The X-ray variable sky as seen by MAXI: the future of dust echo tomography with bright Galactic X-ray bursts
Lia Corrales, Brianna S. Mills, Sebastian Heinz, Gerard M. Williger
DDraft version March 21, 2019
Typeset using L A TEX default style in AASTeX62
The X-ray variable sky as seen by MAXI: the future of dust echo tomography with bright Galactic X-ray bursts
Lia Corrales,
1, 2, 3
Brianna S. Mills,
3, 4, 5
Sebastian Heinz, and Gerard M. Williger
4, 6, 7, 8 LSA Collegiate Fellow, University of Michigan, Ann Arbor, MI 48109, USA Einstein Postdoctoral Fellow University of Wisconsin - Madison, Madison, WI 53706, USA University of Louisville, Louisville, KY 40292, USA University of Virgnia, Charlottesville, VA 22904, USA Jeremiah Horrocks Institute, University of Central Lancashire, Preston, PR1 2HE, England Institute for Astrophysics and Computational Sciences, Catholic University of America, Washington, DC 20064 Konkoly Observatory, 15-17 Konkoly-Thege Mikls t, 1121 Budapest, Hungary
Submitted to ApJABSTRACTBright, short duration X-ray flares from accreting compact objects produce thin, dust scatteringrings that enable dust echo tomography: high precision distance measurements and mapping of theline-of-sight distribution of dust. This work looks to the past activity of X-ray transient outburstsin order to predict the number of sight lines available for dust echo tomography. We search for andmeasure the properties of 3 σ significant flares in the 2-4 keV light curves of all objects available in thepublic MAXI archive. We derive a fluence sensitivity limit of 10 − erg cm − for the techniques usedto analyze the light curves. This limits the study mainly to flares from Galactic X-ray sources. Weobtain the number density of flares and estimate the total fluence of the corresponding dust echoes.However, the sharpness of a dust echo ring depends on the duration of a flare relative to quiescence.We select flares that are shorter than their corresponding quiescent period to calculate a numberdensity distribution for dust echo rings as a function of fluence. The results are fit with a power lawof slope − . ± .
1. Extrapolating this to dimmer flares, we estimate that the next generation ofX-ray telescopes will be 30 times more sensitive than current observatories, resulting in 10-30 dust ringechoes per year. The new telescopes will also be 10-100 times more sensitive than
Chandra to dustring echoes from the intergalactic medium.
Keywords:
X-rays: bursts — X-rays: binaries — dust, extinction — X-rays: ISM — scattering INTRODUCTIONInterstellar dust scatters X-ray light over arcminute-scale angles, producing a diffuse scattering halo with an in-tegrated flux F halo ( E ) = F a (1 − e − τ ), where the optical depth to X-ray scattering, τ ≈ . E − (N H / cm − ),and F a is the absorbed flux of the central X-ray source (Predehl & Schmitt 1995; Corrales et al. 2016). Because thescattered light takes a longer path to reach the observer, the observed scattering halo surface brightness profile is aconvolution of the dust’s line-of-sight position, grain size distribution, and F a ( t ) light curve (Heinz et al. 2015, andreferences therein). When F a ( t ) takes the form of a single burst with high amplitude and short duration, a scatteringhalo will appear as a set of discrete rings, where each ring corresponds to a different foreground dust cloud. These ringsexpand with a characteristic t / time dependency that allows X-ray astronomers to map the line-of-sight distributionof dust (“dust echo tomography”) to much higher resolution than currently available with any other method (Tr¨umper& Sch¨onfelder 1973; Heinz et al. 2015, 2016). Corresponding author: a r X i v : . [ a s t r o - ph . H E ] M a r Corrales et al.
Table 1.
Flare properties of objects with observed dust echoes
Object Telescope(s) Fluence a Gal. N H References (erg cm − ) (10 cm − )GRB 031203 XMM-Newton . − × − XMM-Newton × − Swift × − Swift × − Swift × − XMM-Newton × − Swift , XMM-Newton − × − Chandra
XMM-Newton , Chandra
Swift , Chandra a Mapping the ISM through dust echo tomography is also important for interpreting the time and spectral evolution ofaccreting compact objects. Dust echoes are known to affect the spectral evolution of X-ray variable objects, producinga prolonged soft-tail (e.g., Pintore et al. 2017a; Jin et al. 2018). This confusion is particularly acute for X-ray timingmissions with low imaging resolution: RXTE, MAXI, and NICER.To date, the brightest dust echo rings observed have come from four Galactic X-ray sources – 1E 1547.0-5408(Tiengo et al. 2010; Olausen et al. 2011; Pintore et al. 2017a), Cir X-1 (Heinz et al. 2015), V404 Cygni (Vasilopoulos& Petropoulou 2016; Heinz et al. 2016; Beardmore et al. 2016), and 4U 1630-47 (Kalemci et al. 2018). Dust echoescan also be produced by the X-ray components of gamma-ray bursts (GRBs), which scatter off the nearby Galacticmedium (Vaughan et al. 2004, 2006; Tiengo & Mereghetti 2006; Vianello et al. 2007; Pintore et al. 2017b). Table 1lists the approximate soft X-ray fluence and ISM column for dust echo rings observed around GRBs and XRBs. Inmost of the GRB cases, fluences were measured from the properties of the dust scattering echo, and the results dependon the adopted grain size distribution.One can note from Table 1 that the fluences of GRBs producing dust echoes are particularly low. In these cases, ∼
10% of the X-ray light from the flare is deposited into the dust scattering ring. This level rivals the amount of lightin the telescopes’ point spread function (PSF) wings. However, due to the quick dimming typical of X-ray afterglows,the time delay between the prompt X-ray emission and the dimming afterglow allows the the dust scattering rings tostand out in contrast, even when a central X-ray point source is visible. In theory, X-ray variability from any high-redshift object can produce echoes that propagate off dust from foreground galaxies or the intergalactic medium, butit requires more sensitive telescopes than currently available (Miralda-Escud´e 1999; Corrales & Paerels 2012; Corrales2015).Many Galactic XRBs are persistent sources of X-rays, producing a quiescent dust scattering halo. A source thatexperiences frequent outbursts, or high variation, will create a time variable scattering halo with no clearly definedrings. This study focuses on identifying single, large amplitude outbursts capable of producing thin, high contrastdust echo rings.This work evaluates the X-ray light curves from all sources monitored regularly by MAXI (Monitor of All-sky X-rayImage, Matsuoka et al. 2009), in order to gather the rate of X-ray flares propagating through the interstellar medium(ISM). In Section 2, we describe the algorithm used to identify flares and discuss its limitations. In Section 3, wecalculate the number distribution of flares identified in MAXI. A metric for evaluating the likelihood of an outburst toproduce sharp ring echoes is discussed in Section 3.1. In Section 3.2, we fit a power law to the number distribution offlares and use it to estimate how many X-ray dust ring echoes will be seen with the next generation of X-ray telescopes.We also update the results of Corrales (2015) to estimate the number of X-ray scattering echoes that might be foundarising from dust in the intergalactic medium. All findings are summarized in Section 4. DATA ANALYSIS ust echo tomography with bright Galactic X-ray bursts − erg s cm − ) (Matsuoka et al.2009; Kawai et al. 2014). Because the ISM preferentially removes soft X-rays, the spectral energy distribution of X-rayscattering halos tend to peak around 1-3 keV. We use the publicly available one-day binned 2-4 keV light curves from398 point sources currently available on the MAXI website , from the start of MAXI operations to MJD 58408, toestimate the probability distribution of soft X-ray flares across the sky. For the purposes of this work, a flare is definedas any duration longer than several days for which an object’s flux is > σ above its dimmest state.It should be noted that MAXI is insensitive to most flares that are significantly shorter than a single ISS orbit.Magnetars, Type I neutron star bursts, and X-ray afterglows to GRBs fall into this category. As will be demonstratedbelow, such flares are missed from this study due to limitations of MAXI, not due to data analysis choices.2.1. Detection Algorithm
First, we removed all data points where a monitored object was within 10 degrees of the Sun, which is a large sourceof contamination. All light curves were smoothed using a 3-day Gaussian convolution, to improve the stability of thealgorithm. Limitations imposed by smoothing are discussed in § § . × − erg cm − s − . We used linear interpolation over data gaps to arrive at a totalfluence for each flare interval.Figure 1 shows the results for three light curves of interest. LMC X-3 exhibits erratic behavior with no clearlydefined quiescent state. The algorithm flags the intervals when LMC X-3 is in a bright state. The next two panelsshow Cir X-1 and 4U 1630-47 during the flares leading to dust echoes study by Heinz et al. (2015) and Kalemci et al.(2018), respectively. The calculated fluences are 0.023 erg cm − over 85 days (Cir X-1) and 0.021 erg cm − over 171days (4U 1630-47). These values are consistent with those in the published works.We were unable to check on the dust echo producing flares from 1E 1547.0-5408, which occurred before the launchof MAXI, and V404 Cygni, which was only observable by the degraded GSC3 instrument at the time of the flare(Negoro et al. 2015). The publicly available MAXI light curves do not include data from GSC3. The MAXI view ofV404 Cygni is also affected by source confusion with Cyg X-1, which is usually much brighter. As a result, the lightcurve is poorly calibrated and no flares were measured from V404 Cygni. Sensitivity limits
To examine the accuracy of our analysis, we simulated 1000 MAXI light curves of 900 days long, and injected oneGaussian flare into each. The reported MAXI sensitivity is 4.5 mCrab for one-day binned data (Matsuoka et al. 2009),yielding a fluence theoretical lower limit of 5 × − erg cm − for a five day long flare. As such, the flare propertieswere drawn from a uniform distribution of fluences, log( F cgs ) ∈ [ − , −
1] (where F cgs is fluence in units of erg cm − ),and a uniform distribution of Gaussian widths σ (days) ∈ [1 , The baseline flux and error bars for each simulatedlight curve were drawn randomly from three MAXI light curves of objects with a quiescent flux below the sensitivitylimits, i.e., those exhibiting a light curve consistent with zero flux throughout: 1ES 1101-23.2, WW Cet, and VY Ari.We take these objects as representative of the zero values and error bars arising from the MAXI calibration processes.Figure 2 shows the distribution of detected flares compared to the input distribution. In general, the algorithmreturns a large number of short 10 − erg cm − flares ( < http://maxi.riken.jp/top/lc.html Communication with MAXI calibration staff A 900 day light curve was deemed sufficient to capture flares that are effectively 300 days long (Gaussian σ = 50 days). As shown laterin Section 3.1, these very long outbursts are typically beyond the scope of interest for dust echo tomography. Corrales et al.
Figure 1.
Flare intervals identified from three example light curves. The raw 2-4 keV light curves supplied by the MAXIwebsite (blue) are smoothed with a 3-day Gaussian kernel (black). After subtracting a baseline flux value, identified using thelower 1- σ value of the dataset (dashed black line), intervals with signal-to-noise greater than three are flagged as flares (shadedgrey regions). For X-ray binaries that rarely stay quiescent, such as LMC X-3 (left), any bright state is flagged as a flare. Twodust-echo producing flares from Cir X-1 (middle) and 4U 1630-47 (right) are highlighted. The calculated fluences are consistentwith those reported in the literature. Figure 2.
A histogram of simulated input (light grey) and the histogram derived with the techniques described in Section 2(dark grey). The input flares were drawn from a uniform distribution, and the expected 1 σ variation is shaded in blue. Thedotted black histogram shows how many of the output flares were correct identifications, to within 20% of the input fluence. than five days, and by combining flares that were separated by less than five days. The dotted line in Figure 2 showshow many flares for which the fluence was correctly retrieved to within 20%. For the subset of flares with fluence > − erg cm − , our algorithm was able to identify 90% of all the simulated flares and 100% of those that were ofduration ≤
20 days. We therefore take log F cgs > − Limitations for short outbursts
Using daily binned light curves and three-day smoothing imposes selection effects against short flares. In the extremecase of a flare restricted to a single ISS/MAXI orbit (90 minutes), the signal-to-noise of the flare in one-day binneddata will be reduced by a factor of √ ∼ <
80 mCrab) from detection, corresponding to a fluence < − erg cm − . Thisvalue is several orders of magnitude below the fluence values of interest for dust echo tomography with Galactic X-raysources (lower portion of Table 1), which is the main target of this study. ust echo tomography with bright Galactic X-ray bursts Figure 3.
Left:
A histogram of flares found in 213 MAXI light curves shows the fluence of the flares themselves (black) andthe estimated fluence of the corresponding dust echo (orange).
Right:
The number of sight lines that exhibit a flare (black) ordust echo (orange) larger than a particular fluence, described on the horizontal axis. This represents the number of sight linesavailable for performing dust echo tomography. The vertical dashed lines mark the threshold for flares (black) and correspondingecho brightness (orange) above which dust echoes from Galactic XRBs have been observed today. 34 and 24 of the sight linessatisfy two thresholds, respectively.
In conclusion, smoothing data has the advantage of reducing the number of false positives, because the variance ofthe data is significantly reduced. The critical metric for the detectability of dust scattering echoes of flares is theirfluence, which is preserved in binning and smoothing. Section 2.2 demonstrates that the algorithm retrieved all of theshort duration flares with log F cgs > −
3, which is an order of magnitude below our threshold of interest demonstratedby the lower portion of Table 1. Thus, the benefits of using binned and smoothed data outweigh the reduction ofsensitivity to short flares. RESULTS AND DISCUSSIONOf the 398 sources analyzed, 213 exhibited outbursts that were picked up by the flare detection algorithm. Toaccount for source confusion, we evaluated the light curves of three sources within 2 ◦ of each other: SMC X-1, SMC X-3, and MAXI J0057-720. One flare from SMC X-3 appeared coincidentally in the light curve of MAXI J0057-720,which is 0.6 ◦ away. However, variations from SMC X-1, which is the brightest of the three and 2 ◦ away from the othertwo objects, did not affect the light curves of either. Thus we chose 1 ◦ as the threshold for evaluating the effects ofsource confusion. We identified pairs of sources in the MAXI dataset separated by < ◦ . Within this subset of lightcurves, we searched for flares appearing within 30 days of each other. When coincident flares were found, we kept thelarger fluence event and discarded the other. We also visually evaluated the light curves of sources within 2 ◦ of theGalactic Center, which hosts a large number of variable compact objects that cannot be resolved with MAXI. Theoverall process resulted in the removal of 8 flares that were double counted, leaving a total of 854 distinct outburstswith log F cgs > − Chandra
X-ray Center tool colden to look up the N H value from HI surveys, in order to estimate the optical depth of X-rayscattering at 1 keV. We then multiplied the fluence of each flare by a factor of (1 − e − τ ) to estimate the integratedfluence of the resulting dust echo (orange).A higher instrument background makes it difficult to observe a dust scattering halo. A small fluence (relative to thequiescent state) will produce a small perturbation in the scattering halo brightness that is unlikely to be observable.To avoid modeling the problem, we use the examples of spectacular dust ring echoes from the literature (bottomportion of Table 1) to arrive at approximate thresholds for observation with modern-day X-ray telescopes. We choseflares with log F cgs > − H ≈ × cm − or τ ≈ .
1. The corresponding estimate yields thedimmest available dust echo fluence ( ≈ .
006 erg cm − ) in Table 1, yet V404 Cygni produced some of the clearestmulti-structured dust echo rings (Heinz et al. 2016). We take 0.005 erg cm − as an approximate threshold for effectivedust echo tomography with modern day instruments.Because one object can produce multiple flares, we counted the number of MAXI targets that exhibited a flare withfluence larger than a given threshold, yielding the number of sight lines available for dust echo tomography (Figure 3, Corrales et al. right). We found that 34 of the objects exhibited flares with log F cgs > −
2, and 24 of these have predicted dustechoes over the 0.005 erg cm − threshold during the last 9 years of MAXI operation. However, more analysis isneeded to determine which of these would have produced the thin, high contrast rings that are ideal for measuring theline-of-sight dust distribution. 3.1. Identifying Sources of Dust Echo Rings
High fluence flares are necessary to produce dust scattering halos, but many of them have a large fluence simplybecause they are long. Two other conditions are important for identifying dust echo candidates. First, flares mustbe short enough to produce sharp rings. Second, the bursts must be accompanied by a long period of quiescence sothat the dust echo rings stand out in contrast to the quiescent dust scattering halo. A survey by Valencic & Smith(2015) showed that a majority of X-ray scattering halos are dominated by scattering from a single cloud, rather thanisotropically distributed dust. The time delay associated with a particular angle can be inverted to solve for the angleat which a dust scattering echo will appear ( θ ), from a burst that occurred at some time ( t ) prior to now: θ = (cid:20) c (1 − x ) txD (cid:21) / (1)where D is the distance to the X-ray source, x is the distance to a dust cloud divided by D , and c is the speed of light(Tr¨umper & Sch¨onfelder 1973). This equation can be used to fit dust echo rings with multiple discrete ISM clouds,or, applying a convolution with the flare light curve, can be used to measure contiguous line of sight dust abundances(Heinz et al. 2015, 2016). While clouds or dust material that are extended along the line of sight will alter the perceivedthickness and time delay of a dust echo, a full examination of these geometric effects is beyond the scope of this work.For a fixed dust cloud position, the thickness of a dust echo ring (∆ θ ) will depend on the duration of the flare ( t f )so that ∆ θ ∝ t / f . In contrast, the dust scattering halo will return to its quiescent state out to some angle, θ ∝ t / q where t q is the duration of the quiescent period before or following the flare. We do not set a maximum duration for t f . All scattering halos dim in surface brightness at large angular distance from the central source source, so a returnto a dim quiescent state will always produce the appearance of rings. This was apparent from the outburst of 4U1630-47, lasting over 100 days, which produced an 8 arcminute scale ring (Kalemci et al. 2018). Ideal echoes will havethin rings relative to the size of the quiescent halo, requiring t f /t q << t f /t q for the flares identified in the MAXIdataset. We determined the duration of the quiescence directly before and after each flare, and chose the larger t q value. Smaller values of the t f /t q lead to thinner dust echo rings. The dust echoes arising from the Cir X-1 flare (Heinzet al. 2015) and 4U 1630-47 (Kalemci et al. 2018) were both high fluence with moderate values of 0 . < t f /t q <
1. Theflares from LMC X-3 are highlighted in Figure 4 (orange) to demonstrate a population of flares arising from a highlyvariable source with no persistent quiescent state. We found nine objects that produced bright > − erg cm − flaresdetected by MAXI with ( t f /t q ) < .
1. Of these, four have an estimated dust echo fluence > .
005 erg cm − . Thesefour have not been followed up or published: LS I +61 303, V* BQ Cam, XTE J1752-223, and MAXI J1535-571.Figure 4 (right) shows the number density of flares as a function of 2-4 keV fluence, which follows a power law ofslope − . ± .
03 (black). We also calculated the fluence distribution for dust echoes with t f /t q < F cgs > − . F cgs > − . − . ± . Avenues for Future Study
In the future, more sensitive X-ray telescopes will extend dust echo tomography to dimmer flares, opening up moresight lines for probing the 3D distribution of dust via X-ray scattering. For a fixed exposure time, we solved for thefluence ( f ) for which the signal-to-noise ratio is the same as the signal-to-noise ratio for a telescope with no background( f ). f = f × (cid:16) (cid:112) b/f (cid:17) (2) ust echo tomography with bright Galactic X-ray bursts Figure 4.
Left:
Relationship between flare duration and 2-4 keV fluence of the flare, as measured by MAXI. Naturally, thelarger fluence flares tend to arise from longer duration flares, up to 1000 days. The blue, red, and green circles show data pointsfrom the flares observed from Cir X-1, 4U 1630-47, and LMC X-3, respectively. The flares that led to dust echoes studied byHeinz et al. (2015) and Kalemci et al. (2018) are highlighted by the large blue and red circles, respectively.
Middle:
Plot ofthe dust echo 2-4 keV fluence versus the ring sharpness metric, ( t f /t q ). The larger fluence flares, which are often longer, areless useful because they fill out more of the dust scattering halo and produce broad rings that are more likely to overlap. TheCir X-1, 4U 1630-47, and LMC X-3 flares are highlighted in the same way as the left plot (blue, red, and green). In general,flares with ( t f /t q ) << Right:
A power law fitto the fluence distribution for all flares (black) and dust echoes with t q /t f < − . ± . − . ± .
1, respectively.
Figure 5.
Predicted number of dust scattering echoes observable by different telescopes, depending on the effective area andbackground levels, as compared to
Chandra . For the next generation of telescopes (
Athena , Lynx , and AXIS) we expect about30 times more dust echoes than observable with current instruments, depending on the background levels achieved. where b is the background surface brightness. Since any flux threshold is inversely proportional to the effectivearea ( a ), we substitute f with 1 /a in Equation 2. We calculated f for a grid of effective areas and backgrounds,relative to Chandra . We then calculated the total number of scattering ring echoes expected ( N ) by integrating thepredicted fluence density distribution for echoes, dN/df (Figure 4, orange), extrapolating the power law to fluenceswith log F cgs < −
3. Figure 5 shows several contours for N , predicting the observable number of high signal-to-noisescattering ring echoes, relative to the Chandra effective area and background surface brightness. The background is due to a combination of instrumental, charged particle, and cosmic X-ray background, which change with time andposition on the sky.
Chandra has relatively low, stable, and well documented background rates compared to other currently active X-raytelescopes, making
Chandra a good baseline for comparison.
Corrales et al.
Athena , expected to launch around 2030, will have a 1 keV effective area of 2 m (Barcons et al. 2017), approximately80 times the current soft X-ray effective area for Chandra
ACIS-I.
Athena will thereby observe on the order of 30 timesmore dust echoes than
Chandra can, depending on the instrument background levels. The concept mission,
Lynx ,will have a similar effective area to
Athena with the imaging resolution of
Chandra . The Advanced X-ray ImagingSatellite (AXIS) concept mission has a proposed 1 keV effective area of 7000 cm with 10-20 times lower backgroundthan Chandra (Mushotzky 2018). Thus AXIS would be able to image a similar number of dust echoes to
Athena and
Lynx .The increased sensitivity offered by the next generation of X-ray telescopes will also constrain the abundance anddistribution of dust in the intergalactic medium (IGM) through dust scattering echoes left behind by previously activegalactic nuclei (AGN). Using the formulations of Corrales (2015), a telescope with ten times the
Chandra sensitivitywill be able to image IGM scattering echoes on the order of 20 (cid:48)(cid:48) - 80 (cid:48)(cid:48) in radius, corresponding to AGN activity ∼ - 10 years prior. Using the numbers of bright z > N IGMech ∼ − (cid:18) ν fb − yr − (cid:19) (3)where ν fb is the characteristic frequency for rapid quenching of an AGN accretion flow. We refer the reader to theoriginal work of Corrales (2015) for a detailed discussion on how AGN variability and feedback can be constrained byIGM dust echoes. CONCLUSIONSExamination of nine years of MAXI light curves reveals 34 objects that exhibited bright X-ray flares with fluences > − erg cm − , with durations ∼ H to estimate the dust echo brightness, four of the flares might have produced dust echo rings detectable bycurrent X-ray telescopes. Only one of these sight lines, Cir X-1, has been imaged and studied in detail.With the next generation of X-ray telescopes, dust ring echoes will become common features of the Galactic ISM.We expect Athena , Lynx , and AXIS to be ≥
30 times more sensitive to dust echoes in comparison to
Chandra . Theresult will be hundreds of time-variable X-ray scattering halos. Of these, we expect ∼ t f /t q >
1. The resultingimage will be a blend of broad rings. Interpreting these images will require more advanced dust scattering halo timingtechniques. The results will open an avenue for mapping Galactic and intergalactic structures in an entirely new way.We wish to thank the anonymous referee for their thoughtful comments that greatly improved the clarity of the paper.This research has made use of MAXI data provided by RIKEN, JAXA, and technical support from the MAXI team.Support for this work was provided by NASA through Einstein Postdoctoral Fellowship grant number PF6-170149awarded by the Chandra X-ray Center (CXC), which is operated by the Smithsonian Astrophysical Observatory forNASA under contract NAS8-03060. Additional support for this work came from CXC through grant number TM6-17010X.
Facilities:
MAXI (Matsuoka et al. 2009)
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