text: c c c aa bb dd RNd 6 1.0 1.0 (a) (e) 0.5 0.5 0.0 0.0 1.0 1.0 (b) (f) 0.5 0.5 0.0 0.0 1.0 1.0 (c) (g) 0.5 0.5 0.0 0.0 1.0 1.0 (d) (h) 0.5 0.5 0.0 0.0 0 100 200 300 0 100 200 300 Time [t / 1] Time [t / 1] FIG. 3: Sets of typical quantum trajectories and corresponding detection records for Ω/Γ = 0.5 (a)-(d) and Ω/Γ = 0.1 (e)-(h) ≡ (cid:104) | | (cid:105) with the same initial condition ρc (t = 0) a ρc(t = 0) a = 1. The measurement voltage V/Γ = 10 is within the bias aa | (cid:105) regime 1 [see Fig. 2], such that the state “ c ” as shown in Fig. 1(c) is energetically prohibited. The Fermi energies are far from the excitation energies of the reduced system, such that the Fermi functions can be approximated by either 1 or 0, and thus − temperature is not involved here. The time step used is ∆t=0.01Γ 1. Other plotting parameters are: (cid:15) = (cid:15) = 0, W/Γ = 0.5, q T Γ /Γ = 1/3, and U/Γ = 10. L R The measurement current I¯, zero frequency noise S(0), the intrinsic dynamics of the qubit serves as an additional and the Fano factor F = S(0)/(2eI¯) versus voltage are mechanism that may lead to super-Poissonian shot noise plotted in Fig. 2(a)-(c), respectively. At very low bias in a double dot detector. (cid:28) V kBT, electron transport through the TDQD detec- Speciﬁcally, let us inves−tigate the current and noise in tor is exponentially suppressed. The current ﬂuctuation the bias regime 1: 2(E E ) > V > 2(E + E ) and 4 2 5 2 is dominated by thermal noise described by the hyper- regime 2: V > 2(E + E ). Here the factor of “2” arises 4 2 bolic cotangent behavior [46], which leads to a divergence from the symmetric application of the bias voltage. In of the Fano factor at V = 0, as shown in Fig. 2(c). Each these two wide regions where electrode chemical poten- time when a new excitation energy (as indicated in Table tials are far away from the excitation energies of the dou- I) lies within the energy window deﬁned by the chemical ble dot, the Fermi functions can be well approximated by potentials of the left and right electrodes, a new transport either one or zero. Analytical results of the current and (cid:28) channel opens, which gives rise to plateaus, separated by noise are obtained for (cid:15) = (cid:15) = 0, and Ω, W U, as q T thermally broadened steps. Owing to symmetric appli- listed in Table II. Indeed, the current plateau height de- cation of the bias, the steps take place at bias voltages pend on the coupling parameters Γ and Γ only, while L R twice of the corresponding excitation energy. noise and Fano factor are both sensitive to the interdot The plateau heights of the current are found to be inde- couplings Ω and W. St→rikingly, a→divergent Fano factor pendent on Ω. Variation of Ω changes the eigenenergies is found in the limit Ω 0 or W 0. (see Table I), leading thus only to small shift of the cur- To investigate in detail the underlying physics that rent steps, as displayed in Fig. 2(a). The plateau heights leads to the divergent Fano factor, we now resort to the of noise and Fano factor, however, are sensitively modu- real-time measurement dynamics of the reduced system, lated by Ω, showing shot noise as a more sensitive diag- i.e., the usual single measurement realizations in experi- nostic tool than the current. For Ω/Γ = 0.5, the noise is ments. In what follows, we will consider a typical voltage well below the Poissonian value. An decrease in Ω leads V/Γ = 10 in the bias regime 1 as shown in Fig. 2, such | (cid:105) to a strong enhancement of the Fano factor. In partic- that the state “ c ” [Fig. 1(c)] is energetically prohibited. ular, a prominent super-Poissonian noise is observed for The reason we consider this regime is that the measured | − | Ω/Γ = 0.1, as shown by the dotted curve in Fig. 2(c). current visibility, deﬁned as I I /(I +I ), can reach α β α β In literature, diﬀerent mechanisms responsible for super- the maximum value of 1. Here I (I ) stands for the α β Poissonian noise have been identiﬁed, such as dynamical current through the TDQD when the qubit occupies the | (cid:105) | (cid:105) channel blockade [59–62], dynamical spin blockade [63– logical state α ( β ). Electrons ﬂow in one direction: 65], or cotunneling events [66–68]. Our result reveals that An extra electron injects into the QD1 from the left elec- ##LTFigure## ##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## ##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## ##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## ##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## ##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## ##LTLine## ##LTLine##

text: c

text: c

text: c

text: aa

text: bb

text: dd

text: RNd

text: (a)

text: (e)

text: (b)

text: (f)

text: (c)

text: (g)

text: (d)

text: (h)

text: Time

text: [t

text: Time

text: [t

text: FIG.

text: Sets

text: of

text: typical

text: quantum

text: trajectories

text: and

text: corresponding

text: detection

text: records

text: for

text: Ω/Γ

text: (a)-(d)

text: and

text: Ω/Γ

text: (e)-(h)

text: with

text: the

text: same

text: initial

text: condition

text: ρc

text: (t

text: a

text: ρc(t

text: a

text: The

text: measurement

text: voltage

text: V/Γ

text: is

text: within

text: the

text: bias

text: aa

text: regime

text: [see

text: Fig.

text: such

text: that

text: the

text: state

text: c

text: as

text: shown

text: in

text: Fig.

text: is

text: energetically

text: prohibited.

text: The

text: Fermi

text: energies

text: are

text: far

text: from

text: the

text: excitation

text: energies

text: of

text: the

text: reduced

text: system,

text: such

text: that

text: the

text: Fermi

text: functions

text: can

text: be

text: approximated

text: by

text: either

text: or

text: and

text: thus

text: temperature

text: is

text: not

text: involved

text: here.

text: The

text: time

text: step

text: used

text: is

text: Other

text: plotting

text: parameters

text: are:

text: W/Γ

text: q

text: T

text: Γ

text: /Γ

text: and

text: U/Γ

text: L

text: R

text: The

text: measurement

text: current

text: I¯,

text: zero

text: frequency

text: noise

text: the

text: intrinsic

text: dynamics

text: of

text: the

text: qubit

text: serves

text: as

text: an

text: additional

text: and

text: the

text: Fano

text: factor

text: F

text: versus

text: voltage

text: are

text: mechanism

text: that

text: may

text: lead

text: to

text: super-Poissonian

text: shot

text: noise

text: plotted

text: in

text: Fig.

text: respectively.

text: At

text: very

text: low

text: bias

text: in

text: a

text: double

text: dot

text: detector.

text: V

text: kBT,

text: electron

text: transport

text: through

text: the

text: TDQD

text: detec-

text: Speciﬁcally,

text: let

text: us

text: inves−tigate

text: the

text: current

text: and

text: noise

text: in

text: tor

text: is

text: exponentially

text: suppressed.

text: The

text: current

text: ﬂuctuation

text: the

text: bias

text: regime

text: E

text: V

text: E

text: and

text: is

text: dominated

text: by

text: thermal

text: noise

text: described

text: by

text: the

text: hyper-

text: regime

text: V

text: E

text: Here

text: the

text: factor

text: of

text: “2”

text: arises

text: bolic

text: cotangent

text: behavior

text: which

text: leads

text: to

text: a

text: divergence

text: from

text: the

text: symmetric

text: application

text: of

text: the

text: bias

text: voltage.

text: In

text: of

text: the

text: Fano

text: factor

text: at

text: V

text: as

text: shown

text: in

text: Fig.

text: Each

text: these

text: two

text: wide

text: regions

text: where

text: electrode

text: chemical

text: poten-

text: time

text: when

text: a

text: new

text: excitation

text: energy

text: (as

text: indicated

text: in

text: Table

text: tials

text: are

text: far

text: away

text: from

text: the

text: excitation

text: energies

text: of

text: the

text: dou-

text: I)

text: lies

text: within

text: the

text: energy

text: window

text: deﬁned

text: by

text: the

text: chemical

text: ble

text: dot,

text: the

text: Fermi

text: functions

text: can

text: be

text: well

text: approximated

text: by

text: potentials

text: of

text: the

text: left

text: and

text: right

text: electrodes,

text: a

text: new

text: transport

text: either

text: one

text: or

text: zero.

text: Analytical

text: results

text: of

text: the

text: current

text: and

text: channel

text: opens,

text: which

text: gives

text: rise

text: to

text: plateaus,

text: separated

text: by

text: noise

text: are

text: obtained

text: for

text: and

text: Ω,

text: W

text: U,

text: as

text: q

text: T

text: thermally

text: broadened

text: steps.

text: Owing

text: to

text: symmetric

text: appli-

text: listed

text: in

text: Table

text: II.

text: Indeed,

text: the

text: current

text: plateau

text: height

text: de-

text: cation

text: of

text: the

text: bias,

text: the

text: steps

text: take

text: place

text: at

text: bias

text: voltages

text: pend

text: on

text: the

text: coupling

text: parameters

text: Γ

text: and

text: Γ

text: only,

text: while

text: L

text: R

text: twice

text: of

text: the

text: corresponding

text: excitation

text: energy.

text: noise

text: and

text: Fano

text: factor

text: are

text: both

text: sensitive

text: to

text: the

text: interdot

text: The

text: plateau

text: heights

text: of

text: the

text: current

text: are

text: found

text: to

text: be

text: inde-

text: couplings

text: Ω

text: and

text: W.

text: St→rikingly,

text: a→divergent

text: Fano

text: factor

text: pendent

text: on

text: Ω.

text: Variation

text: of

text: Ω

text: changes

text: the

text: eigenenergies

text: is

text: found

text: in

text: the

text: limit

text: Ω

text: or

text: W

text: (see

text: Table

text: I),

text: leading

text: thus

text: only

text: to

text: small

text: shift

text: of

text: the

text: cur-

text: To

text: investigate

text: in

text: detail

text: the

text: underlying

text: physics

text: that

text: rent

text: steps,

text: as

text: displayed

text: in

text: Fig.

text: The

text: plateau

text: heights

text: leads

text: to

text: the

text: divergent

text: Fano

text: factor,

text: we

text: now

text: resort

text: to

text: the

text: of

text: noise

text: and

text: Fano

text: factor,

text: however,

text: are

text: sensitively

text: modu-

text: real-time

text: measurement

text: dynamics

text: of

text: the

text: reduced

text: system,

text: lated

text: by

text: Ω,

text: showing

text: shot

text: noise

text: as

text: a

text: more

text: sensitive

text: diag-

text: i.e.,

text: the

text: usual

text: single

text: measurement

text: realizations

text: in

text: experi-

text: nostic

text: tool

text: than

text: the

text: current.

text: For

text: Ω/Γ

text: the

text: noise

text: is

text: ments.

text: In

text: what

text: follows,

text: we

text: will

text: consider

text: a

text: typical

text: voltage

text: well

text: below

text: the

text: Poissonian

text: value.

text: An

text: decrease

text: in

text: Ω

text: leads

text: V/Γ

text: in

text: the

text: bias

text: regime

text: as

text: shown

text: in

text: Fig.

text: such

text: to

text: a

text: strong

text: enhancement

text: of

text: the

text: Fano

text: factor.

text: In

text: partic-

text: that

text: the

text: state

text: c

text: [Fig.

text: is

text: energetically

text: prohibited.

text: ular,

text: a

text: prominent

text: super-Poissonian

text: noise

text: is

text: observed

text: for

text: The

text: reason

text: we

text: consider

text: this

text: regime

text: is

text: that

text: the

text: measured

text: Ω/Γ

text: as

text: shown

text: by

text: the

text: dotted

text: curve

text: in

text: Fig.

text: current

text: visibility,

text: deﬁned

text: as

text: I

text: I

text: /(I

text: +I

text: can

text: reach

text: α

text: β

text: α

text: β

text: In

text: literature,

text: diﬀerent

text: mechanisms

text: responsible

text: for

text: super-

text: the

text: maximum

text: value

text: of

text: Here

text: I

text: (I

text: stands

text: for

text: the

text: α

text: β

text: Poissonian

text: noise

text: have

text: been

text: identiﬁed,

text: such

text: as

text: dynamical

text: current

text: through

text: the

text: TDQD

text: when

text: the

text: qubit

text: occupies

text: the

text: channel

text: blockade

text: dynamical

text: spin

text: blockade

text: logical

text: state

text: α

text: β

text: Electrons

text: ﬂow

text: in

text: one

text: direction:

text: or

text: cotunneling

text: events

text: Our

text: result

text: reveals

text: that

text: An

text: extra

text: electron

text: injects

text: into

text: the

text: from

text: the

text: left

text: elec-

text: ##LTFigure##

text: ##LTFigure##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: Figure 3: Schematic representation of the conformal map h (z) and the backward conformal map − t f (w) ζ on the SLE trace. t t of bcc’s. Real-axis to real-axis random curves: As an example of the above discussion, we consider the FIG 2 in which the mentioned preferred point is the ending point of the curve (which does not go to the inﬁnity, but after the exploration process − turns to the real axis). For this set-up, by using the conformal map φ = x∞z/(x∞ z), one can send the end point of the curve to the inﬁnity. Since our model is conformal invariant, we can deduce that ◦ ◦ − the function h = φ g φ 1 describes ordinary (chordal) SLE from which one easily concludes that g t { (cid:48)t − } (cid:48) ≡ t satisﬁes ∂ g = 2/( φ (g )(φ(g ) ζ ) ) in which φ (z) dφ. The other criteria is to make the mapping t t t t t dz hydrodynamically normalized. It has been shown [17] that the stochastic equation of hydrodunamically normalized g is the same as Eq. (1) with the price that ζ acquires a drift term as follows [17]: t t √ − κ 6 dζ = κdB + − dt (3) t t ζ g (x∞) t t − In the other words, this stochastic function is the driving function of the SLE(κ, ρ ) with ρ = κ 6. c c Thus for the critical curves from boundary to boundary, the corresponding driving function acquires a drift term. This generalization of SLE can be generalized further to have multiple preferred real axis points and multi-critical curves [6]. For review see also references [2, 15]. ∞ The other example is the traces which terminate surely to the real axis in the interval [x , ). For − 0 these curves of course the point x is regarded as the preferred point for which ρ = (κ 6)/2 yields 0 c dipolar SLE(κ) [4, 6, 17]. 3 Derivation of Fokker-Planck Equation In this section we are going to ﬁnd the Langevin equation for the tip of the chordal SLE trace. Let us ﬁrst deﬁne the shifted conformal map as follows: ≡ − h (z) g (z) ζ (4) t t t for which one can easily verify that − − h 1(w) =d g 1(w + ζ ). (5) t t t 4 ##LTFigure## ##LTLine## ##LTLine## ##LTLine##

text: Figure

label: paragraph

text: Schematic

label: caption

text: representation

text: of

text: the

text: conformal

text: map

text: h

text: (z)

text: and

text: the

text: backward

text: conformal

text: map

text: t

text: f

text: (w)

text: ζ

text: on

text: the

text: SLE

text: trace.

text: t

text: t

text: of

text: bcc’s.

text: Real-axis

text: to

text: real-axis

text: random

text: curves:

text: As

text: an

text: example

text: of

text: the

text: above

text: discussion,

text: we

text: consider

text: the

text: FIG

text: in

text: which

text: the

text: mentioned

text: preferred

text: point

text: is

text: the

text: ending

text: point

text: of

text: the

text: curve

text: (which

text: does

text: not

text: go

text: to

text: the

text: inﬁnity,

text: but

text: after

text: the

text: exploration

text: process

text: turns

text: to

text: the

text: real

text: axis).

text: For

text: this

text: set-up,

text: by

text: using

text: the

text: conformal

text: map

text: φ

text: x∞z/(x∞

text: z),

text: one

text: can

text: send

text: the

text: end

text: point

text: of

text: the

text: curve

text: to

text: the

text: inﬁnity.

text: Since

text: our

text: model

text: is

text: conformal

text: invariant,

text: we

text: can

text: deduce

text: that

text: the

text: function

text: h

text: φ

text: g

text: φ

text: describes

text: ordinary

text: (chordal)

text: SLE

text: from

text: which

text: one

text: easily

text: concludes

text: that

text: g

text: t

text: t

text: satisﬁes

text: g

text: φ

text: (g

text: )(φ(g

text: ζ

text: in

text: which

text: φ

text: (z)

text: dφ.

text: The

text: other

text: criteria

text: is

text: to

text: make

text: the

text: mapping

text: t

text: t

text: t

text: t

text: t

text: dz

text: hydrodynamically

text: normalized.

text: It

text: has

text: been

text: shown

text: that

text: the

text: stochastic

text: equation

text: of

text: hydrodunamically

text: normalized

text: g

text: is

text: the

text: same

text: as

text: Eq.

text: with

text: the

text: price

text: that

text: ζ

text: acquires

text: a

text: drift

text: term

text: as

text: follows

text: t

text: t

text: κ

text: dζ

text: κdB

text: dt

text: t

text: t

text: ζ

text: g

text: (x∞)

text: t

text: t

text: In

text: the

text: other

text: words,

text: this

text: stochastic

text: function

text: is

text: the

text: driving

text: function

text: of

text: the

text: SLE(κ,

text: ρ

text: with

text: ρ

text: κ

text: c

text: c

text: Thus

text: for

text: the

text: critical

text: curves

text: from

text: boundary

text: to

text: boundary,

text: the

text: corresponding

text: driving

text: function

text: acquires

text: a

text: drift

text: term.

text: This

text: generalization

text: of

text: SLE

text: can

text: be

text: generalized

text: further

text: to

text: have

text: multiple

text: preferred

text: real

text: axis

text: points

text: and

text: multi-critical

text: curves

text: For

text: review

text: see

text: also

text: references

text: The

text: other

text: example

text: is

text: the

text: traces

text: which

text: terminate

text: surely

text: to

text: the

text: real

text: axis

text: in

text: the

text: interval

text: [x

text: For

text: these

text: curves

text: of

text: course

text: the

text: point

text: x

text: is

text: regarded

text: as

text: the

text: preferred

text: point

text: for

text: which

text: ρ

text: (κ

text: yields

text: c

text: dipolar

text: SLE(κ)

text: Derivation

text: of

text: Fokker-Planck

text: Equation

text: In

text: this

text: section

text: we

text: are

text: going

text: to

text: ﬁnd

text: the

text: Langevin

text: equation

text: for

text: the

text: tip

text: of

text: the

text: chordal

text: SLE

text: trace.

text: Let

text: us

text: ﬁrst

text: deﬁne

text: the

text: shifted

text: conformal

text: map

text: as

text: follows:

text: h

text: (z)

text: g

text: (z)

text: ζ

text: t

text: t

text: t

text: for

text: which

text: one

text: can

text: easily

text: verify

text: that

text: h

text: =d

text: g

text: ζ

text: t

text: t

text: t

text: ##LTFigure##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: SN 1994I Progenitor Companion 3 SN 1994I site SN 1994I site (a) F275W 2014 (b) F336W 2014 N N 0.5" 0.5" E E Figure 1. A portion of the WFC3/UVIS images obtained in 2014 September of the SN 1994I site in bands (a) F275W and (b) F336W. The position of the SN in these images is indicated by the tick marks. The rms uncertainty in this position is 0.35 UVIS pixel (13.9 milliarcsec). North is up, and east is to the left. Schuyler D. Van Dyk1, Selma E. de Mink2, and Emmanouil Zapartas2 Keywords: supernovae: individual (SN 1994I) — galaxies: individual (NGC 5194) — binaries (includ- ing multiple): close — stars: massive — stars: evolution position into the WFC3 images and attempted to de- SN 1994I SN 1994I (a) F255W 1994 (b) F336W 1994 tect and measure them above the complex background using Dolphot (Dolphin 2000). However, ﬁrst, we ap- plied a pixel-based correction to the frames for any CTE losses beforehand, using the routines available for this purpose7. Dolphot was then run on the corrected ‘ﬂc’ frames for each band. At F275W we were able to place ∼ a detection limit of > 26.1 mag at 4σ. At F336W the detection limit that we established is > 24.7 mag at ∼ N N 11σ. As a consequence of the higher detection thresh- 0.5" 0.5" E E old in this latter band, the F336W data do not provide as stringent of a constraint as do the F275W data. This Figure 2. A portion of the WFPC2/PC images of SN 1994I ob- is likely a result of the overall higher diﬀuse background tained on 1994 May 12 (as part of GO-5652), in (a) F255W and (b) around the SN site, as can be seen in Figure 1. F336W. These images are shown to the same scale and orientation as those in Figure 1. The SN is indicated by the tick marks. North Next we need to make assumptions about the distance is up, east is to the left. and reddening to the SN. Ergon et al. (2014) adopted a distance to M51 of 7.8+−1.1 Mpc. Vink´o et al. (2012), ap- 3. DATA ANALYSIS plying the Expanding P0h.9otospheres Method to the two We ﬁrst must pinpoint the precise location of SN 1994I Type II SNe in M51, 2005cs and 2011dh, measured a ± in the new HST images. Fortunately, HST image data distance of 8.4 0.5 Mpc (assuming their systematic un- exist, obtained in 1994 by GO-5652 (PI: R. Kirshner) of certainty). These two estimates are essentially consistent the SN itself using the Wide-Field Planetary Camera 2 with each other and with the surface brightness ﬂuctua- ± (WFPC2) in similar bands, F255W and F336W. The SN tion (SBF) distance of 7.7 1.0 Mpc (distance modulus ± was located on the PC chip of WFPC2. We display these 29.42 0.27 mag) measured to M51b by Tonry et al. images in Figure 2. To establish an astrometric grid, (2001). We therefore consider here the full range of pos- we employed 24 isolated, stellar-like objects in common sible distances to SN 1994I, i.e., 6.7–8.9 Mpc. between the WFPC2 F336W image data from 1994 and The reddening to SN 1994I is likely signiﬁcant, but the new F336W image. (This band had an overall higher relatively uncertain. An estimate of the Galactic fore- signal-to-noise ratio for both image datasets than did the ground extinction contribution can be obtained from F255W/F275W ones.) The SN position can be placed in Schlaﬂy & Finkbeiner (2011) to be A = 0.096 mag, − V the WFC3 F336W image with an rms uncertainty of 0.35 i.e., E(B V ) = 0.031 mag. From model ﬁts to the UVIS pixel (13.9 milliarcsec). early-time light curves, Iwamoto et al. (1994) arrive at ± − ± The SN position is indicated in Figure 1. As can be A = 1.4 0.25 mag (E[B V ] = 0.45 0.08 mag). V seen from the ﬁgure, no source is obviously detected in From model ﬁts to the early spectra, Baron et al. (1996) − either WFC3 band. found E(B V ) = 0.29–0.45 mag. From further de- To establish the detection limit in each of the F275W tailed theoretical modeling of early-time spectra, Sauer and F336W bands, we inserted artiﬁcial stars at the SN et al. (2006) concluded that the reddening had to be − ± E(B V ) = 0.30 0.05 mag. Richmond et al. (1996) − ± ± assumed E(B V ) = 0.45 0.16 mag (or A = 1.4 0.5 1 IPAC/Caltech, 100-22, Pasadena, CA 91125 USA V 2 Anton Pannekoek Astronomical Institute, University of Am- sterdam, 1090 GE Amsterdam, The Netherlands 7 Anderson, J., 2013, http://www.stsci.edu/hst/wfc3/tools/cte tools. ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: SN

text: Progenitor

text: Companion

text: SN

font: default

text: site

text: SN

text: site

text: (a)

text: (b)

text: N

text: N

text: E

text: E

text: Figure

text: A

text: portion

text: of

text: the

text: images

text: obtained

text: in

text: September

text: of

text: the

text: SN

text: site

text: in

text: bands

text: (a)

text: and

text: (b)

text: The

text: position

text: of

text: the

text: SN

text: in

text: these

text: images

text: is

text: indicated

text: by

text: the

text: tick

text: marks.

text: The

text: rms

text: uncertainty

text: in

text: this

text: position

text: is

text: UVIS

text: pixel

text: milliarcsec).

text: North

text: is

text: up,

text: and

text: east

text: is

text: to

text: the

text: left.

text: Schuyler

text: D.

text: Van

text: Selma

text: E.

text: de

text: and

text: Emmanouil

text: Keywords:

text: supernovae:

text: individual

text: (SN

text: galaxies:

text: individual

text: (NGC

text: binaries

text: (includ-

text: ing

text: multiple):

text: close

text: stars:

text: massive

text: stars:

text: evolution

text: position

text: into

text: the

text: images

text: and

text: attempted

text: to

text: de-

text: SN

text: SN

text: (a)

text: (b)

text: tect

text: and

text: measure

text: them

text: above

text: the

text: complex

text: background

text: using

text: Dolphot

text: (Dolphin

text: However,

text: ﬁrst,

text: we

text: ap-

text: plied

text: a

text: pixel-based

text: correction

text: to

text: the

text: frames

text: for

text: any

text: CTE

text: losses

text: beforehand,

text: using

text: the

text: routines

text: available

text: for

text: this

text: Dolphot

text: was

text: then

text: run

text: on

text: the

text: corrected

text: ‘ﬂc’

text: frames

text: for

text: each

text: band.

text: At

text: we

text: were

text: able

text: to

text: place

text: a

text: detection

text: limit

text: of

text: mag

text: at

text: At

text: the

text: detection

text: limit

text: that

text: we

text: established

text: is

text: mag

text: at

text: N

text: N

text: As

text: a

text: consequence

text: of

text: the

text: higher

text: detection

text: thresh-

text: E

text: E

text: old

text: in

text: this

text: latter

text: band,

text: the

text: data

text: do

text: not

text: provide

text: as

text: stringent

text: of

text: a

text: constraint

text: as

text: do

text: the

text: data.

text: This

text: Figure

text: A

text: portion

text: of

text: the

text: images

text: of

text: SN

text: ob-

text: is

text: likely

text: a

text: result

text: of

text: the

text: overall

text: higher

text: diﬀuse

text: background

text: tained

text: on

text: May

text: (as

text: part

text: of

text: in

text: (a)

text: and

text: (b)

text: around

text: the

text: SN

text: site,

text: as

text: can

text: be

text: seen

text: in

text: Figure

text: These

text: images

text: are

text: shown

text: to

text: the

text: same

text: scale

text: and

text: orientation

text: as

text: those

text: in

text: Figure

text: The

text: SN

text: is

text: indicated

text: by

text: the

text: tick

text: marks.

text: North

text: Next

text: we

text: need

text: to

text: make

text: assumptions

text: about

text: the

text: distance

text: is

text: up,

text: east

text: is

text: to

text: the

text: left.

text: and

text: reddening

text: to

text: the

text: SN.

text: Ergon

text: et

text: al.

text: adopted

text: a

text: distance

text: to

text: of

text: Mpc.

text: Vink´o

text: et

text: al.

text: ap-

text: DATA

text: ANALYSIS

text: plying

text: the

text: Expanding

text: Method

text: to

text: the

text: two

text: We

text: ﬁrst

text: must

text: pinpoint

text: the

text: precise

text: location

text: of

text: SN

text: Type

text: II

text: SNe

text: in

text: and

text: measured

text: a

text: in

text: the

text: new

text: HST

text: images.

text: Fortunately,

text: HST

text: image

text: data

text: distance

text: of

text: Mpc

text: (assuming

text: their

text: systematic

text: un-

text: exist,

text: obtained

text: in

text: by

text: (PI:

text: R.

text: Kirshner)

text: of

text: certainty).

text: These

text: two

text: estimates

text: are

text: essentially

text: consistent

text: the

text: SN

text: itself

text: using

text: the

text: Wide-Field

text: Planetary

text: Camera

text: with

text: each

text: other

text: and

text: with

text: the

text: surface

text: brightness

text: ﬂuctua-

text: in

text: similar

text: bands,

text: and

text: The

text: SN

text: tion

text: (SBF)

text: distance

text: of

text: Mpc

text: (distance

text: modulus

text: was

text: located

text: on

text: the

text: PC

text: chip

text: of

text: We

text: display

text: these

text: mag)

text: measured

text: to

text: by

text: Tonry

text: et

text: al.

text: images

text: in

text: Figure

text: To

text: establish

text: an

text: astrometric

text: grid,

text: We

text: therefore

text: consider

text: here

text: the

text: full

text: range

text: of

text: pos-

text: we

text: employed

text: isolated,

text: stellar-like

text: objects

text: in

text: common

text: sible

text: distances

text: to

text: SN

text: i.e.,

text: Mpc.

text: between

text: the

text: image

text: data

text: from

text: and

text: The

text: reddening

text: to

text: SN

text: is

text: likely

text: signiﬁcant,

text: but

text: the

text: new

text: image.

text: (This

text: band

text: had

text: an

text: overall

text: higher

text: relatively

text: uncertain.

text: An

text: estimate

text: of

text: the

text: Galactic

text: fore-

text: signal-to-noise

text: ratio

text: for

text: both

text: image

text: datasets

text: than

text: did

text: the

text: ground

text: extinction

text: contribution

text: can

text: be

text: obtained

text: from

text: ones.)

text: The

text: SN

text: position

text: can

text: be

text: placed

text: in

text: Schlaﬂy

text: Finkbeiner

text: to

text: be

text: A

text: mag,

text: V

text: the

text: image

text: with

text: an

text: rms

text: uncertainty

text: of

text: i.e.,

text: E(B

text: V

text: mag.

text: From

text: model

text: ﬁts

text: to

text: the

text: UVIS

text: pixel

text: milliarcsec).

text: early-time

text: light

text: curves,

text: Iwamoto

text: et

text: al.

text: arrive

text: at

text: The

text: SN

text: position

text: is

text: indicated

text: in

text: Figure

text: As

text: can

text: be

text: A

text: mag

text: (E[B

text: V

text: mag).

text: V

text: seen

text: from

text: the

text: ﬁgure,

text: no

text: source

text: is

text: obviously

text: detected

text: in

text: From

text: model

text: ﬁts

text: to

text: the

text: early

text: spectra,

text: Baron

text: et

text: al.

text: either

text: band.

text: found

text: E(B

text: V

text: mag.

text: From

text: further

text: de-

text: To

text: establish

text: the

text: detection

text: limit

text: in

text: each

text: of

text: the

text: tailed

text: theoretical

text: modeling

text: of

text: early-time

text: spectra,

text: Sauer

text: and

text: bands,

text: we

text: inserted

text: artiﬁcial

text: stars

text: at

text: the

text: SN

text: et

text: al.

text: concluded

text: that

text: the

text: reddening

text: had

text: to

text: be

text: E(B

text: V

text: mag.

text: Richmond

text: et

text: al.

text: assumed

text: E(B

text: V

text: mag

text: (or

text: A

text: IPAC/Caltech,

text: Pasadena,

text: CA

text: USA

text: V

text: Anton

text: Pannekoek

text: Astronomical

text: Institute,

text: University

text: of

text: Am-

text: sterdam,

text: GE

text: Amsterdam,

text: The

text: Netherlands

text: Anderson,

text: J.,

text: tools.

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTFigure##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: ∼ using Dolphot, and estimate a very low upper limit to at, say, the 10% level, this would not aﬀect our con- ∼ ≈ detection of 23.8 mag (at 6σ), or 0.5 µJy. We there- clusions here. We would still place a mass limit on a forAecccoepntseiddetrothapepeliakreliinhoAopdJ.of excess dust extinction to comp∼anion at 10 M(cid:12). However, if additional reddening bePlroepwri.ntItfyptheseetSuNsingwLeArTeEXsosmtyleeheomwulaatdeadpijtivo.n12a/ll1y6/r1e1ddened were 20%, the star would then have to be h(cid:38)otter than B1V and the inferred mass limit would be at 17 M(cid:12). CONSTRAINTS ON THE BINARY COMPANION TO THE SN IC 1994I PROGENITOR Schuyler D. Van Dyk1, Selma E. de Mink2, and Emmanouil Zapartas2 Keywords: supernovae: individual (SN 1994I) — galaxies: individual (NGC 5194) — binaries (includ- ing multiple): close — stars: massive — stars: evolution 4. INTERPRETATION upper limits. Also a neutron star or white dwarf com- panion (Path B and C) would not be detectable, based 4.1. Comparison with the original predictions by on our HST data. Nomoto et al. (1994) 4.2. Comparison with new population synthesis Not long after the discovery of SN 1994I, Nomoto et predictions al. (1994) argued that a single star scenario, where the To reassess the original predictions by Nomoto et al. envelope is removed by stellar winds, is inconsistent with (1994) and to provide a theoretical framework to put our the rapid decline of the light curve. The single-star sce- new upper limits in perspective, we performed new pop- nario predicts massive C- and O-rich stars as progenitors. ulation synthesis simulations. We aim to investigate the A high-mass progenitor would imply considerably longer possible progenitor systems that produce “1994I-like” light curve decline times than observed. events, as we will deﬁne below. Instead, Nomoto et al. (1994) proposed three possi- 4.2.1. Method and assumptions ble binary scenarios to explain the observed properties of SN 1994I. Those authors did not present simulations for these scenarios, but they did provide quantitative We employ the binary c synthetic binary evolutionary arguments to estimate the relative contribution of the code developed by Izzard et al. (2004, 2006, 2009), with scenarios. They concluded that the three scenarios are updated treatments for the massive binaries as described roughly equally as likely. (We draw a diﬀerent conclu- in de Mink et al. (2013). This code relies on the ap- sion based on our new simulations, as discussed below in proximate evolutionary algorithms by Tout et al. (1997) Section 4.2.) and Hurley et al. (2000, 2002). These algorithms are so In all three scenarios the SN progenitor is stripped by fast and robust that they allow predictions to be made a companion in two subsequent stages. The ﬁrst stage for entire populations of massive binaries. At present removes the H envelope and leaves behind a naked He such simulations are too demanding for detailed binary (cid:46) star with M 4 M(cid:12). Such low-mass He stars expand evolutionary codes, such as MESA (e.g., Paxton et al. substantially during the He shell burning phase and can 2015); see, however, Eldridge et al. (2008). Future in- reach sizes of tens of solar radii. The expansion can cause vestigation with detailed codes would be desirable, but them to ﬁll their Roche lobe a second time, now removing our method is suitable for the scope of the present study. a large fraction of the He layers. In a forthcoming paper (Zapartas et al., in preparation) The three scenarios diﬀer with respect to the type of we will present an extended discussion based on these the companion. In Path A the SN results from the pri- simulations of the impact of binarity on the statistical mary, i.e., the initially more massive star. The compan- properties of core-collapse SNe in general. A complete ion is a low-mass main sequence star (1–4 M(cid:12)). The high description of the assumptions is provided in de Mink et mass ratio at the onset of the ﬁrst Roche lobe overﬂow al. (2013, and references therein). Below, we provide a ensures highly non-conservative mass transfer. In Paths brief summary of the assumptions for the most relevant B and C the SN Ic results from the secondary, i.e., the physical processes. initially less massive star. For both of these latter two We simulate a population of binary stars assuming con- paths the primary evolves ﬁrst and leaves behind a com- tinuous star formation, choosing initial primary masses, pact remnant: either a neutron star for Path B or a white M , from a Kroupa (2001) initial mass function. The 1 dwarf for Path C. In both cases the compact remnant of compani≡on masses, M2, are chosen such that the mass the primary strips the original secondary star of most of ratio, q M /M , is distributed uniformly between 0.1 2 1 its He. and 1 (e.g., Duchˆene & Kraus 2013; Sana et al. 2012). For Our upper limits on the presence of a companion are the initial orbital periods, we assume a uniform distribu- consistent with all three binary evolutionary paths from tion in log space (“O¨pik’s law;” O¨pik 1924). For systems Nomoto et al. (1994). A low-mass (1–4 M(cid:12)) main se- with initial masses above 15 M(cid:12) we adopt the steeper quence companion (Path A) is well within the observed distribution by Sana et al. (2012). We consider initial or- ≤ ≤ bital periods, p, in the range 0.15 log p(days) 3.5, 10 1 IPAC/Caltech, 100-22, Pasadena, CA 91125 USA cons×istent×with Sana et al. (2012). We simulate a grid of 2 Anton Pannekoek Astronomical Institute, University of Am- 200 200 200 binary systems, varying the initial masses sterdam, 1090 GE Amsterdam, The Netherlands of both stars and the initial orbital period. ##LTLine##

text: using

text: Dolphot,

text: and

text: estimate

text: a

text: very

text: low

text: upper

text: limit

text: to

text: at,

text: say,

text: the

text: level,

text: this

text: would

text: not

text: aﬀect

text: our

text: con-

text: detection

text: of

text: mag

text: (at

text: or

text: µJy.

text: We

text: there-

text: clusions

text: here.

text: We

text: would

text: still

text: place

text: a

text: mass

text: limit

text: on

text: a

label: section

text: excess

text: dust

text: extinction

text: to

text: comp∼anion

text: at

text: However,

text: if

text: additional

text: reddening

text: were

text: the

text: star

text: would

text: then

text: have

text: to

text: be

text: than

text: and

text: the

text: inferred

text: mass

text: limit

text: would

text: be

text: at

text: CONSTRAINTS

text: ON

text: THE

text: BINARY

text: COMPANION

text: TO

text: THE

text: SN

text: IC

text: PROGENITOR

text: Schuyler

label: author

text: D.

text: Van

text: Selma

text: E.

text: de

text: and

text: Emmanouil

text: Keywords:

text: supernovae:

text: individual

text: (SN

text: galaxies:

text: individual

text: (NGC

text: binaries

text: (includ-

text: ing

text: multiple):

text: close

text: stars:

text: massive

text: stars:

text: evolution

text: INTERPRETATION

text: upper

text: limits.

text: Also

text: a

text: neutron

text: star

text: or

text: white

text: dwarf

text: com-

text: panion

text: (Path

text: B

text: and

text: C)

text: would

text: not

text: be

text: detectable,

text: based

text: Comparison

text: with

text: the

text: original

text: predictions

text: by

text: on

text: our

text: HST

text: data.

text: Nomoto

text: et

text: al.

text: Comparison

text: with

text: new

text: population

text: synthesis

text: Not

text: long

text: after

text: the

text: discovery

text: of

text: SN

text: Nomoto

text: et

text: predictions

text: al.

text: argued

text: that

text: a

text: single

text: star

text: scenario,

text: where

text: the

text: To

text: reassess

text: the

text: original

text: predictions

text: by

text: Nomoto

text: et

text: al.

text: envelope

text: is

text: removed

text: by

text: stellar

text: winds,

text: is

text: inconsistent

text: with

text: and

text: to

text: provide

text: a

text: theoretical

text: framework

text: to

text: put

text: our

text: the

text: rapid

text: decline

text: of

text: the

text: light

text: curve.

text: The

text: single-star

text: sce-

text: new

text: upper

text: limits

text: in

text: perspective,

text: we

text: performed

text: new

text: pop-

text: nario

text: predicts

text: massive

text: C-

text: and

text: O-rich

text: stars

text: as

text: progenitors.

text: ulation

text: synthesis

text: simulations.

text: We

text: aim

text: to

text: investigate

text: the

text: A

text: high-mass

text: progenitor

text: would

text: imply

text: considerably

text: longer

text: possible

text: progenitor

text: systems

text: that

text: produce

text: light

text: curve

text: decline

text: times

text: than

text: observed.

text: events,

text: as

text: we

text: will

text: deﬁne

text: below.

text: Instead,

text: Nomoto

text: et

text: al.

text: proposed

text: three

text: possi-

text: Method

text: and

text: assumptions

text: ble

text: binary

text: scenarios

text: to

text: explain

text: the

text: observed

text: properties

text: of

text: SN

text: Those

text: authors

text: did

text: not

text: present

text: simulations

text: for

text: these

text: scenarios,

text: but

text: they

text: did

text: provide

text: quantitative

text: We

text: employ

text: the

text: binary

text: c

text: synthetic

text: binary

text: evolutionary

text: arguments

text: to

text: estimate

text: the

text: relative

text: contribution

text: of

text: the

text: code

text: developed

text: by

text: Izzard

text: et

text: al.

text: with

text: scenarios.

text: They

text: concluded

text: that

text: the

text: three

text: scenarios

text: are

text: updated

text: treatments

text: for

text: the

text: massive

text: binaries

text: as

text: described

text: roughly

text: equally

text: as

text: likely.

text: (We

text: draw

text: a

text: diﬀerent

text: conclu-

text: in

text: de

text: Mink

text: et

text: al.

text: This

text: code

text: relies

text: on

text: the

text: ap-

text: sion

text: based

text: on

text: our

text: new

text: simulations,

text: as

text: discussed

text: below

text: in

text: proximate

text: evolutionary

text: algorithms

text: by

text: Tout

text: et

text: al.

text: Section

text: and

text: Hurley

text: et

text: al.

text: These

text: algorithms

text: are

text: so

text: In

text: all

text: three

text: scenarios

text: the

text: SN

text: progenitor

text: is

text: stripped

text: by

text: fast

text: and

text: robust

text: that

text: they

text: allow

text: predictions

text: to

text: be

text: made

text: a

text: companion

text: in

text: two

text: subsequent

text: stages.

text: The

text: ﬁrst

text: stage

text: for

text: entire

text: populations

text: of

text: massive

text: binaries.

text: At

text: present

text: removes

text: the

text: H

text: envelope

text: and

text: leaves

text: behind

text: a

text: naked

text: He

text: such

text: simulations

text: are

text: too

text: demanding

text: for

text: detailed

text: binary

text: star

text: with

text: M

text: Such

text: low-mass

text: He

text: stars

text: expand

text: evolutionary

text: codes,

text: such

text: as

text: MESA

text: (e.g.,

text: Paxton

text: et

text: al.

text: substantially

text: during

text: the

text: He

text: shell

text: burning

text: phase

text: and

text: can

text: see,

text: however,

text: Eldridge

text: et

text: al.

text: Future

text: in-

text: reach

text: sizes

text: of

text: tens

text: of

text: solar

text: radii.

text: The

text: expansion

text: can

text: cause

text: vestigation

text: with

text: detailed

text: codes

text: would

text: be

text: desirable,

text: but

text: them

text: to

text: ﬁll

text: their

text: Roche

text: lobe

text: a

text: second

text: time,

text: now

text: removing

text: our

text: method

text: is

text: suitable

text: for

text: the

text: scope

text: of

text: the

text: present

text: study.

text: a

text: large

text: fraction

text: of

text: the

text: He

text: layers.

text: In

text: a

text: forthcoming

text: paper

text: (Zapartas

text: et

text: al.,

text: in

text: preparation)

text: The

text: three

text: scenarios

text: diﬀer

text: with

text: respect

text: to

text: the

text: type

text: of

text: we

text: will

text: present

text: an

text: extended

text: discussion

text: based

text: on

text: these

text: the

text: companion.

text: In

text: Path

text: A

text: the

text: SN

text: results

text: from

text: the

text: pri-

text: simulations

text: of

text: the

text: impact

text: of

text: binarity

text: on

text: the

text: statistical

text: mary,

text: i.e.,

text: the

text: initially

text: more

text: massive

text: star.

text: The

text: compan-

text: properties

text: of

text: core-collapse

text: SNe

text: in

text: general.

text: A

text: complete

text: ion

text: is

text: a

text: low-mass

text: main

text: sequence

text: star

text: The

text: high

text: description

text: of

text: the

text: assumptions

text: is

text: provided

text: in

text: de

text: Mink

text: et

text: mass

text: ratio

text: at

text: the

text: onset

text: of

text: the

text: ﬁrst

text: Roche

text: lobe

text: overﬂow

text: al.

text: and

text: references

text: therein).

text: Below,

text: we

text: provide

text: a

text: ensures

text: highly

text: non-conservative

text: mass

text: transfer.

text: In

text: Paths

text: brief

text: summary

text: of

text: the

text: assumptions

text: for

text: the

text: most

text: relevant

text: B

text: and

text: C

text: the

text: SN

text: Ic

text: results

text: from

text: the

text: secondary,

text: i.e.,

text: the

text: physical

text: processes.

text: initially

text: less

text: massive

text: star.

text: For

text: both

text: of

text: these

text: latter

text: two

text: We

text: simulate

text: a

text: population

text: of

text: binary

text: stars

text: assuming

text: con-

text: paths

text: the

text: primary

text: evolves

text: ﬁrst

text: and

text: leaves

text: behind

text: a

text: com-

text: tinuous

text: star

text: formation,

text: choosing

text: initial

text: primary

text: masses,

text: pact

text: remnant:

text: either

text: a

text: neutron

text: star

text: for

text: Path

text: B

text: or

text: a

text: white

text: M

text: from

text: a

text: Kroupa

text: initial

text: mass

text: function.

text: The

text: dwarf

text: for

text: Path

text: C.

text: In

text: both

text: cases

text: the

text: compact

text: remnant

text: of

text: compani≡on

text: masses,

text: are

text: chosen

text: such

text: that

text: the

text: mass

text: the

text: primary

text: strips

text: the

text: original

text: secondary

text: star

text: of

text: most

text: of

text: ratio,

text: q

text: M

text: /M

text: is

text: distributed

text: uniformly

text: between

text: its

text: He.

text: and

text: (e.g.,

text: Duchˆene

text: Kraus

text: Sana

text: et

text: al.

text: For

text: Our

text: upper

text: limits

text: on

text: the

text: presence

text: of

text: a

text: companion

text: are

text: the

text: initial

text: orbital

text: periods,

text: we

text: assume

text: a

text: uniform

text: distribu-

text: consistent

text: with

text: all

text: three

text: binary

text: evolutionary

text: paths

text: from

text: tion

text: in

text: log

text: space

text: (“O¨pik’s

text: law;”

text: O¨pik

text: For

text: systems

text: Nomoto

text: et

text: al.

text: A

text: low-mass

text: main

text: se-

text: with

text: initial

text: masses

text: above

text: we

text: adopt

text: the

text: steeper

text: quence

text: companion

text: (Path

text: A)

text: is

text: well

text: within

text: the

text: observed

text: distribution

text: by

text: Sana

text: et

text: al.

text: We

text: consider

text: initial

text: or-

text: bital

text: periods,

text: p,

text: in

text: the

text: range

text: log

text: p(days)

text: IPAC/Caltech,

text: Pasadena,

text: CA

text: USA

text: cons×istent×with

text: Sana

text: et

text: al.

text: We

text: simulate

text: a

text: grid

text: of

text: Anton

text: Pannekoek

text: Astronomical

text: Institute,

text: University

text: of

text: Am-

text: binary

text: systems,

text: varying

text: the

text: initial

text: masses

text: sterdam,

text: GE

text: Amsterdam,

text: The

text: Netherlands

text: of

text: both

text: stars

text: and

text: the

text: initial

text: orbital

text: period.

text: ##LTLine##


text: MNRAS 000, 1–?? (2015) Preprint 28 May 2020 Compiled using MNRAS LATEX style ﬁle v3.0 Galaxy And Mass Assembly (GAMA): The 325 MHz Radio Luminosity Function of AGN and Star Forming Galaxies Matthew Prescott1(cid:63), T. Mauch2, M.J. Jarvis1,3, K. McAlpine1, D.J.B. Smith4, S. Fine1, R. Johnston1, M.J. Hardcastle4, I.K. Baldry5, S. Brough6, M.J.I. Brown7, M.N. Bremer8, S.P. Driver9,10, A.M Hopkins6, L.S. Kelvin5, J. Loveday11, P. Norberg12, D. Obreschkow9 and E.M. Sadler13 1Department of Physics and Astronomy, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa 2SKA Africa, Third Floor, The Park, Park Road, Pinelands 7405, South Africa 3Oxford Astrophysics, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK 4Centre for Astrophysics Research, Science & Technology Research Institute, University of Hertfordshire, Hatﬁeld, Herts, AL10 9AB, UK 5 Astrophysics Research Institute, Liverpool John Moores University, IC2, Liverpool Science Park, 146 Brownlow Hill, Liverpool, L3 5RF 6 Australian Astronomical Observatory, PO Box 915, North Ryde, NSW 1670, Australia 7 School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia 8 H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK 9 ICRAR, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia 10 SUPA, School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, KY16 9SS, UK 11 Astronomy Centre, University of Sussex, Falmer, Brighton BN1 9QH, UK 12 Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham DH1 3LE, UK 13 School of Physics, University of Sydney, NSW 2006, Australia Accepted 2015 December 30. Received 2015 December 24; in original form 2015 August 27. ABSTRACT Measurement of the evolution of both active galactic nuclei (AGN) and star-formation in galaxies underpins our understanding of galaxy evolution over cosmic time. Radio continuum observations can provide key information on these two processes, in partic- ular via the mechanical feedback produced by radio jets in AGN, and via an unbiased dust-independent measurement of star-formation rates. In this paper we determine radio luminosity functions at 325 MHz for a sample of AGN and star-forming galax- ies by matching a 138 deg2 radio survey conducted with the Giant Metrewave Radio Telescope (GMRT), with optical imaging and redshifts from the Galaxy And Mass Assembly (GAMA) survey. We ﬁnd that the radio luminosity function at 325 MHz for star-forming galaxies closely follows that measured at 1.4 GHz. By ﬁtting the AGN radio luminosity function out to z = 0.5 as a double power law, and parametrizing the ∝ ± evolution as Φ (1 + z)k, we ﬁnd evolution parameters of k = 0.92 0.95 assuming ± pure density evolution and k = 2.13 1.96 assuming pure luminosity evolution. We ﬁnd that the Low Excitation Radio Galaxies are the dominant population in space density at lower luminosities. Comparing our 325 MHz observations with radio con- tinuum imaging at 1.4 GHz, we determine separate radio luminosity functions for steep and ﬂat-spectrum AGN, and show that the beamed population of ﬂat-spectrum sources in our sample can be shifted in number density and luminosity to coincide with the un-beamed population of steep-spectrum sources, as is expected in the orientation based uniﬁcation of AGN. Key words: surveys – galaxies:luminosity function – galaxies: evolution – galaxies: formation – radio continuum: galaxies – galaxies: active 1 INTRODUCTION In recent years it has become apparent that Active Galactic Nuclei (AGN) play an important role in the for- (cid:63) E-mail: mxp@uwcastro.org mation and evolution of galaxies. Every massive galaxy is (cid:13) c 2015 The Authors

text: MNRAS

text: Preprint

text: May

text: Compiled

text: using

text: MNRAS

text: LATEX

text: style

text: ﬁle

text: Galaxy

label: title

text: And

text: Mass

text: Assembly

text: (GAMA):

text: The

text: MHz

text: Radio

text: Luminosity

text: Function

text: of

text: AGN

text: and

text: Star

text: Forming

text: Galaxies

text: Matthew

text: T.

text: M.J.

text: K.

text: D.J.B.

text: S.

text: R.

text: M.J.

text: I.K.

text: S.

text: M.J.I.

text: M.N.

text: S.P.

text: A.M

text: L.S.

text: J.

text: P.

text: D.

text: and

text: E.M.

text: of

text: Physics

text: and

text: Astronomy,

text: University

text: of

text: the

text: Western

text: Cape,

text: Private

text: Bag

text: Bellville

text: South

text: Africa

text: Africa,

text: Third

text: Floor,

text: The

text: Park,

text: Park

text: Road,

text: Pinelands

text: South

text: Africa

text: Astrophysics,

text: Denys

text: Wilkinson

text: Building,

text: Keble

text: Road,

text: Oxford

text: UK

text: for

text: Astrophysics

text: Research,

text: Science

text: Technology

text: Research

text: Institute,

text: University

text: of

text: Hertfordshire,

text: Hatﬁeld,

text: Herts,

text: UK

text: Astrophysics

text: Research

text: Institute,

text: Liverpool

text: John

text: Moores

text: University,

text: Liverpool

text: Science

text: Park,

text: Brownlow

text: Hill,

text: Liverpool,

text: Australian

text: Astronomical

text: Observatory,

text: PO

text: Box

text: North

text: Ryde,

text: NSW

text: Australia

text: School

text: of

text: Physics

text: and

text: Astronomy,

text: Monash

text: University,

text: Clayton,

text: Victoria

text: Australia

text: H.H.

text: Wills

text: Physics

text: Laboratory,

text: University

text: of

text: Bristol,

text: Tyndall

text: Avenue,

text: Bristol

text: UK

text: ICRAR,

text: University

text: of

text: Western

text: Australia,

text: Stirling

text: Highway,

text: Crawley,

text: WA

text: Australia

text: SUPA,

text: School

text: of

text: Physics

text: and

text: Astronomy,

text: University

text: of

text: St

text: Andrews,

text: North

text: Haugh,

text: St

text: Andrews,

text: UK

text: Astronomy

text: Centre,

text: University

text: of

text: Sussex,

text: Falmer,

text: Brighton

text: UK

text: Institute

text: for

text: Computational

text: Cosmology,

text: Department

text: of

text: Physics,

text: Durham

text: University,

text: South

text: Road,

text: Durham

text: UK

text: School

text: of

text: Physics,

text: University

text: of

text: Sydney,

text: NSW

text: Australia

text: Accepted

text: December

text: Received

text: December

text: in

text: original

text: form

text: August

text: ABSTRACT

text: Measurement

text: of

text: the

text: evolution

text: of

text: both

text: active

text: galactic

text: nuclei

text: (AGN)

text: and

text: star-formation

text: in

text: galaxies

text: underpins

text: our

text: understanding

text: of

text: galaxy

text: evolution

text: over

text: cosmic

text: time.

text: Radio

text: continuum

text: observations

text: can

text: provide

text: key

text: information

text: on

text: these

text: two

text: processes,

text: in

text: partic-

text: ular

text: via

text: the

text: mechanical

text: feedback

text: produced

text: by

text: radio

text: jets

text: in

text: AGN,

text: and

text: via

text: an

text: unbiased

text: dust-independent

text: measurement

text: of

text: star-formation

text: rates.

text: In

text: this

text: paper

text: we

text: determine

text: radio

text: luminosity

text: functions

text: at

text: MHz

text: for

text: a

text: sample

text: of

text: AGN

text: and

text: star-forming

text: galax-

text: ies

text: by

text: matching

text: a

text: radio

text: survey

text: conducted

text: with

text: the

text: Giant

text: Metrewave

text: Radio

text: Telescope

text: (GMRT),

text: with

text: optical

text: imaging

text: and

text: redshifts

text: from

text: the

text: Galaxy

text: And

text: Mass

text: Assembly

text: (GAMA)

text: survey.

text: We

text: ﬁnd

text: that

text: the

text: radio

text: luminosity

text: function

text: at

text: MHz

text: for

text: star-forming

text: galaxies

text: closely

text: follows

text: that

text: measured

text: at

text: GHz.

text: By

text: ﬁtting

text: the

text: AGN

text: radio

text: luminosity

text: function

text: out

text: to

text: z

text: as

text: a

text: double

text: power

text: law,

text: and

text: parametrizing

text: the

text: evolution

text: as

text: Φ

text: z)k,

text: we

text: ﬁnd

text: evolution

text: parameters

text: of

text: k

text: assuming

text: pure

text: density

text: evolution

text: and

text: k

text: assuming

text: pure

text: luminosity

text: evolution.

text: We

text: ﬁnd

text: that

text: the

text: Low

text: Excitation

text: Radio

text: Galaxies

text: are

text: the

text: dominant

text: population

text: in

text: space

text: density

text: at

text: lower

text: luminosities.

text: Comparing

text: our

text: MHz

text: observations

text: with

text: radio

text: con-

text: tinuum

text: imaging

text: at

text: GHz,

text: we

text: determine

text: separate

text: radio

text: luminosity

text: functions

text: for

text: steep

text: and

text: ﬂat-spectrum

text: AGN,

text: and

text: show

text: that

text: the

text: beamed

text: population

text: of

text: ﬂat-spectrum

text: sources

text: in

text: our

text: sample

text: can

text: be

text: shifted

text: in

text: number

text: density

text: and

text: luminosity

text: to

text: coincide

text: with

text: the

text: un-beamed

text: population

text: of

text: steep-spectrum

text: sources,

text: as

text: is

text: expected

text: in

text: the

text: orientation

text: based

text: uniﬁcation

text: of

text: AGN.

text: Key

text: words:

text: surveys

text: galaxies:luminosity

text: function

text: galaxies:

text: evolution

text: galaxies:

text: formation

text: radio

text: continuum:

text: galaxies

text: galaxies:

text: active

text: INTRODUCTION

text: In

text: recent

text: years

text: it

text: has

text: become

text: apparent

text: that

text: Active

text: Galactic

text: Nuclei

text: (AGN)

text: play

text: an

text: important

text: role

text: in

text: the

text: for-

text: E-mail:

text: mxp@uwcastro.org

text: mation

text: and

text: evolution

text: of

text: galaxies.

text: Every

text: massive

text: galaxy

text: is

text: c

text: The

text: Authors


text: 2 Matthew Prescott et al. now thought to contain a central supermassive black hole a V/V analysis. ?) also found little or no evolution in max that can undergo periods of rapid gas accretion to produce the FR I population, compared to FR IIs at frequencies of an AGN. The accretion activity of AGN may also have a 151 MHz. The trend that low luminosity sources (L < 1025 − strong interplay with star formation. Indirect evidence for W Hz 1) evolve much less than higher luminosity sources this comes from comparisons made between the evolution of was also seen by ?). At 325 MHz, ?) found no signiﬁcant − − AGN activity and the star-formation rate of the Universe, evolution for sources with L − < 1026.1 W Hz 1 sr 1 325 MHz which have been shown to follow each other over cosmic his- out to z = 0.8, from matching radio data from the Wester- tory (e.g. ?). In the local Universe more evidence comes from bork Northern Sky Survey (WENSS; ?) with optical SDSS the correlation between the black hole and bulge masses of DR1 data and performing a V/V analysis. max galaxies (??). Although more recent results have shown this These results are in contrast to those of ?) who found relationship deviates from being linear when probing lower strong evolution in the low luminosity radio population at masses (?), the relationship for more massive galaxies is 1.4 GHz out to z = 0.55, and by assuming pure lumi- ∝ thought to arise from the regulation of star formation in the nosity density evolution of the form L (1 + z)k found bulge due to ‘AGN feedback’ (for a review see ?). AGN feed- 3 < k < 5 for AGN with 1023 < L − < 1025 − 1.4 GHz back has also been incorporated into semi-analytical models W Hz 1. ?) also found signiﬁcant evolution for AGN with − (??), as a way to quench star formation and produce the 1024 < L − < 1025 W Hz 1 consistent with pure lumi- 1.4 GHz ∝ ± observed colour bimodality of galaxies (??). nosity evolution where L (1+z)2.0 0.3 from z = 0.7, using The radio source population probed by the current gen- the 2SLAQ (?) catalogue combined with Faint Images of the eration of radio surveys probes a mixture of galaxies powered Radio Sky at Twenty-Centimeters (FIRST, ?) and NRAO by star-formation and AGN activity. At 1.4 GHz ﬂux densi- VLA Sky Survey (NVSS, ?). ∼ ties of 10 mJy and above, the majority of radio sources are More recent studies, probing fainter ﬂuxes, have found radio-loud AGN. Below 10 mJy there is an increasing num- milder evolution in low-luminosity AGN. ?) produced 1.4 ber of star-forming galaxies (?). ?) found that radio-loud GHz luminosity functions using the VLA-COSMOS survey − AGN could be subdivided into two types (known as Fanaroﬀ- for AGN with 1021 < L − < 1026 W Hz 1 to z = 1.3 1.4 GHz ∝ ± Riley (FR) types I and II), based on their radio morpholo- and found modest evolution, with L (1 + z)0.8 0.1, or ∝ ± gies, which were found to show a division at approximately Φ (1 + z)1.1 0.1, assuming pure luminosity and density − L − = 1025 W Hz 1. Those having brighter cores and evolution respectively. 178 MHz diﬀuse lobes are labelled as FR I sources and those with ?) found that low-luminosity sources evolve diﬀerently highly collimated jets, which produce ‘hot-spots’ of high sur- from their high-luminosity counterparts out to a redshift of face brightness at their edges, as FR IIs. z = 0.8 and the measured radio luminosity function was A diﬀerent classiﬁcation system based on the presence found to be consistent with an increase in the comoving or absence of narrow emission lines in the optical spectra of space density of low-luminosity sources by a factor of 1.5. radio-loud AGN has also been used over the years (????). ?) using deep S > 100 µJy radio imaging in the 1.4 Those with high-excitation emission lines being referred to Suburu/XMM-Newton Deep Field, produced 1.4 GHz lumi- as High Excitation Radio Galaxies (HERGs) and those with- nosity functions divided into the radio-loud and radio-quiet out as Low Excitation Radio Galaxies (LERGs). HERGs are AGN populations. They found that radio-quiet population − the dominant population above L − = 1026 W Hz 1 evolves more strongly than the radio-loud population. Again 1.4 GHz (?) and are more likely to be associated with the more pow- very little or no evolution in the number density of the radio- ≤ − erful FR II sources, compared to the LERGs which are more loud AGN with L − 1024 W Hz 1 out to z = 1.5 was 1.4 GHz associated with FR Is (although not exclusively). The di- observed. chotomy in these populations is believed to be due to two Using 1.4 GHz VLA data combined with photometric diﬀerent modes of accretion, with the LERG population un- redshifts from the VIDEO survey, ?) found that AGN evolve ∝ ± dergoing radiatively ineﬃcient accretion of hot gas from the as L (1 + z)1.18 0.21 at relatively low radio luminosities, galaxies’ interstellar medium and surrounding galaxies, and assuming pure luminosity evolution. ∼ the HERG population undergoing radiatively eﬃcient ac- Finally, using deep from deep ( 30µJy) 1.4 GHz VLA cretion of cold gas by mergers and interactions between the observations of the Chandra Deep Field South (CDFS) ?) host galaxy and gas rich systems (??????). Both accretion ﬁnd that the number density of radio loud AGN evolves as ∝ modes are thought to be important processes in the AGN (1 + z)2 out to z = 0.5, after which it declines steeply as ∝ − feedback mechanism. In order to fully understand these dif- (1 + z) 4. ferent mechanisms, the evolution of these populations has to As well as tracing the population of AGN, radio emis- be determined, usually conducted by either a V/Vmax anal- sion is produced from electrons in the Hii regions near mas- ysis or by producing radio luminosity functions, whose evo- sive stars (free-free emission) and cosmic ray electrons pro- lution is parametrized in some way. duced by supernova remnants (synchrotron emission), and It is now established that the most powerful radio-loud oﬀers a probe of recent star-formation in galaxies without − AGN (with L1.4−GHz > 1025 W Hz 1) evolve strongly over the need for an uncertain extinction correction (?). It has the course of cosmic history, with studies ﬁnding an increase become well established that the star-formation rate of the ∼ − ∼ in their number densities by a factor of 1000 from z 0 2 Universe has declined by a factor of 10, from z = 1.0 to ∼ (????), which then declines beyond z 3 (?????). At lower z = 0.0 (????). Studies such as ?) for example, incorporated luminosities, however, the picture is much more uncertain. 1.4 GHz measurements into a compilation of star-formation In an early study by ?), observations at 178 MHz con- indicators to show that the star-formation rate in galaxies ∝ ± ducted as part of the 3CRR survey, revealed that sources evolves as L (1 + z)2.7 0.6 for pure luminosity evolution − ∝ ± with L − < 1026 W Hz 1 exhibit no evolution via and φ (1 + z)0.15 0.6 for density evolution. ?) also found 178 MHz MNRAS 000, 1–?? (2015)

text: Matthew

text: Prescott

text: et

text: al.

text: now

text: thought

text: to

text: contain

text: a

text: central

text: supermassive

text: black

text: hole

text: a

text: V/V

text: analysis.

text: also

text: found

text: little

text: or

text: no

text: evolution

text: in

text: max

text: that

text: can

text: undergo

text: periods

text: of

text: rapid

text: gas

text: accretion

text: to

text: produce

text: the

text: FR

text: I

text: population,

text: compared

text: to

text: FR

text: IIs

text: at

text: frequencies

text: of

text: an

text: AGN.

text: The

text: accretion

text: activity

text: of

text: AGN

text: may

text: also

text: have

text: a

text: MHz.

text: The

text: trend

text: that

text: low

text: luminosity

text: sources

text: (L

text: strong

text: interplay

text: with

text: star

text: formation.

text: Indirect

text: evidence

text: for

text: W

text: Hz

text: evolve

text: much

text: less

text: than

text: higher

text: luminosity

text: sources

text: this

text: comes

text: from

text: comparisons

text: made

text: between

text: the

text: evolution

text: of

text: was

text: also

text: seen

text: by

text: At

text: MHz,

text: found

text: no

text: signiﬁcant

text: AGN

text: activity

text: and

text: the

text: star-formation

text: rate

text: of

text: the

text: Universe,

text: evolution

text: for

text: sources

text: with

text: L

text: W

text: Hz

text: sr

text: MHz

text: which

text: have

text: been

text: shown

text: to

text: follow

text: each

text: other

text: over

text: cosmic

text: his-

text: out

text: to

text: z

text: from

text: matching

text: radio

text: data

text: from

text: the

text: Wester-

text: tory

text: (e.g.

text: In

text: the

text: local

text: Universe

text: more

text: evidence

text: comes

text: from

text: bork

text: Northern

text: Sky

text: Survey

text: (WENSS;

text: with

text: optical

text: SDSS

text: the

text: correlation

text: between

text: the

text: black

text: hole

text: and

text: bulge

text: masses

text: of

text: data

text: and

text: performing

text: a

text: V/V

text: analysis.

text: max

text: galaxies

text: Although

text: more

text: recent

text: results

text: have

text: shown

text: this

text: These

text: results

text: are

text: in

text: contrast

text: to

text: those

text: of

text: who

text: found

text: relationship

text: deviates

text: from

text: being

text: linear

text: when

text: probing

text: lower

text: strong

text: evolution

text: in

text: the

text: low

text: luminosity

text: radio

text: population

text: at

text: masses

text: the

text: relationship

text: for

text: more

text: massive

text: galaxies

text: is

text: GHz

text: out

text: to

text: z

text: and

text: by

text: assuming

text: pure

text: lumi-

text: thought

text: to

text: arise

text: from

text: the

text: regulation

text: of

text: star

text: formation

text: in

text: the

text: nosity

text: density

text: evolution

text: of

text: the

text: form

text: L

text: z)k

text: found

text: bulge

text: due

text: to

text: ‘AGN

text: feedback’

text: (for

text: a

text: review

text: see

text: AGN

text: feed-

text: k

text: for

text: AGN

text: with

text: L

text: GHz

text: back

text: has

text: also

text: been

text: incorporated

text: into

text: semi-analytical

text: models

text: W

text: Hz

text: also

text: found

text: signiﬁcant

text: evolution

text: for

text: AGN

text: with

text: as

text: a

text: way

text: to

text: quench

text: star

text: formation

text: and

text: produce

text: the

text: L

text: W

text: Hz

text: consistent

text: with

text: pure

text: lumi-

text: GHz

text: observed

text: colour

text: bimodality

text: of

text: galaxies

text: nosity

text: evolution

text: where

text: L

text: from

text: z

text: using

text: The

text: radio

text: source

text: population

text: probed

text: by

text: the

text: current

text: gen-

text: the

text: catalogue

text: combined

text: with

text: Faint

text: Images

text: of

text: the

text: eration

text: of

text: radio

text: surveys

text: probes

text: a

text: mixture

text: of

text: galaxies

text: powered

text: Radio

text: Sky

text: at

text: Twenty-Centimeters

text: (FIRST,

text: and

text: NRAO

text: by

text: star-formation

text: and

text: AGN

text: activity.

text: At

text: GHz

text: ﬂux

text: densi-

text: VLA

text: Sky

text: Survey

text: (NVSS,

text: ties

text: of

text: mJy

text: and

text: above,

text: the

text: majority

text: of

text: radio

text: sources

text: are

text: More

text: recent

text: studies,

text: probing

text: fainter

text: ﬂuxes,

text: have

text: found

text: radio-loud

text: AGN.

text: Below

text: mJy

text: there

text: is

text: an

text: increasing

text: num-

text: milder

text: evolution

text: in

text: low-luminosity

text: AGN.

text: produced

text: ber

text: of

text: star-forming

text: galaxies

text: found

text: that

text: radio-loud

text: GHz

text: luminosity

text: functions

text: using

text: the

text: VLA-COSMOS

text: survey

text: AGN

text: could

text: be

text: subdivided

text: into

text: two

text: types

text: (known

text: as

text: Fanaroﬀ-

text: for

text: AGN

text: with

text: L

text: W

text: Hz

text: to

text: z

text: GHz

text: Riley

text: (FR)

text: types

text: I

text: and

text: II),

text: based

text: on

text: their

text: radio

text: morpholo-

text: and

text: found

text: modest

text: evolution,

text: with

text: L

text: or

text: gies,

text: which

text: were

text: found

text: to

text: show

text: a

text: division

text: at

text: approximately

text: Φ

text: assuming

text: pure

text: luminosity

text: and

text: density

text: L

text: W

text: Hz

text: Those

text: having

text: brighter

text: cores

text: and

text: evolution

text: respectively.

text: MHz

text: diﬀuse

text: lobes

text: are

text: labelled

text: as

text: FR

text: I

text: sources

text: and

text: those

text: with

text: found

text: that

text: low-luminosity

text: sources

text: evolve

text: diﬀerently

text: highly

text: collimated

text: jets,

text: which

text: produce

text: ‘hot-spots’

text: of

text: high

text: sur-

text: from

text: their

text: high-luminosity

text: counterparts

text: out

text: to

text: a

text: redshift

text: of

text: face

text: brightness

text: at

text: their

text: edges,

text: as

text: FR

text: IIs.

text: z

text: and

text: the

text: measured

text: radio

text: luminosity

text: function

text: was

text: A

text: diﬀerent

text: classiﬁcation

text: system

text: based

text: on

text: the

text: presence

text: found

text: to

text: be

text: consistent

text: with

text: an

text: increase

text: in

text: the

text: comoving

text: or

text: absence

text: of

text: narrow

text: emission

text: lines

text: in

text: the

text: optical

text: spectra

text: of

text: space

text: density

text: of

text: low-luminosity

text: sources

text: by

text: a

text: factor

text: of

text: radio-loud

text: AGN

text: has

text: also

text: been

text: used

text: over

text: the

text: years

text: using

text: deep

text: S

text: µJy

text: radio

text: imaging

text: in

text: the

text: Those

text: with

text: high-excitation

text: emission

text: lines

text: being

text: referred

text: to

text: Suburu/XMM-Newton

text: Deep

text: Field,

text: produced

text: GHz

text: lumi-

text: as

text: High

text: Excitation

text: Radio

text: Galaxies

text: (HERGs)

text: and

text: those

text: with-

text: nosity

text: functions

text: divided

text: into

text: the

text: radio-loud

text: and

text: radio-quiet

text: out

text: as

text: Low

text: Excitation

text: Radio

text: Galaxies

text: (LERGs).

text: HERGs

text: are

text: AGN

text: populations.

text: They

text: found

text: that

text: radio-quiet

text: population

text: the

text: dominant

text: population

text: above

text: L

text: W

text: Hz

text: evolves

text: more

text: strongly

text: than

text: the

text: radio-loud

text: population.

text: Again

text: GHz

text: and

text: are

text: more

text: likely

text: to

text: be

text: associated

text: with

text: the

text: more

text: pow-

text: very

text: little

text: or

text: no

text: evolution

text: in

text: the

text: number

text: density

text: of

text: the

text: radio-

text: erful

text: FR

text: II

text: sources,

text: compared

text: to

text: the

text: LERGs

text: which

text: are

text: more

text: loud

text: AGN

text: with

text: L

text: W

text: Hz

text: out

text: to

text: z

text: was

text: GHz

text: associated

text: with

text: FR

text: Is

text: (although

text: not

text: exclusively).

text: The

text: di-

text: observed.

text: chotomy

text: in

text: these

text: populations

text: is

text: believed

text: to

text: be

text: due

text: to

text: two

text: Using

text: GHz

text: VLA

text: data

text: combined

text: with

text: photometric

text: diﬀerent

text: modes

text: of

text: accretion,

text: with

text: the

text: LERG

text: population

text: un-

text: redshifts

text: from

text: the

text: VIDEO

text: survey,

text: found

text: that

text: AGN

text: evolve

text: dergoing

text: radiatively

text: ineﬃcient

text: accretion

text: of

text: hot

text: gas

text: from

text: the

text: as

text: L

text: at

text: relatively

text: low

text: radio

text: luminosities,

text: galaxies’

text: interstellar

text: medium

text: and

text: surrounding

text: galaxies,

text: and

text: assuming

text: pure

text: luminosity

text: evolution.

text: the

text: HERG

text: population

text: undergoing

text: radiatively

text: eﬃcient

text: ac-

text: Finally,

text: using

text: deep

text: from

text: deep

text: GHz

text: VLA

text: cretion

text: of

text: cold

text: gas

text: by

text: mergers

text: and

text: interactions

text: between

text: the

text: observations

text: of

text: the

text: Chandra

text: Deep

text: Field

text: South

text: (CDFS)

text: host

text: galaxy

text: and

text: gas

text: rich

text: systems

text: Both

text: accretion

text: ﬁnd

text: that

text: the

text: number

text: density

text: of

text: radio

text: loud

text: AGN

text: evolves

text: as

text: modes

text: are

text: thought

text: to

text: be

text: important

text: processes

text: in

text: the

text: AGN

text: out

text: to

text: z

text: after

text: which

text: it

text: declines

text: steeply

text: as

text: feedback

text: mechanism.

text: In

text: order

text: to

text: fully

text: understand

text: these

text: dif-

text: z)

text: ferent

text: mechanisms,

text: the

text: evolution

text: of

text: these

text: populations

text: has

text: to

text: As

text: well

text: as

text: tracing

text: the

text: population

text: of

text: AGN,

text: radio

text: emis-

text: be

text: determined,

text: usually

text: conducted

text: by

text: either

text: a

text: V/Vmax

text: anal-

text: sion

text: is

text: produced

text: from

text: electrons

text: in

text: the

text: Hii

text: regions

text: near

text: mas-

text: ysis

text: or

text: by

text: producing

text: radio

text: luminosity

text: functions,

text: whose

text: evo-

text: sive

text: stars

text: (free-free

text: emission)

text: and

text: cosmic

text: ray

text: electrons

text: pro-

text: lution

text: is

text: parametrized

text: in

text: some

text: way.

text: duced

text: by

text: supernova

text: remnants

text: (synchrotron

text: emission),

text: and

text: It

text: is

text: now

text: established

text: that

text: the

text: most

text: powerful

text: radio-loud

text: oﬀers

text: a

text: probe

text: of

text: recent

text: star-formation

text: in

text: galaxies

text: without

text: AGN

text: (with

text: W

text: Hz

text: evolve

text: strongly

text: over

text: the

text: need

text: for

text: an

text: uncertain

text: extinction

text: correction

text: It

text: has

text: the

text: course

text: of

text: cosmic

text: history,

text: with

text: studies

text: ﬁnding

text: an

text: increase

text: become

text: well

text: established

text: that

text: the

text: star-formation

text: rate

text: of

text: the

text: in

text: their

text: number

text: densities

text: by

text: a

text: factor

text: of

text: from

text: z

text: Universe

text: has

text: declined

text: by

text: a

text: factor

text: of

text: from

text: z

text: to

text: which

text: then

text: declines

text: beyond

text: z

text: At

text: lower

text: z

text: Studies

text: such

text: as

text: for

text: example,

text: incorporated

text: luminosities,

text: however,

text: the

text: picture

text: is

text: much

text: more

text: uncertain.

text: GHz

text: measurements

text: into

text: a

text: compilation

text: of

text: star-formation

text: In

text: an

text: early

text: study

text: by

text: observations

text: at

text: MHz

text: con-

text: indicators

text: to

text: show

text: that

text: the

text: star-formation

text: rate

text: in

text: galaxies

text: ducted

text: as

text: part

text: of

text: the

text: survey,

text: revealed

text: that

text: sources

text: evolves

text: as

text: L

text: for

text: pure

text: luminosity

text: evolution

text: with

text: L

text: W

text: Hz

text: exhibit

text: no

text: evolution

text: via

text: and

text: φ

text: for

text: density

text: evolution.

text: also

text: found

text: MHz

text: MNRAS