-space environment, the experiment is a testbed for new space technologies being developed at INPE. A new attitude control and pointing system for scientific balloon gondolas, including two new star trackers, will be tested, as well as novel data handling and ground support systems.

In Sect. 2 we present the scientific objectives of the experiment. In Sect. 3 we describe the X-ray camera and the other subsystems that protoMIRAX comprises. In Sect. 4 we present the results of Monte Carlo simulations of the camera response at balloon altitudes, showing the expected background level and the detailed sensitivity of protoMIRAX. A simulated image of the Crab region is shown in Sect. 5. We present our conclusions in Sect. 6.

2. Scientific objectives

The protoMIRAX experiment will perform imaging spectroscopy with good energy resolution of bright Galactic hard X-ray sources such as the Crab nebula (and its pulsar) and the Galactic center complex.

In X-ray astronomy, the Crab has been considered as a standard candle owing to its large and nearly constant flux at Earth (see Bühler & Blandford 2014; and Madsen et al. 2015, for recent reviews). At X-ray energies above ~30 keV, the Crab is generally the strongest persistent source in the sky, and it has a diameter of ~1 arcmin. The Crab has experienced some recent flares in the GeV range (Tavani et al. 2011) that were simultaneous or just previous to a particularly active period in hard X-rays (Wilson-Hodge et al. 2011). Those surprising variations represent a few percent of the persistent flux on the 50–100 keV energy range. ProtoMIRAX will be able to measure the Crab spectrum from 30 to 200 keV. These observations will also be used for flux calibrations and imaging demonstrations.

The Galactic center (GC) region is very favorable for protoMIRAX observations thanks to its declination of δ ~ − 29°, since the balloon will fly over a region at latitudes of ~–23°. One of the most interesting sources is 1E 1740.7−2942, the brightest and hardest persistent X-ray source within a few degrees of the GC. Because of a similar hard X-ray spectrum and comparable luminosity to Cygnus X-1 (Liang & Nolan 1984), 1E 1740.7−2942 is classified as a black hole candidate. Because of the two-sided radio jets associated to the source, the object was dubbed the first “microquasar” (Mirabel et al. 1992), an X-ray binary whose behavior mimics quasars on a much smaller scale. Since the GC direction has extremely high extinction, a counterpart has not yet been identified despite deep searches in both the optical and IR bands. The source was recently studied by our group from soft to hard X-rays up to 200 keV (Castro et al. 2014), showing spectra that can be modeled very well by thermal Comptonization of soft X-ray photons. We will image the Galactic center region with protoMIRAX with 1E 1740.7−2942 in the center of the field of view (FOV). Our observations in the hard X-ray band could be useful for measuring flux and spectral parameters, especially because the source is in the hard state most of the time.

Another interesting source that will be in the same FOV is GRS 1758−258, also a microquasar, and one of the brightest X-ray sources near the GC at energies greater than 50 keV (Sunyaev et al. 1991a). Like its sister source 1E 1740.7−2942, GRS 1758−258 spends most of the time in the hard state. Its hard X-ray spectra and variability are also similar to Cyg X-1 (Kuznetsov et al. 1996). GRS 1758−258 also does not have an identified counterpart yet, so its mass and orbital periods are still unknown. The protoMIRAX observations will in principle be capable of attaining spectral and flux information about GRS 1758−258.

The GC field to be observed by protoMIRAX will also include GX 1+4, the best studied accreting pulsar around the GC, with a pulse period on the order of two minutes. This object is the prototype of the small but growing subclass of slowly rotating accreting X-ray pulsars called symbiotic X-ray binaries (SyXB), in which a neutron star accretes from the wind of an M-type giant companion (Masetti et al. 2006). GX 1+4 is a persistent source, but with strong, irregular flux variations on various timescales and extended hard/low states. Its peculiar spin history has been the object of intensive study (Nagase 1989), and Makishima et al. (1988) have shown a clear transition from spin-up to spin-down behavior in the equilibrium period, characterizing a torque-reversal episode. More recent studies (González-Galán et al. 2012) have used data from BeppoSAX, INTEGRAL, Fermi and Swift/BAT to show that the source continues its spin-down trend with a constant change in frequency, and the pulse period has increased by ~50% over the past three decades. Since the source is highly variable, our spectral and timing observations can possibly contribute to the flux and period histories for this peculiar object.

Besides providing new data on astrophysical sources, the experiment will be able to make precise measurements of the hard X-ray background at balloon altitudes for the Brazilian mid-latitudes, which is important for investigating the South Atlantic Anomaly (SAA) and Space Weather phenomena.

3. The protoMIRAX experiment

The protoMIRAX experiment consists basically in a hard X-ray imaging camera mounted in a stratospheric balloon gondola capable of carrying out pointing observations of selected target regions. Table 1 presents an overview of the experiment’s baseline parameters.

3.1. The X-ray camera

The X-ray camera (XRC) is a coded-aperture wide-field hard X-ray imager that consists in an aluminum tower-like structure that supports an array of X-ray detectors, a collimator, a coded mask, passive shields and other electrical shielding and supporting components. In this section we describe each component of the XRC in detail.

3.1.1. The X-ray detectors

The X-ray detectors we use in this experiment are band-gap, room-temperature semiconductors made of an alloy of 90% cadmium telluride (CdTe) and 10% zinc telluride (ZnTe), called CdZnTe or simply CZT. They have high photoelectric efficiency up to hundreds of keV, owing to the high atomic numbers of Cd (Z = 48) and Te (Z = 52) and a density of 6 g cm-3. The probability of photoelectric absorption per unit pathlength is roughly a factor of 4 to 5 times higher than in Ge for typical gamma-ray energies. The relatively large band gap of 1.5 eV precludes significant thermal excitations at room temperature and provides good enough energy resolution (ΔE/E ≲ 10% at 60 keV).

CZT detectors have often been used in X-ray astronomy because of their high efficiency with small thickness (thus reducing background, which scales with volume) and relative ease of handling and mounting. This allows for tiling so that large nearly-contiguous detector planes can be built.

The experiment uses 169 CZT detectors with platinum planar contacts and dimensions of 10 mm × 10 mm, thickness of 2 mm each, out of 200 units acquired from eV Products, USA. They will be configured in a 13 × 13 array, so the total area of the detector plane is 169 cm2. Owing to physical mounting restrictions, the edges of adjacent detectors will be separated by 10 mm. The operational energy range will be from 30 to 200 keV. The lower limit is determined by absorption in the residual atmosphere above balloon altitudes (~42 km), whereas the higher limit is determined by detector photoelectric efficiency given its thickness.

Each detector is connected directly to a printed circuit board (PCB) that carries the front-end analog electronics with a preamp, a low-noise amplifier (LNA) and a shaper. The PCBs were designed in our lab and the first ten were built in house. A contractor will replicate them for the whole detector plane. Figure 1 shows a photo of one detector and its associated board, as well as an exploded view of the detector system. The detectors are mounted at 45° with respect to the boards to minimize the spacing between adjacent detectors.

Fig. 1

Top: one CZT detector (10 mm × 10 mm × 2 mm) and its associated electronics board with preamp, LNA and shaper. The actual components of the LNA are on the opposite side of the board to avoid electrical interference. The thick wire is the high-voltage supply to the detector (the blue wire is a test lead). Bottom: a computer rendering of an exploded view of the detector system. The upper plate is a structural Al frame in which a 0.016 mm-thick aluminum foil will be stretched to provide light and electrical shielding to the detectors. The bottom brass piece provides structure and casing for the detectors and PCBs.

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The readout circuit of each detector has an applied bias voltage of ~–220 V, a 100 MΩ bias resistor and a 150 nF coupling capacitor. The charge released by an X-ray interaction in each detector will feed an AC-coupled charge-sensitive preamplifier that creates an output pulse of typically ≲1 mV. The pulses are then amplified by ~65 dB by the LNA and formatted by a shaper. A Wilkinson-type eight-bit analog-to-digital converter (ADC) converts the pulse amplitudes to time and then measures this time. The digitized times are proportional to the energy deposited on the detector. This conversion technique is highly linear and precise; we find it is very suitable for CZT detectors with not very high count rates.

Figure 2 shows an energy spectrum of a radioactive 241Am source for one detector in the lab. The energy resolution at the 59.5 keV line is 6.6 keV full width at half maximum (FWHM), corresponding to ΔE/E = 11%. Also shown is a peak from a pulse generator that we used to measure the pulse height spread due to electronic noise. The equivalent electronic noise resolution is 4.5 keV FWHM. Since the electronic noise and the Poissonian fluctuations due to the number of charge carriers (electron-hole pairs) within the material must add in quadrature, the intrinsic, purely statistical resolution is 4.8 keV FWHM (8%). The red wing on the 60 keV peak is due to incomplete charge collection within the CZT. The spectrum also shows a blend of Cd and Te escape peaks between the radioactive lines.

Fig. 2

Energy spectrum of a radioactive 241Am source for one of the CZT detectors. The peak on the right (~85 keV) is produced by a pulser and has a FWHM of 4.5 keV. The 59.5 keV peak has a resolution of 6.6 keV FWHM (ΔE/E = 11%).

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3.1.2. The scientific data acquisition subsystem

The pulses generated by X-ray interactions in the detectors are processed individually by a data acquisition scheme that includes the front-end analog electronics, as described above, and digital electronics for processing and formatting. The detector pulses are digitized, tagged with position and time, formatted, and then sent to the onboard data-handling computer for storage and transmission to the ground.

The detector signals of each row of 13 detectors in the detector plane array feed into a box with the conversion electronics (CE) with a Complex Programmable Logic Device (CPLD) and microcontrollers. Each one of the 13 CEs acquires data coming from the 13 detector PCBs on that particular row and feeds the pulses into 13 8-bit ADCs (mentioned above), one for each detector, so the energy of each event is determined in 256 channels. The CEs identify the specific detector that is hit on its associated row. Each event will be time-tagged unambiguously with 5 μs precision by an internal clock whose accuracy is checked each second by a GPS receiver. Each CE box receives PPS signals from the GPS.

The signals processed by the CEs will be read by a multiplexing electronics (MUX) box at a rate of 1 Hz. The MUX is thus responsible for identifying the detector in which the event occurred (the event position), the energy and the relative time of the event. For each acquisition cycle (1 s), the MUX will attach the absolute time information coming from the GPS to the data package, so each event will have its instant of occurrence completely determined within 5 μs.

The MUX will send complete datasets containing all data originating in the 13 CEs to the on-board data handling computer (described in Sect. 3.2.1), at a maximum rate of 115 200 bps. In this way, the time, position and energy of each event will be stored individually so that the position and energy distribution of events for any desired integration time can be determined. With an estimated count rate of ~55 counts/s for the entire detector plane (see Sect. 4), the dead time will be negligible even for very strong sources at levels of several Crabs.

Figure 3 shows a simplified block diagram of the detector data acquisition subsystem.

Fig. 3

Simplified block diagram of the detector data acquisition subsystem. The bias voltage is ~–200 V, the bias resistance is 100 MΩ and the coupling capacitance is 150 nF. LNA: low-noise amplifier; ADC: analog-to-digital converter; MUX: multiplexing electronics; OBDH: onboard data-handing computer.

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3.1.3. The collimator

A collimator will be mounted in front of the detector plane in order to define the FOV, minimize background, and provide a uniform illumination fraction of the detectors at any incidence angle. In this way, the entire FOV, all the way to zero intensity, will be fully coded by the mask, ensuring that the experiment does not have any partially coded field of view (PCFOV). Other coded-mask systems do not use collimators, but only shield materials on the sides of the cameras. In these systems, sources in the PCFOV may create severe difficulties in the reconstruction process by casting incomplete shadowgrams of the mask pattern onto the detector plane. In addition, ambiguities in source positions are introduced. We have decided to use a collimator to avoid these problems and reduce background. The price to be paid is the reduction of the sensitivity with increasing off-axis incidence angle, according to the collimator angular response.

The collimator cell centers will be separated by 20 mm in such a way that the individual CZT detectors will each be in the bottom of a collimator cell. The collimator blades are 81-mm high and have lead cores (0.5 mm) and copper plates (0.5 mm) on each side to absorb the radiation impinging at high angles and also provide a graded shield for lead X-ray fluorescence.

The collimator is surrounded by a graded shield made of lead (1.5 mm) in the outside and copper (0.5 mm) in the inside to suppress radiation from outside the FOV. The shielding walls have the same height as the collimator blades (81 mm) and are separated from the last blades by 20 mm, so that the environment that the last detectors (edges and corners) are subjected to is very similar to the more central ones. This is important for minimizing inhomogeneities in the count distribution over the detector plane.

3.1.4. The coded mask

A coded mask, shown in Fig. 4, will be mounted at a distance of 650 mm from the detector plane. The mask has the function of providing a spatial encoding of the X-ray incoming fluxes (see Dicke 1968, for an introduction of the concept). With the knowledge of the mask pattern and the number of X-rays detected by each CZT detector for a given integration time, one can reconstruct an image of the observed FOV by suitable deconvolution or cross-correlation algorithms (Fenimore & Cannon 1978). The mask is made out of 1 mm-thick lead sheets and the basic cells are blue 20 mm × 20 mm squares. The pattern of closed and open elements are a cyclic extension (2 × 2) of a 13 × 13 Modified Uniformly Redundant Array (MURA) pattern (Gottesman & Fenimore 1989) with 20 mm-side square basic cells. Of the 169 elements of the pattern, 84 are open and 85 closed, giving an open fraction of 0.497. In order not to have complete repetitions of the pattern, which would introduce ambiguities in source positions in the sky, we remove one row and one column from the total 2 × 2 array of basic patterns, so that the final dimensions of the mask are 25 × 25 elements or 500 mm × 500 mm.

Fig. 4

ProtoMIRAX coded mask. The basic elements are 1mm-thick 20 mm × 20 mm lead squares. The basic pattern is a 13 × 13 MURA repeated four times (2 × 2) minus 1 row and 1 column to provide unique shadowgrams for any incident direction (skybin). The total size is 500 mm × 500 mm. The lead pieces are glued to an X-ray transparent, 1 mm-thick acrylic substrate both above and below the mask.

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The MURA patterns belong to a class of aperture patterns that allow images to be produced with no intrinsic noise, which means that the autocorrelation function of the mask pattern is a delta function. (Actually, to be precise, the delta function is the result of the cross-correlation between the mask pattern and the decoding function, which is almost exactly equal to the mask pattern with the exception of one single element.) For a point source, the reconstructed image is “perfect” in the sense that it produces a peak in an otherwise completely flat image (see Gottesman & Fenimore 1989 and Braga et al. 2002 for details about imaging with MURAs). With this configuration, the protoMIRAX X-ray camera will have a total FOV of totally coded by the mask and a geometrical angular resolution (one skybin) of 1°43′. Because there are 10 mm gaps between adjacent detectors, the fraction of the FOV with maximum sensitivity (total detector area illuminated) will be 7°03′ × 7°03′. In other words, the collimator blades will only start shadowing the detectors for incident directions outside this angular range, centered on the camera axis. The source location accuracy (see Caroli et al. 1987) will depend on the incident angle and will be limited by the precision of the pointing system. In the best case, it will be around 10′ for a 10σ source in the center of the FOV.

3.1.5. The passive shield

The detector array and associated electronics, including the detector boards, power supplies and batteries, will be surrounded on the sides and bottom by a gradual passive shield of lead (1.5 mm) and copper (0.5 mm). This shield will be responsible for absorbing most of the radiation coming from directions other than those defined by the collimator. Figure 5 shows computer diagrams with the main parts of the XRC, including the aluminum support structures.

Fig. 5

Computer rendering of the protoMIRAX X-ray Camera. Left: exploded diagram of the XRC, showing, from top to bottom, the coded mask, collimator, aluminum foil support plate, detector system, detector electronics and power supply boxes, and battery pack. Right: the assembled XRC with passive shielding and structural parts, including the elevation axis support. Also shown are one of protoMIRAX’s two star cameras (top right) and the elevation driving mechanism (bottom left) based on a ball screw.

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3.2. The balloon gondola

The protoMIRAX balloon gondola will house the X-ray camera and the various subsystems of the space segment, including the On-Board Data Handling Subsystem (OBDH), the Attitude Control and Pointing Subsystem (ACS), the Telemetry and Command Subsystem (TM&TC), and the Power Supply Subsystem (PSS). Also, there will be a main GPS receiver that will provide universal time to all subsystems and two star cameras that will be part of the control loop. A computer rendering of the gondola is shown in Fig. 6.

Fig. 6

Computer rendering of the protoMIRAX balloon gondola, showing the X-ray camera on the front side. The colored boxes at the bottom of the frame are battery packs and electronics racks. The flat box in the back is the TM&TC subsystem. The reaction wheel can be seen below the XRC. One can also see the two star cameras: one is fixed at the XRC and the other (behind the coded mask) is fixed in the gondola frame. At the top, the decoupling mechanism that connects to the balloon cables is shown. The four brown boxes in the bottom are crash pads. The gondola frame dimensions are 1.4 m × 1.4 m × 2 m.

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The gondola will use a power supply system based on packages of Li-ion batteries. A telemetry system operating in the L band (1.5 GHz) will provide data and housekeeping links to the ground. A command system will provide pointing operations during the balloon flight. The science data will be stored on-board on computer flash memories and will also be entirely transmitted to the ground.

3.2.1. The On-Board Data Handling Subsystem

The On-Board Data Handling Subsystem (OBDH) is responsible for acquiring, formatting and transmitting all data that come from the various subsystems of protoMIRAX’s space segment to the ground station (GS). The OBDH is also responsible for receiving and retransmitting the various commands sent by the GS to the gondola, when necessary. For each X-ray photon detected by the XRC, a six-byte packet is created encasing the time stamp, xy position (detector that was hit) and energy (pulse height) of the event that were formatted and sent by the MUX. These event packets are then sent every one second to the OBDH through a 115.2 kbps RS-422 unidirectional serial communication line. In addition, another 115.2 kbps RS-422 serial interface allows OBDH to send specific commands to the XRC and receive XRC’s housekeeping data.

We devised a cost-effective and robust solution for the experiment timing in which a single Global Positioning System (GPSDXA) unit sends PPS (1 pulse per second) and data to the various subsystems of the experiment: OBDH, XRC, ACS, and the Autonomous Star Trackers (AST). The OBDH attaches the UT data from the GPSDXA to the scientific data files at each second, so absolute timing information at the resolution of 5 μs can be retrieved for every event.

The OBDH also communicates with the GS and the ACS. A 500 kbps synchronous communication channel connects the OBDH with the Flight Control and Telecommunications Subsystem (FCTS). This channel is exclusively dedicated to transmit scientific data to the GS. The FCTS also communicates with the GS via a double transmitter/receiver system operating in the L band. To transmit all housekeeping data generated by the several subsystems of the space segment, the OBDH uses a serial RS-232 channel operating at 115.2 kbps. Ground station commands are received by the OBDH via FCTS by means of a 9.6 kbps RS-232 serial channel. In addition, all ACS data are sent to the OBDH prior to be sent to the GS via another 115.2 kbps RS-422 serial interface standard.

The main hardware unit of OBDH is the Payload Data Handling Computer (PDCpM), which is a PC/104 ultra-low-power AMD Geode LX computer. It operates on 333 MHz, has a 128-MByte SDRAM, and has all the necessary interfaces previously mentioned in addition to analog-digital/digital-analog converters. The PDCpM went through thermal cycling and thermal vacuum testing with temperatures ranging from − 40°C to + 85°C and pressure as low as 1.3 mbar.

The software embedded in the computer (SWPDCpM) has been developed in C language over the real-time operating system RTEMS. The architecture of the SWPDCpM is composed of three layers where the bottom layer is the basic software, the intermediate layer is the flight software library in which there are basic services and reusable components, and the top layer is the application software, the main part of SWPDCpM.

Figure 7 shows a simplified physical architecture of the protoMIRAX experiment with its main subsystems.

Fig. 7

Simplified physical architecture of the protoMIRAX balloon experiment. XRC: X-ray camera; ACS: Attitude Control System; TEMPDXA: Temperature monitoring equipment; GPSDXA: GPS unit; OBDH: On-Board Data Handling Subsystem; PDCpM: Payload Data Handling Computer; DC-DC Conv: DC-DC Converter; PRESN: Pressure Sensor; PSS: Power Supply Subsystem; FCTS: Flight Control and Telecommunications Subsystem.

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3.2.2. The Attitude Control and Pointing Subsystem

The X-ray camera will be placed in an alt-azimuth mount in the balloon gondola, allowing pointing to different targets in the sky and tracking them continuously down to elevation angles of 30°. A ball screw mechanism, with a step motor, will allow smooth and secure motion in elevation, and the azimuth motion will be provided by a system that rotates the entire gondola with respect to the geomagnetic field and the positions of the sun and the stars in the sky. The attitude control system will employ several sensors and actuators. The sensors include an electronic compass, an accelerometer, two star sensors, a sun tracker and both azimuth and elevation angular encoders. The actuators include a reaction wheel for angular momentum exchange and dump, and motors that will drive the motions in both elevation and azimuth. The gondola also has a mechanism at its top for decoupling its rotation with respect to the balloon itself and a motor for desaturating the reaction wheel. The overall pointing accuracy of the control system is ≲0.5°, depending on the elevation angle. High elevations are in general more difficult to control since small changes in the pointing direction near the zenith leads to large azimuthal and roll angle displacements. Also, the accuracy will depend on whether the flight is at daytime or nighttime. At night, the star cameras will provide more accurate control.

The two autonomous star sensors of protoMIRAX are being developed at INPE. They are wide-field (25° × 25°) optical (400−800 nm) cameras with a 35 mm focal length. The imaging sensor is a CMOS APS (active pixel sensor) with 1024 × 1024 pixels and quantum efficiency up to 25%. An especially designed algorithm for star pattern recognition provides attitude knowledge precision better than ten arcseconds (1σ) around the cross-foresight axes (yaw and pitch) and better than 60 arcsec (1σ) around the foresight axis (roll angle). One of the star sensors is fixed in the XRC mechanical frame so that it aids in the precise pointing of the XRC telescope. Its optical axis is tilted 24° with respect to the X-ray axis towards lower elevations, so as to avoid having the balloon in the FOV for high-elevation observations. Even with this misalignment, there will be occasions when the primary star tracker will be obstructed by the balloon. In these cases the XRC attitude will be determined by the secondary star tracker mounted in the gondola, albeit with a somewhat reduced accuracy due to uncertainties from the angular encoders used in the motors that control the XRC mechanical frame elevation. The star trackers are also capable of acquiring images, which will be used for evaluation of the star tracker performance during the flight.

3.3. The ground subsystem

The operations of the protoMIRAX telescope during the balloon flights will make use of the ground facilities already available at INPE. The reuse strategy focused on two subsystems: (i) the balloon flight control (OPS) and (ii) the experiment operation itself, which will be supported by the SATellite Control System (SATCS). SACTS is a software-based architecture developed at INPE for satellite commanding and monitoring. Considering that protoMIRAX is a pathfinder for the MIRAX satellite mission, a ground infrastructure compatible with INPE’s satellite operation approach would be useful and is highly recommended for controlling and monitoring the experiment during the balloon campaigns.

The OPS required investments on information technology. The available balloon GS needed little hardware maintenance, but significant efforts on software updating were necessary. The original stand-alone computer system dedicated to run the flight control software was modernized both in hardware and software by the new system named OPS/ES. In addition, a new server computer, properly configured for Ethernet connections, has extended the existing GS facilities with a network switch, serial converters and a new piece of software named OPS/Server in order to support the available uplink and downlink channels being mapped to TCP/IP gateways. Those communication improvements were necessary to support the interoperability between the balloon GS, SATCS, and protoMIRAX data center.

Some effort in software customization was necessary because SATCS architecture complies with particular operational requirements on different missions by using several customized object-oriented software elements and frameworks. The diagram in Fig. 8 shows the ground solution designed for the ground segment of the protoMIRAX experiment.

4. Effective area and sensitivity

The effective area of a balloon experiment for the observation of cosmic sources is a function of energy (E), atmospheric depth and zenith angle: (1)where Ageo is the geometrical detection area, ϵ ≡ 1 − exp( − μDl) is the detector efficiency, μD(E) is the detector’s attenuation coefficient in cm-1, l is the detector thickness in cm, (μ/ρ)A(E) is the attenuation coefficient of the atmosphere in cm2/g, x is the atmospheric depth in g cm-2 and z is the zenith angle.

For the expected observations of protoMIRAX at 2.7 g cm-2, considering a point source at the zenith, the effective area is shown in Fig. 9, with a maximum value of 52 cm2 at ~80 keV. It is important to note that the geometrical area for a point source at infinity is the total detector area of 169 cm2 multiplied by the open fraction of the mask, which is 0.497 (see Sect. 3.1.4).

The sensitivity of the experiment can be calculated by estimating the background at the altitudes expected for the balloon flight. This was produced by performing Monte Carlo simulations using the software package GEANT4 (Agostinelli et al. 2003), a well-known suite of routines that performs detailed calculations of gamma-ray and particle interactions on all materials. Given the experiment mass model and the environmental particle and photon fields, the code provides the detector spectral response, both prompt and delayed.

Based on detailed GEANT4 calculations we carried out (Penacchioni et al. 2015; Castro et al., in prep.), the estimated background count rate for the entire detector plane, in the 30 to 200 keV energy range, is of ~55 counts/s. In these simulations, we considered both the anisotropic atmospheric X and γ-ray spectra and the cosmic diffuse contribution coming from the telescope aperture. We also considered primary and secondary protons, electrons and neutrons. As shown by Penacchioni et al. (2015), the photon contribution is dominant up to 90 keV, where the contribution due to protons becomes almost equally important. Neutrons are important below 35 keV and the electron contribution is negligible.

In Fig. 10 we show a map of the simulated background counts over the detector plane for an integration of four hours at 2.7 g cm-2 for the entire energy range 30–200 keV. The increased count rates at the edges and corners of the detector plane are most likely due to the closeness of these detectors with the shielding materials and support structures, which produce secondary radiation by scattering. Another factor could be due to the extra shielding produced by the collimator blades to the detector in the central areas of the detector plane.

Fig. 10

Background count distribution over the detection plane in the detector energy range 30–200 keV, for an observation time of 4 h at balloon altitudes.

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Taking the expected background levels at balloon altitudes as a function of energy, one can calculate the sensitivity of the experiment in terms of the minimum detectable flux at a particular statistical significance. As shown by Gottesman & Fenimore (1989), the signal-to-noise ratio (S/NNσ) of a coded mask instrument that uses URAs or MURAs, for a single point source, is given by (2)where NS is the net source counts and NB is the background number of counts for a given integration time in a particular energy range. Solving for NS, one gets (3)If we are interested in a minimum detectable flux, the signal-to-noise ratio will be a small number (≲10), and it is reasonable to assume that for sufficiently long integration times. Therefore, .

Now, if S is the source flux in photons cm-2 s-1 keV-1, then NS = SAeffT ΔE, where Aeff is the effective area in cm2, T is the integration time in seconds and ΔE is the energy interval under consideration (in keV). Similarly, NB = BAgeoT ΔE, where B is the background level in the more suitable units of counts cm-2 s-1 and Ageo is the geometrical area of the whole detector plane.

The minimum source flux that will be detectable at a level of Nσ will then be (4)According to this expression, the 3σ sensitivity (minimum detectable flux) for the whole energy band is found to be approximately 1.9 × 10-5 counts cm-2 s-1 from 30 to 200 keV, considering 8 h of integration at 2.7 g cm-2 and a zenith angle of 30°. This allows protoMIRAX to make detailed observations of the Crab (even at low elevation angles) and also detect a few X-ray binaries in states of high hard X-ray emission. In Fig. 11 we show a 3σ sensitivity curve for protoMIRAX for an integration time of eight hours at 2.7 g cm-2, considering a point source at a zenith angle of 30°. The increased minimum flux values between 70 and 90 keV are due to somewhat strong lead fluorescent lines (reported by Penacchioni et al. 2015) in the estimated background spectrum. We are in the process of studying different shielding configurations that will very likely minimize this problem.

Fig. 11

On-axis sensitivity curve for protoMIRAX. The horizontal bars are the minimum detectable fluxes at a level of 3σ at an atmospheric depth of 2.7 g cm-2 and a zenith angle of 30°. The integration time is 8 hours. Also shown are the spectra of 4 X-ray sources that will be observed in the first balloon flight. The source spectra were taken from Sizun et al. (2004; Crab), Grebenev et al. (1995; 1E 1740.7−2942), Sunyaev et al. (1991b; GRS 1758−258) and Dieters et al. (1991; GX 1 + 4).

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5. Image simulation

To predict the performance of the protoMIRAX imaging system, we have simulated an observation of the Crab nebula during a meridian transit at our flight latitudes (23° S). To calculate the number of counts from the source, we have considered the zenith angle variation with time before and after the transit, which occurs at an elevation of 45°. Based on the Crab hard X-ray spectrum taken from Sizun et al. (2004), we used GEANT4 to build a simulated shadowgram of a Crab observation in the center of the FOV, which is shown in Fig. 12.

Fig. 12

Count distribution (shadowgram) on the detector plane of a simulated observation of the Crab, including the expected background, for an integration time of 4 h around the meridian passage at a latitude of 23° S. The energy range is 30 to 200 keV.

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The image covers the entire FOV of 21° × 21°, and each sky bin corresponds to 1°43′ of the sky. The overall S/N of the image is 109σ (see Penacchioni et al. 2015, for details). This value corresponds to 91% of the theoretical value given by expression (2) above. The loss in detection significance is mainly due to the non-uniformity of the background across the detector plane. In Fig. 13 we show the reconstructed Crab image. It is interesting to note that the Crab will in principle be observable by protoMIRAX at a 5σ level for an integration as short as 63 s, which makes it a very good calibration source for the experiment.

Fig. 13

Simulated image of the Crab nebula region for an integration time of 4 h around the meridian transit at balloon altitudes (2.7 g cm-2). The energy range is 30−200 keV. The S/N of the detection is 109.

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6. Conclusion

The protoMIRAX experiment is a balloon-borne hard X-ray telescope being developed as a scientific and technical pathfinder for the MIRAX satellite mission. In the current configuration, which is under revision owing to restrictions imposed by the Brazilian space program, MIRAX will consist in a set of wide-field coded-mask hard X-ray cameras (5−200 keV) with an angular resolution of ~5−6 arcmin that will operate in scanning mode in a near-equatorial circular low-Earth orbit. MIRAX main goals include the characterization, with unprecedented depth and time coverage, of a large sample of variable and transient phenomena on accreting neutron stars and black holes, as well as active galactic nuclei and GRBs.

Apart from serving as a testbed for several MIRAX subsystems, protoMIRAX will be capable of doing interesting science of its own. The hard X-ray camera, similar to the hard X-ray imager being developed for MIRAX, albeit with a much lower angular resolution and smaller detector area, has a resolution of 1°43′ with a fully coded FOV of 21° × 21°. Detailed background calculations were performed with the GEANT4 package, and the expected background at balloon altitudes at a latitude of − 23° over the SAA region in Brazil provides a 3σ sensitivity for the 30−200 keV range of ~ 1.9 × 10-5 photons cm-2 s-1 for an integration of eight hours. In its first balloon flight, protoMIRAX

will observe the Crab nebula for calibration and imaging demonstration and also the GC region for scientific purposes. The experiment is in a very advanced state of development and we hope to carry out the first ballon flight in late 2015.

Acknowledgments

We thank FINEP, CNPq and FAPESP, Brazil, for financial support. We also thank Fernando G. Blanco, Sérgio Admirábile, Luiz A. Reitano, Wendell P. da Silva, Leonardo Pinheiro, Fernando Orsatti, Paulino Scherer and the engineers from the company COMPSIS in São José dos Campos for invaluable technical support. A.V.P. acknowledges the support by the international Cooperation Program CAPES-ICRANET financed by CAPES – Brazilian Federal Agency for Support and Evaluation of Graduate Education within the Ministry of Education of Brazil. M.C.A. and J.R.S. also acknowledge CAPES for Ph.D. and post-doctoral fellowships, respectively.

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Table 1

ProtoMIRAX baseline parameters.

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