Accurate Mass Determination of the Old White Dwarf G through Astrometric Microlensing

Transcription

1 Hubble Space Telescope Cycle 19 GO Proposal 871 Accurate Mass Determination of the Old White Dwarf G through Astrometric Microlensing Principal Investigator: Dr. Kailash C. Sahu Institution: Space Telescope Science Institute Electronic Mail: Scientific Category: COOL STARS Scientific Keywords: Astrometry, Extra-Solar Planets, Gravitational Lensing, Microlensing, White Dwarfs Instruments: WFC3 Proprietary Period: 12 Orbit Request Prime Parallel Cycle Cycle Cycle Total 8 0 Abstract We propose to determine the mass of the cool, nearby, high-proper-motion white dwarf (WD) G (LHS 1838) through astrometric microlensing. In a reprise of the famous 1919 solar eclipse that verified general relativity, G will pass very close in front of a 19.5-mag background star in June 2012, with an impact parameter of only ~0.08 arcsec. As it passes in front, it will cause a relativistic deflection of the background star's image by >2 milliarcsec, an amount easily detectable with HST/WFC3. The gravitational deflection angle depends only on the distances and relative positions of the stars, and on the mass of the WD. Since the distance to G is already known from an accurate parallax, and the relative positions can be determined precisely before the event, the astrometric measurement offers a unique and direct method to measure the mass of the WD to high accuracy (<5%, potentially <1% for favorable circumstances). One key astrophysical prediction for WDs is the existence of a mass-radius relation (MRR), which depends on the WD's core composition. Since the luminosity and distance of G are known, its radius is known. Our measurements will thus provide a new, precise point in the MRR. The mass of G is of special interest because it is an old and relatively massive WD, which would provide new constraints near the bottom of the WD cooling curve, currently being used to age-date stellar populations.

2 Dr. Kailash C. Sahu : Accurate Mass Determination of the Old White Dwarf G through Astrometric Microlensing Investigators: Investigator Institution Country PI Dr. Kailash C. Sahu Space Telescope Science Institute USA/MD CoI Dr. Howard E. Bond Space Telescope Science Institute USA/MD CoI Dr. Jay Anderson Space Telescope Science Institute USA/MD CoI Dr. Edmund Nelan Space Telescope Science Institute USA/MD Number of investigators: 4 Target Summary: Target RA Dec Magnitude GJ V = Observing Summary: Target Config Mode and Spectral Elements Flags Orbits GJ-3392 WFC3/UVIS Imaging F555W 8 (1x8) Total prime orbits: 8

3 Scientific Justification 1 Introduction: The Importance of White-Dwarf Masses White dwarfs (WDs) are the remnants of stars less massive than 8 M. They provide astrophysical insights into the properties of degenerate matter, and, as stellar chronometers, astronomical insights into the ages of stellar populations. One key astrophysical prediction is the existence of a WD mass-radius relation (MRR), which depends on the mean molecular weight of the electron-degenerate matter. Radii can be inferred when the luminosity and effective temperature (T eff ) are known, so if the mass is also known the core composition can be determined using the theoretical MRR. Because of the strong (inverse) dependence of radius and hence density upon mass, WD cooling rates depend strongly on the mass, and thus masses must be known in order to calibrate the WD cooling timescale. Until now, the only directly measured dynamical masses for WDs have come from binary stars, but very few of these are available, the most accurate being those of Sirius B and Procyon B. Precise masses and radii are also available for WDs in short-period eclipsing binaries like V471 Tauri (O Brien et al. 2001) and NN Ser (Parsons et al. 2010), along with a few pulsar companions but they have been through a very different evolutionary history, and they provide no information on issues like the initial/final mass relation for WDs. An alternative is to determine the surface gravity from a spectroscopic analysis (which of course is model-dependent) or from the gravitational redshift (in those rare cases where the centerof-mass velocity is independently known), and if the radius is also determined as described above, a mass can be calculated; however, the spectroscopic log g determinations generally are not of high accuracy, and in any case can only be determined for the subset of DA or DB WDs that have suitable spectra. Otherwise, the mass has to be inferred from radii and the assumption of a theoretical MRR and core composition, a procedure that of course provides no independent information on the actual mass. Thus, actual fully empirical tests of the MRR are still rare. We propose to measure the mass of a cool, old WD, through a new technique, by imaging an astrometric microlensing event. These observations will provide the first direct, model-independent mass determination for a single WD. 2 Predicting Close Encounters of the Stellar Kind PI Sahu and collaborators have carried out a large-scale search for upcoming events in which high-proper-motion stars will pass closely in front of background sources. The input catalog was the LHS (Luyten 1979 a catalog of all known stars with proper motions greater than 0. 5 yr 1 ), which unfortunately had coordinate errors of about 6. We first updated the coordinates of the entire LHS catalog, using the STScI Digitized Sky Survey (DSS) data, to improve the coordinate accuracy to better than 0. 2; the revised LHS catalog was published by Bakos, Sahu, & Nemeth (2002). Then we projected the positions of all 5,000 LHS stars 1

4 forward over the next 40 years, and have characterized some 100 upcoming close passages near background stars contained in the GSC2 catalog. One of the most interesting events that will occur in the next few years is the close passage of the cool (spectral type DA9) WD G (LHS 1838, GJ 3392) in front of a 19.5-mag background star. To refine the prediction, we imaged G with the the SAAO 1m telescope in 2008, and combined the resulting astrometry with DSS archival images from two earlier epochs, to predict the date and impact parameter of the event. It will occur in June 2012, with a predicted impact parameter of only ± Fig. 1 (left) shows a DSS image from 1953, with G circled. Fig 1 (right) is the DSS-II image from 1990 showing the progress of G toward the background source, which is also circled. 3 The Cool and Old White Dwarf G G is not just a random faint WD, but is among the cooler, older, and intrinsically fainter known WDs. The apparent magnitude of G is V = 16.41, and the proper motion is µ = yr 1. Its distance is 22.7 pc, based on a USNO parallax of 44.0 ±4.2 mas (Dahn et al. 1982). Bergeron et al. (2001), on the basis of a model-atmosphere analysis, give a WD cooling age of 4.3 Gyr. The moderately high transverse velocity (55 km s 1 ) and age suggest that the star is a member of the thick disk. Determining its total age, including its main-sequence lifetime, would require a knowledge of its mass, combined with an initial-mass/final-mass relation. In the absence of a dynamical mass, or knowledge of its gravitational redshift, Bergeron et al. used its log g and a theoretical MRR (for an assumed CO core composition) to infer a mass of 0.76 ± 0.09 M, placing G well above the average mass of WDs, and implying that its progenitor was relatively massive ( 3.5 M ; Kalirai et al. 2008). 4 Astrometric Microlensing Astrometric microlensing provides a powerful technique for the direct determination of stellar mass through the general-relativistic gravitational deflection of the image of a background source. When the light of a background star (the source) passes within or close to the Einstein ring of a foreground object (the lens), it is amplified and split into multiple images (see Fig. 2). For typical stellar parameters, the separation of the images is of the order of milliarcseconds, and thus the images are generally not resolved. However, since one image is brighter than the other, this causes a shift in the apparent centroid of the source image. The angular Einstein ring radius of a point lens is given by θ E = (4GM/c 2 d r ) 1/2, (1) where M is the lens mass and d r is the reduced distance to the lens with respect to the more-distant source, given by 1/d r = 1/D l 1/D s, where D l and D s are the distances from the Earth to the lens and the source, respectively. 2

5 The angular displacement of the source image at any given time is δθ = θ 2 E/ θ, (2) where θ is the angular separation between the lens and the (undeflected) location of the source (cf. Fig. 2 and Dominik & Sahu 2000). (More precisely, Eq. [2] is valid for θ 2θ E. For the case of very small angular separations, where the approximation of Eq. [2] is invalid, see Dominik & Sahu 2000). Adopting a distance of 23 pc for G , and assuming D s D l, its angular Einstein ring radius is 14 mas, and as noted above the impact parameter for the 2012 event is 80 mas. Therefore the maximum angular displacement of the background star due to lensing by G will be δθ (14 mas) 2 /80 mas 2.5 mas. (3) Displacements of this order are readily detectable with HST imaging with WFC3 (Anderson et al. 2004, 2006). (Note that at this large an impact parameter, the source will not brighten appreciably during the event, even though its apparent position will change detectably.) 5 Determining the Mass By combining Eqs. (1) and (2), we see that we can solve for the mass of the lens by measuring the deflection, if we know the reduced distance d r of the lens and its angular separation from the source. As noted earlier, d r depends only on the difference between the parallaxes of the lens and the source. The parallax of the lens is already known from the USNO measurement, and we can estimate the much smaller parallax of the source through multicolor photometry from our proposed HST observations as well as ground-based photometry. The next section discusses our detailed observing plan. The astrometric accuracy that can be achieved with WFC3 imaging is about 0.2 mas in a single measurement. We will obtain a total of about 10 measurements during the microlensing event, and thus be able to determine θ E to an accuracy of better than 0.1 mas. Thus we expect to measure θ E to an accuracy of about 7% (worst-case scenario of a 130 mas impact parameter) to <2% (impact parameter 30 mas), and the mass of G to a similar accuracy. Thus, potentially, G will join Sirius B and Procyon B as the three WDs with the most accurately known masses, and it will be the only single WD with an accurate mass. References Bakos, G., Sahu, K.C., & Nemeth, P. 2002, ApJS, 141, 187 Bergeron, P., Ruiz, M. T., & Leggett, S. K. 2001, ApJS, 133, 413 Dahn, C. C., et al. 1982, AJ, 87, 419 Dominik, M., & Sahu, K.C. 2000, ApJ, 534, 213 Kalirai, J., et al. 2008, ApJ, 676, 594 Luyten, W.J. 1979, LHS Catalog, Univ. of Minnesota, Minneapolis 3

6 Figure 1: (Left): A 1953 image of G taken from STSCI Digitized Sky Survey. The image size is arcsec. North is up, east to the left. G is encircled, and is heading east. (Right): Image of G as seen in a DSS-II image taken in G (circled bright star) is heading towards a fainter, 19.5-magnitude star (circled faint star), which it will lens in The predicted impact parameter is O Brien, M. S., Bond, H. E., & Sion, E. M. 2001, ApJ, 563, 971 Paczyński, B. 1996, Ann. Rev. Astron. Astrophys., 34, 419 Parsons, S. G., et al. 2010, MNRAS, 402, 2591 Description of the Observations We need to know accurate locations and proper motions for G and the source star, in order to predict the precise circumstances of the event, including the date and impact parameter. The existing ground-based measurements do not have the 1 mas accuracy needed for these purposes, especially given the 1.5 mas/day proper motion of G Therefore, we will use direct imaging with WFC3 to determine the astrometric parameters of G , the source star, and the surrounding reference field. These determinations need to be done well in advance of the closest encounter in June 2012, beginning as soon as possible in Cycle 19. The maximum deflection of the source position that is actually observable occurs just before the images of the two stars become blended (at HST resolution), which happens about 40 days before closest approach (and 40 days after closest approach). So, we need to know the time of closest approach as accurately as possible in order to schedule these two critical observations. Additional observations should be scheduled before and after those critical times, when the deflection is changing most rapidly with time. See Fig. 3. These considerations dictate a four-phase observing program: 4

7 Figure 2: This figure shows how the apparent positions and the sizes of the images change at various stages of a microlensing event. In this geometry the position of the lens, indicated by a solid dot, is fixed, and the open circles show the actual positions of the source. The filled circles show the images of the source as it passes close to the lens in the plane of the sky. The dashed circle is the Einstein ring of the lens. At any instant, the source, the lens and the two images lie on a straight line. This clearly shows that the centroid of the source will be shifted during the event. (Taken from Paczyński 1996) (1) Prediction phase. In this phase, we will obtain the HST observations needed to make the final predictions of the circumstances of the event (impact parameter and time of closest approach) with high accuracy. At the beginning of Cycle 19 we will image the field twice at about a 3-month separation for this purpose. (2 Cycle 19 orbits) (2) Course correction. Based on the early Cycle 19 astrometry, we will refine the predicted dates between which the images will be blended, so that we will know the optimal observation dates just before and after those times. (3) Fly-By. We will obtain one more observation in cycle 19 just before the onset of blending (and before the peak of the microlensing), when the astrometric deflection is at its largest observable value. (If this epoch turns turns out to lie in the solar-avoidance interval, May August 2012, we would make sure to obtain this observation just before the solar-avoidance interval.) The estimated times of these cycle 19 observations are shown as blue dots in Fig. 3. (1 Cycle 19 orbit) We will obtain 4 more observations after the peak of the microlensing, beginning just after the time when the source and the lens are no more blended (shown as red dots in Fig. 3). (4 Cycle 20 orbits) (4) Post-encounter phase. Finally, we will obtain 1 more observation in cycle 21 as the lensing deflection subsides (shown as a magenta dot in Fig. 3). (1 Cycle 21 orbit) We thus require 3 orbits in cycle 19, 4 orbits in cycle 20, and 1 orbit in cycle 21. Exposure times: Both the source and the lens are relatively bright, so we will carry out the observations in two different (F814W and F555W) filters, to confirm achromaticity 5

8 Figure 3: This figure shows the expected astrometric shifts as a function of time for an impact parameter of 80 mas. The distance to the lens (WD G ) has been assumed to be 22.7 pc, and its mass to be 0.76M. The pre-encounter observations that we propose will provide the actual value of the impact parameter. The actual size of the deflection then scales linearly only with the true mass of the lens. The lens and source can be resolved separately with HST outside ±40 days of closest approach. The blue, red and magenta points represent our requested observations in cycles 19, 20 and 21, respectively during the event, and to better characterize the spectral type of the source. The exposures will be relatively short: for example, in a single 100 sec exposure the lens will have a S/N 500, and the source will have a S/N 100, avoiding saturation at the same time. The S/N achieved in one orbit will thus be more than adequate to achieve the full astrometric accuracy of 0.2 mas. Special Requirements The observations are time-critical, as described above. However, the requirements are easy to meet. Coordinated Observations Justify Duplications Past HST Usage and Current Commitments HST Programs by PI: PI Sahu has used HST extensively, both on calibration programs as an Instrument Scientist, and as a GO on research projects. One of his programs directly relevant to this 6

9 proposal (GO-9750) involved monitoring of a dense stellar field in the Galactic bulge continuously for 7 days, to look for transiting exoplanets. This program led to the discovery of 16 exoplanet candidates. The analysis of this data set has been completed, and the results have been published as an article in Nature (Sahu et al. 2006, Nature, 443, 534). The analysis of the proper motions of the stars in the SWEEPS field has also been completed, and the results are published in ApJ (Clarkson, Sahu et al. 2008, ApJ, 684, 1110). Other programs include the following: GO-7138: Imaging and spectroscopy of the bright arcs around the most luminous X-ray cluster RXJ The results from this program are published in: Sahu, K.C. et al. ApJ, 492, L125, GO-7592: Follow-up observations of a possible optical counterpart of GRB The results from this program are published in: Sahu, K.C. et al. Nature, 387, 476, 1997 Sahu, K.C. et al. ApJ, 489, L127, GO-11707: Detecting Isolated Black Holes through Astrometric Microlensing. This program is currently in progress. 7