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Optical Studies of 8 AM Herculis-Type Cataclysmic Variable Stars

We report detailed follow-up observations of 8 cataclysmic variable stars (CVs) that are apparently AM Her stars, also called polars. For all, we either determine orbital periods for the first time, or improve on existing determinations. The seven for which we have spectra show the high-amplitude radial velocity curves and prominent HeII 4686 emission lines characteristic of strongly magnetic CVs, and their periods, which range from 81 to 219 minutes, are also typical for AM Her stars. Two objects from the Gaia-alerts index, Gaia18aot and Gaia18aya, are newly identified as CVs. Another, RX J0636.3+6554, eclipses deeply, while CSS080228:081210+040352 shows a sharp dip that is apparently a partial eclipse. The spectrum of Gaia18aya has a cyclotron harmonic near 5500 Angstroms that constrains the surface field to about 49 Megagauss or greater.


INTRODUCTION
Cataclysmic variable stars (Warner 1995) are close binary systems in which a white dwarf accretes material from a more extended companion, usually resembling a main-sequence star, which overflows its Roche lobe (critical equipotential surface). The name arose because the first known examples underwent outbursts -classical nova explosions occur when nuclear fuel accumulated on the white dwarf's surface explodes, and the more common dwarf novae undergo outbursts when gas accumulated in an accretion disk becomes unstable, and rapidly accretes onto the white dwarf.
Magnetic CVs -in which the white dwarf is strongly magnetized -can behave quite differently. They are usually much stronger X-ray emitters than non-magnetic CVs. If the magnetic field is not especially strong, an accretion disk can form far from the white dwarf, but the inner disk is disrupted and the field forces material to fall onto the poles of the white dwarf. Systems of this kind are called DQ Herculis stars (Patterson 1994), or intermediate polars, and they show pulsations in the X-ray and optical bands at the rotation period of the white dwarf and/or the orbital sidebands (e.g. the orbital-spin beat). A still stronger magnetic field can disrupt the formation of an accretion disk entirely; often, magnetic torques force the white dwarf to co-rotate with the orbit, though the coupling is weak enough that the white dwarf can sometimes be temporarily knocked out of co-rotation. In these systems, at least some of the matter lost from the companion threads onto the magnetic field and falls directly onto the white dwarf's magnetic poles via magnetically confined accretion columns. CVs of this kind are classified as AM Herculis stars, after their prototype, and are also called polars (Cropper 1990), because they often show strong circular polarization modulated at the the orbital (= rotational) frequency.
It is often easy to recognize an AM Her star even without polarization measurements. When they are accreting actively, their spectra show strong emission lines, with high excitation; the He II λ4686 emission is usually comparable in strength to Hβ. Because the emission lines arise largely in the accretion column, their radial velocities are often dominated by infall, which can reach velocities much higher than the white dwarf's orbital speed. The rotation of the white dwarf changes our viewing angle, leading to large variations in velocity (up to a few thousand. km s −1 ) periodic on the white dwarf rotation period, which in co-rotating systems is the same as the orbital period P orb . The brighter parts of the accretion column can also disappear over the limb of the white dwarf as it rotates, causing the intensity of both the lines and the continuum to vary. As with any binary system, eclipses also occur if the inclination is high enough. Typically, most of the eclipsed flux arises from the bright base of the accretion column (or columns). Note-Positions, mean G magnitudes, and distances from the GAIA Data Release 2 (DR2; Gaia Collaboration et al. 2016Collaboration et al. , 2018. Positions are referred to the ICRS (essentially the reference frame for J2000), and the catalog epoch (for proper motion corrections) is 2015. The distances and their error bars are the inverse of the DR2 parallax πDR2, and do not include any corrections for possible systematic errors.
We have been observing CVs, mostly spectroscopically, to characterize them and in particular to measure their orbital periods when possible. Here we present studies of 8 CVs that are apparently AM Her stars. Table 1 lists the stars discussed here.
In Section 2, we describe the instrumentation and techniques used for our observations, reductions, and analysis. Section 3 gives detailed information on the individual objects. Section 4 summarizes and draws attention to the results we think are most interesting.

TECHNIQUES
Nearly all of the data presented here are from MDM Observatory, on Kitt Peak, Arizona. Here we only summarize our observing protocols, data reduction, and analysis techniques, since they were mostly similar to those described in previous papers (e.g. Halpern et al. 2018;Thorstensen et al. 2016).

Spectroscopy
Most of our spectra are from the "modspec" spectrograph 1 , usually mounted on the 2.4m Hiltner telescope, though occasionally on the 1.3m McGraw-Hill telescope. A 600 line mm −1 grating gave 2 Å pixel −1 with either of the two SITe CCD detectors (2048 2 or 1024 2 ) we used. We reduced these data with IRAF software driven by python scripts, but extracted the 2-dimensional spectra to 1-dimensional spectra using our own implementation of the optimal extraction algorithm described by Horne (1986). For wavelength calibration we derived a pixel-wavelength relation from comparison lamps taken in twilight, and then adjusted the zero point using the [O I] λ5577 airglow feature, since with this instrument a linear shift accurately compensated the flexure of the Cassegrain-mounted spectrograph as the telescope moved.
The most recent observations are from the Ohio State Multi-Object Spectrometer (OSMOS; Martini et al. 2011) mounted on the 2.4 m, using the blue grism and 'inner' slit, which gave 0.7 Å pixel −1 and ∼ 3 Å resolution. While the reductions were generally similar to modspec, OSMOS required a more elaborate wavelength calibration procedure since the pixel-to-wavelength scale was less stable. To adjust the wavelength scale we either measured airglow features (tabulated by Osterbrock et al. 1996) or took short Hg and Ne lamp exposures adjacent to our science exposures.
We measured radial velocities, mostly of Hα, in the individual exposures by by convolving the line profile with an antisymmetric function as described by Schneider & Young (1980). The choice of convolution function serves to emphasize different parts of the line profile (Shafter 1983). For the most part we chose the derivative of a Gaussian as the convolution function, which provides a measure of the 'overall' location of the line, including the line core.
The emission lines of AM Her stars display complicated profiles that change through their orbits. We display these by creating two-dimensional images as follows. In most cases, we start by rectifying the spectra, that is, dividing them by a smooth function fitted to the continuum. Cosmic rays and other obvious artifacts are then edited out by hand. We compute the orbital phase of each spectrum, divide the orbital cycle into 100 phase bins and average together spectra that fall within a window of each phase point, using a weighting function that is a truncated Gaussian in phase, centered on the phase point. Finally, we stack the averaged spectra into a two-dimesional image, repeating a cycle to avoid discontinuities. The sources studied here are rather faint, so some of our sources required exposure times of 720-900 s for adequate signal-to-noise; this resulted in some phase smearing. Even so, most of the trailed emission line spectrograms show a rather sharp component that is brightest as it swings from red to blue. This behavior is consistent with emission from the side of the companion star irradiated by the X-ray and ultraviolet flux from the white dwarf (see, e.g., Schwope et al. 1997, and for a very early example, Thorstensen et al. 1978).
For one of our targets, CSS080228:081210+040352, we also obtained four spectra with the Southern African Large Telescope (SALT; Buckley et al. 2006); these are described in Section 3.4.

Photometry
The MDM time-series photometry is from the 1.3m telescope, mostly with an Andor IKON CCD frame-transfer CCD. Some of the photometric data were taken with a 1024 2 -pixel SITe CCD, cropped to a 256 2 pixel subarray to reduce the CCD readout time. The reduction script performed aperture photometry on the program star, a comparison star, and several check stars in each frame.
We also include some time-series photometry from the 1-meter telescope at the South African Astronomical Observatory (SAAO), taken using the Sutherland High-speed Optical Camera (SHOC; Coppejans et al. 2013), using an Andor iXon 888 EM-CCD camera.
The OSMOS spectroscopic target acquisition procedure requires at least one direct exposure to place the slit on the target. We took these through a Sloan g filter, and developed an automated program to infer the target's g magnitude. The script detects the stars in the image, matches them to entries in the the PAN-STARRS 1 Data Release 2 catalog, performs aperture photometry, establishes the offset between the instrumental magnitude and the catalogued g, and from this infers the g magnitude of the target just before the spectra were taken. Because the offset between instrumental and catalogued magnitude is common to the program and field stars, the procedure is differential. Given adequate signal-to-noise, it is accurate even in thin clouds and poor seeing.

Gaia18aot
This source was listed in the Gaia Transient Alerts on 2018 March 07, with an alerting magnitude of 17.32. Its Gaia light curve shows irregular fluctuations, mostly between 18th and 19th magnitude, but sometimes fainter than 20th. The Catalina Real Time Survey Data Release 2 light curve is similar, but also shows a brief flare on 2007 Nov. 02 that reaches 16.0.
Most of our spectra are from 2018 September. The mean spectrum ( Fig. 1) shows the strong emission in the Balmer, He I, and He II lines characteristic of magnetic CVs. The emission line velocities vary with P ∼ 114 min, in a non-sinusoidal pattern ( Fig. 1. We obtained some velocities in 2018 November, 2018 December, and 2019 January. Combining these, we found P = 0.078830(2) d, with no ambiguity in cycle count.
On the same observing runs, we obtained multiple orbits of time-series photometry, which are summarized in Fig. 2. The object remained in a similar photometric state through all our runs, and showed modulation at the orbital period, most notably a rapid decrease in flux around phase 0.2 in the radial-velocity ephemeris, and a more gradual recovery around phase 0.7. The small scatter of the phase of the rapid decrease over multiple observing runs corroborates the already-secure choice of cycle count.    . Photometry of Gaia18aot from seven nights spread over four observing runs. The data are folded on the spectroscopic orbital period, but with a new zero in phase defined for each night so as to maintain time ordering through the night. Phase zero corresponds to blue-to-red crossing of the radial velocity. The earliest data are at the top, and each night's data is offset downward by 1 magnitude, as indicated in the legend. The vertical scale is correct for the lowermost trace. The large squares, from OSMOS setup images, were taken with a g filter; the rest of the data are essentially white-light, but adjusted to approximate g using the PAN-STARRS 1 magnitude of the comparison star.

PT Per
Herschel Telescope on three successive nights in 2015 April, at airmass > 3, and in evening twilight, which showed no strong emission or absorption features, but did show weak, Zeeman-split absorption at Hα and Hβ, consistent with a magnetic field of ∼ 25 MG. They suggested that PT Per is a polar, and that their optical spectra were taken in a low state. Their observations indicated a relatively small distance, perhaps as nearby as 90 pc, and indeed its Gaia DR2 distance of 1/π = 185(+5, −4) pc makes in the closest object studied here. In 2019 January, we found PT Per in a much more active state and obtained spectra with OSMOS on two successive nights. The spectrum (Fig. 3, top) showed strong emission lines, in contrast to the Watson et al. (2016) spectra. Large, rapid radial velocity shifts were immediately apparent; an analysis of the two nights' velocities gives a period P = 81.00(4) min, with no cycle-count ambiguity, in reasonable agreement with the 81.7(4) min period found by Watson et al. (2016). The phase-resolved spectra in the middle panel of Fig. 3 shows the large velocity shifts, as well as the asymmetric line wings characteristic of AM Her stars. Large blue-shifted velocity excursions are also seen, near phase ∼0.7, typical of polars. The Hα radial velocities (lower panel) are modulated almost sinusoidally. The velocity half-amplitude, K = 340 ± 14 km s −1 , is much too large to be plausibly orbital, so the infall velocity of the accretion column causes most of the velocity shift.
The high-state data amply confirm that PT Per is an AM Her star, as suggested by Watson et al. (2016). They note that their optical data were taken in a remarkably low state, with no clear emission lines, whereas most AM Her stars continue to show some emission lines even in very low states.
On 2019 Jan 21 and 22, we used the 1.3 m telescope and Andor camera to obtain the time-series photometry shown in Fig. 4. The light curve shows with two maxima per orbit, along with some flickering. There is no sign of an eclipse, so the correspondence between the orbital phase plotted and the locations of the stars in their orbits is not constrained. The double-humped light curve indicates that accretion likely occurs onto two poles.
3.3. RX J0636.3+6554 Appenzeller et al. (1998) discovered this star as the optical counterpart of a ROSAT X-ray source; they noted it was blue, variable on a timescale of hours, and that one of their spectra showed broad Hα emission at rest velocity. It was listed in the Downes et al. (2001) catalog, but apparently no follow-up studies have appeared. The CRTS Data Release 2 light curve (Drake et al. 2009) shows short term variation of about 1 magnitude superposed on a gradual decline from ∼ 17.6 mag in 2006 to about 20.0 mag in 2013.
We took spectra of this star in 2018 February. The mean spectrum (Fig. 5, top panel) shows strong emission lines on a blue continuum, with He II λ4686 nearly as strong as Hβ. Passing the fluxed spectrum through the V response function tabulated by Bessell (1990) gives V ∼ 17.9, so we caught the system in a relatively bright state. The emission lines immediately showed large velocity swings on a period just over 100 min (Fig. 5, middle and lower panels).
The star disappeared from time to time during the spectroscopy, so we obtained time-series photometry on the same observing run (see Fig.6). This showed eclipses ∼ 2 mag deep and lasting ∼6 min on a ∼ 103 min period, as well as out-of-eclipse flickering. Over the last two years we have observed 23 eclipses, including two that were generously observed by Karolina Bąkowska in 2018 April. Table 2 gives the times of eclipse center, along with the cycle count and residuals from the best linear ephemeris, which is BJD mid-eclipse = 2458174.62129(5) + 0.071221298(9). (1) where E is an integer eclipse number and the time base is UTC. Nearly all our time-series photometry was relative to a star ∼ 81 arcsec from the program object in position angle ∼ 63 • , for which Gaia DR2 lists α = 6:36:34.75 and δ =+65:54:51.7. The PAN-STARRS data release 2 gives gives g PSF = 17.07 for this star, which we added to our differential magnitudes. During our 2018 February and April observations , the out-of-eclipse magnitude averaged g ∼ 18.1, while for all our other time-series photometry it was much fainter at ∼ 20.1. Fig. 7 shows the brighter-and fainter-state eclipse light curves in greater detail. In both the brighter and fainter states, the egress is sharply defined and occurs at a very consistent phase. Our exposures (typically 20 sec) do not resolve the sharp rise in egress. In the fainter state, the ingress is also very consistent, but in the brighter state there is significant dispersion in the ingress phase. This suggests that in the bright state, a significant source of light lags behind the trailing side of the white dwarf; a natural candidate for this would be an accretion stream that fades away during the faint state. In some light curves, the ingress starts slightly earlier than in others, suggesting an extra source of obscuration, which might be the outermost parts of the accretion stream.
We also note that in the bright-state egress, following the initial rapid rise, the object consistently undergoes a slower, steady brightening. This may be explained by the gradual uncovering of the inner part of the magnetically threaded accretion stream.
The eclipse in the fainter state appears to be that of the white dwarf alone, and we conservatively estimate the full width as 412 ± 8 seconds. If the secondary star fills its Roche lobe, this implies a minimum q = M 2 /M WD of 0.11 to 0.13 for an edge-on orbit (Chanan et al. 1976). In non-magnetic systems, the relationship between P orb and q has been calibrated at short periods (see e.g. Patterson 2011); dwarf novae at this period have q < 0.2, which if applicable here implies an upper limit for i of ∼ 83 • . Assuming an implausibly large q = 1 gives i ∼ 73 • .
Taking 90 • ≤ i < 83 • constrains the dynamically important quantity sin 3 i to an accuracy of better than 3 per cent, so if we did have a reliable measurement of the secondary's velocity amplitude K 2 , we could in principle determine M WD quite accurately. Although the secondary is likely to be extremely faint, similar systems often have a strong, narrow component in their emission line profiles that arises on the side of the secondary facing the white dwarf. Our spectroscopy shows a hint of this, but at our spectral resolution it is not cleanly defined, so we are unable to draw any useful conclusions.  . Photometry of PT Per from two successive nights. The phase is treated as in Fig. 2. Phase zero corresponds to blue-to-red crossing of the radial velocity. No vertical offset is applied. The large squares, from OSMOS setup images, were taken with a g filter; the time-series points were taken almost unfiltered and were adjusted to agree with the calibrated OSMOS magnitudes obtained simultaneously.
This object (abbreviated CSS0812+04) was detected in 2008 by the Catalina sky survey at a magnitude of 18.8, and listed as an eclipsing CV with a Sloan Digital Sky Survey (SDSS) magnitude of 22.4. However, the PAN-STARRS 1 survey consistently detects it with 18.0 < g < 19.1, suggesting that SDSS caught it in a state of low mass transfer. We selected this object in 2014 for further photometric and spectroscopic studies after it was identified by one of us, MM, as a candidate polar based on its long-term CRTS light curve; this is part of a study to identify candidate polars based on long-term photometric behavior. Independently, Oliveira et al. (2020) obtained a survey spectrum and classified it as a magnetic system.
Our mean spectrum from 2017 March (Fig. 8) shows strong He II λ4686 emission, and also emission at λ 5411, which are typical of magnetic CVs. Four additional spectra were taken with the Robert Stobie Spectrograph (RSS) (RSS; Burgh et al. 2003;Kobulnicky et al. 2003;Smith et al. 2006) on the Southern African Large Telescope (SALT; Buckley et al. 2006) on 4 & 5 January, 10 February and 1 March 2016. The RSS was used in long-slit spectroscopy mode with a slit width 1.5". The PG900 VPH grating was used, set to an incidence angle of 14.75 • , giving a spectral coverage of 4060-7100 and a mean resolution of 5.7 Å. On each night, 2×690 s exposures were taken. The wavelength calibration was done using Ar lamp exposures taken immediately following the observations and relative flux calibration was achieved using standard stars LTT 377 and LTT 4364, depending the night of observation. The SALT spectra are shown in Fig. 9.  Note-Observed times of mid-eclipse. The first column gives the eclipse number E, and the second the barycentric julian date minus 2 450 000., on the UTC system. The penultimate column gives the residual compared to the best-fit linear ephemeris (eqn. 1), and the last the calendar date in UT.
Radial velocities taken over two nights gave P = 162.0 ± 0.3 min. The velocity half-amplitude K = 131 ± 14 km s −1 is much smaller than expected for an AM Her star. Fig. 10 shows a sampling of our time-series photometry. Many of our light curves show a very short dip, resembling a partial eclipse. This feature appeared insignificant until we found the spectroscopic period, which made it evident that dips on successive nights were separated by integer multiples of the orbital period. We were able to connect dips found in 2014, 2017, and 2019 with a unique ephemeris, BJD sharp dip = 2457844.6379(2) + 0.11241902(2)E, which we take to be orbital; Table 3 gives the observed dip times and their assigned cycle numbers. In many light curves, a broader minimum occurs shortly before the dip. The phase of this decline is consistent to better than ∼ 0.05 cycle, which corroborates our choice of period. . Differential photometry of RX J0636.3+6554 on four nights during the brighter state, folded on the best-fit linear ephemeris (eqn. 1). The curves are offset vertically by 3 mag. The data were taken with a UV cutoff filter only; the g magnitude of the reference star has been added to convert to a rough g magnitude. Fig. 11 is a close-up view of the dip, with data from 13 nights plotted. The dip appears to be stable in phase, about 250 seconds wide, and typically about 0.6 mag deep. Its consistency suggests it is caused by a grazing eclipse of the bright accretion column by the secondary star. A compact accretion column disappearing momentarily over the limb of a rotating white dwarf might, in principle, mimic the dip's appearance, but such events tend to have more gradual ingresses and egresses, and not to be as consistent.

SDSS J100516.61+694136.5
Wils et al. (2010) discovered this object (hereafter SDSS1005+69) by mining data from SDSS, Galaxy Evolution Explorer (GALEX), and various astrometric catalogs for dwarf nova candidates. They noted strong emission lines, including He II λ4686 comparable to Hβ, in the SDSS spectrum, and suggested that it is a magnetic CV, varying from 17.9 through 21.2 mag.
We obtained single spectra in 2012 January and 2015 April, but did not find the system bright enough to study. We enjoyed better luck in 2018 February and March and obtained spectra on three nights. The top panel of Fig. 12 shows the mean spectrum, which includes the He II emission characteristic of magnetic CVs. The Hα emission line velocities are strongly modulated at an unambiguous period of 218.6(4) min; the modulation is non-sinusoidal with a rapid rise and a more gradual decline in each cycle. The phase used in the lower panel of Fig. 12 is based on a sinusoidal fit to the velocity data, and is essentially arbitrary. Using the 1.3m telescope, we obtained time-series photometry   Note-Observed times of the sharp dip. The first column gives the dip number E, and the second the barycentric julian date minus 2 450 000., on the UTC system. The penultimate column lists the residual compared to the best-fit linear ephemeris (eqn. 2), and the last gives the UT date. contemporaneous with our 2018 spectroscopy, and also on two nights in 2020 January (see Fig. 13). The comparison star was at α = 10 h 05 m 14 s .34, δ = +69 • 43 23 .4, 108 arcsec from, and almost due north of, the target; the PS1 DR2 lists g = 15.53, r = 14.98 for this star. The light curves show a rise starting around phase zero, and a slower decline, but no definite eclipse. The spectroscopic orbital period is not precise enough to specify phase for the 2020 data; to prepare the figure, we assumed the minimum around phase zero is stable in phase and adjusted the period slightly to force its phase to align with the 2018 data.
For the light curves taken on 26 February and 1 March 2018 (top panel of Fig. 13), we see evidence of possibly periodic fluctuations on a ∼800 s timescales. We therefore produced periodograms of the 2018 light curves using Gatspy, a Python implementation of the Lomb-Scargle method (VanderPlas & Ivezić 2015). The results are shown in Fig. 14, which clearly show period peaks at 810 s and 771 s, respectively, both of which have formal false-alarm probabilities below 1 per cent. In addition, the periodogram of the four combined nights clearly shows the presence of the orbital period and its harmonic (Fig. 15). The fact that the two shorter period peaks are not separated by the orbital frequency would seem to rule out an intermediate polar interpretation, where the two frequencies could be due to the beat and spin modulations, respectively. We therefore conclude that the system probably exhibits quasi-periodic variability from time to time.
The photometric variations seen in polars have variously been characterized as flickering, fluctuations and sometimes quasi-periodic oscillations (QPOs). The latter are variations that show some degree of coherence over a number of cycles of the QPO period. The discovery of ∼Hz frequency QPOs in the visible light of polars is now over 30 years old (e.g. Middleditch 1982), and at the time resulted in a flurry of theoretical studies. The commonly held understanding is that they are due to plasma oscillations in the magnetically confined accretion columns. Until recently, only five systems were known to exhibit such QPOs, with the sixth (V379 Tel) being the only discovery in over two decades, despite attempts to find more examples (Breytenbach, H. et al., in preparation). Longer period QPOs were also seen in AM Her (Bonnet-Bidaud et al. 1991), at 250−280s, while more recently a ∼320 s QPO was detected in IGR J14536-5522 5.4 (Potter et al. 2010). The origin of these longer period QPOs is still debated, with proposed sites suggested near the L1 point (King 1989), the stream coupling region or within the magnetically confined flow, close to the white dwarf surface (Bonnet-Bidaud et al. 1991).
In polars the QPOs seem to occur with typically a few seconds period (accretion column oscillations), or with periods of many minutes. The latter are larger amplitude and are quite a common feature of polars, often seen by eye in the lightcurves, as seems to be the case for SDSS J100516.61+694136.5 (see Fig. 13), where they can appear to show some sort of coherence, but are not necessarily obvious in power spectra; they are often referred to as "QPO-like" (Potter et al. 2010).
3.6. SDSS J133309.20+143706.9 Schmidt et al. (2008) published time-series spectroscopy and polarimetry of this object not long after it was discovered in SDSS. The detection of circular polarization firmly established it as an AM Her star. The radial velocities of Hα varied with K ∼ 250 km s −1 on a period of 2.2 ± 0.1 hr. Southworth et al. (2015) obtained time-series photometry on three nights, but were unable to improve on the period.
On 5 consecutive nights in 2016 February, we obtained time series photometry with the 1.3m and Andor camera. The light curves (Fig. 16) consistently show a flat-topped brightening that recurs on a period of 0.08814(4) d, or 126.92(6) min, consistent with the radial-velocity period found by Schmidt et al. (2008). The daily cycle count is unambiguous.
We also have time series from 2016 June 10 and from 2017 June 21 and 22. The 2016 June time series shows a brightening toward the end that is similar to those seen in the other light curves, but does not cover the decline. The 2017 June light curves show clearly-defined brightenings similar to the others. Only one choice of long-term cycle count fits all the brightening ingress times comfortably, and it implies BJD of brightening = 2457434.8817(4) + 0.0881118(3)E (provisional). ( We label this as provisional because of the lack of redundant timings on the longer baselines; the less precise value from 2016 February is firmly established. One reason for caution is that the three brightenings seen in the Southworth et al. (2015) arrive early in this ephemeris by ∼ 25 min, in contrast to the MDM timings, which all align to better than 2 min. 3.7. SDSS J134441.83+204408.3 Szkody et al. (2011) found this object (hereafter SDSS1344+20) in the SDSS data and noted its apparently magnetic nature. In a short series of spectra, they found the radial velocities of Hα and Hβ varying on a period of ∼ 115 min, with semi-amplitudes K ∼ 400 km s −1 . Szkody et al. (2014) present further observations, including photometry and spectroscopy showing changes of photometric state.
We observed this star most intensively in 2016 February and March. In the mean spectrum (Fig. 17), He II λ4686 is less prominent that usual in AM Her stars, about half the strength of Hβ. The continuum is strong and blue. Hot continua usually show a smooth upward sweep toward the blue; this continuum may have a very broad hump from ∼ 5100−5700Å. If real, this might be a cyclotron feature.
As Szkody et al. (2011) found, the radial velocities of Hα are strongly modulated, and with our more extensive data set we determine P orb = 101.652(6) min. The cycle count between nights and between the two observing runs is unambiguous; the relatively small uncertainty reflects the 21-day span of the time series. Figure 18 shows light curves taken on three different observing runs; the spectroscopic ephemeris used to compute the phases is only valid for the 2016 February data, so the phases in the top and bottom panels are arbitrary. Not all the runs used the same comparison stars, but the magnitude scales have been adjusted using the different stars' r magnitudes from PAN-STARRS. No periodic behavior is evident, though the intervals of rapid fluctuation seen in the middle panel are both centered on a brief interval before phase zero. We speculate that the V-shaped ∼0.5 magnitude dips seen near phase zero in the 2016 data, when the object was brighter than for the other observations, could be a partial grazing eclipses of an accretion hot-spot. The data from 2018-02-26 shows a brightening by ∼ 2 mag over less than one orbit; note that Szkody et al. (2014)     . Light curves of SDSS1333+14 from three observing runs. The differential magnitudes have been adjusted using the r magnitudes of the comparison stars. The lowermost trace is plotted without a vertical offset, and successive trace above it are offset upward by 1.5 mag, as indicated by the color-coded tick marks on the left. The ephemeris used to compute phases is provisional, and is the epoch of the ingress into the bright phase.

Gaia18aya
The Gaia light curve for this source shows it varying between 18 and 19 mag, except for a few days in 2018 April when it triggered an alert at a magnitude of 17.52, and a pair of detections at 17.27 on 2018 May 25.
The mean spectrum (Fig. 19) shows the usual emission lines, but the most striking feature is a cyclotron emission harmonic centered around ∼ 5500 Å. The cyclotron harmonic clinches the AM Her classification. The Hα radial velocities from 2018 September establish an unambiguous orbital period near 120 min. We obtained more observations in 2018 November, December, and January which constrain the period uniquely to 120.165(3) min.
The cyclotron emission hump varies in strength with the orbital period. This can be seen in Fig. 20, which is similar to the middle panel of Fig. 19 but with wider wavelength range. In both these figures the spectra were not rectified (normalized to a continuum) before being averaged and stacked; rather, flux-calibrated spectra were used, so variations in flux can be seen. Fig. 21 shows time series photometry. During 2018 September, the variation is irregular without obvious periodicity, but in 2018 November the source was somewhat brighter and varied smoothly with the orbital period.
The wavelength of the nth cyclotron harmonic is  Figure 18. Light curves of SDSS1344+20 from three observing runs. The differential magnitudes have been adjusted using the r magnitudes of the comparison stars. The lower trace (red) in the lower panel is plotted without a vertical offset, and the upper trace (blue) is offset upward by 1.0 mag. The ephemeris used to compute phase is given in the axis label, but it is only valid for the middle panel, which was contemporaneous with the spectroscopy.
where B 8 is the magnetic field in units of 10 8 Gauss (10 4 Tesla). The ∼ 5500 Å feature is the only harmonic we clearly observe, which implies that the allowable magnetic fields for different assumed cyclotron harmonics in the range n = 2−7, varies from 28−97 MG. If the cyclotron feature at ∼5500 Å is associated with the n = 6 (32 MG) or 7 (28 MG) harmonic, this implies that the shorter and longer wavelength harmonics at n ± 1 ( ∼4800 and ∼4700 Å and ∼6400 and ∼6600 Å respectively) should be detectable in our spectra. For n = 5 (B = 39 MG), we should also see the n = 4 harmonic at ∼6900 Å. The fact that we see no other cyclotron features corresponding to these wavelengths is evidence that n < 5. If we take n = 4, then the neighbouring harmonics should occurs at ∼4400 Å (n = 5) and ∼7300 Å (n = 3), respectively. From Fig. 19 (top panel) we see the flux increases from ∼7000 Å to the red limit, at 7400 Å consistent with a broad cyclotron line at ∼7300Å. Similarly, the flux also increases for wavelengths ≤4900, to the blue limit of our spectra, at 4550 Å also consistent with the expected cyclotron line at ∼4400 Å. So this is all consistent with identifying the clearly observed hump at ∼5500 Å with the n = 4 cyclotron harmonic from a B = 49 MG magnetic white dwarf. Lower harmonics, at n = 2 or 3, are also admittable, with higher field strengths, though the n ± 1 harmonics are now well outside the wavelength range of our spectra. A good far-red or near-infrared spectrum could help determine the field strength by clearly identifying the lower harmnonics and allowing for subtraction of the underlying secondary star flux, which is likely an M-type star given the ∼2 h orbital period.
4. CONCLUSIONS Figure 22 shows a histogram of the orbital periods of AM Her stars listed in the final release (version 7.24) of the Ritter & Kolb (2003) catalog of cataclysmic binaries. The periods of the stars discussed here are also indicated. They all have periods typical of the population. Table 4 summarizes our findings. We classify three objects (Gaia18aot, RX J0636.3+6554, and Gaia18aya) as AM Her stars for the first time; the two Gaia sources are also newly-recognized as CVs. For six of the objects we determine P orb for the first time, and for two more (PT Per and SDSS1344+20) we improve significantly on previous period determinations. We confirm that PT Per is a magnetic CV, as Watson et al. (2016) suggested.
Three of our objects have especially interesting light curves. RX J0636.5+6554 eclipses deeply. CSS0812+04 shows a sharp dip that is stable in phase and appears to be a partial eclipse. Finally, SDSS1333+14 persistently shows a distinctive bump consistent the the appearance of an otherwise self-occulted accretion spot.
The spectrum of Gaia18aya has an apparent cyclotron emission hump near 5500 Å, which constrains the magnetic field to be greater than ∼ 49 MG.
It is worth noting that magnetic CVs appear to be underrepresented in various listings. Pala et al. (2020) constructed a volume-limited sample of 42 CVs within 150 pc, as judged by Gaia DR2 parallaxes, and found that over 30 per cent were magnetic, and that 11 out of the 42 in the total sample were polars, including the prototypical polar, AM Her. High-cadence synoptic sky surveys have found very large numbers of new CVS (see, e.g. Breedt et al. 2014), but they are clearly biased toward dwarf novae, which show distinct, large amplitude outbursts. The objects in this paper no doubt represent a very sizeable population of more subtly variable AM Her stars, as yet unrecognized.   (6) · · · · · · New per., firm 0.0881118 (2) 57434.8818(4) · · · · · · Provisional SDSS J134441.83+204408.3 Spec. 0.070592(4) 57456.8785 (7) 273(17) −50(12) Improved per.

38(8) New CV
Note-A summary of the measurements presented here. Sinusoids, where fitted, are of the form v(t) = γ + K sin 2π(t − T0)/P . Epochs are barycentric Julian dates minus 2,400,000., in the UTC time system; these can be converted to TDB with sufficient accuracy by adding 69 s. a Non-sinusoidal velocity curve; parameters are formal best fits only.