Background

We used SKYNET, a network of robotic telescopes located around the world (Reichart et al. 2005), to conduct our survey. Within SKYNET, we chose to use the 0.4-m PROMPT telescopes located on Cerro Tololo in Chile. PROMPT, like all SKYNET telescopes, can be controlled remotely via a simple web interface (see Figure 1).

Acknowledgements

Stephen M. Vultaggio1

Brad N. Barlow1,2

The SKYNET Team2

A Photometric Survey for Rapidly-Pulsating Hot Subdwarf Stars with SKYNET

1Department of Physics, High Point University, High Point, NC 272622Department of Physics & Astronomy, University of North Carolina, Chapel Hill, NC 27599

Hot subdwarf B (sdB) stars were once red giant branch stars that had their outer layers stripped off due to interactions with a binary companion (Heber 2009). They have around half the mass of the sun and will fuse helium in their cores for approximately 100 Myr on the extreme horizontal branch.

Out of the thousands of known sdB stars, only about 100 are known pulsators. There are three main types of pulsators: (i) sdBVr stars, which show rapid p-mode pulsations, (ii) sdBVs stars, which show slow g-mode oscillations, and (iii) the hybrid sdBVrs stars, which exhibit both types of pulsations.

Our survey focused on finding new rapid pulsators, which have periods from 1-10 minutes and amplitudes <10%. These pulsations are useful because they reveal information about the composition, mass, size, and density of hot subdwarf stars. Similar to white dwarfs, studying these stars helps to shed light on how physics works at temperatures and pressures we cannot easily recreate in laboratories on Earth.

Survey Description

We acknowledge the support of the National Science Foundation, under award AST-0707381 (BNB). We are grateful to SKYNET team members Dan Reichart, Aaron LaCluyze, Josh Haislip, and Kevin Ivarsen for their generous support and ample observing time over the years. Lastly, we also recognize Bart Dunlap and Chris Clemens for their unwavering support and useful insight.

•Targets observed: 288•Telescopes used: 4•Frames taken: ~120,000•Data size: ~480 GB•Total integration time: 988 hr

Survey Stats

FIGURE 1 SKYNET web interface (skynet.unc.edu)

Results & New VariablesCS 1246A new sdBVr star (Barlow et al. 2010)

HE 0341-2449A new sdBVr star(Barlow & Vultaggio, in prep)

EC 10246-2707A new eclipsing HW Vir binary(Barlow et al. 2013)

References

Barlow, B.N., Vultaggio, S., et al., 2014, MNRAS, in prepBarlow, B.N., et al., 2013, MNRAS, 430, 22Barlow, B.N., et al., 2010, MNRAS, 403, 324Heber, U., 2009, ARA&A, 47, 211Kilkenny, D., et al., 2010, Information Bulletin on Variable

Stars, 5927, 1Østensen, R. H., 2006, Baltic Astronomy, 15, 85Reichart, D.E., et al., 2005, Nuovo Cimento C Geophysics

Space Physics C, 28, 767

FIGURE 2 Targets observed in our survey (red circles) plotted over all hot subdwarfs in the Online Subdwarf Database (black points). The celestial poles and equator are marked in blue for reference.

FIGURE 3 (Top) Maximum amplitude detected in the FT of each targetʼs light curve plotted against the mean noise level. Dotted and dashed lines represent the 3- and 4-σ levels, respectively. Variables and pulsators found in the survey are plotted as red stars. (Bottom) Histogram of the mean noise levels of all survey observations.

•Median mean noise level: 0.09%•Best mean noise level: 0.03%•Worst mean noise level: 0.7%

Targets for our survey were selected primarily from the Online Subdwarf Database (Østensen, 2006); those in the Southern-hemisphere and brighter than V=15.5 were given top priority. For each target, we obtained 2-4 hours of continuous time-series photometry with 30 s integration times and a 83% duty cycle. We used our own aperture photometry program in IDL to extract light curves and Period04 to compute discrete Fourier Transforms of the light curves to look for periodic signals.

Survey Name

Sample Size

Variables Found

Yield (%)

Selection Criteria?

South Africa 1200 20 1.7 None

Billeres 74 4 5.4 Yes (Teff)

Dreizler 12 1 8.3 Yes (Teff)

Østensen 309 24 7.8 Yes (Teff)

This work 288 7 2.4 None

TABLE 1 Summary of other photometric sdBV surveys.

Quick Summary:•Targets not observed to vary: 281•Variables found: 7

Overview of Variables Found:•New sdB pulsators: 3•Already known pulsators: 3•New eclipsing sdB binaries: 1

FIGURE 4 (Top) Light curve of CS 1246, a new pulsating hot subdwarf discovered during the survey. (Bottom) Fourier transform of the light curve, which shows one strong signal at a period of 371.7 s.

FIGURE 5 (Top) Light curves of EC 10246-2707, a new eclipsing sdB + M dwarf discovered during the survey. (Bottom) Residual light curves after subtracting the best model fits from the MORO code.

FIGURE 6 (Top) Discovery light curve of HE 0341-2449, a new pulsating hot subdwarf. (Bottom) Fourier transform of the light curve, which shows a single oscillation at a period near 150 s.

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Figure 5. Top panel: SOAR B light curve with the best-fitting theoretical light curve, as determined from the MORO code. Only onefull orbital cycle of the light curve is shown. Bottom panel: Residuals after subtracting the model from the data.

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Figure 6. Simultaneous, multi-colour photometry of EC 10246-2707 obtained with PROMPT on 2009-12-15 (top panel). Lightcurves were taken through the B,V,R, and I filters with PROMPT3, 1, 4, and 5, respectively. Although each data set covered ap-proximately 1.3 orbital cycles, we only show one complete cyclehere. The best-fitting binary light curves from MORO (Solution#3) are plotted with solid black lines. Residuals after subtractionof the models are also shown (bottom panel).

shows the secondary is cool while the lack of any other op-tical light from it implies it is small; these traits are con-sistent with a low–mass M dwarf companion. Accordingly,we used the theoretical mass–radius relationship for lower–main sequence stars from Bara!e et al. (1998) to furtherconstrain our model outputs. We accept only those MOROsolutions with mass–radius combinations for the cool com-

panion falling within conceivable boundaries obtained fromBara!e et al. (1998).

Other adjustable parameters for the modeling includedthe inclination angle (i), secondary albedo (A2), Roche sur-face potentials ("1, "2), mass ratio (q), primary radiationparameter (!1), colour-dependent luminosities (L1, L2), andthe secondary linear limb darkening coe#cient (x1).

MORO encountered no serious problems in the fittingexcept those connected with the usual parameter correla-tions. Di!erent combinations of the inclination angle, limb-darkening coe#cients, and ratio of the stellar radii, can pro-duce essentially indistinguishable light curves of nearly thesame shape and fit quality. Thus, the code finds reason-able light curve solutions for a broad range of mass ratios(q=M2/M1) and corresponding gravitational equipotentials("1, "2). Figure 4 illustrates this degeneracy by present-ing primary and secondary mass–radius diagrams for the 27separate solutions MORO found for the SOAR B light curve(“Solution #1”).

The "–squared values of the models in Figure 4 arecomparable, and consequently, we have no strong statisticalreason to choose one model over the others without applyingadditional constraints. For reference, we overplot the empir-ical M–R relationship for lower–main sequence stars in CVs3

from Knigge et al. (2011), the theoretical M–R relation forsingle M–dwarfs from Bara!e et al. (1998), the ‘canonical’sdB mass, and the minimum mass needed for He–burning.In the sdB panel, we also highlight combinations of massesand radii consistent with our spectroscopic measurement ofthe surface gravity. Several of the models fall within thisshaded region, so the addition of our log g estimate alone isnot su#cient for choosing a single solution. In light of thedegeneracy inherent to the models, we choose to report only

3 we note that the secondary stars in CVs might be slightly ex-panded compared to those in detached systems.

The O-C diagram of CS 1246 3

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Figure 2. (Top) Sample light curve of CS 1246 from 2010 Jan18. The data shown were obtained with PROMPT 3 over 2.9hours using 30-s exposures without a filter. (Bottom) Ampli-tude spectrum of the light curve, which is dominated by a 371.7-s signal.

14000 µHz) after pre-whitening the signal. Low-amplitudesignals appear in some of the nightly Fourier transforms(FTs) at frequencies near the g-mode regime, but we hes-itate to claim these signals as real since 1/f noise and im-properly removed extinction e!ects could easily accountfor those structures.

Our least-squares fits show the amplitude of f1 de-creased from 20 mma3 in 2010 Jan to 16 mma in 2010 Mayat a rate of nearly 0.9 mma month!1. Figure 3 presentsthis trend above its FT. We exclude the 2009 data fromthis plot since they were taken primarily through di!erentpassbands from the 2010 data and the measured ampli-tude of f1 strongly depends on the observed wavelengths(Barlow et al. 2010). If the rate of decline remains linear,f1 will have an amplitude below our detection limits (innightly light curves) by 2011 Nov. As we discuss later,there is no detectable periodic signal in the amplitudes.

The frequencies of f1 in all the light curves agreewithin their error bars, which were typically around 1.2µHz. To investigate smaller changes in the frequency aswell as variations in the phase, we analysed our completedata set using the O-C technique, as discussed in the sec-tion that follows.

3 Amplitudes are given in units of milli-modulation amplitude(mma), or parts-per-thousand. 10 mma corresponds to 1%

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Figure 3. (Top) Amplitudes of f1 taken from the least-squaresfits to the individual 2010 light curves. The data show a de-creasing trend of nearly 0.9 mma month!1, which is marked bya dotted line. (Bottom) Fourier transform of the nightly am-plitudes with the linear trend removed. The mean noise levelis 0.25 mma. The dashed vertical line marks the location of a14.1-day oscillation, and the dotted horizontal line representsthe amplitude at four times the mean noise level.

3 THE O-C DIAGRAM

We began our construction of the O-C diagram4 by calcu-lating a linear ephemeris for the times of maxima in thelight curve (C) of the form

C = Tc + PcE, (1)

where Tc is a reference time of maximum, Pc the pulsa-tion period, and E the cycle number measured from Tc.Since keeping track of E correctly over an extended pe-riod of time requires an exceptionally accurate startingfrequency, we used the period resulting from the least-squares fits to the combined 2010 light curve for Pc. Ourobserving run on 2010 Mar 10 falls near the middle of thiscombined light curve, and, consequently, we employed thetime of maximum determined from its least-squares fit forTc. The observed times of maxima (O) were taken fromthe least-squares fits to the individual light curves, andtheir corresponding cycle numbers were computed usingequation (1).

Figure 4 presents the O-C diagram created by sub-tracting the calculated from the observed times of max-ima. A sinusoidal oscillation dominates the overall struc-ture. The sinusoid is superimposed on a parabolic trendindicative of a secular change in the pulsation period. Thepresence of the sinusoid is even more apparent in the FTof the O-C diagram with the quadratic term removed, as

4 For a review of the basic principles behind the O-C method,we refer the reader to Kepler (1993).

c! 0000 RAS, MNRAS 000, 000–000

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Figure 2.1: Targets observed in our survey (red circles) plotted over all hot subwarfs in theOnline Subdwarf Database (black points). The celestial poles and equator are marked in bluefor reference. EC Zone 2 targets easily stand out as a band of points in the lower right.

Sample Size Variables Fraction Selection CriteriaSouth Africa 1200 20 1.7 noneBilleres 74 4 5.4 Te f f

Dreizler 12 1 8.3 Te f f

Østensen 309 24 7.8 Te f f

THIS WORK 212 6 2.8 none

Table 2.2: Yields of sdBV Surveys

weather conditions, and total length of the run. Although one would typically expect a cor-

respondence between the brightest stars and lowest detection limits, this was not always the

case since brighter targets were often observed for a shorter amount of time and weather

conditions varied greatly from night to night.

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Figure 2.2: (Top) Maximum amplitude detected in the FT of each target’s light curve plot-

ted against the mean noise level. Dotted and dashed lines represent the 3- and 4-σ levels,

respectively. Variables and pulsators found in the survey are plotted as red stars. (Bottom)

Histogram of the mean noise levels of all survey observations.

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Figure 2.2: (Top) Maximum amplitude detected in the FT of each target’s light curve plot-

ted against the mean noise level. Dotted and dashed lines represent the 3- and 4-σ levels,

respectively. Variables and pulsators found in the survey are plotted as red stars. (Bottom)

Histogram of the mean noise levels of all survey observations.

29