document: white dwarf ( wd ) stars represent the end points of stellar evolution for all low - mass stars , and are the fate of more than 97% of all stars in our galaxy . 
   roughly 80% of wds belong to the spectral class da , with atmospheres characteristically dominated by hydrogen @xcite . when da wds cool to the appropriate temperature to foster a hydrogen partial ionization zone , they begin their journey through the zz ceti ( or dav ) instability strip , where global pulsations are driven to observable amplitudes and their fundamental parameters can be determined using asteroseismology ( see reviews by @xcite , @xcite and @xcite ) .    aside from their variability , the zz ceti stars discovered to date appear to be otherwise normal wds , and are therefore believed to be a natural phase in the evolution of all das . although some das within the empirical instability strip have been observed not to vary to modest limits ( e.g. , @xcite ) , follow - up observations have shown that some of these stars really do pulsate at low amplitude ( e.g. , @xcite ) . 
   higher - quality optical and uv spectra have also moved some of these non - variable interlopers out of the instability strip @xcite . 
   thus , it is currently believed that the zz ceti instability strip is pure , and that all da wds will at some point pass through it and pulsate @xcite . 
   much work has been devoted to observationally mapping the zz ceti instability strip , which runs in temperature from roughly @xmath11 k for standard @xmath4  = 8.0 wds @xcite . 
   there is also a dependence on surface gravity , such that wds with lower @xmath4  pulsate at lower effective temperatures . 
   this trend has been observed for wds with masses from 1.1 @xmath1  down to 0.5 @xmath1  @xcite . 
   the blue edge of the zz ceti instability strip , where pulsations are turning on , has been successfully estimated by both convective period arguments @xcite and full non - adiabatic calculations @xcite . 
   a slightly more efficient prescription for convection has to be assumed , by increasing the value of the mixing - length theory parameter ml2/@xmath12 , to make the theory match the observed blue edge , which was most recently mapped empirically by @xcite . 
   however , estimating the temperature at which pulsations should shut down has remained a challenge . 
   modern non - adiabatic calculations do not predict a red edge until around 5600 k @xcite , more than 5000 k cooler than the empirical red edge @xcite . 
   @xcite argue that a surface reflection criterion can be enforced to limit the maximum mode period , which may push a theoretical red edge to hotter temperatures , nearer what is observed in zz ceti stars @xcite . 
   the recent discovery of pulsating extremely low - mass ( elm , @xmath13 0.25 @xmath1 ) wds provides us with an exciting new opportunity to explore the nature of the physics of wd pulsations at cooler temperatures and much lower masses . since the first discovery by @xcite , more than 160 zz ceti stars have been found , all of which have masses @xmath14 0.5 @xmath1  and thus likely harbor carbon - oxygen ( co ) cores . that changed with the discovery of the first three pulsating elm wds @xcite . 
   these elm wds are likely the product of binary evolution , since the galaxy is not old enough to produce such low - mass wds through single - star evolution @xcite . during a common - envelope phase , 
   the elm wds were most likely stripped of enough mass to prevent helium ignition , suggesting they harbor he cores . 
   the pulsating elm wds will be incredibly useful in constraining the interior composition , hydrogen - layer mass , overall mass , rotation rate , and the behavior of convection in these low - mass wds , which may derive a majority of their luminosities from stable hydrogen burning for the lowest - mass objects @xcite . 
   several groups have recently investigated the pulsation properties of he - core wds , and non - adiabatic calculations have shown that non - radial @xmath15- and @xmath10-modes should be unstable and thus observable in these objects @xcite . 
   pulsating elm wds will also extend our empirical studies of the zz ceti instability strip to significantly lower surface gravities .    boosted by the many new elm wds catalogued by the elm survey , a targeted spectroscopic search for elm wds @xcite , we have looked for additional pulsating elm wds throughout a large part of parameter space . 
   the first three pulsating elm wds all have effective temperatures below @xmath16 k , much cooler than any previously known co - core zz ceti star @xcite , which makes up the coolest class of pulsating wds . 
   we now add to that list the two coolest pulsating wds ever found , sdss  j161431.28 + 191219.4 ( @xmath17 mag , hereafter j1614 ) and sdss  j222859.93 + 362359.6 ( @xmath18 mag , hereafter j2228 ) , bringing to five the number of elm wds known to pulsate . 
   in section  [ sec : j1614 ] we detail our discovery of pulsations in j1614 and outline our new spectroscopic observations of this elm wd . in section  [ sec : j2228 ] 
   we describe the discovery of multi - periodic variability in the elm wd j2228 and update its determined atmospheric parameters . 
   we conclude with a discussion of these discoveries , and update the observed da wd instability strip . 
   @xcite found that j1614 had @xmath2  @xmath19 k and @xmath4  @xmath20 , based on a single spectrum of this @xmath17 mag wd from the flwo 1.5 m telescope using the fast spectrograph @xcite . 
   we have obtained an additional 51 spectra using the same instrument and setup . 
   we have co - added our spectroscopic observations to determine the atmospheric parameters of the elm wd j1614 ( figure  [ fig : j1614spec ] ) . 
   our observations cover a wavelength range from @xmath21  . 
   the model atmospheres used for this analysis are described at length in @xcite and employ the new stark broadening profiles from @xcite . 
   models where convective energy transport becomes important are computed using the ml2/@xmath12 = 0.8 prescription of the mixing - length theory ( see * ? ? ? 
   a discussion of our extension of these models to lower surface gravities and more details of our fitting method can be found in section 2.1.1 of @xcite . 
   our final fit to the phased and co - added spectrum of j1614 is shown in the top panel of figure  [ fig : j1614spec ] and yields @xmath2  @xmath3 k and @xmath4  @xmath5 . 
   this corresponds to a mass of @xmath60.20 @xmath1  using the he - core wd models of @xcite , if we assume the wd is in its final cooling stage . 
   the more recent models of @xcite predict a mass of 0.19 @xmath1  given the atmospheric parameters , which we adopt . 
   we have also performed our fit without using the low s / n lines h11@xmath22h12 , but this marginally affects our solution : using only the h@xmath23@xmath22h10 lines of the balmer series , we find @xmath2  @xmath24 k and @xmath4  @xmath25 . to remain consistent with our previous pulsating elm wd atmospheric determinations @xcite , we will include the h11@xmath22h12 lines in our adopted solution for j1614 . 
   @lcccc@ run & ut date & length & seeing & exp . 
   + & & ( hr ) & ( ) & ( s ) +   + a2690 & 2012 jun 21 & 2.6 & 1.7 & 5 + a2692 & 2012 jun 22 & 2.0 & 1.8 & 5 + a2695 & 2012 jun 23 & 3.7 & 1.2 & 5 + a2697 & 2012 jun 24 & 3.5 & 1.4 & 5 + a2699 & 2012 jun 25 & 3.6 & 1.3 & 5 +   + a2521 & 2011 nov 28 & 3.5 & 1.5 & 10 + a2524 & 2011 nov 29 & 1.6 & 2.5 & 10 + a2528 & 2011 nov 30 & 1.9 & 2.2 & 10 + a2707 & 2012 jul 13 & 2.3 & 1.1 & 5 + a2710 & 2012 sep 17 & 2.8 & 2.4 & 10 + a2719 & 2012 sep 20 & 6.4 & 1.6 & 15 + a2721 & 2012 sep 21 & 7.4 & 1.4 & 10 +      elm wds are typically found in close binary systems ; these companions are necessary to strip the progenitor of enough mass to form such a low - mass wd within the age of the universe @xcite . however , using the code of @xcite , we do not detect any significant radial velocity variability in our observations of j1614 . the r.m.s . 
   scatter gives us an upper limit on the rv semi - amplitude : @xmath26 km s@xmath27 . 
   the systemic velocity is @xmath28 km s@xmath27 . 
   we note that this non - detection does not require the lack of a companion to the elm wd in j1614 . 
   rather , the system may be inclined nearly face - on to our line of sight , or the companion may be a much cooler low - mass wd 
   . if the inclination is @xmath29 , which is more than 85% likely if the orientation of the system with respect to the earth is drawn from a random distribution , the companion has @xmath30 @xmath1  if the system has a 7 hr orbital period , the median for elm wd binaries in the elm survey @xcite . empirically , there are similarly low - mass wds in the elm survey with no significant radial velocity variability @xcite . 
   we obtained high - speed photometric observations of j1614 at the mcdonald observatory over five consecutive nights in 2012  june for a total of nearly 15.4 hr of coverage . 
   we used the argos instrument , a frame - transfer ccd mounted at the prime focus of the 2.1 m otto struve telescope @xcite , to obtain @xmath31 s exposures on j1614 . 
   a full journal of observations can be found in table  [ tab : jour ] . 
   observations were obtained through a 3 mm bg40 filter to reduce sky noise . 
   we performed weighted , circular , aperture photometry on the calibrated frames using the external iraf package @xmath32 written by antonio kanaan @xcite . 
   we divided the sky - subtracted light curves by the brightest comparison star in the field , sdss  j161433.39 + 191058.3 ( @xmath33 mag ) , to correct for transparency variations , and applied a timing correction to each observation to account for the motion of the earth around the barycenter of the solar system @xcite . 
   the top panel of figure  [ fig : j1614 ] shows a portion of a typical light curve for j1614 , obtained on 2012 june 23 , and includes the brightest comparison star in the field over the same period . 
   the bottom panel of this figure shows a fourier transform ( ft ) utilizing all @xmath34 light curve points collected thus far . 
   we display the 4@xmath35 significance line at the bottom of figure  [ fig : j1614 ] , calculated from the average amplitude , @xmath35 , of an ft within a 1000 @xmath36hz  region in steps of 200 @xmath36hz , after pre - whitening by the two highest - amplitude periodicities . 
   .frequency solution for sdss j161431.28 + 191219.4 [ tab : j1614freq ] [ cols="<,^,^,^,^ " , ]     we may compare the first five pulsating elm wds to the previously known zz ceti stars by placing them in a @xmath4@xmath2  diagram , shown in figure  [ fig : search ] . 
   doing so , we discover there are at least six elm wds with temperatures and surface gravities between the newfound pulsating elm wd j2228 and the other four known pulsating elm wds . 
   these non - variable elm wds have been observed extensively and do not show significant evidence of pulsations to at least 1% relative amplitude . 
   we have excellent limits on the lack of variability in four of these six , ruling out pulsations larger than 0.3% amplitude . 
   we have put limits on three of these new non - detections , detailed in table  [ tab : null ] . 
   we note that @xcite previously observed psr  1012 + 5307 , but we have put much more stringent limits on a lack of variability on this faint elm wd with 7 hr of observations in excellent conditions . 
   the other three interlopers have been detailed in previous studies . 
   sdss  j0822 + 2753 is a @xmath2  @xmath37 k , @xmath4  @xmath38 wd observed not to vary to 0.2% @xcite . 
   sdss  j1443 + 1509 is a @xmath2  @xmath39 k , @xmath4  @xmath40 wd with exquisite limits on lack of variability , to @xmath41% @xcite . finally , nltt  11748 is the @xmath2  @xmath42 k , @xmath4  @xmath43 primary wd in an eclipsing wd+wd binary @xcite . 
   it was shown by @xcite not to vary out of eclipse to above 0.5% . 
   we have obtained an additional 8 hr of photometry of nltt  11748 out of eclipse at mcdonald observatory and can independently rule out variability larger than 0.3% .    the discovery of pulsations in j2228 , which is considerably cooler than at least a half - dozen other photometrically constant elm wds , questions the purity of the instability strip for he - core wds and confuses the location of an empirical red edge . 
   however , there is no a priori reason to expect the elm wd instability strip to be pure , or for there to exist a connected low - mass extension of the classical co - core zz ceti instability strip ; evolution through a specific temperature - gravity region is not well established for the elm wds , and they may not all cool through the instability strip in as simple a manner as the co - core zz ceti stars . 
   in fact , some of these elm wds may indeed be in the throws of unstable hydrogen shell burning episodes ; they may not be cooling at all , but rather looping through the hr diagram prior to settling on a final cooling track ( e.g. , @xcite ) . 
   such excursions are not expected for co - core zz ceti stars , which are expected to monotonically cool through an observationally pure instability strip . 
   we have plotted the evolution of theoretical cooling tracks for several different wd masses through the effective temperatures and surface gravities in figure  [ fig : search ] . 
   we plot the 0.16 @xmath1 , 0.17 @xmath1 , 0.18 @xmath1 , 0.20 @xmath1 , 0.25 @xmath1 , and 0.35 @xmath1  he - core models of @xcite as dotted magenta lines . 
   we have also used the stellar evolution code mesa @xcite to model the evolution of 0.15 @xmath1 , 0.20 @xmath1 , and 0.25 @xmath1  he - core wds , shown as solid cyan lines in figure  [ fig : search ] . for reference 
   , we have also included 0.6 @xmath1 , 0.8 @xmath1 , and 1.0 @xmath1  co - core cooling tracks @xcite .    where the lowest - mass wd models enter this diagram depends on how we artificially remove mass from the models , and there is a very noticeable discrepancy between the 0.16 @xmath1  @xcite wd models and our 0.15 @xmath1  wd models using mesa . as an added complication , except for the lowest - mass elm wds ( below roughly 0.18 @xmath1 ) , recurrent hydrogen shell flashes cause the elm wd model to loop many times through this @xmath2-@xmath4  plane , further confusing the picture @xcite . 
   thus , it is not entirely surprising to find non - variable elm wds between j2228 and the four warmer pulsating elm wds . 
   further empirical exploration of the entire elm wd instability strip offers a unique opportunity to constrain physical and evolution models of elm wds , specifically these late thermal pulses and the mass boundary for the occurrence of these episodes . 
   long - term monitoring of the rate of period change of pulsating elm wds also affords an opportunity to constrain the cooling ( or heating ) rate of these objects @xcite . 
   in contrast to the confusion along the red edge of the instability strip , the blue edge is more reliably predicted by theory . 
   the theoretical blue edge ( dotted blue line ) in figure  [ fig : search ] has been calculated following @xcite and @xcite . 
   we use the criterion that @xmath44 for the longest period mode that is excited , where @xmath45 is the mode period and the timescale @xmath46 describes the heat capacity of the convection zone as a function of the local photospheric flux , which we compute from a grid of models ( see @xcite for further details ) . 
   we use the criterion @xmath47 s , with the convective prescription ml2/@xmath12=1.5 . 
   we also include the theoretical blue edge of @xcite , which uses a slightly less efficient prescription for convection , ml2/@xmath12=1.0 . 
   we have discovered pulsations in two new extremely low - mass , putatively he - core wds using optical facilities at the mcdonald observatory . 
   spectral fits show that these two elm wds , j1614 and j2228 , are the coolest pulsating wds ever found . 
   this brings to five the total number of pulsating elm wds known , establishing them as a new class of pulsating wd . as with the more than 160 co - core zz ceti stars that have been known for more than four decades , the luminosity variations in these elm wds is so far consistent with surface temperature variations caused by non - radial @xmath10-mode pulsations driven to observability by a hydrogen partial ionization zone . 
   the coolest pulsating elm wd , j2228 , has a considerably lower effective temperature than six similar - gravity elm wds that are photometrically constant to good limits . 
   in contrast to the co - core zz ceti stars , which are believed to represent a stage in the evolution of all such wds , elm wds may not all evolve through an instability strip in the same way , and thus we may not observe their instability strip to be pure . 
   theoretical he - core wd models predict multiple unstable hydrogen - burning episodes , which complicates the evolution of an elm wd through a simple instability strip . empirically discovering elm wds in this space that do or do not pulsate opens the possibility to use the presence of pulsations in elm wds to constrain the 
   binary and stellar evolution models used for low - mass wds , which may better constrain these poorly understood cno - flashing episodes . 
   we acknowledge the anonymous referee for valuable suggestions that greatly improved this manuscript . 
   j.j.h . , m.h.m . and d.e.w . 
   acknowledge the support of the nsf under grant ast-0909107 and the norman hackerman advanced research program under grant 003658 - 0252 - 2009 . 
   m.h.m . additionally acknowledges the support of nasa under grant nnx12ac96 g . b.g.c . 
   thanks the support from cnpq and fapergs - pronex - brazil . 
   the authors are grateful to the essential assistance of the mcdonald observatory support staff , especially dave doss and john kuehne , and to fergal mullally for developing some of the data analysis pipeline used here .
summary: we report the discovery of two new pulsating extremely low - mass ( elm ) white dwarfs ( wds ) , sdss  j161431.28 + 191219.4 ( hereafter j1614 ) and sdss  j222859.93 + 362359.6 ( hereafter j2228 ) . 
   both wds have masses @xmath0 0.25 @xmath1  and thus likely harbor helium cores . 
   spectral fits indicate these are the two coolest pulsating wds ever found . 
   j1614 has @xmath2  @xmath3 k and @xmath4  @xmath5 , which corresponds to a @xmath60.19 @xmath1  wd . 
   j2228 is considerably cooler , with a @xmath2  @xmath7 k and @xmath4  @xmath8 , which corresponds to a @xmath60.16 @xmath1  wd , making it the coolest and lowest - mass pulsating wd known . 
   there are multiple elm wds with effective temperatures between the warmest and coolest known elm pulsators that do not pulsate to observable amplitudes , which questions the purity of the instability strip for low - mass wds . 
   in contrast to the co - core zz ceti stars , which are believed to represent a stage in the evolution of all such wds , elm wds may not all evolve as a simple cooling sequence through an instability strip . both stars 
   exhibit long - period variability ( @xmath9 s ) consistent with non - radial @xmath10-mode pulsations . 
   although elm wds are preferentially found in close binary systems , both j1614 and j2228 do not exhibit significant radial - velocity variability , and are perhaps in low - inclination systems or have low - mass companions . 
   these are the fourth and fifth pulsating elm wds known , all of which have hydrogen - dominated atmospheres , establishing these objects as a new class of pulsating wd . 
   [ firstpage ]    stars : white dwarfs  stars : oscillations ( including pulsations )  galaxy : stellar content  stars : individual : sdss j161431.28 + 191219.4 , sdss j222859.93 + 362359.6