A determination of the space density and birth rate of hydrogen-line (DA) white dwarfs in the Galactic Plane, based on the UVEX survey

Abstract

We present a determination of the average space density and birth rate of hydrogen-line (DA) white dwarfs within a radius
of 1 kpc around the Sun, based on an observational sample of 360 candidate white dwarfs with g < 19.5 and (g − r) < 0.4, selected from the UV-Excess (UVEX) survey of the northern Galactic plane, in combination with a theoretical white
dwarf population that has been constructed to simulate the observations, including the effects of reddening and observational
selection effects. The main uncertainty in the derivation of the white dwarf space density and current birth rate lies in
the absolute photometric calibration and the photometric scatter of the observational data, which influences the classification
method on colours, the completeness and the pollution. Corrections for these effects are applied. We derive an average space
density of DA white dwarfs with Teff > 10 000 K (MV < 12.2) of (3.8 ± 1.1) × 10−4 pc−3, and an average DA white dwarf birth rate over the last 7×107 yr of (5.4 ± 1.5) × 10−13 pc−3 yr−1. Additionally, we show that many estimates of the white dwarf space density from different studies are consistent with each
other, and with our determination here.

Full text

arXiv:1306.5252v1 [astro-ph.SR] 21 Jun 2013
Mon. Not. R. Astron. Soc. 000, 1–17 (2013) Printed 17 June 2014 (MN L
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A determination of the space density and birth rate of
hydrogen-line (DA) white dwarfs in the Galactic Plane,
based on the UVEX survey
Kars Verbeek1⋆, Paul J. Groot1, Gijs Nelemans1, Simone Scaringi1,3,
Ralf Napiwotzki2, Janet E. Drew2, Danny Steeghs4, Jorge Casares5,
Jesus M. Corral-Santana5,6Boris T. G¨ansicke4, Eduardo Gonz´alez-Solares7,
Robert Greimel8, Ulrich Heber9, Mike J. Irwin9, Christian Knigge10,
Nicholas J. Wright2and Albert A. Zijlstra11
1Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
2Centre for Astronomy Research, Science & Technology Research Institute, University of Hertfordshire, Hatfield, AL10 9AB, UK
3Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
4Physics Department, University of Warwick, Coventry, CV4 7AL, UK
5Instituto de Astrof´ısica de Canarias, Via Lactea, s/n E-38205 La Laguna (Tenerife), Spain
6Departamento de Astrof´ısica, Universidad de La Laguna, La Laguna E-38205, S/C de Tenerife, Spain
7Cambridge Astronomy Survey Unit, Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
8Institut f¨ur Physik, Karl-Franzen Universit¨at Graz, Universit¨atsplatz 5, 8010 Graz, Austria
9Dr. Remeis-Sternwarte Bamberg, Universit¨at Erlangen-N¨urnberg, Sternwartstrasse 7, D-96049 Bamberg, Germany
10School of Physics and Astronomy, University of Southampton, Southampton, Hampshire, SO17 1BJ, UK
11 Jodrell Bank Centre for Astrophysics, Alan Turing Building, University of Manchester, M13 9PL, UK
Accepted for publication in MNRAS
ABSTRACT
We present a determination of the average space density and birth rate of hydrogen-
line (DA) white dwarfs within a radius of 1 kpc around the Sun, based on an
observational sample of 360 candidate white dwarfs with g<19.5 and (g−r)<0.4,
selected from the UV-excess Survey of the Northern Galactic Plane (UVEX ), in
combination with a theoretical white dwarf population that has been constructed
to simulate the observations, including the effects of reddening and observational
selection effects. The main uncertainty in the derivation of the white dwarf space
density and current birth rate lies in the absolute photometric calibration and the
photometric scatter of the observational data, which influences the classification
method on colours, the completeness and the pollution. Corrections for these
effects are applied. We derive an average space density of hydrogen-line (DA)
white dwarfs with Teff >10 000K (MV<12.2) of (3.8 ±1.1) ×10−4pc−3, and an
average DA white dwarf birth rate over the last 7×107years of (5.4 ±1.5) ×10−13
pc−3yr−1. Additionally, we show that many estimates of the white dwarf space density
from different studies are consistent with each other, and with our determination here.
Key words: surveys – stars: general – ISM:general – Galaxy: stellar content – Galaxy:
disc – stars: white dwarfs
⋆E-mail:k.verbeek@astro.ru.nl
1 INTRODUCTION
One of the main goals of the European Galactic Plane
Surveys (EGAPS 1) is to obtain a homogeneous sample of
1EGAPS is the combination of the IPHAS (Drew et al.,
2005), UVEX (Groot et al., 2009) and the VPHAS+ surveys.
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2Kars Verbeek et al.
stellar remnants in our Milky Way with well-understood
selection limits. The population of white dwarfs in the
Plane of the Milky Way is relatively unknown due to the
effects of crowding and dust extinction. White dwarf space
densities and birth rates have mostly been derived from
surveys at Galactic latitudes larger than |b|>30◦, such as
the Sloan Digital Sky Survey (SDSS , York et al., 2000,
Yanny et al., 2009, Eisenstein et al., 2006 and Hu 2007),
the Palomar Green Survey (Green et al., 1986 and Liebert
et al., 2005), the KISO Survey (Wegner et al., 1987 and
Limoges & Bergeron, 2010), the Kitt Peak-Downes Survey
(KPD, Downes, 1986) and the Anglo-Australian Telescope
(AAT) QSO Survey (Boyle et al., 1990). However, as shown
in Groot et al. (2009) the distribution of any Galactic
stellar population with absolute magnitude MV<10 is
strongly concentrated towards the Galactic Plane in mod-
ern day deep surveys reaching limiting magnitudes of V∼22.
Within the EGAPS project, the UVEX survey images
a 10×185 degrees wide band (–5◦< b <+5◦) centred on the
Galactic equator in the U, g , r and He iλ5875 bands down
to ∼21st −22nd magnitude using the Wide Field Camera
mounted on the Isaac Newton Telescope on La Palma
(Groot et al., 2009). From the first 211 square degrees
of UVEX data a catalogue of 2 170 UV-excess sources
was selected in Verbeek et al. (2012a; hereafter V12a).
These UV-excess candidates were identified in the (U−g)
versus (g−r) colour-colour diagram and gversus (U−g)
and gversus (g−r) colour-magnitude diagrams by an
automated field-to-field selection algorithm. Less than ∼1%
of these UV-excess sources were previously known in the
literature. A first spectroscopic follow-up of 131 UV-excess
candidates, presented in Verbeek et al. (2012b; hereafter
V12b), shows that 82% of the UV-excess catalogue sources
are white dwarfs. Other sources in the UV-excess catalogue
are subdwarfs type O and B (sdO/sdB), emission line stars
and QSOs.
A determination of the space density and birth rate
of hydrogen-line (DA) white dwarfs in the Galactic Plane
based on an observational sample of hot candidate white
dwarfs from V12a is presented in this work. In Sect. 2
a theoretical Galactic model population is constructed
to simulate a survey such as UVEX . In Sect. 3 the
sample of observed candidate white dwarfs is selected
from the UV-excess catalogue, including an estimate on
completeness and homogeneity due to selection effects. In
Sect. 4 the method is outlined that is used to derive the
effective temperatures, reddening, and, derived from these,
the distances to the observational sample. In Sect. 5 the
method is applied to the observational sample, considering
three sub-samples with slightly different selection biases
and model assumptions. In Sects. 7 and 8 a space density
and birth rate for hydrogen-line (DA) white dwarfs within
a radius of 1 kpc around the Sun are derived. Taking into
account the uncertainties, we give upper and lower limits on
these derived space densities and birth rates. In Sect. 9 the
impact of all assumptions is discussed, the conclusions are
Websites: http://www.iphas.org, http://www.uvexsurvey.org and
http://www.vphasplus.org
1
10
100
100000 1e+06 1e+07 1e+08 1e+09 1e+10
Temperature (kK)
Age (years)
DA log(g)=8 cooling track
Figure 1. Cooling track for DA white dwarfs with log(g)=8 from
Wood (1995).
7
8
9
10
11
0 4e+07 8e+07 1.2e+08
Absolute Magnitude
Age (years)
r
g
U
Figure 2. Age versus absolute magnitude for DA white dwarfs
with log(g)=8 from Holberg & Bergeron (2006) for the UVEX r,
gand Ufilter bands.
summarized and compared with the results of other surveys.
2 A THEORETICAL GALACTIC MODEL
SAMPLE
In the determination of the white dwarf space density
and birth rate, the observations will be compared to a
Galactic model population that has been constructed
and scaled to emulate the observations. The model is
detailed in Nelemans et al. (2004) and is based on the
Galaxy model according to Boissier & Prantzos (1999),
including a Sandage (1972) extinction model. This model
has been presented and used before in Nelemans et al.
(2004), Roelofs, Nelemans & Groot (2007) and Groot et al.
(2009). Note that for the simulated sample in this paper a
constant white dwarf birth rate over the last 8×108years is
assumed. Only the spatial distribution of the white dwarfs
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A determination of the space density and birth rate of hydrogen-line (DA) white dwarfs in the Galactic Plane
Figure 3. g-band magnitude histogram for the modelled white
dwarf sample.
Figure 4. Distance histogram for the modelled white dwarf sam-
ple. The number white dwarfs brighter than g < 19.5 decreases for
distances larger than 0.25 kpc while the number of white dwarfs
in the total simulated sample continues to increase.
comes from the model as described in Nelemans et al. (2004).
A theoretical sample of 8×104DA white dwarfs is
generated by a random distribution over ages 0-8×108years
and a model-weighted position in the Galaxy with a Galac-
tic longitude spread of –180◦<l<+180◦, a Galactic latitude
spread –5◦<b<+5◦(the limits of the EGAPS surveys), a
distance d<1.5 kpc and an extinction AVappropriate to
their distance and Galactic location.
Using the DA white dwarf cooling models by Wood
(1995) the adopted age distribution (<8×108years) trans-
lates into a minimal temperature of Teff >9 000 K. This
cut in temperature is required due to the uncertainties
and incompleteness of colder white dwarfs in the observed
sample (see Sect. 3). The temperature of the white dwarf is
related to an absolute magnitude (M) for each filter band
Figure 5. AVhistogram for the modelled white dwarf sample.
Figure 6. Age histogram for the modelled white dwarf sample.
The number of white dwarfs brighter than g < 19.5 decreases for
older systems, the number of white dwarfs in the total simulated
sample is constant for all bins due to the assumption of a constant
birth rate.
(Figs. 1 and 2). For each object, the absolute magnitude in
the Vega system in the UVEX bands (MU,Mg,Mr) has
been calculated using the colour calculations of Holberg &
Bergeron2(2006), Kowalski & Saumon (2006), Tremblay et
al. (2011) and Bergeron et al. (2011), assuming a surface
gravity log g= 8.0, and the UVEX filter passbands pre-
sented in Groot et al. (2009). The magnitudes are converted
to the Vega system using the AB offsets U=-0.927, g=0.103,
r=-0.164 of Gonz´alez-Solares et al., 2008 and Hewett et al.,
2006. These values need to be added to the AB magnitudes
to convert them to the Vega system. Reddened apparent
magnitudes and Vega colours for each white dwarf were
calculated using Aλ/AV=1.66, 1.16, 0.84 for the U-, g- and
r-bands respectively. To emulate the observational sample
of Sect. 3, only white dwarfs with g<19.5 were selected,
2http://www.astro.umontreal.ca/∼bergeron/CoolingModels
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Figure 7. Temperature histogram for the simulated white dwarf
sample.
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20
30
40
50
60
70
80
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Temperature (kK)
Distance (kpc)
Simulated sample g<19.5
g=13.0
g=19.5
Figure 8. Temperature versus distance for the modelled white
dwarf sample (red). The two lines indicate the survey limits at
g=13 and g=19.5.
keeping 723 systems out of the original model sample. The
reason of the magnitude cut at g<19.5 is to warrant the
completeness of the observational sample. Going deeper
clearly showed a down-turn in the number of systems in the
observational sample, indicative of loss of completeness.
The characteristics of the simulated white dwarf sample
are shown in Figs. 3-9. Figure 3 shows that the number of
white dwarfs keeps on increasing for magnitudes g>19.5
and only turns over around g∼25 due to the combined
effects of a minimum temperature and a limited volume
in the model. White dwarfs detectable in a survey such as
UVEX are only a tip of the iceberg compared to the total
population, even within a limited distance of ∼1 kpc. No
white dwarfs in the sample are brighter than g∼13.3 and all
white dwarfs brighter than g<19.5 are within d<0.92 kpc
(Fig. 4). The observable sample is complete to a distance
of ∼0.2kpc and all systems have extinctions smaller than
AV<1.7 (Figs. 4 and 5). AVpeaks between 0.3 and 0.4 for
0
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0.04
0.06
0.08
0.1
0.12
0.14
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Height above the plane (kpc)
Distance (kpc)
Simulated sample g<19.5
hot DA WDs of V12b
Figure 9. Height above the Galactic Plane versus distance for
the modelled white dwarf sample (red) and the William Herschel
Telescope (WHT) spectroscopically confirmed DA white dwarfs
(black) of V12b.
the white dwarfs brighter than g < 19.5 while it peaks be-
tween 1.7 and 1.8 for the total simulated white dwarf sample.
The age distribution is shown in Fig. 6, and the corre-
sponding white dwarf temperatures in Fig. 7. The fraction
of hot, young white dwarfs is larger than the fraction of
older, colder white dwarfs. The number of white dwarfs
in the complete simulated sample varies with different
Galactic latitude and longitude. While the number of white
dwarfs in the total simulated sample is higher at Galactic
latitude b=0◦and Galactic longitude l=0◦, the number in
the g<19.5 sample is constant over Galactic latitude and
Galactic longitude. The white dwarfs brighter than g<19.5
are equally distributed over different Galactic latitudes and
Galactic longitudes due to the limited distance probed in
this first, relatively shallow sample. The distributions over
distance, temperature and height above the Galactic Plane
of the numerical, observable sample are shown as red points
in Figs. 8 and 9. The lines in Fig. 8 show for the chosen
upper and lower magnitude limits in the observable out
to which distance a survey such as UVEX is sensitive as a
function of temperature.
3 THE OBSERVATIONAL WHITE DWARF
SAMPLE
The UV-excess catalogue of V12a, selected from the first
211 square degrees of UVEX data contains 2 170 UV-excess
sources. In the colour-colour and colour-magnitude dia-
grams an automated algorithm selects blue outliers relative
to other stars in the same field. We have used recalibrated
UVEX photometry to correct for the time-variable U-band
calibration as noted in Greiss et al. (2012). The recalibrated
UVEX data are explained in Appendix A.
Since we are interested in a complete sample of white
dwarfs with minimal pollution we select all sources with
g<19.5 and (g−r)<0.4. The distribution of the observa-
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A determination of the space density and birth rate of hydrogen-line (DA) white dwarfs in the Galactic Plane
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-0.5
0
0.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4
(U-g)
(g-r)
6kK
80kK
AV=1
Total UV-excess sample
WD candidates
Simulated WD sample
Figure 10. Colour-colour diagram with the UV-excess sources of V12a brighter than g<19.5 (black triangles), the white dwarf candidates
in the UV-excess catalogue (blue circles), and the simulated white dwarf sample brighter than g<19.5 (red squares). Overplotted are the
simulated colours of unreddened main-sequence stars (dashed black) and the simulated colours of unreddened Koester DA (solid black)
and DB (dashed green) white dwarfs of V12a. The DA white dwarf colours are shown for different log g=7.0, 7.5, 8.0, 8.5, 9.0, where the
upper line is log g=9.0. The DA white dwarf colours cover the range 80kK> Teff >6kK No photometric error bars are plotted for clarity,
photometric errors range from 0.002 mag at g=16 to <0.025 mag at g=19.5. The simulated DA white dwarfs are distributed over the
Galaxy and reddened to their Galactic position. The simulated sources around the unreddened DB track (dashed green) are reddened
hot DA white dwarfs. The vector (AV=1) shows the direction of the reddening, its length is equal to AV=1.
tional sample for magnitudes fainter than g>19.5 clearly
showed a down-turn indicative of loss of completeness,
therefore a magnitude cut at g=19.5 is applied. The colour
cut at (g−r)<0.4, which corresponds to the colour of
unreddened DA white dwarfs with Teff ∼7 000K, is applied
since all DA white dwarfs in V12b have (g−r)<0.4 (Figs. 1
and 2 of V12b). From spectroscopic follow-up of V12b it
is known that the observational sample with (g−r)<0.4
is dominated by DA white dwarfs, and spectroscopy of
the “subdwarf sample” of V12a shows that the UV-excess
catalogue is complete for white dwarfs. The effects of the
pollution of the observational sample are corrected in Sect.
6. Additionally, sources more than 0.1 magnitude above
the reddened white dwarf locus in the (g−r) vs. (U−g)
colour-colour diagram are not taken into account since they
are more than 0.1 magnitude above the reddened hottest
white dwarf model.
These cuts result in an sample of 360 observed
candidate white dwarfs, which will be used as the basis
of the space density and birth rate calculations in this
paper. The observational white dwarf sample is shown
in the colour-colour and colour-magnitude diagrams of
Figs. 10 and 11, overplotted by the simulated sample of
Sect. 2. The objects in the simulated sample have colours
similar to reddened synthetic colours shifted by a defined
amount of reddening, determined by the Galactic position
of the objects in the theoretical sample. The simulated
white dwarf sample and the observed white dwarf sample
have different colours since the observed sample has a
photometric scatter and an uncertainty on the absolute
calibration. Additionally, from V12b it is known that
the observed sample contains some non-DA sources, such
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6Kars Verbeek et al.
13
14
15
16
17
18
19
-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4
(g)
(g-r)
Total UV-excess sample
WD candidates
Simulated WD sample
Figure 11. Colour-magnitude diagram with the UV-excess sources of V12a brighter than g<19.5 (black triangles), the white dwarf
candidates in the UV-excess catalogue (blue circles), and the simulated white dwarf sample brighter than g<19.5 (red squares). No
photometric error bars are plotted for clarity, photometric errors range from 0.002 mag at g=16 to <0.025 mag at g=19.5.
as DB white dwarfs. We correct for these non-DAs in Sect. 6.
4 SPACE DENSITIES AND BIRTH RATES:
METHOD
The method to derive the space density and birth rate is
first to calculate for each system in the observational sample
its current temperature and distance, and then to scale
and compare the distribution of the observed sample to the
simulated, numerical sample. Herein we adjust the space
density of the numerical sample to match the observed
number of systems. The test we perform here is therefore
how well the observed population resembles a simulated,
numerical sample. In Sect. 9 we will discuss the validity of
our assumptions in constructing the numerical, observable
sample.
To derive temperatures and distances the observed
position of a source in the (g−r) and (U−g) diagram is
compared with a grid of reddened model colours, based on
the hydrogen dominated white dwarf atmosphere models
of Koester et al. (2001) for temperatures in the range
6 0006Teff680 000 K. We assume a fixed surface gravity
of log g= 8.0, as this is the median value found in the
spectroscopic fitting of a representative sample of the white
dwarf systems in V12b (Fig. 5 of V12b, and e.g. Fig. 5 of
Vennes et al., 1997; Fig. 9 of Eisenstein et al., 2006). The
impact of this assumption of a fixed surface gravity of log g
= 8.0 is discussed in Sect. 9. The reddening grid was calcu-
lated at ∆E(B−V)=0.1 intervals. The best-fitting value
for an individual system is taken as the grid point with the
smallest distance to the observed value (see Fig. 12). Error
estimates on the fit values are obtained by projecting the
1σphotometric errors on to the grid axes, often resulting in
asymmetric errors in temperature. The distance to a source
is derived from the combination of the observed g-band
magnitude, the model absolute magnitude corresponding to
the surface gravity and the derived temperature, including
the reddening value derived from the fit.
As the synthetic colour tracks of white dwarfs display
a distinct ‘hook’ in the colour-colour plane at Teff =10 000K
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Figure 12. The temperature and reddening of each white dwarf
in the observational sample are determined from the location
in the colour-colour diagram. The temperature is determined by
tracing the reddening vector (thick line) back to the unreddened
synthetic log g=8.0 DA white dwarfs model colours of V12a. The
reddening corresponds with the length of the reddening vector.
The error on the determined temperature and reddening are re-
lated the photometric error and the error on the temperature de-
pends on the position of the source in the colour-colour diagram.
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0
5000
10000
10000 15000 20000 25000 30000
Temperaturevector method - Temperaturefit V12b (K)
Temperature (K)
case A/B
case C: (U-g)=0.2 shifted
Figure 13. Difference between the temperature determined from
the photometry by the vector method and the temperature de-
termined through line profile fitting in V12b. When the vector
method is applied to the original UVEX data (cases A and B)
the difference in temperature increases for hotter white dwarfs
with a clear trend. For the UVEX with a shift of (U−g)=0.2
magnitude (case C) the difference in temperature is more scat-
tered around zero without this trend. There are two more hot
white dwarfs at 35kK < Teff <40kK that have a temperature
difference larger than 15kK.
(Fig. 10), due to the strength of the Balmer jump, a highly
reddened object may have a dual possible solution: a high
temperature/high reddening, or a low temperature/low
reddening solution. The numerical model shows that in
most of the cases where a dual solution exists, the preferred
one is the hot solution. In observational samples cool white
dwarfs below Teff<10 000K are more rare (Fig. 5 V12b,
Eisenstein et al., 2006 and Finley et al., 1997). Therefore it
is assumed that in all cases the hot solution is correct. The
impact of this assumption will be discussed in Sect. 9.
Fig. 10 shows the colour-colour diagram of the selected
UVEX sample alongside theoretical tracks of cooling white
dwarfs of various surface gravity (log g= 7.0 - 9.0, from
bottom to top). The sp ectroscopic analysis of V12b (Fig. 5)
shows that the vast majority of the DA white dwarfs in the
UVEX sample have log g∼8, and should therefore lie at the
log g=8 line. However, a substantial number of systems in
Fig. 7 of V12b lie below the line, either due to their own
photometric error, the scatter in the absolute calibration
in the U-band magnitude, the lack of a global photometric
calibration in the UVEX survey, or a combination of
all three. To investigate the effect of this scatter on the
determination of the space densities and birth rates three
separate samples are defined and analysed.
•Sample A (only systems above log g=8.0 line): In
sample A, 84 white dwarfs which are located far under/left
of the unreddened synthetic log g=8.0 colour track of Fig.
10 are not taken into account. To allow for some intrinsic
photometric scatter all systems that lie closer than 0.1
magnitude left of the unreddened synthetic log g=8.0
colour track are included, automatically have reddening
E(B−V)=0, and are assigned the temperature of the grid
point on the track most closely located to the measurement.
Sample A contains 276 white dwarf systems.
•Sample B (all systems): In sample B all candidate
white dwarfs shown in Figs. 10 and 11 are included.
Temperatures and reddening vectors are compared to
log g=8.0 models only. For systems below the log g=8.0 line,
temperatures and reddenings are assumed to be those of
the closest grid point on the log g=8.0 line. This sample will
correctly include the number of systems present, but will
overestimate the number of systems at very low reddenings.
Sample B contains 360 systems in our footprint.
•Sample C (shifted U-band): In sample C a shift of
(U−g)=–0.2 is applied to all systems in the observational
sample. This brings the vast majority of systems above
the log g=8.0 line. The magnitude of the shift is the
maximum scatter observed in the U-band calibration and
will therefore in general overestimate the actual calibration
uncertainty. A consequence of the (U−g) shift is that each
white dwarf will get a different colour, and so a different
Teff ,E(B−V) and distance. Sources that are more than 0.1
magnitude above the white dwarf grid after the colour shift
are not taken into account. This sample excludes a fraction
of systems and will lead to an overestimate of the number
of hot, distant systems. Sample C contains 303 systems in
our footprint.
Note that samples A and C do not give the best exact
value of the space density and birth rate, but are presented
to show the effect of a colour shift or cut log g>8. To obtain
a feel for the accuracy in temperature and reddening from
the photometric method, the effective temperature (Teff ),
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8Kars Verbeek et al.
Figure 14. Histogram of g-band magnitudes of the UV-excess
white dwarf candidates of sample B and the simulated white dwarf
sample.
surface gravity (log g) and reddening of the 20 UVEX white
dwarfs with Teff>20 000K in V12b (Table 2, Fig. 5) were
compared with the photometric method, with and without
applying any shifts, and the results are shown in Fig. 13.
For samples A and B, the difference in effective temperature
found by the photometric method and determined through
line profile fitting of V12b appears to increase for hotter
white dwarfs. This trend is less clear for sample C, see Fig.
13.
In the photometric method the error on the temper-
ature depends on the (g−r) and (U−g) colours of the
white dwarf. The errors on the temperature and reddening
due to the method are between ∆Teff =2 000K for white
dwarfs of Teff= 25 000 K and ∆Teff =15 000K for white
dwarfs of Teff=60 000 K and ∆E(B−V)∼0.03 for sources
with a photometric error of ∆g=0.01 mag. However, the
uncertainty in temperature and reddening is larger because
of the lack of a global photometric calibration.
Photometric distances (d) to all systems in the observed
samples were calculated using
d= 0.01 ×100.2(mg−Mg−Ag)(kpc)
, where mgand Mgare the observed and absolute g-band
magnitude and Agis the extinction in the g-band. The
absolute magnitudes of Holberg & Bergeron (2006) are
used, assuming log g=8.0 for all white dwarfs.
5 RESULTS
For illustration purposes only the distribution compar-
isons for sample B are shown here (Figs. 14 to 17). The
histograms of all three samples (A-C) are shown in Figs.
B1 to B4 of Appendix B. For the magnitude, reddening,
distance and temperature distributions, sample B is most
consistent with the simulated sample. Because sample B
is most complete and has the best Kolomogorov-Smirnov
Figure 15. Temperature histogram of the UV-excess candidate
white dwarfs of sample B and the simulated white dwarf sample.
Figure 16. Histogram of E(B−V) of the UV-excess candidate
white dwarfs of sample B and the simulated white dwarf sample.
(KS) results, this sample will be emphasized in the next
sections.
To test whether the distributions in temperature,
distance and reddening between the observational and
numerical sample are consistent with each other, a KS test
was performed on the cumulative distributions in magni-
tude, reddening, distance and temperature, with limiting
values of 13<g<19.5, 0<E(B−V)<0.7, 0<d(kpc)<1.0 and
10 000<T (K)<80 000. The results of the KS-test are sum-
marized in Table 1. The D-value is the maximum distance
between the cumulative distributions and the p-value is the
probability that the observational and numerical samples
are the same distributions. If the D-value is small or the
p-value is high, the hypothesis cannot be rejected that the
distributions of the numerical and observational samples
are the same.
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Table 1. KS tests between the derived, observed, and numerical distributions for samples A-C.
Distribution Sample A Sample B Sample C
(D, p) ((D, p) (D, p )
Magnitude (0.09,0.07) (0.08,0.11) (0.09,0.09)
Reddening (0.40,4.0×10−26) (0.30,1.2×10−18 ) (0.41,9.6×10−30)
Distance (0.07,0.25) (0.06,0.49) (0.22,1.2×10−8)
Temperature (0.20,6.2×10−7) (0.17,3.0×10−6) (0.36,1.1×10−22)
Figure 17. Distance histogram of the UV-excess candidate white
dwarfs of sample B and the simulated white dwarf sample.
Figure 18. Temperature versus distance of the UV-excess can-
didate white dwarfs (sample B) from UVEX (blue) and the sim-
ulated sample (red).
Our main conclusion from Table 1 and the distributions
shown in Figs. 14 to 17 is that the numerical sample repro-
duces the reconstructed observational samples reasonably
accurate, except for the reddening and temperature, where,
for sample B, the reddening gradient is too shallow. There
are not enough observed systems at low reddening, and
too many at high reddening. Note however, that the model
reddening is a very simple Sandage-type relation and can
Figure 19. Height above the plane versus distance of the UV-
excess candidate white dwarfs (sample B) from UVEX (blue) and
the simulated sample (red).
therefore easily underestimate the amount of reddening in
the local volume.
Figs. 18 and 19 show the main similarities and dif-
ferences between the observed white dwarf sample and
the theoretical g<19.5 sample. In Fig. 18 there is a clear
lower limit in the distance-temperature distribution due
to a linear relation between the distance and reddening
for the theoretical white dwarfs, while there are candidate
white dwarf in the observational sample that have little
reddening at a large distance or strong reddening at a small
distance as a result of the method in Sect. 4. Note that due
to the method of Sect. 4 the results of Teff and E(B−V)
are strongly correlated. All white dwarfs have a height
above the plane smaller than 0.07 kpc (Fig. 19), which is
a consequence of the UVEX Galactic latitude limit |b|<5◦,
and all white dwarfs are within a distance of 1.0 kpc due to
the brightness limit of UVEX .
The vector method finds several solutions at Teff =80kK
since that is the hottest model of the white dwarf grid,
see Fig. 15. A small fraction of these sources might be
photometrically scattered DA white dwarfs, white dwarfs
hotter than ∆Teff >80 000K, non-DA white dwarfs (DB,
DA+dM) or subdwarfs. As shown in V12b and follow-up
spectroscopy of the comparable region in the Sloan Digital
Sky Survey (Rau et al., 2010; Carter et al., 2012, and
V12b), the majority of these ob jects are helium-line (DB)
white dwarfs, subdwarfs, DA+dM stars and Cataclysmic
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10 Kars Verbeek et al.
Variables. These hottest solutions also induce the peaks at
0.8<E(B−V)<0.9 and 1.2<d(kpc)<1.3 in Figs. 16 and 17.
The maximum reddening of E(B−V)=0.7 in Fig. 16
corresponds with a maximum extinction of AV=2.2 using
RV=3.1 and is in agreement with Fig. 8 of V12b. The
difference between the theoretical and observational sample
for reddening smaller than E(B−V)<0.2 might be due to
the method to determine the temperature and reddening of
the UV-excess sources below the unreddened white dwarf
track. The method assumes the nearest grid point for these
sources while these sources might be slightly more reddened
in reality.
6 COMPLETENESS OF THE OBSERVED
SAMPLE
Before space densities and birth rates can be derived by
scaling the observed sample to the numerical sample, a num-
ber of corrections to the observed sample need to be applied:
6.1 Non-DA white dwarf selection
In the spectroscopic follow-up of the UV-excess catalogue
presented in V12b, it was concluded that 67% of the
sources with g<19.5 and (g−r)<0.4 were indeed DA
white dwarfs (Fig. 1 and Fig. 2 of V12a). Fifteen percent
was classified as white dwarfs of other types (DB, DAB,
DC, DZ, DA+dM, DAe) and 18% were non-white dwarfs
(Cataclysmic Variables, Be stars, sdO/sdB stars). For a
correct derivation of the space number density and birth
we correct for the fraction of genuine DA white dwarfs and
take the 67% into account. This is the largest correction
made to the observed numbers.
6.2 Non-selection of DA white dwarfs
From spectroscopic follow-up of the ‘subdwarf sample’ (see
V12a) it is concluded that the method described in V12a
selects all observable white dwarfs, so the observational
sample is almost complete in its selection of white dwarfs
with temperatures Teff >10 000K (MV<12.2). In both the
theoretical and observational samples, only white dwarfs
hotter than Teff >10 000K are taken into account, due to the
distinct ‘hook’ in the synthetic colours of white dwarfs in
the (U−g) vs. (g−r) colour-colour diagram The brightest
UV-excess candidates with g<16 and (g−r)<0.4 have a
chance not to be selected, see Fig. 14 of V12a. The sources
brighter than g<16 are a small fraction of only 2% of the
theoretical sample and 3% of the observational sample.
Additionally, in the simulated white dwarf sample there are
3 sources with (g−r)>0.4, so some reddened white dwarfs
could be missed in the observational sample because they
are at (g−r)>0.4. For the derivation of the space number
density and birth, these effects are not taken into account,
since both contributions are negligible.
2
2.5
3
3.5
4
4.5
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Space density (10-4 pc-3)
Distance (kpc)
A
B
C
Figure 20. Space density versus distance for the three different
samples (A, B, C), demonstrating that the space densities derived
only slightly depend on the volume. Here the error bars indicate
the number of white dwarfs (N) used to derive each space density
and are calculated as 1/p(N).
7 DERIVATION OF THE SPACE NUMBER
DENSITY OF DA WHITE DWARFS FROM
UVEX
The observed white dwarf sample from UVEX is selected
from 211 square degrees along the Galactic Plane. The
simulated numerical sample is obtained from the full
Galactic Plane (3 600 square degrees). Since the sample
with g<19.5 shows no longitude or latitude dependence, the
area ratio between the observed sample and the simulated
sample is simply a factor 211/3 600. Assuming equal depths
of 1.0 kpc, the volume of the simulated white dwarf sample
is 0.365 kpc3and the observed white dwarf sample is the
same factor 3600/211 times smaller.
The observed UV-excess samples (A, B, C) contain
(276,360,303) sources and the simulated sample contains
723 white dwarfs in the full Plane. If we correct the
observed sample for the fraction of genuine DA white
dwarfs (67%), there are (185,241,203) DA white dwarf
candidates in a volume within 1.0 kpc. If we correct
the volume of the observed sample there would be 723×
(211/3 600)=42.4 times more theoretical white dwarfs in
the volume. The difference between the number of observed
white dwarfs and number of simulated white dwarfs is a fac-
tor (185,241,203)/42.4 = (4.36,5.68,4.79) for cases (A, B, C).
Using these ratios to scale the observed sample to
the total numerical sample of 8 ×104white dwarfs with
Teff >10 000K, an average space density in a volume within
a radius of 1 kpc around the Sun is obtained of ρA= 2.9 ±
0.8×10−4pc−3,ρB= 3.8 ±1.1×10−4pc−3and ρC= 3.2
±0.9×10−4pc−3. These results are summarized in Table
2. The derivation of the errors here is explained in Sect. 9.
To test the validity of the model assumption on Galac-
tic reddening, and to test the sensitivity of the result as a
function of the actual distance/volume used in the calcula-
tions, the cut-off distance has been varied between 0.1 and
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Table 2. Space densities for DA white dwarfs with Teff >10 000K and birth rates from UVEX .
Case Space density (10−4pc−3) Birth rate (10−13pc−3yr−1) Caveats
A 2.9 ±0.8 5.4 ±1.5 Not complete
B 3.8 ±1.1 5.4 ±1.5 Too many E(B−V)=0
C 3.2 ±0.9 7.3 ±2.0 Too many hot/young, not complete
0
2
4
6
8
10
10 20 30 40 50 60 70 80
Birth rate (10-13 pc-3 yr-1)
Temperature (kK)
sample B
Figure 21. The UVEX birth rate of sample B for different limits
of Teff . The error bars, indicating the number of white dwarfs (N)
used for each birth rate, are calculated as 1/p(N).
1.0 kpc in steps of ∆d=0.1 kpc. The resulting average space
densities are shown in Fig. 20, which shows that the result
is very stable in the range 0.6 - 1.0 kpc. Below 0.5 kpc the
results change rapidly, both within one sample as well as
between the three samples. This is caused by low number
statistics, combined with the relatively large uncertainties
on individual systems, inherent to the photometric method
of deriving temperatures and reddenings.
8 BIRTH RATE OF DA WHITE DWARFS IN
THE GALACTIC PLANE
For the derivation of the birth rate of DA white dwarfs,
only objects with Teff >20 000K are taken into account. The
samples are limited to Teff >20 000K since for the hottest
systems the cooling tracks is less uncertain (see Fig. 1) and
the assumption of a constant birth rate is more realistic,
while for a higher Teff the number of systems in the samples
would become too small. From the cooling tracks of Fig.
1 we assume that all white dwarfs in the samples with
Teff >20 000K are younger than ∼6.9×107years. From the
211 square degrees of V12a there are (153,154,211) white
dwarf candidates with Teff >20 000K for samples A, B and
C of Sect. 4, respectively, taking the 67% into account. This
area of 211 square degrees has a volume of 2.14 ×10−3
kpc3using a depth of 1.0 kpc.
Within the full numerical sample there are 2 024 white
dwarfs with Teff>20 000K within 1.0 kp c, of which 267 have
a magnitude g<19.5 and fall within the simulated sample. If
we correct for the volume and the ratio between simulated
and observed sources the same way as in Sect. 7, the birth
rate for the samples A, B and C is (5.4 ±1.5) ×10−13
pc−3yr−1, (5.4 ±1.5) ×10−13 pc−3yr−1and (7.3 ±2.0) ×
10−13 pc−3yr−1. These results are summarized in Table 2.
The derivation of the errors here is explained in Sect. 9.
So far the birth rate is derived using the samples
limited to Teff >20 000K. Fig. 21 shows that birth rate varies
between 2.5 ×10−13 pc−3yr−1and 6.7 ×10−13 pc−3yr−1
for different limits of Teff . However, the birth rates at
Teff >26 000K are infl uenced by the shape of the cooling
tracks and the age versus absolute magnitude relation (Fig.
2), while the birth rates at the higher temperatures are
affected by low number statistics.
9 DISCUSSION AND CONCLUSIONS
A derivation of the average space density and birth rate
within a radius of 1 kpc around the Sun very much depends
on the ability to construct volume-limited samples, to
estimate the completeness and biases in the observational
sample, and the accuracy of deriving fundamental parame-
ters from observational characteristics. As outlined in Sect.
5, the space densities have been estimated using three ob-
servational samples, each with its own set of biases and/or
corrections. Sample A is a conservative lower limit, since
this sample excludes white dwarfs left from the unreddened
log g=8.0 colour track in the colour-colour diagram. In
sample B all white dwarfs are taken into account, so the
space density derived from this sample is the most complete,
however, the method overestimates the number of systems
with no reddening. For sample C the space density is also a
lower limit, since the sample excludes a fraction of systems
above the grid, while the derived birth rate is too large
due to an overestimate of the number of hot/young systems.
A number of caveats and limitations are in common
between the three samples. The estimated space density
depends on: (i) the distance determination, (ii) uncer-
tainties in the method for estimating the temperature
and reddening of the white dwarfs in the observational
sample, (iii) the assumption about the amount of redden-
ing/extinction, (iv) the magnitude cut g<19.5, (v) the
colour cut (g−r)<0.4, (vi) the assumption of log g=8.0 for
all white dwarfs, (vii) the fraction of genuine white dwarfs
in the UV-excess catalogue and (viii) the binary fraction in
the UV-excess catalogue. The estimated white dwarf birth
rate depends on these points as well, with the additional
assumptions about the cooling time and constant birth rate.
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12 Kars Verbeek et al.
The distance estimates to individual systems strongly
depend on the assumed absolute g-band magnitudes
from Holberg & Bergeron (2006), assuming log g=8.0 for
all white dwarfs. The absolute magnitudes follow from
the temperature and reddening determined from the
UVEX photometry. If the absolute magnitude would be
brighter than derived, the white dwarfs would be detectable
over a larger volume. In the most extreme cases, for example
due to a maximal shift in (U−g) of –0.2 magnitudes,
the temperature determinations are off by ∆Teff =+6 000K
for cool white dwarfs and up to ∆Teff =+30 000K for the
hottest white dwarfs. The surface gravity determination
could be off by ∆ log g=0.5 (Fig. 5 of V12b). We note that
although in the last case we would strongly overestimate an
absolute bolometric magnitude, the effect is ameliorated by
the fact that the change in the absolute g-band magnitude
is less severe at these very hot temperatures. In these
cases the absolute magnitude would be overestimated by
Mg∼1 magnitude on an individual basis. If the apparent
magnitude of a source at 1.0 kpc would change by mg=0.1
magnitude, the distance would typically change by 5%.
If this would be the case for the total sample, this would
mean a maximal increase or decrease of 15% of the total
survey volume. There might be a Malmquist-type bias in
the distance-selected observational sample. There will be
distance uncertainties since the observational sample will
include white dwarfs which are outside the chosen distance
limit, but brought in because of distance errors, and it will
exclude objects which are moved to outside of the distance
limit because of distance errors. There is no direct effect
since the observational sample is compared to the simulated
sample, and the space densities, calculated using different
volumes in Fig. 20, depend only slightly on the volume. For
the derivation of an error on the space number density (see
below), the effect of this bias is taken into account within
the factor of 15 per cent of the photometric scatter.
The colour cut (g−r)<0.4 and the magnitude cut
g<19.5 will cause a loss of systems on the total number of
white dwarfs in the observational sample. In the simulated
sample there are three white dwarfs with (g−r)>0.4 and
g<19.5: a fraction of ∼0.4%, negligible compared with
the other correction factors applied (see Fig. 14). In the
observed UV-excess sample there are no sources with
(g−r)>0.4 spectroscopically confirmed as white dwarfs
in V12b. The probability that a source with g<19.5 and
(g−r)<0.4 will be picked-up by the selection algorithm
(Fig. 14 of V12a) drops for sources brighter than g=16
and redder than (g−r)>0.2 to ∼50%. Unreddened white
dwarfs cooler than Teff <7 000K have synthetic colours
(g−r)>0.4, due to the colour cut the final white dwarf
sample is incomplete for these cool white dwarfs. However,
in the comparison with the numerical model these cool
dwarfs have also been excluded, and their exclusion from
the observational sample therefore does not influence
the estimate on the space density of hotter white dwarfs
(T>10 000 K).
The magnitude cut at g<19.5 is applied due to the
difference between the magnitude distributions of the simu-
lated sample and the observational samples for magnitudes
fainter than g>19.5. For fainter magnitudes the number
of white dwarfs in the simulated sample increases strongly
while the number of white dwarfs in the observational sam-
ple starts to drop. For magnitudes g>19.5 the observational
sample is not complete which would influence the result
of the space density. If a magnitude limit of g<20.0 was
chosen, the space densities would have been (2.4 ±0.7) ×
10−4pc−3, (3.2 ±0.9) ×10−4pc−3and (2.7 ±0.8) ×10−4
pc−3for the three samples (A, B, C), which is ∼16% smaller.
The UV-excess catalogue was selected from 726
partially contiguous‘direct’ fields, as defined in Gonz´alez-
Solares et al. (2008). Because of the tiling pattern of the
IPHAS and UVEX surveys a completely contiguous area of
this number of fields would result in an overlap in area of
<5%, which is the maximal correction on the 211 square
degree area that could be applied. Over the covered area
a number of sources might be missed because they fell on
dead pixels or very near the edges of the CCDs. However,
the WFC consists of high quality CCDs and the total dead
area is <1%.
An assumption that may strongly affect the estimates
is the assumption of log g=8.0 for all sources. This has
been motivated by the findings in V12b (Fig. 5) and the
well known strong biases in previous studies of the white
dwarf population towards log g=8.0 (e.g. Fig. 5 of Vennes
et al., 1997 and Fig.9 of Eisenstein et al., 2006.). At face
value Fig. 10 suggests that in the Plane a substantial
number of sources exist with log g < 8, although this is
not substantiated by the spectroscopic fitting in V12b.
However, if a large number of lower gravity systems are
present, this would lead to an overestimate of the space
density since lower gravity systems are more luminous at
a given temperature and the observed sample therefore
occupies a larger volume. At a given temperature log g=7.5
gravity white dwarfs will have larger absolute magnitudes of
∼0.8-0.9 mag compared to log g=8.0 of DA white dwarfs.
Their distance would be underestimated, and so also the
space density would be overestimated by a factor of ∼25%.
For the derivation of an error on the space number density
(see below), an error on the surface gravity of ∆ log g=0.1,
which is a typical value of the scatter in the white dwarf
surface gravity (Fig. 5 of V12b), will be taken into account.
Combining the uncertainties mentioned above leads
to an upper and lower limit on the space number density
derived in Sect. 7. If we consider the most optimistic case,
the upper limit is due to a combination of the method
of Sect. 4 and photometric scatter of 0.5 mag (15%), an
error of ∆ log g=0.1 (6%) non-selected DA white dwarfs at
(g−r)>0.4 (1%), non-selected by the algorithm of V12a
(1%) (see Sect. 6.2) and non-selected white dwarfs due to
tiling of the fields and errors on the CCD chips (5%). The
error on the birth rate is estimated in a similar way as for
the space density. If the same uncertainties are taken into
account, the birth rate would be 28% larger in the most
optimistic case. Now for sample C, the distributions are less
similar to the modelled theoretical sample, and the method
finds too many hot solutions. For this reason the birth rate
for sample C is larger than for sample B.
Fundamentally the analysis discussed here tests how
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0.01
0.1
1
10
10 11 12 13 Inf
Space density (10-3 pc-3)
Limiting Magnitude (MV)
Volume limited
Vennes(1997)
Fleming(1986)
Ishida(1982) Liebert(2005)
Hu(2007)
Ishida(1982)
Downes(1986)
Limoges(2010)
Boyle(1989)
Green(1980)
Space densities from different surveys
Extrapolated space density from UVEX
Space density from UVEX
’-’
Figure 22. The UVEX space density of sample B (blue squares) extrapolated for different MVoverplotted on the space number densities
from other surveys (black dots). The dots at “Inf” represent the space densities of the volume limited surveys indicated in Table 3.
well the numerical Galactic model resembles the observed
distribution of white dwarfs. The Galactic model includes
an idealized dust distribution that may not resemble the
actual distribution. Since UVEX observes directly in the
Galactic Plane in blue colours, the effect of the dust
distribution and the ensuing reddening may be substantial.
The theoretical dust distribution in the Sandage model
may behave different than the actual distribution in our
pointings, also because we are looking at a local population,
while the extinction on exactly this local scale is very poorly
known (Sale et al., 2009 and Giammanco et al., 2011). As
can be seen in Fig. 16 there is a difference between the
reddening distributions, which is partly due to the crude
determination of E(B−V) for the observational sample,
with bins of ∆E(B−V)=0.1. The effect of reddening for the
white dwarfs in UVEX was already shown in Fig. 8 of V12b.
The reddening is smaller than E(B−V)=0.7 (AV<2.2) for
all white dwarfs as shown in Fig. 16 and Fig. 8 of V12b.
In the simulated observable sample there are no sources
with E(B−V)>0.7. The most reddened white dwarfs
have E(B−V)=0.55. In the observational sample the
reconstruction method of Sect. 4 finds E(B−V)=1.0 and
Teff =14kK for only one source, five sources with Teff >40kK
have E(B−V)=0.7 and all other sources have E(B−V)<0.7.
When the local population of white dwarfs is well-
known and spectroscopically characterized it can conversely
be used to derive a 3D extinction map of the local
(d < 1kpc) environment.
Finally, we note that no correction has been made for
the binary fraction of systems dominated by a DA white
dwarf in the UV-excess catalogue. The binary fraction
estimates range from 12% to 50% (e.g. Nelemans et al.,
2001, Han 1995, Miszalski et al., 2009 and Brown et al.,
2011). The space density and birth rate number derived
here are therefore DA white dwarf dominated systems
that fall within our colour selection criteria, including an
unknown binary fraction.
9.1 Comparison with other surveys
The space density of (3.8 ±1.1) ×10−4pc−3, derived for
sample B for white dwarfs with MV<12.2 or Teff >10 000K,
and a birth rate of (5.4 ±1.5) ×10−13 pc−3yr−1over the
last 7×107years, can be compared with the results of other
surveys (Tables 3 and 4). All previous estimates have been
obtained either from bright samples (in particular the early
surveys) and/or at high Galactic latitudes. The current
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14 Kars Verbeek et al.
Table 3. Space number densities from other surveys.
Reference Space density (10−3pc−3) Limits
UVEX 0.38±0.11 MV<12.2
Giammichele (2012)∗4.39 local
Limoges (2010) 0.280 MV<12.75, DA WDs in Kiso
Limoges (2010)∗0.549 All Teff in Kiso DA WD sample
Sion (2009)∗4.9±0.5 local, 20 pc
Holberg (2008)∗4.8±0.5 local, 13 pc (122 WDs)
Holberg (2008)∗5.0±0.7 HOS sample
Hu (2007) 0.0881 531 SDSS DA WDs, 12kK < Teff <48kK (MV<11.65)
Hu (2007) 1.94 531 SDSS DA WDs, Teff <48kK
Harris (2006)∗4.6±0.5 local
Liebert (2005) 0.158 Teff >13kK (MV<11.52)
Holberg (2002)∗5.0±0.7 local, 13 pc
Knox (1999)∗4.16 local, PM survey
Tat (1999)∗4.8 local, 15 pc
Leggett (1998)∗3.39 local, 1/Vmax
Vennes (1997) 0.019±0.003 EUVE sample of 110 DA WDs
Vennes (1997) 0.0049±0.0007 hot DA WDs Teff >40kK (MV<9.45)
Oswalt (1996)∗7.6±3.7 local, wide binaries
Weidemann (1991)∗5 local, in 10pc
Boyle (1989) 0.60±0.09 MV<12.75
Liebert (1988)∗3.2 local, 1/Vmax
Downes (1986) 0.72±0.25 MV<12.25
Fleming (1986) 0.45±0.04 MV<10, PG WD sample: 353 obj.
Shipman (1983)∗4.6 local, astrom. binaries
Ishida (1982) 0.088 MV<11.0, 588 KUV obj.
Ishida (1982) 0.500 MV<12.0, 588 KUV obj.
Green (1980) 1.43±0.28 MV<12.75
Sion (1977)∗5 local, 23 WDs in 10 pc
∗Volume limited
Table 4. Birth rates from other surveys.
Reference Birth rate (10−13pc−3yr−1) Limits
UVEX 5.4±1.5 Teff >20kK
Frew (2008) 8±3 PN birthrate
Hu (2007) 2.579 12kK < Teff <48kK, 531 SDSS DA WDs
Hu (2007) 2.794 Teff <48kK, 531 SDSS DA WDs
Liebert (2005) 6 PG WD sample: 348 obj.
Liebert (2005) 10±2.5 overall, in local disk
Holberg (2002) 6 over 8 Gyr
Phillips (2002) 21 local PN birth rate
Vennes (1997) 8.5±1.5 local
Pottach (1996) 4-80 local PN birth rate
Weidemann (1991) 23 derived from star/WD formation model
Boyle (1989) ∼6 derived WD birth rate
Boyle (1989) ∼20 obs. PN birthrate
Ishida (1987) 80 local PN birth rate
Green (1980) 20±10 from MV<12.75 sample
Koester (1977) 20 from Mbol <15.5 sample
study is the first to be obtained in the Galactic Plane itself
where the majority of systems resides. For that reason,
and due to different magnitude limits, it is not possible
to automaticaly compare different surveys. As is evident
from Tables 3 and 4, the estimates on the space densities
and birth rates strongly vary. To compare our results to
those of the other studies, the Galactic model is used to
calculate the effective space density at various limiting
magnitudes, calibrated to our result. Fig. 22 shows that,
when a correction is made for the vaying limiting absolute
magnitude, many surveys are quite consistent with each
other, despite the fact that they observe different white
dwarf samples. Surveys that claim to be volume limited
derive an average space density of ∼4.6 ×10−4pc−3,
which is consistent with the extrapolated, continued slope
of the space density as a function of absolute magnitude
of Fig. 22. However, it is not possible to extrapolate the
UVEX -based result to the coolest/faintest systems since
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A determination of the space density and birth rate of hydrogen-line (DA) white dwarfs in the Galactic Plane
the star formation history in the Galaxy will start to play
a dominant role. For the same reason also the birth rate
results of the different surveys in Table 4 strongly vary. If
we compare the birth rate of 5.4 ±1.5 (10−13 pc−3yr−1),
derived for sample B in this paper, the result of UVEX is
consistent with other estimates.
ACKNOWLEDGEMENTS
This paper makes use of data collected at the Isaac Newton
Telescope, operated on the island of La Palma by the Isaac
Newton Group in the Spanish Observatorio del Roque de
los Muchachos of the Inst´ıtuto de Astrof´ısica de Canarias.
The observations were processed by the Cambridge Astron-
omy Survey Unit (CASU) at the Institute of Astronomy,
University of Cambridge. Hectospec observations shown
in this paper were obtained at the MMT Observatory, a
joint facility of the University of Arizona and the Smith-
sonian Institution. KV is supported by a NWO-EW grant
614.000.601 to PJG and by NOVA. The authors would like
to thank Detlev Koester for making available his white
dwarf model spectra. The colour tables and model calcula-
tions of Pierre Bergeron can be obtained from this website
(http://www.astro.umontreal.ca/∼bergeron/CoolingModels)
and are explained in Holberg & Bergeron (2006, AJ, 132,
1221), Kowalski & Saumon (2006, ApJ, 651, L137), Trem-
blay et al. (2011, ApJ, 730, 128), and Bergeron et al. (2011,
ApJ, 737, 28).
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0.05
0.1
0.15
0.2
0.25
-0.2 -0.1 0 0.1 0.2 0.3
No of sources
(U-g)Old - (U-g)Recalibrated
jun2006
may2007
jul2007
sep2007
oct2007
Figure A1. Difference in (U−g) between the original UVEX
data and recalibrated UVEX data for the 5 different months used
for the UV-excess catalogue of V12a.
APPENDIX A: RECALIBRATED UVEX DATA.
There is a possible systematic shift in the original UV-excess
catalogue (U−g) data, which would influence the result
of methods in Sect. 4. For that reason we use recalibrated
UVEX data, as explained in Greiss et al. (2012). The
differences in (U−g) between the original UVEX data and
recalibrated UVEX data for the 5 different months used
in V12a are plotted in Fig. A1. The shift in the original
UVEX data does not influence the content of the UV-excess
catalogue because the selection in V12a was done relative
to the reddened main-sequence population. The magnitudes
and colours of the UV-excess sources might still show a
small scatter, similar to the early IPHAS data (Drew et al.,
2005), since a global photometric calibration is not applied
to the UVEX data yet.
APPENDIX B: DISTRIBUTIONS OF
SIMULATED AND OBSERVATIONAL
SAMPLES
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18 Kars Verbeek et al.
Figure B1. Magnitude distributions and cumulative distributions of the UV-excess white dwarf candidates from the 3 samples A-C and
the simulated white dwarf sample.
Figure B2. Temperature distributions and cumulative distributions of the UV-excess white dwarf candidates from the 3 samples A-C
and the simulated white dwarf sample.
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Figure B3. Reddening distributions and cumulative distributions of the UV-excess white dwarf candidates from the 3 samples A-C and
the simulated white dwarf sample.
Figure B4. Distance distributions and cumulative distributions of the UV-excess white dwarf candidates from the 3 samples A-C and
the simulated white dwarf sample.
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