text: GAMA: The 325 MHz Radio Luminosity Function 13 eﬃcient accretion of cold gas, determined by their emission- line properties (e.g. ???). Historically the vast majority of continuum surveys that have produced RLFs have been conducted at 1.4 GHz. Our result is in agreement with the only other comparable study concerned with the evolution of radio sources at 325 MHz by ?), who by matching SDSS DR1 data with the Westerbork Northern Sky Survey (WENSS), found no evolution in low- luminosity AGN via a V/V analysis, out to z = 0.8. max 8 CONCLUSIONS We have produced 1/V radio luminosity functions for max ∼ samples of AGN and star forming galaxies out to z 0.5, by combining data from the largest survey conducted to date at 325 MHz from the GMRT, with the GAMA survey. Our main results are as follows: Figure 17. Figure showing that the RLF (in the redshift slice (i) By cross-matching a 325 MHz GMRT survey covering 0.002 < z < 0.25) for ﬂat-spectrum sources (blue line) can be 138 deg2 of the GAMA spectroscopic survey, we are able to shifted in number density and luminosity (grey region), to in- produce a GMRT/GAMA matched sample of 499 objects ≤ ≥ ≤ cide with an extrapolation of the steep-spectrum sources (red), as with z 0.6, nQ 3 and r 19.8. Inspection of the optical is expected from the orientation based uniﬁcation of radio-loud spectra in our sample allows us to divide the sample into 45 AGN. star forming galaxies and 453 AGN. (ii) The mean spectral index of AGN remains constant with redshift as found in ?) (Fig. 8). Higher luminosity AGN Our measured 325 MHz RLF of AGN is in broad agree- are found to have slightly steeper spectral indices than those ment with the 1.4 GHz RLF measued by (?) when converted − with lower luminosities possibly due to the increase in frac- to 325 MHz using a spectral index of α = 0.7. The ?) LF tion of FR II sources (Fig. 9). also consistent with the local 20 GHz LF of ?), it therefore (iii) We determine the local luminosity function of star appears that the local AGN population is remarkably uni- forming galaxies at 325 MHz, which is broadly consistent form over a large range in frequency (325 MHz to 20 GHz). with the local 1.4 GHz luminosity function of ?) converted to We note that, at the faint end, the 1.4 GHz RLF is − 325 MHz assuming spectral index of α = 0.7. We estimate consitently higher than our 325 MHz RLF, assuming the that the lower limit on the local star formation rate density spectral index correction. The increased space density of 1.4 of the Universe is ρ = 0.013 ± 0.002 M(cid:12) yr−1 Mpc−3 SFR GHz selected galaxies may be due to doppler boosting of (Fig. ??). the population, whereby beamed 1.4 GHz sources are shifted (iv) We determine RLFs of radio-loud AGN for two red- to higher luminosity. Radio-loud AGN samples selected at shift slices. Fitting a double power mild evolution out to lower frequency are not as likely to detect signiﬁcant num- z ∼ 0.5. Parametrizing the evolution as ∝ (1 + z)k, we ﬁnd bers of sources with beamed cores, as at lower frequency the ± a best ﬁtting values k = 0.92 0.95 assuming pure number lobes of galaxies should dominate. This implies that the 325 ± density and 2.13 1.96 assuming the pure luminosity den- MHz LFs presented here are not biased with respect to ori- sity (Fig. ??). From ﬁtting single power law functions to the entation and are more representative of the mechanical jet RLFs we show that low-luminosity sources evolve less than power in the local radio-loud AGN population. high-luminosity sources. Regarding evolution, we detect mild but poorly con- (v) We produce RLFs for the HERG and LERG popu- strained evolution from ﬁts to the 325 MHz RLF for AGN ± lations of AGN. LERGs are the dominant population at out to z = 0.5, with evolution paramete±rs of k = 0.92 0.95 luminosities between 1023 < L − < 1026. At higher 325 MHz for pure density evolution and k = 2.13 1.96 for pure lumi- luminosities the space densities of the populations become nosity evolution. Considering just the low-luminosity popu- − comparable (Fig. ??). lation (those with L − < 25.5 W Hz 1) the evolution 325 MHz (vi) After dividing the AGN sample into steep and appears to be much less. This is in line with previous stud- ﬂat-spectrum sources, we show that the extrapolation of ies (see Table ??), principally based on smaller samples from the steep-spectrum sources agrees with the shifted ﬂat- deep ﬁelds, where the low-luminosity population evolves sig- spectrum, as expected from the orientation-based uniﬁcation niﬁcantly less strongly that the high-luminosity population. of radio-loud AGN (Fig. ??). Our results are also consistent with ?) and although they did not estimate an evolution parameter, they found that In order to fully understand the link between AGN- the number density of low-luminosity AGN increases by a driven feedback and the shutting down or continuous ∼ factor of 1.5, out to z = 0.55, which implies an evolution quenching of star formation in galaxies, a full understanding ∼ parameter of k 0.93. of the link between radio power, accretion mode and environ- Low-luminosity sources are thought to be the popula- ment as a function of redshift is required. In the near future tion that dominates the mechanical feedback in the z < 1 radio data obtained from the LOw-Frequency ARray (LO- Universe (e.g. ?????), and thus constraining their evolution FAR; ?), the Australian Square Kilometre Array Pathﬁnder is key to our understanding of the relevance of such feedback (ASKAP; ?) and MeerKAT (?), along with the VLA, will in studies of galaxy evolution. However, we note that some provide much greater sample sizes for AGN and star forming fraction of such sources are thought to be powered by the galaxies allowing more stringent constraints on the evolution MNRAS 000, 1–?? 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text: GAMA:

text: The

text: MHz

text: Radio

text: Luminosity

text: Function

text: eﬃcient

text: accretion

text: of

text: cold

text: gas,

text: determined

text: by

text: their

text: emission-

text: line

text: properties

text: (e.g.

text: Historically

text: the

text: vast

text: majority

text: of

text: continuum

text: surveys

text: that

text: have

text: produced

text: RLFs

text: have

text: been

text: conducted

text: at

text: GHz.

text: Our

text: result

text: is

text: in

text: agreement

text: with

text: the

text: only

text: other

text: comparable

text: study

text: concerned

text: with

text: the

text: evolution

text: of

text: radio

text: sources

text: at

text: MHz

text: by

text: who

text: by

text: matching

text: SDSS

text: data

text: with

text: the

text: Westerbork

text: Northern

text: Sky

text: Survey

text: (WENSS),

text: found

text: no

text: evolution

text: in

text: low-

text: luminosity

text: AGN

text: via

text: a

text: V/V

text: analysis,

text: out

text: to

text: z

text: max

text: CONCLUSIONS

text: We

text: have

text: produced

text: radio

text: luminosity

text: functions

text: for

text: max

text: samples

text: of

text: AGN

text: and

text: star

text: forming

text: galaxies

text: out

text: to

text: z

text: by

text: combining

text: data

text: from

text: the

text: largest

text: survey

text: conducted

text: to

text: date

text: at

text: MHz

text: from

text: the

text: GMRT,

text: with

text: the

text: GAMA

text: survey.

text: Our

text: main

text: results

text: are

text: as

text: follows:

text: Figure

text: Figure

text: showing

text: that

text: the

text: RLF

text: (in

text: the

text: redshift

text: slice

text: (i)

text: By

text: cross-matching

text: a

text: MHz

text: GMRT

text: survey

text: covering

text: z

text: for

text: ﬂat-spectrum

text: sources

text: (blue

text: line)

text: can

text: be

text: of

text: the

text: GAMA

text: spectroscopic

text: survey,

text: we

text: are

text: able

text: to

text: shifted

text: in

text: number

text: density

text: and

text: luminosity

text: (grey

text: region),

text: to

text: in-

text: produce

text: a

text: GMRT/GAMA

text: matched

text: sample

text: of

text: objects

text: cide

text: with

text: an

text: extrapolation

text: of

text: the

text: steep-spectrum

text: sources

text: (red),

text: as

text: with

text: z

text: nQ

text: and

text: r

text: Inspection

text: of

text: the

text: optical

text: is

text: expected

text: from

text: the

text: orientation

text: based

text: uniﬁcation

text: of

text: radio-loud

text: spectra

text: in

text: our

text: sample

text: allows

text: us

text: to

text: divide

text: the

text: sample

text: into

text: AGN.

text: star

text: forming

text: galaxies

text: and

text: AGN.

text: (ii)

text: The

text: mean

text: spectral

text: index

text: of

text: AGN

text: remains

text: constant

text: with

text: redshift

text: as

text: found

text: in

text: (Fig.

text: Higher

text: luminosity

text: AGN

text: Our

text: measured

text: MHz

text: RLF

text: of

text: AGN

text: is

text: in

text: broad

text: agree-

text: are

text: found

text: to

text: have

text: slightly

text: steeper

text: spectral

text: indices

text: than

text: those

text: ment

text: with

text: the

text: GHz

text: RLF

text: measued

text: by

text: when

text: converted

text: with

text: lower

text: luminosities

text: possibly

text: due

text: to

text: the

text: increase

text: in

text: frac-

text: to

text: MHz

text: using

text: a

text: spectral

text: index

text: of

text: α

text: The

text: LF

text: tion

text: of

text: FR

text: II

text: sources

text: (Fig.

text: also

text: consistent

text: with

text: the

text: local

text: GHz

text: LF

text: of

text: it

text: therefore

text: (iii)

text: We

text: determine

text: the

text: local

text: luminosity

text: function

text: of

text: star

text: appears

text: that

text: the

text: local

text: AGN

text: population

text: is

text: remarkably

text: uni-

text: forming

text: galaxies

text: at

text: MHz,

text: which

text: is

text: broadly

text: consistent

text: form

text: over

text: a

text: large

text: range

text: in

text: frequency

text: MHz

text: to

text: GHz).

text: with

text: the

text: local

text: GHz

text: luminosity

text: function

text: of

text: converted

text: to

text: We

text: note

text: that,

text: at

text: the

text: faint

text: end,

text: the

text: GHz

text: RLF

text: is

text: MHz

text: assuming

text: spectral

text: index

text: of

text: α

text: We

text: estimate

text: consitently

text: higher

text: than

text: our

text: MHz

text: RLF,

text: assuming

text: the

text: that

text: the

text: lower

text: limit

text: on

text: the

text: local

text: star

text: formation

text: rate

text: density

text: spectral

text: index

text: correction.

text: The

text: increased

text: space

text: density

text: of

text: of

text: the

text: Universe

text: is

text: ρ

text: SFR

text: GHz

text: selected

text: galaxies

text: may

text: be

text: due

text: to

text: doppler

text: boosting

text: of

text: (Fig.

text: the

text: population,

text: whereby

text: beamed

text: GHz

text: sources

text: are

text: shifted

text: (iv)

text: We

text: determine

text: RLFs

text: of

text: radio-loud

text: AGN

text: for

text: two

text: red-

text: to

text: higher

text: luminosity.

text: Radio-loud

text: AGN

text: samples

text: selected

text: at

text: shift

text: slices.

text: Fitting

text: a

text: double

text: power

text: mild

text: evolution

text: out

text: to

text: lower

text: frequency

text: are

text: not

text: as

text: likely

text: to

text: detect

text: signiﬁcant

text: num-

text: z

text: Parametrizing

text: the

text: evolution

text: as

text: z)k,

text: we

text: ﬁnd

text: bers

text: of

text: sources

text: with

text: beamed

text: cores,

text: as

text: at

text: lower

text: frequency

text: the

text: a

text: best

text: ﬁtting

text: values

text: k

text: assuming

text: pure

text: number

text: lobes

text: of

text: galaxies

text: should

text: dominate.

text: This

text: implies

text: that

text: the

text: density

text: and

text: assuming

text: the

text: pure

text: luminosity

text: den-

text: MHz

text: LFs

text: presented

text: here

text: are

text: not

text: biased

text: with

text: respect

text: to

text: ori-

text: sity

text: (Fig.

text: From

text: ﬁtting

text: single

text: power

text: law

text: functions

text: to

text: the

text: entation

text: and

text: are

text: more

text: representative

text: of

text: the

text: mechanical

text: jet

text: RLFs

text: we

text: show

text: that

text: low-luminosity

text: sources

text: evolve

text: less

text: than

text: power

text: in

text: the

text: local

text: radio-loud

text: AGN

text: population.

text: high-luminosity

text: sources.

text: Regarding

text: evolution,

text: we

text: detect

text: mild

text: but

text: poorly

text: con-

text: (v)

text: We

text: produce

text: RLFs

text: for

text: the

text: HERG

text: and

text: LERG

text: popu-

text: strained

text: evolution

text: from

text: ﬁts

text: to

text: the

text: MHz

text: RLF

text: for

text: AGN

text: lations

text: of

text: AGN.

text: LERGs

text: are

text: the

text: dominant

text: population

text: at

text: out

text: to

text: z

text: with

text: evolution

text: paramete±rs

text: of

text: k

text: luminosities

text: between

text: L

text: At

text: higher

text: MHz

text: for

text: pure

text: density

text: evolution

text: and

text: k

text: for

text: pure

text: lumi-

text: luminosities

text: the

text: space

text: densities

text: of

text: the

text: populations

text: become

text: nosity

text: evolution.

text: Considering

text: just

text: the

text: low-luminosity

text: popu-

text: comparable

text: (Fig.

text: lation

text: (those

text: with

text: L

text: W

text: Hz

text: the

text: evolution

text: MHz

text: (vi)

text: After

text: dividing

text: the

text: AGN

text: sample

text: into

text: steep

text: and

text: appears

text: to

text: be

text: much

text: less.

text: This

text: is

text: in

text: line

text: with

text: previous

text: stud-

text: ﬂat-spectrum

text: sources,

text: we

text: show

text: that

text: the

text: extrapolation

text: of

text: ies

text: (see

text: Table

text: principally

text: based

text: on

text: smaller

text: samples

text: from

text: the

text: steep-spectrum

text: sources

text: agrees

text: with

text: the

text: shifted

text: ﬂat-

text: deep

text: ﬁelds,

text: where

text: the

text: low-luminosity

text: population

text: evolves

text: sig-

text: spectrum,

text: as

text: expected

text: from

text: the

text: orientation-based

text: uniﬁcation

text: niﬁcantly

text: less

text: strongly

text: that

text: the

text: high-luminosity

text: population.

text: of

text: radio-loud

text: AGN

text: (Fig.

text: Our

text: results

text: are

text: also

text: consistent

text: with

text: and

text: although

text: they

text: did

text: not

text: estimate

text: an

text: evolution

text: parameter,

text: they

text: found

text: that

text: In

text: order

text: to

text: fully

text: understand

text: the

text: link

text: between

text: AGN-

text: the

text: number

text: density

text: of

text: low-luminosity

text: AGN

text: increases

text: by

text: a

text: driven

text: feedback

text: and

text: the

text: shutting

text: down

text: or

text: continuous

text: factor

text: of

text: out

text: to

text: z

text: which

text: implies

text: an

text: evolution

text: quenching

text: of

text: star

text: formation

text: in

text: galaxies,

text: a

text: full

text: understanding

text: parameter

text: of

text: k

text: of

text: the

text: link

text: between

text: radio

text: power,

text: accretion

text: mode

text: and

text: environ-

text: Low-luminosity

text: sources

text: are

text: thought

text: to

text: be

text: the

text: popula-

text: ment

text: as

text: a

text: function

text: of

text: redshift

text: is

text: required.

text: In

text: the

text: near

text: future

text: tion

text: that

text: dominates

text: the

text: mechanical

text: feedback

text: in

text: the

text: z

text: radio

text: data

text: obtained

text: from

text: the

text: LOw-Frequency

text: ARray

text: (LO-

text: Universe

text: (e.g.

text: and

text: thus

text: constraining

text: their

text: evolution

text: FAR;

text: the

text: Australian

text: Square

text: Kilometre

text: Array

text: Pathﬁnder

text: is

text: key

text: to

text: our

text: understanding

text: of

text: the

text: relevance

text: of

text: such

text: feedback

text: (ASKAP;

text: and

text: MeerKAT

text: along

text: with

text: the

text: VLA,

text: will

text: in

text: studies

text: of

text: galaxy

text: evolution.

text: However,

text: we

text: note

text: that

text: some

text: provide

text: much

text: greater

text: sample

text: sizes

text: for

text: AGN

text: and

text: star

text: forming

text: fraction

text: of

text: such

text: sources

text: are

text: thought

text: to

text: be

text: powered

text: by

text: the

text: galaxies

text: allowing

text: more

text: stringent

text: constraints

text: on

text: the

text: evolution

text: MNRAS

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text: GAMA: The 325 MHz Radio Luminosity Function 7 Figure 5. Redshift distribution of GAMA-GMRT matched AGN Figure 7. The spectral index distribution for AGN (red, solid (solid red line) and star forming galaxies (dashed blue line). The line) and star forming galaxies (blue, dashed line). The spectral median redshift for the AGN is z = 0.36, and 0.06 for the star indices of the sources are calculated from the ratios between 325 forming galaxies. MHz GMRT and 1.4 GHz NVSS ﬂux densities. Figure 8. The spectral index distribution for AGN (red dots) Figure 6. The luminosity-redshift distribution of the matched and star forming galaxies (blue stars) as a function of redshift. GAMA-GMRT sources, showing single component AGN (red The black crosses and error bars indicate the mean and standard ﬁlled circles), multiple component AGN (red diamonds), and star error on the mean of the spectral index for the AGN in bins forming galaxies (blue stars). Star forming galaxies become the of ∆z = 0.05. The red line shows the line of best ﬁt for the dominant radio sources at z < 0.1 at the limits of the GMRT AGN datapoints. The average spectral indices remains more or survey. less constant with increasing redshift. is the maximum comoving volume within which a galaxy could lie within a redshift slice and within the ﬂux limits of V was computed from z , the maximum max,optical max,optical the survey (?). The RLF for a given luminosity bin is given redshift in which a galaxy can be observed, calculated via by: (cid:88) SED ﬁtting of the optical spectra described fully in ?). As the GMRT mosaics have non-uniform sensitivity, the eﬀec- N 1 tive area of the survey changes as a function of the ﬂux Φz(L) = C × V , (1) limit. The volume of space available to a source of a given i=1 i max,i luminosity L(Vmax,radio) has to be calculated by taking into account the variation of survey area as a function of ﬂux Here C is the completeness of the survey. We determine i density limit. Figure ?? shows how the cumulative area of upper and lower 1σ Poisson conﬁdence limits using the ap- the survey varies as a function of rms noise for each of the proximation prescribed in ?). As our sample is a matched GMRT mosaics covering G09, G12 and G15. We use the radio/optical sample we have to take into account both the same method of calculating V described in ?). Firstly optical and radio limits of the surveys, where V is the max,radio max the diﬀerential area in the survey in small bins of rms noise taken as the minimum from the optical and radio V for max is determined for each ﬁeld from Figure ??. To calculate each source: V for a radio source with luminosity L, we compute max,radio the maximum redshift (z ) that the source would have max,i V = min(V , V ) (2) in each diﬀerential rms bin i across the 3 survey ﬁelds. z max max,radio max,optical max,i MNRAS 000, 1–?? 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text: GAMA:

label: paragraph

text: The

text: MHz

text: Radio

text: Luminosity

text: Function

text: Figure

text: Redshift

label: caption

text: distribution

text: of

text: GAMA-GMRT

text: matched

text: AGN

text: Figure

text: The

text: spectral

text: index

text: distribution

text: for

text: AGN

text: (red,

text: solid

text: (solid

text: red

text: line)

text: and

text: star

text: forming

text: galaxies

text: (dashed

text: blue

text: line).

text: The

text: line)

text: and

text: star

text: forming

text: galaxies

text: (blue,

text: dashed

text: line).

text: The

text: spectral

text: median

text: redshift

text: for

text: the

text: AGN

text: is

text: z

text: and

text: for

text: the

text: star

text: indices

text: of

text: the

text: sources

text: are

text: calculated

text: from

text: the

text: ratios

text: between

text: forming

text: galaxies.

text: MHz

text: GMRT

text: and

text: GHz

text: NVSS

text: ﬂux

text: densities.

text: Figure

text: The

text: spectral

text: index

text: distribution

text: for

text: AGN

text: (red

text: dots)

text: Figure

text: The

text: luminosity-redshift

text: distribution

text: of

text: the

text: matched

text: and

text: star

text: forming

text: galaxies

text: (blue

text: stars)

text: as

text: a

text: function

text: of

text: redshift.

text: GAMA-GMRT

text: sources,

text: showing

text: single

text: component

text: AGN

text: (red

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text: black

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text: error

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text: the

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text: ﬁlled

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text: Star

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text: GMRT

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text: datapoints.

text: The

text: average

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text: remains

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text: survey.

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text: increasing

text: redshift.

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text: the

text: maximum

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text: redshift

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text: ﬂux

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text: z

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text: RLF

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text: given

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text: given

text: redshift

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text: galaxy

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text: be

text: observed,

text: calculated

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text: SED

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text: of

text: the

text: optical

text: spectra

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text: the

text: GMRT

text: mosaics

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text: non-uniform

text: sensitivity,

text: the

text: eﬀec-

text: N

text: tive

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text: survey

text: ﬁelds.

text: z

text: max

text: max,radio

text: max,optical

text: max,i

text: MNRAS

text: ##LTFigure##

text: ##LTFigure##

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text: LETTER A prevalence of dynamo-generated magnetic ﬁelds in the cores of intermediate-mass stars Dennis Stello1,2, Matteo Cantiello3, Jim Fuller4,3, Daniel Huber1,5,2, Rafael A. Garc´ıa6, Tim R. Bedding1,2, Lars Bildsten3,7, Victor Silva Aguirre2 halfway between successive radial-quadrupolar pairs. The octupolar Magnetic ﬁelds play a role in almost all stages of stellar evolution 1. modes ((cid:96) = 3) are weak or undetectable. The dipolar modes have Most low-mass stars, including the Sun, show surface ﬁelds that are turned out to be particularly useful probes of internal structure 12. They generated by dynamo processes in their convective envelopes 2,3. have been used to distinguish between hydrogen-shell and helium-core Intermediate-mass stars do not have deep convective envelopes 4, burning stars 13–15 and to measure radial differential rotation 16,17. This although 10% exhibit strong surface ﬁelds that are presumed to be usefulness arises because each acoustic non-radial mode in the enve- residuals from the stellar formation process 5. These stars do have lope couples to multiple gravity modes in the core, forming several convective cores that might produce internal magnetic ﬁelds 6, and observable mixed modes with frequencies in the vicinity of the acous- these might even survive into later stages of stellar evolution, but tic mode 16. This coupling is strongest for dipole modes, making them information has been limited by our inability to measure the ﬁelds the most useful probes of the core 18. below the stellar surface 7. Here we use asteroseismology to study Figure 1 shows the oscillation power spectra of red giants at three the occurrence of strong magnetic ﬁelds in the cores of low- and different evolutionary stages observed by NASA’s Kepler mission. For intermediate-mass stars. We have measured the strength of dipolar “normal” stars (upper panels), the dipolar modes (red peaks) have sim- oscillation modes, which can be suppressed by a strong magnetic ilar power to the radial modes (black peaks). However, at each stage ﬁeld in the core 8, in over 3600 red giant stars observed by Kepler. of evolution we also ﬁnd stars with greatly suppressed dipolar modes About 20% of our sample show mode suppression but this fraction (lower panels). Suppressed dipolar modes have been reported in a few is a strong function of mass. Strong core ﬁelds only occur in red dozen red giant stars, with an occurrence rate of about 20% 19,20. The giants above 1.1 solar masses (1.1M(cid:12)), and the occurrence rate is cause of this phenomenon has been puzzling until recent theoretical at least 60% for intermediate-mass stars (1.6–2.0M(cid:12)), indicating work, which showed that the suppression can be explained if waves that powerful dynamos were very common in the convective cores entering the stellar core are prevented from returning to the envelope. of these stars. This occurs for dipolar modes if there are strong magnetic ﬁelds in the Red giants are formed when a low- or intermediate-mass star has core, giving rise to a “magnetic greenhouse effect” 8. ﬁnished burning the hydrogen in its core. This leaves an inert helium We measured the amount of suppression by comparing the inte- core surrounded by a thin hydrogen-burning shell and a very thick outer grated power of the dipolar and radial modes (the dipole mode visi- convective envelope. Like the Sun, red giants oscillate in a broad comb- bility, V 2), averaged over the four orders centred on ν . While the like frequency spectrum of radial and non-radial acoustic modes that ≈ max normal stars show dipole mode visibilities of V 2 1.5, independent of are excited by the turbulent surface convection 9. The observed power ν , 19,21, the stars with suppressed modes have V 2 ≈ 0.5 for ν spectrum has a roughly Gaussian envelope whose central frequency, (cid:39)max max 70 µHz and down to almost zero for the least evolved red giants νmax, decreases as a star expands during the red giant phase 10,11. The oscillating above 200 µHz (Fig. 1). comb structure of the spectrum arises from a series of overtone modes In Fig. 2 we show the dipole mode visibility for about 3600 red separated by the so-called large frequency separation, ∆ν. One of these giants observed over the ﬁrst 37 months of the Kepler mission. Our overtone sequences is seen for each spherical degree, (cid:96). For observa- analysis is restricted to a sample of stars with ν larger than 50µHz tions of unresolved distant stars, geometric cancellation prevents de- max and masses below 2.1M(cid:12) which, assuming no observational uncertain- tection of modes with (cid:96) > 3. Their spectra are characterised by a ties, is expected to include only red giants that have not started burn- pattern of radial ((cid:96) = 0) and quadrupolar ((cid:96) = 2) modes that form ing helium in their cores 14. We cross-matched our sample with those close pairs, interspersed with dipolar ((cid:96) = 1) modes located roughly of known helium-burning stars 14,15, which allowed us to identify and remove a small fraction of evolved stars burning helium that, due to 1Sydney Institute for Astronomy (SIfA), School of Physics, Univer- measurement uncertainty, had entered our sample (2% of our sample, sity of Sydney, NSW 2006, Australia 2Stellar Astrophysics Centre, Department of Physics and Astronomy, almost all with νmax < 70µHz). Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark The stars in Fig. 2 form two distinct branches that gradually merge 3Kavli Institute for Theoretical Physics, University of California, Santa as the stars evolve leftwards towards lower ν . Most stars fall on Barbara, CA 93106 ≈ max 4TAPIR, Walter Burke Institute for Theoretical Physics, Mailcode 350-17 the “normal” upper branch of V 2 1.5, in agreement with previous California Institute of Technology, Pasadena, CA 91125 results 19. The lower branch, with suppressed dipole modes, agrees 5SETI Institute, 189 Bernardo Avenue, Mountain View, CA 94043, USA remarkably well with theoretical predictions (black curve). This pre- 6Laboratoire AIM, CEA/DSM – CNRS – Univ. Paris Diderot – IRFU/SAp diction assumes that all the wave energy leaking into the stellar core Centre de Saclay, 91191 Gif-sur-Yvette Cedex, France is trapped by a magnetic greenhouse effect caused by strong internal 7Department of Physics, University of California, Santa Barbara, CA 93106 magnetic ﬁelds 8. The decrease of the suppression towards lower νmax is a consequence of the weaker coupling between acoustic waves in the 1 ##LTLine##

text: LETTER

text: A

label: title

text: prevalence

text: of

text: dynamo-generated

text: magnetic

text: ﬁelds

text: in

text: the

text: cores

text: of

text: intermediate-mass

text: stars

text: Dennis

label: author

text: Matteo

text: Jim

text: Daniel

text: Rafael

text: A.

text: Tim

text: R.

text: Lars

text: Victor

text: Silva

text: halfway

text: between

text: successive

text: radial-quadrupolar

text: pairs.

text: The

text: octupolar

text: Magnetic

label: abstract

text: ﬁelds

text: play

text: a

text: role

text: in

text: almost

text: all

text: stages

text: of

text: stellar

text: evolution

text: modes

text: are

text: weak

text: or

text: undetectable.

text: The

text: dipolar

text: modes

text: have

text: Most

text: low-mass

text: stars,

text: including

text: the

text: Sun,

text: show

text: surface

text: ﬁelds

text: that

text: are

text: turned

text: out

text: to

text: be

text: particularly

text: useful

text: probes

text: of

text: internal

text: structure

text: They

text: generated

text: by

text: dynamo

text: processes

text: in

text: their

text: convective

text: envelopes

text: have

text: been

text: used

text: to

text: distinguish

text: between

text: hydrogen-shell

text: and

text: helium-core

text: Intermediate-mass

text: stars

text: do

text: not

text: have

text: deep

text: convective

text: envelopes

text: burning

text: stars

text: and

text: to

text: measure

text: radial

text: differential

text: rotation

text: This

text: although

text: exhibit

text: strong

text: surface

text: ﬁelds

text: that

text: are

text: presumed

text: to

text: be

text: usefulness

text: arises

text: because

text: each

text: acoustic

text: non-radial

text: mode

text: in

text: the

text: enve-

text: residuals

text: from

text: the

text: stellar

text: formation

text: process

text: These

text: stars

text: do

text: have

text: lope

text: couples

text: to

text: multiple

text: gravity

text: modes

text: in

text: the

text: core,

text: forming

text: several

text: convective

text: cores

text: that

text: might

text: produce

text: internal

text: magnetic

text: ﬁelds

text: and

text: observable

text: mixed

text: modes

text: with

text: frequencies

text: in

text: the

text: vicinity

text: of

text: the

text: acous-

text: these

text: might

text: even

text: survive

text: into

text: later

text: stages

text: of

text: stellar

text: evolution,

text: but

text: tic

text: mode

text: This

text: coupling

text: is

text: strongest

text: for

text: dipole

text: modes,

text: making

text: them

text: information

text: has

text: been

text: limited

text: by

text: our

text: inability

text: to

text: measure

text: the

text: ﬁelds

text: the

text: most

text: useful

text: probes

text: of

text: the

text: core

text: below

text: the

text: stellar

text: surface

text: Here

text: we

text: use

text: asteroseismology

text: to

text: study

text: Figure

text: shows

text: the

text: oscillation

text: power

text: spectra

text: of

text: red

text: giants

text: at

text: three

text: the

text: occurrence

text: of

text: strong

text: magnetic

text: ﬁelds

text: in

text: the

text: cores

text: of

text: low-

text: and

text: different

text: evolutionary

text: stages

text: observed

text: by

text: NASA’s

text: Kepler

text: mission.

text: For

text: intermediate-mass

text: stars.

text: We

text: have

text: measured

text: the

text: strength

text: of

text: dipolar

text: “normal”

text: stars

text: (upper

text: panels),

text: the

text: dipolar

text: modes

text: (red

text: peaks)

text: have

text: sim-

text: oscillation

text: modes,

text: which

text: can

text: be

text: suppressed

text: by

text: a

text: strong

text: magnetic

text: ilar

text: power

text: to

text: the

text: radial

text: modes

text: (black

text: peaks).

text: However,

text: at

text: each

text: stage

text: ﬁeld

text: in

text: the

text: core

text: in

text: over

text: red

text: giant

text: stars

text: observed

text: by

text: Kepler.

text: of

text: evolution

text: we

text: also

text: ﬁnd

text: stars

text: with

text: greatly

text: suppressed

text: dipolar

text: modes

text: About

text: of

text: our

text: sample

text: show

text: mode

text: suppression

text: but

text: this

text: fraction

text: (lower

text: panels).

text: Suppressed

text: dipolar

text: modes

text: have

text: been

text: reported

text: in

text: a

text: few

text: is

text: a

text: strong

text: function

text: of

text: mass.

text: Strong

text: core

text: ﬁelds

text: only

text: occur

text: in

text: red

text: dozen

text: red

text: giant

text: stars,

text: with

text: an

text: occurrence

text: rate

text: of

text: about

text: The

text: giants

text: above

text: solar

text: masses

text: and

text: the

text: occurrence

text: rate

text: is

text: cause

text: of

text: this

text: phenomenon

text: has

text: been

text: puzzling

text: until

text: recent

text: theoretical

text: at

text: least

text: for

text: intermediate-mass

text: stars

text: indicating

text: work,

text: which

text: showed

text: that

text: the

text: suppression

text: can

text: be

text: explained

text: if

text: waves

text: that

text: powerful

text: dynamos

text: were

text: very

text: common

text: in

text: the

text: convective

text: cores

text: entering

text: the

text: stellar

text: core

text: are

text: prevented

text: from

text: returning

text: to

text: the

text: envelope.

text: of

text: these

text: stars.

text: This

text: occurs

text: for

text: dipolar

text: modes

text: if

text: there

text: are

text: strong

text: magnetic

text: ﬁelds

text: in

text: the

text: Red

text: giants

text: are

text: formed

text: when

text: a

text: low-

text: or

text: intermediate-mass

text: star

text: has

text: core,

text: giving

text: rise

text: to

text: a

text: “magnetic

text: greenhouse

text: effect”

text: ﬁnished

text: burning

text: the

text: hydrogen

text: in

text: its

text: core.

text: This

text: leaves

text: an

text: inert

text: helium

text: We

text: measured

text: the

text: amount

text: of

text: suppression

text: by

text: comparing

text: the

text: inte-

text: core

text: surrounded

text: by

text: a

text: thin

text: hydrogen-burning

text: shell

text: and

text: a

text: very

text: thick

text: outer

text: grated

text: power

text: of

text: the

text: dipolar

text: and

text: radial

text: modes

text: (the

text: dipole

text: mode

text: visi-

text: convective

text: envelope.

text: Like

text: the

text: Sun,

text: red

text: giants

text: oscillate

text: in

text: a

text: broad

text: comb-

text: bility,

text: V

text: averaged

text: over

text: the

text: four

text: orders

text: centred

text: on

text: ν

text: While

text: the

text: like

text: frequency

text: spectrum

text: of

text: radial

text: and

text: non-radial

text: acoustic

text: modes

text: that

text: max

text: normal

text: stars

text: show

text: dipole

text: mode

text: visibilities

text: of

text: V

text: independent

text: of

text: are

text: excited

text: by

text: the

text: turbulent

text: surface

text: convection

text: The

text: observed

text: power

text: ν

text: the

text: stars

text: with

text: suppressed

text: modes

text: have

text: V

text: for

text: ν

text: spectrum

text: has

text: a

text: roughly

text: Gaussian

text: envelope

text: whose

text: central

text: frequency,

text: max

text: µHz

text: and

text: down

text: to

text: almost

text: zero

text: for

text: the

text: least

text: evolved

text: red

text: giants

text: νmax,

text: decreases

text: as

text: a

text: star

text: expands

text: during

text: the

text: red

text: giant

text: phase

text: The

text: oscillating

text: above

text: µHz

text: (Fig.

text: comb

text: structure

text: of

text: the

text: spectrum

text: arises

text: from

text: a

text: series

text: of

text: overtone

text: modes

text: In

text: Fig.

text: we

text: show

text: the

text: dipole

text: mode

text: visibility

text: for

text: about

text: red

text: separated

text: by

text: the

text: so-called

text: large

text: frequency

text: separation,

text: ∆ν.

text: One

text: of

text: these

text: giants

text: observed

text: over

text: the

text: ﬁrst

text: months

text: of

text: the

text: Kepler

text: mission.

text: Our

text: overtone

text: sequences

text: is

text: seen

text: for

text: each

text: spherical

text: degree,

text: For

text: observa-

text: analysis

text: is

text: restricted

text: to

text: a

text: sample

text: of

text: stars

text: with

text: ν

text: larger

text: than

text: tions

text: of

text: unresolved

text: distant

text: stars,

text: geometric

text: cancellation

text: prevents

text: de-

text: max

text: and

text: masses

text: below

text: which,

text: assuming

text: no

text: observational

text: uncertain-

text: tection

text: of

text: modes

text: with

text: Their

text: spectra

text: are

text: characterised

text: by

text: a

text: ties,

text: is

text: expected

text: to

text: include

text: only

text: red

text: giants

text: that

text: have

text: not

text: started

text: burn-

text: pattern

text: of

text: radial

text: and

text: quadrupolar

text: modes

text: that

text: form

text: ing

text: helium

text: in

text: their

text: cores

text: We

text: cross-matched

text: our

text: sample

text: with

text: those

text: close

text: pairs,

text: interspersed

text: with

text: dipolar

text: modes

text: located

text: roughly

text: of

text: known

text: helium-burning

text: stars

text: which

text: allowed

text: us

text: to

text: identify

text: and

text: remove

text: a

text: small

text: fraction

text: of

text: evolved

text: stars

text: burning

text: helium

text: that,

text: due

text: to

text: Institute

text: for

text: Astronomy

text: (SIfA),

text: School

text: of

text: Physics,

text: Univer-

text: measurement

text: uncertainty,

text: had

text: entered

text: our

text: sample

text: of

text: our

text: sample,

text: sity

text: of

text: Sydney,

text: NSW

text: Australia

text: Astrophysics

text: Centre,

text: Department

text: of

text: Physics

text: and

text: Astronomy,

text: almost

text: all

text: with

text: νmax

text: Aarhus

text: University,

text: Ny

text: Munkegade

text: Aarhus

text: C,

text: Denmark

text: The

text: stars

text: in

text: Fig.

text: form

text: two

text: distinct

text: branches

text: that

text: gradually

text: merge

text: Institute

text: for

text: Theoretical

text: Physics,

text: University

text: of

text: California,

text: Santa

text: as

text: the

text: stars

text: evolve

text: leftwards

text: towards

text: lower

text: ν

text: Most

text: stars

text: fall

text: on

text: Barbara,

text: CA

text: max

text: Walter

text: Burke

text: Institute

text: for

text: Theoretical

text: Physics,

text: Mailcode

text: the

text: “normal”

text: upper

text: branch

text: of

text: V

text: in

text: agreement

text: with

text: previous

text: California

text: Institute

text: of

text: Technology,

text: Pasadena,

text: CA

text: results

text: The

text: lower

text: branch,

text: with

text: suppressed

text: dipole

text: modes,

text: agrees

text: Institute,

text: Bernardo

text: Avenue,

text: Mountain

text: View,

text: CA

text: USA

text: remarkably

text: well

text: with

text: theoretical

text: predictions

text: (black

text: curve).

text: This

text: pre-

text: AIM,

text: CEA/DSM

text: CNRS

text: Univ.

text: Paris

text: Diderot

text: IRFU/SAp

text: diction

text: assumes

text: that

text: all

text: the

text: wave

text: energy

text: leaking

text: into

text: the

text: stellar

text: core

text: Centre

text: de

text: Saclay,

text: Gif-sur-Yvette

text: Cedex,

text: France

text: is

text: trapped

text: by

text: a

text: magnetic

text: greenhouse

text: effect

text: caused

text: by

text: strong

text: internal

text: of

text: Physics,

text: University

text: of

text: California,

text: Santa

text: Barbara,

text: CA

text: magnetic

text: ﬁelds

text: The

text: decrease

text: of

text: the

text: suppression

text: towards

text: lower

text: νmax

text: is

text: a

text: consequence

text: of

text: the

text: weaker

text: coupling

text: between

text: acoustic

text: waves

text: in

text: the

text: ##LTLine##


text: | Figure 1 Oscillation spectra of six red giants observed with Kepler. The stars are ordered in three pairs, each representing a different evolution stage ranging from the most evolved (lowest oscillation frequencies) on the left to the least evolved (highest frequencies) to the right. The coloured regions mark the power dominated by modes of different degree (cid:96) = 0–3. For clarity the spectra are smoothed by 3% of the frequency separation between overtone modes, which for the most evolved stars tend to create a single peak at each acoustic resonance, even if it comprises multiple closely-spaced mixed modes (red peaks in the left and centre panels). The slightly downward sloping horizontal dashed line indicates the noise level. Observations of each star were made during the ﬁrst 37 months of the Kepler mission (observing quarters Q0–Q14). envelope and gravity waves in the core 8. With this large sample we Considering again the low-mass stars (< 1.1M(cid:12)), of which none have been able to separate the stars in Fig.2 into ﬁve different mass show suppression, we see from Figure 4 that magnetic ﬁelds above ≈ intervals, from 0.9 to 2.1M(cid:12). It is striking how strongly the relative 10 kG are not present at the hydrogen-burning shell when the stars ≈ − population on the lower branch (stars with suppressed dipole modes) are just below the red giant luminosity bump (ν 70 100 µHz). max depends on mass. Assuming magnetic ﬂux conservation from the main-sequence phase, ≈ We quantify the mass dependence in Fig. 3 by showing the relative this suggests that ﬁelds above 5 kG do not exist within the cores of number of dipole-suppressed stars (those below the dashed line in Fig. Sun-like stars 8. Large scale ﬁelds in the solar interiors have been dis- 2) in narrow mass intervals. We see no suppression in red giants below cussed in order to explain the properties of the tachocline 25. However, 1.1M(cid:12), which coincides with the mass below which they did not have our results do not rule out strong horizontal ﬁelds near the radiative- convective cores during the core-hydrogen-burning phase 4. The on- convective boundary because those ﬁelds would be outside the core set of magnetic suppression above this threshold suggests that at least and could not cause mode suppression when the star evolves into a red some of those stars had convectively driven magnetic dynamos in their giant. cores during the core-hydrogen-burning (main-sequence) phase. This Turning to higher masses we see that, for a given ν , stars above max is supported by 3D hydrodynamical modeling of these stars 6. Red gi- 1.4M(cid:12) require increasingly strong magnetic ﬁelds to suppress their ants no longer contain convective cores, leading us to conclude that the dipolar modes. From Figure 4, there is no clear upper limit to the ﬁeld strong magnetic ﬁelds in suppressed oscillators are the remnants of the strengths present in red giant cores, given that dipole-suppressed stars ﬁelds produced by core dynamos during the main sequence. are common even when ﬁeld strengths B > 1 MG are required for Figure 3 shows that the incidence of magnetic suppression in- suppression. However, the hint of a decline in the occurrence of dipole- creases with mass, with red giants above 1.6M(cid:12) showing a remarkable suppressed stars above 2M(cid:12) seen in Fig. 3 suggests there may be a suppression rate of 50-60%. These have evolved from main-sequence mass above which dynamo-generated magnetic ﬁelds can no longer ≈ A-type stars, among which only up to 10% are observed to have cause oscillation mode suppression in intermediate-mass stars. strong ﬁelds at their surfaces 5. We conclude that these magnetic A The high occurrence rate of dipole mode suppression demonstrates stars represent only the tip of the iceberg, and that a much larger frac- that core-dynamo-generated ﬁelds can remain through the red giant tion of A stars have strong magnetic ﬁelds hidden in their cores. phase, more than 108 yr after the dynamo has shut off at the end of In Fig. 4 we show the observed ν and inferred mass of all core-hydrogen-burning. This indicates that dynamo-generated ﬁelds max the stars superimposed on a contour plot of minimum magnetic ﬁeld are frequently able to settle into long-lived stable conﬁgurations, a strengths required for mode suppression 8. For stars with suppressed result that was not certain from magnetohydrodynamical simulations modes (ﬁlled red circles), the underlying colour provides a lower bound 26–28. The occurrence rate of suppressed dipole modes in intermediate- to the ﬁeld strength at the hydrogen-burning shell. For stars without mass red giants is much higher than the occurrence rate of strong ﬁelds suppressed modes (open black circles), the underlying colour repre- at the surfaces of the main-sequence A stars from which they evolved. sents an upper limit to the ﬁeld at the hydrogen-burning shell; above or The latter ﬁelds are thought to have been generated by a pre-hydrogen- below the shell the ﬁeld could potentially be larger. Hence, normal and core burning dynamo during star formation 29. We conclude that ﬁelds dipole-suppressed stars that fall in the same regions of Fig. 4 may have generated during core-hydrogen-burning are able to settle into stable core ﬁeld strengths that are only slightly different. However, we expect equilibrium conﬁgurations much more commonly (more than 60% of that the dipole-suppressed stars on average exhibit stronger core ﬁelds the time) than ﬁelds generated during star formation (less than 10% of than their normal counter parts. the time). 2 ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: Figure

text: Oscillation

text: spectra

text: of

text: six

text: red

text: giants

text: observed

text: with

text: Kepler.

text: The

text: stars

text: are

text: ordered

text: in

text: three

text: pairs,

text: each

text: representing

text: a

text: different

text: evolution

text: stage

text: ranging

text: from

text: the

text: most

text: evolved

text: (lowest

text: oscillation

text: frequencies)

text: on

text: the

text: left

text: to

text: the

text: least

text: evolved

text: (highest

text: frequencies)

text: to

text: the

text: right.

text: The

text: coloured

text: regions

text: mark

text: the

text: power

text: dominated

text: by

text: modes

text: of

text: different

text: degree

text: For

text: clarity

text: the

text: spectra

text: are

text: smoothed

text: by

text: of

text: the

text: frequency

text: separation

text: between

text: overtone

text: modes,

text: which

text: for

text: the

text: most

text: evolved

text: stars

text: tend

text: to

text: create

text: a

text: single

text: peak

text: at

text: each

text: acoustic

text: resonance,

text: even

text: if

text: it

text: comprises

text: multiple

text: closely-spaced

text: mixed

text: modes

text: (red

text: peaks

text: in

text: the

text: left

text: and

text: centre

text: panels).

text: The

text: slightly

text: downward

text: sloping

text: horizontal

text: dashed

text: line

text: indicates

text: the

text: noise

text: level.

text: Observations

text: of

text: each

text: star

text: were

text: made

text: during

text: the

text: ﬁrst

text: months

text: of

text: the

text: Kepler

text: mission

text: (observing

text: quarters

text: envelope

text: and

text: gravity

text: waves

text: in

text: the

text: core

text: With

text: this

text: large

text: sample

text: we

text: Considering

text: again

text: the

text: low-mass

text: stars

text: of

text: which

text: have

text: been

text: able

text: to

text: separate

text: the

text: stars

text: in

text: into

text: ﬁve

text: different

text: mass

text: show

text: suppression,

text: we

text: see

text: from

text: Figure

text: that

text: magnetic

text: ﬁelds

text: above

text: intervals,

text: from

text: to

text: It

text: is

text: striking

text: how

text: strongly

text: the

text: relative

text: kG

text: are

text: not

text: present

text: at

text: the

text: hydrogen-burning

text: shell

text: when

text: the

text: stars

text: population

text: on

text: the

text: lower

text: branch

text: (stars

text: with

text: suppressed

text: dipole

text: modes)

text: are

text: just

text: below

text: the

text: red

text: giant

text: luminosity

text: bump

text: (ν

text: µHz).

text: max

text: depends

text: on

text: mass.

text: Assuming

text: magnetic

text: ﬂux

text: conservation

text: from

text: the

text: main-sequence

text: phase,

text: We

text: quantify

text: the

text: mass

text: dependence

text: in

text: Fig.

text: by

text: showing

text: the

text: relative

text: this

text: suggests

text: that

text: ﬁelds

text: above

text: kG

text: do

text: not

text: exist

text: within

text: the

text: cores

text: of

text: number

text: of

text: dipole-suppressed

text: stars

text: (those

text: below

text: the

text: dashed

text: line

text: in

text: Fig.

text: Sun-like

text: stars

text: Large

text: scale

text: ﬁelds

text: in

text: the

text: solar

text: interiors

text: have

text: been

text: dis-

text: in

text: narrow

text: mass

text: intervals.

text: We

text: see

text: no

text: suppression

text: in

text: red

text: giants

text: below

text: cussed

text: in

text: order

text: to

text: explain

text: the

text: properties

text: of

text: the

text: tachocline

text: However,

text: which

text: coincides

text: with

text: the

text: mass

text: below

text: which

text: they

text: did

text: not

text: have

text: our

text: results

text: do

text: not

text: rule

text: out

text: strong

text: horizontal

text: ﬁelds

text: near

text: the

text: radiative-

text: convective

text: cores

text: during

text: the

text: core-hydrogen-burning

text: phase

text: The

text: on-

text: convective

text: boundary

text: because

text: those

text: ﬁelds

text: would

text: be

text: outside

text: the

text: core

text: set

text: of

text: magnetic

text: suppression

text: above

text: this

text: threshold

text: suggests

text: that

text: at

text: least

text: and

text: could

text: not

text: cause

text: mode

text: suppression

text: when

text: the

text: star

text: evolves

text: into

text: a

text: red

text: some

text: of

text: those

text: stars

text: had

text: convectively

text: driven

text: magnetic

text: dynamos

text: in

text: their

text: giant.

text: cores

text: during

text: the

text: core-hydrogen-burning

text: (main-sequence)

text: phase.

text: This

text: Turning

text: to

text: higher

text: masses

text: we

text: see

text: that,

text: for

text: a

text: given

text: ν

text: stars

text: above

text: max

text: is

text: supported

text: by

text: hydrodynamical

text: modeling

text: of

text: these

text: stars

text: Red

text: gi-

text: require

text: increasingly

text: strong

text: magnetic

text: ﬁelds

text: to

text: suppress

text: their

text: ants

text: no

text: longer

text: contain

text: convective

text: cores,

text: leading

text: us

text: to

text: conclude

text: that

text: the

text: dipolar

text: modes.

text: From

text: Figure

text: there

text: is

text: no

text: clear

text: upper

text: limit

text: to

text: the

text: ﬁeld

text: strong

text: magnetic

text: ﬁelds

text: in

text: suppressed

text: oscillators

text: are

text: the

text: remnants

text: of

text: the

text: strengths

text: present

text: in

text: red

text: giant

text: cores,

text: given

text: that

text: dipole-suppressed

text: stars

text: ﬁelds

text: produced

text: by

text: core

text: dynamos

text: during

text: the

text: main

text: sequence.

text: are

text: common

text: even

text: when

text: ﬁeld

text: strengths

text: B

text: MG

text: are

text: required

text: for

text: Figure

text: shows

text: that

text: the

text: incidence

text: of

text: magnetic

text: suppression

text: in-

text: suppression.

text: However,

text: the

text: hint

text: of

text: a

text: decline

text: in

text: the

text: occurrence

text: of

text: dipole-

text: creases

text: with

text: mass,

text: with

text: red

text: giants

text: above

text: showing

text: a

text: remarkable

text: suppressed

text: stars

text: above

text: seen

text: in

text: Fig.

text: suggests

text: there

text: may

text: be

text: a

text: suppression

text: rate

text: of

text: These

text: have

text: evolved

text: from

text: main-sequence

text: mass

text: above

text: which

text: dynamo-generated

text: magnetic

text: ﬁelds

text: can

text: no

text: longer

text: A-type

text: stars,

text: among

text: which

text: only

text: up

text: to

text: are

text: observed

text: to

text: have

text: cause

text: oscillation

text: mode

text: suppression

text: in

text: intermediate-mass

text: stars.

text: strong

text: ﬁelds

text: at

text: their

text: surfaces

text: We

text: conclude

text: that

text: these

text: magnetic

text: A

text: The

text: high

text: occurrence

text: rate

text: of

text: dipole

text: mode

text: suppression

text: demonstrates

text: stars

text: represent

text: only

text: the

text: tip

text: of

text: the

text: iceberg,

text: and

text: that

text: a

text: much

text: larger

text: frac-

text: that

text: core-dynamo-generated

text: ﬁelds

text: can

text: remain

text: through

text: the

text: red

text: giant

text: tion

text: of

text: A

text: stars

text: have

text: strong

text: magnetic

text: ﬁelds

text: hidden

text: in

text: their

text: cores.

text: phase,

text: more

text: than

text: yr

text: after

text: the

text: dynamo

text: has

text: shut

text: off

text: at

text: the

text: end

text: of

text: In

text: Fig.

text: we

text: show

text: the

text: observed

text: ν

text: and

text: inferred

text: mass

text: of

text: all

text: core-hydrogen-burning.

text: This

text: indicates

text: that

text: dynamo-generated

text: ﬁelds

text: max

text: the

text: stars

text: superimposed

text: on

text: a

text: contour

text: plot

text: of

text: minimum

text: magnetic

text: ﬁeld

text: are

text: frequently

text: able

text: to

text: settle

text: into

text: long-lived

text: stable

text: conﬁgurations,

text: a

text: strengths

text: required

text: for

text: mode

text: suppression

text: For

text: stars

text: with

text: suppressed

text: result

text: that

text: was

text: not

text: certain

text: from

text: magnetohydrodynamical

text: simulations

text: modes

text: (ﬁlled

text: red

text: circles),

text: the

text: underlying

text: colour

text: provides

text: a

text: lower

text: bound

text: The

text: occurrence

text: rate

text: of

text: suppressed

text: dipole

text: modes

text: in

text: intermediate-

text: to

text: the

text: ﬁeld

text: strength

text: at

text: the

text: hydrogen-burning

text: shell.

text: For

text: stars

text: without

text: mass

text: red

text: giants

text: is

text: much

text: higher

text: than

text: the

text: occurrence

text: rate

text: of

text: strong

text: ﬁelds

text: suppressed

text: modes

text: (open

text: black

text: circles),

text: the

text: underlying

text: colour

text: repre-

text: at

text: the

text: surfaces

text: of

text: the

text: main-sequence

text: A

text: stars

text: from

text: which

text: they

text: evolved.

text: sents

text: an

text: upper

text: limit

text: to

text: the

text: ﬁeld

text: at

text: the

text: hydrogen-burning

text: shell;

text: above

text: or

text: The

text: latter

text: ﬁelds

text: are

text: thought

text: to

text: have

text: been

text: generated

text: by

text: a

text: pre-hydrogen-

text: below

text: the

text: shell

text: the

text: ﬁeld

text: could

text: potentially

text: be

text: larger.

text: Hence,

text: normal

text: and

text: core

text: burning

text: dynamo

text: during

text: star

text: formation

text: We

text: conclude

text: that

text: ﬁelds

text: dipole-suppressed

text: stars

text: that

text: fall

text: in

text: the

text: same

text: regions

text: of

text: Fig.

text: may

text: have

text: generated

text: during

text: core-hydrogen-burning

text: are

text: able

text: to

text: settle

text: into

text: stable

text: core

text: ﬁeld

text: strengths

text: that

text: are

text: only

text: slightly

text: different.

text: However,

text: we

text: expect

text: equilibrium

text: conﬁgurations

text: much

text: more

text: commonly

text: (more

text: than

text: of

text: that

text: the

text: dipole-suppressed

text: stars

text: on

text: average

text: exhibit

text: stronger

text: core

text: ﬁelds

text: the

text: time)

text: than

text: ﬁelds

text: generated

text: during

text: star

text: formation

text: (less

text: than

text: of

text: than

text: their

text: normal

text: counter

text: parts.

text: the

text: time).

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