Lyman- α photons through rotating outflows
MMNRAS , 000–000 (0000) Preprint 6th November 2018 Compiled using MNRAS L A TEX style file v3.0
Lyman- α photons through rotating outflows Maria Camila Remolina-Guti´errez (cid:63) & Jaime E. Forero-Romero † Departamento de F´ısica, Universidad de los Andes, Cra. 1 No. 18A-10 Edificio Ip, CP 111711, Bogot´a, Colombia
ABSTRACT
Outflows and rotation are two ubiquitous kinematic features in the gas kinematics ofgalaxies. Here we introduce a semi-analytic model to quantify how rotating outflowsimpact the morphology of the Lyman- α emission line. The model is contrasted againstMonte Carlo radiative transfer simulations of outflowing gas with additional solid bodyrotation. We explore a range of neutral Hydrogen optical depth of 10 ≤ τ H ≤ ,rotational velocity 0 ≤ v rot / km s − ≤
100 and outflow velocity 0 ≤ v out / km s − ≤ τ H = 10 , respectively, and within 2% and 1% for an optical depthof τ H = 10 . Using this model we also show that the peaks of integrated spectra takenfrom opposite sides of an edge-on rotating gas distribution should have a separationof v rot . The semi-analytic model presented here is a convenient tool to introducerotational kinematics as a post-processing step of idealized Monte Carlo simulations;it provides a framework to interpret Ly α spectra in systems where rotation is expectedor directly measured through kinematic maps. Key words: galaxies:ISM — line:profiles — radiative transfer — methods: numerical
Recent advances in instrumentation have revealed the pres-ence of gas rotation on vastly different physical scales. For in-stance, spatially resolved spectra on compact dwarf galaxieshave measured clear signs of gas showing pure rotation kin-ematics (Cair´os et al. 2015; Cair´os & Gonz´alez-P´erez 2017)and the recent mapping of high redshift circumgalactic re-gions have also revealed kinematic evidence for large scalerotation (Arrigoni Battaia et al. 2018). Systems with starformation, neutral gas and low dust contents can producea Ly α emission line (Partridge & Peebles 1967) motivatingthe observational work to phenomenologically link tracersof galaxy rotation such as H α to Ly α spectra (e.g. Herenzet al. 2016).What is then the expected imprint of rotation on a res-onant emission line such as the Ly α line? To what extent isit possible to constrain rotational kinematics from the Ly α emission line? Detailed radiative transfer (RT) Ly α model-ing of rotating systems started until recently by Garavito-Camargo et al. (2014). In that work the authors studiedthe influence of pure solid body rotation on the Ly α line’s (cid:63) [email protected] † [email protected] morphology. They found that rotation indeed introduceschanges, the most noticeable being the dependence of thespectra with the viewing angle with respect to the rotationaxis.Garavito-Camargo et al. (2014) also presented a simplesemi-analytical approximation that accounted for the mainfeatures of the Ly α spectra from a rotation sphere. Recently,this semi-analytic solution was used to perform a MarkovChain Monte Carlo exploration to fit the observed spectraCompact Dwarf Galaxy (Forero-Romero et al. 2018) withatypical features that could be explained by pure rotation.However, the gas dynamics in Lyman Alpha Emitter(LAE) galaxies are more complex than pure rotation. Inmany observations the Ly α line profile has a single peakredwards from the line’s center, in other cases there is adouble peak but the peak on the red side is stronger (e.g.Steidel et al. 2010; Erb et al. 2014; Trainor et al. 2016). Thesefeatures have been explained as the consequence of multipleLy α photon scatterings through a homogeneous outflowingshell of neutral Hydrogen (Verhamme et al. 2006; Orsi et al.2012; Gronke et al. 2015).Nevertheless, a study of the combined effects of outflowsand rotation has not been presented in the literature. Herewe report on such a study with the main aim of quantifyingthe validity of the semi-analytic approximation presented c (cid:13) a r X i v : . [ a s t r o - ph . GA ] N ov M.C. Remolina-Gutierrez & J.E. Forero-Romero by Garavito-Camargo et al. (2014) in the case where out-flows are also present. We investigate a simplified geomet-rical configuration corresponding to a spherical gas cloudwith symmetrical radial outflows and solid body rotationand contrast the semi-analytic model against the results ofa Monte-Carlo radiative transfer code.The structure of the paper is the following. We intro-duce first our theoretical tools and assumptions in Section2. We continue in Section 3 with the results from the Monte-Carlo simulation, the comparison against the semi-analyticalapproximation which we use to make a thorough explorationof the effect of rotation. In Section 4 we discuss our resultsand their possible implications for observational analysis tofinally present our conclusions in Section 5.Throughout the paper we use a thermal velocity for aneutral Hydrogen gas of v th = 12 .
86 km s − , which corres-ponds to a temperature of T = 10 K. We use CLARA (Forero-Romero et al. 2011), a Monte Carlocode that follows the propagation of individual photonsthrough a neutral Hydrogen medium characterized by itstemperature, velocity field and global optical depth. Thecode assumes an homogeneous density throughout the sim-ulated volume. In the current implementation we neglect theinfluence of dust. Our basic model is an spherical distribu-tion of neutral hydrogen, an approximation commonly usedin the literature that explains a wide variety of observationalfeatures (Ahn et al. 2003; Verhamme et al. 2006; Dijkstraet al. 2006).We use a velocity field that captures both outflows androtation. Outflows are described by a Hubble-like radial velo-city profile with the speed increasing linearly with the radialcoordinate; this model is fully characterized by v out , the ra-dial velocity at the sphere’s surface. Rotation follows a solidbody rotation profile fully characterized by v rot the linearvelocity at the sphere’s surface.The total velocity field is the superposition of rotationand outflows. The cartesian components take the followingform: v x = xR v out − yR v rot , (1) v y = yR v out + xR v rot , (2) v z = zR v out , (3)where x , y and z are the cartesian position coordinates withthe origin at the sphere’s center, R is the radius of the sphereand the direction of the angular velocity vector is the z axis.For each run we follow 10 individual photons generatedfrom the origin at the Ly α line’s center as they propagatethrough the volume and finally escape. We store the fre-quency and propagation direction for each photon at its lastscattering.As input parameters we use τ H = { , , } , v out = { , , } km s − and v rot = { , , } km s − , for a totalof 27 models with all the possible parameter combinations. The values for the outflow velocity are lower than valuescommonly used in the literature to allow for an interplaybetween the two kinematic features. This range of paramet-ers also produce emission lines with standard deviation andskewness in the same range to those of high redshift LAESin recent observations (Herenz et al. 2017).We also define the viewing angle, θ , as the angle betweenthe rotation axis and the line of sight of a potential observer.Garavito-Camargo et al. (2014) presented an analyticalmodel that accounts for the effects of pure rotation on theLy α line morphology. The basic assumption of the modelis that each differential surface element on the sphere Dop-pler shifts (DS) the photons that it emits. In this paper weintroduce this ansatz by post-processing the results of theoutflows simulations without rotation. The frequency of eachphoton is Doppler shifted as follows x (cid:48) = x + (cid:126)v rot · ˆ kv th (4)where x (cid:48) is the photon’s new adimensional frequency, x isthe photon’s frequency after being processed only by theoutflow, v rot is the rotational velocity at the point of escapeof the photon, ˆ k is the photon’s direction of propagation and v th is the thermal velocity of the sphere. We fix v th through-out the paper. This factor is a multiplying constant thatcould be changed without running new Monte-Carlo simu-lations, as the code works with the adimensional frequency x . This semi-analytic model allows us to produce new Ly α spectra from the outflow-only results and compare themwith the full radiative transfer solution including both out-flows and rotation. Figure 1 summarizes the most important trends from theRT simulations. In the left side, the six panels correspondto τ = 10 and a viewing angle of θ = 90 ◦ , that is, per-pendicular to the rotation axis of the galaxy. In every panelthe thin black line corresponds to the pure outflow solution,i.e. without rotation. From top to bottom we see the effectof increasing the outflow velocity, which is the expected in-creasing asymmetry towards the red peak.The thick black line corresponds to the solution thatincludes both outflows and rotation. Comparing the left andright columns (lower versus higher rotational velocity) wecan see two immediate effects. First, the line broadens andsecond, the intensity at the line’s center increases.The thick gray line corresponds to the pure outflowsolution with the Doppler shift added to model rotation’sinfluence. At τ H = 10 the Doppler shift does a good jobat capturing the broad morphological features introducedby rotation: the angle dependence, the broadening and theintensity increase at the line’s center.In the right side of Figure 1 we show the same results asin the left one, but for a viewing angle of θ = 0 ◦ , that is par-allel to the rotation axis. In this case we confirm the resultpresented by Garavito-Camargo et al. (2014), namely thatpure rotation introduces a strong dependence with viewing MNRAS , 000–000 (0000) yman- α photons through rotating outflows . . . . . v rot = 50 km s − v rot = 100 km s − v o u t = k m s − . . . . . I n t e n s i t y v o u t = k m s − − −
100 0 100 200 300V ( km s − ) . . . . . OutflowsOutflowsRotationOutflowsDoppler − −
100 0 100 200 300V ( km s − ) v o u t = k m s − . . . . . v rot = 50 km s − v rot = 100 km s − v o u t = k m s − . . . . . I n t e n s i t y v o u t = k m s − − −
100 0 100 200 300V ( km s − ) . . . . . OutflowsOutflowsRotationOutflowsDoppler − −
100 0 100 200 300V ( km s − ) v o u t = k m s − Figure 1. Qualitative trends of changing outflow and rotational velocity viewed perpendicular/paralell to the rotationaxis . Here we fix τ H = 10 . The six panels on the left correspond to θ = 90 ◦ and the panels on the right to θ = 0 ◦ We vary v rot increasingfrom left to right and v out increasing from top to bottom. The thin black line corresponds to the Ly α line obtained with CLARA withoutany rotation and the indicated outflow velocity. The thick black line corresponds to CLARA’s results including both outflows androtation. The thick gray line shows the results of modifying the pure outflow solution (thin black line) by the Doppler shift presented inEquation 4 using the respective v rot . angle, a trend that we find also holds for rotation mixedwith outflows.The quality of the results from the Doppler shift im-proves for higher τ H values. In the Appendix we show thesame plots as Figure 1, there it is evident that for τ H = 10 the results are not as good as they are for τ H = 10 , andthat for τ H = 10 the Doppler shift provides a remarkablegood approximation. After finding the qualitative influence of the different para-meters we move onto a quantitative study. To do this wesummarize the line morphology by four different scalars:standard deviation (STD), skewness (SKW), bimodality(BI) and valley/peak ratio. These quantities are defined bythe following equations (Kokoska & Zwillinger 1999):STD = √ m , (5)SKW = m m / , (6)BI = KURTOSIS − SKW = m m − m m , (7)where each m i is the i-th moment about the mean. TheSTD has velocity units and quantifies the line’s width. TheSKW is adimensional and quantifies the peaks’ asymmetry.In the case of a bimodal distribution, SKW > < ≥ . Figure 2 summarizes the standard deviation results for allour models. Each panel shows the STD as a function of v rot .All panels were computed using a viewing angle of θ = 90 ◦ (perpendicular to the rotation axis), which has the mostextreme influence from rotation. The black triangles corres-pond to the full RT solution and the line to the DS approx-imation. The optical depth increases from top to bottom andthe outflow velocity from left to right. This quantitative plotconfirms that the line width increases with rotational velo-city and optical depth. These trends are expected; higherrotational velocities can be seen as an addition of differentDoppler shifts that smear out the line, while a higher opticaldepth translates into a larger number of scatterings that in-crease the probability of a photon to diffuse in frequencyresulting in a broader line.The DS successfully reproduces all trends with the op-tical depth, rotational velocity and outflow velocity. How-ever, the DS consistently underestimates the STD. The dif-ference between the RT and DS increases with the outflowvelocity and the rotational velocity, and decreases with in-creasing optical depth. In the range of parameter space ex-plore, this difference has as an upper bound of ∼ ∼
2% for τ H = 10 , 10 and 10 , respectively. MNRAS000
2% for τ H = 10 , 10 and 10 , respectively. MNRAS000 , 000–000 (0000)
M.C. Remolina-Gutierrez & J.E. Forero-Romero v rot ( km s − ) . . . S t a nd a r d D e v i a t i o n ( k m s − ) τ H = 10 v out = 5 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 25 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 50 km s − DSRT v rot ( km s − ) . . . S t a nd a r d D e v i a t i o n ( k m s − ) τ H = 10 v out = 5 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 25 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 50 km s − DSRT v rot ( km s − ) . . . S t a nd a r d D e v i a t i o n ( k m s − ) τ H = 10 v out = 5 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 25 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 50 km s − DSRT
Figure 2. Standard Deviation trends.
Results for all the Radiative Transfer simulations (in triangles) compares against the DopplerShift model (lines). All panels correspond to a viewing angle of θ = 90 ◦ (perpendicular to the rotation axis). The optical depth increasesfrom top to bottom and the outflow velocity from left to right. Figure 3 presents the skewness results for all the models to-gether with the DS comparison following the same layoutas Figure 2. In all cases the skewness is negative showingthat all the lines are unbalanced towards the red side ofthe spectrum. Skewness increases with rotational velocityand decreases with optical depth; rotation tries to smooththe line diminishing the asymmetries while a higher opticaldepth reinforces the line asymmetries. The skewness doesnot have a monotonous trend with outflow velocity becausethere is a transition between double and single peak line;for low outflow velocities the skewness signals the balancebetween the two existing peaks while for high outflow velo-cities it quantifies the asymmetry of the already dominantread peak.The DS reproduces the main trends, again with an un-derestimation that decreases at higher optical depths andincreases with larger values of the rotational velocity andoutflow velocity. In this case the differences between RT andDS have an upper bound of 85%, 35% and 5% for τ H = 10 ,10 and 10 , respectively. Figure 4 shows the results for the bimodality using thesame layout as in the two previous Figures. Following thereasoning about the skewness, we observe that increasingthe outflow velocity increases the value of bimodality, thatis, it transitions to a more pronounced single peak. Thetrend as a function of the rotational velocity and the op-tical depth are not monotonous. When the outflow velocityis low ( v out <
50 km s − ), an increasing rotational velo-city smears the two asymmetrical peaks pushing the linemorphology towards a single peaks, making the bimodalitystatistics increase. On other situations ( v out = 50 km s − and τ H ≥ ) higher rotational velocities the bimodalitystatistics decreases, which means that it manages to slightlyenlarge the already dominant red peak.The DS reproduces the main trends while underestim-ating the bimodality statistics. As expected from the previ-ous results the difference between RT and DS decreases athigher optical depths and increases with increasing values ofthe rotational and outflow velocities. In this case the differ- MNRAS , 000–000 (0000) yman- α photons through rotating outflows v rot ( km s − ) − . − . − . S k e w n e ss τ H = 10 v out = 5 km s − DSRT v rot ( km s − ) − . − . − . τ H = 10 v out = 25 km s − DSRT v rot ( km s − ) − . − . − . τ H = 10 v out = 50 km s − DSRT v rot ( km s − ) − . − . − . S k e w n e ss τ H = 10 v out = 5 km s − DSRT v rot ( km s − ) − . − . − . τ H = 10 v out = 25 km s − DSRT v rot ( km s − ) − . − . − . τ H = 10 v out = 50 km s − DSRT v rot ( km s − ) − . − . − . S k e w n e ss τ H = 10 v out = 5 km s − DSRT v rot ( km s − ) − . − . − . τ H = 10 v out = 25 km s − DSRT v rot ( km s − ) − . − . − . τ H = 10 v out = 50 km s − DSRT
Figure 3. Skewness trends.
Results for all the Radiative Transfer simulations (in triangles) compares against the Doppler Shift model(lines). Follows the same layout as Figure 2. ences have an upper bound of 4%, 2% and 1% for τ H = 10 ,10 and 10 , respectively. In Figure 5 we quantify how the intensity at the line’s center(i.e. the valley) changes with the viewing angle, the outflowvelocity and the optical depth. These results correspond to afixed rotational velocity of v rot = 100 km s − . The trianglescorrespond to the RT simulations and the line representsthe DS results. The valley intensity is expressed as a frac-tion of the maximum peak intensity in the line, as such thevalley/peak ratio is always <
1. In every panel we see thatthe valley/peak ratio decreases as the observer moves from aline of sight perpendicular to the rotation axis onto a paral-lel line of sight. This is a clear demonstration of the viewingangle dependency introduced by rotation.The valley/peak ratio at cos θ = 1 matches resultswithout rotation, this shows that for increasing rotationalvelocity the valley/peak ratio increases. In turn, for increas-ing optical depth or outflowing velocity this ratio decreases.Once again, the DS results correctly follow the trends for the full RT simulations. This time the differences have anupper bound of 55%, 2% and 1% for τ H = 10 , 10 and 10 ,respectively. In this section we discuss how the results we have presentedcan be connected to the interpretation of observational data.
The effects of the semi-analytic model on the pure outflow-ing spectra are similar to the expected results from a gaus-sian smoothing, such smoothing can also be a natural con-sequence of the intruments used to measure the LAE spec-tra. As a consequence, natural experimental artifacts couldbe mistaken as an indication for rotation.To understand to what extent the effects of rotationcan be seen as a simple smoothing, we model the effects
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M.C. Remolina-Gutierrez & J.E. Forero-Romero v rot ( km s − ) . . . B i m o d a li t y τ H = 10 v out = 5 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 25 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 50 km s − DSRT v rot ( km s − ) . . . B i m o d a li t y τ H = 10 v out = 5 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 25 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 50 km s − DSRT v rot ( km s − ) . . . B i m o d a li t y τ H = 10 v out = 5 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 25 km s − DSRT v rot ( km s − ) . . . τ H = 10 v out = 50 km s − DSRT
Figure 4. Bimodality trends.
Results for all the Radiative Transfer simulations (in triangles) compares against the Doppler Shiftmodel (lines). Follows the same layout as Figure 2. of gaussian smoothing with a similar ansatz as the semi-analytic model by changing the frequency of each photon bya Gaussian random variable centered on zero and standarddeviation σ x : x (cid:48) = x + N (0 , σ x ) . (8)We find that the results of the semi-analytic model onthe total spectra at a given angle θ can be approximatedusing σ x = (1 / × ( v rot /v th ) × sin θ . This approximationreproduces within a few porcent all quantities measured inSection 3.2 for the semi-analytic model, it only works wellfor τ = 10 and τ = 10 .This result can be used as an order of magnitude estim-ate of the mimum espectral resolution required to observethe effects of a rotational velocity of v rot . The Space Tele-scope Imaging Spectrograph (STIS) on the Hubble SpaceTelescope (HST) can provide resolutions around 20 kms − (Hayes 2015), which could allow for the detection ofrotation features in nearby galaxies with at least 40 kms − and a rotation axis perpendicular to the line of sight.Other instruments such as the Cosmic Origins Spectro-graph (COS) have varying resolutions between 20km s − and 200km s − according to the angular size of the source (Orl-itov´a et al. 2018). α Kinematic Maps
Current observational facilities have the capability of spa-tially resolving the extent of a LAE. For instance Prescottet al. (2015) presented observational results of a Dopplershift when taking spectra at two opposite sides of a large( ≈ α emission around a quasar. In this caseone could measure the displacement between the peaks inthe two different spectra. The interest of this test is that thelocation of the peaks only depends on the kinematic proper-ties of the sources and does not change by convolution witha gaussian window function due to limited instrumental res-olution, as discussed in the previous section.In Figure 6 we present a toy model ( v rot = 50 km s − , v out = 25 km s − and τ H = 10 ) for the spectrum of aLAE taken from to different sides of the galaxy. As the LAEis rotating, one side is being redshifted while the other isblueshifted. We see that the full spectrum is a weighted line, MNRAS , 000–000 (0000) yman- α photons through rotating outflows . . . θ . . . V a ll e y / P e a k R a t i o τ H = 10 v out = 5 km s − DSRT . . . θ . . . . τ H = 10 v out = 25 km s − DSRT . . . θ . . . . τ H = 10 v out = 50 km s − DSRT . . . θ . . . . V a ll e y / P e a k R a t i o τ H = 10 v out = 5 km s − DSRT . . . θ . . . . τ H = 10 v out = 25 km s − DSRT . . . θ . . . . τ H = 10 v out = 50 km s − DSRT . . . θ . . . . V a ll e y / P e a k R a t i o τ H = 10 v out = 5 km s − DSRT . . . θ . . . . . τ H = 10 v out = 25 km s − DSRT . . . θ . . . . τ H = 10 v out = 50 km s − DSRT
Figure 5. Valley Intensity.
We show for each τ H the dependency that the viewing angle θ has on the line’s the valley intensity. v rot = 100km s − is fixed for all panels. − −
50 0 50 100 150V ( km s − ) . . . . . . . I n t e n s i t y ( A r b i tr a r y U n i t s ) Full SpectraRedBlue
Figure 6. Spectra from receding/approaching sides of atoy model LAE.
These results correspond to the RT simulationwith v out = 25km s − , v rot = 50km s − , τ H = 10 . The spectrawere computed for a viewing angle of θ = 90 ◦ . This toy modelillustrates to what extent spectra from opposite sides of a galaxyhave an imprint of the rotational kinematics. in solid black, that is found between these two. We noticethat the distance between the maxima of the blue and redspectra is not twice the rotational velocity as it could benaively expected.In this toy model the distance between the peaks ofthe receding/approaching spectra is close to ∼
25 km s − ,which is a fourth of the naively expected value of 2 v rot =100 km s − , due to the fact that only a small fraction of thephotons are emitted at the extreme of the galaxy having themaximum rotational velocity of 50 km s − . Although it is agood approximation to think the rotating spectra by a sumof Doppler shifts, the peak of the spectra is also weightedby the amount of mass with a given line-of-sight velocity.Spectrographs like the Multi Unit Spectroscopic Ex-plorer (MUSE) could obtain kinematic information fromlarge samples of LAEs to build velocity maps in Ly α . Thiscould be a natural extension of the work reported by Her-enz et al. (2016) on the velocity maps of several LARS (Ly-man Alpha Reference Sample) galaxies. The interpretationof such data could take into account the insights and trendswe have presented in this paper. MNRAS000
25 km s − ,which is a fourth of the naively expected value of 2 v rot =100 km s − , due to the fact that only a small fraction of thephotons are emitted at the extreme of the galaxy having themaximum rotational velocity of 50 km s − . Although it is agood approximation to think the rotating spectra by a sumof Doppler shifts, the peak of the spectra is also weightedby the amount of mass with a given line-of-sight velocity.Spectrographs like the Multi Unit Spectroscopic Ex-plorer (MUSE) could obtain kinematic information fromlarge samples of LAEs to build velocity maps in Ly α . Thiscould be a natural extension of the work reported by Her-enz et al. (2016) on the velocity maps of several LARS (Ly-man Alpha Reference Sample) galaxies. The interpretationof such data could take into account the insights and trendswe have presented in this paper. MNRAS000 , 000–000 (0000)
M.C. Remolina-Gutierrez & J.E. Forero-Romero
In this paper we explore, for the first time in the literature,the results of a model for the emergent Ly α line from rotat-ing outflows. We use a semi-analytic model first presented byGaravito-Camargo et al. (2014) to capture the main effectsof rotation and confront it against results from Monte-Carloradiative transfer simulations. The semi-analytic model onlytakes into account the Doppler shift computed as productof quantities at the surface of last scattering, namely (cid:126)v rot · ˆ k ,where (cid:126)v rot is the velocity due to rotation and ˆ k is the direc-tion of the photon’s propagation.To address the first question we posed in the introduc-tion ( What is the expected imprint of rotation on a resonantemission line such as the Ly α line? ) we find from the fullRT simulations that the effects of rotation on the Ly α linemorphology are: • Inducing a dependency on the viewing angle. • Broadening the line. • Increasing the intensity at the line’s center.All these effects can be qualitatively explained by theproposed semi-analytic model. Quantitatively speaking thesemi-analytic model provides a satisfactory answer for aneutral Hydrogen optical depth equal or larger than 10 .Addressing the second question we posed in the in-troduction ( To what extent is it possible to constrain ro-tational kinematics from the Ly α emission line? ) we showthat the most straightforward approach is measuring Ly α spectra from two different regions of a galaxy to detect ap-proaching/receding gas motions (Prescott et al. 2015; Arri-goni Battaia et al. 2018). In that case, we also show thatthe distances between these two peaks is four times shorterthan the naively expected value of 2 × v rot . This differenceis produced by the different geometric weights at the emit-ting surface. Here the semi-analytic model also provides thecorrect quantitative insight.To summarize, our works shows that the Doppler Shiftoffers an easy-to-implement approximation to explore suchinfluence into already existing radiative transfer simulationsthat include outflows, providing a versatile tool to interpretcurrent and future Ly α kinematics maps (e.g Arrigoni Bat-taia et al. 2018; Erb et al. 2018). References
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APPENDIX A: ADDITIONAL FIGURES
MNRAS , 000–000 (0000) yman- α photons through rotating outflows . . . . . . v rot = 50 km s − v rot = 100 km s − v o u t = k m s − . . . . . . I n t e n s i t y v o u t = k m s − −
100 0 100 200V ( km s − ) . . . . . . OutflowsOutflowsRotationOutflowsDoppler −
100 0 100 200V ( km s − ) v o u t = k m s − . . . . . . v rot = 50 km s − v rot = 100 km s − v o u t = k m s − . . . . . . I n t e n s i t y v o u t = k m s − −
200 0 200 400V ( km s − ) . . . . . . OutflowsOutflowsRotationOutflowsDoppler −
200 0 200 400V ( km s − ) v o u t = k m s − Figure A1. Qualitative trends of changing outflow and rotational velocity.
Same layout as Figure 1. On the left: τ H = 10 and θ = 90 ◦ ; on the right: this time τ H = 10 and θ = 90 ◦ .MNRAS000