Pulsation among TESS A and B stars and the Maia variables
aa r X i v : . [ a s t r o - ph . S R ] M a r MNRAS , 1–10 (2011) Preprint 6 March 2020 Compiled using MNRAS L A TEX style file v3.0
Pulsation among
TESS
A and B stars and the Maiavariables
L. A. Balona ⋆ and D. Ozuyar South African Astronomical Observatory, P.O. Box 9, Observatory 7935, South Africa Ankara University, Faculty of Science, Dept. of Astronomy and Space Sciences, 06100, Tandogan, Ankara, Turkey
Accepted .... Received ...
ABSTRACT
Classification of over 50000
TESS stars in sectors 1–18 has resulted in the detectionof 766 pulsating main sequence B stars as well as over 5000 δ Scuti, 2300 γ Doradusand 114 roAp candidates. Whereas it has been assumed that high frequency pulsationamong B-type main sequence stars are confined to the early B-type β Cephei stars, theobservations indicate that high frequencies are to be found over the whole B-star range,eventually merging with δ Scuti stars. The cool B stars pulsating in high frequenciesare called Maia variables. It is shown that Maia variables are not rapidly-rotating andthus cannot be β Cephei pulsators which appear to have lower temperatures due togravity darkening. In the region where β Cephei variables are found, the proportion ofpulsating stars is larger and amplitudes are higher and a considerable fraction pulsatein a single mode and low rotation rate. There is no distinct region of slowly-pulsatingB stars (SPB stars). Stars pulsating solely in low frequencies are found among all Bstars. At most, only one-third of B stars appear to pulsate. These results, as well asthe fact that a large fraction of A and B stars show rotational modulation, indicate aneed for a revision of current ideas regarding stars with radiative envelopes.
Key words: stars: early-type – stars: oscillations
The advent of space photometry, particularly from the
Ke-pler and
TESS missions, has radically changed perceptionson stellar pulsation in the upper main sequence. For exam-ple, from
CoRoT data, Degroote et al. (2009) find evidencefor a new class of low-amplitude B-type pulsators betweenthe SPB and δ Scuti instability strips. Prior to
Kepler , itwas believed that the opacity κ mechanism offered a com-plete and satisfactory explanation for the δ Scuti, SPB and β Cephei pulsating variables. At the cool end of the δ Sct in-stability strip, pulsations in the γ Doradus variables were at-tributed to the convective blocking mechanism (Guzik et al.2000). Photometric time series observations from space wereexpected to confirm model predictions and perhaps resolvea few minor problems.The first surprise was the discovery that low-frequency γ Dor pulsations are visible throughout the δ Sct instabilitystrip (Grigahc`ene et al. 2010). We know now that the dis-tinction between the two types of variable is merely oneof mode selection and not of pulsation mechanism sincethey share the same instability region (Balona 2018). Thissuggests a problem with assumptions regarding convection ⋆ E-mail: [email protected] on the upper main sequence. Bowman & Kurtz (2018) andBalona (2018) find that a non-negligible fraction of main-sequence δ Sct stars exist outside theoretical predictions ofthe classical instability boundaries. Recent calculations us-ing time-dependent perturbation theory (Antoci et al. 2014;Xiong et al. 2016) including turbulent convection do not re-solve the issue.Among the main-sequence B stars, the κ mechanismoperating in the ionization zone of iron-group elements ap-pears to be responsible for the high-frequency pulsations ofthe β Cephei stars as well as the low-frequency pulsationsamong the cooler SPB variables. These were the only tworecognized classes of pulsating variable in main-sequencestars hotter than the blue edge of the δ Sct instabilitystrip. Stankov & Handler (2005) provide a list of 93 con-firmed β Cep variables with an additional 14 stars discov-ered by Pigulski (2005). Most recently, Labadie-Bartz et al.(2019) presented results of a search for β Cep stars fromthe
KELT exoplanet survey. They identify 113 β Cepstars, of which 86 are new discoveries. Burssens et al.(2019) found 3 new β Cep stars observed by the K2 mis-sion. Ground-based surveys for SPB stars have been madeby several groups (Aerts et al. 1999; Mathias et al. 2001;De Cat & Aerts 2002; De Cat et al. 2007).The CoRoT space mission (Fridlund et al. 2006) con- c (cid:13) L. A. Balona and D. Ozuyar tributed considerably to our knowledge of pulsation amongthe B stars. For example, observations of the O9V starHD 46202 show β Cep-like pulsations, but none of the ob-served frequencies are excited in the models (Briquet et al.2011). A global magnetic field was found in the hybrid B-type pulsator HD 43317 (Briquet et al. 2013). Unexpectedmodes with short lifetimes in HD 180642 were initially inter-preted as stochastic modes excited by turbulent convection(Belkacem et al. 2009), but this conclusion was subsequentlydisputed (Aerts et al. 2011; Degroote 2013). At least 15 newSPB candidates were detected by
CoRoT (Degroote et al.2009).Due to the high galactic latitude of the field observedby the
Kepler space mission (Borucki et al. 2010), relativelyfew B stars were observed. Balona et al. (2011) found 15pulsating stars, all of which show low frequencies character-istic of SPB stars. Seven of these stars also show a few weak,isolated high frequencies.From time to time, ground-based observations reportedthe possible presence of high frequencies in a few starstoo hot to be δ Scuti, but too cool to be β Cephei(McNamara 1985; Lehmann et al. 1995; Percy & Wilson2000; Kallinger et al. 2004). These were called Maia vari-ables following a report by Struve (1955) of short-periodvariations in the star Maia, a member of the Pleiades clus-ter. Struve (1955) later disclaimed the variability. It is nowknown from the K2 space mission that Maia itself is a ro-tational variable with a 10-d period (White et al. 2017) andno sign of high frequencies.One of the most interesting results from the CoRoT mission is evidence for a new class of low-amplitude B-typepulsator between the SPB and δ Sct instability strips, witha very broad range of frequencies extending well into the β Cep range (Degroote et al. 2009). These are probably thesame as the Maia variables described above. B stars withhigh frequencies too cool to be β Cep variables have alsobeen detected in the
Kepler field (Balona et al. 2015, 2016).From ground-based photometry, Mowlavi et al. (2013);Lata et al. (2014); Mowlavi et al. (2016) discovered anoma-lous high frequencies in rapidly-rotating late to mid-B stars.At this time, it is not clear if these stars can be consid-ered as Maia variables. From pulsating models of rotat-ing B stars, Salmon et al. (2014) found that frequenciesas high as 10 d − may be visible in mid- to late B stars.They therefore suggest that these could be fast-rotating SPBstars in which the apparent effective temperature is low-ered by gravity darkening at the equator. More recently,Szewczuk & Daszy´nska-Daszkiewicz (2017) have computedthe instability domains for B stars including the effects ofslow-to-moderate rotation. They find that unstable progradehigh radial order g modes may have quite high frequencieswhich could account for these anomalous variables and theMaia stars.The advent of TESS (Ricker et al. 2015) has opened anew opportunity to study pulsation among the B stars. Asample of over 50000 stars hotter than 6000 K from sectors1–18 were examined and classified according to variabilitytype. The classification is based on a visual inspection ofthe periodogram and light curve for each star. Accordingto current knowledge, apart from the chemically peculiarroAp stars, the only A and B main sequence stars with fre-quencies higher than about 5 d − are the δ Sct (DSCT) and β Cep (BCEP) variables, the distinction being made accord-ing to the effective temperature. It is, however, necessaryto introduce the Maia class to account for the anomaloushigh-frequency B-type variables just described. This doesnot imply that the Maia variables are necessarily a sepa-rate group of pulsating stars. If Maia variables are simplyrapidly-rotating β Cep or SPB stars, then they must havehigher than normal projected rotational velocities, allowinga test of this idea to be made.The effective temperatures, T eff , in the TESS Input Cat-alogue (TIC) (Stassun et al. 2018) are unreliable for B starsbecause most are derived from multicolour photometry lack-ing the U band. Without photometric measurements in theU band, the Balmer jump cannot be measured and it is notpossible to distinguish stars with T eff > TESS stars. Manystars that we originally classified as DSCT or γ Doradus(GDOR) on the basis of temperatures listed in the TIC,were re-classified as BCEP, MAIA or SPB variables becausethey have B-type spectra.In this paper, we use the best available estimates of T eff and luminosities using Gaia DR2 parallaxes to locate thestars in the H–R diagram and the pulsation period vs T eff (P–T) diagram. The locations of stars classified as SPB orBCEP in the P–T diagram are compared to the predictedlocations derived from pulsation models. In this way, currentideas regarding pulsation instability among the B stars canbe tested. In particular, we investigate the status of the Maiavariables and the connection between pulsation in A and Bstars. TESS light curves for thousands of stars with two-minute ca-dence are available according to sector number. There are 26partially overlapping sectors covering the whole sky and eachsector is observed for approximately one month. The wide-band photometry has been corrected for long-term drifts us-ing pre-search data conditioning (PDC, Jenkins et al. 2010).Each
TESS pixel is 21 arcsec in size which is similar to thetypical aperture size used in ground-based photoelectric pho-tometry. Working groups 4 and 5 of the
TESS asteroseismicconsortium were involved in target selection (Pedersen et al.2019; Handler et al. 2019).Effective temperatures are listed for most
TESS starsin the TIC, but for reasons already mentioned, they can-not be used for B stars. To resolve this problem, a catalog ofover 600000 stars brighter than 12-th magnitude with knownspectroscopic classifications was created and matched withthe TIC. This allows the proper assignment to be made re-garding the type of variability.As far as possible, it is necessary to assign the vari-ability class in accordance with the well-established typesused in the
General Catalogue of Variable Stars (GCVS,Samus et al. 2017). One major consideration is that vari-ation due to rotational modulation seems to be present inall types of star, including the B stars (Balona 2019). Thismay be due to chemical peculiarities (the SX Ari class), butmost often there is no indication of spectral peculiarity, inwhich case the new ROT class is assigned. Rotation always
MNRAS000
MNRAS000 , 1–10 (2011) ulsation among TESS A and B stars needs to be considered when examining the periodograms atlow frequencies.Variability classification for stars with T eff > β Cep and SPB stars show a clear separation between thetwo kinds of variable in a plot of pulsation period as a func-tion of T eff (see Fig. 4 of Miglio et al. 2007a). SPB starsmostly have frequencies less than 2.5 d − , whereas β Cepstars all have higher frequencies. Most β Cep stars are con-fined to T eff > − . ForSPB stars it was decided that for T eff > − separates BCEP from SPB, but for cooler starsthe boundary between low and high frequencies was movedto 5 d − to allow more flexibility for rotational effects. A staris classified as MAIA if 10000 < T eff < − .In many cases the amplitudes in the low-frequencyrange are comparable to those in the high frequencies inwhich case we use BCEP+SPB or SPB+BCEP, depend-ing on which range seems to dominate. These would be the β Cep/SPB hybrids. The hybrid classes MAIA+SPB andSPB+MAIA are also assigned.In Table 1, 327 β Cep variables (the majority of whichare previously unknown), 308 pure SPB stars (i.e. non-hybrids) and 131 Maia stars are listed. In Fig. 1, the β Cep, SPB and Maia stars are shown in the theoreti-cal H-R diagram. Also shown are the theoretical instabil-ity strips for metal abundance Z = 0 .
02, using OP opaci-ties and the AGS05 mixture as calculated by Miglio et al.(2007a). A more recent calculation of the instability regionby Walczak et al. (2015) using updated opacities gives muchthe same result. A few stars lie below the zero-age main se-quence and may be previously unrecognized pulsating sub-dwarfs.It should be noted that the calculated instability stripsshrink quite rapidly with decreasing metallicity. The fig-ure shows the instability strips for solar abundance andOP opacities from Miglio et al. (2007a). These define ap-proximately the maximum extent of instability in non-rotating models. Rotation will tend to reduce the appar-ent effective temperature of a star if it is rapidly rotat-ing and with high inclination due to gravity darkeningat the equator (von Zeipel 1924). This means that somestars may appear outside the cool edge of the instabilitystrip. Szewczuk & Daszy´nska-Daszkiewicz (2017) computedthe instability domains for gravity and mixed gravity-Rossbymodes, including the effects of slow-to-moderate rotation.The main result is that g-mode instability domains are muchmore extended towards higher masses and higher effective eff l og L / L ⊙ Figure 1.
The H–R diagram showing the β Cep, SPB and Maiastars observed by
TESS . Also shown is the theoretical zero-agemain sequence (solid line) and the instability regions of the β Cepand SPB pulsating stars for Z = 0 .
02 and spherical harmonicdegree l ≤ temperatures, mainly as a result of using OPAL rather thanOP opacities. The effective temperature is a crucial component in estab-lishing the type of variability. The most reliable estimates of T eff are those which use spectroscopic observations combinedwith model atmospheres. The PASTEL compilation of spec-troscopic parameters (Soubiran et al. 2016) are particularlyuseful in this regard. The literature was searched for morerecent measurements, and a catalogue of over 101500 starscomprising nearly 170000 individual T eff measurements ofvarious kinds was compiled.Each method of deriving T eff was assigned a priority MNRAS , 1–10 (2011)
L. A. Balona and D. Ozuyar
Table 1.
List of β Cep, SPB and Maia stars in
TESS sectors 1–18.The priority code of effective temperature, T eff , is given in column4 as follows: 1 - spectroscopy; 2 - narrow-band photometry; 3 -UBV photometry; 4 - BV photometry; 5 - Spectral type or other.The complete table is available in electronic form. TIC Var Type T eff Pr log LL ⊙ v sin i Sp. Type99010 SPB 9931 1 2.13 164 B9.5III3300381 BCEP+ROT 20400 3 4.09 B2IIIn4207261 SPB+BCEP 24012 1 4.03 10 B1.5V6110321 MAIA+SPB 14200 4 2.85 B8e:7429754 SPB 15546 2 2.96 B6V9887122 SPB+MAIA 11324 1 2.38 150 B6(V)10510382 SPB 22570 5 3.85 37 B3Vp shell10891640 BCEP+EB 28000 5 4.29 B0.5III:11400562 SPB+BCEP 23940 1 4.13 75 B2IV-V11411724 BCEP+SPB 24068 2 3.15 200 B1.5V11696250 BCEP 26169 1 5.07 116 B0.5III11698190 BCEP 20200 3 4.29 B0.5V class. First priority is given to spectroscopic modelling. Val-ues of T eff from Str¨omgren or Geneva photometry were as-signed second priority. Values using Johnson UBV photom-etry and the Q method of de-reddening were applied tomany stars, but assigned third priority. Fourth priority wasgiven when only BV photometry is available. In this casethe reddening can be estimated using a 3D reddening mapby Gontcharov (2016). The Torres (2010) calibration giv-ing T eff as a function of ( B − V ) was used for the lat-ter two methods. Finally, when no other way of obtaining T eff was possible, the spectral type and luminosity class andthe Pecaut & Mamajek (2013) calibration were used and as-signed fifth priority. The adopted value of T eff is the averageof measurements of highest priority only, even if many moremeasurements of lower priority are available. For most stars,only one measurement method (i.e. one priority) is available.Stellar luminosities were derived from Gaia DR2 par-allaxes (Gaia Collaboration et al. 2016, 2018). The bolo-metric correction was obtained from T eff using thePecaut & Mamajek (2013) calibration. The reddening cor-rection was derived from a three-dimensional reddening mapby Gontcharov (2017). From the error in the Gaia
DR2 par-allax, the typical standard deviation in log(
L/L ⊙ ) is esti-mated to be about 0.05 dex, allowing for standard deviationsof 0.01 mag in the apparent magnitude, 0.10 mag in visualextinction and 0.02 mag in the bolometric correction in ad-dition to the parallax error.A catalogue of projected rotational velocities, v sin i consisting of over 58000 individual measurements of 35200stars was compiled. The bulk of these measurementsare from Glebocki & Gnacinski (2005). The catalogue wasbrought up to date by a literature search. Miglio et al. (2007b) studied the effect of different opacitytables and metallicities on the pulsational stability of non-rotating B stars. A useful visual representation of these re-sults is a plot of the periods of unstable modes as a functionof T eff (the P-T diagram). This leads to two non-overlappingregions, as shown in Fig. 2, which define the instability re-gions of β Cep and SPB stars in the models. One may expecta larger spread of pulsation periods and a displacement in P ( d ) log T eff Figure 2.
Location of
TESS pulsating stars stars in the pe-riod/effective temperature diagram. For each star, the frequencyof maximum amplitude is plotted with size proportional to loga-rithm of the amplitude. The two oval regions show the location ofunstable modes of low degree calculated by Miglio et al. (2007b).The regions demarcated by the dashed lines are the adopted lo-cations of the β Cep, SPB, Maia, δ Sct and γ Dor stars. the observed T eff to lower values in the more rapidly-rotatingstars.Also shown in Fig. 2 are the pulsating stars observedby TESS where the symbol size is related to the maxi-mum amplitude. To obtain the period in the P-T diagram,the peak of highest amplitude with frequency ν > . − was used for a star classified as BCEP. For BCEP+SPB orSPB+BCEP, two periods are extracted, one above 2.5 d − and the other below this frequency. For SPB, only one periodwith ν < . − is extracted. For stars with T eff < β Cep instability strip, one period with ν < − was extracted. For SPB+MAIA or MAIA+SPB,two periods are extracted and for MAIA stars, the peak ofhighest amplitude with ν > − is used. For comparison,Fig. 2 also shows the DSCT, GDOR and ROAP stars. Thedashed lines in the figure represent the regions for the dif-ferent variability classes as defined above.In Fig. 2 there is a concentration of stars with relativelyhigh amplitudes in the predicted β Cep region (though some-what displaced to higher T eff ), mostly with frequencies in therange 5–10 d − . There is no obvious concentration of SPBstars, but there are quite a number of stars cooler than the β Cep stars with high frequencies. These are the Maia vari-ables. β CEP STARS
The frequency distribution of β Cep stars, as revealed by theperiodograms, is much sparser than that of δ Sct stars. Veryfew β Cep stars have more than a dozen significant peaks andabout 20-30 percent pulsate in just one dominant frequency.Very often harmonics are present in these single-mode stars.The median amplitude of the maximum-amplitude peak for
MNRAS , 1–10 (2011) ulsation among TESS A and B stars R e l a t i v e nu m be r Figure 3.
The distribution of projected rotational velocities, v sin i , for main sequence stars (open boxes) and for β Cep, SPBand Maia stars (filled boxes). all β Cep stars is 3.9 ppt, while for the β Cep stars withone dominant mode it is 13.3 ppt. The average projectedrotational velocity for all β Cep stars is h v sin i i = 131 ± − (129 stars). For stars with a single pulsation mode h v sin i i = 70 ±
15 km s − (23 stars). Thus single-mode β Cepstars have significantly higher amplitudes and significantlylower rotation rates than other β Cep stars. The implicationof this result is not clear at present.For all B stars in the same temperature range h v sin i i =142 ± − (2730 stars). The rotational frequency distri-bution for β Cep stars is therefore the same as for all mainsequence stars in the same temperature range, as shown inFig. 3.It is reasonable to presume that the dominant high-amplitude mode could have the same spherical harmonicdegree, l , in these stars. The dimensionless frequency, σ = ω p R /GM where ω is the angular pulsation frequency, R the stellar radius, M the stellar mass and G the gravita-tional constant, is a useful indicator of the pulsation mode.Given T eff and the stellar luminosity, M can be estimatedfrom interpolation of evolutionary tracks which enables σ to be found. From 71 β Cep stars having a single domi-nant frequency, it is found that h σ i = 5 . ± .
3. The mainsource of error is the effective temperature. An uncertaintyof 1000 K in T eff leads to an uncertainty of 0.7 in σ . Com-parison with theoretical models calculated using the code byDziembowski (1977) suggests that a radial mode l = 0 , n = 3or l = 2 , n = 3, where n is the radial order, as the most prob-able identification.About 8 percent of β Cep stars have a curious feature.This is the presence of just two peaks of similar ampli-tude, perhaps a result of rotational splitting or tidal inter-action. These stars are quite noticeable in visual inspection -1 ) 0 10 20 TIC 42365645 A m p li t ude ( pp t ) -1 ) 0 10 20 30 TIC 293680998 0 20 40 TIC 75703490 Figure 4.
Examples of β Cep stars with just a single periodogrampeak (left hand panels) and with a single double peak (right handpanels). of the periodograms and deserve careful study. Examplesare shown in Fig. 4. About half the β Cep stars contain lowfrequencies typical of SPB stars, i.e. they are β Cep/SPBhybrids.
As can be seen in Fig. 1, stars with only low frequencies (i.e.the SPB stars with peaks below 2.5 d − or 5 d − ) are preva-lent right across the B star region, including a substantialnumber within the β Cep instability region. Although hy-brid stars are expected in this region, models do not predictstars where only low frequencies are unstable. There are 90pure SPB stars (i.e. no frequencies exceeding 2.5 d − ) with T eff > TESS field.The median amplitude for all 308 SPB stars is 1.3 ppt,which is considerably smaller than for β Cep stars.From ground-based observations, the SPB stars havebeen found to be slow rotators ( h v sin i i = 60 ±
10 km s − ,Balona 2009). The mean projected rotational velocity for 121 TESS
SPB stars with 10000 < T eff < h v sin i i =147 ± − , while for all main sequence stars in the sametemperature range h v sin i i = 138 ± − (1672 stars). Forhotter SPB stars h v sin i i = 148 ±
12 km s − (61 stars), whilefor main-sequence stars in the same T eff range h v sin i i =140 ± − (2545 stars). Clearly, the rotation rate of SPBstars is the same as for main sequence stars in the same T eff range as shown in Fig. 3. Perhaps the most interesting result is the presence of a sig-nificant number of stars with high frequencies cooler thanthe red edge of the β Cep region. This confirms the de-tection of such stars by
CoRoT (Degroote et al. 2009). Ifthese are rapidly-rotating β Cep or SPB stars, then all of
MNRAS , 1–10 (2011)
L. A. Balona and D. Ozuyar -1 ) 0 0.05 0.1 0.15 TIC 191142098 0 0.5 1 TIC 66594335 0 5 10 TIC 31921921 A m p li t ude ( pp t ) -1 ) 0 0.05 TIC 235459271 0 0.5 TIC 225263020 0 0.05 TIC 202431888 0 0.05 0.1 0.15 TIC 144517863 0 0.2 0.4 0.6 0.8 0 5 10 15 20 25TIC 174662768 0 0.05 0 10 20 30 40 50TIC 469421586Frequency (d -1 ) 0 0.5 TIC 357310008 0 0.1 0.2 TIC 308769611 0 0.5 0 5 10 15 20 25TIC 450935207 0 0.5 1 TIC 323246065 0 0.2 0.4 TIC 306548914 Figure 5.
Periodograms of some Maia stars in Table 2. these Maia variables should have v sin i considerably largerthan main sequence stars in the same T eff range. Projectedrotational velocities are available for 41 of the 131 Maiastars (Table 2). The mean projected rotational velocity is h v sin i i = 173 ±
17 km s − , while the for main sequence starsin the same temperature range h v sin i i = 138 ± − from 1672 stars. There is a difference of two standard de-viations between the two values, which is not consideredstatistically significant. The frequency distribution is shownin Fig. 3.Clearly, Maia stars are not rapidly rotating β Cep orSPB stars. They could possibly be composite objects con-sisting of a non-pulsating B star and a δ Sct star. Anotherpossible explanation is that the effective temperatures are inerror and that Maia stars are actually δ Sct variables. Themost reliable measure of T eff has been used. As can be seenfrom Table 2, a large proportion of stars have T eff measuredby modelling the spectrum, so this explanation is unlikely.The median amplitude for all 131 Maia stars is only0.36 ppt, which perhaps explains why these stars were neverconfirmed to exist from ground-based observations.The distribution of high frequencies in Maia variablesresembles that in δ Sct stars rather than in β Cep variables.Whereas, dominant frequencies as high as 20 d − or more arecommon among the Maia variables, the frequency of highestamplitude in BCEP variables rarely exceeds 10 d − . Of theMaia stars with dominant frequencies higher than 20 d − ,10 percent have values of T eff estimated from spectroscopy and 20 percent from spectroscopy and narrow-band photom-etry. All have spectral classifications of A0 and earlier. Table 3 shows the number of β Cep, SPB and Maia stars indifferent ranges of effective temperature as well as the totalnumber of main sequence stars in the same range observedby
TESS . It is clear that pulsation among B stars is notvery common. While it is possible that pulsations below thedetection level may be present in all B stars, it is likely thatpulsational instability is confined to only certain stars forreasons unknown. The same result applies for δ Sct stars(Balona & Dziembowski 2011; Balona 2018; Murphy et al.2019). This poses a challenge for current models which donot consider possibly small differences in the composition,structure, magnetism, rotation etc in the outer layers. Evenif two stars have the same effective temperature, luminosity,global abundance and projected rotational velocity, thesedifferences may affect pulsational stability and mode selec-tion.
MNRAS000
MNRAS000 , 1–10 (2011) ulsation among TESS A and B stars Table 2.
List of Maia stars with known projected rotational ve-locities (km s − ). The effective temperature, T eff (K), and thepriority level (Pr) is given. The priority codes are as follows: 1- spectroscopic modeling; 2 - narrow-band photometry; 3 - UBVphotometry; 4 - BV photometry; 5 - Spectral type. The stellar lu-minosity, log L/L ⊙ , is derived from the Gaia DR2 parallax. Theprojected rotational velocity, v sin i (km s − ), and the spectraltype is also listed.TIC T eff Pr log LL ⊙ v sin i Sp. Type9887122 11324 1 2.38 150.0 B6(V)12339621 10363 1 2.27 52.5 B9.5III+25425217 10404 2 2.29 230.0 B9III31921921 16575 2 2.84 75.0 B1I/IIIk36557487 13922 2 2.84 255.7 B8IIIn52684359 14624 2 2.90 52.8 B8IV (shell)66594335 16008 1 2.94 300.0 B2IV-V71580820 17024 1 3.35 55.0 B5III116273716 12910 1 2.59 156.7 B5/7III129533458 12742 1 2.84 69.5 B7III144028101 13520 5 2.74 266.7 B8Ve144517863 12151 1 2.27 290.0 B9V160704414 13183 1 2.40 367.3 B7:V:nn169551936 12439 1 2.85 123.0 B8III174662768 13918 2 2.66 42.0 B5Vn191142098 10864 1 1.56 212.0 B8.5Vn191493281 15915 1 2.97 167.2 B3III/V:202431888 12024 1 2.46 44.3 B9IVSi:225263020 10028 2 1.51 214.0 A0/1V234887704 13520 5 2.12 286.0 B8Ve235459271 11967 1 2.57 170.8 B8Vn239219717 11776 1 2.17 333.8 B6III241660076 11508 1 2.11 249.5 B9.5V250137613 14670 1 3.11 22.8 B5IV264540595 11583 2 2.06 270.0 B9.5V270219259 13520 5 2.96 301.2 B8III shell271971626 11412 1 2.29 17.0 B9IV277674241 10789 1 1.85 308.0 B9Vn:301100741 12000 2 2.25 84.2 B9Si306548914 17466 2 2.95 155.7 B5V308769611 10116 1 1.80 172.0 A0V323246065 12214 1 2.12 343.0 B9IV331268750 13552 1 2.71 88.2 B6/7 + B7/8341040976 12900 2 2.63 25.0 B9Si354793407 14900 2 2.78 51.4 B8Hewk.Si357310008 13100 2 2.46 30.0 B9Si400445441 14562 2 2.74 65.0 B5/6IV408382023 17140 5 3.08 272.6 B6V(e)450935207 15975 1 2.67 320.0 B6Vn469421586 13520 5 2.85 205.0 B8IV/V469906369 10069 1 2.09 220.5 B9.5IVn δ SCUTI AND γ DORADUS STARS
The δ Sct and γ Dor variables (Antoci et al. 2019) seem tobe driven by the same mechanism and distinguished onlyby different mode selection (Balona 2018). However, theyclearly occupy well-defined regions in the H–R diagram asshown in Fig. 6, even though the classification is based onthe presence or absence of peaks with frequencies in excessof 5 d − , which is independent of its effective temperatureor luminosity. From this point of view, it is still useful to Table 3.
Number of β Cep, SPB and Maia stars, N var , and totalnumber of main sequence stars, N tot , within a given effective tem-perature range. The last column gives the percentage of pulsatingvariables relative to the total number of main sequence stars.Type T eff range N var N tot PercentBCEP 18000–35000 284 1242 22.9SPB 18000–35000 162 1242 13.0SPB 10000–35000 289 2605 11.1SPB 10000–18000 127 1363 9.3MAIA 10000–18000 91 1363 6.7 distinguish between γ Dor and δ Sct stars, even though lowfrequencies are present in both types of variable.The same is not true for β Cep and Maia stars. Bothare characterised by the presence of high frequencies and,if considered as a single group, would occupy the whole Bstar range. The imposed boundary of 18000 K between thetwo groups is purely arbitrary, guided by the fact that somecorrespondence between the models and observations needsto be made. In other words, unlike the δ Sct and γ Dor stars,there is no information in the light curve or periodogramwhich relates to the location of the star in the H-R diagram.In Fig. 2 it can be seen that stars that correspond tomodels of β Cep variables can be distinguished not onlyby the presence of high frequencies, but also by higher pul-sation amplitudes. However, classification using amplitudesalso requires an arbitrary choice of amplitude. Moreover, alow amplitude does not distinguish Maia from β Cep becausethere are many β Cep stars with low amplitudes similar toMaia variables. In other words, there is no observationalcriterion that offers a clean distinction between β Cep andMaia variables and which is independent of spectral type.Likewise, there is no distinct instability strip for SPBstars. Stars with low frequencies occur right across thewhole B-star main sequence as well as in blue supergiants(Bowman et al. 2019). Clearly, there is a problem with cur-rent pulsation models which need to be refined.This study is about pulsation among the B stars and,as a consequence, it was initially restricted to stars with T eff > T eff whichsuggests that both these variables should be present amongthe early A stars. This is indeed the case, as can be seenin Fig. 6. In this figure we show the locations of over 5000 δ Sct and over 2300 γ Dor variables in the H-R diagramfrom
TESS sectors 1–18. Also included are 113 roAp stars(Cunha et al. 2019), of which 68 are new candidates. Theseare included for completeness.It should be noted that there are a considerable numberof stars classified as DSCT, even though they are hotter thanthe observed δ Sct blue edge at about log T eff ≈ .
95. It isnot possible to distinguish between these hot δ Sct starsand the Maia variables. An artificial boundary of 10000 Kwas chosen to separate MAIA and DSCT variables.Similarly, stars classified as GDOR (i.e. frequencymostly less than 5 d − ) seem to be present which are muchhotter than the observed blue edge of the γ Dor stars atabout 7500 K (Balona et al. 2016). These hot γ Dor starscannot be distinguished from the SPB stars. Once again, a
MNRAS , 1–10 (2011)
L. A. Balona and D. Ozuyar l og L / L ⊙ log T eff Figure 6.
The top panel shows the Maia stars (left of log T eff =4 .
0) and the DSCT stars (to the right of log T eff = 4). SomeDSCT stars hotter than 10000 K have spectral types indicatingcooler temperatures. Also shown is the ZAMS (dash-dotted lines)and the theoretical cool edge of the SPB stars (dotted line). Thebottom panel shows the same for the SPB and GDOR stars ob-served by TESS . purely arbitrary boundary of 10000 K was chosen betweenSPB and GDOR stars. The Maia stars seem to be a con-tinuation of the δ Sct variables which then merge into the β Cep stars. The γ Dor stars, which cannot really be consid-ered as separate from the δ Sct variables, seem to merge intothe SPB stars. Of course, this may be a result of incorrecteffective temperatures, and further research is required.In Fig. 7 the fraction of high-frequency pulsating stars( δ Sct, Maia and β Cep variables) and of low-frequency pul-sating stars ( γ Dor and SPB variables) is shown as a functionof T eff . Even at a minimum of T eff ≈
10 CONCLUSIONS
Light curves and periodograms of over 50000 stars in
TESS sectors 1–18 were visually examined. Where appro-priate, each star was assigned a variability type. Using theTIC effective temperatures, many stars classified as DSCT F r a c t i on o f s t a r s T eff (K) HighLow Figure 7.
The fraction of pulsating stars with high frequencies(i.e. δ Sct, Maia and β Cep, filled circles) and with low frequencies( γ Dor and SPB, open circles) as a function of effective temper-ature. ( δ Scuti) or GDOR ( γ Doradus) were later re-classified asBCEP ( β Cephei), MAIA or SPB based on more reliableestimates of T eff and/or their spectral types. The Maia classis necessary because many B stars with high frequencies aretoo cool to be classified as β Cep variables.With the period–effective temperature diagram as aguideline, it became clear that a stricter definition of thedifferent types of B-type variables is required. For stars hot-ter than about 18000 K, a frequency of 2.5 d − was chosen todistinguish between BCEP and SPB stars. For cooler starsa frequency of 5 d − was chosen as the boundary betweenMaia and SPB stars. Using this classification, 327 β Cep,131 Maia and 308 SPB stars were detected. These resultsconfirm the
CoRoT detections of Maia variables and SPBstars extending well into the β Cep region (Degroote et al.2009).In estimating T eff we used a system of priorities wherethe most reliable estimates (priority 1) are those where T eff isderived by modelling the stellar spectrum. The least preciseestimate (priority 5) uses the spectral type and luminosityclass. The effective temperature for B stars is still poorlyknown and badly neglected because modern CCDs are notvery sensitive in the UV range.It seems that all three groups of pulsating variables haveprojected rotational velocities similar to non-pulsating starsin the same temperature range. In particular, the Maia starsrotate no faster than other main sequence stars in the same T eff range. Therefore this anomalous group cannot be ex-plained as rapidly-rotating β Cep or SPB stars. Becausemany Maia stars have values of T eff derived from spectrummodelling, it is also unlikely that they are a result of erro-neous temperature estimates.If the pulsating A stars are considered, there appearsto be no distinct grouping of high-frequency pulsators. The δ Sct, Maia and β Cep stars seem to merge smoothly witheach other. The δ Sct and β Cep groups form two distinctmaxima in the relative population and also have amplitudessignificantly larger than other pulsating stars, but they arenot isolated groups. The relatively large number of stars ofhigh frequencies outside the traditional instability strips of δ Sct and β Cep stars remains unexplained.
MNRAS , 1–10 (2011) ulsation among TESS A and B stars The β Cep stars observed by
TESS have frequencieswhich span a relatively narrow range, mostly between 3–10 d − . Their amplitudes are relatively large compared tothe SPB and Maia stars. A significant fraction of the β Cepstars pulsate in only a single dominant frequency which, bymatching the dimensionless frequency with models, may bethe second radial ( l = 0) or quadrupole ( l = 2) overtone.These stars have high amplitudes and low rotation rates.Why a particular mode with these properties should be se-lected is not clear.Low-frequency pulsations seem to be present across thewhole main sequence from the γ Dor stars to the domain ofthe β Cep variables. In fact, a substantial number of SPBstars with no high frequencies and T eff > CoRoT (Degroote et al. 2009). Their rotationrates are, however, quite normal. Although there are rela-tively few of the anomalous “hot γ Dor” stars, they meritfurther study.The Be stars are not considered here. There is awidespread opinion that the mass-loss mechanism is a resultof nonradial pulsation coupled with near-critical rotation(Rivinius 2013). Recent results from
TESS do not supportthis conclusion (Balona & Ozuyar 2019) since the variationsare incoherent, though quasi-periodic. Recent analyses of theprojected rotational velocities also indicate that they do notrotate at near-critical velocity (Cranmer 2005; Zorec et al.2016).These results, though different from what may havebeen expected based on current knowledge, are not entirelysurprising. For some time it has been clear that the simplepicture of static radiative envelopes in A and B stars is inneed of revision (Balona 2012, 2013, 2016, 2017). The de-tection of rotational modulation among a large fraction ofB stars (Balona 2019) shows that current concepts of B staratmospheres are not compatible with observations. It seemsthat the multitude of questions relating to pulsation amongthe A and B stars needs to await a better understanding ofthe physics of the upper envelopes of these stars.
ACKNOWLEDGMENTS
LAB wishes to thank the National Research Foundation ofSouth Africa for financial support. Discussions with Dr PeterDe Cat, Dr Gerald Handler and Dr Keivan Stassun are alsogratefully acknowledged.Funding for the
TESS mission is provided by the NASAExplorer Program. Funding for the
TESS
Asteroseismic Sci-ence Operations Centre is provided by the Danish NationalResearch Foundation (Grant agreement no.: DNRF106),ESA PRODEX (PEA 4000119301) and Stellar AstrophysicsCentre (SAC) at Aarhus University.This work has made use of data from the EuropeanSpace Agency (ESA) mission Gaia, processed by the GaiaData Processing and Analysis Consortium (DPAC). Fund-ing for the DPAC has been provided by national institutions,in particular the institutions participating in the Gaia Mul-tilateral Agreement.This research has made use of the SIMBAD database,operated at CDS, Strasbourg, France. Data were obtainedfrom the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities forResearch in Astronomy, Inc., under NASA contract NAS5-2655.
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