text: growth of the majority of star-forming galaxies have been of the AGN population over a broad range of luminosities ∼ regulated more by internal secular processes rather than (41 < log L − (erg/s) < 45) out to z 5, provid- 0.5 10 keV by merger process (e.g. Elbaz et al. 2011; Rodighiero et ing a unique opportunity of studying AGN evolution. al. 2011; Wuyts et al. 2011). X-ray surveys are the most eﬃcient way for selecting Controversial results were found for AGN host galax- AGNs over a wide range of luminosities and redshifts be- ies: some studies have indicated equivalent or enhanced cause they are less aﬀected by obscuration, and also the star formation compared to normal star-forming galax- contamination from non-nuclear emission, mainly due to ies (e.g. Silverman et al. 2009; Mullaney et al. 2012; star-formation processes, is far less signiﬁcant than in Rosario et al. 2012; Santini et al. 2012; Juneau et al. optical and infrared surveys (Donley et al. 2008, 2012; 2013), whereas some others have shown that AGN host Lehmer et al. 2012; Stern et al. 2012). Therefore, the X- galaxies lie below the MS of star-forming galaxies, sug- ray emission is a relatively clean signal from the nuclear gesting that AGN accretion might suppress and even- component. Furthermore, using the AGN sample with tually quench star formation via a process of feedback the large, uniform X-ray depth and coherent observations (e.g. Barger et al. 2015; Mullaney et al. 2015; Riguccini in the COSMOS ﬁeld, we can minimize the systematic et al. 2015; Shimizu et al. 2015). Furthermore, several selection eﬀects (e.g. Lauer et al. 2007; Rosario et al. studies have addressed that the majority of AGN host 2013; Caplar et al. 2015). The already existing extensive galaxies in the local universe are preferentially found in compilation of multi-wavelength data in the COSMOS the green valley on the color-magnitude diagram, tran- ﬁeld allows us to investigate AGN host galaxies to have sitioning from star-forming galaxies in the blue cloud to a better understanding of nuclear activity and its con- passive galaxies on the red sequence (e.g. Schawinski nection with star formation. et al. 2009; Trump et al. 2013). Therefore, the ques- In this paper, we investigate the properties of AGN tion of whether AGN activity can signiﬁcantly enhance host galaxies in the Chandra COSMOS-Legacy survey. or quench star formation in galaxies is still unsettled. Since the SMBH-powered emission contributes signiﬁ- Diﬀerent results can be produced by either physical cantly to the ultraviolet-to-optical parts of the spectra properties of the sources, or observational biases, or both. of Type 1 AGNs (e.g. Elvis et al. 2012; Hao et al. 2013), The sample selection including completeness and biases it is extremely diﬃcult to determine reliable stellar mass due to a speciﬁc selection method (X-ray versus infrared for Type 1 AGNs (e.g. Maiolino et al. 2010). A detailed selected AGNs, for example), as well as the use of diﬀer- analysis of the Type 1 AGN host galaxies in the Chandra ent SFR indicators could introduce systematics since the COSMOS Legacy Survey, including spectroscopic anal- contribution of AGN emission may signiﬁcantly hamper ysis in the optical and near-infrared wavelength ranges, the precise determination of SFRs of AGN host galaxies. will be presented in a second paper, Suh et al. (in prepa- The Herschel Space Observatory (Pilbratt et al. 2010; ration). Thus, we focus on the non-broad-line and/or Poglitsch et al. 2010; Griﬃn et al. 2010) covers the far- obscured AGN host galaxies based either on the spectro- infrared emission from dust including the characteristic scopic or the photometric classiﬁcation. Hereafter, we far-IR bump typically seen in star-forming galaxies, al- refer to non-broad-line and/or obscured sources as “Type lowing us for more precise measurements of the total IR 2” AGNs. We utilize multi-wavelength data from near- luminosity, especially for dusty galaxies and AGN host ultraviolet to far-infrared of a large sample of AGNs in galaxies, since many of the often used SFR indicators the Chandra COSMOS Legacy ﬁeld. We use the Spec- (e.g. Hα, UV continuum) can be substantially contam- tral Energy Distribution (SED) ﬁtting to disentangle the inated by AGN-related emission (e.g. Dale et al. 2007; galaxy and nuclear contributions in order to measure the Schweitzer et al. 2007; Netzer et al. 2007; Lutz et al. stellar masses and the SFRs accurately. Finally we dis- 2016). cuss the eﬀects of the nuclear activity on the star forma- Deep, large-area X-ray observations with Chandra in tion in Type 2 AGN host galaxies by comparing to the thDe rCafOtSvMerOsiSonﬁMelady(3i0.e,.202C0handra-COSMOS, Chandra- normal star-forming galaxies. COPrSeMpriOntStyLpeesgeatcuysinSguLrAvTeEyX;sEtyllveiesmeutlaatel.ap2j0v0.90;3/C0i7v/a0n7o et al. Throughout this paper we assume a ΛCDM−cosmolo−gy 2016) open up a new regime for studying a large sample with Ω = 0.3, Ω = 0.7, and H = 70 km s 1 Mpc 1. m Λ 0 TYPE 2 AGN HOST GALAXIES IN THE CHANDRA-COSMOS LEGACY SURVEY: NO EVIDENCE OF AGN-DRIVEN QUENCHING Hyewon Suh1, Francesca Civano2, Gu¨nther Hasinger1, Elisabeta Lusso3,17, Giorgio Lanzuisi4,5, Stefano Marchesi6, Benny Trakhtenbrot7, Viola Allevato8,9, Nico Cappelluti10, Peter L. Capak11,12, Martin Elvis2, Richard E. Griffiths13, Clotilde Laigle14, Paulina Lira15, Laurie Riguccini16, David J. Rosario17, Mara Salvato18, Kevin Schawinski7, Cristian Vignali3,4 Subject headings: galaxies: active — galaxies: nuclei — quasars: general — black hole physics 1 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Italy Drive, Honolulu, HI 96822, USA 4 Dipartimento di Fisica e Astronomia, Universit`a di Bologna, 2 Harvard-Smithsonian Center for Astrophysics, Cambridge, MA viale Berti Pichat 6/2, 40127 Bologna, Italy 02138, USA 3 INAF Osservatorio Astroﬁsico di Arcetri, I-50125 Florence, 5 INAF Osservatorio Astronomico di Bologna, Via Ranzani 1,

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text: spectra

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text: sources,

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text: biases,

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text: both.

text: of

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text: Hao

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text: covers

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text: photometric

text: classiﬁcation.

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text: and/or

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text: as

text: “Type

text: lowing

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text: more

text: precise

text: measurements

text: of

text: the

text: total

text: IR

text: 2”

text: AGNs.

text: We

text: utilize

text: multi-wavelength

text: data

text: from

text: near-

text: luminosity,

text: especially

text: for

text: dusty

text: galaxies

text: and

text: AGN

text: host

text: ultraviolet

text: to

text: far-infrared

text: of

text: a

text: large

text: sample

text: of

text: AGNs

text: in

text: galaxies,

text: since

text: many

text: of

text: the

text: often

text: used

text: SFR

text: indicators

text: the

text: Chandra

text: COSMOS

text: Legacy

text: ﬁeld.

text: We

text: use

text: the

text: Spec-

text: (e.g.

text: Hα,

text: UV

text: continuum)

text: can

text: be

text: substantially

text: contam-

text: tral

text: Energy

text: Distribution

text: (SED)

text: ﬁtting

text: to

text: disentangle

text: the

text: inated

text: by

text: AGN-related

text: emission

text: (e.g.

text: Dale

text: et

text: al.

text: galaxy

text: and

text: nuclear

text: contributions

text: in

text: order

text: to

text: measure

text: the

text: Schweitzer

text: et

text: al.

text: Netzer

text: et

text: al.

text: Lutz

text: et

text: al.

text: stellar

text: masses

text: and

text: the

text: SFRs

text: accurately.

text: Finally

text: we

text: dis-

text: cuss

text: the

text: eﬀects

text: of

text: the

text: nuclear

text: activity

text: on

text: the

text: star

text: forma-

text: Deep,

text: large-area

text: X-ray

text: observations

text: with

text: Chandra

text: in

text: tion

text: in

text: Type

text: AGN

text: host

text: galaxies

text: by

text: comparing

text: to

text: the

text: thDe

text: Chandra-

text: normal

text: star-forming

text: galaxies.

text: et

text: al.

text: Throughout

text: this

text: paper

text: we

text: assume

text: a

text: ΛCDM−cosmolo−gy

text: open

text: up

text: a

text: new

text: regime

text: for

text: studying

text: a

text: large

text: sample

text: with

text: Ω

text: Ω

text: and

text: H

text: km

text: s

text: Mpc

text: m

text: Λ

text: TYPE

text: AGN

text: HOST

text: GALAXIES

text: IN

text: THE

text: CHANDRA-COSMOS

text: LEGACY

text: SURVEY:

text: NO

text: EVIDENCE

text: OF

text: AGN-DRIVEN

text: QUENCHING

text: Hyewon

text: Francesca

text: Gu¨nther

text: Elisabeta

text: Giorgio

text: Stefano

text: Benny

text: Viola

text: Nico

text: Peter

text: L.

text: Martin

text: Richard

text: E.

text: Clotilde

text: Paulina

text: Laurie

text: David

text: J.

text: Mara

text: Kevin

text: Cristian

text: Subject

text: headings:

text: galaxies:

text: active

text: galaxies:

text: nuclei

text: quasars:

text: general

text: black

text: hole

text: physics

text: Institute

text: for

text: Astronomy,

text: University

text: of

text: Hawaii,

text: Woodlawn

text: Italy

text: Drive,

text: Honolulu,

text: HI

text: USA

text: Dipartimento

text: di

text: Fisica

text: e

text: Astronomia,

text: Universit`a

text: di

text: Bologna,

text: Harvard-Smithsonian

text: Center

text: for

text: Astrophysics,

text: Cambridge,

text: MA

text: viale

text: Berti

text: Pichat

text: Bologna,

text: Italy

text: USA

text: INAF

text: Osservatorio

text: Astroﬁsico

text: di

text: Arcetri,

text: Florence,

text: INAF

text: Osservatorio

text: Astronomico

text: di

text: Bologna,

text: Via

text: Ranzani


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text: ApJ,

text: M.

text: ApJ,

text: Xue,

text: Y.

text: Q.,

text: Grandt,

text: W.

text: N.,

text: Luo,

text: B.,

text: et

text: al.

text: ApJ,

text: Symeonidis,

text: M.

text: MNRAS,

text: Tomczak,

text: A.

text: R.,

text: Quadri,

text: R.

text: F.,

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text: K.,

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text: B.,

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text: C.

text: M.,

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text: F.,

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text: al.

text: Sci,


text: Star formation in Type 2 AGN host galaxies 5 E(B-V) values in the range between 0 and 0.5 with steps the far-IR and those that are not. Speciﬁcally, for the of 0.05, and the range between 0.5 and 1 with a step of sources detected at 24µm but not in any far-IR Her- 0.1. We show some examples of stellar population tem- schel wavelength, there are large uncertainties in the es- plates with various combinations of τ=[0.1, 1, 3], and timate of C and C , because both could substantially 2 3 t =[50 Myr, 2 Gyr] with E(B-V)=[0.0, 0.3] in Figure 2 contribute in the observed 24µm band, introducing a de- age (green curves). generacy in the SED ﬁtting. This implies that the ﬁtting In general, the SED of an obscured AGN is character- can produce two diﬀerent probable solutions with a sim- ized by the near-infrared bump that is a result of the ilar χ2. One is a prominent AGN dominating in the IR absorption of intrinsic nuclear radiation by dust clouds range with no contribution from the dust emission heated in the proximity of the central region (so-called torus) by stars, and the other is a negligible AGN contribution on parsec scales, which subsequently re-radiate at in- in the 24µm band with the infrared emission dominated frared frequencies (Barvainis 1987). The dust torus SED by star-forming regions. Therefore, we perform two dif- templates are taken from Silva et al. (2004), as con- ferent ﬁts for the sources which are not detected at any structed from the study of a large sample of Seyfert far-IR wavelength. (1) the best-ﬁt model with a possi- galaxies for which clear signatures of non-stellar nuclear ble star-forming component using Herschel upper limits, emission were detected in the near-IR and mid-IR, and adopting the same approach as described by Calistro et also using the radiative transfer code GRASIL (Silva al. (2016). Speciﬁcally, we consider Herschel detection et al. 1998). There are three diﬀerent templates de- limits in each Herschel band (ﬂux ) to make mock limit pending on the amount of nuclear obscuration in terms data points in the far-IR wavelength range, assuming the − ± of hydrogen column density, 1022 < N < 1023 cm 2, ﬂux to be ﬂux /2 with an uncertainty ﬂux /2, to − −H limit limit 1023 < N < 1024 cm 2, N > 1024 cm 2 for Seyfert 2. ﬁt the possible star-forming component. (2) We assume H H The three templates of Type 2 AGN dust torus are plot- a negligible contribution from star formation in the IR ted in Figure 2 with yellow curves. The larger the column range, L =0, and a signiﬁcant contribution from the FIR density, the higher is the nuclear contribution to the IR AGN at 24µm. Thus, we have a range of possible L FIR emission. Although the X-ray data for our AGNs con- values for Herschel-undetected sources (i.e., minimum to tains some information on the N towards each source maximum). H (see Marchesi et al. 2016), we chose to allow N to be a We show examples of the SED ﬁts for the sources which H free parameter in our SED ﬁtting. are detected in far-IR photometry (top two panels; LID- For the starburst component in the far/mid-IR region, 1688, CID-360), and the sources which are undetected we adopted 169 starburst templates (105 from Chary & in the far-IR (bottom two panels; CID-1771, LID-617) Elbaz 2001 and 64 from Dale & Helou 2002) for ﬁtting in the left panels of Figure 3. The rest-frame photomet- the cold dust emission (i.e. far-IR emission). It has been ric data (black points) and the detection limits (arrows) shown that measuring the far-IR luminosity from ﬁtting are shown with the best-ﬁt model (black solid curve). the far-IR region to libraries of SED (Chary & Elbaz For the far-IR faint sources (CID-1771, LID-617), we 2001; Dale & Helou 2002) gives roughly the same results show two diﬀerent best ﬁt models in the IR wavelength as the modiﬁed blackbody plus power-law model (Casey range: possible star-forming component using upper lim- 2012; U et al. 2012; Lee et al. 2013). The Chary & El- its (solid curve) and negligible star formation contribu- baz (2001) templates are generated based on the SEDs tions (dashed curve). The galaxy template (green), the of four prototypical starburst galaxies (Arp220, ULIRG; AGN dust torus template (yellow), and the starburst NGC6090, LIRG; M82, starburst; and M51, normal star- component (red) are also indicated. The residuals are forming galaxy). The Dale & Helou (2002) templates are also shown in the lower panel of each SED ﬁt. based on 69 normal star-forming galaxies, representing a The χ2 minimization is used to determine the best ﬁt wide range of SED shapes and IR luminosities, comple- among all the possible template combinations. However, menting each other. A small subset of starburst tem- its absolute value is not a reliable indicator, because sys- plates are shown in Figure 2 as red curves. tematic uncertainties may dominate the statistical errors. 3.2. Multi-component SED ﬁtting Therefore, we compute a complementary statistic on the quality of ﬁt, which is the variation of the residual from We developed a 3-component SED ﬁtting procedure in ∼ the ﬁt. We remove 1% (27/2056) sources which show which the observed photometric data is ﬁtted at a ﬁxed large variations in their residuals (> 0.5), since this indi- redshift of the source with a large grid of models obtained cates that their high χ2 is not due to an underestima- by combining the templates described above. The ob- red tion of the photometric errors but either caused by the served ﬂux can be expressed as the sum of 3 components lack of suitable templates or by the bad photometry. as 3.3. Estimation of physical parameters While the use of the χ2 minimization technique can f = C f + C f + C f (1) obs 1 stellarpopulation 2 AGN 3 starburst give an indication of the overall quality of the ﬁtting, the best-ﬁt value could not be a good estimate of representa- where the C , C , and C are coeﬃcients that repro- 1 2 3 tive of physical parameter values in a multi-dimensional duce the observed data by χ2 minimization. The best-ﬁt parameter space with degeneracies. We, therefore, use SED solution could be a stellar population with a negli- Bayesian statistics to derive the most representative gible contribution from AGN/starburst components, or a value for each parameter of galaxy physical properties, stellar population with the central AGN component, or a and to evaluate the robust uncertainties since it accounts stellar population with starburst component, or a stellar for the degeneracies inherent in our SED templates. population with both AGN and starburst components. We explore any possible combination of SED parame- The ﬁt is performed diﬀerently for sources detected in

text: Star

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text: curves).

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text: taken

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text: the

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text: wavelength.

text: the

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text: model

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text: galaxies

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text: ble

text: star-forming

text: component

text: using

text: Herschel

text: upper

text: limits,

text: emission

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text: near-IR

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text: and

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text: the

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text: GRASIL

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text: al.

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text: we

text: consider

text: Herschel

text: detection

text: et

text: al.

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text: three

text: diﬀerent

text: templates

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text: each

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text: band

text: (ﬂux

text: to

text: make

text: mock

text: limit

text: pending

text: on

text: the

text: amount

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text: nuclear

text: obscuration

text: in

text: terms

text: data

text: points

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text: the

text: far-IR

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text: assuming

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text: ﬂux

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text: uncertainty

text: ﬂux

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text: limit

text: limit

text: N

text: cm

text: N

text: cm

text: for

text: Seyfert

text: ﬁt

text: the

text: possible

text: star-forming

text: component.

text: We

text: assume

text: H

text: H

text: The

text: three

text: templates

text: of

text: Type

text: AGN

text: dust

text: torus

text: are

text: plot-

text: a

text: negligible

text: contribution

text: from

text: star

text: formation

text: in

text: the

text: IR

text: ted

text: in

text: Figure

text: with

text: yellow

text: curves.

text: The

text: larger

text: the

text: column

text: range,

text: L

text: and

text: a

text: signiﬁcant

text: contribution

text: from

text: the

text: FIR

text: density,

text: the

text: higher

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text: the

text: nuclear

text: contribution

text: to

text: the

text: IR

text: AGN

text: at

text: Thus,

text: we

text: have

text: a

text: range

text: of

text: possible

text: L

text: FIR

text: emission.

text: Although

text: the

text: X-ray

text: data

text: for

text: our

text: AGNs

text: con-

text: values

text: for

text: Herschel-undetected

text: sources

text: (i.e.,

text: minimum

text: to

text: tains

text: some

text: information

text: on

text: the

text: N

text: towards

text: each

text: source

text: maximum).

text: H

text: (see

text: Marchesi

text: et

text: al.

text: we

text: chose

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text: allow

text: N

text: to

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text: a

text: We

text: show

text: examples

text: of

text: the

text: SED

text: ﬁts

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text: the

text: sources

text: which

text: H

text: free

text: parameter

text: in

text: our

text: SED

text: ﬁtting.

text: are

text: detected

text: in

text: far-IR

text: photometry

text: (top

text: two

text: panels;

text: LID-

text: For

text: the

text: starburst

text: component

text: in

text: the

text: far/mid-IR

text: region,

text: and

text: the

text: sources

text: which

text: are

text: undetected

text: we

text: adopted

text: starburst

text: templates

text: from

text: Chary

text: in

text: the

text: far-IR

text: (bottom

text: two

text: panels;

text: Elbaz

text: and

text: from

text: Dale

text: Helou

text: for

text: ﬁtting

text: in

text: the

text: left

text: panels

text: of

text: Figure

text: The

text: rest-frame

text: photomet-

text: the

text: cold

text: dust

text: emission

text: (i.e.

text: far-IR

text: emission).

text: It

text: has

text: been

text: ric

text: data

text: (black

text: points)

text: and

text: the

text: detection

text: limits

text: (arrows)

text: shown

text: that

text: measuring

text: the

text: far-IR

text: luminosity

text: from

text: ﬁtting

text: are

text: shown

text: with

text: the

text: best-ﬁt

text: model

text: (black

text: solid

text: curve).

text: the

text: far-IR

text: region

text: to

text: libraries

text: of

text: SED

text: (Chary

text: Elbaz

text: For

text: the

text: far-IR

text: faint

text: sources

text: we

text: Dale

text: Helou

text: gives

text: roughly

text: the

text: same

text: results

text: show

text: two

text: diﬀerent

text: best

text: ﬁt

text: models

text: in

text: the

text: IR

text: wavelength

text: as

text: the

text: modiﬁed

text: blackbody

text: plus

text: power-law

text: model

text: (Casey

text: range:

text: possible

text: star-forming

text: component

text: using

text: upper

text: lim-

text: U

text: et

text: al.

text: Lee

text: et

text: al.

text: The

text: Chary

text: El-

text: its

text: (solid

text: curve)

text: and

text: negligible

text: star

text: formation

text: contribu-

text: baz

text: templates

text: are

text: generated

text: based

text: on

text: the

text: SEDs

text: tions

text: (dashed

text: curve).

text: The

text: galaxy

text: template

text: (green),

text: the

text: of

text: four

text: prototypical

text: starburst

text: galaxies

text: ULIRG;

text: AGN

text: dust

text: torus

text: template

text: (yellow),

text: and

text: the

text: starburst

text: LIRG;

text: starburst;

text: and

text: normal

text: star-

text: component

text: (red)

text: are

text: also

text: indicated.

text: The

text: residuals

text: are

text: forming

text: galaxy).

text: The

text: Dale

text: Helou

text: templates

text: are

text: also

text: shown

text: in

text: the

text: lower

text: panel

text: of

text: each

text: SED

text: ﬁt.

text: based

text: on

text: normal

text: star-forming

text: galaxies,

text: representing

text: a

text: The

text: χ2

text: minimization

text: is

text: used

text: to

text: determine

text: the

text: best

text: ﬁt

text: wide

text: range

text: of

text: SED

text: shapes

text: and

text: IR

text: luminosities,

text: comple-

text: among

text: all

text: the

text: possible

text: template

text: combinations.

text: However,

text: menting

text: each

text: other.

text: A

text: small

text: subset

text: of

text: starburst

text: tem-

text: its

text: absolute

text: value

text: is

text: not

text: a

text: reliable

text: indicator,

text: because

text: sys-

text: plates

text: are

text: shown

text: in

text: Figure

text: as

text: red

text: curves.

text: tematic

text: uncertainties

text: may

text: dominate

text: the

text: statistical

text: errors.

text: Multi-component

text: SED

text: ﬁtting

text: Therefore,

text: we

text: compute

text: a

text: complementary

text: statistic

text: on

text: the

text: quality

text: of

text: ﬁt,

text: which

text: is

text: the

text: variation

text: of

text: the

text: residual

text: from

text: We

text: developed

text: a

text: SED

text: ﬁtting

text: procedure

text: in

text: the

text: ﬁt.

text: We

text: remove

text: sources

text: which

text: show

text: which

text: the

text: observed

text: photometric

text: data

text: is

text: ﬁtted

text: at

text: a

text: ﬁxed

text: large

text: variations

text: in

text: their

text: residuals

text: since

text: this

text: indi-

text: redshift

text: of

text: the

text: source

text: with

text: a

text: large

text: grid

text: of

text: models

text: obtained

text: cates

text: that

text: their

text: high

text: χ2

text: is

text: not

text: due

text: to

text: an

text: underestima-

text: by

text: combining

text: the

text: templates

text: described

text: above.

text: The

text: ob-

text: red

text: tion

text: of

text: the

text: photometric

text: errors

text: but

text: either

text: caused

text: by

text: the

text: served

text: ﬂux

text: can

text: be

text: expressed

text: as

text: the

text: sum

text: of

text: components

text: lack

text: of

text: suitable

text: templates

text: or

text: by

text: the

text: bad

text: photometry.

text: as

text: Estimation

text: of

text: physical

text: parameters

text: While

text: the

text: use

text: of

text: the

text: χ2

text: minimization

text: technique

text: can

text: f

text: C

text: f

text: C

text: f

text: C

text: f

text: obs

text: stellarpopulation

text: AGN

text: starburst

text: give

text: an

text: indication

text: of

text: the

text: overall

text: quality

text: of

text: the

text: ﬁtting,

text: the

text: best-ﬁt

text: value

text: could

text: not

text: be

text: a

text: good

text: estimate

text: of

text: representa-

text: where

text: the

text: C

text: C

text: and

text: C

text: are

text: coeﬃcients

text: that

text: repro-

text: tive

text: of

text: physical

text: parameter

text: values

text: in

text: a

text: multi-dimensional

text: duce

text: the

text: observed

text: data

text: by

text: χ2

text: minimization.

text: The

text: best-ﬁt

text: parameter

text: space

text: with

text: degeneracies.

text: We,

text: therefore,

text: use

text: SED

text: solution

text: could

text: be

text: a

text: stellar

text: population

text: with

text: a

text: negli-

text: Bayesian

text: statistics

text: to

text: derive

text: the

text: most

text: representative

text: gible

text: contribution

text: from

text: AGN/starburst

text: components,

text: or

text: a

text: value

text: for

text: each

text: parameter

text: of

text: galaxy

text: physical

text: properties,

text: stellar

text: population

text: with

text: the

text: central

text: AGN

text: component,

text: or

text: a

text: and

text: to

text: evaluate

text: the

text: robust

text: uncertainties

text: since

text: it

text: accounts

text: stellar

text: population

text: with

text: starburst

text: component,

text: or

text: a

text: stellar

text: for

text: the

text: degeneracies

text: inherent

text: in

text: our

text: SED

text: templates.

text: population

text: with

text: both

text: AGN

text: and

text: starburst

text: components.

text: We

text: explore

text: any

text: possible

text: combination

text: of

text: SED

text: parame-

text: The

text: ﬁt

text: is

text: performed

text: diﬀerently

text: for

text: sources

text: detected

text: in


text: linear and higher orders. The existence of a bilocal model adapted to describing gravity at linear order [11], whereas not suitable for higher orders may reﬂect the especial role of linearized gravity as a complete theory in its own. Let us take the ansatz Φ(1)(X, r) = rµC¯ rνe−α2 r2eiPX, (4.9) µν 2 × ¯ where C is an yet undetermined 4 4 matrix. The momentum P is a 4-vector µν µ with dimension of mass. Substituting (4.9) into (4.7) leads to − 2ηµνC¯ P 2rµrνC¯ = 0 (4.10) µν µν and substituting (4.9) into (4.8) leads to P µC¯ rµ = 0. (4.11) µν Now, since the above conditions should hold for all rµ we see that equations (4.7) and (4.8) imply ηµνC¯ = 0, (4.12) µν P µP = 0, (massless) (4.13) µ P µC¯ = 0. (4.14) µν From Eq.(4.12) and the symmetric nature of ηµν it follows that C¯ is symmetric as µν well. Then it follows from Eqs.(4.12) and (4.14), that the general solution (4.9) is of the form ≡ P P C¯ = C + cP , P µ ν , (p2 = P 2), (4.15) µν µν µν µν p2 0 where C is a symmetric matrix. The matrix elements P are deﬁned in (4.15) to be µν µν dimensionless. From eq. (4.12), we see that all solutions with shape (4.9) are massless, 14 ##LTLine## ##LTLine##

text: linear

text: and

text: higher

text: orders.

text: The

text: existence

text: of

text: a

text: bilocal

text: model

text: adapted

text: to

text: describing

text: gravity

text: at

text: linear

text: order

text: whereas

text: not

text: suitable

text: for

text: higher

text: orders

text: may

text: reﬂect

text: the

text: especial

text: role

text: of

text: linearized

text: gravity

text: as

text: a

text: complete

text: theory

text: in

text: its

text: own.

text: Let

text: us

text: take

text: the

text: ansatz

label: equation

text: r)

text: rµC¯

text: rνe−α2

text: µν

text: where

text: C

text: is

text: an

text: yet

text: undetermined

text: matrix.

text: The

text: momentum

text: P

text: is

text: a

text: µν

text: µ

text: with

text: dimension

text: of

text: mass.

text: Substituting

text: into

text: leads

text: to

text: 2ηµνC¯

text: P

text: µν

text: µν

text: and

text: substituting

text: into

text: leads

text: to

text: P

text: µC¯

text: rµ

text: µν

text: Now,

text: since

text: the

text: above

text: conditions

text: should

text: hold

text: for

text: all

text: rµ

text: we

text: see

text: that

text: equations

text: and

text: imply

text: ηµνC¯

text: µν

text: P

text: µP

text: (massless)

text: µ

text: P

text: µC¯

text: µν

text: From

text: and

text: the

text: symmetric

text: nature

text: of

text: ηµν

text: it

text: follows

text: that

text: C¯

text: is

text: symmetric

text: as

text: µν

text: well.

text: Then

text: it

text: follows

text: from

text: and

text: that

text: the

text: general

text: solution

text: is

text: of

text: the

text: form

text: P

text: P

text: C¯

text: C

text: cP

text: P

text: µ

text: ν

text: P

text: µν

text: µν

text: µν

text: µν

text: where

text: C

text: is

text: a

text: symmetric

text: matrix.

text: The

text: matrix

text: elements

text: P

text: are

text: deﬁned

text: in

text: to

text: be

text: µν

text: µν

text: dimensionless.

text: From

text: eq.

text: we

text: see

text: that

text: all

text: solutions

text: with

text: shape

text: are

text: massless,

text: ##LTLine##

text: ##LTLine##


text: ≡ where Φ¯(1)(x, z) Φ(1)(X, r) and Φ(1)(X, r) are the solutions of the ﬁrst order equa- (cid:48) (cid:48) tions (4.9) with (4.16). The points x , y of (4.18) are deﬁned as (cid:48) (cid:48) (cid:48) − (cid:48) − x + y = x + y, x y = 2(x y), (4.20) which gives (cid:48) (cid:48) X = X, r = 2r. (4.21) The speciﬁc form of the RHS of (4.18) is explained as follows. The prefactor eα2 r2 2 ∝ − serves to force Φ(2)(X, r) e 1α2r2, as Φ(1)(X, r) does. So the global solution, Φ = 2 · · · − Φ(1) + κ Φ(2) + has an overall Gaussian decay e 1α2r2. This condition for the global B 2 solution, which does not seem essential but simpliﬁes the treatment when compared to gravity, could apply to every higher order interacting terms resulting in similar pre- factors 8. The change of coordinates (4.21) is necessary to assure that the the second order solutions are Φ(2)(X, r) ∝ P (4)(r)e−α2 r2, as we will see later. As shown in section 2 , the details of the polynomial P (4)(r) will eventually encode h¯(2). The same happens at µν ﬁrst order where Φ(1)(X, r) ∝ P (2)(r)e−α2 r2, and P (2)(r) encodes gravitational waves. In 2 ∝ general, we propose to constraint the higher order interaction terms so that Φ(n)(X, r) P (2n)(r)e−α2 r2, and then the contribution h¯(n) can be read from P (2n)(r). This will result 2 µν into an essentially unique shape for V (φ) which could encode the exact gravity self- interacting terms. One can compute the integral that appears on the RHS of (4.18), we do it in Appendix (cid:90) . In that calculation we see that the integral splits as (cid:48) (cid:48) (cid:48) (cid:48) I (X, r) = Φ¯(1)(x , z)Φ¯(1)(z, y )dz = I (r)ei2PX. (4.22) Next, we plug in the ansatz (cid:2) (cid:3) 1 Φ(2)(X, r) = A(r) + Bσ(r)X ei2PX, (4.23) σ 2i ∝ − 8In the absence of the prefactor, one has Φ(2)(X, r) e α2r2, and subsequent orders in the pertur- bative expansion would have diﬀerent (sharper) Gaussians. As mentioned above, since this does not aﬀect the treatment in an essential way, we will consider dropping this factor in future works. 16 ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: where

text: z)

text: r)

text: and

text: r)

text: are

text: the

text: solutions

text: of

text: the

text: ﬁrst

text: order

text: equa-

text: tions

text: with

text: The

text: points

text: x

text: y

text: of

text: are

text: deﬁned

text: as

text: x

text: y

text: x

text: y,

text: x

text: y

text: y),

text: which

text: gives

text: X

text: X,

text: r

text: The

text: speciﬁc

text: form

text: of

text: the

text: RHS

text: of

text: is

text: explained

text: as

text: follows.

text: The

text: prefactor

text: serves

text: to

text: force

text: r)

text: e

text: as

text: r)

text: does.

text: So

text: the

text: global

text: solution,

text: Φ

text: κ

text: has

text: an

text: overall

text: Gaussian

text: decay

text: e

text: This

text: condition

text: for

text: the

text: global

text: B

text: solution,

text: which

text: does

text: not

text: seem

text: essential

text: but

text: simpliﬁes

text: the

text: treatment

text: when

text: compared

text: to

text: gravity,

text: could

text: apply

text: to

text: every

text: higher

text: order

text: interacting

text: terms

text: resulting

text: in

text: similar

text: pre-

text: factors

text: The

text: change

text: of

text: coordinates

text: is

text: necessary

text: to

text: assure

text: that

text: the

text: the

text: second

text: order

text: solutions

text: are

text: r)

text: P

text: as

text: we

text: will

text: see

text: later.

text: As

text: shown

text: in

text: section

text: the

text: details

text: of

text: the

text: polynomial

text: P

text: will

text: eventually

text: encode

text: The

text: same

text: happens

text: at

text: µν

text: ﬁrst

text: order

text: where

text: r)

text: P

text: and

text: P

text: encodes

text: gravitational

text: waves.

text: In

text: general,

text: we

text: propose

text: to

text: constraint

text: the

text: higher

text: order

text: interaction

text: terms

text: so

text: that

text: Φ(n)(X,

text: r)

text: P

text: and

text: then

text: the

text: contribution

text: h¯(n)

text: can

text: be

text: read

text: from

text: P

text: This

text: will

text: result

text: µν

text: into

text: an

text: essentially

text: unique

text: shape

text: for

text: V

text: (φ)

text: which

text: could

text: encode

text: the

text: exact

text: gravity

text: self-

text: interacting

text: terms.

text: One

text: can

text: compute

text: the

text: integral

text: that

text: appears

text: on

text: the

text: RHS

text: of

text: we

text: do

text: it

text: in

text: Appendix

text: In

text: that

text: calculation

text: we

text: see

text: that

text: the

text: integral

text: splits

text: as

text: I

text: (X,

text: r)

text: y

text: )dz

text: I

text: Next,

text: we

text: plug

text: in

text: the

text: ansatz

text: r)

text: A(r)

text: Bσ(r)X

text: σ

text: the

text: absence

text: of

text: the

text: prefactor,

text: one

text: has

text: r)

text: e

text: and

text: subsequent

text: orders

text: in

text: the

text: pertur-

text: bative

text: expansion

text: would

text: have

text: diﬀerent

text: (sharper)

text: Gaussians.

text: As

text: mentioned

text: above,

text: since

text: this

text: does

text: not

text: aﬀect

text: the

text: treatment

text: in

text: an

text: essential

text: way,

text: we

text: will

text: consider

text: dropping

text: this

text: factor

text: in

text: future

text: works.

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##

text: ##LTLine##


text: [11] P. Diaz, S. Das and M. Walton, Bilocal theory and gravity I, arXiv:1609.08631. [12] H. Yukawa, Quantum Theory of Nonlocal Fields. 1. Free Fields, Phys.Rev. 77 (1950) 219-226. H. Yukawa, Quantum Theory of Nonlocal Fields. 2: Irreducible Fields and Their Interaction, Phys.Rev. 80 (1950) 1047-1052. H. Yukawa, Structure and Mass Spectrum of Elementary Particles. 1: General Considerations, Phys.Rev. 91 (1953) 415. H. Yukawa, Structure and Mass Spectrum of Elementary Particles. 2: Oscillator Model, Phys.Rev. 91 (1953) 416. [13] T. Takabayasi, Relativistic Mechanics of Conﬁned Particles as Extended Model of Hadrons -The Bilocal Case, Supplement of the Progress of Theoretical Physics, No. 67, 1979. A. Z. Capri and C.C. Chiang, Extended meson ﬁelds. An alternative to quark conﬁnement, Nuov Cim A 36 (1976) 331. [14] T. Shirafuji, Green’s Function of Bilocal Field Equations, Prog. Theor. Phys. (1968) 39 (4): 1047-1068. T. Takabayasi, Prog. Theor, Phys. Suppl. E65, 339 (1965) and papers quoted therein. K. Fujimura, T. Kobayashi and M. Namiki, Nucleon Electromagnetic Form Factors at High Momentum Transfers in an Extended Particle Model Based on the Quark Model, Prog. Theor. Phys. (1970) 43 (1): 73-79. T. Goto and S. Naka, On the Vertex Function in the Bi-Local Field, Prog. Theor. Phys. (1974) 51 (1): 299-308. [15] R. P. Feynman, M. Kislinger and F. Ravndal, Current Matrix Elements from a Relativistic Quark Model, Phys. Rev. D 3 (1971), 2706. [16] S. R. Das and A. Jevicki, Large-N Collective Fields and Holography, Phys.Rev. D68 (2003) 044011. [17] K. Kamimura, Elimination of relative time in bilocal model, Prog. Phys. 58 (1977) 1947. [18] A. Jevicji, K. Jin, Q. Ye, Collective dipole model of AdS/CFT and higher spin gravity, J. Phys. A 44 (2011) 465402. [19] I. Bars, Gauge Symmetry in Phase Space Consequences for Physics and Spacetime, Int. J. Mod. Phys. A 25 (2010) 5235 [20] A. Jevicki and J.Yoon, Bulk from Bi-locals in Thermo Field CFT, JHEP 1602 (2016) 090. A. Jevicki, K. Suzuki and J. Yoon, Bi-Local Holography in the SYK 27

text: P.

text: Diaz,

text: S.

text: Das

text: and

text: M.

text: Walton,

text: Bilocal

text: theory

text: and

text: gravity

text: I,

text: H.

text: Yukawa,

text: Quantum

text: Theory

text: of

text: Nonlocal

text: Fields.

text: Free

text: Fields,

text: Phys.Rev.

text: H.

text: Yukawa,

text: Quantum

text: Theory

text: of

text: Nonlocal

text: Fields.

text: Irreducible

text: Fields

text: and

text: Their

text: Interaction,

text: Phys.Rev.

text: H.

text: Yukawa,

text: Structure

text: and

text: Mass

text: Spectrum

text: of

text: Elementary

text: Particles.

text: General

text: Considerations,

text: Phys.Rev.

text: H.

text: Yukawa,

text: Structure

text: and

text: Mass

text: Spectrum

text: of

text: Elementary

text: Particles.

text: Oscillator

text: Model,

text: Phys.Rev.

text: T.

text: Takabayasi,

text: Relativistic

text: Mechanics

text: of

text: Conﬁned

text: Particles

text: as

text: Extended

text: Model

text: of

text: Hadrons

text: -The

text: Bilocal

text: Case,

text: Supplement

text: of

text: the

text: Progress

text: of

text: Theoretical

text: Physics,

text: No.

text: A.

text: Z.

text: Capri

text: and

text: C.C.

text: Chiang,

text: Extended

text: meson

text: ﬁelds.

text: An

text: alternative

text: to

text: quark

text: conﬁnement,

text: Nuov

text: Cim

text: A

text: T.

text: Shirafuji,

text: Green’s

text: Function

text: of

text: Bilocal

text: Field

text: Equations,

text: Prog.

text: Theor.

text: Phys.

text: T.

text: Takabayasi,

text: Prog.

text: Theor,

text: Phys.

text: Suppl.

text: and

text: papers

text: quoted

text: therein.

text: K.

text: Fujimura,

text: T.

text: Kobayashi

text: and

text: M.

text: Namiki,

text: Nucleon

text: Electromagnetic

text: Form

text: Factors

text: at

text: High

text: Momentum

text: Transfers

text: in

text: an

text: Extended

text: Particle

text: Model

text: Based

text: on

text: the

text: Quark

text: Model,

text: Prog.

text: Theor.

text: Phys.

text: T.

text: Goto

text: and

text: S.

text: Naka,

text: On

text: the

text: Vertex

text: Function

text: in

text: the

text: Bi-Local

text: Field,

text: Prog.

text: Theor.

text: Phys.

text: R.

text: P.

text: Feynman,

text: M.

text: Kislinger

text: and

text: F.

text: Ravndal,

text: Current

text: Matrix

text: Elements

text: from

text: a

text: Relativistic

text: Quark

text: Model,

text: Phys.

text: Rev.

text: D

text: S.

text: R.

text: Das

text: and

text: A.

text: Jevicki,

text: Large-N

text: Collective

text: Fields

text: and

text: Holography,

text: Phys.Rev.

text: K.

text: Kamimura,

text: Elimination

text: of

text: relative

text: time

text: in

text: bilocal

text: model,

text: Prog.

text: Phys.

text: A.

text: Jevicji,

text: K.

text: Jin,

text: Q.

text: Ye,

text: Collective

text: dipole

text: model

text: of

text: AdS/CFT

text: and

text: higher

text: spin

text: gravity,

text: J.

text: Phys.

text: A

text: I.

text: Bars,

text: Gauge

text: Symmetry

text: in

text: Phase

text: Space

text: Consequences

text: for

text: Physics

text: and

text: Spacetime,

text: Int.

text: J.

text: Mod.

text: Phys.

text: A

text: A.

text: Jevicki

text: and

text: J.Yoon,

text: Bulk

text: from

text: Bi-locals

text: in

text: Thermo

text: Field

text: CFT,

text: JHEP

text: A.

text: Jevicki,

text: K.

text: Suzuki

text: and

text: J.

text: Yoon,

text: Bi-Local

text: Holography

text: in

text: the

text: SYK


text: Model, JHEP 1607 (2016) 007. A. Jevicki and K. Suzuki, Bi-Local Holography in the SYK Model: Perturbations, arXiv:1608.07567. S. R. Das, A. Jevicki, K. Suzuki, Three Dimensional View of the SYK/AdS Duality, arXiv:1704.07208. [21] R. de Mello Koch, A. Jevicki, K. Jin, J. P. Rodrigues, AdS4/CFT3 Construction from Collective Fields, Phys.Rev. D83 (2011) 025006. [22] R. Aldrovandi, J. G. Pereira, R. da Rocha and K. H. Vu, Nonlinear Gravitational Waves: Their form and Eﬀects, Int J Theor Phys (2010) 49: 549. arXiv:0809.2911v2. [23] R. M Wald, General Relativity, The University of Chicago Press, 1984. [24] T. Takabayasi, Relativistic Mechanics of Two Interacting Particles and Bilocal The- ory, Prog. Theor. Phys. 54 (1975) 563. [25] X. Beakaert, N. Boulanger, P. Sundell, How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples, Rev. Mod. Phys. 84, 987. arXiv:1007.0435. [26] T. Takabayasi, Relativistic Mechanics of Bilocal and Trilocal Structures, Prog. Theor. Phys. 57 329 (1977). [27] T. Takabayasi, Theory of Relativistic String and Multilocal Model, Prog. Theor. Phys. Supplement 86 (1986) 81. 28

text: Model,

text: JHEP

text: A.

text: Jevicki

text: and

text: K.

text: Suzuki,

text: Bi-Local

text: Holography

text: in

text: the

text: SYK

text: Model:

text: Perturbations,

text: S.

text: R.

text: Das,

text: A.

text: Jevicki,

text: K.

text: Suzuki,

text: Three

text: Dimensional

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text: SYK/AdS

text: Duality,

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text: de

text: Mello

text: Koch,

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text: Jevicki,

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text: J.

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text: Rodrigues,

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text: Fields,

text: Phys.Rev.

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text: Aldrovandi,

text: J.

text: G.

text: Pereira,

text: R.

text: da

text: Rocha

text: and

text: K.

text: H.

text: Vu,

text: Nonlinear

text: Gravitational

text: Waves:

text: Their

text: form

text: and

text: Eﬀects,

text: Int

text: J

text: Theor

text: Phys

text: R.

text: M

text: Wald,

text: General

text: Relativity,

text: The

text: University

text: of

text: Chicago

text: Press,

text: T.

text: Takabayasi,

text: Relativistic

text: Mechanics

text: of

text: Two

text: Interacting

text: Particles

text: and

text: Bilocal

text: The-

text: ory,

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text: Theor.

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text: Beakaert,

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text: gravity

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text: Mechanics

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text: Theor.

text: Phys.

text: Supplement


text: 2 Revision of the perturbative method Since we will compare bilocal theory and gravity perturbatively in this paper, we brieﬂy review the perturbative method in this section. 2.1 Perturbative models As it is customary in perturbation theory, we assume that there exist a one-parameter family of solutions Φ(κ ), where κ is a parameter of the theory. We expand the solution B B in powers of the (small) parameter κ as B Φ(κ ) = Φ(1) + κ Φ(2) + κ2 Φ(3) . . . . (2.1) B B B We write the bilocal model as (cid:0) (cid:1) O Φ(κ ) = V Φ(κ ), κ , (2.2) B B B O where is a linear diﬀerential operator and V (Φ) stands for self-interactions, also expanded in powers of k . Then, equating the same powers of k on both sides of B B Eq.(2.2), one gets an inﬁnite set of diﬀerential equations, one for each Φ(i), all linear, and each of them sourced by lower order solutions. These equations can be solved in ascending order, with ﬁrst equation being O Φ(1) = 0. The method we have just sketched is quite general. In section we will give a precise O form of the diﬀerential operator and the terms in the expansion of V (Φ) for the bilocal model we use. 2.2 Perturbative gravity In this case, we start by assuming the existence of a one-parameter family of solutions g(κ) to Einstein’s equations µν − 1 R g R + Λg = 8πGT . µν µν µν µν 2 The perturbation equations are generated as the Einstein’s equations are expanded in powers of κ and the terms with equal powers are equated. In this paper, for simplicity, 5 ##LTLine##

label: section

text: Revision

text: of

text: the

text: perturbative

text: method

text: Since

text: we

text: will

text: compare

text: bilocal

text: theory

text: and

text: gravity

text: perturbatively

text: in

text: this

text: paper,

text: we

text: brieﬂy

text: review

text: the

text: perturbative

text: method

text: in

text: this

text: section.

text: Perturbative

text: models

text: As

text: it

text: is

text: customary

text: in

text: perturbation

text: theory,

text: we

text: assume

text: that

text: there

text: exist

text: a

text: one-parameter

text: family

text: of

text: solutions

text: Φ(κ

text: where

text: κ

text: is

text: a

text: parameter

text: of

text: the

text: theory.

text: We

text: expand

text: the

text: solution

text: B

text: B

text: in

text: powers

text: of

text: the

text: (small)

text: parameter

text: κ

text: as

text: B

text: Φ(κ

text: κ

text: κ2

text: B

text: B

text: B

text: We

text: write

text: the

text: bilocal

text: model

text: as

text: O

text: Φ(κ

text: V

text: Φ(κ

text: κ

text: B

text: B

text: B

text: O

text: where

text: is

text: a

text: linear

text: diﬀerential

text: operator

text: and

text: V

text: (Φ)

text: stands

text: for

text: self-interactions,

text: also

text: expanded

text: in

text: powers

text: of

text: k

text: Then,

text: equating

text: the

text: same

text: powers

text: of

text: k

text: on

text: both

text: sides

text: of

text: B

text: B

text: one

text: gets

text: an

text: inﬁnite

text: set

text: of

text: diﬀerential

text: equations,

text: one

text: for

text: each

text: Φ(i),

text: all

text: linear,

text: and

text: each

text: of

text: them

text: sourced

text: by

text: lower

text: order

text: solutions.

text: These

text: equations

text: can

text: be

text: solved

text: in

text: ascending

text: order,

text: with

text: ﬁrst

text: equation

text: being

text: O

text: The

text: method

text: we

text: have

text: just

text: sketched

text: is

text: quite

text: general.

text: In

text: section

text: we

text: will

text: give

text: a

text: precise

text: O

text: form

text: of

text: the

text: diﬀerential

text: operator

text: and

text: the

text: terms

text: in

text: the

text: expansion

text: of

text: V

text: (Φ)

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text: 8 Metzger & Pejcha cases where the shock power is suﬃcient to keep the ejecta ionized If the forward shock dominates the shock power (eq. 7), then at the nominal time of the secondary peak. the peak luminosity of the shock-powered second light curve peak (cid:29) We begin by estimating the velocity of the cold central shell. is given by (in the limit v v ) sh w The radiative shock interaction is momentum-conserving, so the (cid:18) (cid:19) ≈ shell velocity equals the ratio of the swept-up momentum p (t) Mejv¯ej fΩ + Mw,sh(t)vw and the swept-up mass Msh(t) ≈ fΩsMh ej + Lpk ≈ Lf(tpk) ≈ 329f vv3sh (cid:32)Mt w e(cid:33)− vvws(cid:18)httrpukn (cid:19)(cid:32) (cid:33) M (t), Ω w run w,sh ≈ (cid:32) × (cid:33) (cid:32) −(cid:33) (cid:32) f (cid:33) −1 (cid:32) M (cid:33) v −1 where the sv(cid:40)v¯wsehjep=t-uv¯1epj mMpsashhss≈of1th+e1(pv+rwe/-Mvd¯eywj)n,s(ahM/m(wif,cΩshaM/l fweΩj)iMndej)is,(cid:41)given b(y17) × 9 v¯ej10340 ertgruns 1−ξ13 M0.Ω3 5/2 0.1awM −5v/2esecw−/(cid:18)4vvwshttrpukn (cid:19), ((2223)) v 10t M(cid:12) 10R(cid:12) esc orb ≈ M (t) ≈ Mw(Rsh/vwtrun) Mw(t/tend), t ∼< tend (18) where we have used equations (1,2). Normalizing again to the w,sh Mw, t ∼> tend. main sequence radius, (cid:32) (cid:33) (cid:18) (cid:19)(cid:32) (cid:33) tlhuetioonuatnoedfr evtedsnhgdies=ocfotrtmuhne(pvlpwirc/eav-tdsehyd)nbiasymtthihceeatliimomupetlﬂircoeiqwtu.diAerepldtehnfodouergnshchetohocekftiMtmower,seehavocohn- Lpk ≈ 9(cid:32) × 1(cid:33)040(cid:32)ergs−1(cid:33)−ξ3(cid:32) 0f.Ω3(cid:33) −1 (cid:32)0M.1wM (cid:33)−vevscw/4(cid:18) −1 (cid:19) vasfha,cwtoerﬁonfdtwthoatfrfoomr ﬁidtsuacsiaylmppatroatmicetvearlsuietsovfalue varies by less than × vv¯ej 3 1t0rutn 1 MM(cid:12) 1/2 10aR 5/2 e− vvwshttrpukn , (24) esc orb ms v∞ = 1 + vv¯wej fΩMMwej ≈ 0.5 − 1, (19) where the argument of the exponential is (assuming vw = v¯ej 1 + fΩMMwej vesc/4) wvwh/ev¯reej i=n 0th.2e5ﬁ.nIanloliunreawnaelyhtaicveesttaikmeanteMs wtha∼<t fMoll≈eoj,wfΩw−e=a0ss.3u,maenda vsh tpk (cid:32) (cid:33) (cid:32) (cid:33) (cid:32) (cid:33) (cid:32) (cid:33) (cid:32) (cid:33) temporarily constant value of vsh = ξv¯ej, where ξ 0.5 1. vw trun − − − − Emission escapes on (cid:32)t(cid:90)he photon d(cid:33)iﬀusion timescale through ≈ t 1 M 1/2 v¯ 1/2 M 1/4 a 5/4 the fast ejecta, which at the shock radius Rsh ≈ vsht is given by 3ξ1/2κ01./32 10rutonrb 0.1eMj veesjc M(cid:12) 10Rms td,sh ≈ τej,sh Rcsh ≈ Rsh ρejκejdr Rcsh ≈ 6πMξe(jv¯κeejjt), (20) (25) where we have used equation (3) for δo = 5 and δi = 2. The luminosity of the shock-powered emission increases with If the opacity remains roughly constant in time, then equat- the binary mass, and is also generally stronger for collisions be- ing this to the expansion time t gives the timescale for the shock- tween more compact stars or shorter runaway times t , up to the run powered e(cid:32)mission (cid:33)to rise to its peak (Arnett 1982) point when the exponential suppression term becomes ∼> 1. The most luminous predicted transients are those from high mass stars ≈ close to the main sequence a 2R with long pre-dynamical tpk ≈ 6πMξecjvκ¯ej (cid:32)1/2 (cid:33) (cid:32) (cid:33)− (cid:32) (cid:33) (cid:32) (cid:33) mnoassisty-loisssLtpikm∼>es3ca×le1s0t4r1uner∼>g s1−010,tcoorbn,sfiosmtreswnthwicihthththeepmreodsitcltuedmliunmouis- ≈ 27d κ01./32 (cid:32) Mej (cid:33)1/2 (cid:32) v¯ej (cid:33) 1/2 (cid:32) M (cid:33)1/4 (cid:32) a 1(cid:33)/4 LRN (Fig. 1). ξ1/2 0.1M vesc M(cid:12) 10R(cid:12) Figure 6 summarizes the above results, showing contours − in the parameter space of stellar mass and radius for the peak ≈ 27d κ01./32 Mej 1/2 v¯ej 1/2 M 9/20 a 1/4 ,(21) timescale (top panel) and peak luminosity/temperature (bottom ξ1/2 0.1M vesc M(cid:12) 10Rms panels), the latter for two assumptions about the timescale of pre- where κ0.3 ≡ κ/(0.3cm2 g−1) is normalized to a typical value d4y.2namDiucasltmFoarssmlaotsiso,ntrun = 10,100torb. (Fig. 4). In the second line we have normalized the ejecta mass to a ﬁxed fraction of the total stellar mass; the fast ejecta velocity to Near- and mid-IR interferometric observations of V838 Mon the binary escape speed; and the semi-major axis of the binary to revealed a resolved ﬂattened disk-like equatorial overdensity of ≈ 10 times the main sequence stellar radius Rms R(cid:12)(M/M(cid:12))0.8. dust with a major axis that aligns with the position angle inferred All else being equal, equation (21) shows that mergers be- from polarimetric studies (Chesneau et al. 2014). Likewise, V1309 tween more massive stars, or evolved stars with radii much larger Sco formed a slowly-expanding, dense, and optically-thick dusty than their main sequence values, will result in later peaking light envelope during its 2008 outburst (Tylenda & Kamin´ski 2016). curves, consistent with our full numerical solutions (Fig. 5). How- Spitzer observations of the LRN V4332 Sagittarii (Martini et al. ever, overall the dependence on binary parameter is relatively weak, 1999) revealed evidence for dust formation (Banerjee et al. 2007). ≈ con−sistent with th∼e fac−tor of ∼< 5 range∼of ob−served values tpk The observed strengths of emission lines suggest that only a small 30 150 d for a 2 100Rms and M 1.5 30M(cid:12) (Fig. 1, Ta- fraction of the emission from the central object is observed, pre- ble 1). Also note that, by assuming a ﬁxed, relatively high value of sumably due to a dusty disk viewed edge on (Kamin´ski et al. 2010), the opacity in deriving equation (21), we cannot account for cases consistent with evidence from linear polarization for dust scatter- when the shock heating is insuﬃcient to keep the ejecta ionized ing in an equatorially-focused disk (Kamin´ski & Tylenda 2011). (e.g. the 2M(cid:12) model in Fig. 5). Mauerhan et al. (2017) also provide evidence, based on the mid- (cid:13) c 2017 RAS, MNRAS 000, 1–12 ##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: Metzger

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text: We

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text: shell

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text: Mw,sh(t)vw

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