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Issue
A&A
Volume 530, June 2011
Article Number A28
Number of page(s) 14
Section Stellar structure and evolution
DOI https://doi.org/10.1051/0004-6361/201015316
Published online 02 May 2011

© ESO, 2011

1. Introduction

Subluminous B stars (sdBs) are core helium-burning stars with very thin hydrogen envelopes and masses around 0.5 M⊙ (Heber 1986). A large fraction of the sdB stars are members of short period binaries (Maxted et al. 2001; Napiwotzki et al. 2004a). After the discovery of close binary subdwarfs, several studies aimed at determining the fraction of hot subdwarfs residing in such systems. Samples of hot subdwarfs checked for radial velocity (RV) variations imply the binary fraction ranges from 39% to 78% (e.g. Maxted et al. 2001; Napiwotzki et al. 2004a). The orbital periods of subdwarf binaries for which orbital parameters could be determined range from 0.07 to  >10 d with a peak at 0.5−1.0 d (e.g. Edelmann et al. 2005; Morales-Rueda et al. 2003a).

For close binary sdBs common envelope ejection is the most probable formation channel (Han et al. 2002; 2003). In this scenario two main sequence stars of different masses evolve in a binary system. The more massive one will reach the red giant phase first and fill its Roche lobe near the tip of the red-giant branch. If the mass transfer to the companion is dynamically unstable, a common envelope is formed. Friction causes the two stellar cores to lose orbital energy, which is deposited within the envelope, and the period of the binary decreases. Eventually, the common envelope is ejected, and a close binary system is formed containing a core helium-burning sdB and a main sequence companion. A binary consisting of a main sequence star and a white dwarf (WD) may evolve to a close binary sdB with a white dwarf companion in a similar way. Tight constraints can be placed on the nature of the sdB companions only in the rare cases where the systems show eclipses or other features indicative of a companion in their light curves (see the catalogue of Ritter & Kolb 2009, and references therein).

Subdwarf binaries with massive WD companions are candidates for SN Ia progenitors because these systems lose angular momentum due to the emission of gravitational waves and start mass transfer. Transfer of mass or the subsequent merger of the system may cause the WD to approach the Chandrasekhar limit, ignite carbon under degenerate conditions, and explode as a SN Ia (Webbink 1984; Iben & Tutukov 1984). One of the best-known candidate systems for this double degenerate merger scenario is the sdB+WD binary KPD 1930+2752 (Maxted et al. 2000a; Geier et al. 2007). Mereghetti et al. (2009) showed that in the X-ray binary HD 49798 a massive (>1.2 M⊙) white dwarf accretes matter from a closely orbiting subdwarf O companion. The predicted amount of accreted material is sufficient for the WD to reach the Chandrasekhar limit. This makes HD 49798 another candidate SN Ia progenitor, should the companion be a C/O white dwarf (Wang et al. 2009). SN Ia play a key role in the study of cosmic evolution since they are utilised as standard candles for determining the cosmological parameters (e.g. Riess et al. 1998; Leibundgut 2001; Perlmutter et al. 1999). Most recently Perets et al. (2010) showed that helium accretion onto a white dwarf may be responsible for a subclass of faint and calcium-rich SN Ib events.

Due to the tidal influence of the companion in close binary systems, the rotation of the primary1 becomes synchronised to its orbital motion. In this case it is possible to constrain the mass of the companion, if mass, projected rotational velocity and surface gravity of the sdB are known. Geier et al. (2008, 2010a,b) analysed high resolution spectra of 41 sdB stars in close binaries, half of all systems with known orbital parameters. In 31 cases, the mass and nature of the unseen companions could be constrained. While most of the derived companion masses were consistent with either late main sequence stars or white dwarfs, the compact companions of some sdBs may be either massive white dwarfs, neutron stars (NS) or stellar mass black holes (BH). However, Geier et al. (2010b) also showed that the assumption of orbital synchronisation in close sdB binaries is not always justified and that their sample suffers from huge selection effects.

Binary evolution theory (Podsiadlowski et al. 2002; Pfahl et al. 2003) predicts the existence of sdB+NS/BH systems formed after two phases of unstable mass transfer and one supernova explosion. The predicted fraction of sdB+NS/BH systems ranges from about 1% to 2% of the close sdB binaries (Geier et al. 2010b; Yungelson & Tutukov 2005; Nelemans 2010).

2. Project overview

The work of Geier et al. (2010b) indicates that a population of non-interacting binaries with massive compact companions may be present in our Galaxy. The candidate sdB+NS/BH binaries have low orbital inclinations (15−30°, Geier et al. 2010b), but high inclination systems must exist as well. A lower limit can be placed on the companion mass by determining the orbital parameters and calculating the binary mass function. (1)The RV semi-amplitude K and the period P can be derived from the RV curve; the sdB mass MsdB, the companion mass Mcomp and the inclination angle i remain free parameters. We adopt MsdB = 0.47 M⊙ and i < 90° to derive a lower limit for the companion mass. Depending on this minimum mass a qualitative classification of the companions’ nature is possible in certain cases. For minimum companion masses lower than 0.45 M⊙ a main sequence companion can not be excluded because its luminosity would be too low to be detectable in the spectra (Lisker et al. 2005). If the minimum companion mass exceeds 0.45 M⊙ and no spectral signatures of the companion are visible, it must be a compact object. If it exceeds the Chandrasekhar mass and no sign of a companion is visible in the spectra, the existence of a massive compact companion is proven without the need for any additional assumptions. This is possible if such a binary is seen at high inclination. The project Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS2 (MUCHFUSS) aims at finding sdBs with compact companions like supermassive white dwarfs (M > 1.0 M⊙), neutron stars or black holes. First results of our follow-up campaign are published in Geier et al. (2011).

There is an interesting spin-off from this project: the same selection criteria we applied to find binaries with massive compact companions are also well-suited to single out hot subdwarf stars with constant high radial velocities in the Galactic halo, which may be extreme population II or even hypervelocity stars. We have coined the term Hyper-MUCHFUSS to refer to this extended project, the first results of which are presented in Tillich et al. (2011).

3. Target selection

The high fraction of sdB stars in close binary systems was initially discovered by the detection of RV shifts using time resolved spectroscopy (Maxted et al. 2001). In the past decade, orbital parameters for about 80 of these systems have been determined. We summarize the orbital parameters of all known sdB binaries and give references in Table A.1 (see also Fig. 1).

To the extent that the companion masses of the known sdB binaries could be constrained, it turned out that most companions should be either late main sequence stars with masses lower than half a solar mass or compact objects like white dwarfs. Targets for spectroscopic follow-up were selected in different ways depending on the specific aims of each project.

For the MUCHFUSS project the target selection is optimised to find massive compact companions in close orbits around sdB stars. In order to discover rare objects applying the selection criteria explained in the forthcoming sections, a huge initial dataset is necessary. The enormous SDSS database (Data Release 6, DR6) is therefore the starting point for our survey. Best sky coverage is reached in the Northern hemisphere close to the galactic poles. SDSS data are widely used and therefore also well evaluated in terms of errors and accuracy (York et al. 2000; Abazajian et al. 2009). Moreover, they are supplemented by additional spectroscopic observations of appropriate quality from other sources.

thumbnail Fig. 1

The RV semiamplitudes of all known sdB binaries with spectroscopic solutions plotted against their orbital periods (see Table A.1). Binaries which were initially discovered in photometric surveys due to indicative features in their light curves (eclipses, reflection effects, ellipsoidal variations) are marked with open circles. Binaries discovered by detection of RV variation from time resolved spectroscopy are marked with filled diamonds. The dashed, dotted and solid lines mark the regions to the right where the minimum companion masses derived from the binary mass function (assuming 0.47 M⊙ for the sdBs) exceed 0.45 M⊙, 1.00 M⊙ and 1.40 M⊙. The two post-RGB objects in the sample have been excluded, because their primary masses are much lower.

3.1. Colour selection and visual classification

Hot subdwarfs are found most easily by applying a colour cut to Sloan photometry. All spectra of point sources with colours u − g < 0.4 and g − r < 0.1 were selected. This colour criterion corresponds to a limit in the Johnson photometric system of U − B < −0.57 (Jester et al. 2005), similar to the cut-off chosen by UV excess surveys, such as the Palomar Green survey (Green et al. 1986). The corresponding effective temperature of a BHB star is  ≃15 000 K (Castelli & Kurucz 2003), well below the observed range for sdB stars (>20 000 K). The limit of g − r = +0.1 corresponds to B − V = +0.3 (Jester et al. 2005). This ensures that sdBs in spectroscopic binaries are included if the dwarf companion is of spectral type F or later, e.g. the sdB+F system PB 8783 at B − V = +0.13 and U − B = −0.65 (Koen et al. 1997). On the other hand the colour criteria exclude the huge number of QSOs (quasi stellar objects) which were the priority objects of SDSS in the first place. We selected 48 267 point sources with spectra in this way.

thumbnail Fig. 2

Left panel. SDSS g − r-colours plotted against u − g of all stars. The grey dots mark all stellar objects with spectra available in the SDSS database. Most of them are classified as DA white dwarfs. The solid diamonds mark (He-)sdO stars, the solid squares sdB and sdOB stars. Open squares mark hot subdwarfs with main sequence companions visible in the spectra. Most of these objects are white dwarfs of DA type. Right panel. Only subdwarfs with g < 18 mag are plotted. The sequence of composite objects is clearly separated from the single-lined stars. Synthetic colours from Castelli & Kurucz (2003) for stars with temperatures ranging from 14 000 K to 50 000 K (log g = 5.0) are marked with upward triangles and connected. The stepsize of the colour grid is 1000 K. The labels mark models of certain temperatures.

The spectra from SDSS are flux calibrated and cover the wavelength range from 3800 Å to 9200 Å with a resolution of R = 1800. Rebassa-Mansergas et al. (2007) verified the wavelength stability to be  <14.5 km s-1 from repeat sub-spectra using SDSS observations of F-stars. We obtained the spectra of our targets from the SDSS Data Archive Server3 and converted the wavelength scale from vacuum to air. The spectra were classified by visual inspection.

First, we excluded spectra of extragalactic objects and spectra with low quality (S/N < 5) or unknown features, leaving us with 10 811 spectra of 10 153 stars. Figure 2 (left panel) shows a two-colour plot of all selected objects. To classify the selected spectra, we compared them visually to reference spectra of hot subdwarfs and white dwarfs. Existence, width, and depth of helium and hydrogen absorption lines as well as the flux distribution between 4000 and 6000 Å were used as criteria. Subdwarf B stars show broadened hydrogen Balmer and He i lines, sdOB stars He ii lines in addition, while the spectra of sdO stars are dominated by weak Balmer and strong He ii lines depending on the He abundance. A flux excess in the red compared to the reference spectrum as well as the presence of spectral features such as the Mg i triplet at 5170 Å or the Ca ii triplet at 8650 Å were taken as indications of a late type companion (for a few examples see Fig. 3, for spectral classification of hot subdwarf stars see the review by Heber 2009).

Our selection criteria led to a sample containing a total of 1100 hot subdwarfs. 725 belong to the class of single-lined sdBs and sdOBs. Because distinguising between these two subtypes from their spectral appearances alone can be difficult, we decided to treat them as one class. Features indicative of a cool companion were found for 89 of the sdBs. 9 sdOs have main sequence companions, while 198 of them, most of which show helium enrichment, are single-lined. A unique classification was not possible for 79 objects in our sample. Most of these stars are considered candidate sdBs with low temperatures, which cannot be distinguished clearly from blue horizontal branch (BHB) stars or low-mass DA or DB white dwarfs.

Eisenstein et al. (2006) used a semi-automatic method for the spectral classification of white dwarfs and hot subdwarfs from the SDSS DR4, and it is instructive to compare their sample to ours. Our colour cut-off is more restrictive and the confusion limit (S/N > 5) is brighter than that of Eisenstein et al. (2006). Due to the redder colour cuts, blue horizontal branch stars enter the Eisenstein et al. sample, which we do not consider as hot subdwarf stars (see Heber 2009). Applying our colour cuts to the hot subdwarf sample of Eisenstein et al. (2006) yields 691 objects. The stars missing in our sample are mostly fainter than g = 19 mag as expected. Most recently, Kleinman (2010) extended the classifications to the SDSS DR7 and found 1409 hot subdwarf stars. Since no details are published, the sample can not be compared to ours yet. Considering our more restrictive colour cuts and confusion limit, the numbers compare very well with ours. This gives us confidence that our selection method is efficient.

In Fig. 2 (right panel) only the subdwarf stars brighter than g = 18 mag are plotted. With less pollution by poor spectra, two sequences become clearly visible. The solid symbols mark single-lined sdBs and sdOs, while the open squares mark binaries with late type companions of most likely K and G type visible in the spectra. The contribution of the cool companions shifts the colours of the stars to the red. As can be seen in Fig. 2 the upper sequence also contains apparently single stars. Since the spectra are not corrected for interstellar reddening, some of these objects may show an excess in the red not due to the presence of a cool companion. Spectral features indicative of a late-type companion and small excesses in the red may have been missed for the faintest targets with the noisiest data.

thumbnail Fig. 3

Flux calibrated SDSS spectra of a single-lined sdB, a helium rich sdO and an sdB with main sequence companion visible in the spectrum. Note the different slopes of the sdB and the sdB+MS spectra.

In Fig. 2 (right panel) we also compare the sample to synthetic colours suitable for hot subdwarf stars. We chose the grid of Castelli & Kurucz (2003)4 and selected models with high gravity (log g = 5.0). The models reproduce the lower envelope of the targets in the colour-colour-diagram very well for effective temperatures ranging from 20 000 to 50 000 K as expected for hot subdwarf stars. Different surface gravities, chemical compositions and interstellar reddening are not accounted for but would explain the observed scatter of the stars.

It is interesting to note that there is an obvious lack of blue horizontal branch (BHB) stars with effective temperatures below 20 000 K compared to the sdBs with higher temperatures. This gap is not a result of selection effects because the BHB stars are brighter than the sdBs at optical wavelengths. We conclude that the number density of BHB stars in the analysed temperature range must be much smaller than that of sdBs. Newell (1973) was the first to report the existence of such a gap in the two-colour diagram of field blue halo stars, which was subsequently also found in some globular clusters (Momany et al. 2004). The reason for this gap remains unclear (see the review by Catelan 2009).

thumbnail Fig. 4

Heliocentric radial velocities of 1002 subdwarfs plotted against g-magnitude. The two dashed lines mark the RV cut of  ± 100 km s-1.

3.2. High radial velocity sample (HRV)

The radial velocities of all identified hot subdwarf stars (both single- and double-lined) were measured by fitting a set of mathematical functions (Gaussians, Lorentzians and polynomials) to the hydrogen Balmer lines as well as helium lines, if present, using the FITSB2 routine (Napiwotzki et al. 2004a) and the Spectrum Plotting and Analysis Suite (SPAS) developed by Hirsch. Figure 4 shows the RVs of 1002 hot subdwarf stars.

Most of the known sdB binaries are bright objects (V ≃ 10−14 mag), and the vast majority of them belong to the Galactic disk population (Altmann et al. 2004). Due to the fact that these binary systems are close to the Sun they rotate around the Galactic centre with approximately the same velocity. For this reason, the system velocities of most sdB binaries are low relative to the Sun. One quarter of the known systems have |γ| < 10 km s-1, 85% have |γ| < 50 km s-1 (see Table A.1). In order to filter out normal thin-disk binaries, which in most cases have RV semiamplitudes less than 100 km s-1 (see Fig. 1), we excluded sdBs with RVs lower than  ±100 km s-1.

Typical hot subdwarf stars fainter than g ≃ 17 mag have distances exceeding 4 kpc and therefore likely belong to the Galactic halo population. Most of the stars in our sample are fainter than that (see Fig. 4). The velocity distribution in the halo is roughly consistent with a Gaussian of 120 km s-1 dispersion (Brown et al. 2005). Figure 5 shows the velocity distributions of our selected objects when separated into bright and faint subsamples. The distribution of the bright subsample (g < 16.5 mag) is roughly similar to the one of the faint subsample (g > 16.5 mag), the latter extending to more extreme velocities and being somewhat asymmetric. Selecting objects with heliocentric radial velocities exceeding  ±100 km s-1 we aim to find halo stars with extreme kinematics as well as close binaries with high RV amplitudes.

Another selection criterion is the brightness of the stars. The accuracy of the RV measurements depends on the S/N of the spectra and the existence and strength of the spectral lines. Furthermore, the classification becomes more and more uncertain as soon as the S/N drops below  ≃10 and the probability of including DAs rises. Objects of uncertain type and RV (errors larger than 50 km s-1) have therefore been excluded. Most of the excluded objects are fainter than g = 19 mag. Altogether the target sample consists of 258 stars.

thumbnail Fig. 5

Radial velocity distribution of the hot subdwarf stars (see Fig. 4). The bright sample (g < 16.5 mag, black histogram) contains a mixture of stars from the disk and the halo population. The faint sample (g > 16.5 mag, grey histogram) contains the halo population. The peak in the bright subsample around zero RV is caused by the thin disk population. The asymmetry in the faint subsample where negative RVs are more numerous than positive ones may be due to the presence of large structures in the halo and the movement of the solar system relative to the halo.

Table 1

Survey observations.

thumbnail Fig. 6

Hγ-line of two consecutively taken individual SDSS spectra (Δt = 0.056 d) of the sdB binary J113840.68−003531.7. The shift in RV (≃140 km s-1) between the two exposures is clearly visible.

Second epoch medium resolution spectroscopy was obtained starting in 2008 using ESO-VLT/FORS1 (R ≃ 1800,λ = 3730−5200 Å), WHT/ISIS (R ≃ 4000,λ = 3440−5270 Å), CAHA-3.5m/TWIN (R ≃ 4000,λ = 3460−5630 Å) and ESO-NTT/EFOSC2 (R ≃ 2200,λ = 4450−5110 Å). A log of our observations is given in Table 1. Up to now we have reobserved 88 stars. We discovered  ≃30 halo star candidates with constant high radial velocity (see Tillich et al. 2011) as well as 46 systems with radial velocities that were most likely variable.

3.3. Rapid radial velocity variable sample (RRV)

All SDSS spectra are co-added from at least three individual “sub-spectra” with typical exposure times of 15 min. In most cases, the sub-spectra are taken consecutively; however, they may be split occasionally over several nights.

Several SDSS objects are observed more than once, either because the entire spectroscopic plate is re-observed, or because they are in the overlap area between adjacent spectroscopic plates; up to 30 sub-spectra are available for some objects. Consequently, SDSS spectroscopy can be used to probe for radial velocity variations, a method pioneered by Rebassa-Mansergas et al. (2007) to identify close white dwarf plus main-sequence binaries. We have obtained the sub-spectra for all sdBs brighter than g = 18.5 mag from the SDSS Data Archive Server. The quality of individual spectra of stars fainter than this is not sufficient for our analysis. The object spectra were extracted from the FITS files for the blue and red spectrographs, and merged into a single spectrum using MIDAS. From the inspection of these data, we discovered 81 new candidate sdB binaries with radial velocity variations on short time scales,  ≃0.02−0.07 d (see Fig.  6 for an example).

The individual SDSS spectra are perfectly suited to search for close double degenerate binaries. Ongoing projects like SWARMS (Badenes et al. 2009; Mullally et al. 2009) focus on binaries with white dwarf primaries (see also Kilic et al. 2010; Marsh et al. 2010) and use a similar method.

3.4. Selecting high mass companions

Time resolved follow-up spectroscopy with a good phase coverage is needed to determine the orbital solutions of the RV variable systems. In order to select the most promising targets for follow-up, we carried out numerical simulations and estimated the probability for a subdwarf binary with known RV shift to host a massive compact companion. We created a mock sample of sdBs with a close binary fraction of 50%.

We adopted the distribution of orbital periods of all known sdB binaries (see Table A.1) approximated by two Gaussians centered at 0.7 d (width 0.3 d) and 5.0 d (width 3.0 d) and assumed that 82% of the binaries belong to the short period population. The short period Gaussian was truncated at 0.05 d, which is considered the minimum period for an sdB binary, because the subdwarf primary starts filling its Roche lobe for shorter periods and typical companion masses. Since stable Roche lobe overflow and the accretion onto the companion would dramatically change the spectra of these stars, we can safely presume that our sample does not contain such objects.

The orbital inclination angles are assumed to be randomly distributed, but for geometrical reasons binaries at high inclinations are more likely to be observed than binaries at low inclinations. To account for this, we used the method described in Gray (1992) and adopted a realistic distribution of inclination angles.

We assumend the canonical value of 0.47 M⊙ for the sdB masses. The distribution of companion masses was based on the results of Geier et al. (2010b). The distribution of the low mass companions was approximated by a Gaussian centered at 0.4 M⊙ (width 0.3 M⊙). The fraction of massive compact companions is estimated as 2% of the close binary population based on binary population synthesis models (Geier et al. 2010b). The mass distribution of these companions was approximated by a Gaussian centered at 2.0 M⊙ (width 1.0 M⊙).

We adopted a Gaussian distribution for the system velocities with a dispersion of 120 km s-1, a typical value for halo stars (Brown et al. 2005). Two RVs were taken from the model RV curves at random times and the RV difference was calculated for each of the 106 binaries in the simulation sample. This selection criterion corresponds to the HRV sample. For given RV difference and timespan between the measurements the fraction of systems with minimum companion masses exceeding 1 M⊙ was computed.

Figure 7 shows the fraction of massive compact companions with unambiguous mass functions plotted against the RV shift between two measurements taken at random times (solid curve). It is quite obvious that binaries with high RV shifts are more likely to host massive companions. The probability for a high mass companion (>1 M⊙) at high inclination is raised by a factor of ten as soon as the RV shift exceeds 200 km s-1.

In order to check whether the selection of high velocities rather than high velocity shifts has an impact on the probability of finding sdB binaries with massive compact companions we used the same simulation. In Fig. 8 the fraction of these binaries is plotted against only one RV measurement taken at a random time. It can be clearly seen that the detection probability rises significantly for stars with high RVs. Selecting the fastest stars in the halo therefore makes sense when searching for massive compact companions to sdBs.

thumbnail Fig. 7

Probability for an sdB binary to host a massive compact companion and to be seen at sufficiently high inclination to unambiguously identify it from its binary mass function plotted against the RV shift within random times (solid curves, HRV sample) or on short timescales (dotted curve, RRV sample).

thumbnail Fig. 8

Same as Fig. 7 except that the probability is plotted against RV at random time.

Since the individual SDSS spectra were taken within short timespans, another simulation was performed corresponding to the RRV sample. The first RV was taken at a random time, but the second one just 0.03 d later. The dotted curve in Fig. 7 illustrates the outcome of this simulation. As soon as the RV shift exceeds 30 km s-1 within 0.03 d, the probability that the companion is massive rises to  ≃10%. The reason the probability does not increase significantly with increasing RV shift is that the most massive companions in our simulation have maximum RV shifts as high as 1000 km s-1. At the most common periods (≃0.5 d), the maximum RV shift within 0.03 d is then of the order of 100 km s-1. RV shifts higher than this within comparable time intervals are not physically plausible.

Our simulation provides quantitative estimates based on our current knowledge of the sdB binary populations. We note that these numbers should be considered as rough estimates only. The observed period and companion mass distributions, for example, are highly susceptible to selection effects. The derived numbers are therefore only used to create a priority list and select the best targets for follow-up.

3.5. Final target sample

Our sample of promising targets consists of 69 objects in total. 52 stars show significant RV shifts (>30 km s-1) within 0.02−0.07 d and are selected from the RRV sample, while 17 stars show high RV shifts (100−300 km s-1) within more than one day and are selected from the HRV sample (see Fig. 9).

In Geier et al. (2011) we showed that the SDSS spectra are well suited to determine atmospheric parameters by fitting synthetic line profiles to the hydrogen Balmer lines (Hβ to H9) as well as He i and He ii lines. In order to maximize the quality of the data the single spectra were shifted to rest wavelength and coadded. The quality of the averaged spectra is quite inhomogeneous (S/N ≃ 20−180, see Table 2), which affects the accuracy of the parameter determination.

thumbnail Fig. 9

Highest radial velocity shift between individual spectra plotted against time difference between the corresponding observing epochs. The dashed horizontal line marks the selection criterion ΔRV > 100 km s-1, the dotted vertical line the selection criterion ΔT < 0.1 d. All objects fulfilling at least one of these criteria lie outside the shaded area and belong to the top candidate list for the follow-up campaign. The filled diamonds mark sdBs, while the blank squares mark He-sdOs.

thumbnail Fig. 10

Example fits of hydrogen and helium lines with model spectra for an sdB (left panel), an sdOB (middle panel) and a He-sdO star (right panel). The atmospheric parameters of these stars are given in Tables 3 and 4.

A quantitative spectral analysis was performed in the way described in Lisker et al. (2005) and Ströer et al. (2007). Due to the fact that our sample consists of different subdwarf classes, we used appropriate model grids in each case. For the hydrogen-rich and helium-poor (log y < −1.0) sdBs with effective temperatures below 30 000 K a grid of metal line blanketed LTE atmospheres with solar metallicity was used. Helium-poor sdBs and sdOBs with temperatures ranging from 30 000 K to 40 000 K were analysed using LTE models with enhanced metal line blanketing (O’Toole & Heber 2006). Metal-free NLTE models (Ströer et al. 2007) were used for hydrogen-rich sdOBs with temperatures below 40 000 K showing moderate He-enrichment (log y = −1.0...0.0) and for hydrogen-rich sdOs. Finally, the He-sdOs were analysed with NLTE models taking into account the line-blanketing caused by nitrogen and carbon (Hirsch & Heber 2009).

Spectral lines of hydrogen and helium were fitted by means of chi-squared minimization using SPAS, and statistical errors were calculated with a bootstrapping algorithm. Minimum errors reflecting systematic shifts when using different model grids (ΔTeff = 500 K; Δlog g = 0.05; Δlog y = 0.1, for a discussion see Geier et al. 2007) have been adopted in cases where the statistical errors were lower. Example fits for a typical sdB, an sdOB and a He-sdO star are shown in Fig. 10.

In addition to statistical uncertainities, systematic effects have to be taken into account in particular for sdB stars. The higher Balmer lines (Hϵ and higher) at the blue end of the spectral range are very sensitive to changes in the atmospheric parameters. However, the SDSS spectral range restricts our analysis to the Balmer lines from Hβ to H9. In high S/N data these lines are sufficient to measure accurate parameters as has been shown in Geier et al. (2011). In spectra of lower quality the bluest lines (H9 and H8) are dominated by noise and cannot be used any more. In order to check whether this leads to systematic shifts in the parameters as reported in Geier et al. (2010b) we made use of the individual SDSS spectra. We chose objects with multiple spectra, which have a S/N comparable to the lowest quality data in our sample (≃20). The atmospheric parameters were obtained from each individual spectrum. Average values of Teff and log g were calculated and compared to the atmospheric parameters derived from the analysis of the appropriate coadded spectrum. For effective temperatures ranging from 27 000 K and 39 000 K no significant systematic shifts were found. This means that the error is dominated by statistical noise. However, for temperatures as low as 25 000 K systematic shifts of the order of −2500 K in Teff and −0.35 in log g are present. For sdBs with low effective temperatures and signal-to-noise, the atmospheric parameters are therefore systematically underestimated. Only three stars in our sample have temperatures in this range. Since their coadded spectra are of reasonable quality (S/N = 34−167), systematic shifts should be negligible in these cases. Because all important lines of He i and He ii are well covered by the SDSS spectral range, systematic effects should be negligible in the case of He-rich sdO/Bs as well.

The parameters of the sample are given in Tables 3 and 4. Seven stars have already been analysed in Geier et al. (2011). The sample consists of 38 hydrogen rich sdBs, 13 sdOBs and 3 hydrogen rich sdOs. Thirteen stars are helium rich sdOs (He-sdOs) and J134352.14+394008.3 belongs to the rare class of helium rich sdBs.

thumbnail Fig. 11

Teff − log g diagram of our target sample. The helium main sequence (HeMS) and the EHB band (limited by the zero-age EHB, ZAEHB, and the terminal-age EHB, TAEHB) are superimposed with EHB evolutionary tracks for subsolar metallicity (log z = −1.48) from Dorman et al. (1993).

Our SDSS sample reaches down to fainter magnitudes and hence, larger distances than any previous survey. In an ongoing project Green et al. (2008) analyse all hot subdwarfs from the PG survey down to  ≃14.0 mag. The sample of hot subdwarf stars analysed in the course of the SPY survey reaches down to  ≃16.5 mag (Lisker et al. 2005; Ströer et al. 2007), quite similar to the sample of sdBs from the Hamburg Quasar Survey analysed by Edelmann et al. (2003).

Spectroscopic distances to our stars have been calculated as described in Ramspeck et al. (2001) assuming the canonical mass of 0.47 M⊙ for the subdwarfs and using the formula given by Lupton5 to convert SDSS-g and r magnitudes to Johnson V magnitudes. Interstellar reddening was once again neglected in these calculations, too. The distances range from 1 kpc to  >16 kpc. Since the SDSS footprint is roughly perpendicular to the Galactic disk, these distances tell us something about the population membership of our stars. These subdwarfs most likely belong to the thick disk or the halo with small contributions of thin disk stars.

Figure 11 shows a Teff − log g diagram of the top target sample. Most of our stars were born in an environment of low metallicity (thick disk or halo). Dorman et al. (1993) calculated evolutionary tracks for different metallicities of the subdwarf progenitor stars. For lower metallicities, the evolutionary tracks (and with them, the location of the EHB) are shifted towards higher temperatures and lower surface gravities. In Fig. 11 the Teff − log g diagram is superimposed with evolutionary tracks and an EHB calculated for a subsolar metallicity of log z = −1.48, which is consistent with a mixture between thick disk and halo population. Evolutionary tracks for solar metallicity are given in Fig. 12 for comparison.

thumbnail Fig. 12

Teff − log g diagram of the hot subdwarfs from the SPY project (Lisker et al. 2005; Ströer et al. 2007). The helium main sequence (HeMS) and the EHB band (limited by the zero-age EHB, ZAEHB, and the terminal-age EHB, TAEHB) are superimposed with EHB evolutionary tracks for solar metallicity from Dorman et al. (1993).

Most of the sdB stars with hydrogen-rich atmospheres are found on or slightly above the EHB band implying an evolutionary status as core helium-burning EHB or shell helium-burning post-EHB stars. The sample contains only three hydrogen rich sdOs, which are thought to be evolved post-EHB stars in a transition state. The He-sdOs cluster near the HeMS at temperatures of  ≃45 000 K. This is fully consistent with the results from the PG and the SPY surveys (Green et al. 2008; Lisker et al. 2005; Ströer et al. 2007) and illustrates that our sample is not biased (see Fig. 12).

Compared to other studies, we find only a few stars with temperatures lower than 27 000 K. Furthermore, the scatter around the EHB seems to be systematically shifted towards higher temperatures and lower surface gravities. According to our study of systematic errors in the parameter determination, it is unlikely that this causes the effect. However, higher quality data would be necessary to verify this. Another possible explanation might be related to the volume of the sample. Since hot subdwarfs of lower temperature are brighter in the optical range because of the lower bolometric correction, we may already see all of them in a fixed volume, while the fraction of hot stars is still rising at fainter magnitudes.

In Fig. 13 the helium abundance is plotted against effective temperature. The general correlation of helium abundance with effective temperature and the large scatter in the region of the sdB stars have been observed in previous studies as well. Two sequences of helium abundance among the sdB stars as reported by Edelmann et al. (2003) could not be identified.

thumbnail Fig. 13

Helium abundance log y plotted against effective temperature (see Tables 3, 4). The solid horizontal line marks the solar value. Lower and upper limits are marked with upward and downward triangles.

One has to keep in mind that our sample consists of RV variable stars only. In Fig. 11 a lack of such stars at the hot end of the EHB is visible. Green et al. (2008) reported similar systematics in their bright PG sample. The reason for this behaviour is not fully understood yet. According to the model of Han et al. (2002; 2003) and Han (2008) sdBs with thin hydrogen envelopes situated at the hot end of the EHB may be formed after the merger of two helium WDs. Since merger remnants are single stars, they are not RV variable.

The top target sample includes 13 He-sdOs for which RV shifts of up to 100 km s-1 have been detected within short timespans of 0.01−0.1 d. In total 20 He-sdOs show signs of RV variability. This fraction was unexpected since the fraction of close binary He-sdOs from the SPY sample turned out to be 4% at most (Napiwotzki 2008)6.

4. Summary and outlook

In this paper we introduced the MUCHFUSS project, which aims at finding sdBs in close binaries with massive compact companions. We identified 1100 hot subdwarf stars from the SDSS by colour selection and visual inspection of their spectra. Stars with high absolute radial velocities have been selected to efficiently remove normal sdB binaries from the thin disk population and were reobserved. We have found 46 binary candidates with significant RV shifts. Additionally, 81 stars with RV shifts on short timescales were found from the analysis of individual SDSS spectra.

Targets for follow-up spectroscopy were chosen using numerical simulations based on the properties of the known sdB close binary population and theoretical predictions about the relative fraction of massive compact companions. We selected 69 binaries with high RV shifts as well as significant RV shifts on short timescales as good candidates for massive compact companions and have determined their atmospheric parameters, spectroscopic distances, and population memberships.

The multi-site follow-up campaign started in 2009 and is being conducted with medium resolution spectrographs mounted on several different telescopes, most of which are 4-m class. First results are presented in Geier et al. (2011).

Online material

Table 2

Priority targets for follow-up.

Table 3

Priority targets for follow-up (HRV subsample).

Table 4

Priority targets for follow-up (RRV subsample).

Appendix A: Close binary subdwarfs from literature

Table A.1

Orbital parameters of all known hot subdwarf binaries from literature.

1

The more massive component of a binary is usually defined as the primary. However, in most close sdB binaries with unseen companions the masses are unknown and it is not possible to decide a priori which component is the most massive one. For this reason we call the visible sdB component of the binaries the primary throughout this paper.

2

Sloan Digital Sky Survey.

6

Green et al. (2008) suggested that the binary fraction of He-sdO stars may be comparable to the binary fraction of sdBs.

Acknowledgments

A.T., S.G. and H.H. are supported by the Deutsche Forschungsgemeinschaft (DFG) through grants HE1356/45-1, HE1356/49-1, and HE1356/44-1, respectively. R.Ø. acknowledges funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement No. 227224 (prosperity), as well as from the Research Council of K.U.Leuven grant agreement GOA/2008/04. B.N.B. acknowledges the support of the National Science Foundation, under award AST-0707381. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.

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All Tables

Table 1

Survey observations.

In the text
Table 2

Priority targets for follow-up.

In the text
Table 3

Priority targets for follow-up (HRV subsample).

In the text
Table 4

Priority targets for follow-up (RRV subsample).

In the text
Table A.1

Orbital parameters of all known hot subdwarf binaries from literature.

In the text

All Figures

thumbnail Fig. 1

The RV semiamplitudes of all known sdB binaries with spectroscopic solutions plotted against their orbital periods (see Table A.1). Binaries which were initially discovered in photometric surveys due to indicative features in their light curves (eclipses, reflection effects, ellipsoidal variations) are marked with open circles. Binaries discovered by detection of RV variation from time resolved spectroscopy are marked with filled diamonds. The dashed, dotted and solid lines mark the regions to the right where the minimum companion masses derived from the binary mass function (assuming 0.47 M⊙ for the sdBs) exceed 0.45 M⊙, 1.00 M⊙ and 1.40 M⊙. The two post-RGB objects in the sample have been excluded, because their primary masses are much lower.
In the text
thumbnail Fig. 2

Left panel. SDSS g − r-colours plotted against u − g of all stars. The grey dots mark all stellar objects with spectra available in the SDSS database. Most of them are classified as DA white dwarfs. The solid diamonds mark (He-)sdO stars, the solid squares sdB and sdOB stars. Open squares mark hot subdwarfs with main sequence companions visible in the spectra. Most of these objects are white dwarfs of DA type. Right panel. Only subdwarfs with g < 18 mag are plotted. The sequence of composite objects is clearly separated from the single-lined stars. Synthetic colours from Castelli & Kurucz (2003) for stars with temperatures ranging from 14 000 K to 50 000 K (log g = 5.0) are marked with upward triangles and connected. The stepsize of the colour grid is 1000 K. The labels mark models of certain temperatures.
In the text
thumbnail Fig. 3

Flux calibrated SDSS spectra of a single-lined sdB, a helium rich sdO and an sdB with main sequence companion visible in the spectrum. Note the different slopes of the sdB and the sdB+MS spectra.
In the text
thumbnail Fig. 4

Heliocentric radial velocities of 1002 subdwarfs plotted against g-magnitude. The two dashed lines mark the RV cut of  ± 100 km s-1.
In the text
thumbnail Fig. 5

Radial velocity distribution of the hot subdwarf stars (see Fig. 4). The bright sample (g < 16.5 mag, black histogram) contains a mixture of stars from the disk and the halo population. The faint sample (g > 16.5 mag, grey histogram) contains the halo population. The peak in the bright subsample around zero RV is caused by the thin disk population. The asymmetry in the faint subsample where negative RVs are more numerous than positive ones may be due to the presence of large structures in the halo and the movement of the solar system relative to the halo.
In the text
thumbnail Fig. 6

Hγ-line of two consecutively taken individual SDSS spectra (Δt = 0.056 d) of the sdB binary J113840.68−003531.7. The shift in RV (≃140 km s-1) between the two exposures is clearly visible.
In the text
thumbnail Fig. 7

Probability for an sdB binary to host a massive compact companion and to be seen at sufficiently high inclination to unambiguously identify it from its binary mass function plotted against the RV shift within random times (solid curves, HRV sample) or on short timescales (dotted curve, RRV sample).
In the text
thumbnail Fig. 8

Same as Fig. 7 except that the probability is plotted against RV at random time.
In the text
thumbnail Fig. 9

Highest radial velocity shift between individual spectra plotted against time difference between the corresponding observing epochs. The dashed horizontal line marks the selection criterion ΔRV > 100 km s-1, the dotted vertical line the selection criterion ΔT < 0.1 d. All objects fulfilling at least one of these criteria lie outside the shaded area and belong to the top candidate list for the follow-up campaign. The filled diamonds mark sdBs, while the blank squares mark He-sdOs.
In the text
thumbnail Fig. 10

Example fits of hydrogen and helium lines with model spectra for an sdB (left panel), an sdOB (middle panel) and a He-sdO star (right panel). The atmospheric parameters of these stars are given in Tables 3 and 4.
In the text
thumbnail Fig. 11

Teff − log g diagram of our target sample. The helium main sequence (HeMS) and the EHB band (limited by the zero-age EHB, ZAEHB, and the terminal-age EHB, TAEHB) are superimposed with EHB evolutionary tracks for subsolar metallicity (log z = −1.48) from Dorman et al. (1993).
In the text
thumbnail Fig. 12

Teff − log g diagram of the hot subdwarfs from the SPY project (Lisker et al. 2005; Ströer et al. 2007). The helium main sequence (HeMS) and the EHB band (limited by the zero-age EHB, ZAEHB, and the terminal-age EHB, TAEHB) are superimposed with EHB evolutionary tracks for solar metallicity from Dorman et al. (1993).
In the text
thumbnail Fig. 13

Helium abundance log y plotted against effective temperature (see Tables 3, 4). The solid horizontal line marks the solar value. Lower and upper limits are marked with upward and downward triangles.
In the text

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