NGC 300 ULX1: Spin Evolution, Super-Eddington Accretion

arXiv:1905.03740v2 [astro-ph.HE] 24 Jul 2019 G 0 L1 pneouin ue-digo crto an accretion super-Eddington outflows evolution, spin ULX1: 300 NGC n neoeaon t( ob it an creating around thus envelope NS, the ing by produced radiation X-ray the to .Haberl F. MNRAS eneieti hi -a ih uvs(e.g. curves 2014 light al. X-ray et Motch their in periodici super-orbital evident while been timing, pulsar from derived ( object compact ac stellar-mass for computed a as onto limit Eddington the of tha excess systems in radiation binary are (ULXs) sources X-ray Ultra-luminous INTRODUCTION 1 ue vdnewspoie ytedsoeyo h rtultr first the ( of X-2 discovery M82 (ULXP) the pulsar by X-ray luminous provided was evidence puted osaentshrcladXryrdaincnsilecp f escape still ( can region radiation cone hollow X-ray central and spherical not are flows dis accretion will inner mass the accreted total from the launched of ( outflows, fraction through a that lost expected is it rates. neut super-Eddington ( a at engine creting with central properti the consistent spectral being are (NS) X-ray star ULXs the non-pulsating that and shown pulsating been has it addition, e.g. f black-holes; (hosting postulated systems been have rates transfer mass super-Eddington cetdXX eevdYY noiia omZZZ form original in YYY; Received XXX. Accepted © ⋆ 1 3 6 2 5 4 hkr uye 1973 Sunyaev & Shakura .Vasilopoulos G. aeUiest,P o 011 e ae,C 62-11 US 06520-8101, CT Haven, New 208101, Box PO University, Yale RP NS vned ooe oh,B 44,F308Toul F-31028 44346, BP Roche, Colonel du avenue 9 CNRS, IRAP, -a srpyisLbrtr,NS odr pc lgtC Flight Space Goddard NASA Laboratory, Astrophysics X-Ray eateto srpyia cecs rneo Universi Princeton Sciences, Astrophysical of Department a-lnkIsiu Ãj xrtreticePyi,Gi Physik, Extraterrestrische fÃijr Max-Planck-Institut pc cec iiin ..NvlRsac aoaoy Wa Laboratory, Research Naval U.S. Division, Science Space -al [email protected] E-mail: 05TeAuthors The 2015 o he ftekonUXs ria eid aebeen have periods orbital ULXPs, known the of three For ie h ue-digo asaceinrtsi ULXPs, in rates accretion mass super-Eddington the Given 000 , 1 – 5 7 .Gendreau K. , (2015) .M2X2hsa ria eidof period orbital an has X-2 M82 ). otnne l 2007 al. et Poutanen .Teeotoscnb pial thick optically be can outflows These ). 1 ige l 2017 al. et King ⋆ .Petropoulou M. , ige l 2001 al. et King oipnse l 2017 al. et Koliopanos rmaot16st esta 0si ny4yas ossetwi consistent w years, system 4 the only monitoring in been s have 20 we discovery than its less un Following to an s showing 126 pulsar, about X-ray from ultra-luminous an is ULX1 300 NGC ABSTRACT td t rpris efudta vntog h observed the though even of that factor found a We properties. its study e words: Key absorpt increased disc. of accretion result precessing a a is or outflows flux observed the in decrease niiul G 0 ULX1 300 NGC individual: arte l 2017 al. et Kaaret 6 ahtie l 2014 al. et Bachetti ; ig&Lst 2019 Lasota & King .Hwvr h out- the However, ). arte l 2006 al. et Kaaret & ,tefis undis- first the ), sebcsrß,878Grhn,Germany Garching, 85748 essenbachstraße, 0 h pnu aermie lotcntn.Apsil ex possible A constant. almost remained rate spin-up the 20, -as iais–glxe:idvda:NC30–sas ne stars: – 300 NGC individual: galaxies: – binaries X-rays: y v ae rneo,N 84,USA 08544, NJ Princeton, Lane, Ivy 4 ty, .Although ). ∼ hntn C235 USA 20375, DC shington, . and d 2.5 2 ishave ties n ac- and ) ne,Genet D271 USA 20771, MD Greenbelt, enter, .Koliopanos F. , rULX or cretion A o a rom emit t ueCdx4 France 4, Cedex ouse sof es scur- .In ). ron be a- ). c ; rpit2 uy21 oplduigMRSL MNRAS using Compiled 2019 July 26 Preprint osat(ihnafco of factor rema a 2018 early (within and it constant 2010 that shown between has luminosity ULX1 300 X-ray NGC intrinsic of spectra X-ray the of Analysis ( period pulse d their of lution. study accretion timing any precessing by confirmed been a never super-orbi from on obscuration changes ( flux the the is explain timescales to scenario possible A of period orbital an has P13 7793 NGC 2019 idre l 2011 al. et Binder 2018 a .–0kVband) keV 0.3–30 ( eid( period NuSTAR bevdflxbigatiue oavral bopincomp absorption variable a to attributed being flux observed ih-uv a a has light-curve oaipso,atri eaeatv n21 S 2010da; (SN 2010 in active became it after impostor, nova nlsso aaotie ysimultaneous by obtained data of analysis hsscnvr yafco f10 ihn vdneof evidence no with 100, of tra factor accretor-to-propeller a from ( expected by changes vary spectral can phases ria eidrsetvl ( respectively period orbital irne l 2005 al. et 2018 Gieren al. et Carpano 2017 al. et Fürst 1975 Sunyaev & Illarionov ∼ 4dsprobtlpro ( period super-orbital d 64 G 0 L1i eetydsoee ULXP discovered recently a is ULX1 300 NGC .Teosre -a u ( flux X-ray observed The ). super- and orbital d 78 and d 5.3 a has ULX1 5907 NGC ). P bevtosi eebr21,wihyeddaspin a yielded which 2016, December in observations 3 of ) .S Ray S. P. , ∼ 1sada nbobdXrylmnst i the (in luminosity X-ray unabsorbed an and s 31 ; ∼ .IsUX lsicto a ae nthe on based was classification ULXP Its ). ideo ta.2018 al. et Middleton L 7dsprobtlproiiy(e.g. periodicity super-orbital d 67 .Tesse a lsie sasuper- a as classified was system The ). X ,lctda itneo .8Mpc 1.88 of distance a at located ), ∼ 4.7 4 ; .B Bailyn B. C. , sale l 2017 al. et Israel × ahtie l 2014 al. et Bachetti obt1996 Corbet ∼ o fosuigmtra u to due material obscuring of ion 10 ) ihaylrecagsi its in changes large any with 3), u ftesse rpe by dropped system the of flux ith 39 hsed asaceinrate. accretion mass steady th F rcdne pnevolution, spin precedented r s erg Swift X uigteesuper-orbital these during ) .Hwvr h atrhas latter the However, ). − 1 ; and ∼ apn ta.2018 al. et Campana ( 4d hl t X-ray its while d, 64 lnto sta the that is planation apn ta.2018 al. et Carpano ; XMM-Newton NICER üs ta.2017 al. et Fürst to pulsars: – utron ; A T rgta tal. et Brightman 1 E tl l v3.0 file style X , d üs tal. et Fürst ofurther to nsitions onent ined evo- and isc tal ). ). ). s 2 G. Vasilopoulos et al.

(Carpano et al. 2018; Vasilopoulos et al. 2018; Koliopanos et al. 2.2 Results 2019). Analysis of archival X-ray data revealed a remarkable Carpano et al. (2018) found that the multi-epoch broadband spec- spin up of the NS, whose spin period changed from 126 s to tra of NGC 300 ULX1 are best fitted by a multi-component con- 19 s between November 2014 and April 2018 (Vasilopoulos∼ et al. ∼ tinuum, where the spectrum can be phenomenologically described 2018). Further X-ray monitoring of NGC 300 ULX1 during the by a power-law (Γ 1.5) with cut-off (E 6.6 keV, E 4.8 first half of 2018 with NICER revealed only small changes in the cut fold keV), with a soft excess∼ (i.e., below 1.0 keV)∼ attributed to a black∼ observed F and confirmed a constant spin-up rate (Ray et al. X body component (kT 0.17 keV). Most importantly, the authors 2018). showed that the spectral∼ continuum is partially absorbed by mate- In this work, we study the evolution of NGC 300 ULX1 using rial with high column density, showing no clear low-energy cutoff X-ray monitoring observations that cover the time period between but a rather complicated spectral shape (see also Koliopanos et al. August 2018 and December 2018. We show that the observed X- 2019). The Swift/XRT data do not provide enough statistics for a ray flux of NGC 300 ULX1 dropped by a factor of &20-30 from its detailed spectral fit and, as a result, we cannot constrain the par- peak value in 2018, but the NS spin-up rate remained roughly con- tial absorption component. Thus, for the conversion of Swift/XRT stant (§2). The latter requires a constant accretion rate, and thus a count rates to F (0.3-30.0 keV) we used the spectral properties de- steady energy release (i.e. intrinsic L ) assuming the radiative effi- X X rived by Carpano et al. (2018) for the continuum spectrum, a con- ciency remains the same. Our results can be understood in the con- stant absorption (accounting only for Galactic absorption), and as- text of super-Eddington accretion onto a magnetized NS (§3), with sumed distance of 1.88 Mpc. In other words, the derived X-ray light the required absorption being caused by either obscuration from a curve, shown in Fig. 1, is not corrected for the intrinsic absorp- precessing accretion disc or mass outflows launched from the inner tion of the system2. Within the period August-November 2018 (see parts of the disc due to very high accretion rates (§4). grey shaded area in Fig. 1; MJD 58350-58450), the observed FX of NGC 300 ULX1 rapidly decreased.∼ As already noted, due to the limited statistics we can put no constraints on the spectral change that accompanied this transition. 2 X-RAY MONITORING OBSERVATIONS Prior to this work, Vasilopoulos et al. (2018) have investi- Our findings are based on Swift/XRT and NICER observations of gated the spin evolution of NGC 300 ULX1 by analysing archival NGC 300 ULX1 that were obtained mainly in 2018. Between Jan- X-ray data and searching for periodic signals using the acceler- uary 2018 and July 2018 the X-ray flux of NGC 300 ULX1 grad- ated epoch-folding method (Leahy et al. 1983). Both P and P˙ were ually declined by a factor of 2, but still remained at a super- measured, with small uncertainties, for 3 epochs where XMM- Eddington level (Ray et al. 2018∼). In August-September 2018 the Newton, Chandra, and NuSTAR data with high statistics were avail- 10 10 observed FX rapidly declined and the system was no longer visible able. The derived values ofν ˙ are 5.5 10− , 4.5 10− , and 10 2 × × with either NICER or Swift/XRT. The latest spin period measure- 3.8 10− s− (Vasilopoulos et al. 2018). We used NICER mon- × ment, on August 21 2018, yielded P = 17.52 0.04 s. itoring data to extend these measurements. During 2018 the evolu- ± In November 2018, Swift/XRT monitoring observations (PI: tion of the NS spin frequency follows an almost linear trend with Kennea, J) indicated a re-brightening of the system. We thus time (see bottom panel in Fig. 1). To derive precise period mea- requested NICER target of opportunity (ToO) observations (PI: surements, we employed a maximum likelihood technique to mea- Vasilopoulos, G) to measure the NS’s pulse period. NICER mea- sure pulsed frequencies and their significance (see details Ray et al. sured a spin period of 16.58 0.04 s on November 28 2019 (MJD 2011, 2018). For this purpose, we only used “good” detections3. 58451), revealing a spin change± of 1 s within 100 days. We fitted the time series of the NS frequencies with a Bayesian ∼ ∼ approach to linear regression (Kelly 2007) and derived a slope of 10 2 (4.031 0.026) 10− s− (90% confidence level). When fitting the data± with a polynomial× model instead, we derive an ephemeris 2.1 Data analysis 1 10 2 with ν = 0.053347 0.000003 s− ,˙ν = (4.23 0.03) 10− s− and ± 18 3 ± × We used Swift/XRT to measure the X-ray flux of NGC 300 ULX1. ν¨ = (4.4 0.5) 10− s− at epoch MJD 58243.515. The secular ± × Swift/XRT data products are available though the UK Swift science frequency evolution as derived above is in agreement ( 20% devi- ∼ data centre1 (Evans et al. 2007, 2009). ation) with the instantaneousv ˙ measured by Carpano et al. (2018); Basic information about spectral changes of the observed Vasilopoulos et al. (2018). spectrum can be derived from the hardness ratio (HR). This is de- In the following section, we show that the spin evolution of fined as the ratio of the difference over the sum of the number of the NS in NGC 300 ULX1 during 2018 requires a roughly constant 18 1 counts in two subsequent energy bands: HR = (R + R )/(R + + accretion rate in excess of the Eddington limit ( 2 10 g s− ), i 1 − i i 1 ∼ × Ri), where Ri is the background-subtracted count rate in a specific whereas the light curve clearly shows a decrease of the observed energy band. FX. This controversy can be naturally resolved, if one attributes the We used data obtained by NICER from 2018 February 6 decay of the observed FX to an increased absorption due to extra through 2019 February 4. to obtain accurate measurements of the material present in the line of sight. The absorbing material can be spin frequency evolution of NGC 300 ULX1. We followed the max- the result of outflows launched from the accretion disc and/or of the imum likelihood procedure described by Ray et al. (2018) on seg- disc precession. ments of data with gaps less than 1000 s and spanning no more than 3000 s. The points plotted in Figure 1 are the detections where the 2 data span at least 360 seconds with a significance of at least 4.5 σ. In this context the observed flux FX, plotted in Fig. 1, when corrected for the distance modulus of NGC 300, is the LX. 3 These have likelihood test statistic less than 21, span of observation greater than 360 s, and more than 70% of good exposure time within that 1 http://www.swift.ac.uk/user_objects/ span (see also Ray et al. 2018).

MNRAS 000, 1–7 (2015) NGC 300 ULX1: spin evolution 3

5×1039 erg/s −11 ) 10 2

−12

(erg/s/cm 10 LEdd X F

10−13 0.6

0.3

0.0 HR

−0.3

−0.6 0.062

0.058

f (Hz) 0.054

0.050 100 200 300 400 500 MJD − 58000

Figure 1. Top panel: X-ray light-curve (0.3–30 keV band) of NGC 300 ULX1 as derived from Swift/XRT observations (black points) performed within 2018. We used the spectral properties derived by Carpano et al. (2018), assuming a constant absorption, to convert Swift/XRT count rates to FX (see text). Horizontal dashed blue lines mark characteristic luminosity levels converted to expected flux for a distance of 1.88 Mpc. The shaded area indicates the period of the rapid X-ray flux decline and recovery discussed in text. Middle panel: temporal evolution of the hardness ratio (HR) as derived from the soft (0.3–1.5 keV) and hard (1.5–10.0 keV) energy bands. Bottom panel: temporal evolution of the measured spin frequencies derived from NICER observations (see Ray et al. 2018). The black dashed line denotes the best linear fit to the data, which yields M˙ = 2.3 1019 gs 1 (see text for details; §3.1). Red points are the NICER detections × − with the highest significance (see Ray et al. 2018, for details) just before the decay and after the rise of the FX.

3 ACCRETION AND TORQUES IN ULX PULSARS the inner part of the accretion disc, thus leading to a reduced accre- tion rate onto the compact object. This occurs inside the spheriza- The Eddington luminosity of an accreting object is obtained by tion radius Rsph, where the disc thickness becomes comparable to equating the outward radiation pressure with the gravitational its radius (Shakura & Sunyaev 1973) or, equivalently, the disc lumi- force: nosity becomes equal to LEdd (see eq. 18 in Poutanen et al. 2007): 4πGMNSc 38 1 LEdd = 1.5 10 m1 erg s− , (1) κ ≈ × GM m˙ R NS 0 m m , 2 1 sph 10 2 15 1 ˙ 0 km (3) where G is the gravitational constant, κ = 0.2(1 + X) cm g− is ≈ c ≃ the Thomson opacity, X is the hydrogen mass fraction for solar wherem ˙ 0 is the mass accretion rate at Rsph in units of M˙ Edd. In this abundances (X = 0.7), and m1 MNS/M is the NS mass (in units ≡ ⊙ regime, the outflows launched from within the spherization radius of the solar mass). are re-configuring accretion in a way that the local disc accretion At low mass accretion rates, the disc is locally sub-Eddington rate is sub-Eddington (Shakura & Sunyaev 1973). In the classical and its inner part is gas-pressure dominated (regime 1). For mass mass-loss model of Shakura & Sunyaev (1973), the mass accretion ˙ accretion rates exceeding the critical rate MEdd: rate at R < Rsph can be written as:

48πGMNS 18 1 R M˙ Edd = 2 10 m1 g s− , (2) ˙ ˙ cκ M(R) m˙ 0 MEdd. (4) ≃ × ≃ Rsph part of the dissipated energy is used to launch mass outflows from

MNRAS 000, 1–7 (2015) 4 G. Vasilopoulos et al.

This is only an approximate relation, as it does not take into account Regime 1 Regime 2 Regime 3 the effects of heat advection in the disc. Inclusion of the latter re- sults in a more gradual decrease of M˙ with radius than the one 20 5 10 dictated by eq. (4) (Poutanen et al. 2007; Chashkina et al. 2019; Mushtukov et al. 2019).

4 km) 7

In contrast to non-magnetized accreting objects, the accretion (g/s) M R discs around magnetized NSs do not extend to the innermost sta- . (10

3 M M

ble orbit, but they are truncated at much larger radii due to the in- R 1019 teraction with the NS magnetic field. The magnetospheric radius 2 provides an estimate of the disc inner radius (Ghosh et al. 1977):

12 4 1/7 RNS B −9 RM = ξ , (5) 10 2 2GMNS M˙ ! )

where RNS is the neutron star radius and ξ 0.5 (Campana et al. −2 ∼ 12 2018). For typical B values in X-ray pulsars (e.g., 10 G), very high (s

. ν mass accretion rates are required (e.g.,m ˙ 0 > 10) to make Rsph > RM (regime 2). Although heat advection is operating in the disc even at sub- 10−10

Eddington rates, where no outflows are present, it begins to play 19 20 an increasingly important role in the energy balance of the inner 10 . 10 M0 (g/s) disc at super-Eddington rates, i.e.,m ˙ 0 & 20 (regime 3) and even- tually becomes the dominant process at extremely high rates, i.e., Figure 2. Top panel: Schematic dependence of the magnetospheric (inner & m˙ 0 100 for typical X-ray pulsar magnetic fields (see Fig. 12 of disc) radius RM (red line) and the mass accretion rate at that radius M˙ (RM) 4 Chashkina et al. 2019) . Because of the heat advection, the radia- (black line) as a function of the mass accretion rate at the spherization radius tion energy flux transported by diffusion in the vertical direction M˙ 0 (for detailed calculations, see Mushtukov et al. 2019; Chashkina et al. is less than the one released locally in the disc (Mushtukov et al. 2019). The spherization (Rsph) and magnetospheric radii are defined by 2019). The advection process effectively leads to a reduced mass eqs. (3) and (7), respectively. The condition Rsph = RM marks the transition loss from the disc. The outflow rate in this regime is a constant between regimes 1 and 2. For the definitions of the accretion regimes indi- cated in the plot, see §3. Bottom panel: Derived spin-up rate using eq. (6). fraction of the mass accretion rate at Rsph and cannot exceed ∼ Horizontal lines mark the variousν ˙ measurements based on XMM-Newton, 50% 60% (see e.g., Fig. 3 in Mushtukov et al. 2019). 10 10 10 − Chandra, NuSTAR, and NICER data: 5.5 10− , 4.5 10− , 4.0 10− , × × × In what follows, we interpret our findings (see Fig. 1 and § 2.2) and 3.8 10 10 s 2 (Vasilopoulos et al. 2018; Ray et al. 2018). in the context of the three regimes described above and schemati- × − − cally shown in Fig. 2.

45 2 where INS (1 1.7) 10 g cm is the moment of inertia of the 3.1 Spin-evolution without outflows NS (e.g., Steiner≃ − et al.× 2015). The spin evolution of a sub-Eddington accreting NS can be theo- For an almost constant mass accretion rate (within a fac- tor of 2), the standard torque model can explain the NS retically predicted, if two parameters are known, the accretion rate ∼ and the surface magnetic field of the NS (Wang 1995). In X-ray spin period evolution for the entire period prior to MJD 58300 pulsars, material is deposited onto the magnetic pole of the NS, (Vasilopoulos et al. 2018), when the X-ray flux of NGC300ULX1 forming the so-called accretion column (e.g. Becker & Wolff 2007; started to decline. Observations of NGC 300 ULX1 performed by Mushtukov et al. 2015). The bolometric X-ray luminosity of the XMM-Newton, NuSTAR, and Chandra have been used to deter- system, which originates from the accretion column, can be con- mine the system’s LX andv ˙ at different epochs, thus allowing the estimation of the NS magnetic field, which was found to be verted to a mass accretion rate M˙ assuming some efficiency ηeff ˙ 2 ffi B 6 1012 G(Vasilopoulos et al. 2018). Upon inserting the av- (i.e., LX ηeff Mc ). This is generally assumed to be the e ciency ≃ × with which≈ gravitational energy is converted to radiation, namely erage spin-up rate for NGC 300 ULX1 as inferred by the fit to the 10 2 = ˙ = = 6 = NICER data (˙v = 4.031 10− s− ) into equations (5)-(6) and set- LX GMNS M/R. For R RNS 10 cm and MNS 1.4M , one × 2 ⊙ ting ξ = 0.5, n(ω ) = 7/6, m = 1.4 and I = 1.3, we find finds LX 0.2Mc˙ . Henceforth, we adopt ηeff = 0.2. fast 1 NS,45 ≈ R M˙ R . 19 1 The induced torque due to the mass accretion is Nacc M 800 km and ( M) 2 3 10 g s− (see first column in ≈ Table≃ 1). ≃ × M˙ √GMNSRM. The total torque can be expressed in the form of Ntot = n(ωfast)Nacc where n(ωfast) is a dimensionless function that We next explored if the same model can reproduce the spin- accounts for the coupling of the magnetic field lines to the accretion evolution of the NS for the 100-day period during which the ob- disc and takes the value 7/6 for slow rotators (for more details served FX rapidly decayed and recovered (see grey shaded region see Wang 1995; Parfrey et≈ al. 2016). The spin-up rate of the NS is in Fig. 1). For this purpose, we solved eq. (6) assuming a constant magnetic field strength of B = 6 1012 G and a radiative effi- then given by: × ciency of ηeff = 0.2. We performed our calculations for (i) various n(ωfast) v˙ = M˙ GM R , (6) constant values of the accretion rate (or equivalently intrinsic LX) 2πI NS M NS p and (ii) a variable accretion rate that best describes the observed temporal evolution of FX, assuming no correction due to obscu- 4 Note that Chashkina et al. (2019) normalize the accretion rates to ration or extreme absorption. The derived spin-period evolution- ary tracks for the two cases are plotted in Fig. 3. It is clear that 4πGMNS /cκ, which introduces a factor of 12 difference with the normal- ization adopted here. the observed spin evolution does not match the one predicted for a

MNRAS 000, 1–7 (2015) NGC 300 ULX1: spin evolution 5

Table 1. Physical parameters of NGC 300 ULX1 inferred from its spin evo- lution, assuming different accretion regimes. 18.0 Parameters Regime 1(a) Regime 2(b) B [G] 6 1012 fixed(c) 1.4 1012 1 (d) × 19 × 19 M˙ (RM)[gs ] 2.3 10 4.0 10 − × × 17.5 RM [km] 800 300

(a) (b) RM > Rsph; accretion without outflows. The mass-accretion rate at the magnetosphere is assumed constant. (c) Fixed at the value derived by Vasilopoulos et al. (2018). (d) Value of an effective constant M˙ (R ) that 17.0 M

P (s) would result in the observed average spin-up rate measured by the NICER . M (g/s) data. 2.0×1018 1.0×1019 16.5 1.3×1019 1.6×1019 2.0×1019 Swift/XRT 16.0 350 400 450 10 7/4 1/2 3 3/2 3/2 3/2 B 3.9 10 ξ− m1− RNS− ,6 INS,45 ν˙ 10 [n(ωfast)]− G (8) MJD−58000 ≃ × − Figure 3. Predicted evolution of NS spin period P based on the Wang (1995) model for various accretion rates marked on the plot. Two red points mark ˙ 19 1/3 2/3 2/3 2/3 1 M(RM) 1.6 10 m1− INS,45 ν˙ 10 [n(ωfast)]− g s− , (9) the measured spin period from the NICER observations, as shown also in ≃ × − 6 10 2 the lower panel of Fig. 1. Black lines denote the evolution of P after the where RNS,6 RNS/10 cm,ν ˙ 10 ν/˙ 10− s− and NICER measurement (first red point) for different constant accretion rates I I /1045≡g cm2. By inserting the− average≡ spin-up rate for NS,45 ≡ NS (at RM) marked on the plot. The evolutionary track predicted for a variable NGC300ULX1 as inferred by the fit to the NICER data (˙v = M˙ that follows the observed Swift/XRT count rate (shaded area in upper 10 2 4.031 10− s− ) into equations (7)-(9) and setting ξ = 0.5, panel of Fig. 1) is plotted with a solid blue line. This solution is obtained n(ω )×= 7/6, m = 1.4 and I = 1.3, we find B 1.4 1012 using the best fit spectral model of Carpano et al. (2018) with no changes in fast 1 NS,45 ≃ × G, R 300 km and M˙ (R ) 4 1019 g s 1 (see second column absorption and η = 0.2. M M − eff in Table≃ 1). For these parameters,≃ × the inner disc is expected to be radiation-pressure dominated (see e.g., Fig. 7 in Mönkkönen et al. 2019). variable mass accretion rate that matches the observed rapid decay We can also compute the luminosity that would be released of the X-ray flux (solid blue line). On the contrary, the observed as the mass reaching RM is accreted onto the NS by adopting the spin evolution demands a constant super-Eddington accretion rate value of M˙ (RM) we derived above. This yields an isotropic X-ray 19 1 39 1 (M˙ 1.6 10 g s− ) that translates to an absorption-corrected luminosity of 6.6 10 erg s− (for ηeff = 0.2), which is a fac- ≃ × 39 1 × luminosity LX 3 10 erg s− , in agreement with the findings of tor of 2 higher than the observed luminosity attributed to the pul- Vasilopoulos et∼ al.×(2018). sating hard component of the X-ray spectrum in NGC 300 ULX1 (Koliopanos et al. 2019; Carpano et al. 2018). Unless the radiative efficiency is much lower than 10% 20%, no beaming is needed to explain the spectral and temporal properties− of NGC 300 ULX1.

3.2 Spin-evolution with outflows Using the derived value of RM and the condition Rsph > RM, we can derive a lower limit on the mass accretion rate at the spher- Here, we expand the calculations for the spin evolution of ization radius, i.e.,m ˙ & 14. We can also place a rough upper limit NGC 300 ULX1 presented by Vasilopoulos et al. (2018), by tak- 0 onm ˙ by noting thatν ˙ does not vary much (see Fig. 1), suggesting ing into account the effects of outflows expected during super- 0 an approximately constant accretion rate at the magnetospheric ra- Eddington accretion (Shakura & Sunyaev 1973). A major differ- dius. The latter condition can be realized only for a narrow range ence of the following analysis with that presented in §3.1, is that of super-Eddington accretion rates (for a schematic illustration see (under certain conditions) one can estimate the unknown parame- grey-shaded region in the top panel of Fig. 2). This range of ac- ters of the system (R , B, M˙ (R )) from just one observable (i.e., M M cretion rates was found to be only weakly dependent on the mag- the spin-up rateν ˙). netic field strength of the NS (see Figs. 12-13 in Chashkina et al. Equation 3 suggests that ifm ˙ is sufficiently high so that 0 2019). Beyond this range, the time-derivative of the NS spin fre- R > R , by further increasingm ˙ , both R and M˙ (R ) remain sph M 0 M M quency is expected to depend more strongly on the accretion rate, constant and all the excess mass is lost through outflows (Lipunov as schematically shown in the bottom panel of Fig. 2. This state- 1982). These arguments have provided the baseline for the recent ment is true regardless of the specific dependence of R onm ˙ (see study of King et al. (2017), where it was shown that by just mea- M 0 e.g., Fig. 12 in Chashkina et al. 2019), which is determined by the suring the spin-up rate of the NS in ULXPs one can estimate B, R M interplay of mass loss through outflows and advection of heat in and M˙ (R ), without any knowledge of its actual X-ray luminosity M the inner disc and is model-dependent. As the long-term spin evo- (see §3.1 for comparison). Using equations (3), (4), (5), and (6) we lution of NGC 300 ULX1 is consistent with an almost constantν ˙ obtain R , B, and M˙ (R ): M M (see Fig. 1), we can place a rough upper limit on the accretion rate 1/3 2/3 2/3 2/3 . 12 RM 119 m1− INS,45 ν˙ 10 [n(ωfast]− km (7) at the spherization radius, i.e.,m ˙ 0 50 for B 10 G. ≃ − ∼ MNRAS 000, 1–7 (2015) 6 G. Vasilopoulos et al.

4 ON THE ORIGIN OF THE OBSCURING MATERIAL opening angles lead to non-spherical photospheres by introducing a dependence of Rph on θc. Any information about changes in the We have demonstrated that the NS continues to spin up with an al- inflow due to the Lense-Thirring torque must be communicated to most constantν ˙ during the period of decreasing flux (MJD 58350- all parts of the outflow within the photosphere, for it to precess out 58450), suggesting an almost constant accretion rate at the NS mag- to that radius. It is possible, however, that the outflow becomes su- netospheric radius. Thus, the decrease of the observed X-ray flux personic at R Rph, thus becoming decoupled from the inflow. cannot be intrinsic to the source but it can rather be caused by ab- A lower limit on≪ the predicted precession period can be derived, if sorption. the outflow remains subsonic within the spherization radius. In this Radiatively driven outflows launched from the disc can be case, Rout & Rsph. An accurate calculation of Pprec requires detailed optically thick to the hard radiation produced by the NS, act- knowledge of the outflow thermodynamical properties and geome- ing effectively as obscuring envelopes (e.g., Poutanen et al. 2007; try (i.e., density and pressure radial profile, opening angle) and, as Abolmasov et al. 2009). However, radiation can still escape from such, lies beyond the scope of this paper (see also Middleton et al. a central conical region (with opening angle θc) that is devoid of 2019). obscuring material (Poutanen et al. 2007). For a radiation-pressure Assuming that the observed X-ray flux decay is associated dominated accretion disc, truncated at RM < Rsph, the mass outflow with Lense-Thirring precession, the corresponding period should rate up to a radius R, lying within the spherization radius, can be be longer than a year, since we have only observed one such event estimated by: within one year of continuous monitoring. For the current spin pe- 5 R riod PNS = 16 s, RM = 300 km, andm ˙ 0 = 20 (50) we find dM˙ (R′) R RM M˙ out(R) = dR′ m˙ 0 M˙ Edd − , (10) Pprec 2.3 yr (300 yr), if Rout = Rph and Pprec 0.4 yr (3.0 yr), ZR dR′ ≈ Rsph ≃ ≃ M if Rout = 2Rsph. As the spin-up of the NS continues, shorter Pprec where eq. (4) was used. Following Poutanen et al. (2007) (see are expected. Due to the strong dependence of Pprec onm ˙ 0, we can eqs. (27), (28), and (30) therein), we calculate the maximum Thom- place upper limits on the latter by detecting future periodic dips in son optical depths in the directions perpendicular (τ ,max) and par- the X-ray flux due to precession. Future monitoring observations ⊥ allel (τ//,max) to the accretion disc plane: could provide crucial insights on this phenomenon.

τ0m˙ 0 rM τ ,max = √rsph (11) ⊥ βrsph − √rsph ! 5 CONCLUSIONS τ0m˙ 0 1/2 1/2 τ//,max = 2 √rsph √rM + 2rM r− r− β cot θ r sph M c sph h  −   −  We have analysed monitoring observations of NGC 300 ULX1 ob- rM tained with Swift/XRT within 2018, and presented an updated X- + √rsph 1 , (12) − rsph !# ray light-curve. We showed that within a 100 days period the ob- served flux of the system rapidly decayed. Moreover, we triggered where β 1 is the ratio of the outflow speed to the Keplerian ve- NICER target of opportunity observations to follow the spin evo- ∼ √ ˙ = 2 locity at Rsph, θc π/4, τ0 6κMEdd/4πcR0, R0 6GMNS/c , lution on the NS during the low-flux epoch. We showed that the ∼ = ≡ & and r R/R0. For RM 300 km (see Table 1) andm ˙ 0 20, we NS of NGC 300 ULX1 continues to spin up with a rate that trans- ≡ & find τ//,max τ ,max 5. This corresponds to a maximum column lates to a constant mass accretion rate within 2018, even at epochs &≈ ⊥ 24 2 density NH 7.5 10 cm− for a line-of-sight cutting through the where the observed flux dropped by a factor of 50. We interpreted × ffi outflow, and it is su cient to explain the X-ray flux decay due to the changes in the observed flux as a result of∼ increased absorp- absorption (see also Carpano et al. 2018). tion and obscuration. Outflows from a radiation-dominated accre- The accretion disc around a black hole or a NS can pre- tion disc can provide an optically thick structure that could be re- cess due to the Lense-Thirring effect (Bardeen & Petterson 1975; sponsible for the increased absorption. In this regime, the observed Truemper et al. 1986). Recently, it has been postulated that this LX under-predicts the mass accretion rate assuming typical radia- mechanism can explain the super-orbital modulation in the ob- tive efficiency for the accretion column, thus no strong beaming (if served flux of ULXPs (Middleton et al. 2018). According to this any) is needed to explain the observed super-Eddington luminos- scenario, the drop in the observed flux is due to changes in the ge- ity. Based on the inferred properties of NGC 300 ULX1 we expect ometrical configuration of the inner accretion disc and the outflow. the orientation of the outflows to change on year-long timescales Thus, in ULXPs the observer can only see the NS when the wind- due to Lense-Thirring precession. The detection of multiple (quasi- free region of the outflow aims directly at him/her. The timescale periodic) dips in the X-ray flux within the next decade will pro- of the outflow precession is (see eq. 5 of Middleton et al. 2018): vide a firm confirmation for the Lense-Thirring precession being

3 2 3 2 the mechanism responsible for the X-ray obscuration. Rsphc 1 (RM/Rsph) Rout Pprec PNS − , (13) ≈ 6GINS ln(Rsph/RM) Rsph ! where R is the radius at which the precession of the outflow out ACKNOWLEDGEMENTS ceases. An upper limit on the precession period can be derived if Rout Rph, where the photospheric radius Rph is estimated by the The authors would like to thank the anonymous referee for their ∼ condition τ = 1: constructive review. GV would like to thank D. Walton, F. Fürst, ⊥ τ m˙ R M. Bachetti, and M. Heida for discussions on NGC 300 ULX1 R 0 0 0 r r . (14) ph ≈ β r sph − M √ sph   For β 1, R = 300 km, andm ˙ = 20 (50), we obtain R 5 ∼ M 0 ph ≃ This calculation is just introduced as an order of magnitude estima- 2000 km (2 104 km). Similar values of the photospheric radius tion. For a discussion about the uncertainties, we point the reader to × can be obtained by requiring τ = 1, if θ π/4. We note that other Middleton et al. (2018, 2019). // c ∼ MNRAS 000, 1–7 (2015) NGC 300 ULX1: spin evolution 7 that took place at the HEAD17 meeting. MP acknowledges sup- Steiner A. W., Gandolfi S., Fattoyev F. J., Newton W. G., 2015, port from the Lyman Jr. Spitzer Postdoctoral Fellowship and Fermi Phys. Rev. C, 91, 015804 Guest Investigator grant 80NSSC18K1745. We thank Z. Arzouma- Truemper J., Kahabka P., Oegelman H., Pietsch W., Voges W., 1986, ApJ, nian and the NICER team for their help and assistance during the 300, L63 execution of the NICER ToO observations. NICER work at NRL is Vasilopoulos G., Haberl F., Carpano S., Maitra C., 2018, A&A, 620, L12 Wang Y.-M., 1995, ApJ, 449, L153 funded by NASA. We acknowledge the use of public data from the Swift data archive. This paper has been typeset from a TEX/LATEX file prepared by the author.

REFERENCES Abolmasov P., Karpov S., Kotani T., 2009, PASJ, 61, 213 Bachetti M., et al., 2014, Nature, 514, 202 Bardeen J. M., Petterson J. A., 1975, ApJ, 195, L65 Becker P. A., Wolff M. T., 2007, ApJ, 654, 435 Binder B., Williams B. F., Kong A. K. H., Gaetz T. J., Plucinsky P. P., Dal- canton J. J., Weisz D. R., 2011, ApJ, 739, L51 Brightman M., et al., 2019, ApJ, 873, 115 Campana S., Stella L., Mereghetti S., de Martino D., 2018, A&A, 610, A46 Carpano S., Haberl F., Maitra C., Vasilopoulos G., 2018, MNRAS, 476, L45 Chashkina A., Lipunova G., Abolmasov P., Poutanen J., 2019, A&A, 626, A18 Corbet R. H. D., 1996, ApJ, 457, L31 Evans P. A., et al., 2007, A&A, 469, 379 Evans P. A., et al., 2009, MNRAS, 397, 1177 Fürst F., Walton D. J., Stern D., Bachetti M., Barret D., Brightman M., Harrison F. A., Rana V., 2017, ApJ, 834, 77 Fürst F., et al., 2018, A&A, 616, A186 Ghosh P., Lamb F. K., Pethick C. J., 1977, ApJ, 217, 578 Gieren W., Pietrzynski´ G., Soszynski´ I., Bresolin F., Kudritzki R.-P., Minniti D., Storm J., 2005, ApJ, 628, 695 Illarionov A. F., Sunyaev R. A., 1975, A&A, 39, 185 Israel G. L., et al., 2017, Science, 355, 817 Kaaret P., Simet M. G., Lang C. C., 2006, ApJ, 646, 174 Kaaret P., Feng H., Roberts T. P., 2017, ARA&A, 55, 303 Kelly B. C., 2007, ApJ, 665, 1489 King A., Lasota J.-P., 2019, MNRAS, 485, 3588 King A. R., Davies M. B., Ward M. J., Fabbiano G., Elvis M., 2001, ApJ, 552, L109 King A., Lasota J.-P., Klu´zniak W., 2017, MNRAS, 468, L59 Koliopanos F., Vasilopoulos G., Godet O., Bachetti M., Webb N. A., Barret D., 2017, A&A, 608, A47 Koliopanos F., Vasilopoulos G., Buchner J., Maitra C., Haberl F., 2019, A&A, 621, A118 Leahy D. A., Darbro W., Elsner R. F., Weisskopf M. C., Sutherland P. G., Kahn S., Grindlay J. E., 1983, ApJ, 266, 160 Lipunov V. M., 1982, Soviet Ast., 26, 54 Middleton M. J., et al., 2018, MNRAS, 475, 154 Middleton M., Fragile P. C., Ingram A., Roberts T. P., 2019, arXiv e-prints, p. arXiv:1905.02731 Mönkkönen J., Tsygankov S. S., Mushtukov A. A., Doroshenko V., Suleimanov V. F., Poutanen J., 2019, arXiv e-prints, p. arXiv:1905.05593 Motch C., Pakull M. W., Soria R., Grisé F., Pietrzynski´ G., 2014, Nature, 514, 198 Mushtukov A. A., Suleimanov V. F., Tsygankov S. S., Poutanen J., 2015, MNRAS, 454, 2539 Mushtukov A. A., Ingram A., Middleton M., Nagirner D. I., van der Klis M., 2019, MNRAS, 484, 687 Parfrey K., Spitkovsky A., Beloborodov A. M., 2016, ApJ, 822, 33 Poutanen J., Lipunova G., Fabrika S., Butkevich A. G., Abolmasov P., 2007, MNRAS, 377, 1187 Ray P. S., et al., 2011, The Astrophysical Journal Supplement Series, 194, 17 Ray P. S., et al., 2018, arXiv e-prints, p. arXiv:1811.09218 Shakura N. I., Sunyaev R. A., 1973, A&A, 24, 337

MNRAS 000, 1–7 (2015)