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Analysis of Pulsating Subdwarf B Stars from NASA's K2 Campaign 7

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Analysis of Pulsating Subdwarf B Stars from NASA's K2 Campaign 7 Analysis of pulsating Subdwarf B Stars from NASA’s K2 Campaign 7 Alyssa Slayton Department of Physics, Astronomy, and Materials Science Missouri State University Advisor: Dr. Mike Reed Abstract Asteroseismology is the study of stars using vibrations (pulsations). There are two types of pulsations: pressure modes (p-modes) and gravity modes (g-modes). P-modes have a much higher frequency and come from the outer regions of the star. G-modes have a lower frequency and come from the star’s core. All of the data used was collected using the seventh field of the extended mission of NASA’s Kepler Space Telescope (K2), of which we observed 9 subdwarf B (sdB) stars of which four were discovered to be pulsators. Introduction NASA’s Kepler Space Telescope orbits the Sun directly in an Earth-trailing orbit. Originally it pointed perpendicular to its orbit, but after failures in two reaction wheels, it began its second mission, known as K2. During K2, the telescope points parallel to its orbit and uses solar pressure for a force along a third axis. However the telescope is not perfectly balanced in this third axis and so pointing drifts with time and needs to be restored by firing thrusters. Thrusters are only fired at intervals of six hours, so any signal introduced has a known period. Overall, the stellar drift is less than one pixel, but because pixels cannot be recalibrated in space, the aging CCD imager now has significant pixel-to-pixel variations. For additional information about the Kepler program, see Matt Yeager’s paper in these proceedings. Campaign 7 of K2 took place between October 4, 2015 and December 26, 2015. At the beginning of the campaign, communication was switched to an alternate antenna which caused the roll drift to increase, adversely affecting data that was being taken. This was apparent in our data as discontinuities in the beginning of the lightcurve of each star from field 7 (F7 star). We applied for nine prospective pulsating stars and all were observed in short cadence mode, which obtains a new image every 58 seconds. For the purposes of analyzing sdBV (subdwarf B Variable) stars, short cadence data has been found to be optimal as pulsations can occur even near to that period. Of the nine stars observed from our proposal, only 4 were found to be variable. Data Processing Each star in this campaign was processed in two different ways. The first method is using Pyraf software and is referred to as the “PyKE” method. The other is a custom method developed by our collaboration, mostly by Dr. Andrzej Baran. Our custom method uses IRAF and is an improvement over PyKE as it allows custom apertures which can drift along with the stars, to better decorrelate pixel sensitivity. Our custom method is vastly superior to the PyKE processing and so all our analyses use our custom method and not the PyKE processing. F7 STARS 2 Pulsating Stars Star light only leaves the surface of stars, and so analogous to Earth seismologists, we use stellar vibrations to probe stellar interiors. There are two types of these vibrations or pulsations: g- modes and p-modes1. P-modes are also referred to as pressure modes and are caused by pressure waves. They are formed in the outer regions of the star and have periods of a few minutes. G- modes (gravity modes) are formed deeper and have periods up to several hours. They are caused by buoyancy within the star. Sometimes a pulsation will be split into several closely-spaced peaks called multiplets. Multiplets are caused by stellar rotation and each peak represents slightly different stellar geometry and the separation indicates how fast a star is spinning. To analyze pulsations and look for multiplets, a Fourier transform (FT) is created. An FT shows which frequencies have the highest amplitudes, indicating the presence of a pulsation. The frequency of each pulsation is noted and used to calculate the period (inverse frequency). For a complete discussion, see the paper of Matt Yeager, these proceedings. In addition to our K2 data, spectroscopic observations were obtained at the Nordic Optical Telescope by our collaborator Dr. John Telting and effective temperatures and gravities were determined using model fits by our collaborator Dr. Roy Ostensen. The average sequence for gmode l=1 period spacing has been determined to be about 250 seconds2 and the spacing for the l=2 sequence is that result divided by the square root of 3. Campaign 7 Stars No multiplets were identified in campaign 7, so rotation velocities were unable to be determined. An echelle diagram plots the period of a star versus the modulus of the period and the identified mode sequence should make a nearly vertical line. Mode identifications represent the number a certain period is in the sequence (the relative radial node of pulsation). J19416-2333 J19416-2333 has a temperature of 27860K and a surface gravity of 5.45dex (cgs). F7 STARS 3 Figure 1. Fourier Transform of J19416-2333. G-mode pulsations can be seen on the left. Number Frequency (μz) Period (s) Mode (l=1) Mode (l=2) 1 110.400 9057.971 43 70 2 136.603 7320.483 36 58 3 197.032 5075.318 27 42 4 214.556 4660.788 39 5 221.306 4518.630 38 6 258.640 3866.378 22 7 348.721 2867.622 18 8 372.877 2681.850 17 25 9 390.702 2559.495 10 419.79 2382.143 16 23 11 1005.770 994.263 13 Table 1. A list of detected pulsations in J19416-2333. From left to right: Pulsation ID, frequency, period (1/frequency), relative radial order in l=1 sequence, relative radial order in l=2 sequence. No multiplets were found in this star. The asymptotic sequence was not obvious at first but was eventually found to be 245.43 seconds for l=1 and 141.70 seconds for l=2. This is consistent with other sdBV stars. F7 STARS 4 J19155–2051 The the temperature of J19155-2051 is 22770K and the surface gravity is 5.01dex. J19155-2051 is the only star in the seventh campaign that has p-modes. There are only 3 and so no sequence was discernable. Figure 2. Fourier Transform of J19155–2051. G-mode pulsations can be seen to the left and p-mode pulsations can be seen to the right, reflected by the nyquist. Number Frequency (μz) Period (s) Mode (l=1) Mode (l=2) 1 60.425 16549.387 62 110 2 65.288 15316.774 57 102 3 75.454 13253.038 49 4 86.558 11552.987 42 76 5 147.652 6772.682 23 6 156.544 6387.980 40 7 161.638 6186.664 8 285.743 3499.648 10 20 9 7876.390 10 7879.890 11 7930.700 Table 2. A list of detected pulsations in J19155–2051. From left to right: Pulsation ID, frequency, period (1/frequency), relative radial overtone for the l=1 sequence, relative radial overtone for the l=2 sequence. F7 STARS 5 No multiplets were found in this star. The asymptotic sequence was not obvious at first but was eventually found to be 250.92 for l=1 and 144.87 for l=2. This is consistent with other sdBV stars. J19348–1855 The temperature of J19348-1855 was found to be 28160K and the surface gravity 5.44 dex. J19348-1855 is the richest pulsator of the stars from field 7, though no multiplets were found. Figure 3. Fourier Transform of J19348–1855. G-mode pulsations can be seen to the left. Number Frequency (μz) Period (s) Mode (l=1) Mode (l=2) 1 119.945 8337.142 32 56 2 127.638 7834.659 30 3 136.773 7311.392 49 4 141.552 4064.527 27 5 152.926 6539.126 25 44 6 159.091 6285.717 24 42 7 165.698 6035.081 23 8 172.580 5794.428 22 39 9 178.679 5596.613 10 181.005 5524.698 21 37 11 188.826 5295.884 20 F7 STARS 6 12 209.051 4783.531 18 32 13 221.076 4523.339 17 30 14 236.030 4236.755 28 15 244.820 4084.631 27 16 249.782 4003.483 15 17 254.659 3926.817 26 18 264.374 3782.514 14 25 19 267.029 3744.915 14 20 275.184 3633.935 24 22 278.543 3590.104 23 283.244 3530.522 13 24 286.534 3489.982 23 25 289.181 3458.040 26 313.565 3189.135 21 27 326.205 3065.556 20 28 330.446 3026.212 11 20 30 342.134 2922.829 19 31 360.526 2773.728 10 18 32 377.650 2647.951 33 424.882 2353.594 15 34 472.046 2118.438 35 541.427 1846.970 36 613.733 1629.373 10 37 651.577 1534.738 39 661.036 1512.777 5 40 708.144 1412.142 41 802.573 1245.992 4 F7 STARS 7 Table 3. A list of detected pulsations in J19348–1855. From left to right: Pulsation ID, frequency, period (1/frequency), relative radial overtone of the l=1 sequence, and relative radial overtone of the l=2 sequence. J19348-1855 has a very strong l=1 sequence at 256.28 with a l=2 sequence of 146.13. This is consistent with other sdBV stars. J1937-1817 The temperature of J1937-1817 is 24470K and the surface gravity is 5.17 dex.
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