© The Authors 2023

1. Introduction

The Gaia mission has revealed important features of the white dwarf population with unprecedented precision. That is the case, for instance, with respect to the existence of two well-defined branches in the colour-magnitude diagram (roughly between 0.0 ≲ G_BP − G_RP ≲ 0.5) referred to as the A and B branches, which correspond to the majority of white dwarfs with hydrogen-rich and helium-rich atmospheres (see Gaia Collaboration 2018). The most plausible explanation to reproduce the B branch invokes the presence of small amount of hydrogen or carbon into helium-dominated atmospheres (Bergeron et al. 2019; Camisassa et al. 2023; Blouin et al. 2023). These models are based on well-studied physical processes that can alter the composition of the outer layers, such as convective mixing and convective dilution, among others (e.g. Rolland et al. 2018, and references therein). The specific characteristics of each model, such as the hydrogen content, the depth of the convective zone as a function of the effective temperature, or even the possibility of accreting material from surrounding asteroids, give rise to different channels of formation and evolution of white dwarf spectral types¹ (e.g., Rolland et al. 2018; Ourique et al. 2018; Cunningham et al. 2019, 2020; Bédard et al. 2020). Therefore, accurate observational data is required to constrain these models.

The proper explanation for the formation of the Gaia A and B branches extends beyond the effective temperature range of these branches, encompassing a broader issue. A crucial observational factor in analysing the spectral evolution of white dwarfs is the ratio of non-DA to DA stars as a function of effective temperature². Extensive efforts have been made since the pioneering work of Sion (1984) to obtain statistically significant spectral distributions (e.g., Tremblay & Bergeron 2008). However, the advent of large spectroscopic and photometric surveys such as the Sloan Digital Sky Survey (SDSS; York et al. 2000), Galaxy Evolution Explorer (GALEX; Morrissey et al. 2007), and Gaia (Gaia Collaboration 2016) has significantly increased both the quantity and quality of available data (e.g., Ourique et al. 2018; Genest-Beaulieu & Bergeron 2019; Blouin et al. 2019; Cunningham et al. 2020; McCleery et al. 2020; López-Sanjuan et al. 2022). However, complete spectroscopic samples have been limited to a distance of up to 40 pc. In other cases, magnitude-selection effects introduce significant biases in the final distribution.

Nevertheless, we can leverage the exceptional quality of astrometric and photometric data provided by the Gaia mission. The third data release (DR3) of Gaia includes low-resolution spectra for nearly 100 000 white dwarfs (Montegriffo 2023), making it the largest sample of white dwarfs available for analysis. In our recent study (Jiménez-Esteban et al. 2023), we classified 8150 white dwarfs within a nearly volume-complete 100 pc sample into DA or non-DA categories. The achieved accuracy of 90% was remarkable and allowed us to derive a detailed spectral distribution within the range of temperatures from 5500 K up to 23 000 K.

In this paper, we extend our previous analysis to a distance of 500 pc, significantly increasing the expected number of white dwarfs, particularly for hotter effective temperatures. Our goal is to derive, for the first time, the spectral distribution in the entire range of temperatures between 5500 K and 40 000 K, where spectral evolution is significant.

The paper is structured as follows. In Sect. 2, we describe the selection procedure used to obtain our white dwarf sample from Gaia data. We provide a summary of the main steps of our classification methodology in Sect. 3. Once our sample is classified and validated, Sect. 4 focuses on analysing selection effects and addressing the completeness correction of the sample. In Sect. 5, we present our spectral distribution, discuss our findings, and compare them to previous works. We summarise our key results and draw our main conclusions in Sect. 6.

2. The Gaia-DR3 white dwarf sample

We selected our objects from Gaia-DR3 catalogue³ following the criteria used in Jiménez-Esteban et al. (2023) but extended up to 500 pc: (1) ω − 3σ_ω ≥ 2 mas and ω/σ_ω ≥ 10; (2) F_BP/σ_FBP ≥ 10 and F_RP/σ_FRP ≥ 10; (3) with a renormalised unit weight error (RUWE) of less than 1.4, aimed at preventing poor astrometric solutions (Lindegren et al. 2021); (4) |C^*|< 3σ_C^*, where |C^*| is an estimate of the BP and RP flux excess factor and σ_C^* is its scatter, following the prescription by Riello et al. (2021).

Selected objects were corrected from extinction following the 3D interstellar Galactic extinction maps from Lallement et al. (2022)⁴. In principle, we selected only those objects falling below the 0.45 M_⊙ cooling track on the Hertzsprung–Russell (HR) diagram. Additionally, as the atmospheric models we used (see Sect. 3) provide a reliable estimate of the effective temperature in the range from 5500 K up to 40 000 K, we chose those objects with unreddened colour between −0.5 < BP − RP < 0.86. A total number of 100 173 objects were selected, from which 76 657 have Gaia low-resolution spectra available.

Figure 1 displays the distance distribution (left panel) and cumulative distribution of apparent magnitude G (right panel) for our entire sample (red histogram) and white dwarfs with Gaia spectra (blue histogram). The use of inverse parallax as a distance estimator, combined with a parallax error threshold of less than 10%, introduces negligible discrepancies (less than ≈4%) compared to other distance estimators (Bailer-Jones et al. 2021). Most of our selected white dwarfs (73%) are within 250 pc, with a long tail extending up to 500 pc. The cumulative G magnitude distribution reveals a deficit of objects starting at G ∼ 20 mag for the entire sample and around G ∼ 19.5 mag for white dwarfs with Gaia spectra. Although the nominal limiting Gaia magnitude is ∼21.0, we adopted a conservative value of G_lim = 19.5 mag for our completeness analysis (see Sect. 4).

Fig. 1. Distance distribution (left panel) and apparent G magnitude cumulative distribution (right panel) for the entire sample of white dwarfs that fulfil our selection criteria (red histogram) and for the subsample of objects that have Gaia spectra (blue histogram). A constant cumulative slope is shown (black line) as indicative of the completeness of the sample.

3. White dwarf spectral classification

For those sources of our selected sample with available Gaia spectra, we followed the same procedure described in Jiménez-Esteban et al. (2023). A brief description of the methodology for classifying white dwarfs into DA and non-DA types used in that work is provided as follows.

First, for each white dwarf of our sample with available Gaia spectrum we determined, by means of the Python package Gaia XPy⁵ and taking into account all the coefficients of the Gaia spectrum, the synthetic Javalambre-Physics of the Accelerating Universe Astrophysical Survey (J-PAS; Benitez et al. 2014) filter system (Marín-Franch et al. 2012) photometry. We focused on those filters covering the range from 4000 to 9590.54 Å and discarding those filters with effective wavelength shorter than 4000 Å. Second, for each object we built a spectral energy distribution (SED) using the derived J-PAS photometry. Although most of the SEDs have 56 photometric points, in some noisy spectra the number of points is lower, due to our threshold in the photometric error of 10% to each individual photometric measurement obtained with Gaia XPy.

We analysed 67 340 new white dwarfs spectra, which had not previously been studied in our 100 pc sample (Jiménez-Esteban et al. 2023). For those objects with more than four photometric points (57 155), their SEDs were fitted using either pure hydrogen white dwarf atmospheric models (DA) or models with helium and a small trace of hydrogen (non-DA, log N(H)/N(He) = −6). Both DA and non-DA models covered the temperature range of interest for this study (5500–40 000 K) and surface gravities from 7 to 9 dex (see Sect. 3.1 in Jiménez-Esteban et al. 2023 for detailed model information). The fitting process was performed using the Virtual Observatory spectral energy distribution Analyser⁶ (VOSA; Bayo et al. 2008), a powerful tool developed by the Spanish Virtual Observatory. Among the new 57 155 analysed objects, only three had Vgf_b⁷ greater than 15 and were disregarded. For each object, two reduced chi-squared values (${\chi }_{\text{DA}}^2$ and ${\chi }_{\text{non-DA}}^2$) were obtained. Finally, the estimator of the probability of being a DA white dwarf (P_DA) was defined as:

$$\begin{array}{c}\hfill P_{\mathrm{DA}}=\frac{1}{2}(\frac{{\chi }_{\text{non-DA}}^2-{\chi }_{\mathrm{DA}}^2}{{\chi }_{\text{non-DA}}^2+{\chi }_{\mathrm{DA}}^2}+1),\end{array}$$(1)

where we classified an object as DA if P_DA ≥ 0.5, otherwise as a non-DA.

We validated our classification procedure by means of the spectroscopically labelled white dwarf sample of the Montreal White Dwarf Database⁸ (MWDD; Dufour et al. 2017). A total of 8482 objects from the MWDD were used in our validating test (including those at distances closer than 100 pc). We adopted all MWDD objects whose primary spectral type is DA as DA class, regardless of their secondary types. The rest of the objects were considered as non-DA. In the left panel of Fig. 2, we show the distribution of the probability of being a DA, P_DA, for white dwarfs labelled as DA (blue histogram) or non-DA (red histogram) in the MWDD. The distribution confirms that the adopted threshold at P_DA = 0.5 effectively separates both populations and that the percentage of misclassified object is reasonable small, ≲7%. In the right panel of Fig. 2, we show the confusion matrix, where rows represent the number of already labelled spectral objects, while columns are the prediction of our classification (in parentheses the percentages with respect to the total population). The results of the confusion matrix reveal that the performance of our spectral type estimator is excellent, as it is corroborated by the derived metrics⁹: accuracy of 0.94, F1-score of 0.96, recall of 0.94, and precision of 0.98.

Fig. 2. Probability distribution of being DA for the white dwarf labelled as DA or non-DA (blue and red histograms, respectively) in the MWDD (top panel). Confusion matrix of our estimator of being DA (bottom panel). Displayed values represent the total number of objects, while in brackets the percentages with respect to the total population.

A last check was performed before applying our classification method to the observed Gaia white dwarf sample. In Fig. 3, we depicted the distribution of the G apparent magnitude for the entire sample of white dwarfs with Gaia spectra (blue histogram) and those with spectral classification in MWDD (gray histogram). We verified that the MWDD sample covers the full range of magnitudes and closely resemble the observed Gaia sample distribution. These facts guarantee the proper use of the MWDD sample for testing our classification method. Moreover, in Fig. 3, we present the magnitude distribution of the white dwarfs misclassified by our method (red histogram). As expected, the fainter the magnitude the larger the fraction of misclassified objects. Considering the percentage of error as a function of magnitude and extrapolating it to the Gaia sample, we estimated that the error in the final classification should not exceed 10%.

Fig. 3. Distribution of G apparent magnitude for the entire sample of white dwarfs with Gaia spectra (blue histogram), those with spectral classification in MWDD (grey histogram) and those of the previous sample misclassfied by our method (red histogram).

Once we have validated the reliability of our classification method, we applied it to the sample of white dwarfs with Gaia spectra within 500 pc. A total of 65 310 white dwarfs (including those previously classified in Jiménez-Esteban et al. 2023) have been classified into the spectral types DA (50 189; 77%) and non-DA (15 121; 23%) with an accuracy of 0.94. The catalogue with the spectral classification is available at the CDS and at The SVO archive of Gaia white dwarfs¹⁰ at the Spanish Virtual Observatory portal¹¹.

In Fig. 4, we show the HR diagram of the corresponding DA and non-DA populations. For visual reference, we also show the cooling sequence of a 0.58 M_⊙ DA white dwarf (Camisassa et al. 2016). The distribution of DA and non-DA white dwarfs clearly follows different tracks, with the latter group being, on average, less luminous for a certain colour (in particular for BP − RP > ;0) than the first one. It is worth mentioning that our classification into DA and non-DA groups is less model-dependent than H- vs. He-rich classification. However, such a classification is still needed for a correct astrophysical interpretation. Thus, higher resolution spectroscopy is required to flag misclassified objects, identify He-rich DAs and magnetic DAH with distorted Balmer jumps, as well as DZ and DQ with unusual colours, among other cases.

Fig. 4. Gaia HR diagram for the population of white dwarfs classified by our probability estimator as DA (left panel) and non-DA (right panel). As a visual reference, we plotted the cooling sequence of a 0.58 M⊙ DA white dwarf according to La Plata models.

4. Completeness correction

We analysed the different selection effects and how they can be corrected or at least mitigated. First of all, as our sample is initially built as a magnitude-selected sample, objects fainter than a certain magnitude limit would be absent from our sample. A standard 1/𝒱_max method (Schmidt 1968) will provide an unbiased estimate of the space density. However, it requires extra conditions of completeness and homogeneity to be fulfilled (see Geijo et al. 2006, and references therein). These conditions are not guaranteed in our sample, as the requirement to have a Gaia spectrum adds a new selection effect and also mainly because DA and non-DA populations have, as previously stated, a different distribution in the colour–magnitude diagram (see Fig. 4).

In order to avoid this bias that would distort the spectral distribution, we developed a strategy in which we consider objects contributing to the spectral distribution only if they are brighter than a certain magnitude and hotter than a certain temperature (colour). We adopted the cooling sequence for a 1.05 M_⊙ white dwarf as our faint limiting region. For a given distance of the white dwarf, the Gaia limiting magnitude we adopted is G_lim = 19.5 (see Sect. 2), which is meant to fix the absolute observable magnitude limit. The corresponding colour at this magnitude for the 1.05 M_⊙ white dwarf cooling sequence delimits the possible contribution to the spectral distribution. Only objects with a bluer colour than this value will contribute, while redder objects will be disregarded. In the left panel of Fig. 5, we present an example of this strategy. White dwarfs beyond a distance of 250 pc are highlighted in the Gaia HR diagram. Only those objects (marked in blue) above the horizontal line are observable and those to the left of the vertical line and above the 1.05 M_⊙ track are included in the final sample to construct our spectral distribution. Thus, we prevented non-DA objects (which, on average, are fainter than DAs for a given colour; see Fig. 4) from being underestimated in the spectral distribution. It should be noted that this procedure automatically eliminates any massive white dwarf from our sample. However, their contribution is estimated to be less than ≈3% of the entire population (e.g., Kilic et al. 2020; Jiménez-Esteban et al. 2023).

Fig. 5. Gaia colour–magnitude diagram of our population of DA and non-DA white dwarfs, shown as yellow dots in the left panel. Highlighted in blue are those objects at distances d > ;250 pc. Assuming a limiting magnitude of Glim = 19.5, only those brighter than MG < 12.5 (horizontal red line) are observable. The cooling track for a 1.05 M⊙ white dwarf (black line) is adopted as our lower selection function limit. For a given distance, only objects (marked in dark blue) at the left of the corresponding colour value (vertical red line) contribute to the final spectral distribution. The white dwarfs selected for building our spectral distribution are highlighted in red in the right panel. Objects above or below the cooling track for a 0.51 M⊙ helium-rich and a 1.05 M⊙ hydrogen-rich white dwarf, respectively, were discarded.

A second important source of incompleteness comes from the fact that not all white dwarf sources have an available Gaia spectrum. Moreover, even those sources that have it may not have a good VOSA determination of the probability of being DA or non-DA. It is expected that the number of sources without a determination of this probability increases for fainter and distant objects. We take into account this fact by introducing a weight function that depends on the distance, d, of the object and its specific location within the HR diagram, w(G_BP − G_RP,  M_G,  d). For a given source with parameters (G_BP − G_RP,  M_G,  d)₀, we computed the number of sources, n_sources, within a volume of 𝒱 = Δ(G_BP − G_RP)×ΔM_G × Δd centred at the previous value and with Δ(G_BP − G_RP) = 0.1, ΔM_G = 0.1 and Δd = 50 pc. Besides the number of sources within 𝒱, we also computed the number of objects with available Gaia spectra, n_Gaia-sp, and the number of those who have a VOSA estimation of the probability of being DA, n_VOSA-PDA. Assuming that the completeness weight function should be inversely proportional to the probability of an object of belonging to the final sample, a straightforward application of the Bayes’ theorem for conditional probability leads to:

$$\begin{array}{c}\hfill w(G_{\mathrm{BP}}-G_{\mathrm{RP}},M_G,d)={(\frac{n_{\text{Gaia-sp}}}{n_{\mathrm{sources}}}\times \frac{n_{\text{VOSA-PDA}}}{n_{\text{Gaia-sp}}})}^{-1}=\frac{n_{\mathrm{sources}}}{n_{\text{VOSA-PDA}}}.\end{array}$$(2)

Finally, in addition to the selection function previously described (i.e., the selection of objects hotter than a given colour determined by the 1.05 M_⊙ evolutionary track for a given distance), we considered objects located in the HR diagram below the cooling track for a 0.51 M_⊙ helium-rich white dwarf. This way, we avoid unresolved binary white dwarf systems and the contribution of white dwarfs evolved from binary evolution (Jiménez-Esteban et al. 2023). Furthermore, the existence of low-mass white dwarfs with helium-rich atmospheres has not been proven (see, for instance, Genest-Beaulieu & Bergeron 2019; Battich et al. 2020). Thus, we adopted the 0.51 M_⊙ low-mass limit as a conservative criterion. For each object of our final sample we determined the effective temperature by interpolating the Gaia photometry in the La Plata models. Those objects classified as DA were interpolated in the models of Camisassa et al. (2016), while for those labelled as non-DA, we used the hydrogen-deficient cooling models of Camisassa et al. (2017); in both cases, for carbon-oxygen-core white dwarfs (see Jiménez-Esteban et al. 2023, for details). Atmospheric models where those used in the SED analysis (see Sect. 3.1 from Jiménez-Esteban et al. 2023), namely, Koester’s models with pure hydrogen composition for DAs and helium with a small trace of hydrogen (log N(H)/N(He) = −6) for non-DAs (Koester 2010). It is worth noting here that recent studies have emphasised the importance of considering the carbon content in non-DA atmospheres (Camisassa et al. 2023; Blouin et al. 2023). Assuming the maximum non-observable carbon enrichment prescription from Camisassa et al. (2023), that is, carbon sequence −1 dex, the difference with respect to a pure helium model is ∼10% at 12 000 K, and approximately 5% at 6000 K. The differences are not larger than 1500 K, which corresponds to the bin width of our spectral distribution. Thus, no major effects are expected in this regard. Our final sample to estimate the spectral fraction, consisting of 33 997 white dwarfs, is shown in Fig. 5, with 25 984 (76.4%) classified as DAs and 8013 (23.6%) as non-DAs.

5. The spectral type-temperature distribution

The spectral type-temperature distribution, f, is defined as the ratio of weighted non-DA white dwarfs, to the total number of weighted objects, N_w, per effective temperature interval. We adopted that the contribution of each object to its temperature bin depends on its weight function, w, and the probability of classification, P_i (that is P_DA, i for DAs, 1 − P_DA, i for non-DAs). Hence, the weighted number of objects is defined as:

$$\begin{array}{c}\hfill N_{\mathrm{w}}={\displaystyle \sum _i^{N}w{(G_{\mathrm{BP}}-G_{\mathrm{RP}},M_G,d)}_i\times P_i,}\end{array}$$(3)

where N is the number of objects in that interval, w the weighted function and P_i the probability aforementioned. Error bars were estimated taking into account Poissonian error and the corresponding object weight, that is ${\sigma }_f=\sqrt{f\times (1-f)/N_{\mathrm{w}}}$.

In Fig. 6, we displayed our final spectral distribution (black solid circles and black line). To evaluate the extent of the completeness correction introduced in our sample, we included the ratio distribution of the entire classified white dwarf population (raw sample consisting of 65 310 objects) when no selection function is applied at all (blue open triangles). For purposes of comparison, we also plotted the spectral distribution for the sample of 100 pc (red circles; Jiménez-Esteban et al. 2023). The analysis of the different spectral distributions revealed that the effects due to completeness correction are of minor order. The general trend is practically coincident, and only small discrepancies appear for the coolest bin, where the error bars underestimate the fact that the classification is less certain. In any case, we can conclude that our weighted spectral distribution provides a robust estimate of the ratio of DA vs. non-DA white dwarfs.

Fig. 6. Spectral distribution presented in this work (black lines and solid circles) and when no selection criteria and correction function is applied at all (blue open triangles). The one obtained for the 100 pc sample (Jiménez-Esteban et al. 2023, red circles) is also shown.

In Fig. 7, we show a comparison of the spectral distribution found in this work (black solid circles) with some of the most recent ratio distributions found in the literature. The first remarkable characteristic of the spectral distribution found in this work is the wider range of effective temperatures covered by it, thus constituting a solid estimate of the spectral evolution of white dwarfs. While a detailed analysis of the implications for spectral evolution is outside the scope of this work, in what follows, we present a brief analysis of the most relevant points found.

Fig. 7. Spectral distribution for our final white dwarf sample (black points and lines). For comparison, we also show the spectral distributions from other works found in literature.

At the hottest end, that is, T_eff ≈ 35 000 − 40 000 K, the lowest ratio of non-DAs was found. As previously reported, there is not a complete absence of non-DAs in this region, but an average ∼5% is indicative of the presence of the so called “DB-gap” (e.g., Bergeron et al. 2011; Koester & Kepler 2015, and references therein). An additional statistical significant deficit of non-DAs was also found for effective temperatures in the range of 22 000 ≲ T_eff ≲ 25 000 K, in perfect agreement with the ratios found by Ourique et al. (2018) and López-Sanjuan et al. (2022). Finally, for temperatures cooler than ∼18 000 K, coinciding with the onset of convection mixing in DAs (e.g., Cunningham et al. 2020), a marked increase in the ratio of non-DAs was found, leading from ∼10% at 18 000 K up to ∼40% at 8000 K and in agreement with most of the spectral distributions found in the literature.

It is worth mentioning that our spectral distribution presented a peak around T_eff ≈ 7000 K with a ratio of non-DA objects of f ≈ 0.41. This maximum is found at lower temperatures than that of our previous work (Jiménez-Esteban et al. 2023) and others retrieved in literature such as Ourique et al. (2020), probably as a consequence of an unweighted distribution in these cases. However, the weighted distribution presented here is in agreement with the 40 pc spectroscopic complete sample analysed in McCleery et al. (2020). Moreover, a statistically significant decrease in the ratio of non-DAs is found at the coolest bin, T_eff ≈ 6000 K, dropping to f ≈ 0.35. This behaviour was also reported in our previous work (Jiménez-Esteban et al. 2023) and is also in agreement with Blouin et al. (2019) and McCleery et al. (2020), although no known physical mechanism can be associated with it (Blouin et al. 2019).

6. Conclusions

Following the methodology presented in Jiménez-Esteban et al. (2023), we have expanded our white dwarf study sample up to 500 pc. A total of 65 310 white dwarfs have been classified as DAs and non-DAs based on their Gaia spectra, with an accuracy of 94%. This has allowed us to construct a statistically significant and precise distribution of the DA vs. non-DA ratio as a function of effective temperature. Nearly 34 000 white dwarfs have contributed to the final selected sample, making it the largest sample to date in terms of the number of objects and the range of effective temperatures analysed, from 5500 K to 40 000 K.

The comparative analysis of our distribution with others found in the literature reveals statistically significant features such as: the deficit of DBs within the effective temperature range of approximately 35 000 − 40 000 K and between 22 000 − 25 000 K, along with a gradual rise starting from 18 000 K up to around 7000 K, where the proportion of non-DA white dwarfs peaks at 41%, followed by a decline for lower temperatures.

Finally, we can state that selection effects have been taken into account in the construction of the final sample. This fact, along with the high number of objects per interval in the sample, ensures that our spectral distribution can be considered a robust and precise element in the analysis of the spectral evolution of white dwarfs.

Acknowledgments

We acknowledge support from MINECO under the PID2020-117252GB-I00 grant and by the AGAUR/Generalitat de Catalunya grant SGR-386/2021. P.C. acknowledges financial support from the Government of Comunidad Autónoma de Madrid (Spain) via postdoctoral grant ‘Atracción de Talento Investigador’ 2019-T2/TIC-14760. R.M.O. is funded by INTA through grant PRE-OBSERVATORIO. MC acknowledges grant RYC2021-032721-I, funded by MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR. RR acknowledges support from Grant RYC2021-030837-I funded by MCIN/AEI/ 10.13039/501100011033 and by “European Union NextGenerationEU/PRTR”. F.J.E. acknowledges support from ESA through the Faculty of the European Space Astronomy Centre (ESAC) – Funding reference 4000139151/22/ES/CM. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This work has made use of the Python package Gaia XPy, developed and maintained by members of the Gaia Data Processing and Analysis Consortium (DPAC) and in particular, Coordination Unit 5 (CU5), and the Data Processing Centre located at the Institute of Astronomy, Cambridge, UK (DPCI). This publication makes use of VOSA, developed under the Spanish Virtual Observatory (https://svo.cab.inta-csic.es) project funded by MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00. We extensively made used of Topcat (Taylor 2005). This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. We acknowledge use of the ADS bibliographic services.

References

All Figures

	Fig. 1. Distance distribution (left panel) and apparent G magnitude cumulative distribution (right panel) for the entire sample of white dwarfs that fulfil our selection criteria (red histogram) and for the subsample of objects that have Gaia spectra (blue histogram). A constant cumulative slope is shown (black line) as indicative of the completeness of the sample.
In the text

	Fig. 2. Probability distribution of being DA for the white dwarf labelled as DA or non-DA (blue and red histograms, respectively) in the MWDD (top panel). Confusion matrix of our estimator of being DA (bottom panel). Displayed values represent the total number of objects, while in brackets the percentages with respect to the total population.
In the text

	Fig. 3. Distribution of G apparent magnitude for the entire sample of white dwarfs with Gaia spectra (blue histogram), those with spectral classification in MWDD (grey histogram) and those of the previous sample misclassfied by our method (red histogram).
In the text

	Fig. 4. Gaia HR diagram for the population of white dwarfs classified by our probability estimator as DA (left panel) and non-DA (right panel). As a visual reference, we plotted the cooling sequence of a 0.58 M⊙ DA white dwarf according to La Plata models.
In the text

Fig. 5. Gaia colour–magnitude diagram of our population of DA and non-DA white dwarfs, shown as yellow dots in the left panel. Highlighted in blue are those objects at distances d > ;250 pc. Assuming a limiting magnitude of Glim = 19.5, only those brighter than MG < 12.5 (horizontal red line) are observable. The cooling track for a 1.05 M⊙ white dwarf (black line) is adopted as our lower selection function limit. For a given distance, only objects (marked in dark blue) at the left of the corresponding colour value (vertical red line) contribute to the final spectral distribution. The white dwarfs selected for building our spectral distribution are highlighted in red in the right panel. Objects above or below the cooling track for a 0.51 M⊙ helium-rich and a 1.05 M⊙ hydrogen-rich white dwarf, respectively, were discarded.

In the text

	Fig. 6. Spectral distribution presented in this work (black lines and solid circles) and when no selection criteria and correction function is applied at all (blue open triangles). The one obtained for the 100 pc sample (Jiménez-Esteban et al. 2023, red circles) is also shown.
In the text

	Fig. 7. Spectral distribution for our final white dwarf sample (black points and lines). For comparison, we also show the spectral distributions from other works found in literature.
In the text