THE POLAR CATALYSMIC VARIABLE 1RXS J173006.4+033813

We observed 1RXS J1730+03 with the Palomar Robotic 60 inch telescope (P60; Cenko et al. 2006) from UT 2009 April 17 to UT 2009 June 5 and with the Large Format Camera (LFC; Simcoe et al. 2000) at the 5 m Hale telescope at Palomar on UT 2009 August 26. Here, we give details of the photometry.

We define a photometric epoch as observations from a single night when the source could be observed. We obtained 28 epochs with the P60, subject to scheduling and weather constraints. A typical epoch consists of consecutive 90–120 s exposures spanning between 30 and 300 minutes (Table 1). We obtained g ', r ', i ' photometry on the first and third epochs. After the third epoch, we continued monitoring the source only in the i ' band.

We reduced the raw images using the default P60 image analysis pipeline. LFC images were reduced in IRAF.⁴ We performed photometry using the IDL⁵ DAOPHOT package (Landsman 1993). Fluxes of the target and reference stars (Figure 1) were extracted using the APER routine. For aperture photometry, the extraction region was set to one seeing radius, as recommended by Mighell (1999). The sky background was extracted from an annular region 5–15 seeing radii wide. We used flux zero points and seeing values output by the P60 analysis pipeline. Magnitudes for the reference stars were calculated from a few images (Table 2). The magnitude of 1RXS J1730+03 was calculated relative to the mean magnitude of 9 reference stars for LFC images and 15 reference stars for P60 images. The LFC images (Figure 1) resolve out a faint nearby star (m_i' = 20.8), 34 from the target. The median seeing in P60 data is 21 (Gaussian FWHM): so there is a slight contribution from the flux of this star to photometry of 1RXS J1730+03. We do not correct for this contamination. The statistical uncertainty in magnitudes is ∼ 0.2 mag for P60 and ∼0.05 mag for LFC, and the systematic uncertainty is 0.16 mag in the g ' band, 0.14 mag in the r ' band, and 0.06 mag in the i ' band.

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The resultant light curves are shown in Figures 2–4. Table 1 provides the photometry.

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We obtained optical and near-infrared spectra of 1RXS J1730+03 at various stages after outburst (Figure 5). The first optical spectra were taken 13 days after the first photometric epoch. We used the Low Resolution Imaging Spectrograph on the 10 m Keck-I telescope (LRIS; Oke et al. 1995), with upgraded blue camera (McCarthy et al. 1998; Steidel et al. 2004), covering a wavelength range from 3200 Å to 9200 Å. We acquired more optical data 34 days after outburst, with the Double Beam Spectrograph on the 5 m Hale telescope at Palomar (DBSP; Oke & Gunn 1982). We took five exposures spanning one complete photometric period, covering the 3500–10000 Å wavelength range. We took late-time spectra covering just over one photometric period for the quiescent source with the upgraded LRIS.⁶ At this epoch, we aligned the slit at a position angle of 45°to cover both the target and the contaminator, 34 to its southwest (Figure 1). We also obtained low-resolution J-band spectra with the Near Infrared Spectrograph on the 10 m Keck-II telescope (NIRSPEC; McLean et al. 1998). Twelve spectra of 5 minutes each were acquired, covering the wavelength region from 11500 Å to 13700 Å. For details of the observing set up, see the notes to Table 5 later.

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We analyzed the spectra using IRAF and MIDAS⁷ and flux calibrated them using appropriate standards. Wavelength solutions were obtained using arc lamps and with offsets determined from sky emission lines. Figure 6 shows an optical spectrum from each epoch, while the IR spectrum is shown in Figure 7.

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The second LRIS epoch had variable sky conditions. Here, we extracted spectra of the aforementioned contaminator. This object is also a M dwarf, hence both target and contaminator spectra will be similarly affected by the atmosphere. We estimate the i ' magnitude of the contaminator in each spectrum and compare it to the value measured from the LFC images to estimate and correct for the extinction by clouds.

We observed the 1RXS J1730+03 with the X-ray telescope (XRT) and the UV-Optical Telescope (UVOT) on board the Swift X-ray satellite (Gehrels et al. 2004) during UT 2009 May 3–6 for a total of about 12.5 ks. The level-two event data were processed using Swift data analysis threads for the XRT (Photon counting mode; PC) using the HEASARC FTOOLS⁸ software package. The source was not detected in the X-ray band.

We follow the procedures outlined by Poole et al. (2008) for analyzing the UVOT data. The measured fluxes are given in Table 3. The contaminator is within the recommended 5'' extraction radius. Hence, flux measurements are upper limits.

Shevchuk et al. (2009) had observed 1RXS J1730+03 on UT 2006 February 9 with the Swift satellite as a part of investigations of unidentified ROSAT sources. They detected the source with a count rate of 0.02 counts s⁻¹. The best-fit power law has a photon index Γ = 1.8 ± 0.5 and a 0.5–10 keV flux of 1.2 × 10⁻¹² erg cm^-2 s⁻¹. After converting to the ROSAT bandpass assuming the XRT model parameters, this value is approximately a factor of two lower than the archival ROSAT flux. They report a much higher UV flux in their observations, which suggests that the source was in an active state during their observations.

The column density inferred from the XRT data is low, N_H ∼ 7 × 10²⁰  cm⁻². From ROSAT data, this column density corresponds to A_V = 0.39, which gives A_UVM2 = 0.84 (Cox 2000). For comparison, Schlegel et al. (1998) give the Galactic dust extinction toward this direction (l = 267, b = 197) to be E(B − V) = 0.141 mag (A_V = 0.44), corresponding to a column density of about 8 × 10²⁰ cm⁻².

The red component of 1RXS J1730+03 is typical of a late-type star. In Figure 8, we compare the red side spectrum of 1RXS J1730+03 with several M dwarfs. From the shape of the TiO bands at 7053–7861 Å, we infer that the spectral type to be M3 ± 1. This is consistent with the relatively featureless J-band spectrum (McLean et al. 2003). The spectral type indicates an effective temperature of 3400 K (Cox 2000). The presence of a sodium doublet at 8183/8195 Å implies a luminosity class V.

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We also fit the spectrum with model atmospheres calculated by Munari et al. (2005). For late-type stars, these models are calculated in steps of ΔT = 500 K, Δlog  g = 0.5, and Δ[M/H] = 0.5. We use model atmospheres with no rotational velocity (V_rot = 0 km s⁻¹) and convolve them with a kernel modeled on the seeing, slit size, and pixel size. We ignore the regions contaminated by the telluric A and B bands (7615 Å and 6875 Å). The unknown contribution from the WD was fit as a low-order polynomial. We correct for extinction using A_V = 0.39 from X-ray data (Section 2.3). To measure log  g, we use the spectrum in the 8000–8700 Å region, which is expected to have fairly little contamination from the blue component. This region includes the Ca ii lines at 8498, 8542 Å, and the Na i doublet, which are sensitive to log  g. We then fit the spectra in the 6700–8700 Å range to determine the temperature and metallicity. The best-fit model has T = 3500 K, log  g = 5.0, and solar metallicity, consistent with our determination of the spectral type.

Kolb et al. (2001) state that unevolved donors in CVs follow the spectral type–mass relation of the zero-age main sequence (ZAMS), as the effects of thermal disequilibrium on the secondary spectral type are negligible. For an M3 star, this yields a mass of 0.38 M_☉. As the secondaries evolve, the spectral type is no longer a good indicator of the mass and gives only an upper limit on the mass. The lower limit can simply be assumed to be the hydrogen-burning limit of 0.08 M_☉.

The blue component of 1RXS J1730+03 is consistent with a highly magnetic WD. The blue spectrum is suggestive of a hot object, but does not show any prominent absorption/emission features. Hα is seen in emission, but other Balmer features are not detected. The spectrum (Figure 6) shows cyclotron humps, suggesting the presence of a strong magnetic field. The polar nature of the object is supported by the absence of an accretion disk and the transition from an active state to an off state in X-rays (Section 1, Section 2.3).

For analyzing the WD spectrum, we subtracted a scaled spectrum of the M dwarf GL 694 from the composite spectrum of 1RXS J1730+03. The resultant spectrum (Figure 9) clearly shows cyclotron harmonics. The hump seen in the J-band spectrum (Figure 7) is also inferred to be a cyclotron harmonic. A detailed modeling of the magnetic field is beyond the scope of this work, but we use a simple model to estimate the magnetic field. We fit the cyclotron humps with Gaussians and measure the central wavelengths (Table 4). We then fit these as a series of harmonics and infer that the cyclotron frequency is ν_cyc = 1.17 × 10¹⁴ Hz. The magnetic field in the emission region is given by B = (ν_cyc/2.8 × 10¹⁴ Hz) · 10⁸ G = 42 × 10⁶ G.

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As a conservative error estimate, we consider the worst case scenario where our identified locations for the cyclotron humps are off by half the spacing between consecutive cyclotron harmonics. Using this, we estimate the errors on the magnetic field: B = 42⁺⁶₋₅ MG.

We use the best-fit (Munari et al. 2005) model atmosphere to measure radial velocities of the M dwarf. We vary the radial velocity of the model and minimize the χ² over the 6500–8700 Å spectral region, excluding the telluric O₂ bands. After a first iteration, the spectra are re-fit to account for motion of the M dwarf during the integration time. For the 12 spectra taken at the second LRIS epoch, we also measure the radial velocity for the contaminator star on the slit and find it to be constant. This serves as a useful test for our radial velocity measurement procedure. The barycentric corrected velocities are given in Table 5.

We fit a circular orbit (v₂ = γ₂ + K₂sin([2π(t − t₀)]/P)) to the measured velocities. We define the superior conjunction⁹ of the WD as phase 0.

The 2009 June 16 spectroscopic data (Table 5) give an orbital period P_est = 123 ± 3 min. We then use the photometric variability (Section 4.2) to determine an accurate period in this range. Next, we refine the solution with velocity measurements from the other two spectroscopic epochs. The best-fit solution gives a period P = 120.2090 ± 0.0013 minutes and K₂ = 390 ± 4 km s⁻¹ (Table 6 and Figure 10).

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Figure 11 shows sections of the last epoch spectra around Hα and the Na i doublet at 8184/8195 Å. The Na i doublet clearly matches the velocity of the M dwarf in the orbit, but the Hα emission seems to have a smaller velocity amplitude. A possible explanation for this is that the Hα emission comes from the M dwarf surface that is closest to the WD, which may be heated by emission from the WD or the accretion region.

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The light curve of 1RXS J1730+03 shows clear periodicity (Figures 2–4), with two peaks per spectroscopic period. Most of the photometric data were acquired in the i ' band, which contains contribution from both the M dwarf and a cyclotron harmonic from the emission region near the WD.

A Fourier transform of the data (Figure 12) shows a strong peak at 60 minutes. We interpret this as a harmonic of the orbital period. To determine the exact period, we analyze the data as follows. As the object has a short orbital period, we convert all times to Heliocentric Julian Date for analysis. We fit a sinusoid (m₀ + m_Asin([2π(t − t₀)]/P)) to each epoch, allowing m₀ and m_A to vary independently for each epoch, but we use the same reference time t₀ and period P for the entire fit. The mean magnitude is correlated with the amplitude (Figure 5). Note that the amplitude measured for the sinusoidal approximation for each epoch is always less than the actual peak-to-peak variations of the source during that epoch, as expected. The source is in the active state in the first few epochs, and we exclude epochs 1–5 from the fit to avoid contamination from the accretion stream and/or the accretion shock.

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The best-fit solution is overplotted in blue in Figures 3 and 4. Since epochs 1–5 were not included in the fit, a sinusoid is overplotted in dashed green to indicate the expected phase of the variations. The best-fit period is 60.1059 ± 0.0005 minutes. This formally differs from the spectroscopically determined orbital period by 2.1σ. However, this error estimate includes only statistical errors. There is some, difficult to determine, systematic error component in addition, so we do not claim any significant inconsistency.

Periodic photometric variability for 1RXS J1730+03 can be explained as a combination of two effects: cyclotron emission from the accretion region and ellipsoidal modulation. The active state is characterized by a higher mass transfer rate from the donor to the WD and results in higher cyclotron emission. This emission is beamed nearly perpendicular to the magnetic field lines, creating an emission fan beam. For high inclination systems, the observer crosses this fan beam twice, causing two high amplitude peaks per orbit (Figure 2). In the active state when the emission is dominated by cyclotron radiation, the minimum leads the superior conjunction by ∼47°.

In ellipsoidal modulation, the photometric minima coincide with the superior conjunction. It is observed that in quiescence, the photometric minimum leads the superior conjunction of the WD by ∼14°. This suggests that the 0.29 ± 0.13 mag variation is caused by a combination of ellipsoidal modulation and cyclotron emission from the accretion region.

The semi-amplitude of the M dwarf radial velocity, K2, gives a lower limit on the mass of the WD. For a circular orbit, one can derive from Kepler's laws that

$$\begin{equation} M_{1, {\rm min}} = \frac{P K_2^3}{2\pi G} = 0.52\,M_{\odot }. \end{equation} \tag{ 1 }$$

Tighter constraints can be placed on the individual component masses M₁, M₂ by considering the geometry of the system. Eggleton (1983) expresses the volume radius R₂ of the secondary in terms of the mass ratio q = M₂/M₁:

$$\begin{equation} \frac{R_2}{a} = \frac{0.49 q^{2/3}}{0.6q^{2/3} + \ln (1 + q^{1/3})}, \end{equation} \tag{ 2 }$$

where the separation of the components is given by a = [P²G(M₁ + M₂)/4π²]^1/3. Thus for a fixed period P, R₂ depends only on M₂. The radius of the WD is much smaller than that of the M dwarf. Hence, the M dwarf will eclipse the accretion region if the inclination of the system is i < sin⁻¹(R₂/a). Figures 3 and 4 show that we do not detect any eclipses in the system.

Figure 13 shows the allowed region for 1RXS J1730+03 in a WD mass—M dwarf mass phase space. The orange dotted region is excluded as the orbital velocity would be greater than the measured projected velocity. The red hatched region is excluded by non-detection of eclipses. The allowed mass of the primary ranges from the minimum mass (M₁>0.52 M_☉) to the Chandrasekhar limit. The mass of the secondary is bounded above by the ZAMS mass for an M3 dwarf (M₂ = 0.38 M_☉).

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For a given M₂ and a known orbital period, we can determine the radius of the secondary using Equation (2) and can calculate the surface gravity (log  g). For 0.38 M_☉ ≳ M₂ ≳ 0.05 M_☉, log  g ranges from 5.1 to 4.8. This is consistent with log  g = 5.0 for the best-fit M dwarf spectrum (Section 3.1).

The donor stars in CVs are expected to corotate. For 1RXS J1730+03, the highest possible rotational velocity vsin i is ∼160 km s⁻¹ for a 0.38 M_☉, 0.27 R_☉ M dwarf, and a 1.1 M_☉ WD (Figure 13). vsin i will be lower if the WD is heavier or if the M dwarf is lighter. To measure rotational broadening in the spectra, we use a higher resolution (R = 20,000) template of the best-fit model from Zwitter et al. (2004). We take a template with zero rotation velocity and broaden it to different rotational velocities using the prescription by Gray (2005). Then we use our fitting procedure (Section 3.1) to find the best-fit value for vsin i. For this measurement, we use only the 12 relatively high-resolution spectra from the second LRIS epoch (UT 2009 June 16). The weighted vsin i from the 12 spectra is 97 ± 22 km s⁻¹, but the measurements show high scatter, with a standard deviation of 54 km s⁻¹. We compared our broadened spectra with rotationally broadened spectra computed by Zwitter et al. (2004) and found that our methods systematically underestimate vsin i by ∼20 km s⁻¹. We do not understand the reason for this discrepancy, hence do not feel confident enough to use this value in our analysis. A reliable measurement of vsin i will help to better constrain the masses of the two components.

We estimate the distance to 1RXS J1730+03 as follows. Our fitting procedure (Section 3.1) corrects for extinction and separates the WD and M dwarf components of the spectra. We correct for varying sky conditions by using a reference star on the slit. The ratio of measured flux to the flux of the best-fit model atmosphere (T = 3500 K, log g = 5.0) is

$$\begin{equation} \frac{f_{\rm measured}}{f_{\rm model}} = \left(\frac{R_2}{d}\right)^2 = (6.1\pm 1.6)\times 10^{-23}, \end{equation} \tag{ 3 }$$

where d is the distance to the source and R₂ is given by Equation (2).

For 1RXS J1730+03, the maximum mass of the M dwarf is 0.38 M_☉, and the corresponding radius is R₂ = 0.27 R_☉. Equation (3) then gives d = 800 ± 110 pc. This calculation assumes the largest possible M dwarf radius, hence is an upper limit to distance. If the M dwarf is lighter, say 0.1 M_☉, we get R₂ = 0.17 R_☉, yielding d = 500 ± 70 pc.