Selection effects among WDMS binaries in SDSS

The large amount of data presented in this Chapter is of quality enough to study the selection effects of WDMS binaries in SDSS in a more complete way than discussed in Chapter 7. For this purpose we have collected the stellar parameters and distances provided in Table 9.3, and obtained in the top, middle and bottom panels of Fig. 9.14 the (log Teff,dwd), (Sp,dwd)

and (log Teff,Sp) density maps, respectively for the systems in our catalogue. Only objects

in which the relative errors in their (average) white dwarf parameters are less than 25% were selected for this purpose6, resulting in a sample of 597, 692, and 1052 systems respectively in the top, middle and bottom panels of Fig. 9.14.

The top panel in Fig. 9.14 shows the (log Teff,dwd) density map. It becomes clear

that whilst binaries in which the white dwarf primaries are cooler than 10000 K are detected at shorter distances, systems with hotter white dwarf components can be observed at a wider range of (longer) distances, the hottest among them the farthest. Cooler white dwarfs are then too faint to be detected at relatively long distances, and moderately hot white dwarfs saturate the lower magnitude limit of SDSS at shorter distances. The majority of objects are hence concentrated at ∼400-500 pc, with white dwarf effective temperatures between

∼15000-25000 K. This is in agreement with the effective temperature distribution provided in Fig. 9.11.

Having analysed how distance effects affect the detection of our white dwarf pri- maries in SDSS, we study in the middle panel of Fig. 9.14 the same effect for our secondary stars. Early-type M-dwarfs are hotter, and consequently saturate the SDSS lower magnitude limit at relatively short distances. On the contrary, later-type secondaries are cold enough

6_{We could, in principle, have also used the distances measured to the secondaries. Note though that magnetic} activity is expected to affect the spectral type (and consequently the radii and the distances) of a large fraction of secondary stars (Sect. 9.6.3). We consequently considered here the distances measured to the white dwarfs, and quote them simply as distances in what follows.

Figure 9.14: Selection effects in SDSS WDMS binaries can be understood by analysing the density maps obtained from their stellar parameters. From top to bottom the (log Teff,dwd),

to be detected at shorter distances, but too dim to be observed at long distances. Thus hotter (earlier) companions are generally detected at d>_∼300pc, and cooler (later) secondaries are concentrated at∼100−200pc.

In the bottom panel of Fig. 9.14 we show the (Teff,Sp) density map. A clear trend

of decreasing the Teff of the white dwarfs for later-type companions can clearly be seen.

In other words, high white dwarf temperatures are too hot for a late-type companion to be detected (in the optical). In the same way early spectral type secondaries are too hot for a cool white dwarf primary to be detected. With the above analysis the cut-off at early spectral types in Fig. 9.11 can be easily explained in a natural way. Selection effects then dominate the bottom left region of the (Teff,Sp) density map. The scarcity of systems with

later-type (>M6) secondaries can also be seen here, and has been already discussed in Sect.9.6.2. This feature might be also related to the above selections effects. Nevertheless, as discussed in Chapter 7, spectral type distributions of field low-mass and ultracool stars [e.g. Reid et al., 2007, 2008] peak at Sp≃M4-5, and decline towards later spectral types. Hence we suggest that the lack of WDMS binaries with late-type companions is probably both an intrinsic property of the WDMS binary population and a consequence of selection effects. Distance effects play also an important role. Thus for example, those WDMS binaries which contain both a hot primary and secondary components can not be observed at short distances, since they saturate the SDSS magnitude limit. On the contrary, WDMS binaries containing faint stars can only be observed at short distances.

From the analysis of Fig. 9.14 we conclude that a “typical” SDSS WDMS binary contains a M3–4 companion, a ∼10000-20000 K primary, and is observed at a distance

∼400-500 pc. Note though that the distributions presented in Fig. 9.14 are a combination of the real distribution of WDMS binary properties and the selection effects in the sample. Consequently a typical SDSS WDMS binary is unlikely to be representative of the “real” (corrected for selection effects) WDMS binary population.

The top and middle panels of Fig. 9.14 help in understanding brightness limited selection effects of WDMS binaries in SDSS. In order to avoid this it becomes necessary to use different magnitude limited surveys from SDSS, with lower and larger magnitude cuts respectively. The bottom panel of Fig. 9.14 helps to understand selection effects related to

the spectral appearance of WDMS binaries. Detection of systems with hotter white dwarfs and later-type companions is then most likely to arise from the use of infrared magnitude surveys such us UKIDSS or 2MASS. In the same way, to identify cool white dwarfs with early-type dominated M-dwarfs it is necessary to make use of blue surveys such as GALEX.

9.7

Conclusions

We have presented a catalogue of 1591 WDMS binaries from the spectroscopic SDSS DR6. We have used a decomposing/fitting technique to measure the effective temperatures, sur- face gravities, masses and distances to the white dwarfs, as well as the spectral types and distances to the companions in our catalogue. Distributions and density maps obtained from these stellar parameters have been used to study both the general properties and the selec- tion effects of WDMS binaries in SDSS. A comparison between the distances measured to the white dwarfs and the MS companions shows dsec >dwd for∼20% of the systems, a

tendency found in previous Chapters. We suggest that the possibility that magnetic activity raises the temperature of the inter-spot regions in active stars that are heavily covered by cool spots, leading to a bluer optical colour compared to inactive stars, remains the best explanation for this behaviour. We also provide RVs for 1062 WDMS binaries measured from the NaIλλ8183.27,8194.81 absorption doublet and/or the Hαemission line. Among

the systems with multiple SDSS spectroscopy, we find four new WDMS binaries exhibiting significant RV variations, identifying them as PCEB candidates.