783, 1997 May 10 Procyon B is one of a select group of white dwarf stars which are members of visual binary systems and represents a critically important object for testing the fundamental physics of stellar degeneracy. We have accurate measurements of the binary period and the white dwarf mass. However, the extreme brightness ratio and the small separation between primary and secondary makes accurate ground-based determinations of basic characteristics, such as effective temperature and chemical composition, which we require to derive stellar radius, impossible to obtain. Furthermore, since the age of this system is known, a temperature determination for Procyon B constrains its cooling age, providing an estimate of the progenitor mass, a stringent test of theories of stellar mass loss. We present the results of photometry from a series of WFPC2 images, from which we determine an apparent magnitude of mV = 10.92 ± 0.05, and an effective temperature of 8688 ± 200 K, based on Hubble Space Telescope equivalent UBVRI filter measurements. Our more uncertain, problematic, narrow filter results argue a helium composition is more plausible for Procyon B. The stellar radius we derive from these parameters, assuming a mass of 0.622 ± 0.023 M
, is 0.0096 ± 0.0005 R, inconsistent with the carbon-core, zero-temperature mass-radius relation of Hamada & Salpeter. This implies that Procyon B has a heavier core than carbon, calling into question the assumption of carbon-core composition commonly used for white dwarf stars.
Subject headings: stars: individual (Procyon B)
stars: interiorsstars: white dwarfsultraviolet: stars
1 Department of Physics and Astronomy, University of Delaware, Newark, DE 19716; jlp@chopin.udel.edu.
2 Département de Physique, Université de Montréal, C. P. 6128, Succ. Centre Ville, Montréal, Québec, Canada H3C 3J7.
3 Lockheed Martin Electronic Systems Canada, 6111 Avenue Royalmount, Montréal, Québec, Canada H4P 1K6.
4 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218.
5 Department of Astronomy and Steward Observatory, University of Arizona, Tucson, AZ 85721.
6 Department of Astronomy and Astrophysics, Villanova University, Villanova, PA 19085.
White dwarfs, the final evolutionary endpoints for the majority of stars, are the Rosetta stones of astrophysics. Determination of their physical properties influences such diverse fields as stellar evolution, star formation, and cosmology. Their interior composition and structure are fingerprints of processes occurring in contemporary main-sequence stars such as our Sun; their surface abundances uncover information about red giant evolution and interactions with the interstellar medium; their masses and cooling ages combine to define the dependence of white dwarf mass on progenitor mass, constraining the total amount of material each star loses throughout its evolution; and finally, their number distribution with temperature reveals the history of star formation in and the age of the galactic disk.
Procyon B is the third brightest white dwarf known, yet we know very little about it, as nature has conspired to place it a maximum of 5
from one of the brightest stars in the sky. Its obvious influence on the motion of Procyon A led to its discovery as one of the first known white dwarfs (Eggen & Greenstein 1965). Its orbital period is 40.82 ± 0.06 yr, and its mass is 0.622 ± 0.023 M (Girard et al. 1996). Eggen & Greenstein (1965) outline the first attempt to measure the apparent magnitude of Procyon B, providing a uncertain estimate of mv 
10.7. Walker et al. (1994) combine speckle interferometry, the novel high-resolution camera, and the Canada-France-Hawaii Telescope to obtain mv = 11.3, B - V = +0.26, and B - I = +0.62. Unfortunately, their technique is not designed with photometry in mind, their photometric passbands are nonstandard, and the authors do not quote error estimates. This brief introduction outlines the extent of our knowledge of Procyon B. We do not know its temperature, chemical composition, and do not have an accurate value for its visual magnitude.
Procyon B belongs to a handful of white dwarfs that are members of visual binary systems (Table 1) and represents a critical object for testing the fundamental physics of stellar degeneracy. A generation ago, Chandrasekhar was awarded the Nobel prize for his description of the equation the state of the electron degenerate matter comprising white dwarfs, predicting the existence of a relationship between mass and radius for a degenerate configuration (Chandrasekhar 1933). Today, the mass-radius relation for white dwarfs, assuming carbon cores, is an underlying assumption in many of our techniques of determining white dwarf masses. The best method, and the one most devoid of extraneous assumptions, is to find objects in nearby binary systems. For those systems, a knowledge of the white dwarf mass, combined with its temperature and distance, reveals the stellar radius. Observational confirmation of stellar degeneracy rests on the three objects in Table 1 for which ground-based measurements are sufficient to determine the white dwarf's characteristics, allowing these objects to be placed on the theoretical mass-radius relation: 40 Eri B (Koester & Weidemann 1991), Stein 2051 B (Liebert 1976), and Sirius B (Shipman 1979). The resounding success of the Hubble Space Telescope (HST) repair mission now gives us access to the remaining white dwarfs in visual binaries, the best known of which is Procyon B.
Procyon B also offers the tantalizing possibility of directly measuring the amount of mass its progenitor main-sequence star lost during its red giant evolutionary phase, adding this object to the small group of stars defining the initial-final mass relation (IFMR) for white dwarfs. A determination of its temperature leads to a cooling age for the white dwarf. Subtracting the cooling age from the age of the system, as estimated by the main-sequence lifetime of Procyon A, will determine the nuclear burning lifetime, and hence the mass, of the white dwarf progenitor. Our theories of mass loss in the late stages of stellar evolution are tied to our knowledge of white dwarfs' narrow mass distribution, both of which are incomplete. Procyon B offers a rare opportunity to add a concrete observational point testing our understanding.
With Procyon B currently at its largest separation (5), we obtained a series of Wide Field Planetary Camera (WFPC2) images of the Procyon system with a wide variety of filters, with several goals in mind. The first and foremost was to accurately determine Procyon B's effective temperature. Combining this information with the well known parallax of the system, we will derive the white dwarf's radius and cooling age. Finally, through images acquired in narrow as well as wide bands, we hope to obtain general information about Procyon B's chemical composition.
In 1995 May, we obtained a series of 16 WFPC2 images of Procyon B, using a wide variety of both narrow- and broadband filters (Table 2). All images were taken at a temperature of -88° C, with an analog-to digital (A/D) conversion gain of 14.
The reduction process transforming raw images into usable form consisted of six major steps (Holtzman et al. 1995a). The first corrected for A/D conversion errors, related to the use of switching power supplies which generate noise, influencing the A/D conversion in a systematic way. The second step subtracted a bias level, and the third subtracted a superbias frame, removing additional structures remaining after the initial bias correction, such as the slightly different bias levels of alternating odd and even pixels, and the secondary effects of individual pixel dark currents. The fourth step in data reduction corrected the overall dark count by subtracting a superdark frame. Dark frames are taken approximately 5 times a week and used to create new superdark frames which are placed in the HST reduction pipeline. The preferred method of reduction, which we employed here, uses these well-determined superdark frames and ignores individual pixels with significantly different dark rates in local darks. The remaining reduction steps included shaded shutter corrections and, finally, the flat-field correction. Most of the reductions were accomplished using the HST pipeline calibration routines in STSDAS. Procyon B's proximity to Procyon A provided a relatively high background, so we did not correct for charge transfer efficiency (CTE) effects.
We performed aperture photometry on individual Procyon B images using the QPHOT routine included in IRAF's NOAO package. QPHOT computes accurate centers, sky values, and magnitudes from IRAF images. We specified a centering box of 5 pixels, an inner radius of the sky annulus of 6 pixels, and an annulus width of 4 pixels. To insure the inclusion of all photons from Procyon B, we repeated the measurement using five different aperture widths and corrected the UV count rate for time-dependent throughput.
We converted the counts output by QPHOT to two separate magnitude systems, the WFPC2 and stmag systems (Holtzman et al. 1995b, hereafter H95b), to ensure consistency in our results. The steps involved calculating a zeropoint for each combination of passband and chip in each magnitude system, using
The WFPC2 system, based on Vega, is defined such that a star of zero color has WFPC2 magnitudes equal to its UBVRI magnitudes. For such stars, the physical fluxes corresponding to its WFPC2 magnitude are the same as those for UBVRI magnitudes. Unfortunately, H95b presents WFPC2 zeropoints only for the wideband filters. The stmag system, on the other hand, is based on a spectrum with constant flux per unit wavelength, and we have stmag zeropoints for all filters.
The final steps in the reduction process converted our WFPC2 and stmags to physical fluxes ( Fig. 1) and Johnson UBVRI magnitudes, using the SYNPHOT package supplied with STSDAS within IRAF, and the zeropoints and techniques described by H95b (Table 3). The broadband filters were converted using the various zeropoints in Table 9 of H95b, while we derived the narrow and UV fluxes from equations (11) and (10) of H95b, respectively. Our results in both the WFPC2 and stmag systems agreed quite well, except in the UV range. A detailed account of ongoing problems of UV calibration is given in H95b.
Fig. 1
The conversion to Johnson UBVRI magnitudes was far more subtle. The filters F336W, F439W, F569W, F675W and F791W approximate the Johnson system often used in ground-based observing. In theory, these filters can be transformed to Johnson magnitudes with an estimated error of 0.05 mags, with the exception of F336W, which differs significantly from the Johnson U bandpass and also suffers from a red leak requiring additional correction (H95b). HST maintains a set of calibration stars which are sufficient for the transformation of main-sequence star observations to Johnson magnitudes. White dwarfs, however, are blanketed quite differently, and the white dwarf calibration stars observed by HST do not include one as cool as Procyon B. Our closest calibration white dwarf was HZ 4, a DA with an effective temperature of 13,000 K. The unknown surface composition of Procyon B, combined with the lack of a close calibration star, introduced additional uncertainties into our transformation, particularly in the UV region. Using SYNPHOT, we artificially passed spectra of HZ 4 through both the HST filter bandpasses, obtaining stmags, and the corresponding Johnson UBVR bandpasses, obtaining Johnson magnitudes. The differences between these determinations gave us correction factors as appropriate as possible for Procyon B. These factors were applied to our stmags to obtain Johnson UBVRI magnitudes of U = 10.62 ± 0.1, B = 11.13 ± 0.05, V = 10.92 ± 0.05, R = 10.72 ± 0.06, and I = 10.97 ± 0.08.
Although Procyon B is one of the brightest known white dwarfs, its proximity to Procyon A makes ground-based spectroscopy of this object impossible, forcing reliance on our HST broadband photometry to obtain Procyon B's temperature. A first estimate of the atmospheric parameters of Procyon B can be obtained by making use of our derived Johnson color indices, together with the grid of photometric calibrations (for log g = 8.0) published by Bergeron, Wesemael, & Beauchamp (1995) for both DA and non-DA white dwarf models. Our broadband photometry provides the color indices of U - B = -0.50 ± 0.07, B - V = 0.22 ± 0.04, and V - R = 0.19 ± 0.06. Interpolating between the hydrogen models from Table 3 of Bergeron et al. (1995) results in individual temperatures of 7200 ± 1000 K (U - B), 9000 ± 500 K (B - V), and 7700 ± 700 (V - R) K. Combining all three measurements and giving the greatest weight to the B - V value results in an optimal temperature of 8200 ± 700 K. If we assume Procyon B is helium dominated, we find individual temperatures of 7800 ± 1000 K (U - B), 8900 ± 500 K (B - V), and 8100 ± 700 K (V - R), giving an optimal temperature of 8100 ± 700 K. This value matches our hydrogen temperature, and demonstrates that, at this level, our temperature determination is essentially independent of chemical composition.
The uncertainties associated with the transformation to the Johnson system are sufficiently troublesome that we must consider a more direct method to determine the effective temperature. We now attempt to fit our entire energy distribution with atmosphere models. We also hope to make use of our narrowband filters and determine the general composition of Procyon B. Our results are presented in Figures 2 5. Figure 2 presents the fits to filters F336W, F439W, F569W, F675W, and F791W (Johnson UBVRI) only for both hydrogen and helium models at log g = 8.0. Both fits are adequate and point to rather high effective temperatures of 8931 ± 325 K (hydrogen) and 8688 ± 187 K (helium). While the gravity assumed in these fits remains arbitrary at this stage, experiments show that the effective temperature derived on the basis of helium-rich models is not affected if gravities between 7.5 and 8.5 are adopted. For hydrogen-rich models, the sensitivity is larger and the derived effective temperature ranges from 9000 K at log g = 7.5 to 8690 K at log g = 8.5. In Figure 3, we added two narrowband filters, F487N and F502N, to the fit. F487N, centered on H
, and F502N, 30 Å away, contain discriminating information on composition. The hydrogen-rich temperature decreases significantly, from 8931 K to 8344 ± 240 K (log g = 8.0), while the temperature based on the helium-rich models is barely affected (8692 ± 187 K). The H point (F487N) is clearly discrepant in the hydrogen fit, and, combined with the self-consistent helium temperatures, argues strongly for a helium-rich composition for Procyon B.
Fig. 2 
Fig. 3 
Fig. 4 
Fig. 5
The situation becomes confusing when we add the three narrowband filters F631N, F656N, and F658N. F656N is centered on H
, while F631N and F658N are centered 250 Å and 30 Å away, respectively. All three flux points are inconsistent with a helium-rich model containing no Balmer lines, yet the observed overall flux level in this region is far too high to account for the rapidly varying flux level within the Balmer lines of a DA white dwarf. Clearly, the flux level in the region around H looks quite unlike that of a 
normal
energy distribution (Fig. 1) and cannot be reproduced by any of our models. We confront additional problems when we consider the UV fluxes (filters F160BW, F218W, and F255W). The measured fluxes are inconsistent with either pure hydrogen or pure helium models (Fig. 4), and the temperatures required to fit the UV fluxes do not agree with the optical determinations. We believe this disagreement has two causes: firstly our insufficient understanding of the HST UV and narrow filter calibrations (H95b), and, secondly, the inability of current models to accurately describe the far-ultraviolet flux in cool white dwarfs (see Koester & Allard 1995).
To sum up our temperature determination efforts, we find a best temperature of 8650 ± 200 K, consistent with both broadband color determinations and model atmosphere fits to our Johnson UBVRI equivalent data points (Fig. 5). Using our narrow filters to isolate composition information, we also find that a pure helium composition is more plausible than a pure hydrogen composition for Procyon B.
We can now proceed to combine our determination of Procyon B's effective temperature with our knowledge of its apparent magnitude and parallax in order to derive the white dwarf's radius. The parallax of the Procyon system is well known, and we adopt the USNO value of 0
2864 ± 00023 (Harrington et al. 1993), giving a distance of 3.49 ± 0.03 pc. We then determine Procyon B's absolute magnitude, using
to be 13.20 ± 0.04.
We followed the footsteps of Shipman (1979), using
where H
is the monochromatic Eddington flux which we took from the model atmospheres of Bergeron et al. (1995). To insure consistency, we also took advantage of another link between stellar luminosity and radius, using
We arrive at a best radius of 6.70 ± 0.05 × 108 cm, or 0.0096 ± 0.0005 R, with errors are dominated by our uncertainties in temperature and magnitude.
Figure 6 displays the zero temperature mass-radius relation of Hamada & Salpeter (1961) for He, C, Mg, and Fe core compositions. The dotted line represents a 30,000 K mass-radius relation from Wood (1996), appropriate for Sirius B. The dashed lines are Wood (1996) T = 8,000 K and T = 15,000 K mass-radius relations bracketing Procyon B. All Wood (1996) relations assume carbon cores, have log q(He) = -4, and no hydrogen. Stein 2051 B, Sirius B, and 40 Eri B mark the three objects previously defining the white dwarf mass-radius relation (Shipman & Sass 1980), with error bars defining the 1 
errors in radius and mass. We now add our results for Procyon B to the figure.
Fig. 6
Our purpose in determining Procyon B's radius is to compare our results with the predictions of the various white dwarf mass-radius relations. An important underlying assumption used in the spectroscopic determination of white dwarf masses is the validity of the mass-radius relationship for a given core composition, usually assumed to be carbon. Our results show that Procyon B is not consistent with either the Hamada & Salpeter zero temperature relation for a carbon core (3 below), or the corresponding Wood (1996) relationship (5 below). This conclusion is further supported by our determination of Mv = 13.20 for Procyon B. Bergeron et al. (1995) find a value, based on log g = 8.0 model atmospheres of pure helium, of Mv = 12.770 for a 8500 white dwarf. However, they assume the carbon-core mass-radius relation of Wood (1995), therefore it is not surprising that Procyon B's observed magnitude does not agree.
We must now consider two distinct possibilities. The first is that the astrometric mass of 0.622 ± 0.023 (Irwin et al. 1992) for Procyon B is erroneous. But what stellar mass would we need to ensure self consistency? Our method of analysis gives us some handle on this problem. Our energy distribution fit, rather than being carried out at log g = 8.0, as we have done above, can also be carried out at a surface gravity which is consistent with the fitted solid angle and known distance of Procyon B. If we assume the validity of the Wood (1996) mass-radius relationship for carbon, this value of log g comes out to 8.34, corresponding to a stellar mass of 0.780.80 M. On the other hand, the astrometric masses determined by Strand (1951), Irwin et al. (1992), and Girard et al. (1996) are too self-consistent to be so far in error.
The second possibility negates the assumption of carbon-core composition commonly used for white dwarf stars. Our results for Procyon B are consistent with a heavier core, perhaps as heavy as iron, and hence smaller radius. To narrow the possible core compositions, we would require an improved temperature measurement, which at this point is obtainable only through an actual spectrum of the object. Procyon B, at 0.622 M, is above the white dwarf mean mass of 0.58 M (Bergeron, Saffer, & Liebert 1992). All four objects plotted in Figure 6 are members of binaries, which may or may not affect their individual evolution, perhaps holding a key to a correlation between progenitor mass, white dwarf mass, and core composition.
Our second goal is to constrain Procyon B's progenitor mass, adding this white dwarf to the small group of stars outlining the initial-final mass relation (IFMR). The IFMR constrains the total amount of mass lost by a star during its evolution and, in turn, provides insight into the amount of material returned to the interstellar medium, its enrichment with processed materials (Weidemann 1987), and the evolution of the mass budget of the Galaxy (Renzini & Buzzoni 1986). Procyon B is an important test case; the masses of most white dwarfs are not directly obtainable, but are inferred via spectral determination of temperatures and gravities. Procyon B's mass is directly determined from its binary orbit, eliminating much of the uncertainties associated with spectral determination.
Many studies examining the upper initial mass limit for white dwarf formation probe open clusters, where the system age is determined by the turnoff point. Procyon A and B can be thought of as a cluster containing two members, with the age of the system based on the observation that Procyon A is leaving the main sequence (Shipman 1995). Extensive literature does exist outlining the conflict of Procyon A's position on the HR diagram and its estimated mass with current evolution theory (Guenther & Demarque 1993). The conflict was recently resolved with a reanalysis of Procyon A's astrometric mass (Girard et al. 1996). Girard et al. (1996) redetermine the component masses of the Procyon system based on two recent separation measurements, one using a ground-based coronographic camera (Wang et al. 1994), and the second employing the WFPC2 images we discuss here. The authors find a systematically lower mass than previous determinations of MA = 1.75 ± 0.1 M, although their results from the coronographic camera (M = 1.626 M) differ from the WFPC2 results (M = 1.465 M) at the 1.5 level. We do not believe this debate affects our ability to determine Procyon B's progenitor mass. Our use of Procyon A as a turnoff point in our two-member cluster will only be affected if the solution to this problem places Procyon A back on or near the zero age main sequence, an unlikely event.
An estimate of Procyon B's progenitor mass is quite straightforward. An 8650 ± 200 K 0.60 M helium-surface, carbon-core white dwarf has a cooling age of 1.25 ± 0.10 × 109 yr (Bergeron et al. 1995). Based on WFPC2 images, Girard et al. (1996) give the mass of Procyon A, an F5 IVV star currently leaving the main sequence, as 1.47 ± 0.04 M. The nuclear lifetime of Procyon A is therefore 3.88 × 109 yr, providing an estimate of the system lifetime. The cooling age of the white dwarf subtracted from the system lifetime yields the nuclear burning lifetime of the white dwarf progenitor, 2.63 × 109 yr. This in turn gives a progenitor mass of 1.7 ± 0.1 M. If Procyon A's mass is closer to the estimates of Irwin et al. (1992), we derive a progenitor mass of 2.1 ± 0.1 M. We stress that these numbers represent estimates only. We use a carbon-core model in determining the Procyon B's cooling age, yet our determination of the white dwarf's radius is inconsistent with this assumption. Core compositions heavier than carbon will, in general, increase the white dwarf's cooling age, influencing the progenitor mass (Bradley 1996, private communication).
Our HST observations of Procyon B have broadened our knowledge of this elusive white dwarf. Where we previously knew only its mass and orbital period, our broadband photometry has revealed its temperature, apparent magnitude, and probable surface composition. From these characteristics, we determine a radius for the white dwarf of 0.0096 ± 0.0005 R, inconsistent with the expected values of Hamada & Salpeter (1961) or Wood (1996), for carbon cores. If Procyon B does have a heavier core, we must reconsider our theories of stellar evolution to allow for a low-mass star to produce such a white dwarf.
Procyon B is the first step on the road to completing our observational exploration of stellar degeneracy, HST will give us access to the remaining white dwarfs in visual binaries, but we will still be limited by a small number of data points. We continue to pursue the problem of accurate mass determination for single, field white dwarfs. Spectroscopic determinations are limited by our understanding of the physics we put in our models. For example, Bergeron, Saffer, & Liebert (1992) were the first to point out that spectroscopic masses could be underestimated by as much as 0.04 M if white dwarfs have thick hydrogen layers. Observational evidence, from more accurate nonadiabatic pulsation calculations attempting to reproduce the observed blue edge of the ZZ Ceti instability strip (Fontaine et al. 1994; Bradley & Winget 1994), from recent interpretations of the opacity sources responsible for Extreme Ultraviolet Explorer (EUVE)/X-ray flux deficiencies in the hot DAs (Barstow et al. 1993), and from pulsational analysis of ZZ Ceti stars as a class (Clemens 1993), strongly support this view. Perhaps asteroseismologically determined masses (Winget et al. 1994) or accurate parallaxes from Hipparcos will prove helpful. Until we are able to accurately determine the masses of single white dwarfs, we can not satisfactorily test the common assumption of carbon or carbon/oxygen cores for all white dwarfs.
Finally, we determine Procyon B's progenitor's mass to be 1.7 ± 0.1 M, based on the results of Girard et al. (1996). It is clear that a large range of stellar masses will produce white dwarfs of very similar mass, and a great deal of emphasis has been placed on finding the maximum progenitor mass producing white dwarfs (Weidemann & Koester 1983). The minimum stellar mass has been largely ignored, with a large gap between the IFMR for the Hyades and the single point provided by 40 Eri B (Weidemann & Koester 1983). Procyon B has narrowed this gap slightly by demonstrating that a 1.7 M star will produce a white dwarf of unremarkable mass. Yet, in the Hyades, for example, stars much more massive have left behind white dwarfs of similar mass. However, we point out that both Procyon B and 40 Eri B are members of binaries, and Procyon B's mass is higher than the white dwarf mean mass. Procyon B, combined with similar studies of additional white dwarfs in visual binaries, offers the possibility of determining not only the amount of mass lost during stellar evolution but also effects of binary evolution on the IFMR.
Procyon B is an interesting and important object requiring further study. The next, and very difficult, step is to obtain actual spectra of the white dwarf. We conservatively estimate that high quality Space Telescope Imaging Spectrograph spectra will reduce our errors in effective temperature to ±60 K, from ±200 K. This, in turn, will reduce our errors in radius by 75%. We will be able to demonstrate, at a far higher confidence level than achieved here, whether or not Procyon B lies on the theoretical mass-radius relation. Spectra are also vital to confirm a spectral type and explore the discrepancies we find in the H and UV fluxes.
This work was based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract No. NAS 5-26555. This work was also supported in part by NASA grant NAG 5-2405, Nos. GO-2593.0187A and GO-3816.01 from the Space Telescope Science Institute, NSERC Canada, and by the fund FCAR (Québec). Participation by E. M. S. was supported by NASA grants NAGW-5726 and by NSF grant AST 90-16283 to Villanova University. H. S. also acknowledges the long term support of the NSF, and J. L. P. would like to thank Adrienne Cool and D. Dave Wilhelm for helpful discussions. This research made use of the Simbad database, operated at Centre de Données de Strasbourg (CDS), Strasbourg, France.
. 1995b, PASP, 107, 1065 First citation in article | IOPscience | ADS. 1995, in Proc. 9th European Workshop on White Dwarfs, ed. D. Koester & K. Werner (Berlin: Springer-Verlag), 248 First citation in article
Full image (13kb) | Discussion in textFluxes for Procyon B. The error bars denote 1 errors. The filled circles are UV broadband filters (400 Å wide), the open circles represent HST's interpretation of Johnson UBVR filters (400, 470, 900, and 1200 Å wide), and the triangles are narrowband filters (30 Å wide). The wavelengths given are mean filter wavelengths.
Full image (57kb) | Discussion in textPure hydrogen (Teff = 8931 ± 325 K) and helium (Teff = 8688 ± 187 K) model atmosphere fits to filters F336W, F439W, F569W, F675W, and F791W (Johnson UBVRI). The fit errors are standard errors generated by the fitting program. The plotted error bars denote our observations, the open circles are helium models, and the filled circles are hydrogen. Both models use log g = 8.00.
Full image (74kb) | Discussion in textHydrogen and helium model atmosphere fits including the narrowband filters F487N and F502N. The hydrogen-rich temperature decreases significantly, from 8931 K to 8344 ± 240 K, while the He-rich temperature is stable at 8692 ± 187 K. The inclusion of these two filters is critical for our composition determination, as they exclude the H-rich composition.
Full image (73kb) | Discussion in textModel atmosphere fits now including the UV points in addition to the seven already included (UBVRI + F487N + F502N). The UV fluxes are inconsistent with results for the optical data.
Full image (68kb) | Discussion in textOur best fits to the optical data plotted with all available points, showing the (dis)agreement achieved.
Full image (18kb) | Discussion in textZero-temperature relations of Hamada & Salpeter (1961; solid lines) and the mass-radius relation of Wood (1996; dotted line) for 30,000 K (dots), 15,000 K, and 8,000 K (dashed lines) white dwarfs with a carbon cores, MH = 10-4 M*, and MHe = 10-2 M*. The positions of Sirius B, Stein 2051 B, 40 Eri B, and our results for Procyon B are given. The error bars indicate 1 errors in mass and radius.
| Object |  (arcsec) |
Mass (M ) |
Radius (R ) |
Orbital Period (yr) |
| Sirius B... | 0.3756 ± 0.003 | 1.03 ± 0.015 | 0.0074 ± 0.0007 | 50.09 |
| Stein 2051B... | 0.1812 ± 0.0011 | 0.48 ± 0.045 | 0.0115 ± 0.0015 | >300 |
| 40 Eri B... | 0.2084 ± 0.0023 | 0.43 ± 0.02 | 0.0124 ± 0.0005 |  |
| 0.53 ± 0.04 | 0.0127 ± 0.002 | |
||
| G107-70... | 0.0883 ± 0.0025 | 0.65 ± 0.15 | |
0.94 |
| 0.0883 ± 0.0025 | 0.64 ± 0.15 | |
|
|
| Procyon B... | 0.2899 ± 0.0074 | 0.622 ± 0.017 | |
40.5 |
Sources of information in this table include Harrington et al. 1993; Shipman 1979; Shipman & Sass 1980; Koester & Weidemann 1991; Liebert 1976; Bois, Lanning, & Mochnacki 1988; Borgman & Lippincott 1983; and Heintz 1974.| Observation | Filter | Width (Å) |
Mean  (Å) |
Max (Å) |
Exposure (s) |
| u2my010ht... | F160BW | 542 | 1591 | 1797 | 600 |
| u2my0102t... | F218W | 373 | 2174 | 2174 | 35 |
| u2my0103t... | F218W | 373 | 2174 | 2174 | 160 |
| u2my0104t... | F255W | 421 | 2609 | 2611 | 0.11 |
| u2my0105t... | F255W | 421 | 2609 | 2611 | 35 |
| u2my0107t... | F336W | 379 | 3321 | 3205 | 5 |
| u2my0108t... | F439W | 474 | 4303 | 4175 | 1 |
| u2my0106t... | F569W | 969 | 5618 | 5688 | 0.23 |
| u2my0109t... | F675W | 871 | 6700 | 6618 | 0.23 |
| u2my010at... | F791W | 1189 | 7374 | 7790 | 0.23 |
| u2my010et... | F469N | 25 | 4695 | 4700 | 10 |
| u2my010ft... | F487N | 25.8 | 4865 | 4864 | 10 |
| u2my010gt... | F502N | 26.9 | 5013 | 5010 | 10 |
| u2my010dt... | F658N | 28.4 | 6595 | 6591 | 5 |
| u2my010bt... | F631N | 30.7 | 6283 | 6281 | 5 |
| u2my010ct... | F656N | 21.4 | 6564 | 6561 | 5 |
| Filter | Counts (s-1) |
WFPC2 (mag) |
stmag | f (×10-26) |
 (Å) |
| F160BW... | 0.94 | 13.97 | 13.72 | 1.06 | 1491 |
| F218W... | 60.55 | 11.26 | 11.07 | 22.4 | 2189 |
| F255W... | 175.4 | 10.60 | 10.62 | 46.6 | 2587 |
| F336W... | 2123 | 10.19 | 10.34 | 102.3 | 3341 (U) |
| F439W... | 3569 | 11.19 | 10.48 | 145.3 | 4300 (B) |
| F569W... | 15480 | 10.94 | 11.03 | 150.9 | 5614 (V) |
| F675W... | 15178 | 10.79 | 11.44 | 145.6 | 6697 (R) |
| F791W... | 10317 | 10.67 | 11.85 | 136.2 | 7828 (I) |
| F469N... | 164.3 | |
10.69 | 138.7 | 4695 |
| F487N... | 231.0 | |
10.69 | 149.1 | 4865 |
| F502N... | 273.5 | |
10.82 | 144.4 | 5013 |
| F631N... | 660.8 | |
11.07 | 171.1 | 6306 |
| F656N... | 368.8 | |
11.12 | 172.2 | 6564 (H) |
| F658N... | 499.4 | |
11.18 | 165.0 | 6591 |
W denotes broadband filters, and N denotes narrow. Equivalent Johnson filters are marked U, B, V, R and I. Fluxes are in units of ergs cm-2 s-1 Hz-1.